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Tool-part interaction in composites processing Twigg, Graham 2001

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TOOL-PART INTERACTION IN COMPOSITES PROCESSING by G R A H A M TWIGG B A . S c . (Materials and Metallurgical Engineering), Queen's University, 1997  A THESIS SUBMITTED IN PARTIAL F U L F I L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E O F M A S T E R OF APPLIED SCIENCE  in  T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Metals and Materials Engineering)  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A January, 2001 © Graham A. Twigg, 2001  In  presenting  degree freely  at  this  the  available  copying  of  department publication  of  in  partial  fulfilment  University  of  British  Columbia,  for  this or  thesis  reference  thesis by  this  for  his  and  scholarly  or  thesis  for  her  Department The University of British C o l u m b i a Vancouver, Canada  DE-6  (2/88)  R>6  /9  900/  I  I further  purposes  gain  the  shall  requirements  agree  that  agree  may  representatives.  financial  permission.  Date  study.  of  be  It not  that  the  Library  by  understood be  an  advanced  shall  permission for  granted  is  for  allowed  the  make  extensive  head  that  without  it  of  copying my  my or  written  ABSTRACT  The ability to process composite structures with a high degree of dimensional control remains a barrier to the further implementation of composite materials in commercial applications. Poor control over final part shape can necessitate custom shimming of composite parts or remachining of tooling, resulting in excessive manufacturing costs.  Mechanical interaction  between the tool and part has been identified as a significant contributor to dimensional control problems yet this phenomena remains poorly understood.  Tool-part interaction can often manifest itself in the warpage of initially flat laminates. In the present work an experimental study was performed to identify the effect that part geometry and process variables had on this warpage. Part geometry had a much greater influence on warpage than autoclave process pressure did, while tool surface condition was not observed to have any significant effect.  A second experimental study was performed whereby a thin aluminum tool was instrumented with strain gages. The mechanical strain induced in the instrumented tool provided a means for estimating the magnitude and distribution of shear stress operative at the tool-part interface. Both sliding and sticking interface conditions were observed to occur at various times throughout the cure cycle. The interfacial shear stress increased with increasing part degree of cure.  An analytical model to predict warpage was developed based on the conclusions of the instrumented tool investigation. This model agreed well with the trends in part warpage which were identified experimentally. Process induced warpage was also simulated using an existing  numerical process model. The current method of accounting for tool-part interactions via an elastic shear layer was unable to correctly represent the interface behavior, however, reasonable agreement with experimental results was possible by using a sufficiently low modulus shear layer.  The value assigned to the shear modulus of the part was also observed to have a  significant effect on the success with which part warpage could be modelled.  -in-  T A B L E OF  CONTENTS  Abstract  ii  Table of Contents  iv  List of Tables  vii  List of Figures  ix  Nomenclature  .  xvi  Acknowledgements  xix  Chapter 1: Introduction  1  1.1  Autoclave Processing Overview  2  1.2  Material Property Evolution  4  1.3  Aspects of Dimensional Control  5  1.4  Research Obj ective and Approach  6  1.5  Tables  7  1.6  Figures  :  Chapter 2: Literature Review  8 9  2.1  Warpage Theories  10  2.2  Quantitative Warpage Studies  12  2.3  Warpage Modelling  15  2.4  Friction Theories  19  2.5  Tool-Part Interface Characterization  20  2.6  Summary  23  2.7  Tables  25  2.8  Figures  26  Chapter 3: Experimental Warpage Specimens 3.1  33  Sample Fabrication  33  Tool Preparation  34  3.1.2 Lay-Up and Cure  34  3.1.1  3.2  Sample Measurement  35  3.3  Results  37  -iv-  3.3.1 Warpage Results  37  3.3.1.1  Warpage - Length Effect  37  3.3.1.2  Warpage - Thickness Effect  38  3.3.1.3  Warpage - Pressure Effect  38  3.3.1.4  Warpage - T o o l Surface Effect  39  3.3.1.5  Warpage - Specimen Variability  .'  39  3.3.2 Curvature Results  40  3.3.3 Curvature Distribution  41  3.4  Discussion  42  3.5  Summary  44  3.6  Tables  46  3.7  Figures  48  Chapter 4 : Instrumented Tool Experiments  67  4.1  Experimental  68  4.2  Instrumented Tool Theory  69  4.2.1 Sliding Friction Condition  71  4.2.2 Stick Condition 4.3  72  Instrumented Tool Results  76  4.3.1 High Pressure / Release Agent 4.3.1.1  76  Strain Development - C o o l - d o w n  77  4.3.1.1.1 Estimate ofL  78  s  4.3.1.1.2 Estimate of T  80  4.3.1.1.3 Estimate of tsndmg  °^  Debond  4.3.1.2  Strain Development - Isothermal H o l d  82  4.3.1.3  Strain Development - Heat-up  83  4.3.2 Instrumented Results - Other Experimental Conditions  84  4.3.2.1  Other Experimental Conditions - Heat-up  84  4.3.2.2  Other Experimental Conditions - Isothermal H o l d and C o o l - d o w n  85  4.4  Discussion  86  4.5  Summary  88  4.6  Tables  90  4.7  Figures  91  Chapter 5: Analytical and Numerical Modelling 5.1  Analytical Model  110 110  -v-  5.1.1  Comparison with Experimental Results  5.1.2 Analytical Model - Discussion  5.2  114 116  Numerical Warpage Modelling  120  5.2.1 Numerical Model - Parametric Study  121  5.2.1.1  Parametric Study - Results  122  5.2.2 Numerical Modelling - Discussion  123  5.2.2.1  Interfacial Shear Stress with Elastic Shear Layer  124  5.2.2.2  In-Plane Stress Gradient  125  5.3  Summary  127  5.4  Tables  129  5.5  Figures  131  Chapter 6: Conclusions and Future Work  143  6.1  144  Future Work  References  147  Appendix A : Warpage Specimen Measurement Error  150  A. 1  Scanner Method - 300 mm and 600 mm Specimens  150  A.2  Manual Method - 1200 mm Specimens  150  A.3  Tables  152  A. 4  Figures  153  Appendix B: Strain Gage Thermal Compensation  154  B. 1  Strain Gage Calibration  155  B.2  Stability of Calibration Factors  157  B. 3  Figures  158  Appendix C : Calculations  165  C. 1  Warpage due to Bi-Material Strip Effect  165  C.2  Warpage of Parts with L > L  166  C. 3  Figures  169  c  Appendix D: Instrumented Tool Results  170  D. l  Tables  171  D.2  Figures  176  -vi-  LIST OF TABLES  Table 1.1: Typical carbon fibre and epoxy matrix properties  7  Table 1.2: Typical tooling material Coefficient of Thermal Expansions  7  Table 2.1: Sources of processed induced deformation in composite laminates  25  Table 2.2: Experimentally determined coefficients of friction (Flanagan, 1997)  25  Table 3.1: Maximum warpage and average curvature for the experimental warpage specimens  46  Table 3.2: Warpage specimen variability for 300 mm specimens  46  Table 3.3: Warpage specimen variability for 1200 mm specimens  47  Table 4.1: Material properties used for calculation purposes expressed as a function of temperature. Note that T refers to the temperature in °C Table 5.1: LQ values for a uni-directional CFRP laminate fabricated on tools of varying  90  CTE  129  Table 5.2: Design and results of COMPRO parametric study  129  Table 5.3: Average experimental results for all part geometries  130  Table A . l : Coordinate data for calculation of  SMeasure  for 300 and 600 mm specimens  152  Table A.2: Coordinate data for calculation of  SMeasure  for 1200 mm specimens  152  Table D . l : Elastic constraint evolution for 586 kPa / release agent experimental conditions (Figure 4.21 and Figure 4.22)  171  Table D.2: Elastic constraint evolution for 103 kPa / release agent experimental conditions (Figure 4.33)  171  Table D.3: Elastic constraint evolution for 586 kPa / FEP experimental conditions (Figure 4.34)  171  Table D.4: Elastic constraint evolution for 586 kPa / FEP experimental conditions (Figure 4.3 5)  172  Table D.5: Temperature and strain data corresponding to instrumented tool - part debonding during cool-down. 586 kPa / release agent experimental conditions (Figure 4.18)  172  Table D.6: Temperature and strain data corresponding to instrumented tool - part debonding during cool-down. 103 kPa / release agent experimental conditions (Figure 4.36)  172  Table D.7: Strain reading versus location for various times during the cure cycle. 586 ' kPa / release agent interface (Figure 4.19 and Figure 4.24)  173  -vii-  Table D.8: Strain reading versus location for various times during the cure cycle. 103 kPa / release agent interface (Figure 4.29)  173  Table D.9: Strain reading versus location for various times during the cure cycle. 586 kPa / FEP interface (Figure 4.30)  173  Table D.10: Strain reading versus location for various times during the cure cycle. 103 kPa / FEP interface (Figure 4.31)  174  Table D. 11: Change in Tsndtng with respect to part degree of cure for 586 kPa / release agent interface conditions (Figure 4.25)  174  Table D.12: Change in rsndmg with respect to part degree of cure for 103 kPa / release agent interface conditions (Figure 4.32)  174  Table D. 13: Change in rsndmg with respect to part degree of cure for 586 kPa / FEP interface conditions (Figure 4.32)  175  Table D.14: Change in rsndmg with respect to part degree of cure for 103 kPa / FEP interface conditions (Figure 4.32)  175  -viii-  LIST OF FIGURES  Figure 1.1: Tool-Part-Vacuum Bag assembly  8  Figure 2.1: Proposed mechanism for warpage due to tool-part interaction, a) Tool expands thermally on heating to pre-preg cure temperature. Friction at interface induces tensile fibre stresses in lay-up. b) Layer slippage relieves fibre stresses preferentially in layers furthest from tool face. Non-uniform stresses locked in when pre-preg cures, c) Laminate bows away from tool face (Ridgard, 1993)  26  Figure 2.2: Experimental and numerical warpage results for 16 ply, uni-directional laminates of various lengths. Samples were fabricated at 586 kPa on steel tooling with release agent (fk0_16) and FEP(rfO_16) interfaces (Flanagan, 1997)  27  Figure 2.3: Experimental and numerical warpage results for 300 mm, uni-directional laminates of various thicknesses. Samples were fabricated at 586 kPa on steel tooling with a release agent interface (Flanagan, 1997)  27  Figure 2.4: Experimental and numerical warpage results for 300 mm, 8 ply, unidirectional laminates at various pressures. Samples were fabricated on steel tooling with release agent (fk0_8) and FEP(rfO_8) interfaces (Flanagan, 1997)  28  Figure 2.5: Experimental and numerical warpage results for 300 mm, 8 ply, unidirectional laminates with various tooling materials. Samples were fabricated on steel tooling with release agent (fk0_8) and FEP(rf0_8) interfaces (Flanagan, 1997)  28  Figure 2.6: Curvature versus temperature for various tool materials and surface conditions. A l l samples were 250 mm long, 4 ply, uni-directional laminates fabricated without the use of bleeder plies (Radford et al., 1999)  29  Figure 2.7: Curvature versus temperature for various bleeder arrangements and tool surface conditions. A l l samples were 250 mm long, 4 ply, uni-directional laminates fabricated on aluminum tooling (Radford et al., 1999)  29  Figure 2.8: Arrangement of layers and sub-layers in the analytical warpage model developed by Melo and Radford (1999)  30  Figure 2.9: Theoretical in-plane stress gradients for a) [0/90]s , b) [0]4 , c) [0]6 laminates fabricated on aluminum tooling (Melo and Radford, 1999)  30  Figure 2.10: Test rig used by Hubert et al. (1996) for observation of shear flow during the compaction of laminates  31  Figure 2.11: Coefficient of friction test rig (Flanagan, 1997)  31  -ix-  Figure 2.12: Measured strain in the flat aluminum tool during heat-up and cool-down with no mould release on the tool. The CFRP was uncured prior to heat-up and that the temperature was held at 177°C for two hours before cool-down. Fernlund et al. (2000)  32  Figure 3.1: Target cure cycle for manufacture of warpage specimens  48  Figure 3.2: Run data from a typical autoclave cure cycle used for the manufacture of warpage specimens  48  Figure 3.3: Document scanner as set-up for scanning deformed part shape  49  Figure 3.4: The greyscale image on the left shows a segment of the part profile after scanning. The image contrast was then increased, and image brightness adjusted to create the sharply defined image on the right. The clear black and white image was then used for locating part edge coordinates using image analysis software  49  Figure 3.5: Photograph depicting the magnitude of warpage for 4 ply parts of various lengths. 586 kPa / FEP interface  50  Figure 3.6: Part shapes for 300 mm specimens  50  Figure 3.7: Part shapes for 600 mm specimen  51  Figure 3.8: Part shapes for 1200 mm specimens  51  Figure 3.9: Maximum part warpage variation with length for 4 ply specimens  52  Figure 3.10: Maximum part warpage variation with length for 8 ply specimens  52  Figure 3.11: Maximum part warpage variation with length for 16 ply specimens  53  Figure 3.12: Normalized maximum warpage versus length for all thicknesses and process conditions  53  Figure 3.13: Normalized maximum warpage averaged for all specimen conditions contrasted with various theoretical warpage - length relationships.  54  Figure 3.14: Maximum part warpage variation with thickness, 300 mm specimens  54  Figure 3.15: Maximum part warpage variation with thickness, 600 mm specimens  55  Figure 3.16: Maximum part warpage variation with thickness, 1200 mm specimens  55  Figure 3.17: Normalized maximum warpage versus part thickness for all lengths and process conditions  56  Figure 3.18: Normalized maximum warpage averaged for all specimen conditions contrasted with various theoretical warpage - thickness relationships  56  Figure 3.19: Autoclave pressure effect on maximum warpage for 300 mm specimens  57  Figure 3.20: Autoclave pressure effect on maximum warpage for 600 mm specimens  57  Figure 3.21: Autoclave pressure effect on maximum warpage for 1200 mm specimens  58  Figure 3.22: Normalized maximum warpage versus autoclave pressure for specimens with an FEP interface  58  -x-  Figure 3.23: Normalized maximum warpage versus autoclave pressure for specimens with a release agent interface condition^  59  Figure 3.24: Average experimental result plotted against various pressure warpage relations  59  Figure 3.25: Maximum part warpage versus tool surface condition for 300 mm specimens  60  Figure 3.26: Maximum part warpage versus tool surface condition for 600 mm specimens  60  Figure 3.27: Maximum part warpage versus tool surface condition for 1200 mm specimens  61  Figure 3.28: Normalized maximum warpage versus tool surface condition for specimens fabricated at 103 kPa  61  Figure 3.29: Normalized maximum warpage versus tool surface condition for specimens fabricated at 586 kPa  62  Figure 3.30: Warpage of 300 mm replicate specimens  62  Figure 3.31: Warpage of 1200 mm replicate specimens  63  Figure 3.32: Average part curvature versus part length for 4 ply specimens  63  Figure 3.33: Average curvature versus part length for 8 ply specimens  64  Figure 3.34: Average curvature versus part length for 16 ply specimens  64  Figure 3.35: Curvature distribution for 600 mm specimens  65  Figure 3.36: Curvature distribution for 1200 mm specimens  65  Figure 3.37: Experimental data compared with empirical relationship predicting maximum warpage  66  Figure 4.1: Arrangement of strain gages on the instrumented tool  91  Figure 4.2: Instrumented tool - part - baseplate cross section  91  Figure 4.3: Instrumented tool experimental set-up  92  Figure 4.4: Geometry of thin tool loading under sliding friction conditions  92  Figure 4.5: Interfacial shear stress distribution for the case of a sliding friction interface  93  Figure 4.6: In-plane stress distribution for the case of a sliding friction interface  93  Figure 4.7: Geometry of the thin tool loading under sticking interface conditions  94  Figure 4.8: Interfacial shear stress distribution for the case of a perfectly bonded toolpart interface  94  Figure 4.9: In-plane stress distribution for the case of a perfectly bonded tool-part interface  95  Figure 4.10: Theoretical interfacial shear stress development as a function of interface displacement  95  -xi-  Figure 4.11: Typical thermal cycle used for the instrumented tool experiments  96  Figure 4.12: Mechanical strain evolution in the instrumented tool for the entire process cycle. 586 kPa / release agent interface  96  Figure 4.13: Mechanical strain evolution during the cool-down portion of the cure cycle. 586 kPa / release agent interface  97  Figure 4.14: Illustration of interfacial shear stress distribution as the debond front travels from the tool end towards the centre  97  Figure 4.15: Interfacial shear stress distribution corresponding to the peak strain gage reading prior to debonding  98  Figure 4.16: Interfacial shear stress distribution corresponding to the post-debond plateau strain gage reading  98  Figure 4.17: Strain evolution at a single gage during the debond event  99  Figure 4.18: Debond front migration with respect to part temperature  99  Figure 4.19: Post debond strain versus gage location. The slope of the fitted line is used: for calculation of rsndmg- 586 kPa / release agent interface  100  Figure 4.20: Mechanical strain evolution during the isothermal hold. 586 kPa / release agent interface  100  Figure 4.21: Elastic constraint with respect to time. 586 kPa / release agent interface  101  Figure 4.22: Elastic constraint plotted with respect to part degree of cure. 586 kPa / release agent interface  101  Figure 4.23: Mechanical strain evolution during the heat-up portion of the cure cycle. 586 kPa / release agent interface  102  Figure 4.24: Strain reading versus gage location for various times during the cure cycle. The slope of the best fit lines is used for estimating rsndmg- 586 kPa / release agent interface  102  Figure 4.25: Change in Tsuding with respect to part degree of cure. 586 kPa / release agent interface  103  Figure 4.26: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / release agent interface  103  Figure 4.27: Instrumented tool mechanical strain development for the entire cure cycle. 586kPa/FEP interface  104  Figure 4.28: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / FEP interface  104  Figure 4.29: Strain reading versus gage location for various times during the cure cycle. 103 kPa / release agent interface  105  Figure 4.30: Strain reading versus gage location for various times during the cure cycle. 586 kPa / FEP interface  105  -xii-  Figure 4.31: Strain reading versus gage location for various times during the cure cycle. 103 kPa / FEP interface Figure 4.32: Change in  Tsuding  with respect to part degree of cure  106 106  Figure 4.33: Elastic constraint with respect to degree of cure. 103 kPa / release agent interface  107  Figure 4.34: Elastic constraint with respect to degree of cure. 586 kPa / FEP interface  107  Figure 4.35: Elastic constraint with respect to degree of cure. 103 kPa / FEP interface  108  Figure 4.36: Post debond strain versus gage location. The slope of the fitted line is used for calculation of Tsuding- 103 kPa / release agent interface Figure 4.37: Schematic illustration of the development of agent interface  toebond  Figure 4.38: Schematic illustration of the development of interface  Toebond  and  Tsuding  108  for a release 109  and  Tsuding  for an FEP 109  Figure 5.1: Part geometry for the analytical model. Sliding friction is occurs at both the tool-part interface and at the interply region  131  Figure 5.2: In-plane stress distribution for the analytical model with sliding friction at the 1 p l y - 2 ply interface  131  Figure 5.3: Comparison of numerical modelling results from Flanagan with L warpage relationship  132  Figure 5.4: Comparison of numerical modelling results from Flanagan with 1 / t warpage relationship  132  Figure 5.5: Interfacial shear stress distribution corresponding to a part where the part length, L , is greater than Lc •  133  Figure 5.6: In-plane stress distribution corresponding to a part where the part length, L , is greater than Zc •  133  st  n d  2  Figure 5.7: Difference in 1st ply in-plane stress distributions for a 4 metre long parts fabricated on aluminum and invar tooling. For the part fabricated on invar tooling, L > Lc, hence the stress reaches the limiting value, <JMOX- In contrast, stress continues to build for the part fabricated on aluminum tooling  134  Figure 5.8: Warpage versus length predictions for parts fabricated on tooling with different CTEs. The maximum warpage predictions differ when the part length, L , becomes greater than Lc for the tooling material  134  Figure 5.9: Representative F E mesh used for COMPRO modelling runs. The laminate is 8 plies thick  135  Figure 5.10: Effect of mesh refinement on deformed part shape (4 Ply / 600 mm part, Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa)  135  3  -xiii-  4  Figure 5.11: Agreement between COMPRO and experimental deformed shape for an 8 ply, 600 mm part  136  Figure 5.12: Effect of initial resin modulus and shear layer modulus on COMPRO warpage results for 4 ply / 1200 mm specimens  136  Figure 5.13: Effect of initial resin modulus and shear layer modulus on COMPRO warpage results for 8 ply / 600 mm specimens  137  Figure 5.14: Effect of initial resin modulus and shear layer modulus on COMPRO warpage results for 16 ply / 300 mm specimens  137  Figure 5.15: COMPRO prediction versus average experimental result for 4 ply specimens. (Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa)  138  Figure 5.16: COMPRO prediction versus average experimental result for 8 ply specimens. (Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa)  138  Figure 5.17: COMPRO prediction versus average experimental result for 16 ply specimens. (Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa)  139  Figure 5.18: Interfacial shear stress distribution for a model with high shear layer stiffness (8 ply / 600 mm part, Initial Resin Modulus = 4.1 x 10 Pa)  139  Figure 5.19: Interfacial shear stress distribution for models with low shear layer stiffness (8 ply / 600 mm part, Initial Resin Modulus = 4.1 x 10 Pa)  140  Figure 5.20: Effect of initial resin modulus on in-plane stress distribution. The cross section considered is at the part centre. (8 ply / 600 mm part, Shear Layer Modulus = 6.9 x 10 Pa)  141  3  4  3  4  3  4  5  5  4  Figure 5.21: Development of in-plane stress with respect to time (8 ply / 600 mm part, Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa) 4  6  Figure 5.22: COMPRO prediction of resin modulus development with respect to time  141 142  Figure 5.23: Development of bending moment with respect to time for models with different initial resin modulus. (8 ply / 600 mm part, Shear Layer Modulus = 6 . 9 x l 0 Pa)  142  4  Figure A . l : Replicate measurement trials on a single 300 mm specimen  153  Figure A.2: Replicate measurement trials on a single 1200 mm specimen  153  Figure B . l : Strain gage calibration run showing raw thermal output, empirical thermal output equation and the residual. Gage A  158  Figure B.2: Strain gage calibration run. Gage B  158  Figure B.3: Strain gage calibration run. GageT  159  Figure B.4: Strain gage calibration run. Gage C Figure B.5: Strain gage calibration run. Gage C  159 160  -xiv-  Figure B.6: Strain gage calibration run. Gage T'  160  Figure B. 7: Strain gage calibration run. Gage B '  161  Figure B.8: Strain gage thermal output during a calibration check. The residual represents the error associated with this technique. Gage A  161  Figure B.9: Strain gage thermal output during a calibration check. Gage B  162  Figure B.10: Strain gage thermal output during a calibration check. Gage T.  162  Figure B. 11: Strain gage thermal output during a calibration check. Gage C  163  Figure B.12: Strain gage thermal output during a calibration check. Gage C'.  163  Figure B.13: Strain gage thermal output during a calibration check. Gage T'  164  Figure B.14: Strain gage thermal output during a calibration check. Gage B'.  164  Figure C . l : Deformation of the instrumented-tool / part assembly due to autoclave pressure compared with the deformation due to the bi-material strip effect. Even 103 kPa of autoclave pressure is sufficient to force the tool-part assembly to remain flat Figure D . l : Instrumented tool mechanical strain development for the entire cure cycle. 586 kPa / release agent interface condition  169 176  Figure D.2: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / release agent interface condition  176  Figure D.3: Instrumented tool mechanical strain development for the entire cure cycle. 586 kPa / FEP interface condition  177  Figure D.4: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / FEP interface condition  177  -xv-  NOMENCLATURE  c  distance from ply centroid to laminate neutral axis  C, Cj, C2, C3  arbitrary constants  Ci  coefficient of tool-part interaction  c  coefficient of interaction between sub-layers  CTE  Coefficient of Thermal Expansion  cv  coefficient of variation  E  Young's modulus  2  Ep rt  Young's modulus of the part  ETOOI  Young's modulus of tool  F  fit-up load  G  shear modulus  a  hi, h  thickness of adherends  I  section moment of inertia  L  length  2  L  critical length  L  strain gage length  Ls  stress transfer length  M  bending moment  n  number of layers  P  pressure  R  radius of curvature  s  sample standard deviation  t  thickness  T  temperature  t  thickness of adhesive layer  TAir  air temperature  T  glass transition temperature  TGage  strain gage temperature  c  G  A  -xvi-  tham  laminate thickness  tpiy  ply thickness  hool  tool thickness  U], U2  displacement of adherends  v  volume fraction  ^max  maximum part warpage  X  length coordinate  X  sample mean  z  height coordinate  a  degree of cure  r  shear strain  8  deflection  8jnterface  interface displacement  AT  temperature change  s  in-plane strain  Si  mechanical strain in sub-layer sk  „sk+l Si  mechanical strain in sub-layer sk+1  „ sn Si  strain in sub-layer n  „T f  free thermal strain of the fibre  F  S  final strain s  initial strain  SMechanical  mechanical strain  SMismatch  thermal strain mismatch  Smm  thermal output correction supplied by Micro Measurements  SThermal Output  strain gage thermal output  STotal  mechanical strain  si  free thermal strain of the tool  K  curvature  A  arbitrary constant  M  coefficient of friction  1  -XVll-  a  in-plane stress  0~Max  maximum in-plane stress  T  shear stress  TCr  critical interfacial shear stress  ^Debond  critical stress for debonding  Tlnterply  shear stress at the interply region under sliding friction conditions  ^Interface  interfacial shear stress under sliding friction conditions  TNet  net shear stress  ^Sliding  interfacial shear stress under sliding friction conditions  -xviii-  ACKNOWLEDGEMENTS  As with all such efforts, this thesis would not have been possible without the contributions of a number of individuals. I would firstly like to thank my supervisor Dr. Anoush Poursartip for the guidance he provided to my research, while still ensuring I was given sufficient freedom to make and learn from my own mistakes.  Perhaps more importantly I would like to acknowledge his  role in creating the working community which I had the privilege to be part of for the past three years. The technical assistance, encouragement and perspective offered by Dr. Goran Fernlund was also invaluable to me during the course of my work. I would like to express my appreciation to my friend and colleague, Mr. Robert Courdji who was always willing to share his abundant knowledge through countless hours of discussion.  The  input of Dr. Reza Vaziri on modelling issues was appreciated as well. Mr. Roger Bennett is to be thanked for his tireless efforts in maintaining an ailing autoclave, without which I could not have completed my experimental work. Mr. Serge Millaire and Dr. Pascal Hubert provided me with valuable assistance in setting up the instrumentation required for my research. Mr. Kurtis Willden and Mr. Chris Harris of The Boeing Company gave me an opportunity to learn about composites in the real world, an experience for which I am grateful. Many thanks to my colleagues in the Composites Group who each contributed in their own way to both my academic and social experiences at U B C . My extended family of friends and housemates have helped to make my life here in Vancouver the way it should be: a lot of fun. For that I thank you all. Last, but certainly not least, I recognize the unconditional love and support of Mom, Dad, Stewart and John. The generous contributions of the Bank of M & D and line of credits offered by the Rossland Savings Co. were also greatly appreciated.  -xix-  CHAPTER 1 : INTRODUCTION  Due to their exceptional specific strength and stiffness, fibre reinforced polymer composites are a preferred material for use in weight critical structures.  The premium placed on weight in  military aviation and space exploration applications is such that these industries were quick to adopt composites, despite a sometimes significant increase in product cost. Raw material costs for composite parts have reduced in recent years, however, they remain considerably higher than those of competitive light metal alloys.  For the affordable structures demanded by commercial aerospace applications, the high price of material must be balanced by lower manufacturing costs. Composite structures can be fabricated with less machining, fewer fasteners and reduced overall part count compared to their metal counterparts. Indeed the savings in manufacturing can more than offset the high initial material cost of composites.  A vital aspect of affordable composite manufacturing is the ability to fabricate parts within tight dimensional tolerances.  Manufacturing induced deformations are an unavoidable consequence  of processing and must be accounted for in the initial design of the tooling in order to ensure correct final part shape. Standard industrial practice relies on empirical experience, or a costly iterative approach to achieve the correct mold profile.  Furthermore, the issue of part-to-part  variability is typically addressed through the custom shimming of assemblies.  Recent efforts have enabled the development of process models, with which one can perform virtual tool design iterations, prior to the actual machining of the mold. This approach has  Chapter 1 Introduction  shown promise toward the goals of shimless assembly and the elimination of tool revisions. However, further improvement in the predictive abilities of process models is required to secure the cost-effective status of composites structures. For this improvement to occur, an enhanced understanding of the underlying causes of process induced deformation is required.  1.1  AUTOCLAVE PROCESSING OVERVIEW  The advanced composites considered here consist of continuous, high strength, high modulus reinforcing fibres embedded in a thermosetting polymer matrix. More specifically the scope of this study is limited to carbon fibre / epoxy composite systems. Typical fibre and matrix properties are listed in Table 1.1. The starting material for the manufacture of advanced composite structures is pre-preg: a thin sheet of material in which the fibres have been impregnated with a carefully controlled amount of resin. Pre-preg is commonly available in the form of uni-directional tape, approximately 0.2 mm thick. Prior to use, the pre-preg is stored in a freezer to prevent advancement of the curing reaction. Plies of pre-preg are cut to shape and draped on a rigid mold or tool, which will impart the desired shape. Multiple plies or laminae, are stacked together to create a laminate of the required thickness. By varying the orientation and stacking sequence of the plies, the aniosotropy of the composite tape can be exploited to tailor mechanical properties of the laminate to the anticipated loading. To ensure that the part can be removed from the tool after curing a chemical release agent is applied to the tool or alternatively, a thin polymer film is placed between tool and part.  Chapter 1 Introduction  Common tooling materials for autoclave processing are composite, aluminum, steel and invar. A key parameter in the selection of tooling is the Coefficient of Thermal Expansion (CTE) of the material.  Low C T E tools are generally preferred because their dimensions remain stable  throughout the cure cycle. Composite tools are advantageous because their C T E is usually quite low and also is tailorable but their service life is shorter than that of metal tools. Aluminum and steel are favourable for their relatively low cost, however, the industrial trend is towards tool materials which have greater dimensional stability. This explains why invar is commonly used as a tooling material, despite its relatively high cost.  Table 1.2 lists the common tooling  materials and their respective CTEs.  After the laminate stack is completed the part is covered with a resin impermeable parting film, a layer of porous breather cloth, and a sheet of air impermeable rubber or polymer film. Thermocouples used for process control may also be inserted into the part at this time. The rubber / polymer film outer layer is sealed against the perimeter of the tool to create an airtight bag. The vacuum bag assembly is illustrated in Figure 1.1. Vacuum is applied to the airtight bag causing compaction of the laminate stack.  Vacuum may also be applied in this fashion as  required during the lay-up in order to de-bulk the laminate.  The entire assembly is then placed in an autoclave where the part will be subjected to the heat required to bring the resin cure to completion. A common cure cycle would involve a slow (2 °C/min) heat-up to a cure temperature of 180 °C (355 °F) followed by a hold of approximately 2 hours. During processing the autoclave is pressurized, typically between 103 kPa (15 psi) to 1  586 kPa (85 psi), while the vacuum bag is vented to the atmosphere. This provides increased  1  A l l pressures refer to gage pressure, relative to atmospheric pressure.  -3-  Chapter 1 Introduction  force for laminate compaction and encourages any entrapped volatiles to remain in solution in the resin.  1.2  MATERIAL PROPERTY EVOLUTION  The structure and properties of the reinforcing fibres remain unchanged throughout the cure cycle, however, the resin matrix undergoes a considerable transformation from a low molecular weight liquid monomer to a rigid, crosslinked polymer. The advancement of the curing reaction is quantified by the parameter a, the degree of cure. Degree of cure is typically defined as the fraction of total heat of reaction which has been released up to the time of measurement (e.g. Osswald and Menges, 1995). Given the degree of microstructural change associated with curing, it is not surprising that resin material properties are highly dependent on both temperature and degree of cure.  During pre-preg manufacturing the resin is slightly cured (B-staged) such that it is semi-solid at room temperature during the lay-up. Once in the autoclave, as the process temperature rises, molecular mobility increases and the viscosity of the resin drops dramatically. The viscosity decrease due to temperature is soon countered by an increase in molecular length as the polymerization reaction commences.  Bond forming occurs and the resin eventually reaches  gelation, considered to be the point at which a molecule of infinite molecular weight is formed (Berglund and Kenny, 1991). The matrix now behaves as a visco-elastic solid but the processing temperature is well above the material glass transition temperature, T . Though the matrix is g  now capable of supporting stresses, they will decay quickly.  After gelation, cross-linking  continues and the material T rises, eventually increasing past the processing temperature. This g  Chapter 1 Introduction  transition is referred to as vitrification and is associated with an increase in elastic modulus of several orders of magnitude.  1.3  ASPECTS OF DIMENSIONAL CONTROL  Residual stresses invariably arise during the processing of composite structures and these often result in part dimensional changes. Common manifestations of residual stress are the spring-in of flanges on angled sections and the warpage of parts fabricated on flat tooling. A number of sources of residual stress have been identified, some intrinsic to the material itself and others dependent on external variables.  These mechanisms usually act collectively and furthermore  their relative contributions can vary depending on a number of parameters.  A common  observation amongst composite manufacturers and researchers is that there is a component of shape change which cannot readily be attributed to the well understood sources of residual stress such as material anisotropy (e.g. Pagliuso, 1982; Radford and Rennick, 2000). In particular, thin, balanced laminates fabricated on flat tooling are often seen to exhibit a concave down warpage after processing.  The explanation often invoked to account for this deformation is a mismatch between tool and part CTEs. This results in a shear interaction between the tooling and the curing part along their interface, inducing residual stresses in the part which lead to warpage. There is a large body of anecdotal evidence confirming the occurrence of tool-part interaction but there is very little information about the conditions under which it acts, the extent to which it can influence part shape or the variability associated with this phenomena. Efforts to incorporate this behaviour into process models have shown that tool-part interaction can have a tremendous influence on the magnitude of predicted deformation (Johnston et al., 1998). At the present time though, there is  Chapter 1 Introduction  a lack of experimental basis for the selection of input parameters for these models. A n increased understanding of tool-part interaction is required if the manufacturing dimensional control of composite structures is to improve.  1.4  RESEARCH OBJECTIVE AND APPROACH  Tool-part interaction induced deformations are currently an industrially significant problem but the physics of this interaction remain poorly understood. The current research aims to better establish the mechanics of tool-part shear interaction through experimental investigation.  It is  believed that this will provide a basis for improved quantitative modelling of this phenomena. The approach used is as follows:  1)  The state of understanding of tool-part interaction as presented in the current literature is examined in Chapter 2. The findings from this literature review provide the basis for the subsequent experimental studies.  2)  Chapter 3 presents a set of experiments examining the effects of various process and geometry parameters on tool-part interaction induced warpage. The results are later used for evaluation of the models discussed in Chapter 5.  3)  In Chapter 4, an experimental technique developed for identifying the magnitude and distribution of tool-part interfacial shear stress during the cure cycle is presented.  4)  Chapter 5 examines two models for the prediction of tool-part interaction induced warpage. The first model is a semi-quantitative analytical model (developed as part of the present work) based on the results of Chapter 4. The second model is a commercially available 2dimensional finite element composites process modelling code, COMPRO.  Chapter 1 Introduction  1.5  TABLES Table 1.1: Typical carbon fibre and epoxy matrix properties  Carbon Fibre  Property  1  Epoxy Matrix  Density (g / cc) Modulus (CPa)  220 - 440  4.1  Strength (Ml*a)  3800 - 6300  45 - 100  1.8  2  1.3  'AS4, U H M and IM7 Fibre Property Data Sheet, Hexcel Corporation 8551-7 and 3501-6 Resin Property Data Sheet, Hexcel Corporation  2  Table 1.2: Typical tooling material Coefficient of Thermal Expansions  Material  Average C T E , 20-100°C (^ / °C)  Aluminum (6061-T6) Steel (AISI 1020)  Invar 36  1  23.6 11.7  1  CFRP(AS4/3501-6)  1  2  -0/28 2.43  'ASM Metals Handbook 10th Ed. Theory of Composites Design, Tsai. - Properties for Longitudinal and Transverse Directions Respectively  2  Chapter 1 Introduction  1.6  FIGURES Vacuum Bag Film Vacuum Port  \  Breather  F E P Parting Film  Sealant Tape  Figure 1.1: Tool-Part-Vacuum Bag assembly.  CHAPTER 2: LITERATURE REVIEW  The problem of residual stress and associated shape change in composite parts is complex because of the large number of sources of residual stress and the potential for interaction between them. Those sources generally regarded as the most significant are listed in Table 2.1 along with a description of the mechanism by which they act, their manifestation and the prerequisites for their occurrence.  Of the sources / mechanisms listed in Table 2.1, those involving laminate anisotropy have been characterized most thoroughly. Tool-part interaction has often been invoked as an explanation for the poor agreement between experiment and analytical predictions which only account for thermal anisotropy (Radford and Rennick, 2000). Finite Element (FE) modelling work such as that presented by Wiersma et al. (1998) also shows that interactions between tool and part were significant in that tooling C T E had a direct impact on the total magnitude of predicted spring-in.  Nowhere is the deviation between anisotropy based prediction and experimental results greater than in the case of flat symmetric laminates. A concave down warpage is generally observed in laminates of this type which is not attributable, even in part, to laminate anisotropy. Tool-part shear interaction is one of the few viable mechanisms for the occurrence of this generally observed deformation. Because it represents a manifestation of tool-part interaction which is not obscured by other dimensional control issues, studies on the warpage of flat parts are of primary interest in this review. For this discussion, warpage refers to the distance measured between the part profile and a straight line connecting the part end points.  Chapter 2 Literature Review  2.1  WARPAGE THEORIES  Pagliuso (1982) offered a qualitative explanation of how tooling might affect sandwich panels manufactured on flat aluminum and composite tooling.  The hypothesis was that a laminate  forced against the tool by autoclave pressure, is stretched by the higher C T E tooling during the temperature ramp phase of the cure cycle.  In the case of sandwich panels, the lower skin is  stretched directly by the tooling expansion while the effect on the upper skin is diminished due to the compliant core which separates the facesheets. The imbalance in facesheet stresses causes a bending moment resulting in warpage of the panels away from the tool.  Experiments showed that the warpage effect scaled with tooling C T E in a qualitative sense. Experiments were also performed to identify the dependence of warpage on the type of release ply used but no relationship was apparent.  Nelson and Cairns (1989) presented a similar description for tool-part interaction acting in angled sections. It was suggested that the entire laminate is stretched by the high C T E tooling, but in the outer layers of the laminate this stress is relieved by resin flow and fibre motion. The suggestion was also made that the length of the laminate will be influential in the amount of deformation because more load will be transferred to a laminate with a longer frictional interface. No experimental evidence was presented to support this contention, however.  As part of a classification scheme of dimensional errors occurring in the fabrication of laminates, Ridgard (1993) identified what was referred to as a Type Ilia Thermomechanical Distortion error. Similar to the intuitive explanation offered by Pagliuso (1982), it was suggested that this type of error may occur when three conditions are met.  Firstly the tool must have a C T E  significantly greater than that of the fibre reinforcement in the pre-preg. Secondly, the laminate  -10-  Chapter 2 Literature Review  must be clamped to the tool by autoclave pressure and finally, the entire assembly must be subjected to a large temperature rise. Under such conditions the expansion of the tool will place all of the fibres of the laminate in tension. As this occurs prior to any significant curing in the matrix, fibres which are distant from the tool are able to relieve this stress through interply slippage. Again, this causes a net bending moment which will warp an otherwise flat part. This is illustrated schematically in Figure 2.1.  Ridgard (1993) noted that this type of error is highly variable from part to part and can depend on parameters such as pre-preg age, resin viscosity, as well as process variables such as the rate and magnitude of pressure and temperature application. No quantitative information was given about the relative significance of these parameters but a number of strategies were recommended for addressing this type of error. Matching the tooling C T E to that of the part, or using low temperature curing resins was said to render the deformations negligible. Also, for tooling made of composite materials a suggestion was made to join together multiple small sections of laminate, rather than using one continuous length.  This implies that there is also a length  dependence to the magnitude of this type of dimensional error.  A unique mechanism for the occurrence of warped parts fabricated on flat tooling was put forth by Radford (1993).  Many early generation pre-pregs were fabricated with an excess resin  content which, during processing, is drawn out of the laminate into a porous material known as a bleeder. It was suggested that when a top bleed process is used, a non-uniform volume fraction (Vp) through the thickness of the part is the result. This volume fraction gradient was identified and characterized via image analysis of part cross sections. By considering the resulting nonuniform cure shrinkage and C T E in a Classical Lamination Theory (CLT) analysis, attempts were made to predict the experimentally observed warped shape.  Chapter 2 Literature Review  The key assumption to Vp gradient induced warpage is the occurrence of non uniform resin bleeding. Current generation material systems are fabricated with net-resin content and require no bleeding so this assumption becomes questionable. In fact, in subsequent research Radford et al. (1999) noted that the Vp gradients were only a small contributor to the total curvature.  2.2 An  QUANTITATIVE WARPAGE STUDIES effort to verify the qualitative explanations of tool-part interaction proposed by earlier  researchers was performed by Flanagan (1997). Building on the notion of interply slippage as expressed by Ridgard (1993), it was assumed that sliding occurred at the tool-part and interply interfaces. The critical value of shear stress at which sliding occurs at a given interface  was  assumed to follow the classical friction relation:  r  C r  =ju-P  (l.l)  where r<> is the critical interfacial shear stress, ju is the coefficient of friction and P is the pressure acting normal to the interface.  Interface and interply friction coefficients were measured experimentally for various tool surface conditions and pressures and by incorporating the experimental coefficient of friction data into a finite element simulation, the deformation arising during the actual fabrication process  was  modelled.  The  A number of specimens were also fabricated for model validation purposes.  results from the warpage experiments are examined in this section while the warpage modelling efforts and friction experiments of Flanagan (1997) are considered in Section 2.3 and Section 2.5 respectively.  -12-  Chapter 2 Literature Review  The parametric warpage study performed by Flanagan (1997) was mainly focused on 8 ply laminates with either uni-directional or cross-ply lay-ups. aluminum and CFRP.  The tooling materials were steel,  The cure cycle used was a standard single hold 180 °C (355 °F) with  varying process pressures of 103 kPa (15 psi), 275 kPa (40 psi) and 586 kPa (85 psi). Both Freekote release agent and FEP release film interfaces were used.  Flanagan (1997) noted the experiments showed a relatively linear increase in maximum part warpage with increasing part length as shown in Figure 2.2. No comment was made regarding the trend of warpage with respect to part thickness, however, the data in Figure 2.3 shows a significant decrease in warpage as ply count was increased. A strong pressure dependence and tool surface condition effect was also observed in the experimental results.  Higher process  pressures resulted in greater warpage magnitudes as did the use of release agent compared to FEP (Figure 2.4).  A proportionality between part warpage and tool C T E was noted but not quantified (Figure 2.5). An interesting result was the fact that there was still measurable warpage for parts fabricated on CFRP tooling, despite the matched C T E between tool and part.  As previously mentioned, Radford et al. (1999) proposed that the warpage of flat laminates is, at least in part, related to V F gradients induced by the top bleed process.  A distinguishing  characteristic of this mechanism is that the curvature of the laminate should change with respect to temperature due to the non-uniform laminate C T E . By subjecting the cured laminate to a range of temperatures and carefully measuring the change in deformed shape, the contribution of V F induced warpage to the total warpage was estimated. The remaining amount of warpage was then attributed to tool-part interaction effects.  -13-  Chapter 2 Literature Review  A parametric study was performed whereby a number of parts were fabricated using a single hold, 120 °C (250 °F) cure cycle. A l l specimens were 4 ply laminates with nominal dimensions of 25 mm x 250 mm (1" x 10"). Tooling materials considered were aluminum, steel and ceramic (CTE = 5.82 ju I °C). FEP and release agent interfaces were also compared, furthermore, specimens were fabricated under 2 bleeder ply, 1 bleeder ply and no-bleed conditions.  The results were analyzed in two groupings as shown in Figure 2.6 and Figure 2.7. As noted by the authors, the Vp contribution to the total curvature indicated by the slopes of the curvature versus temperature plots, was negligible.  The specimens represented in Figure 2.6 were all  fabricated without any resin bleeding. It was also noted that there was no consistent tool C T E effect, nor any apparent effect of tool-surface finish under these conditions.  Figure 2.7 examines the interaction between the amount of bleeder and the tool surface condition for specimens fabricated on aluminum tooling. Radford et al. (1999) noted specimens fabricated with an FEP interface showed very little bleeder effect, while for those with a release agent interface, the effect was dramatic with more bleeder plies leading to larger specimen curvatures. They proposed that with increasing amounts of resin bled from the part, there would be greater stress transfer at the tool-part interface due to increased fibre bed interaction. Furthermore, it was suggested that with the use of an FEP interface, the part was de-coupled from the tool which defeated the action of increased resin bleeding.  Some of the above results are in conflict with those presented by Melo and Radford (1999). Using the previously described measurement technique for isolating the components of warpage, they examined parts which were fabricated using a 2 hold cure cycle. Specimens of 19 mm x  -14-  Chapter 2 Literature Review  250 mm (0.75" x 10") were fabricated with various uni-directional and cross-ply lay-ups, using 2 bleeder plies and a release agent interface. The tooling was either ceramic or aluminum.  In this research the authors reported that the V F contribution to the total warpage was very large, in some cases the entire amount of room temperature warpage being attributable to the V F effect. The reason for this discrepancy with previous results was not discussed. Tool C T E effects were inconclusive, a result which was attributed to a difference in surface finish between the aluminum and ceramic tools.  2.3  WARPAGE MODELLING  The modelling approach utilized by Flanagan (1997) consisted of  two steps.  The first  considered the strains arising during the early portion of the cure cycle when interfacial / interply sliding was assumed to be occurring while the second step was an elastic analysis considering post gelation developments.  In the first segment, temperature dependent friction coefficients  determined through the  previously mentioned friction experiments were incorporated into a contact surface model in HKS Abaqus.  Slippage was considered at the tool-part interface and between the first and  second plies only. Initial modelling runs which incorporated contact surfaces between all plies showed that only the 1 ply /2 st  nd  ply interface slipped, hence the other contact surfaces were  unnecessary.  The contact surface model yielded an in-plane strain distribution for the part which was then incorporated into an elastic F E model. The strains arising due to the interlayer friction were  -15-  Chapter 2 Literature Review  expressed as initial thermal strains in the elastic analysis. From this analysis a deformed part shape could be predicted.  Flanagan (1997) noted agreement between the trend of induced warpage in the numerical and experimental results as is apparent in Figure 2.2 through Figure 2.5. In particular, the modelling approach was successful at predicting the experimentally observed dependence of warpage on tool surface condition, and pressure. The modelling results greatly overpredicted warpage as the part length was increased, with the model essentially predicting an exponential increase in warpage as length was increased. The author suggested that a shortcoming of the modelling approach was the inability of the pure friction model to distinguish between tools of different CTE.  A different approach to modelling tool-part shear interaction was followed in the research presented by Johnston et al. (1998, 2000). A 2-D F E modelling program was created which utilizes an incremental elastic approach to predict the development of residual stresses arising during autoclave processing. For a complete description of the model development the reader is referred to Johnston (1997).  Instead of employing a sliding friction tool-part interface as Flanagan (1997) did, a single layer of low modulus elements was incorporated into the F E mesh between the tool and part. By adjusting the modulus of this "shear layer", the amount of stress transferred between tool and part could be tailored. At the one extreme, by setting shear layer properties equivalent to that of the tooling material, the part was effectively perfectly bonded to the tool throughout the cure cycle. At the other end of the spectrum, by setting the in-plane and shear modulii of the shear layer very low, ~ 10 Pa (while maintaining the same out of plane modulus as the tooling 5  -16-  Chapter 2 Literature Review  material to prevent the part from penetrating the shear layer) the response of a compliant interface could be approximated. With the use of experimental data the shear layer properties were calibrated to an appropriate value.  Johnston et al. (1998) reported that modelling results were highly dependent on the shear layer properties with the predicted deformations of a given panel spanning several orders of magnitude.  By pre-calibrating the shear layer against a single, experiment, however, good  predictions could be made for other parts.  No general study concerning the effects of part geometry or process conditions on the warpage of flat parts was performed but examination of the results from a number of more complex structures suggests some strengths and weaknesses of this approach. The shear layer was shown to be able to account for the effect that tool-part C T E mismatch has on deformation, at least qualitatively. Pressure effects would not be predicted by the elastic shear layer itself, however it is plausible that the shear layer properties could be calibrated for each pressure.  The main  shortcoming of this approach is the lack of physical basis for selection of the shear layer properties.  Furthermore, the fact that there are three main shear layer variables:  in-plane  modulus, shear modulus and thickness, can add substantial complexity to the model.  In contrast to the numerical modelling efforts described above, Melo and Radford (1999) developed a analytical model to predict tool-part interaction induced warpage in cross-ply and uni-directional laminates.  As with Flanagan (1997) the model was based on the mechanism  suggested by Ridgard (1993). Stresses in the laminate were assumed to be borne solely by the fibres and were expected to develop only during the heat-up, after which the stresses are locked  -17-  Chapter 2 Literature Review  in by the curing of the resin. Slippage was assumed to occur between the fibres thereby creating the requisite stress gradient.  The authors considered adjacent plies of the same orientation to be a single layer. Based on this a uni-directional laminate was considered a single layer, while a cross ply laminate would have n layers as shown in Figure 2.8. Furthermore, because stresses were considered to be supported only by the fibres, transversely oriented layers were assumed to have no modulus and hence, transfer no stress to layers adjacent to them. In order to generate a gradient in stress, the layer closest to the tool (layer n) was divided into sub-layers, also depicted in Figure 2.8.  The amount of strain transferred to the sub-layer closest to the tool was expressed as:  sr=c -(s -s/) where sf  n  (1.2)  T  l  t  is the mechanical strain induced in sub-layer sn (closest to the tool), Cj is the T  T  coefficient of tool-part interaction and e and Sf are the free thermal strains (or AT) of the tool t  and fibre respectively. The mechanical strain in the other sub-layers was given as:  e* = C -e 2  where £i  sk  sk+i  l  (1.3)  is mechanical strain in sub-layer sk, C2 is the coefficient of interaction between sub-  layers,.and sf  k+1  is the mechanical strain in sub-layer sk+1. Multiplying by the modulus yielded  a stress in each sub-layer, from which the bending moment and curvature of the laminate could be calculated using C L T .  -18-  Chapter 2 Literature Review  The distribution of in-plane stress for various lay-ups with different values of C; and Cj is shown in Figure 2.9. The researchers noted that they were not able to determine a unique set of values for the coefficients which was able to generally predict the experimentally observed results. Furthermore, they suggested that an experimental technique needs to be developed to measure the coefficients.  The work presented by Melo and Radford (1999) was, in the authors' admission, a preliminary model hence there was relatively little comparison between modelling and experimental results. Considering the model formulation, however, some comments can be made even without experimental results.  The total force transferred to the part by means of friction is expected to vary with location along the length of the part, and also to depend on the total length of the tool-part interface (Nelson and Cairns, 1989; Flanagan, 1997). By contrast the model of Melo and Radford (1999) assumes that the stress distribution through the part thickness is unchanging with respect to location or total part length. The formulation is consistent with stresses being introduced into the laminate as an end effect rather than through stress transfer along the length of the interface.  2.4  FRICTION THEORIES  The two empirical laws which are commonly used to describe friction phenomena were first articulated by Amonton. (e.g. Arnell et al., 1991).  1. Friction is independent of the apparent area of contact of the two bodies.  2. The force due to friction is proportional to the normal load.  -19-  Chapter 2 Literature Review  T h e s e c o n d l a w i s u s u a l l y expressed i n the f o r m p r e v i o u s l y i n t r o d u c e d :  T =jU-P  (1.1)  Cr  E v e n w i t h the c o n s i d e r a b l e amount o f research c o n d u c t e d i n the f i e l d o f t r i b o l o g y , the a c c u r a c y w i t h w h i c h f r i c t i o n coefficients c a n be p r e d i c t e d r e m a i n s l o w .  T h e r e are t w o theoretical  m e c h a n i s m s g e n e r a l l y put forth as c o n t r i b u t i n g to the total coefficient o f f r i c t i o n : theory a n d d e f o r m a t i o n theory.  adhesion  I n b o t h cases it is important to understand that the surfaces o f  m a c r o s c o p i c a l l y s m o o t h materials are c o v e r e d i n m i c r o s c o p i c u n d u l a t i o n s or asperities.  True  contact b e t w e e n t w o surfaces o n l y o c c u r s at the tips o f the asperities w h i c h have d i m e n s i o n s o n the order o f m i c r o n s . F o r this reason, the actual contact area is m u c h s m a l l e r than the apparent contact area.  A s the n a m e i m p l i e s , adhesion theory proposes that adhesive b o n d i n g takes p l a c e b e t w e e n asperities. T h e nature o f b o n d i n g at p o l y m e r - m e t a l interfaces i s c o m p l e x and b e y o n d the scope o f interest here, h o w e v e r , the force o f f r i c t i o n c a n be regarded as the force r e q u i r e d to break the bonds b e t w e e n the asperities ( L e e , 1991). I n contrast, d e f o r m a t i o n theory assumes n o b o n d i n g at the interface.  R a t h e r the force o f f r i c t i o n arises due to the m e c h a n i c a l i n t e r a c t i o n o f the  asperities, w h i c h must d e f o r m i n order to a c c o m m o d a t e s l i d i n g at the interface.  The physical  basis for A m o n t o n ' s first l a w b e c o m e s clear g i v e n that it i s o n l y the asperities w h i c h  are  interacting rather than the entire apparent contact area. F u r t h e r m o r e , the n u m b e r o f asperities i n contact w i l l increase w i t h i n c r e a s i n g force n o r m a l to surface e x p l a i n i n g the s e c o n d e m p i r i c a l relation.  -20-  Chapter 2 Literature Review  2.5  TOOL-PART INTERFACE CHARACTERIZATION  As part of a study of the compaction and flow of composite laminates, Hubert et al. (1996) used an environmental scanning electron microscope to observe the tool-part interfacial region of a laminate during processing. The procedure involved compacting a laminate between two plates, thereby forcing the material to flow perpendicular to the applied load. The apparatus used is shown in Figure 2.10.  By monitoring the migration of tungsten markers placed at locations  throughout the laminate, the change in displacement profile with respect to time was determined. This displacement profile in turn could be related to the interfacial conditions. Initially a no slip condition was observed, resulting in shear deformation of the laminate near the tool. However, after a critical shear stress was exceeded at the laminate interface a fractional sliding condition occurred. While the experiments were only performed at low temperatures (50 °C) and degrees of cure, the result is significant in that it suggests that there are two conditions which can be operative at the tool part interface. As previously mentioned, Flanagan (1997) experimentally characterized friction coefficients using a test apparatus shown schematically in Figure 2.11. Friction coefficients were determined for the cases of a tool coated with release agent (Freekote), a tool covered with an FEP release ply and for the interface between two plies.  Experiments were performed with deadweight  loading up to a pressure of 240 kPa (35 psi).  All friction coefficients were found to be  insensitive to pressure, however, there were significant changes in p with respect to temperature. Efforts were made to have the heat-up rate in the friction experiments representative of the recommended autoclave cure cycle, hence, friction coefficients were expressed solely as  -21-  Chapter 2 Literature Review  functions of temperature rather than considering degree of cure as a second state variable. The values determined from the friction experiments are presented in Table 2.2.  Flanagan (1997) noted that the measurement of interply friction coefficients was considerably more difficult than for the interface coefficients. For the interply case, the critical shear stress at which sliding commenced corresponded to a /j. of approximately 0.15.  After interply slippage  had commenced, however, ju reduced dramatically to a value which was estimated to be 0.01. If the loading was stopped and then resumed, ju returned to its initial higher value. The suggestion was that after slippage had commenced, a lubricating resin layer reduced the apparent interply friction coefficient.  For modelling purposes Flanagan (1997) assumed that ju= 0.01 was  representative. Friction coefficients were evaluated for both 0°-0° and 0°-90° interfaces with the latter being approximately 10% lower.  Some comments can be made about this technique for measuring friction coefficients.  •  Experimental measurements were only performed up to pressure of 240 kPa, whereas actual process pressures range as high as 586 kPa.  This assumes a large range of  applicability of the friction coefficients.  •  Pressure loading was achieved using deadweight on top of the tool surface. While this is statically equivalent to the loading experienced by a vacuum bagged part subjected to autoclave pressurization, the effect at the tool-part interface is different.  As an  illustration of this concept consider two identical parts resting on a tool under ambient pressure, with one of the tool-part assemblies enclosed in a vacuum bag. In both cases the pressure loading on the tool-part interface is equivalent to atmospheric pressure and  -22-  Chapter 2 Literature Review  the apparent tool-part contact area is identical. The vacuum bag, however, encourages intimate contact at the tool-part interface, greatly increasing the  actual  contact area. The  effect of this would be to increase the apparent ju considerably.  A qualitative means of examining the interactions between tool and part during processing was presented by Fernlund et al. (2000). A strain gage rosette was mounted on a thin aluminum tool, measuring strain in the two perpendicular directions. A stack of pre-preg was placed on the opposite side of the tool plate. After lay-up, the tool and part were enveloped in a vacuum bag and subjected to a cure cycle during which time the strain in the tool was measured. No external autoclave pressure was applied to the curing assembly.  In one case the experiment was  performed with a roughened tool surface and no release agent at the interface, while in the other case two sheets of Mylar release film were placed at the tool-part interface.  The results showed that for the Mylar interface, the strain measured in the tool-plate during both the heat-up and cool-down was approximately the same as that due to the free thermal expansion of aluminum. This indicated that there was little or no mechanical interaction between the tool and part. Similarly the untreated interface experiment showed no interaction during the heat-up until the point of gelation.  After gelation, and in particular during the cool-down there was  significant interaction. This was indicated by the fact that changes in strain as a function of temperature were more representative of longitudinal and transverse CTEs of the CFRP part rather than the C T E of the aluminum plate. This is illustrated in Figure 2.12.  For the material and cure cycle considered, the resin was expected to reach gelation just prior to the isothermal hold. The conclusion of the researchers was that prior to gelation, there was no appreciable mechanical interaction between tool and part, regardless of tool surface condition.  -23-  Chapter 2 Literature Review  For the untreated interface, stress transfer between the tool and part was evident after part gelation, whereas the use of the Mylar film at the interface prevented any significant interaction regardless of degree of cure.  2.6  SUMMARY •  There is general agreement that C T E mismatch between the tool and part results in shear stress transfer to the part. Most researchers assume the stress is transferred to fibres in the laminate via sliding friction condition at the interface. Slippage between fibres within the laminate results in a through-thickness residual stress gradient, causing the commonly observed concave down warpage of flat parts.  •  Experimental studies have shown that the following parameters influence tool-interaction induced warpage:  part geometry, process pressure, tool surface condition, amount of  resin bleeding and tooling. There is no consensus on the relative significance of these effects, however.  •  Part to part variability was a significant issue noted in experimental studies.  •  The limited characterization of the tool-part interface which has been performed suggests that depending on the tool surface condition (FEP or release agent) and degree of cure of the part, either a sticking interface or sliding interface condition may occur.  •  Efforts to model tool-part interaction have met with mixed success.  -24-  Chapter 2 Literature Review  2.7  TABLES Table 2.1: Sources of processed induced deformation in composite laminates  Keierence Source Necessary Conditions Mechanism Manifestation Nelson and Cairns (1989) CTE / cure shrinkage mistmatch Jain et al. (1997) Anisotropic Part Curved laminate between laminate in-plane and out ofSpring-in of angled parts Wiersmaet al. (1998) Properties plane directions Fernlund and Poursartip (1999) Radford and Rennick (2000) White and Hahn (1992b) CTE / cure shrinkage mismatch above Ridgard(1993) Anisotropic Part Unbalanced lay-up Warpage of flat parts Properties and below laminate mid-plane Johnston (1997) Cho et al. (1998) Bogetti and Gillespie (1992) Part Temperature / Thick parts and / or high Gradient in thermal strains and Various Fernlund and Poursartip (1999) Degree of Cure temperature ramp rates material properties Gradients Nelson and Cairns (1989) Jain et al. (1997) Tooling Constraints Curved laminate, tool-part CTE Normal stresses applied to part Various mismatch, pressure Johnston et al. (1998) Radford and Rennick (2000) Pagliuso (1982) Ridgard(1993) Flat Laminate, Tool-part CTE Interfacial shear stresses applied to Warpage of flat parts and Flanagan (1997) Tooling Constraints mismatch, pressure part others Melo and Radford (1999) Fernlund et al. (2000) Hubert et al. (1996) Laminate Flow and Resin Pressure Gradients Material migration, material property Thickness variation, Compaction gradients others  Table 2.2: Experimentally determined coefficients of friction (Flanagan, 1997).  Temperature Range ( ° C ) 22 - 165 Tool-Part Interlace, Release Agent Tool-Part Interlace, F E P Interply  -25-  0.18 0.07 0.01  165 - 170 170 -179  0.25 0.15 0.18  0.32 0.21 0.30  Chapter 2 Literature Review  2.8  FIGURES  A u t o c l a v e Pressure  A u t o c l a v e Pressure  Figure 2.1: Proposed mechanism for warpage due to tool-part interaction, a) Tool expands thermally on heating to pre-preg cure temperature. Friction at interface induces tensile fibre stresses in lay-up. b) Layer slippage relieves fibre stresses preferentially in layers furthest from tool face. Non-uniform stresses locked in when pre-preg cures, c) Laminate bows away from tool face (Ridgard, 1993).  -26-  Chapter 2 Literature Review  60  Ply Length (mm)  Figure 2.2: Experimental and numerical warpage results for 16 ply, uni-directional laminates of various lengths. Samples were fabricated at 586 kPa on steel tooling with release agent (fk0_16) and FEP(rfO_16) interfaces (Flanagan, 1997).  1.2  Ply Numbers  Figure 2.3: Experimental and numerical warpage results for 300 mm, uni-directional laminates of various thicknesses. Samples were fabricated at 586 kPa on steel tooling with a release agent interface (Flanagan, 1997).  -27-  Chapter 2 Literature Review  0  0.1  0.2  0.3  0.4  0.5  0.6  Pressure (N/mm ) J  Figure 2.4: Experimental and numerical warpage results for 300 mm, 8 ply, unidirectional laminates at various pressures. Samples were fabricated on steel tooling with release agent (fk0_8) and FEP(rfO_8) interfaces (Flanagan, 1997).  aluminium  steel  carbon fibre  Tool Material  Figure 2.5: Experimental and numerical warpage results for 300 mm, 8 ply, unidirectional laminates with various tooling materials. Samples were fabricated on steel tooling with release agent (fk0_8) and FEP(rf0_8) interfaces (Flanagan, 1997).  -28-  Chapter 2 Literature Review  ~  s  ~ Ceramic/Spray  -  • • " •Ceramic/Film  A  —  Stee^Spray  °  • * • - Steel/Film  " *  Aluminum/Spray •AJurninunVFilm  0.25  0.00  F i g u r e 2.6:  • 20  Curvature  1  1  1  1  1  40  60  80  100  120  versus temperature  conditions.  surface  long, 4 ply, uni-directional  laminates  t h e u s e o f b l e e d e r plies ( R a d f o r d et a l . , 1 9 9 9 ) .  ®"~ No Bleeder/Spray  -*  for various tool materials a n d  A l l samples were 250 m m  fabricated without  —  Temperature (C)  1 140  &  •No Bleeder/Film  1 Bteeder/Spray  ""2  ~~*~ 1 Bfeeder/Film  Bleeders/Spray  " * " "2 Bleeders/Film  0,7 o.e  B-  ,-vO.S  -B-  g 03 0.2  -e-  0.1 o.o -i  1  1  1  1  1  20  40  60  80  100  120  i  140  Temperature (C)  F i g u r e 2.7:  Curvature  versus temperature  surface conditions.  for various bleeder arrangements  A l l samples were 250 m m  laminates fabricated on aluminum  -29-  long, 4 ply,  and  tool  uni-directional  t o o l i n g ( R a d f o r d et a l . , 1 9 9 9 ) .  Chapter 2 Literature Review  ,  •0.30  C1-0.2. C2-0.9  . .-C1=0.3. C2=0.69|-  -0.16 s a! £ 0.00 0.15 55  B  .^..01=0.4. C2=0.52  tn E °-  -37.50  -50.00  -25.00  O 0.30 a 0.00  -12.50  INDUCED STRESSES IN THE LAMINATE, MPa  __»_C1=0.i C2=0.9 ..o—C1=0.3, C2=0. .. ...C1=0.4, C2=0.52. A  •50.00  -37.50  -25.00  -12.50  0.00  INDUCED STRESSES IN THE LAMINATE, MPa  .C1=0.2. C2-0.9 .C1=0.3, C2=0. . C1=0.4, C2=0.52  50.00  -37.50  -25.00  -12.50  INDUCED STRESSES IN THE LAMINATE, MPa  Figure 2.9: Theoretical in-plane stress gradients for a) [0/90] , b) [0] , c) [0] laminates fabricated on aluminum tooling (Melo and Radford, 1999). s  -30-  4  6  Chapter 2 Literature Review  E S E M observation  XX  Marker Sample  Fibre orientation Applied displacement Oblate)  Aluminium shims  Teflon film  Figure 2.10: Test rig used by Hubert et al. (1996) for observation of shear flow during the compaction of laminates.  Temperature readout for thermocouples Universal Tensile Testing Machine  y middle o f the stack  P 1  from  Dead weight loading  Connected to computer Transducers & ^racket  Laminate stack  Figure 2.11: Coefficient of friction test rig (Flanagan, 1997).  -31-  Chapter 2 Literature Review  200 Temperature (°C)  Figure 2.12: Measured strain in the flat aluminum tool during heat-up and cool-down with no mould release on the tool. The C F R P was uncured prior to heat-up and that the temperature was held at 177°C for two hours before cool-down. Fernlund et al. (2000).  -32-  C H A P T E R 3 : EXPERIMENTAL W A R P A G E SPECIMENS  In order to experimentally quantify the effect of tool-part interaction, a number of uni-directional CFRP samples were fabricated on flat tooling and measured for deformation. To the greatest extent possible, process conditions and part sizes were selected to reflect industrial practice. The following parameters were selected as experimental variables:  •  Part thickness - [0]4 , [0]s and [0]i6 ply lay-ups were examined.  •  Part length - 300 mm, 600 mm and 1200 mm part nominal lengths.  •  Autoclave Pressure - 103 kPa (15 psi) and 586 kPa (85 psi).  •  Tool Surface Condition - 2 plies of FEP and Freekote 700 N C release agent.  3.1  SAMPLE FABRICATION  All specimens in this study were fabricated by hand cutting and lay-up of a carbonfibre/ epoxy pre-preg material, followed by autoclave curing. The material used was T-800H/3900-2 unidirectional tape manufactured by the Toray Company. The autoclave was operated under leadlag control with four J-type thermocouples located on a single part. As many as four parts were cured in each autoclave run, so thermocouples were placed on the thickest part of a given batch to  ensure  the  lagging  thermocouples  were  -33-  representative  of  the  coolest  regions.  Chapter 3 Experimental Warpage Specimens  3.1.1  T O O L PREPARATION  All parts were fabricated on the same aluminum (Al-6061 T-6) tool with dimensions of 1400 mm x 640 mm x 6.35 mm.  The experiments were conducted on aluminum tooling in order to  maximize tool-part C T E mismatch. Flatness of the tool as set up in the autoclave was checked using a straight edge and feeler gauge. Deviation from flat was not more than 0.075 mm over 1200 mm. Prior to use the tool was prepared in the following fashion: Firstly the tool was abrasively cleaned using water and wet-dry paper progressing from 400 grit through 600 grit. The tool was then degreased using acetone. Freekote 700 N C , a release agent manufactured by the Dexter Company, was applied using a cloth. After the solvent from the first coat had dried, a second coat was applied and left to dry for at least 15 minutes prior to lay-up.  In industry it is a common procedure to scrape bonded resin from the tool and locally touch up the release agent coat between runs. Complete tool cleaning is performed only when the release agent coating has degraded enough to render part removal excessively difficult. It was felt that this practice, however, might increase the run-to-run tool surface condition variability. As such, each time a part was fabricated without the use of FEP parting film, the tool was completely cleaned and re-coated as described above.  3.1.2  L A Y - U P AND CURE  Plies of pre-preg were cut to a nominal width of 100 mm and stacked, with vacuum compaction performed every 4 plies. The vacuum bag arrangement was similar to that shown in Figure 1.1. For specimens with an FEP interface, each part was placed on two new, separate sheets of film.  Both the high and low pressure cure cycles used the same thermal cycle: a standard 180 °C (355 °F) cure cycle with a temperature ramp rate of 2.2 °C/ min (4 °F/ min).  -34-  The high and low  Chapter 3 Experimental Warpage Specimens  pressure target cure cycles are shown in Figure 3.1 and actual run data from two representative runs is shown in Figure 3.2.  3.2  SAMPLE MEASUREMENT  After curing, part edges were trimmed by approximately 10 mm to provide a straight edge for measurement purposes. For most of the specimens, deflections due to part self weight were significant with respect to overall warpage. To negate this effect, all measurements were taken with the part on its side. Warpage measurement was performed in one of two ways depending on the part length. For 300 mm and 600 mm specimens the following procedure was used: parts were placed edge down on a flatbed document scanner. The arrangement is shown in Figure 3.3. The scanner was an HP Scanjet 4C with optical resolution of 600 dpi. After the part was arranged, a black housing was placed over the scanner to prevent obscuring of the image by other light sources. A grey scale image of the part profile was created, with the scanner set at maximum resolution without software enhancement.  It is important to note that document scanners may cause some degree of image distortion, the severity of which varies with respect to location on the scanner bed. Prior to part measurement, a full mapping of this distortion was carried out for the scanner in question (Fidler, 1998). Parts were placed in a zone of the scanner known to be unaffected by this distortion.  Image post-processing was performed using Ulead PhotoImpact.  The image contrast was  increased to the maximum, and then image brightness was adjusted until the part edge was sharply defined.  Examples of pre and post-processed images are shown in Figure 3.4.  The  edited image was then opened using Measure 6, an image analysis software (Paris, 1996). The Measure 6 software was calibrated using a standard of known dimensions, after which pixel  -35-  Chapter 3 Experimental Warpage Specimens  coordinates were recorded and exported to MS Excel for data post-processing. Edge coordinates were measured at approximately 12 mm intervals along the part length.  An additional step was required for the 600 mm specimens as their edge length exceeded the length of the scanner bed. A n image of half of the part edge was captured, and then the part was rearranged to permit scanning of the remaining edge portion. A n overlap of approximately 75 mm was common to both images. Prior to scanning two characteristic marks were made with a scalpel blade, approximately 50 mm apart and located near the part centre. The coordinates of the characteristic points as well as the edge coordinates were then recorded for the two images. Then during data post processing, a rotation of coordinates was applied to bring the characteristic points into coincidence. In this manner coordinates from the two half edges could be spliced together to create a composite data set.  The length of the 1200 mm parts meant that measurement using the scanning method was impractical. Instead, the warpage profile of these parts was traced onto paper. The distance of the profile from a straight edge reference was measured using Vernier calipers, at locations every 100 mm along the part length.  Measurement error estimates were based on replicate measurements of the same part. Details of the error estimate are presented in Appendix A. The scanner technique used for 300 and 600 mm parts had an associated error estimated to be ± 0.03 mm per coordinate point. The measurement error estimate of the method used for the 1200 mm parts was ± 0.5 mm, considerably larger than that of the scanner method. The magnitude of warpage demonstrated by parts of this length was also greater though, hence the error magnitude was still small with respect to the measurement  -36-  Chapter 3 Experimental Warpage Specimens  data. Measurement error bars are included in subsequent figures for reference purposes unless measurement error was negligible with respect to the magnitude of warpage.  3.3  RESULTS  Specimens generally deformed in a smooth, symmetrical arc, concave down towards the tooling. A photograph showing the magnitude of warpage which can occur is shown in Figure 3.5. Part shapes are shown in Figure 3.6 to Figure 3.8.  The effects of part geometry and process  conditions were examined with respect to maximum part warpage, and with respect to part curvature.  Replicate runs were performed for a few selected specimens in order to provide  information regarding batch to batch variability. Conditions for which replicate specimens were made have the average part profile shown here, while specimen variability is addressed in Section 3.3.1.5.  3.3.1 WARPAGE RESULTS For this discussion warpage refers to the distance measured between the part profile and a straight line connecting the part end points. The maximum warpage, w  max  exhibited by a part,  provided a useful basis for comparison of part shape. Table 3.1 lists the maximum warpage and average curvature for each specimen fabricated. The effects of the 4 experimental variables on maximum part warpage will be discussed individually.  3.3.1.1  Warpage - Length Effect  Longer parts were seen to warp considerably more than shorter parts, regardless of process conditions or part thickness.  Maximum part warpage versus length is plotted in Figure 3.9  through Figure 3.11. To isolate the length effect, the data was condensed onto a single plot by  -37-  Chapter 3 Experimental Warpage Specimens  normalizing the  w  max  for a given part with respect to the w  thickness and process conditions.  max  for a 1200 mm part of the same  The length normalized warpage is shown in Figure 3.12.  Curves representing warpage magnitudes proportional to L  2  ,L  3  and L , where L refers to part 4  length, are shown in Figure 3.13. along with the average experimental result for all thicknesses and process conditions. The L proportionality best represents the experimental data.  3.3.1.2  Warpage - Thickness Effect  Thinner parts were observed to warp considerably more than thick parts over all part lengths and process conditions. Maximum part warpage with respect to the number of plies is shown in Figure 3.14 to Figure 3.16. Similar to the method described above, the data was collapsed onto a single plot by normalizing (Figure 3.17).  with respect to the  w  max  of corresponding 4 ply specimens  As shown in Figure 3.18, the trend of maximum warpage with respect to  thickness is best predicted by an inverse  ti 2  am  proportionality, where  4  a m  is the laminate  thickness.  3.3.1.3  Warpage - Pressure Effect  The effect of pressure on maximum warpage as shown in Figure 3.19 to Figure 3.21 is quite weak. For viewing convenience the data is collapsed in Figure 3.22 and Figure 3.23, by being normalized with respect to the  w  max  of the 586 kPa specimen of the same length, thickness and  tool surface condition. Figure 3.22 shows that for specimens with an FEP interface, 8 of 9 data pairs show a decrease in  w  ,  max  when autoclave pressure is reduced from 586 kPa to 103 kPa. A  single data pair shows the opposite trend. Similar results are apparent for specimens with a release agent interface, again with a single outlier pair. Disregarding the two anomalous results, the average pressure effect is shown in Figure 3.24. The experiments are best represented by a P  proportionality, where P is the autoclave pressure.  -38-  Chapter 3 Experimental Warpage Specimens  3.3.1.4  Warpage - Tool Surface Effect  The effect of tool surface condition on warpage is shown in Figure 3.25 through Figure 3.27. As above, the data can be collapsed by normalizing with respect to  w  max  measured on the release  agent specimen of a given pair. From plots shown in Figure 3.28 and Figure 3.29 it is apparent that there is no predictable effect of tool surface condition. 3.3.1.5  Warpage - Specimen Variability  Replicate specimens were fabricated for 5 geometry / process condition combinations as shown in Figure 3.30 and Figure 3.31. From each set of replicate specimens a sample standard deviation of the MW was calculated. The standard deviation estimates were then pooled for parts of the same length as shown in Table 3.2 and Table 3.3. Not surprisingly, the absolute magnitude of the sample standard deviation was much larger for longer parts where the absolute magnitude of the  w  max  was also greater. A more meaningful representative of part to part  variability in this case is the sample coefficient of variation:  cv = ~ x  (3.1)  where cv is the coefficient of variation, s is the sample standard deviation and 3c is the sample mean. In all cases the coefficient of variation was seen to be an appreciable percentage of the maximum warpage, rangingfrom14% to 65%.  -39-  Chapter 3 Experimental Warpage Specimens  3.3.2 CURVATURE RESULTS Examination of average part curvature provides an alternate basis for the comparison of deformed part shapes.  The average part curvature, k, can be calculated from Equation (3.2)  below (Cho et al., 1998):  1  8-w  K = — = — R L + 4 - w „ m  2  a  x  ,  (3.2)  2  max  where R is the part radius of curvature. By describing the part curvature as above, it is implicitly assumed that the part has a constant radius of curvature along its length. As will be shown, this assumption was not strictly correct for the high aspect ratio parts. Nonetheless, describing the curvature with a single number is a common practice because of the convenience of part to part comparisons which it affords.  There is no advantage to be gained by examining the effects of part thickness or process conditions with respect to curvature. Looking at equation (3.2), under the circumstances that L > w  ,  max  the average curvature will be directly proportional to the maximum warpage for a given  part length. Therefore, trends in curvature will be identical to the trends in maximum warpage already examined.  What is of interest are the changes in average curvature which occur with respect to part length. Recalling the previous observation that  is proportional to  w  max  L  3  and substituting this result into  equation (3.2) yields the following:  u  q . - H ^ L  U  q . ^ - „ c  -40-  3  - L  (3.3)  Chapter 3 Experimental Warpage Specimens  Based on the statement that increase linearly with L .  w  max  is approximately proportional to  L  , it follows that  K  should  This is confirmed by Figure 3.32 through Figure 3.34 where it is  observed that the average curvature generally increases with part length. The trend is obscured for low aspect ratio specimens, however, this can be attributed largely to the increasing significance of measurement error for parts with this geometry.  3.3.3 CURVATURE DISTRIBUTION The variation in local curvature along the length of the part was also examined. The curvature at a given point, x, along a curve can be expressed as (Bickford, 1993):  where z is the out-of-plane warpage at x and k(x) is the is the curvature at x. When z' is small, as in the warpage specimens, the following approximation is reasonable:  (x)*z" On parts with an aspect ratio, L /1,  (3.5)  of less than 750 the measurement error proved too large to  permit effective estimates of local curvature. For the remaining specimens (4 ply/600 mm, 4 ply/1200 mm and 8 ply/1200 mm parts) a 4  th  deformed shape. Differentiating twice yielded a 2  degree polynomial was fit to describe their nd  order function which described the variation  in local curvature. The curvature plots are shown in Figure 3.35 and Figure 3.36.  It should be noted that the parabolic shape apparent in the curvature distributions is an artifact of the order of function assumed to describe the part profile. In an attempt to provide an estimate of the curvature distribution less biased with respect to shape, the part profile was discretized into a  -41-  Chapter 3 Experimental Warpage Specimens  number of segments.  A n average curvature for each segment was estimated and when  considered collectively, a distribution could be drawn. This method was abandoned, however, because it was overly affected by the part measurement error as each local curvature estimate was based only on a small number of measurement points.  Keeping in mind the inherent weakness of the 4  th  order polynomial fit approach, one can state  that the curvature was greatest in the centre of parts, tending towards zero near the part ends. Conclusions about whether the curvature distribution was parabolic, linear or some other shape were not possible, however, given the quality of the measurement data.  3.4  DISCUSSION  The warpage data showed that part geometry had a much greater effect on maximum warpage than process variables did. For the parameters examined, the collective effect on warpage can be expressed by the following proportionality:  p0.2. 3 z  Wn,*  0 0  —2  t Lam  ("> 3  6  This relationship is illustrated in Figure 3.37.  This result is important from the perspective of the composite manufacturer concerned about the fit-up forces required when assembling multiple parts.  Consider the case of a simple beam  which must be bent into place to accommodate process induced deformations. The deflection, 5, under a given fit-up load, F, is:  (3.7)  5 -  C-E-I  -42-  Chapter 3 Experimental Warpage Specimens  where C is a dimensionless constant depending on the loading arrangement, E is the modulus of the beam and / is the section moment of inertia. Thus for a given 8, the required load is:  Fozd-I  (3.8)  FozS-t  (3.9)  3  Assuming the required displacement is due to the warpage of the specimen, one can substitute Equation (3.6) to give:  Eccw -t  3  maK  Feet  (3.10) (3.11)  Thus, while the absolute magnitude of warpage may be smaller for thick parts, larger fit-up forces will be required to overcome the warpage.  The scaling of warpage with respect to length also has implications regarding the selection of appropriate laboratory test specimen sizes. The 1200 mm specimens fabricated in this study are representative of the upper limit of specimen size which can be fabricated in most research facilities, with typical "coupon" type specimens being on the order of 300 mm. In contrast, structures fabricated in industry are often on the order of several metres in length. It is clear from the results that process induced deformations, like many other phenomena, do not scale linearly with part dimensions. This should be kept in mind when considering the applicability of laboratory results to industrial scale structures.  Considering the warpage data collectively, there was no predictable effect of tool surface condition, however, for high aspect ratio parts fabricated at low pressures, there was a conspicuous difference between parts manufactured at different interface conditions.  -43-  For the  Chapter 3 Experimental Warpage Specimens  cases of 4 ply / 600 mm, 4 ply / 1200 mm and 8 ply / 1200 mm specimens manufactured at 103 kPa, the release interface gave considerably less warpage than any other specimens of the same geometry (Figure 3.7 and Figure 3.8). This trend was significant with respect to the part to part variability demonstrated (Figure 3.31), but was not apparent at other pressures or part geometries, nor can it attributed to any known differences in fabrication conditions. The cause of these anomalous results is not clear at this time.  Part to part variability was seen to be relatively large, particularly with respect to the small differences in part warpage due to autoclave process conditions. This variability is somewhat surprising given the efforts to ensure consistency between batches. The issue of high variability is certainly well known to large scale composite manufacturers and it appears that controlled laboratory environments are susceptible to similar problems. This suggests that in addition to the parameters studied, part shape is dependent on factors not adequately controlled during the process.  3.5 •  SUMMARY The maximum warpage demonstrated by parts was affected by their length, thickness and the process pressure.  Maximum part warpage can be predicted by the following  proportionality:  w.  max  OC  P'  (3.6)  t Lam  •  Tool surface condition did not affect the part warpage in a predictable way.  •  Batch to batch variability was significant for the type of deformations considered.  -44-  Chapter 3 Experimental Warpage Specimens  •  Average part curvature tended to increase linearly with part length.  •  For the parts examined, curvature was greatest at the part centres, diminishing towards the ends.  The exact shape of the curvature distribution could not be determined,  however.  •  When creating an assembly of composite parts, the fit-up load required to overcome process induced warpage is greater for thicker parts. This occurs despite the fact that the absolute magnitude of part warpage decreases with increasing part thickness,  -45-  Chapter 3 Experimental Warpage Specimens  3.6  TABLES  Table 3.1: Maximum warpage and average curvature for the experimental warpage specimens  Number of Plies Part Length (mm) Pressure (kPa) 4 366 m 8 300 103 16 300 103 4 600 103 8 600 103 16 600 103 4 1200 103 8 1200 103 16 1200 103 4 300 586 8 300 586 16 300 586 4 600 586 8 600 586 16 600 586 4 1200 586 8 1200 586 16 1200 586 4 300 103 8 300 103 16 300 103 4 600 103 8 600 103 16 600 103 4 1200 103 8 1200 103 16 1200 103 4 300 586 8 300 586 16 300 586 4 600 586 8 600 586 16 600 586 4 1200 586 8 1200 586 16 1200 586  Interface Condition Maximum Warpage (mm) Average Curvature (mm") 2 Plies of FEP 676 6.3E-65 2 Plies of FEP 0.13 1.2E-05 2 Plies of FEP 0.04 3.5E-06 2 Plies of FEP 3.84 8.9E-05 2 Plies of FEP 0.81 1.8E-05 2 Plies of F£P 0.12 2.8E-06 2 Plies of FEP 29.10 1.6E-04 2 Plies of FEP 7.26 3.9E-05 2 Plies of FEP 1.18 6.4E-06 2 Plies of FEP 0.43 3.9E-05 2 Plies of FEP 0.15 1.3E-05 2 Plies of FEP 0.16 1.4E-05 2 Plies of FEP 3.94 8.9E-05 2 Plies of FEP 0.86 1.9E-05 2 Plies of FEP 0.28 6.2E-06 2 Plies of FEP 39.57 2.1E-04 2 Plies of FEP 8.97 4.8E-05 2 Plies of FEP 1.31 7.1E-06 Release Agent 0.67 5.7E-05 Release Agent 0.26 2.3E-05 Release Agent 0.07 6.4E-06 Release Agent 2.03 4.5E-05 Release Agent 0.97 2.2E-05 Release Agent 0.31 7.0E-06 Release Agent 15.72 8.5E-05 Release Agent 2.67 1.4E-05 Release Agent 1.56 8.4E-06 Release Agent 0.78 7.1E-05 Release Agent 0.25 2.3E-05 Release Agent 0.08 7.6E-06 Release Agent 4.09 9.4E-05 Release Agent 1.23 2.7E-05 Release Agent 0.11 2.5E-06 Release Agent 42.04 2.3E-04 Release Agent 7.71 4.1E-05 Release Agent 1.58 8.5E-06  Table 3.2: Warpage specimen variability for 300 mm specimens.  Specimen Description 8 ply, 586 kPa,FEP Specimen 1 (mm) 0.21 Specimen 2 -  16 Fly, 586 kFa, Release 0.09  (mm)  0.08  0.07  Mean W ^ , (mm)  0.15  0.08  0.09  0.01  65%  14%  Standard Deviation of  (mm)  Coefficient oi" Variation of Pooled Standard Deviation of  (mm)  0.05  Pooled Coefficient of Variation of  40%  -46-  Chapter 3 Experimental Warpage Specimens  Table 3.3: Warpage specimen variability for 1200 mm specimens  Specimen Description 4 ply, 11)3 kPa, FEP Specimen 1 - W (mm) 28.4 Specimen 2 - W (mm) 24.6 Specimen 3 - W (mm) 37.6 m a i  m l I  m a l  Specimen 4 - W  m a l  (mm)  ( ) Standard Deviation of W (mm) Coefficient of Variation of W M  e  a  n  mm  w  m a l  mal  maj  Pooled Standard Deviation of W  m a i  (mm)  Pooled Coefficient of Variation of W  mal  25.8 29.1 5.9 20% 5.22 25%  -47-  4 ply, 1UJ kl'a, Release 12.0 19.4  8 ply, 103 kPa, Release 8.8 5.8  -  -  -  -  15.7 5.2 33%  7.3 2.1 29%  Chapter 3 Experimental Warpage Specimens  3.7  FIGURES  200  JL  600  temperature hold at 180 °C for 140 minutes, after lagging [thermocouple reaches 175 °C ^^jAutoclave heating rate ~ 2.2 °C / min  |  .Autoclave Air Temperature - Cycles A and B Autoclave Pressure - Cycle A Autoclave Pressure - Cycle B •Bag Pressure | Vacuum bag is vented to the atmosphere when autoclave pressure reaches 103 kPa  Depressurize after UL 400 part has cooled to at least 55 C. Natural pressure drop due to cooldown is permitted  Temperature ramp starts when autoclave is at full pressure  «  -100  Time (not to scale)  Figure 3.1: Target cure cycle for manufacture of warpage specimens.  r  100  150  200 250 Time (min)  800  400  Figure 3.2: Run data from a typical autoclave cure cycle used for the manufacture of warpage specimens.  -48-  Chapter 3 Experimental Warpage Specimens  Figure 3.3: Document scanner as set-up for scanning deformed part shape.  Figure 3.4: The greyscale image on the left shows a segment of the part profile after scanning. The image contrast was then increased, and image brightness adjusted to create the sharply defined image on the right. The clear black and white image was then used for locating part edge coordinates using image analysis software.  -49-  Chapter 3 Experimental Warpage Specimens  Figure 3.5: Photograph depicting the magnitude of warpage for 4 ply parts of various lengths. 586 kPa / FEP interface.  5  c  3$0  X Coordinate (mm)  Figure 3.6: Part shapes for 300 mm specimens.  -50-  Chapter 3 Experimental Warpage Specimens  X Coordinate (mm)  Figure 3.7: Part shapes for 600 mm specimen.  586 kPa - Release 103 kPa - Release 586 kPa - FEP 103kPa-FEP  X Coordinate (mm)  Figure 3.8: Part shapes for 1200 mm specimens.  -51-  Chapter 3 Experimental Warpage Specimens  200  400  600  800  1000  1200  1400  Part Length (mm)  Figure 3.9: Maximum part warpage variation with length for 4 ply specimens.  10 9 8 7 o o> ra Q.  I  n 0.  E 3  -»-103 k P a - FEP - • - 5 8 6 kPa - FEP  6  -A-103 kPa - Release Agent  5  - • - 5 8 6 kPa - Release Agent  4 3  E  2 1 0 200  400  600  800  1000  1200  1400  Part Length (mm)  Figure 3.10: Maximum part warpage variation with length for 8 ply specimens  -52-  Chapter 3 Experimental Warpage Specimens  1.8,  0  200  400  600  800  1000  1200  1400  Part Length (mm)  Figure 3.11: Maximum part warpage variation with length for 16 ply specimens.  586 kPa - Release 103 kPa - Release 586 kPa - FEP 103kPa-FEP  . 4 Plies 8 Plies 16 Plies  0.8  0.6  0.2  0.0  4200  400  600  800  1000  1200  X Coordinate (mm)  Figure 3.12: Normalized maximum warpage versus length for all thicknesses and process conditions.  -53-  Chapter 3 Experimental Warpage Specimens  1400 Part Length (mm)  Figure 3.13: Normalized maximum warpage averaged for all specimen conditions contrasted with various theoretical warpage - length relationships.  Figure 3.14: Maximum part warpage variation with thickness, 300 mm specimens.  -54-  Chapter 3 Experimental Warpage Specimens  Figure 3.15: Maximum part warpage variation with thickness, 600 mm specimens.  Figure 3.16: Maximum part warpage variation with thickness, 1200 mm specimens.  -55-  Chapter 3 Experimental Warpage Specimens  Figure 3.17: Normalized maximum warpage versus part thickness for all lengths and process conditions.  Figure 3.18: Normalized maximum warpage averaged for all specimen conditions contrasted with various theoretical warpage - thickness relationships.  -56-  Chapter 3 Experimental Warpage Specimens  0.9 0.8 • 0.7  I 0.6 0.5 .  i  t. ra Q . X ra S  0.4 0.3 .  4 Ply - FEP -8 Ply FEP -16 Ply FEP 4 Ply - Release -8 Ply - Release .16 Ply - Release  0.2  100  200  300  400  500  600  700  Autoclave Pressure (kPa)  Figure 3.19: Autoclave pressure effect on maximum warpage for 300 mm specimens.  4.5 4.0  a - 4 Ply-FEP  I 3.0  -B—8 D>  Ply FEP  -•—16 Ply FEP  2.5  .»- 4 Ply - Release —•—8 Ply - Release  2.0  Q. E  -^—16 Ply - Release  1.5  x  ra S  0.5  100  200  300  400  500  600  700  Autoclave Pressure (kPa)  Figure 3.20: Autoclave pressure effect on maximum warpage for 600 mm specimens.  -57-  Chapter 3 Experimental Warpage Specimens  45.0  40.0  35.0  Measurement Error Bar j  a - 4 Ply - FEP  1 30.0  -•—8 Ply FEP - • — 1 6 Ply FEP  25.0  •» - 4 Ply - Release 8 Ply - Release  20.0  r  10 a.  -^—16 Ply - Release  15.0  10.0  0.0  100  200  300  400  500  600  700  Autoclave Pressure (kPa)  Figure 3.21:  A u t o c l a v e p r e s s u r e effect o n m a x i m u m  w a r p a g e f o r1 2 0 0 m m s p e c i m e n s .  3.0 .4 Ply - 300  - 8 Ply - 300  mm mm  -16 Ply - 300mm .4 Ply - 600 mm  - 8 Ply - 600 mm -16 Ply - 600 mm • 4 Ply - 1200 mm  -8 Ply - 1200 mm -16 Ply 1200 mm  0>  Ui ro a  •o N  ra E i_  o z  100  200  300  400  500  600  700  Autoclave Pressure (kPa)  Figure 3.22: Normalized  m a x i m u m  w a r p a g e v e r s u s a u t o c l a v e p r e s s u r e f o rs p e c i m e n s w i t h  an F E P interface.  -58-  Chapter 3 Experimental Warpage Specimens  o.o-l 0  ,  ,  ,  100  200  300  , 400  , 500  , 600  1 700  Autoclave Pressure (kPa)  Figure 3.23: Normalized maximum warpage versus autoclave pressure for specimens with a release agent interface condition.  1.2  Figure 3.24: Average experimental result plotted against various pressure warpage relations.  -59-  Chapter 3 Experimental Warpage Specimens  0.7 -  m-  4 Ply -103 kPa  - • — 8 - P l y - 1 0 3 kPa - B — 1 6 Ply-103 kPa  0.5 .  •» - 4 Ply - 586 kPa 0.4 .  ill  - • — 8 Ply - 586 kPa 16 Ply - 586 kPa  2 Plies of FEP  Release Agent Tool Surface Condition  Figure 3.25: Maximum part warpage versus tool surface condition for 300 mm specimens.  - e - 4Ply-103kPa —•—8 -Ply-103 kPa —•—16 Ply-103 kPa . ^ . 4Ply-586kPa —•—8 Ply - 586 kPa 16 Ply-586 kPa  2 Plies of FEP  Release Agent Tool Surface Condition  Figure 3.26: Maximum part warpage versus tool surface condition for 600 mm specimens.  -60-  Chapter 3 Experimental Warpage Specimens  45.0 -  40.0 -  |  35.0 -  Measurement Error Bar j  30.0 -  a-  4Ply-103kPa  - B — 8-Ply -103 kPa 16Ply-103kPa  25.0 -  4Ply-586kPa g  - • — 8 Ply - 586 kPa  20.0 -  —H—16 Ply-586 kPa 15.0 -  10.0 .  2 Plies of F E P  Release Agent  Tool Surface Condition  Figure 3.27: Maximum part warpage versus tool surface condition for 1200 mm specimens.  Figure 3.28: Normalized maximum warpage versus tool surface condition for specimens fabricated at 103 kPa.  -61-  Chapter 3 Experimental Warpage Specimens  Figure 3.29: Normalized maximum warpage versus tool surface condition for specimens fabricated at 586 kPa.  0.25  Figure 3.30: Warpage of 300 mm replicate specimens.  -62-  Chapter 3 Experimental Warpage Specimens  Figure 3.31: Warpage of 1200 mm replicate specimens.  Figure 3.32: Average part curvature versus part length for 4 ply specimens.  -63-  Chapter 3 Experimental Warpage Specimens  6.0E-05 -103 kPa - FEP 5.0E-05  -586kPa-FEP -103 kPa - Release Agent  S 4.0E-05  -586 kPa - Release Agent  = 3.0E-05 OJ  2.0E-05  1.0E-05  0.0E+00 200  400  600  800  1000  1200  1400  Part Length (mm)  Figure 3.33: Average curvature versus part length for 8 ply specimens.  1.8E-05 - H - 1 0 3 kPa - FEP  1.6E-05  - • - 5 8 6 k P a - FEP - A - 1 0 3 k P a - Release Agent  1.4E-05  - • - 5 8 6 k P a - Release Agent 1.2E-05 1.0E-05 8.0E-06 6.0E-06 4.0E-06 2.0E-06 0.0E+00 200  400  600  800  1000  1200  Part Length (mm)  Figure 3.34: Average curvature versus part length for 16 ply specimens.  -64-  1400  Chapter 3 Experimental Warpage Specimens  1.0E-04  5.0E-05  -3.0E-04  X Coordinate (mm)  Figure 3.35: Curvature distribution for 600 mm specimens.  1.0E-04  5.0E-05  -3.0E-04  X Coordinate (mm)  Figure 3.36: Curvature distribution for 1200 mm specimens.  -65-  Chapter 3 Experimental Warpage Specimens  45 , 40  0.0E+00  1.0E+09  2.0E+09  3.0E+09 4.0E+09 p0.2 3 L  5.0E+09  6.0E+09  7.0E+09  8.0E+09  / t 2  Figure 3.37: Experimental data compared with empirical relationship predicting maximum warpage.  -66-  CHAPTER 4 : INSTRUMENTED TOOLING EXPERIMENTS  The literature examined in Chapter 2 showed that shear stress at the tool-part interface arising from C T E mismatch is a viable mechanism for the occurrence o f warpage in initially flat laminates.  However, the success o f warpage predictions over a practical range o f part  geometries and process conditions depends on having an accurate picture o f the distribution o f interfacial shear stress. A n experimental technique based on the work presented by Fernlund et al. (2000) was developed with the goal of quantifying the development o f tool-part interface shear stress throughout the cure cycle.  No  stress can be measured directly, but the interfacial shear stress acting on a body may be  inferred from the normal strains exhibited by material close to the interface. Strain gages can be sufficiently robust to survive an autoclave cycle, hence they are well suited for this type o f measurement.  When examining this interfacial phenomena one has the option o f examining  strains from the tool side or from the part side. Strain gage placement in the part itself has been utilized successfully for the examination o f residual stresses which arise after part gelation but there are inherent difficulties i n this technique (Crasto et al., 1999).  In order to measure  accurately, a strain gage must be well bonded to the substrate. Prior to, and during resin curing, the bond between gage and resin is uncertain. Furthermore, there is no provision for separating the component o f strain arising from specimen imposed stresses.  thermal expansion and that arising due to  Finally, in-situ gage placement does not permit re-use of the strain gage  arrangement which can be important to allow for error calibration.  -67-  Chapter 4 Instrumented Tool Experiments  For these reasons, it was decided to place strain gages on the tool itself.  To ensure that the  magnitudes of the strain induced in the tool were sufficiently large to be measurable, a thin, compliant tool was used.  Several gages were placed along the length of the tool and the  constraint or stretching to which the tool was subjected during the entire process cycle was monitored. From this measurement it was possible to estimate the magnitude and distribution of shear stresses at the tool-part interface.  4.1  E X P E R I M E N T A L  The instrumented tool was a piece of 6061-T6 aluminum with dimensions of 100 mm x 600 mm x 0.762 mm.  Eight strain gages were placed on the tool, 6 oriented longitudinally and 2  transversely, as shown in Figure 4.1.  The eight Micro Measurements EA-13-250BG-120-  Option-LE gages were adhesively bonded to the aluminum tool using Micro Measurements M Bond 43B adhesive. The pre-attached leadwires were soldered to 26 A W G wires for connection to the data acquisition (DAQ) system.  A [0]i6 CFRP part with the same length and width as the instrumented tool was placed on a 6.35 mm thick aluminum baseplate. The CFRP material was T-800H/3900-2 from the same batch as that used for the warpage specimens.  Two sheets of FEP separated the part and the baseplate.  The instrumented tool was then placed on top of the CFRP part. The instrumented tool surface was prepared in the same manner as the tool surface for the warpage specimens. The baseplateCFRP part-thin tool assembly is illustrated schematically in Figure 4.2 and shown in a photo in Figure 4.3. The assembly was vacuum bagged and subjected to a modified version of the 180 °C (355 °F) cure cycles described in Figure 3.1. The modifications to the cure cycle are addressed  -68-  Chapter 4 Instrumented Tool Experiments  in Section 4.3. As with the warpage specimens, two interface and two pressure conditions were examined:  •  2 plies of FEP, and Freekote release agent.  •  103 kPa and 586 kPa autoclave pressures.  As the cure cycle progressed, strains measured in the thin tool were recorded with the DAQ system.  Compensation for the free thermal output of the strain gages was performed  subsequently using pre-calibrated constants. The product of this experimental technique was a history of the in-plane, mechanical strain in the thin tool throughout the cure cycle. Appendix B presents a detailed explanation of the procedure used for thermal compensation of the strain gage data. The experimental error associated with this technique was estimated to be ± 9 LIE.  4.2  I N S T R U M E N T E D T O O L  T H E O R Y  When the conditions of a differing CTE between tool and part are combined with a change in temperature, the tool and part will attempt to adopt different shapes. As a measure of this shape mismatch one can consider, SMismatch, the difference between the unconstrained thermal expansion of the tool and part:  £ , =(CTE -CTE )-(AT) M malch  where CTET I 00  and CTEp  art  Tool  Part  (4.1)  are the respective thermal expansion coefficients and AT is the  temperature change. This strain mismatch results in shear stresses along the tool-part interface. The strain data generated from the instrumented experiments represents the in-plane strain induced in the tool due to this shear interaction. The following section presents the theory by  -69-  Chapter 4 Instrumented Tool Experiments  which the tool-part interface conditions can be related to the measured in-plane strains. For the scope of this study it is sufficient to consider two interface conditions:  the sliding friction  condition and the sticking interface condition.  Regardless of the interface condition present, the following assumptions are implicit in the thin instrumented tool approach used here. Firstly, it was assumed that temperatures were constant along the part length. This assumption was confirmed by experiment where it was shown that temperatures did not vary more than 1 °C over the entire part length.  Secondly, it was assumed that through-thickness in-plane strain gradients in the thin tool were negligible, that is to say that the strains induced at the tool part interface were equal in magnitude to the strains measured on the tool free surface. This assumption is based on the fact that the tool thickness is small, and the tool shear modulus is relatively high, so the decay of strain through the instrumented tool thickness is minimal.  Finally, it was assumed that the instrumented tool was not subject to bending deformations which would cause erroneous strain readings. Bending deformations will occur in a bi-material strip subjected to a temperature change, if it is not constrained in the out-of-plane direction. However, as the instrumented tool-part assembly was forced against the baseplate by autoclave pressure, no out of plane bending deformations were possible.  Calculations performed to  confirm this assumption are presented in Appendix C.  A real cause of erroneous bending strain was encountered during the course of the experiments. While the material system used was a non-bleed system, there is invariably a region of material near the laminate edges out of which resin will bleed. As a result the laminate thins locally, hence the instrumented tool bends to accommodate this thickness change.  -70-  By sectioning the  Chapter 4 Instrumented Tool Experiments  laminate and examining the thickness profile, the error associated with this was estimated. The edge thinning effect was limited to the gages at location A / A', and was calculated to cause the gages to read 20 LIE too high. It was not possible to identify the exact time at which this error was introduced, however, the edge thinning was assumed to be complete by the time the isothermal hold started. For this reason, the strain versus time plots presented are not corrected for this error but a correction was incorporated into any subsequent calculations.  4.2.1  S L I D I N G F R I C T I O N  C O N D I T I O N  The first theoretical case for consideration is that of the sliding frictional interface.  This  condition implies that the shear stress along the entire tool-part interface is a constant value. The magnitude of the shear stress is often assumed to be proportional to the normal stress acting on the interface, as suggested by the Coulomb friction model:  *swn = V-P  (4-2)  g  where  tsuding  is the interfacial shear stress, // is the dimensionless friction coefficient and P is the  autoclave pressure. It is important to note that under these conditions, the interfacial shear stress will be independent of the  SMismatch  term from Equation (4.1).  The loading condition for a thin tool of length 2L is shown in Figure 4.4. Examining the force equilibrium on a tool element with dimensions tr oi by dx by unit depth yields the following: 0  dcr -a y  +  xx  xx  t  Tool  + r -dx = 0 xz  In the remaining text, the subscripts for the stress terms will be omitted, hence simply as a and  as r. Rearranging gives:  -71-  (4.3) is referred to  Chapter 4 Instrumented Tool Experiments  d<7 = ——-dx  (4.4)  ^Tool  a  x  \da  =  0  j  dx  (4.5)  L ^Tool  In the case of sliding friction r = Tsndmg along the entire interface, hence integrating Equation (4.5) yields: Ts,i« <L-x)  a=  ng  (  4  6  )  *Tool  The shear stress and in-plane stress distributions for this condition are shown schematically in Figure 4.5 and Figure 4.6. The strains as measured by the gages are related to the in-plane stress by the Young's modulus, ET I, of the thin tool. 00  , w(*-»> =  F  -t  ^Tool Tool l  Considering Equation (4.7) in the context of the instrumented tool experiment, in the case that sliding friction is prevalent at the interface and the tool-part combination is subjected to a temperature change, the following characteristic behaviour should be observed:  •  Strain magnitudes as measured by the gages should be directly proportional to their distance from the end of the tool.  •  Strain magnitudes should be independent of Smsmatch, and hence independent of the temperature change to which the tool-part assembly is subjected. The exception to this would be the case in which Tsudmg is increasing at the same time the tool-part assembly is subjected to a temperature change.  -72-  Chapter 4 Instrumented Tool Experiments  4.2.2  S T I C K  C O N D I T I O N  The second interface condition to be considered is that representing sticking between the tool and part. Solutions for similar problems in adhesive bonding research have been developed so these will serve as a basis for the development presented here (Fernlund, 1999; Reddy and Roy, 1991). This situation also has many similarities to the stress transfer which occurs between fibre and matrix in a composite material. This class of problem is often solved using what is referred to as a shear lag solution. Consider the general case of two elastic adherends separated by an adhesive layer, with geometries as depicted in Figure 4.7. For simplification purposes the adherends are assumed to undergo no shearing, while the adhesive is assumed to experience no extensional strains. Examining the force equilibrium on an element dx in length by unit depth gives (Figure 4.7):  da, r =  , L  do*. ,  -h =—--rh, l  dx  (4.8)  dx  Considering Hooke's law and the strain-displacement relation, one can relate the stresses in the adherends to their displacements:  ^ L = s =^ dx  ^  dx  1  r  E  +  CTE AT  (4.9)a  r  = s = ^ + CTE • AT 2  2  E  (4.9)b  where uj and U2 are the displacements of the bottom and top adherends respectively, E is the modulus of the adherends and CTEi  and CTEj  are the respective thermal expansions.  Differentiating again, and incorporating Equation (4.8) gives:  -73-  Chapter 4 Instrumented Tool Experiments  d u,  da,  1  dx  E  dx  d w, 2  dx  1  da, -  2  dx  (4.10)a  E-h\  E  T  -  (4.10)b  E-r\  Now considering the adhesive layer:  t = G-y = G—  1  (4.11)  L  where G is the shear modulus of the adhesive layer. Differentiating Equation (4.11) twice and incorporating Equations (4.10)a and (4.10)b gives a differential equation for r.  dr 2  dx  1  2  _ =  G-jh.+h^) : E-t -h\-h A  (4-12)  1  The solution of this equation can be shown to be:  I * -M\ = {e**-e**)  G-AT-(CTE -CTE.) —ir~— 2  (4-13)  where:  X=  ^3  (4.14)  Putting representative values into Equation (4.13) yields an interfacial shear stress distribution like that depicted in Figure 4.8. This is characterized by zero shear occurring over much of the interface length, with the shear stress increasing exponentially over a short region near the end of the interface. This region is referred to as the stress transfer length, Ls. Regarding the form of Equation (4.13) it is apparent that the magnitude of the shear stress is proportional to the EMismatch term from Equation (4.1)  -74-  Chapter 4 Instrumented Tool Experiments  Recalling Equation (4.5), and incorporating Hooke's law gives:  S-E —  1 CT  X  (4.15)  =  Too/ L  Equation (4.15) states that the in-plane stress and strain at a given point will be proportional to the integral of the shear stress from the interface end to that point. A n in-plane stress distribution corresponding to the perfect bonding condition is shown schematically in Figure 4.9. Based on this distribution, for the sticking interface condition one can expect strain in the tool to develop as follows:  •  Strains in the thin tool will be constant along the length, unless the gages are located close enough to the tool end to be within the zone over which the shear stress is building.  •  The magnitude of the interfacial shear stress and hence the in-plane strain, will increase as the SMismatch term increases.  A temperature change will thus cause tool strains to  increase.  •  The interfacial shear stress will be a maximum at the tool end.  The sliding friction and sticking interface conditions are analogous to plastic and elastic material deformations respectively. displacement, Si / , nter  4.10.  ace  A schematic illustration of interfacial shear stress versus interface  for an arbitrary point along the tool-part length is presented in Figure  At low values of 8i„ f ,  ^interfaceTDebond-  ter  ace  the elastic condition governs, with T being proportional to  As Surface increases so does r, until it reaches the critical shear stress for debonding, After debonding, the sliding condition is in effect, thus as 8i„ f ter  the interfacial shear stress remains constant at rsndmg-  -75-  ace  is increased further,  Chapter 4 Instrumented Tool Experiments  It should be noted that the critical shear stress at which debonding occurs, same value as  zsiidmg-  Toebond,  need not be the  It is a common observation that for a given interface, the coefficient of  static friction, corresponding to  zoebond,  is greater than the coefficient of sliding friction. For the  materials considered presently, the magnitude of  zoebond  may also be increased by adhesive  bonding of the tool and part.  4.3  I N S T R U M E N T E D T O O L  R E S U L T S  Before examining the strain gage response, a brief explanation of the temperature cycle used is warranted. The state of mechanical strain in the thin tool changes mainly when the tool part assembly is subjected to a change in temperature. In order to provide greater insight into the progress of tool-part interaction during the isothermal portion of the cure cycle in particular, temperature modulations were programmed into the autoclave controller.  These temperature  dips were also used during the heat-up portion of the cure. A typical thermal cycle used is shown in Figure 4.11 along with the part degree of cure and resin modulus estimates based on cure kinetics model # 6 and modulus development model #2 presented in Johnston (1997). The other minor difference between this cycle and that described in Section 3.1.2 was that for the instrumented experiments, autoclave pressure was not permitted to drop during the cool-down period.  4.3.1  H I G H  P R E S S U R E  / R E L E A S E  A G E N T  The results from the 586 kPa / Release Agent interface condition set will be presented in detail after which the results from other conditions can be compared. Figure 4.12 shows the evolution of mechanical strain in the thin tool throughout the cure cycle. Only gages from one side of the tool symmetry line are shown for the sake of clarity. Complete results can be found in Appendix  -76-  Chapter 4 Instrumented Tool Experiments  D.  Again it should be emphasized that the strains shown in all plots have their free thermal  output removed, meaning that the strains depicted are those corresponding directly to stresses in the thin tool.  4.3.1.1  Strain Development - Cool-down  While the end of the cure cycle is not expected to be significant in terms of developing residual stresses in the part, it is instructive to examine the experimental results starting with the cooldown portion of the cure cycle because the strain magnitudes are very large making trends easier to identify. Furthermore, at this time the part degree of cure is unchanging and part properties can be assumed to be fully elastic.  An expanded view of the cool-down portion of the cycle is shown in Figure 4.13. Recall that the C T E of the aluminum tool is approximately 24 LIE / °C compared to 0 us / °C and 44 LIS / °C for the CFRP in the longitudinal and transverse directions respectively. The elastic properties of the CFRP laminate and aluminum tool used for calculation purposes are shown in Table 4.1. Despite the use of a release agent, as the tool and part cool, the two are perfectly bonded. In the longitudinal direction the aluminum tool is prevented from thermally contracting, resulting in a tensile stress which increases as the temperature drops further from the cure temperature. In the transverse direction the opposite trend is seen owing to the greater C T E of the part in that direction. Strain in the toolplate continues to increase until a sharp discontinuity occurs. The discontinuity is associated with debonding of the tool and part.  This occurs in a manner consistent with theory for a perfectly bonded bi-material strip. Recall from Section 4.2.2 that for the elastic distribution, interfacial shear stress is expected to be zero over most of the part length but increases to a maximum over a short region near the tool end,  -77-  Chapter 4 Instrumented Tool Experiments  while the resulting in-plane strain should be constant over most of the tool length. Experimentally, it is observed that as the cooling progresses, in-plane strains build at the same rate for each gage location. Debonding occurs first at the part end, where interfacial shear stress is a maximum. The debond front then progresses towards the part centre, reflected by the order in which the gages debond.  After debonding the in-plane strain drops considerably and then remains constant as the temperature drops further. The gages show a strain level proportional to their distance from the tool end suggesting that after debonding a sliding friction interface condition is operative for the rest of the cool-down (Note that the autoclave pressure remains applied for the entire duration of the cool-down).  This results in part of the interface being subjected to the sliding friction  condition while the rest remains adhesively bonded as illustrated in Figure 4.14.  4.3.1.1.1  Estimate of Ls  Having first developed a qualitative picture of the distribution of interfacial shear stress, it is possible to determine the magnitudes of  Toebond,  L and s  Tsuding.  The peak strain which a given  gage reads immediately prior to debonding, d, occurs the instant prior to the stress transfer length, Ls, reaching that gage.  The interfacial shear stress distribution corresponding to this  situation is shown in Figure 4.15. The plateau strain value after debonding, / , is reached at the moment when Ls has travelled past the gage, corresponding to Figure 4.16.  It is important to  note that the finite dimensions of the strain gage are significant in the following arguments. In the period over which the strain is dropping from i to / , the debond front travels a total distance of Ax:  Ax = L + L s  G  -78-  (4.16)  Chapter 4 Instrumented Tool Experiments  where LG is the active gage length of the strain gage. For the gages considered in the present work, the gage length was 6.4 mm.  The distance Ax, and hence the stress transfer length, Ls, can be calculated based on two related quantities: the temperature span of the debond event, AT, and the rate of debond migration with Ax respect to temperature, — . Both these quantities are readily identified from the experimental output, enabling a calculation of Ls as follows: (4.17)  AT-L  G  (4.18)  This calculation is performed with respect to temperature rather than time because as will be seen, the debond migration rate is constant with respect to temperature whereas it varies with respect to time.  Figure 4.17 examines the strain evolution at a single gage during debonding, illustrating that this event actually occurs over a period of approximately 2 minutes. Alternatively one can express the duration of this event in terms of the temperature span, AT, over which it occurs. The average temperature span for Ls to pass a given gage was 2.8 °C .  Recall that the peak strain which a gage reads occurs the instant prior to Ls reaching that gage. This enables one to identify the exact location of the debond front at 4 separate moments during the cool-down. Figure 4.18 shows a plot of debond front location versus tool temperature. The  1  2  The active gage length is considered as opposed to the overall length of the gage including the backing. The complete strain, time and temperature data are presented in Appendix D.  -79-  Chapter 4 Instrumented Tool Experiments  Ax  slope of this line, — , represents the debond front migration rate. From this plot it is apparent that the debond migration rate of 7.1 mm / °C is constant with respect to temperature. Incorporating these values into Equation (4.17) gives:  A x L  s  =  ~ £ f '  A  T  ~  L  G  ( 4  -  1 ? )  mm  L = 7.\— s  4.3.1.1.2  -2.8 °C-635mm  = Umm  (4.19)  Estimate of tDebond  Now that an estimate of Ls is available, one can also calculate Toebond- Recalling Equation (4.5), one can relate the strain measured by a gage to the integral of the shear stress between the interface end and the gage location, x:  1 * £= =— J - r -\-T-dx tfx t'Too/ '-F J ^Tool L  (4.5)  The change in strain measured by the gage during the debond event can thus be related to the change in the integral of the shear stress.  L\E=£  J  -S  =  /  (4.20)  •F  Tool ^Tool  l  During the cool-down, the shear stress distribution cannot be described by a single integrable function, but a reasonable approximation of the required quantities can be determined by estimating areas from schematic r versus x coordinate curves. Recall that Figure 4.15 shows the shear stress distribution corresponding to the time at which the peak strain, d, is recorded at a  -80-  Chapter 4 Instrumented Tool Experiments  given gage, while Figure 4.16 corresponds to the post debond value, / . As Ls passes a given gage, the area under the curve between the interface end and the gage changes by an amount approximately equal to the area of the shaded triangle in Figure 4.16. Moreover, in the event that TDebond Tsiiding, >>  this area can be approximated as follows:  jjf-r-^j - j j - r - ^ j  « ~ r  0  e  W  - Z  s  (4.21)  Combining Equations (4.20) and (4.21) and solving for Toebond gives:  2-{s -e ')-t-E f  *Debond =  j  —  (4-22)  AsUsing an average value for (s/- £j) and the value for Ls as calculated above yields an estimate of ^Debond of 3.8 MPa. For comparison, the bond strength for metal adherends with a typical structural epoxy adhesive can be expected to be on the order of 22 to 40 MPa (Hexcel, 2000). 4.3.1.1.3  Estimate of tsuding  Finally, the magnitude of  Tsuding  can be estimated from the strain measurements during the post  debond period. Differentiating Equation (4.7) and rearranging gives:  -ds  *'sliding—-E-t  dx  A plot of post debond strain versus gage location is shown in Figure 4.19.  (4.23)  The strain value  reported for a given location is the average of appropriate gages on both sides of the part symmetry line. A straight line was fitted to the data, and forced to go through zero strain at the tool end (to reflect the fact that the tool is stress free at the end). The slope of the line in Figure  -81-  Chapter 4 Instrumented Tool Experiments  4.19 represents — , and applying values of 70 GPa and 0.762 mm for the tool modulus and dx thickness respectively yields a value for  Tsuding  of 167 kPa.  The error associated with this  technique was determined from the effect which the strain measurement error had on the slope estimate. The strain measurement error of ± 10 LIE translated into an error of ± 5.4 kPa for the Tsuding  4.3.1.2  estimate.  Strain Development - Isothermal Hold  Strain in the longitudinal direction stays at a constant value for the hold portion of the cure cycle, with the exception of the temperature dips (Figure 4.20). In the transverse direction a decrease in strain which is assumed to correspond to resin cure shrinkage is noted. Examining the strain gage behaviour during the temperature dips suggests a sticking condition at the interface. The strain induced by the temperature fluctuation is the same for all gage locations, whereas if a sliding condition were in effect the gage response should be proportional to their distance from the interface end.  The degree to which the tool is constrained and / or stretched during the temperature dips reflects the changing modulus of the curing part. This elastic interaction can be quantified by comparing the apparent C T E demonstrated by the tool, to the stress free C T E of the tool. For the purposes of this discussion, the term Elastic Constraint will be defined as follows:  Elastic Constraint = CTE  Measured  - CTE  Free  (4.24)  The theoretical minimum value for elastic constraint is zero, which would indicate that the tool was not influenced to any degree by the part. The absolute maximum elastic constraint possible is the difference between the C T E of the tool and part, which would occur in the case that the  -82-  \ Chapter 4 Instrumented Tool Experiments  tool was completely dominated by the part. The elastic constraint is measured by the slope of a strain versus temperature plot during a given temperature dip.  The development of elastic  constraint with respect to time is shown in Figure 4.21, while Figure 4.22 shows the change with respect to part degree of cure. Each elastic constraint value displayed is the average of the two gages at the same distance from the part symmetry line. Also shown are lines indicating the estimates from a C L T software, Promal (Kaw, 1997), for the longitudinal and transverse directions.  Calculations were performed using the fully cured composite properties given in  Table 4.1.  Early in the cure cycle the elastic constraint is negligible in the transverse direction yet at the same time there is approximately 10 p /°C of constraint in the longitudinal direction.  With  increasing degree of cure the elastic constraint increases in both directions, approaching the estimate for a fully cured composite part.  4.3.1.3  Strain Development - Heat-up  Mechanical strain evolution during the heat-up portion of the cure cycle is shown in Figure 4.23. Identifying trends in strain development which occur during the heat-up is difficult because the strain magnitudes are relatively small. Prior to 60 minutes, gages show no significant response. Shortly after the first temperature dip, however, strain measurements at each respective location start to diverge slightly. By the time the isothermal hold is reached, the longitudinal gages show a negative strain approximately proportional to their distance from the tool free end.  As with the post debond strain distribution, this is indicative of a sliding friction condition at the interface.  Following the method outlined in Section 4.3.1.1.3, one can estimate an interfacial  shear stress corresponding to this strain distribution using Equation (4.23).  -83-  A plot of strain  Chapter 4 Instrumented Tool Experiments  versus gage location for various times during the heat-up is shown in Figure 4.24.  From the  slope of this plot, values of rsndmg throughout the cure cycle were estimated. A plot of rsndmg against resin degree of cure is shown in Figure 4.25 from which it is apparent that rsndmg is strongly related to the degree of advancement of the resin cure.  4.3.2  INSTRUMENTED RESULTS - O T H E R EXPERIMENTAL CONDITIONS  Having examined the results of a single experiment thoroughly, the results from other experimental conditions can be contrasted. The strain versus time plots for the other process and tool surface conditions examined are shown in Figure 4.26 through Figure 4.28.  Again, only  gages on one side of the tool symmetry line are shown for the sake of clarity. Complete results are presented in Appendix D.  4.3.2.1  Other Experimental Conditions - Heat-up  During the heat-up portion of the cure cycle, the sliding interface condition is dominant for all of the experiments.  As before, the evolution of rsndmg with respect to degree of cure can be  examined by first plotting measured strain versus gage location as shown in Figure 4.29 through Figure 4.31. A plot of rsndmg with respect to degree of cure for all experimental conditions is shown in Figure 4.32. In all cases rsndmg increases with increasing resin degree of cure.  By the end of the cure cycle there are substantial differences in rsndmg between the various experimental conditions, with the value of rsndmg being much greater for the higher pressure conditions. Taking into account the error associated with the estimate of rsndmg as well as the expected variability in this parameter, there is no significant pressure or tool surface effect at the low degrees of cure encountered during the heat-up.  -84-  Chapter 4 Instrumented Tool Experiments  The evolution of elastic constraint during the temperature dips is shown in Figure 4.33 through Figure 4.35. 4.35).  The behaviour is similar for all runs except for the 103 kPa / FEP case (Figure  For the other three cases elastic constraint builds with increasing degree of cure,  approaching the C L T estimate by the end of the cure cycle. However, for the case of the 103 kPa / FEP condition the term elastic constraint is not strictly correct. As is apparent from Figure 4.35, gage response in the longitudinal direction is proportional to the distance from the end, indicative of a sliding condition. For this experimental case, toebond was evidently low enough to be reached during the temperature dips.  4.3.2.2  Other Experimental Conditions - Isothermal Hold and Cool-down  Gage response during the isothermal hold was similar for all experimental conditions, except for during the previously discussed temperature dips.  During the cool-down marked differences  become apparent, however.  For the case of 103 kPa / release agent (Figure 4.26), as with the previously examined 586 kPa / release agent condition the tool and part are perfectly bonded at the start of the cool-down. In the low pressure case though, the debond front does not travel at a constant rate along the length of the tool. For gages A and B, debonding occurs simultaneously, after which the debond front travels at a rate of approximately 26.2 mm / °C as shown in Figure 4.36. On the other side of the tool symmetry line, gages A' through C debond simultaneously (Figure D.2). It is apparent that under the low pressure condition, the debonding event does not progress in as stable a manner as under the high pressure condition.  Using the same methods outlined in Section 4.3.1.1, L$ and Toebond can be estimated from the evolution of strain during the debond events. The time, temperature and strain data required for  -85-  Chapter 4 Instrumented Tool Experiments  the calculations are presented in Appendix D. For the 103 kPa / Release Agent case, Ls and ^Debond were calculated to be 16 mm and 3.0 MPa respectively. These values are not significantly different from those for the 586 kPa / Release Agent case (14 mm and 3.8 MPa respectively).  The experiments performed with an FEP interface also show a sticking condition during the initial cool-down (Figure 4.27 and Figure 4.28).  In contrast to the release agent cases the  transition from a sticking condition to a sliding condition does not have any associated drop in strain for the FEP interface. This result implies that for the FEP interface there is no difference between toebond and the previously calculated cool-down values of rsndmg- Regarding the 586 kPa / FEP case there is an apparent increase in Tsuding after the start of the sliding friction condition. In Figure 4.30 this is illustrated by the difference in slope between the initial and final cool-down lines. The reason for this is not clear but one possibility is that with increasing Si rface, the FEP nte  layers at the interface may be wrinkling causing an apparent increase in the interface friction coefficient.  4.4  DISCUSSION  The events of the entire cure cycle can now be considered collectively in the following summary. During the heat-up portion of the cure cycle all the process conditions exhibit a sliding friction interface condition, with Tsuding initially being a negligible value but increasing with resin degree of cure. During the temperature dips the interface behaves elastically, however. A n analogy to this behaviour can be drawn by considering a tensile test in which material is taken into the plastic regime.  Upon unloading, the material follows a stress-strain path determined by its  elastic properties.  In the same manner, during the temperature dips the interface behaves  elastically until the interfacial shear stress exceeds Toebond, after which the interface slides again.  -86-  Chapter 4 Instrumented Tool Experiments  Early in the cure cycle it is apparent that TDebond ~ ?sndmg because there is no abrupt jump in strain associated with the transition between the two regimes.  During the isothermal hold there is no relative motion between the tool and part and during this period marked differences arise between the FEP and release agent conditions. For the release agent interface, TDebond increases substantially due to the adhesive characteristic of the curing resin. By the end of the cure cycle, TDebond has increased to a value several orders of magnitude above Tsuding- For the FEP interface the impermeable ply prevents any adhesive bonding between tool and part. During the initial portion of the cool-down the sticking condition operates until the interfacial shear stress builds to TDebond and debonding occurs, starting at the tool end and travelling towards the centre.  After debonding the sliding friction condition dominates again.  The evolution of interfacial shear stress versus Si face is illustrated schematically for release nler  agent and FEP interfaces in Figure 4.37 and Figure 4.38 respectively.  The evolution of Tsuding and TDebond with degree of cure has implications with respect to the effect of cure cycle on part shape. The massive tools used in industry often force the temperature ramp rates of the cure cycle to be very low. Because of this, the resin may have already achieved a substantial degree of cure prior to the hold, and hence a higher value of Tsuding would be operative while still on the heat-up.  Alternatively, some cure cycles employ a hold at an intermediate  temperature before the ramp to the final cure temperature.  It is also possible that during an  intermediate isothermal dwell, TDebond would increase sufficiently to change the interface from a sliding dominated condition to a stick condition. Parts which are subject to these intermediate dwells or slow heat-up rates would be subject to higher interfacial stresses than parts with a single rapid ascent to cure temperature.  -87-  Chapter 4 Instrumented Tool Experiments  As noted in Section 4.3.1.2, even early in the cure cycle while the resin is essentially liquid there is appreciable tool-part interaction in the fibre direction, but little or none in the transverse direction. This is significant in that it indicates a degree of fibre bed interaction with the tool. The majority of researchers assume that prior to gelation, a laminate is unable to develop and store residual stresses, however, fibre bed interaction is a mechanism by which this might occur.  4.5  S U M M A R Y  •  During the heat-up portion of the cure cycle when part residual stress development due to tool-part interaction is most significant, a sliding friction condition is prevalent at the tool-part interface.  •  The degree of elastic constraint at low degrees of cure shows an interaction between the fibre bed and the tool.  This indicates that even prior to resin gelation, the part can  support stresses.  •  The value of rsiidmg increases significantly with degree of cure. During the heat-up Tsnding is on the order of 30 kPa, while at the end of the cure cycle values can reach as high as 165 kPa. This suggests that temperature ramp rate or intermediate isothermal dwells can influence interfacial shear stress history and hence change final part shapes.  •  At high degrees of cure Tsnding is much greater for higher autoclave pressures.  •  A sticking interface condition can occur, particularly during temperature modulations and after isothermal dwells.  -88-  Chapter 4 Instrumented Tool Experiments  •  Adhesive bonding between the tool and part occurs despite the use of release agent on the tool. The TDebond corresponding to adhesive bonding is on the order of 3-4 MPa.  •  The use of FEP prevents any degree of tool-part adhesive bonding.  -89-  Chapter 4 Instrumented Tool Experiments  4.6  T A B L E S  Table 4.1: Material properties used for calculation purposes expressed as a function of temperature. Note that T refers to the temperature in °C.  Material Young's Modulus, E (GPa) C T E (m  1 C) U  T-800/3900-2  1  T-800 / 3900-2  1  Aluminum  2  Longitudinal  Transverse  6061-T6  126-0.0125(T-20)  9.7 - 0.0369(T-20)  0.0374 - 0.000786(1-20)  33.3 + 0.0894(T-20)  69 22.3 + 0.0204(1-20)  1 Toray T-800 / 3900-2 Material Data Sheet 2 ASM Metals Handbook, 10th Ed.  -90-  Chapter 4 Instrumented Tool Experiments  4.7  F I G U R E S  51  51  51  '<—H<—*—102  T 51  • A'  B'  T'  C*  C  u • T  B  A  51  1 305  All dimensions in mm  Strain Gage Axis  Figure 4.1: Arrangement of strain gages on the instrumented tool.  FEP or Release  Figure 4.2: Instrumented tool - part - baseplate cross section  -91-  Chapter 4 Instrumented Tool Experiments  Figure 4.4: Geometry of thin tool loading under sliding friction conditions.  -92-  Chapter 4 Instrumented Tool Experiments  (fi Ui (D -t—«  CO 1_  CD d)  x:  V) "ro  o ^  T  Sliding  Tool  X Coordinate  Tool E n d  Centre  Figure 4.5: Interfacial shear stress distribution for the case of a sliding friction interface.  Tool  X Coordinate  Tool E n d  Centre  Figure 4.6: In-plane stress distribution for the case of a sliding friction interface.  -93-  Chapter 4 Instrumented Tool Experiments  Figure 4.7: Geometry of the thin tool loading under sticking interface conditions.  Tool  x  Coordinate  Tool E n d  Centre  Figure 4.8: Interfacial shear stress distribution for the case of a perfectly bonded tool-part interface  -94-  Chapter 4 Instrumented Tool Experiments  Figure 4.9: In-plane stress distribution for the case of a perfectly bonded tool-part interface.  Sticking </) 2?  Condition x  Debond|  T  Sliding  -f->  Sliding Condition  CO s_  ro x: CO  "ro o  •e  'Interface  Figure 4.10: Theoretical interfacial shear stress development as a function of interface displacement.  -95-  Chapter 4 Instrumented Tool Experiments  0  50  100  150  200  250  300  350  Time (min)  Figure 4.11: Typical thermal cycle used for the instrumented tool experiments.  Figure 4.12: Mechanical strain evolution in the instrumented tool for the entire process cycle. 586 kPa / release agent interface.  -96-  Chapter 4 Instrumented Tool Experiments  Figure 4.13: Mechanical strain evolution during the cool-down portion of the cure cycle. 586 kPa / release agent interface.  Sticking Condition $ <D i_ -i—'  T  Sliding Condition  Debond  CO  D e b o n d Front Migration  CO <D  .c CO "ro  o .ro 0)  c  Sliding  Tool  <  Le"" X Coordinate 5  Tool End  Centre  Figure 4.14: Illustration of interfacial shear stress distribution as the debond front travels from the tool end towards the centre.  -97-  Chapter 4 Instrumented Tool Experiments  Figure 4.15: Interfacial shear stress distribution corresponding to the peak strain gage reading prior to debonding.  $  x  Debond  0) i_  CO  Debond Front Migration  C O C D  •4  _rz CO  "ro o  •i C  Sliding  Tool Centre  Tool E n d  X Coordinate  Figure 4.16: Interfacial shear stress distribution corresponding to the post-debond plateau strain gage reading.  -98-  Chapter 4 Instrumented Tool Experiments  1000  Gage B  C  Tool End  X Coordinate  700 Gage B  Strain = £,  400 280  282  290  292  294  296  Time (min)  Figure 4.17: Strain evolution at a single gage during the debond event.  110  115  140  145  Part Temperature (°C)  Figure 4.18: Debond front migration with respect to part temperature.  -99-  150  Chapter 4 Instrumented Tool Experiments  900  800  350  X Coordinate (mm)  Figure 4.19: Post debond strain versus gage location. The slope of the fitted line is used for calculation of Tsuding- 586 kPa / release agent interface.  Figure 4.20: Mechanical strain evolution during the isothermal hold. 586 kPa / release agent interface.  -100-  Chapter 4 Instrumented Tool Experiments  Figure 4.21: Elastic constraint with respect to time. 586 kPa / release agent interface.  0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0  Part Degree of Cure, a  Figure 4.22: Elastic constraint plotted with respect to part degree of cure. 586 kPa / release agent interface  -101-  Chapter 4 Instrumented Tool Experiments  300  o  100  hC I-  a  S  -200  -300 125  Time (min)  Figure 4.23: Mechanical strain evolution during the heat-up portion of the cure cycle. 586 kPa / release agent interface.  3*0  X Coordinate (mm)  Figure 4.24: Strain reading versus gage location for various times during the cure cycle. The slope of the best fit lines is used for estimating Tsuding- 586 kPa / release agent interface.  -102-  Chapter 4 Instrumented Tool Experiments  180.0 -  160.0 -  140.0 -  120.0 -  _ (0  0.  100.0 .  J£ «?  I H  80.0  w  60.0 -  40.0  20.0 .  0.0 0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0  Part Degree of Cure, a  Figure 4.25: Change in Tsuding with respect to part degree of cure. 586 kPa / release agent interface.  Figure 4.26: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / release agent interface  -103-  Chapter 4 Instrumented Tool Experiments  Figure 4.27: Instrumented tool mechanical strain development for the entire cure cycle. 586 kPa / F E P interface.  Figure 4.28: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / F E P interface.  -104-  Chapter 4 Instrumented Tool Experiments  Figure 4.29: Strain reading versus gage location for various times during the cure cycle. 103 kPa / release agent interface.  Figure 4.30: Strain reading versus gage location for various times during the cure cycle. 586 kPa / F E P interface.  -105-  Chapter 4 Instrumented Tool Experiments  900  086 Minutes • 1 0 8 Minutes • 132 Minutes  ~ .3,  700  ^Cooldown  O O  500  £  300  c 10 J= o CD  100  5  350 -100  -300  X Coordinate (mm)  Figure 4.31: Strain reading versus gage location for various times during the cure cycle. 103 kPa / F E P interface.  180 160 140 586 kPa / Release Agent  120  -a—103 kPa / Release Agent 586 kPa / FEP  £ 100  o- 103 k P a / F E P  ca  H  IW  80 60 40 • -- "  - - • "T  20 0 0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  Part Degree of Cure, tx  Figure 4.32: Change in tsnding with respect to part degree of cure.  -106-  0.9  1.0  Chapter 4 Instrumented Tool Experiments  Figure 4.33: Elastic constraint with respect to degree of cure. 103 kPa / release agent interface.  o  o  O  O  ra  LU  0.4  0.5  0.6  Part Degree of Cure, a  Figure 4.34: Elastic constraint with respect to degree of cure. 586 kPa / F E P interface.  -107-  Chapter 4 Instrumented Tool Experiments  Figure 4.35: Elastic constraint with respect to degree of cure. 103 kPa / F E P interface.  Figure 4.36: Post debond strain versus gage location. The slope of the fitted line is used for calculation of tsuding- 103 kPa / release agent interface.  -108-  Chapter 4 Instrumented Tool Experiments  (fi (fi  Sliding Condition  Sticking Condition  a = 0.9 a = 0.5 a = 0.1 ^ 'Interface  Figure 4.37: Schematic illustration of the development of agent interface.  TDebond  and  Tsuding  for a release  (fi (fi  (D 1_  -I—«  CO ro  Sticking Condition  Sliding Condition a = 0.9 a = 0.5 a = 0.1  'Interface  Figure 4.38: Schematic illustration of the development of T b d and Tsuding for an F E P interface. De  -109-  on  Chapter 5 Analytical and Numerical Modelling  C H A P T E R 5: A N A L Y T I C A L AND N U M E R I C A L M O D E L L I N G  The results of the previous chapters provide useful empirical rules and general insight for understanding tool-part interaction.  However, to be of even greater value the results of the  previously detailed experimental studies should serve as a basis for validating or improving current process models. Towards this end a semi-quantitative model based on the results of the instrumented tool experiments is presented. Secondly, the quality of warpage predictions using the current version of the COMPRO (V.2.42) composites process modelling software are examined with respect to the trends identified in Chapter 3.  5.1  A N A L Y T I C A L  M O D E L  The qualitative descriptions of tool-part interaction found in the literature offer little information about how part warpage will scale with length, thickness or process variables.  These  descriptions can serve as a basis for complex numerical models such as those developed by Flanagan (1997) or Johnston et al. (2000).  However, an analytical model is still useful for  illustrating relationships between the part geometry, process parameters and final part shape.  The results of Chapter 4 indicate that during the heat-up portion of the cure cycle, sliding friction is the dominant interface condition, that is the interfacial shear stress is constant along the length of the part. Interfacial shear stress alone is insufficient to cause warpage in a part, however. For warpage to occur, the interfacial shear stress must induce a through-thickness stress gradient in the part. As discussed in the literature study, other researchers have assumed that slip also occurs between the plies of the laminate itself.  This causes a non-uniform distribution of in-  -110-  Chapter 5 Analytical and Numerical Modelling  plane stress, cr, with the tool side plies being stretched to a greater extent than plies near the laminate top. The non-uniform stress gradient is locked in as the part cures, and upon removal from the tool this residual stress distribution results in a net bending moment causing the part to warp.  For simplicity one can assume that the sliding friction condition occurs only at 2  interfaces: between 1 ply and 2 st  nd  ply, and at the tool-part interface. This was the basis for the  numerical model developed by Flanagan (1997) and will be the starting point for the simple model presented here. Other assumptions are as follows:  •  The interply sliding friction coefficient is smaller than the interface sliding friction coefficient.  This assumption is based on experimental evidence presented by Flanagan  (1997).  •  The bending moment which causes warpage is solely due to the residual stress induced in the 1 ply. There is no through thickness stress gradient in the upper plies. st  •  The effect of part degree of cure on part modulus and interface friction coefficients is neglected.  •  The laminate is uni-directional and hence the modulus and thermal expansion of each ply is identical.  The loading scenario for the first ply of a laminate stack is nearly equivalent to that considered for the thin tool in Section 4.2.1  A slight refinement is necessary, to recognize that the top  surface of the first ply is not a free surface but is subject to a shear stress transferred from the plies above it (Figure 5.1). The designations Ti„ rface and rj te  -111-  i  nterp  y  refer to the values of Tsnding at  Chapter 5 Analytical and Numerical Modelling  the bottom and top sides of the first ply respectively. Modifying the force equilibrium presented in Equation 4.3 accordingly:  (a + da-a)-t  + {r  Ply  lnlerface  -r  )-dx  Imerply  =0  (5.1)  Following through the same procedure as in Section 4.2.1, yields the following expression for stress in the first ply:  a ^ ' i L - x )  where x^ = et  tinter/ace - Tj„t piy er  (  5  2  )  and tpiy is the thickness of a single pre-preg ply. This is the tensile  stress in the first ply caused by tool-part interaction during the heat-up portion of the cure cycle. The stress in the rest of the laminate is:  a  Tl  =  y<L-x)  ^  nlerp!  ^Lam ~tpty  To the extent that  TMerface »  finterpty  and  tiam »  tpiy,  the stress supported by the rest of the  laminate will be small compared to that in the first ply. The in-plane stress gradient which this results in is discontinuous as Figure 5.2 illustrates for a cross-section at an arbitrary x coordinate.  As the material cures, this stress is locked in as a residual stress. The effect of the residual stress on final part shape can be calculated by applying a stress of the same magnitude as the residual stress but opposite in sign, to a stress free laminate. This stress causes a net bending moment, warping the part. The bending moment due to the residual stress in the first ply is:  M = cr-t -C ply  -112-  (5.4)  Chapter 5 Analytical and Numerical Modelling  where c is the distance from the ply centroid to the neutral axis of the laminate.  For  simplification purposes one can make the following approximation:  c =  ^-  tj  (5.5)  Substituting Equations (5.2) and (5.5) into Equation (5.4) yields:  t  M=r -(L-x)-^  (5.6)  Nel  Incorporating the moment-curvature relation gives:  dz  M  dx  E-I  2  2  dz  r „ -r '•Net Lam  2  _  l  2  where E  Part  -  E  P a n -  (5.7)  (L-x)  (5.8)  1  is the part modulus and / is the second moment of area for the part. Integrating twice  and incorporating boundary conditions one can get an expression for the warpage of the part as a function of x:  dz —  dx  z =  z  _  at  = 0  ^ Nel '  at  0  '  x =  x =  L-x  {  Lam  2  V 2  0  0  x^  6 ,  (5.9)  Substituting for /, one can calculate the maximum part warpage at x = L  ,3  T  1=  I  Lam  12  -113-  (5.10)  Chapter 5 Analytical and Numerical Modelling  2-T Maximum Part Warpage, w  5.1.1  m a x  =  -If  ^ — Epart' * to™  (5.11)  COMPARISON WITH EXPERIMENTAL RESULTS  Recalling the empirical warpage relation expressed in Equation (3.6):  p  0  . 2 .  z  3  ^ m a x * — 2  t  ( -6) 3  Lam  the similarities to Equation (5.11) are apparent. Both geometric parameters ti  am  and L are in  agreement between the two relations.  The P  02  term in Equation (3.6) describes the pressure effect, which is embodied in the zm term  in Equation (5.11).  To check for consistency between Equation (3.6) and Equation (5.11),  consider the change in warpage which was experimentally observed between the low pressure and high pressure conditions. From Equation (3.6):  W  5 8 6  e  (5S6  (P ) -L \ 02  W 5 8 6  02  (\03kPa)  3  m  where  kPa)  0.2  = 1.4  (5.12)  and w^s are the warpages at the high and low pressure conditions respectively. For  consistency, predictions made using Equation (5.11) should also show the same change in warpage between high and low pressure conditions.  2' ^586 _ E  part  102  W  Z  ^586  L  '  -t Lam _ T  s86  ' M03 ' 2  L  ^103  t  Epart ' ^ Lam  Combining the results of Equation (5.12) and Equation (5.13):  -114-  Chapter 5 Analytical and Numerical Modelling  W  W  586  =  103  T 586 7  = 1.4  (5.14)  103  Equation (5.14) suggest that one should observe a 1.4 fold increase in r^, from the low pressure condition to the high pressure condition.  The instrumented tool experiments performed in  Chapter 4 do not measure r^, directly but rather r/„ / te/  tinterpiy  ace  (Tsnding). However, if one assumes that  remains unchanged with respect to pressure, a 1.4 fold increase in  expected.  Ti rface nte  would be  Regarding the instrumented tool experimental results in Figure 4.32, when residual  stress is expected to be building (during the heat-up), the average value of Tsnding is on the order of 25 kPa. One should therefore see approximately 10 kPa of distinction between Tsnding for the high and low pressure conditions , however, the experimental error in the Tsnding estimates is on 1  the order of 5 kPa. It was felt that this offered insufficient resolution to confirm an effect of that scale.  As a verification, the analytical model can be used in order to calculate what value of T^ is el  necessary to induce the experimentally observed part warpage. Solving Equation (5.11) for T^ t e  gives:  ,  1  _  Net ~  Max "Epart ' ^ Lam  W  2 £  For the example calculation the following inputs will be used:  W  M  O  X  =  8.34 mm - average of the 2 experimental results for 8 ply/1200 mm/586 kPa parts.  E = 125 GPa - longitudinal Young's modulus for fully cured laminate.  1  (1.4 x 25 kPa) - 25 kPa = 10 kPa  -115-  Chapter 5 Analytical and Numerical Modelling  tLam  =1.6 mm - 8 ply laminate.  L = 600 mm - half part length for 1200 mm specimens.  The resulting value for r  Net  is 6.2 kPa. By contrast the average value of  Ti f nter  ace  for the 586 kPa  pressure condition prior to the hold, as measured by the instrumented tool experiments was 29.4 kPa.  The result is consistent insomuch as the required z^ is smaller than the experimentally et  measured  The value of  Ti„i f . er  ace  Ti i  nterp y  which this implies is:  * Interply = ? Interface ~ *Net =  29.4 kPa ~ 6.2 kPa = 23.2 kPa  (5.16)  The question of whether this is a realistic value is outside the scope of the experimental study undertaken here, however for comparison purposes Flanagan (1997) reported measurements of Tinterpiy  spanning from 6 kPa to 176 kPa.  5.1.2  ANALYTICAL M O D E L - DISCUSSION  The purpose of the above calculation is not to suggest that the analytical model is suitable for quantitative calculations; variation in  tinterpiy  potentially important factors such as resin cure shrinkage and the  and r/„ / ter  ace  with degree of cure are ignored. However, it does illustrate the  basis for the relationship between part geometry and part warpage. A key aspect of the model is the severe through thickness stress gradient in the part, meaning that a more sophisticated process model which incorporates this distribution should give reasonable quantitative results. Indeed, while they were not presented in such a fashion, plotting the numerical warpage results presented in by Flanagan (1997) against length and thickness, shows that they match the L and 3  l/t relations very well as shown in Figure 5.3 and Figure 5.4.  -116-  Chapter 5 Analytical and Numerical Modelling  The analytical model presented above also has interesting implications with respect to parts fabricated on tooling with different CTEs. Equation (5.2) suggests that stress and strain in the 1  st  ply will continue to increase indefinitely as part length is increased. However, there is a limiting condition governed by e  ismatch  M  between the tool and part. At a certain critical part length, L , the c  strain in the 1 ply at x = 0, will be equal to EMismatch- Incorporating Hooke's Law into Equation st  5.2, one can express strain in the 1 ply at x=0 as: st  ^ Net '  = —m. F -t '-'Part  •  (5_ ) 2  Pfy  l  The critical condition is the following:  (CTE -CTE ).AT= ^' T  Too!  Lc  (5.17)  Parl  ^Part  ' *Pfy  Solving for Lc gives: (CTE  r  Tooj  - CTE ) • AT Part  ' Epart  L  '  tpiy  • Net  c  (5.18)  As part length is increased past Lc, there will be a portion in the centre of the part where there is no longer a strain mismatch between the tool and 1 ply and hence no sliding will occur. The st  interfacial shear stress in this region falls to zero and the in-plane stress in the first ply will not increase past, CTMOX, the limiting value dictated by  SMismatch'-  <J ={CTE -CTE \AT-E Max  Tml  Pm  Part  (5.19)  The stress distributions associated with this scenario are depicted in Figure 5.5 and Figure 5.6. This implies that depending on tooling material, two parts of identical dimensions can have different stress distributions and hence different warpages. .  -117-  Chapter 5 Analytical and Numerical Modelling  As an example calculation, consider two parts fabricated on aluminum and invar tooling respectively, both with a total part length of 4 metres. To calculate Lc for the part cured on invar tooling, one can assume the following values:  CTE  = 2 u/°C  CTE  = Q\xl C  Tool  0  Part  zfT=160°C  tpiy = 0.2 mm  tNet = 6.2 kPa  L  (5.18)  c  (2.4 fil'C) • (160 °C)-(125-10 /V / m ) • (2 • 10" m) — = — -&\.5m 6.2-10 N/m 9  Z =^ c  3  2  2  4  (5.18)  As Equation (5.18) states, the value of Lc varies with the C T E mismatch between tool and part. Table 5.1 shows the value for Lc for a uni-directional CFRP laminate on tools of various materials. For the part on the invar tool the stress distribution at any section beyond 1.5 metres from the part end will be unchanging . In contrast, for the part fabricated on aluminum tooling the stress in the first ply will continue to increase as illustrated in Figure 5.7. This would result in a greater bending moment (and greater curvature) active over much of the length of the part fabricated on aluminum tooling.  -118-  Chapter 5 Analytical and Numerical Modelling  The maximum warpage for parts o f lengths less than, and greater than LQ respectively can be shown to be (Appendix C ) :  ^=\-C -L'  L<L  x  w „ = m  C  C .^.Z -Z, -i.Ic3j 2  1  L>L  c  C  (C.5)  (CM)  where:  Q _ 1  L  Net Lam l  2-F  •I  The maximum warpage as a function o f length for parts fabricated on different tooling materials is shown i n Figure 5.8.  The figure illustrates that the maximum part warpage would be identical  for the various tooling materials, until the part length reaches LQ for a given tooling material. A s part length is increased past LQ the maximum part warpage no longer follows the L relation. A 3  number o f simplifying assumptions were made for the calculation o f Lc, but it illustrates two important points:  •  Even with a sliding frictional interface, there are situations under which the C T E o f the tooling material can influence part shape.  •  The critical length at which sliding between tool and part no longer occurs is within the realm o f industrially relevant part dimensions.  Strictly speaking, due to the shear stress transferred from the 1 ply, the stress in plies 2.. .n will still be increasing as one moves closer to the part centre. However, recalling the assumption that the bending moment is derived entirely from the first ply means that the bending moment contributing to part warpage remains unchanged beyond 1.4 metres from the part end.  2  st  -119-  Chapter 5 Analytical and Numerical Modelling  5.2  N U M E R I C A L W A R P A G E  M O D E L L I N G  As discussed in Chapter 2, Johnston et al. (2000) created a 2-dimensional, plane-strain finite element program, COMPRO, for modelling residual stress development during the autoclave processing of composites.  The details of the model are presented in entirety in Hubert (1996)  and Johnston (1997) so only a cursory explanation of the model is included here.  A representative cross-section of both the tool and part is typically modelled.  COMPRO  contains three modules to examine the heat transfer and thermochemical aspects of the process, compaction and flow of the material, and finally the development of residual stresses in the part. The lead-lag control algorithms used by real autoclave controllers are incorporated into the program, so the virtual autoclave cycle will closely mirror its real counterpart. C O M P R O timesteps through the cycle, first running the thermochemical module to calculate temperatures and also the degree of cure for appropriate materials. Material property models based on extensive experimental characterization express the changing properties of the composite material as a function of both temperature and degree of cure. After the thermochemical module completes a step, the flow module or stress module is run depending on whether the material in question is at a degree of cure prior to, or after gelation.  Material properties for the stress module are considered to be linear-elastic during any given time increment, however, with appropriately small time-steps, the evolving properties of composite materials can be captured. As the cycle progresses, residual forces can accumulate in the part due to cure shrinkage, part anisotropy, thermal gradients and tooling constraints. The last step of the model is the removal of all tooling constraints from the part, yielding the final equilibrium part shape.  -120-  Chapter 5 Analytical and Numerical Modelling  A representative mesh for an 8 ply, flat part on aluminum tooling is shown in Figure 5.9. Note that in C O M P R O there may be more than one ply per element. To permit a means of tailoring the amount of shear stress transfer between the tool and part, an elastic shear-layer is incorporated into the finite element mesh as shown in Figure 5.9. Depending on the value of elastic modulus assigned to the shear layer, a range of tool part interface conditions can be simulated. At the one extreme, i f the properties of the shear layer are the same as the tooling, high shear stresses arise between the tool and part. At the other extreme, by giving the shear layer low values for E n and G o , relatively little stress is transferred between tool and part. It should be noted that the shear layer is considered to be part of the tooling and as such is removed during the final tool removal calculation .  5.2.1  NUMERICAL M O D E L - PARAMETRIC STUDY  A parametric study was performed using C O M P R O (V.2.42) to examine the effect of varying shear layer and part properties over the range of part geometries examined experimentally. Because of part symmetry, only half of each geometry was modelled. Mesh size was held constant for each geometry and mesh sensitivity was tested in order to confirm that through thickness effects were adequately represented. Doubling the number of elements through the thickness of the part had less than 5% change on warpage as shown in Figure 5.10.  The following parameters were examined in the numerical study:  •  Shear layer stiffness - with the exception of E n and G13, the shear layer properties were always the same as that of the aluminum tool and the shear layer geometry was held  As a result of the current work, there is a version of COMPRO currently in development (Decemeber 2000) which incorporates a sliding interface, as well as the current elastic implementation.  3  -121-  Chapter 5 Analytical and Numerical Modelling  Values of E n and G13 were lowered by identical order of magnitude  constant.  decrements to create an increasingly soft shear layer . 4  •  Part shear modulus - COMPRO uses standard micromechanics equations to calculate the properties of a laminate based on its constituents properties. The shear modulus, G13, is a resin dominated property while the in-plane modulus, E n , is fibre dominated. By using a lower initial elastic modulus for the resin, G13 of the laminate is reduced substantially while E n remains virtually unchanged. The nominal value for initial resin modulus is 4.1 x 10 Pa. In a similar fashion to the shear layer, resin modulus was lowered by order of magnitude decrements from its nominal value of 4.1 x 10 Pa. The final resin modulus 7  was held constant at 4.1 GPa.  •  Part length - 300mm, 600 mm and 1200 mm part lengths were examined.  •  Part thickness - 4, 8 and 16 ply laminates were modelled.  5.2.1.1  Parametric Study - Results  The results of the parametric study are presented in Table 5.2 and for comparison purposes the average of all experimental specimens for a given geometry are presented in Table 5.3. Both shear layer modulus and initial resin modulus can cause part warpage to vary over many orders of magnitude.  The warpage demonstrated by a single part geometry can be matched by  appropriate selection of the shear layer and resin modulii as shown in Figure 5.11, moreover there are several combinations of the two parameters which can reasonably approximate the actual part shape.  When a value for shear layer modulus is given in the following discussion, only the value of E is quoted. However, It should be understood that the shear modulus of the layer has also been adjusted to the same order of 4  u  -122-  Chapter 5 Analytical and Numerical Modelling  In addition to matching part shape, it is of primary interest to be able to capture the trends in warpage with respect to part geometry.  Figure 5.12 through Figure 5.14 show the effect of  varying shear layer modulus and resin initial modulus for the high, middle and low aspect ratio part geometries examined.  The following trends were observed:  •  Increasing the stiffness of the shear layer had the effect of increasing part warpage  •  Decreasing the part initial resin modulus also increased warpage.  •  For parts with high initial resin modulus there was little difference in warpage between parts of various thicknesses. Decreasing the initial resin modulus increased the effect of part thickness on warpage.  The  combination of parameters which provided the best agreement  with the  average  experimental results was a shear layer modulus of 6.9 x 10 Pa and a part initial resin modulus of 4.1 x 10 Pa. The model predictions for this parameter set are compared with experimental 4  results in Figure 5.15 through Figure 5.17.  This data set gives reasonable agreement for the  trends with respect to part length and good agreement for trends with respect to part thickness.  5 . 2 . 2 N U M E R I C A L M O D E L L I N G - DISCUSSION The key to correctly capturing warpage trends lies in the distributions of tool-part interfacial shear stress and in-plane stress within the part. The stress distributions which determine final part shape develop mainly during the heat-up portion of the cure cycle.  For the following  magnitude. F o r instance, shear layer modulus o f 6.9 x 10 P a represents the following: En = 6.9 x 10 P a , Gn = 2.6 x 10 P a and E 3 3 = 6.9 x 1 0 Pa. 5  5  10  -123-  5  Chapter 5 Analytical and Numerical Modelling  discussion it is sufficient to compare distributions at a single instant during the isothermal hold. Figure 5.17 through Figure 5.19 all refer to stress distributions at a point during the isothermal hold, 200 minutes into the cure cycle.  5.2.2.1  Interfacial Shear Stress with Elastic Shear Layer  The interfacial shear stress which is applied to the part is represented by the shear stress in the shear layer elements. The magnitude and distribution of this stress is governed largely by the properties assigned to the shear layer. Figure 5.18 shows that for a high shear layer stiffness, the elastic F E model considered here yields the same type of distribution predicted by the closed form solution in Section 4.2.2 with shear stress building over a short region near the part end. However, the magnitude of the shear stress is on the order of 10 Pa, which is quite in excess of 6  the values which were experimentally determined to be operative at the tool-part interface.  By lowering the shear layer stiffness, more of the strain mismatch between tool and part is accommodated by the shear layer. The result of this is shown in Figure 5.19 for modelling runs with shear layer properties of 6.9 x 10 and 6.9 x 10 respectively. The reduced shear layer 4  3  stiffness has the effect of increasing the stress transfer length (such that it now spans the entire part length) and reducing the magnitude of shear stress applied to the part. The reduction in interfacial shear stress results in less part warpage.  By adjusting the shear layer properties, the interfacial shear stress can be reduced such that its magnitude at least spans the value suggested by the instrumented tool experiments. However, the experiments in Chapter 4 suggest that interfacial shear stress should be constant along the part length and this distribution cannot be captured using the elastic shear layer model. Furthermore, as part length increases the interfacial shear stress will increase indefinitely with  -124-  Chapter 5 Analytical and Numerical Modelling  the COMPRO (V.2.42) implementation, whereas experimentally it was determined that there is a limiting stress, Tsnding, which the interface can support. This clearly has implications about the ability of the shear layer approach to capture interface behaviour over all part lengths.  5.2.2.2  In-Plane Stress Gradient  The other factor which greatly influences the magnitude and trends of part warpage is the distribution of in-plane stress through the part cross-section.  In particular this distribution has a  strong effect on the relationship between warpage and laminate thickness.  Recall that for the  analytical model presented in Section 5.1 the assumed stress distribution was discontinuous, with the 1 ply bearing most of the stress transferred from the tool. This distribution resulted in the st  bending moment which in turn caused part warpage.  The important characteristic of the discontinuous distribution is the severe in-plane stress gradient through the part thickness.  For the elastic case considered in COMPRO the decay of  stress through the thickness of the part is strongly related to the shear modulus of the part. As discussed earlier, the shear modulus can be adjusted by altering the modulus of the resin. Figure 5.20 shows the in-plane stress distribution through the thickness of the part for modelling runs performed with various initial resin modulii. The distribution illustrated is for a cross section at the part centre. For the high initial modulus case all plies carry nearly the same load whereas for the low initial modulus case, the stress is concentrated near the tool-part interface as in the discontinuous distribution.  The bending moment resulting from a given stress distribution can be calculated using Equation (5.4):  M = cr-t  -C  Elemem  -125-  (5.4)  Chapter 5 Analytical and Numerical Modelling  where  tEkment  is the element thickness. The moment arising from the respective in-plane stress  distributions is much greater when the gradient in stress through the thickness is large.  In fact, this relationship between part shear modulus and through-thickness stress distribution explains how the moment can be 'locked-in' as residual stress in the model.  Figure 5.21  examines the in-plane stress for a cross section (at the part centre) as it evolves through the cure cycle. Early in the cycle the resin modulus is low as shown in Figure 5.22 and because of this, stress builds to a greater extent in the lower plies.  The resin modulus increases dramatically  during the hold such that on the cool-down, while the magnitudes of the part stresses change, the distribution does not.  The result is that the bending moment builds during the heat-up, and  remains practically unchanged for the rest of the cure cycle. This is illustrated in Figure 5.23 for two parts of different initial resin modulus. Also note that the bending moment resultant is greater for the lower initial resin modulus case.  The resin modulus input for COMPRO is typically characterized by Dynamic Mechanical Analysis (DMA), however, the measurement of composite material properties at low degrees of cure is exceedingly difficult.  The material dataset used for the present COMPRO modelling  work was generated by Johnston (1997) who found good agreement between the material model and the tests at high degrees of cure. Initially the resin modulus has no practically measurable value, hence for modelling purposes an arbitrarily low value of 4.1 x 10 Pa was selected. The 7  reported value is apparently too high to adequately capture the through thickness gradient which is necessary to match the experimentally observed warpage trends.  Both the analytical and numerical models illustrate that the magnitude of warpage for a given part is determined by a complex interaction between part geometry, part properties and interface  -126-  Chapter 5 Analytical and Numerical Modelling  properties. A significant result which both models lead to is that the effect which part thickness has on warpage suggests a severe gradient in stress through the thickness of the part. The question of which model better represents the actual stress distribution within the laminate is outside the scope of the experimental efforts undertaken in the present work. The discontinuous model corresponds to the assumption of interply slippage while the elastic model assumes a part which is easily sheared.  Both views seem equally plausible when considering laminate  mechanical properties during the heat-up portion of the cure cycle. Both assumptions also yield similar results, suggesting that the approach one takes when modelling this phenomena can be based on other factors such as the ease of characterizing the required material properties or how readily the assumptions can be incorporated into existing numerical models.  5.3  S U M M A R Y  •  A n analytical model assuming slip occurs between the 1 and 2 st  nd  plies as well as at the  tool part interface can predict the experimentally observed relationship between part geometry and warpage.  •  There is a complex interaction between part geometry, part properties and interface properties which act collectively to determine the magnitude of part warpage.  •  The elastic shear layer currently used in COMPRO (V.2.42) is unable to adequately capture the distribution of shear stress which arises due to the sliding friction condition at the tool-part interface.  Moreover, with the elastic shear layer, shear stress increases  indefinitely as part length increases in contrast with the experimental observation of a  -127-  Chapter 5 Analytical and Numerical Modelling  limiting shear stress, rsudmg-  This affects the ability of COMPRO (V.2.42) to predict  warpage over a large range of laminate lengths.  •  The distribution of in-plane stress through the thickness of the part is critical for accurate modelling of the warpage phenomena.  By reducing the initial shear modulus for the  laminate, a more severe stress gradient is created, resulting in good agreement between COMPRO predictions and experimental results.  -128-  Chapter 5 Analytical and Numerical Modelling  5.4  T A B L E S  Table 5.1: L values for a uni-directional C F R P laminate fabricated on tools of varying C T E . c  Tooling C T E  Tooling Material  L  c  (M/°C)  (m)  Aluminum  'B.6  Steel  11.7 2.5 2.4  15.2 7.5 1.6 1.5  CFRP (Quasi-lsotropic) Invar  Table 5 2: Design and results of C O M P R O parametric study  Shear Layer Modulus (6.9 x 10» Pa)  Part Kesin Modulus  3  3  3  4  (4.1 x 10* Pa)  Number of Plies  Part Warpage (mm) 300 mm Part Length 600 mm Part Length 1200 mm Part Length  4 8 16 4  0.12 0.03 0.01 0.12 0.03 0.01  16  3  5  3  6  3  7  4  3  4  4  4  5  4  6  4  7  4 8 16 4 8 16 4 8 16 4 8 16 4 8 16 4 8 16 4 8 16 4 8 16  0.09  0.03 0.01 0.03 0.02 0.01 0.00 0.00 0.00 1.93 0.55 0.14 1.85 0.54 0.14 1.34 0.47 0.13 0.36 0.24 0.10 0.04 0.04 0.03  -129-  2.90 0.83 0.22 2.50 0.78 0.21 1.08 0.53 0.18 0.16 0.15 0.09 0.02 0.02 0.02 28.65 8.23 2.14 25.01 7.80 2.11 11.02 5.52 1.86 1.69  1.52 0.97 0.18 0.18 0.17  46.09 13.61 3.59 28.93 11.19 3.31 6.28 4.70 2.26 0.70 0.71 0.61 0.07 0.07 0.07 232.24 98.00 25.88 232.24 90.31 26.79 56.54 43.15 20.93 6.57 6.87 6.03 0.66 0.72 0.73  Chapter 5 Analytical and Numerical Modelling  Table 5.3: Average experimental results for all part geometries.  JNumber ol Flies iUU mm Fart Length 6UU mm Fart Length 12UU mm Part Length  4 16  0.64 0.20 0.09  3.48 0.97 0.21  -130-  31.61  6.65  1.41  Chapter 5 Analytical and Numerical Modelling  5.5  F I G U R E S  Figure 5.1: Part geometry for the analytical model. Sliding friction occurs at both the toolpart interface and at the interply region.  n-Plane Stress, a  Figure 5.2: In-plane stress distribution for the analytical model with sliding friction at the 1 ply-2 ply interface. st  nd  -131-  Chapter 5 Analytical and Numerical Modelling  1.2  0  200  400  600  800  1000  1200  Part Length (mm)  Figure 5.3: Comparison of numerical modelling results from Flanagan with L warpage relationship.  1.2  Number of Plies  Figure 5.4: Comparison of numerical modelling results from Flanagan with 1 / 1 warpage relationship 2  -132-  Chapter 5 Analytical and Numerical Modelling  CO W  0)  CO i_  C O 0  SZ CO "ro  o  -e £  C  x Sliding  Part Centre  X Coordinate  Part E n d  Figure 5.5: Interfacial shear stress distribution corresponding to a part where the part length, L, is greater than Lc.  Figure 5.6: In-plane stress distribution corresponding to a part where the part length, L, is greater than L&  -133-  Chapter 5 Analytical and Numerical Modelling  Aluminum tool  Invar tool  Figure 5.7: Difference in 1 ply in-plane stress distributions for a 4 metre long parts fabricated on aluminum and invar tooling. For the part fabricated on invar tooling, L > Lc, hence the stress reaches the limiting value, o-Max- In contrast, stress continues to build for the part fabricated on aluminum tooling. st  1.2  0  5  10  15  20  25  Part Length (m)  Figure 5.8: Warpage versus length predictions for parts fabricated on tooling with different C T E s . The maximum warpage predictions differ when the part length, L, becomes greater than Lc for the tooling material.  -134-  Chapter 5 Analytical and Numerical Modelling  Regions 1  2  x  Figure 5.9: Representative FE mesh used for COMPRO modelling runs. The laminate is 8 plies thick.  -0.5  ro a CD  ro CL  150  200  250  300  350  Z Coordinate (mm)  Figure 5.10: Effect of mesh refinement on deformed part shape (4 Ply / 600 mm part, Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa) 3  -135-  4  Chapter 5 Analytical and Numerical Modelling  u_J X Coordinate (mm)  Figure 5.11: Agreement between ply, 600 mm part.  C O M P R O  and experimental deformed shape for an 8  250 ,  Initial Resin Modulus -4.1 x 10"  Figure 5.12: Effect of initial resin modulus and shear layer modulus on warpage results for 4 ply / 1200 mm specimens.  -136-  C O M P R O  Chapter 5 Analytical and Numerical Modelling  9.0 ,  Initial Resin Modulus -4.1 x 10"  Figure 5.13: Effect of initial resin modulus and shear layer modulus on warpage results for 8 ply / 600 mm specimens.  0.16  C O M P R O  T  Initial Resin Modulus - 4.1 x 10"  Figure 5.14: Effect of initial resin modulus and shear layer modulus on warpage results for 16 ply / 300 mm specimens.  -137-  C O M P R O  Chapter 5 Analytical and Numerical Modelling  35.0 ,  X Coordinate (mm)  Figure 5.15: C O M P R O prediction versus average experimental result for 4 ply specimens. (Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa). 3  4  12.0 ,  1400 X Coordinate (mm)  Figure 5.16: C O M P R O prediction versus average experimental result for 8 ply specimens. (Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa). 3  -138-  4  Chapter 5 Analytical and Numerical Modelling  3.5 -,  X Coordinate (mm)  Figure 5.17: C O M P R O prediction versus average experimental result for 16 ply specimens. (Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa). 3  4  Figure 5.18: Interfacial shear stress distribution for a model with high shear layer stiffness (8 ply / 600 mm part, Initial Resin Modulus = 4.1 x 10 Pa). s  -139-  Chapter 5 Analytical and Numerical Modelling  -100  -I 0  ,  ,  50  100  ,  150  ,  200  ,  ,  250  300  1  350  X Coordinate (mm)  Figure 5.19: Interfacial shear stress distribution for models with low shear layer stiffness (8 ply / 600 mm part, Initial Resin Modulus = 4.1 x 10 Pa). s  Figure 5.20: Effect of initial resin modulus on in-plane stress distribution. The cross section considered is at the part centre. (8 ply / 600 mm part, Shear Layer Modulus = 6.9 x 10 Pa) 4  -140-  Chapter 5 Analytical and Numerical Modelling  Figure 5.21: Development of in-plane stress with respect to time (8 ply / 600 mm part, Shear Layer Modulus = 6.9 x 10 Pa, Initial Resin Modulus = 4.1 x 10 Pa). 4  6  Figure 5.22: C O M P R O prediction of resin modulus development with respect to time.  -141-  Chapter 5 Analytical and Numerical Modelling  -Initial Resin Modulus = 4.1 E+6 -Initial Resin Modulus = 4.1 E+4 -Part Temperature <D  m  100  150  200  Time (min)  Figure 5.23: Development of bending moment with respect to time for models with different initial resin modulus. (8 ply / 600 mm part, Shear Layer Modulus 6.9 x 10 Pa) 4  -142-  C H A P T E R 6: CONCLUSIONS AND F U T U R E W O R K  The objective of this thesis was to develop a fundamental understanding of the mechanics and constitutive behaviour of the tool-part interface during processing, with the ultimate goal of improving the predictive capabilities of current process models. Toward this end two experimental studies were undertaken, the insight from which provided a basis for the development and improvement of models to predict tool-part interaction induced warpage. The major accomplishments of the current work include:  •  A n empirical relation to predict tool-part interaction induced warpage was determined.  A parametric study examining the effects of geometry and process parameters on warpage was conducted.  The relationship between part warpage and part length,  thickness and processing pressure can be embodied in a single equation. Tool surface condition did not have a significant effect on part warpage.  •  The magnitude and distribution of tool-part interfacial shear stress during processing were measured.  A new technique for characterizing the interfacial shear stress operative at the tool-part interface was developed. Both interfacial sliding and sticking interface conditions were observed to occur at various times throughout the cure cycle. During the heat-up when part residual stresses are developing, a sliding friction condition occurred for the cure cycles considered. For a release agent tool-part interface, adhesive bonding can increase  -143-  Chapter 6 Conclusions and Future Work  the interface strength by orders of magnitude. The use of FEP at the interface prevented any adhesive bonding between the tool and part but there can still be appreciable interaction between the two.  •  A n analytical model to predict part warpage was developed.  An analytical warpage model was developed, based on the simplifying assumption that slip occurs at the tool-part and 1 ply-2 ply interfaces only. There was good agreement st  nd  between the analytical model and the experimental results.  •  A n existing numerical model was used to successfully model part warpage.  The experimentally observed warpage could be modelled reasonably using COMPRO (V.2.42). A key parameter which related part thickness and the magnitude of warpage was the shear modulus of the part during the heat-up. A low part shear modulus creates a severe gradient in stress through the laminate thickness which is required for accurate warpage predictions. However, the current implementation of tool-part interaction via the elastic shear layer approach cannot correctly represent the interface behaviour over a general range of part lengths.  6.1  F U T U R E  W O R K  A recurring observation, consistent with published research, was the significance of batch to batch variability for the experimental specimens. Given that at present the drivers of this variability remain unknown, this must be taken into account when designing future experimental studies. Replicate specimens should be fabricated over the entire range of experimental conditions examined.  This would provide both an increased level of  -144-  Chapter 6 Conclusions and Future Work  confidence in the warpage values for a given condition and perhaps more importantly, one could map the relationship between processing parameters and variability. Other recommendations for future work include:  •  Examination of alternate cure cycles  The examination of 2-step cure cycles would be of value for confirming hypotheses with respect to the evolution of interfacial shear stress through the cure cycle. Moreover, this type of cycle is of interest because a significant number of commercial structures are processed this way.  •  Experiments using other tooling materials and part lay-ups  Both part lay-up and tooling material are expected to have a significant effect on part warpage.  The scope of future experimental warpage studies should include these two  industrially relevant variables.  •  Improved instrumented tooling experiments  At low degrees of cure, the strains measured using the instrumented tool approach were very small. The resulting resolution limited the extent to which one could differentiate between various processing conditions during the heat-up portion of the cure cycle. A simple remedy for this would be to make the instrumented tool longer. A longer tool part interface results in greater measurable strains for a given interfacial shear stress. Furthermore, this would permit the location of gages well away from the part ends where bending deformation in the tool due to local resin bleeding was an issue.  -145-  Chapter 6 Conclusions and Future Work  •  Measurement of strains within the part  Ultimately, one would like to measure the strain distribution within the part itself as it evolves through the cure cycle. Given that the expected magnitude of the strains is very small compared with the potential error sources, measurement tools such as traditional strain gages or fibre optic sensors are perhaps ill suited to this task. Indirect inferring of the final stress / strain state of the part may be possible using a modification of the "make and measure" technique employed in the present study. By selectively removing plies from the laminate and re-measuring, a more complete picture of the part stress state could be developed.  •  Modelling - improved interface representation  The current shear layer method of representing tool-part interaction in COMPRO (V.2.42) is inadequate for representing a sliding friction condition.  Future versions  should be able to represent both plastic/sliding and elastic/sticking interface conditions.  •  Improved characterization of composite material properties at low degrees of cure  The properties of the laminate at low degrees of cure were shown to be important for proper representation of the through thickness decay of stresses in the laminate. The current practice of arbitrarily setting the initial resin modulus to a value assumed to be low enough has been shown to be problematic.  Improved characterization of part  mechanical properties at low degrees of cure is essential for accurate process modelling of the tool-part interaction phenomena.  -146-  REFERENCES  Arnell, R.D., Davies, P.B., Hailing, J., et al. "Tribology: Principles and Design Applications", Springer-Verlag, New York, 1991. Berglund, L . A . and Kenny, J.M., "Processing Science for High Performance Composites", SAMPE Journal, Vol. 27, 1991, pp. 27-37.  Thermoset  Bickford, W.B., "Mechanics of Solids Concepts and Applications", Irwin, Boston, 1993. Bogetti, T.A. and Gillespie, J.W., Jr., "Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates", Journal of Composite Materials, Vol. 26, No. 5, 1992, pp. 626-659. Cho, M . , Kim, M . H . , Choi, H.S., et al., "A Study on the Room-Temperature Curvature Shapes of Unsymmetric Laminates Including Slippage Effects", Journal of Composite Materials (USA), Vol. 32, No. 5, 1998, pp. 460-482. Crasto, A., Kim, R Y . and Russell, J.D., "In Situ Monitoring of Residual Strain Development During Composite Cure", 44th International SAMPE Symposium, 1999, pp. 1706-1717. Daniel, I.M., Liber, T., Cairns, C C , "Measurement of Residual Strains in Boron-Epoxy and Glass Epoxy Laminates", Composite Reliability, A S T M STP 580, American Society for Testing and Materials, 1975, pp. 340-351. Fernlund, G., "Stresses in Adhesively Bonded Substrates", Personal Communication, April 7, 1999. Fernlund, G. and Poursartip, A . , "The Effect of Tooling Material, Cure Cycle and Tool Surface Finish on Spring-In of Autoclave Processed Curved Composite Parts", 12th International Conference on Composite Materials, July-1999, Paper 690. Fernlund, G., Rahman, N . , Courdji, R., et al., "Experimental and Numerical Study of the Effect of Cure Cycle, Tool Surface, Geometry and Lay-up on the Dimensional Fidelity of AutoclaveProcessed Composite Parts", Submitted to Composites Part A: Manufacturing. Fidler, F., "The Scanner Method: An Optical Method for Measuring Angularity of Composite Parts", Internal Report, Composites Group, University of British Columbia, 1998. Flanagan, R. "The Dimensional Stability of Composite Laminates and Structures", Ph.D. Thesis, Queen's University of Belfast, 1997. Hexcel Corporation Product Data Sheet, "Hexcel Fibres".  -147-  References  Hexcel Corporation Product Data Sheet, "8551-7". Hexcel Corporation Product Data Sheet, "3501-6". Hexcel Corporation Product Data Sheet, "Redux 330". Hubert, P. "Aspects of Flow and Compaction of Laminated Composite Shapes During Cure", Ph.D. Thesis, University of British Columbia, 1996. Hubert, P., and Poursartip, A., "Study of the Interaction Between Percolation and Shear Flow in Processing of Thermoset Matrix Composites", American Society for Composites, College Station, Texas, September 2000. Hubert, P., Poursartip, A . , and Bradley, W.L., "Direct Observations of Transverse Flow in Fibre Reinforced Composite Materials During Processing", Proceedings of The 11 Technical Conference on Composite Materials of the American Society for Composites, Atlanta, G A , October 7-9 1996. th  Jain, L . K . , Lutton, B . G . , Mai, Y.W., et al, "Stresses and Deformations Induced During Manufacturing. Part II: A Study of the Spring-In Phenomenon", Journal of Composite Materials, Vol. 31, No. 7, 1997, pp. 696-719 ;  Johnston, A., "An Integrated Model of the Development of Process Induced Deformation in Autoclave Processing of Composite Structures.", Ph.D. Thesis, University of British Columbia, 1997. Johnston, A.; Hubert, P., Fernlund, et al., "A Sensitivity Analysis of Modelling Predictions of the Warpage of a Composite Structure", Proceedings of the 43 International SAMPE Symposium and Exhibition, Anaheim, C A , May 31-June 4, 1998. r  Johnston, A., Vaziri, R., and Poursartip, A., "A Plane Strain Model for Process-Induced Deformation of Composite Structures" accepted for publication in Journal of Composite Materials, August 2000. Kaw, A . K., "Promal", (1.0), 1997. Lee, L . H . , "Recent Studies in Polymer Adhesion Mechanisms", In: Adhesive Bonding, ed. L.J.Lee, Plenum Press, New York, 1991, pp. 1-26. Micro-Measurements Division of Measurements Group, Inc. "Strain Gage Technical Data, Part B", 1988. Melo, J.D. and Radford, D.W., "Modeling Manufacturing Distortions in Flat Symmetric, Composite Laminates", 31st International SAMPE Technical Conference, 1999, pp. 592-603. Nelson, R.H. and Cairns, D.S., "Prediction of Dimensional Changes in Composite Laminates During Cure", In: International SAMPE Symposium and Exhibition Book 2 (of 2). Publ by  -148-  References  SAMPE, Covina, C A , USA, p 2397-2410, Anonymous, SAMPE, Covina, CA, U S A , 1989, pp. 2397-2410. Osswald, T.A. and Menges, G., "Solidification of Thermosets", In: Materials Science of Polymers for Engineers, Anonymous, Hanser / Gardner, Cincinnati, 1995, pp. 222-233. Pagliuso, S., "Warpage, A Nightmare for Composite Parts Producers", Progress in Science and Engineering of Composites, 1982, pp. 1617-1623. Paris, I., "Measure6", University of British Columbia Composites Group, 1996. Radford, D.W., "Cure Shrinkage Induced Warpage in Flat Uni-Axial Composites", Journal of Composites Technology & Research, Vol. 15, No. 4, 1993, pp. 290-296. Radford, D.W., Fu, S., Derringer, D., et al, "Measurement of Manufacturing Distortion in Flat Composite Laminates", 12th International Conference on Composite Materials, July-1999, Paper 574. Radford, D.W. and Rennick, T., "Separating Sources of Manufacturing Distortion in Laminated Composites", Journal of Reinforced Plastics and Composites, Vol. 19, No. 8, 2000, pp. 621-641. Reddy, J.N. and Roy, S., "Finite Element Analysis of Adhesive Joints", In: Adhesive Bonding, ed. L.H.Lee, Plenum Press, New York, 1991, pp. 359-392. Ridgard, C , "Accuracy and Distortion of Composite Parts and Tools: Causes and Solutions", Tooling for Composite '93, 1993. Tsai, S.W., "Theory of Composites Design", Think Composites, Dayton, O H , 1988. White, S.R. and Hahn, H.T., "Process Modeling of Composite Materials: Residual Stress Development During Cure. Part II. Experimental Validation", Journal of Composite Materials, Vol. 26, No. 16,1992, pp. 2423-2453. Wiersma, H.W., Peeters, J.B., and Akkerman, R., "Prediction of Springforward in ContinuousFibre/Polymer L Shaped Parts", Composites Part A , Vol. 29A, No. 11, 1998, pp. 1333-1342. Window, A . L . and Holister, G.S., "Strain Gage Technology", Elsevier Applied Science, New York, 1982.  -149-  APPENDIX A : W A R P A G E SPECIMEN M E A S U R E M E N T ERROR  The error associated with warpage specimen profiles was estimated from replicate measurements on the same part. Measurement error values were determined for both the scanner technique used for 300 mm and 600 mm parts, and the manual technique used for 1200 mm parts.  A. 1  S C A N N E R  «  M E T H O D  -  300  M  M A N D 600  M  M S P E C I M E N S  For the scanner method, 4 repeated measurement trials were performed on a single 300 mm specimen. The profiles from the replicate measurements are shown in Figure A . l . The warpage at three exact locations along the length of the part was used as a basis for the estimate of error. The locations were: x = 75 mm, x = 150 mm and x = 225 mm. The z coordinate at this point was estimated by linearly interpolating between the two nearest data points. The coordinate values are presented in Table A . l . For each location a sample standard deviation, therefore gave a value of  SMeasure,  SMeasure  of the warpage was calculated.  with 3 degrees of freedom. The  Each location  SMeasure  values from  each location then were pooled, to yield an estimate with 9 degrees of freedom. The measurement standard deviation was calculated to be 0.03 mm for the scanner technique.  A.2  M A N U A L  M E T H O D  -1200  M  M S P E C I M E N S  The method for calculation of measurement error was similar for the 1200 mm parts, except that in this case profile data points were always located at the same JC coordinate  -150-  Appendix A: Warpage Specimen Measurement Error  interval.  This afforded 11 locations along the part length for comparison of z  coordinates, without the need for interpolation.  Three measurement trials were  performed on the part to yield an SMeasure value with 30 degrees of freedom.  The  coordinate data is presented in Table A.2. The measurement standard deviation was estimated to be 0.5 mm for the manual measurement technique.  -151-  Appendix A:  A.3  Warpage Specimen Measurement Error  T A B L E S  Table A . l :  Coordinate data for calculation of SMeasure for 300 and 600 m m specimens.  X Location  Trial 1 Trial 2 Trial 3 Trial 3  i Point 2 Interpolated Point  X C o o r d i n a t e (mm)  Point 1 70.0  Z C o o r d i n a t e (mm)  0.146  0.134  X C o o r d i n a t e (mm)  70.1  76.5  Z C o o r d i n a t e (mm)  0.192  0.168  X C o o r d i n a t e (mm)  69.8  76.2  Z C o o r d i n a t e (mm)  0.133  0.129  X C o o r d i n a t e (mm)  63.7  76.5  Z C o o r d i n a t e (mm)  0.097  0.206  76.3  S t a n d a r d Deviation of Z C o o r d i n a t e s  76.0  Point 1 146.2  2 Point 2 Interpolated Point 150.0  229.1  225.0  0.209  0.172  0.157  0.161  150.0  222.4  228.8  225.0  0.169  0.186  152.6  0.231 iSo.O  222.3  228.8  0.176  0.185  0.179  0.141  0.141  140.8  152.4  0.181 150.0  217.2  229.9  225.0  0.231  0.251  0.247  0.209  0.178  0.190  152.6  0.191  0.221  75.0  146.2  152.5  0.173  0.221  0.237  146.3  0.136  75.0 0.130 7S.0 0.193  i Point 2 Interpolated Point  Point 1 216.3  0.030  0.028  225.0 0.141  0.021  (mm) Pooled Standard Deviation (mm)  Table A . 2 :  0.03  Coordinate data for calculation of SMeasure  x Location  —  1  —T~  for 1200  3  4  5  6  7  mm specimens  8  9  10  II  -  Trial 1  i. Coordinate (mm)  9.9  18.8  26.5  32.2  36.6  37.6  35.7  31.6  25.5  17.9  8.6  Trial 2  Z Coordinate (mm)  10.2  18.7  26.7  32.8  36.9  38.5  36.6  32.2  25.6  18.1  9.3  Trial 3  Z Coordinate (mm)  10.0  18.2  25.5  31.0  35.5  37.4  35.6  31.5  25.4  17.5  8.6  0.15  0.34  0.67  0.91  0.73  0.58  0.54  0.37  0.10  0.33  0.37  Standard Deviation of Z Coordinates (mm) Pooled Standard  0.5  Deviation (mm)  -152-  Appendix A: Warpage Specimen Measurement Error  A.4  F I G U R E S  100  150  200  250  300  350  X Coordinate (mm)  Figure A . l : Replicate measurement trials on a single 300 mm specimen.  600  800  X Coordinate (mm)  Figure A.2: Replicate measurement trials on a single 1200 mm specimen.  -153-  APPENDIX B: STRAIN G A G E T H E R M A L COMPENSATION  Thermally induced error represents the largest source of error associated with strain gage measurement in an autoclave environment.  There are many strategies available to  counter thermally induced error and the techniques utilized in the present work warrant some explanation.  The difference between the C T E of the strain gage and the C T E of the substrate material will cause an apparent strain reading when a specimen is subjected to a temperature change (e.g. Micro Measurements, (1988); Window and Holister, (1982)). Modern strain gages typically offer some degree of Self Temperature Compensation (STC) in order to offset this error, however the STC of the gage and the exact thermal strain of the sample may still differ slightly.  Furthermore, the leadwires connecting the gage to the data  acquisition system may also have a thermal output associated with them.  These errors are often compensated by the use of a dummy gage connected to an adjacent arm of the strain gage bridge circuitry. The dummy gage should be placed on the same sample material and subjected to the same environment as the test specimen, but not subjected to stress. Standard practice for dummy gages involves using gages from the same manufacturing batch, with identical lengths of leadwire.  Furthermore, to the  greatest extent possible dummy gages and specimen gages must be subjected to exactly the same temperature, along the entire length of their respective circuits.  -154-  Appendix B Strain Gage Thermal Compensation  The suitability of dummy gage compensation for the present work was tested, however, upon performing an initial calibration run it was noted that even after dummy compensation there was still a significant thermal output for each gage. Furthermore, the thermal output was observed to be different for each of the gages mounted on the instrumented tool, despite efforts to use identical gages, leadwires and leadwires paths. It was noted however, that for a given gage the thermal error was consistent from run to run.  The requirement that dummy gage and specimen gage be subjected to exactly the same temperatures also proved problematic for the experimental arrangement in question. This was due to the thermal mass of the pre-preg stack being sufficiently large to cause a temperature lag between the instrumented tool and dummy gage.  In order to address, and/or avoid the above problems a thermal compensation technique described in Micro Measurements (1988) was used. The instrumented tool was subjected to a complete cure cycle, without a part present.  Both the autoclave air temperature  (which affects leadwire thermal outputs directly) and strain gage temperatures were recorded during the run. Using this data, an equation was determined, describing the thermal output of each individual gage as a function of air and strain gage temperatures. In subsequent intstrumented runs it was then possible to correct for gage thermal output using the pre-calibrated correction factors along with temperature data.  B.l  S T R A I N G A G E  C A L I B R A T I O N  In Figure B . l through Figure B.7 the raw thermal output the strain gages during a calibration run is shown. The manufacturer of the gage, Micro Measurements, supplies  -155-  Appendix B Strain Gage Thermal Compensation  an initial correction factor to account for non-linearity in the strain gage thermal output. For the gages used the equation is as follows:  = 1.06 x 10 + 5.33 x 10" T 1  1  where £MM  - 5.02 x 10" T 2  Gage  2  + 3.78x 10" T 4  Gage  3  - 5.88x 10" T\ 7  Gage  age  (B. 1)  is the Micro Measurements supplied correction and Toage is the strain gage  temperature.  After this initial correction the gage thermal output could be expressed as a linear function of strain gage and air temperature. The equation was fit using a least squares curve fit strategy. The total thermal output of a given gage is given by the following:  £  Thermal Output  MM  =  £  Q ' ^Qage ~*~ ^ 2 " ^Air  (B.2)  where C / and C2 are unique constants for each gage. Figure B . l through Figure B.7 compares the raw thermal output against the estimate based on gage and air temperature measurements.  The residual difference between the calibrated estimate and the raw  thermal output is also shown for each graph.  This unique thermal output curve for each strain gage was used for the post processing of strain data from the instrumented runs. The mechanical strain which a gage measured could simply be calculated as the total strain minus the apparent strain due to the thermal output.  Mechanical ~  £  £  Total ~ Thermal Output £  -156-  (B-3)  Appendix B Strain Gage Thermal Compensation  B.2  S T A B I L I T Y O F C A L I B R A T I O N  F A C T O R S  The stability of the thermal output is an extremely important factor for accurate strain measurement.  The calibration of the strain gages was checked periodically. In Figure  B.2 through B.8 the thermal output of each of the 8 strain gages mounted on the instrumented tool is shown, as measured on a date subsequent to performing the instrumented tool experiments. Also shown is the thermal output estimate based on the previously calibrated constants.  The deviation between the raw thermal output and the  calibrated thermal output represents the error associated with this technique. The pooled average residual from all the gages was 9.8 pe.  -157-  Appendix B Strain Gage Thermal Compensation  B.3  F I G U R E S  Figure B . l : Strain gage calibration run showing raw thermal output, empirical thermal output equation and the residual. Gage A .  Figure B.2: Strain gage calibration run. Gage B.  -158-  Appendix B Strain Gage Thermal Compensation  1200 —Strain Gage Raw Thermal Output 1000  . Strain Gage Fitted Equation — Residual  800  ._  600  w 400  E  200  Tnermal Output ~~ M M E  100  +  3.95  X  150  T  G a g e  + 3.52  200  X  T  Air  250  300  350  -200  Time (min)  Figure B.3: Strain gage calibration run. Gage T .  1200 —Strain Gage Raw Thermal Output 1000  . Strain Gage Fitted Equation — Residual  100  150  200  -200  Time (min)  Figure B.4: Strain gage calibration run. Gage C .  -159-  250  300  350  Appendix B Strain Gage Thermal Compensation  1200 -Strain Gage Raw Thermal Output Strain Gage Fitted Equation - Residual  1000  800  _ 600 c  J5 co 400  200  250  300  350  -200 Time (min)  Figure B.5: Strain gage calibration run. Gage C \  1400 ^ S t r a i n Gage Raw Thermal Output . Strain Gage Fitted Equation — Residual  1200 1000 800 £ 600 n  (0  400 200 v *  r—'  150  200  -200 Time (min)  Figure B.6:  Strain gage calibration run. Gage T \  •160-  250  300  350  Appendix B Strain Gage Thermal Compensation  1200  ^—Strain Gage Raw Thermal Output . Strain Gage Fitted Equation Residual  1000  800  600  c  '55 w  400  200  350  -200  Time (min)  Figure B.7: Strain gage calibration run. Gage B \  1400  1200  -Strain Gage A - Raw Thermal Output Strain Gage A - Predicted Thermal Output -Residual  100  150  200  250  300  350  - 2 0 0 -1  Time (min)  Figure B.8: Strain gage thermal output during a calibration check. The residual represents the error associated with this technique. Gage A .  -161-  Appendix B Strain Gage Thermal Compensation  1400  1200  •Strain Gage B - Raw Thermal Output Strain Gage B - Predicted Thermal Output - Residual  100  Y  150  200  250  300  350  -200  Time (min)  Figure B . 9 : Strain gage thermal output during a calibration check. Gage B .  1400  -r  1200  300  350  -200  Time (min)  Figure B . 1 0 : Strain gage thermal output during a calibration check. Gage T .  -162-  Appendix B Strain Gage Thermal Compensation  1400  T  1200  -200 J  Time (min)  Figure B . l l : Strain gage thermal output during a calibration check. Gage C .  1200 ,  -200 J  Time (min)  Figure B.12: Strain gage thermal output during a calibration check. Gage C ' .  -163-  Appendix B Strain Gage Thermal Compensation  1400  1200  1000  800  600  400  -Strain Gage T' - Raw Thermal Output Strain Gage T - Predicted Thermal Output  200  -Residual  100  150  200  250  300  350  -200  Time (min)  Figure B.13: Strain gage thermal output during a calibration check. Gage T \  1200  —  Strain Gage B' - Raw Thermal Output  . Strain Gage B' - Predicted Thermal Output — Residual  50  100  150  200  250  300  350  -200  Time (min)  Figure B.14: Strain gage thermal output during a calibration check. Gage B \  -164-  APPENDIX C: CALCULATIONS  The appendix describes the calculations referred to in Chapter 4, which confirm that global bending effects for the instrumented tool were negligible.  Also shown are  calculations in support of Section 5.1.2.  C. 1  W A R P A G E  D U E T O B I - M A T E R I A L  STRIP  E F F E C T  As stated in Section 4.2, a bi-material strip subjected to a change in temperature will tend to bend if it is not constrained in the out-of-plane direction.  To confirm that the  autoclave pressure during processing was sufficient to force the laminate to remain flat, the curvatures arising due to the bi-material strip effect were examined using Promal C L T software and compared with the deformations due to the pressure loading.  To provide the most conservative estimate possible, the aluminum-CFRP assembly was assumed to be perfectly bonded for the entire temperature ramp. The material properties used for all calculations in this section are shown in Table 4.1. For the purposes of the Promal analysis, properties at a temperature of 100 °C were assumed to be representative for the entire temperature range in consideration. The C L T analysis yielded a curvature which can be related to the part deformation as follows. Recalling Equation 3.5, if the curvature is small one can assume:  , \  d  2  z  dx  Integrating twice, and incorporating boundary conditions:  -165-  Appendix C Calculations  dz  n  — =0  at  z=0  a/  dx  L  x=—  (Cl)  2  (C.2)  x=0  gives the profile for a part with a constant curvature:  Z(X) = ^Y"(X-L)  (C.3)  The deformations which arise due to the out-of-plane loading of the autoclave pressure can also be calculated (Bickford, 1993):  P-x z(x) =  (L -2-L-x 3  24-E-I  +x )  2  (CA)  3  V  ;  The deformations due to the pressure loading are compared with those from the bimaterial strip effect in Figure C l . To provide a conservative calculation, the section properties for Equation (C.4) were estimated assuming that the entire tool-part assembly was made of fully cured CFRP and subjected to 103 kPa of autoclave pressure. As is apparent from Figure C l the pressure loading was more than adequate to overcome the deformation due to the bi-material strip effect.  C.2  L>L  W A R P A G E O F PARTS W I T H  C  In Section 5.1 it was shown the curvature for a part with length L<Lc  = ^' ^> .(L-x) 2-E -l T  dx  t  was:  (5.8)  Part  Integrating this twice and incorporating boundary conditions yielded an expression for part warpage as a function of x:  -166-  Appendix C Calculations  ^ Net '^Lam  L-x  (  2  x^ 3  (5.9)  2 " Epart ' IV 2  The maximum part warpage which occurs at x = L can be expressed as:  1 max =  W  •»  3 • r C  V  L  a  l  i  d  f  0  r  L  <  L  C  (C5)  where C/ is given as:  C, =  m  (C.6)  L a m  From developments in presented Section 5.1.2 it was apparent that for parts of length L > Lc the stress in the first ply reached a maximum value at x = L - Lc- Following the same procedure as in Section 5.1 one can relate the stress in the first ply to the local curvature. This distribution in curvature which this results in is no longer smooth function, but rather has a change in slope at x = L - Lc. The curvature for a part with length L > Lc is:  '- Q •L dx  d  Z  2  d z.'2  c c  1  0<x<L-L  (C.7)  L-L <x<L  (C.8)  c  2  dx  = C (L-x) r  c  where zj and z/ denote the transverse displacements on the respective intervals. Integrating both Equation (C.7) and Equation (C.8) twice with respect to x and incorporating the following boundary and continuity conditions:  dz L  — = 0andz =0 dx  atx = 0  1  -167-  Appendix C Calculations  dz,  dz-,  dx  dx  ,  — - = — - and z, - z  at x = L - Lc  2  gives two equations for the warpage of parts with length L > Lc'-  'Zi\ i  —  *  2  i  * fJf *  c  x  (C.9)  which is valid on the interval, 0 < x < L- Lc, and:  z = C, 2  -1  , 1  x + — -L-X + \—-L +L-L ---L 3  2  2  C  2 C  1  1  \-x + --L ---L -L 6  3  2  2  r  +--L  2 r  -L---L.  (CIO)  which is valid on the interval, L - L < x < L. From Equation (C.10) one can calculate c  the maximum warpage at x = L as:  w ax m  ,1 1 = C,-(--I -Z - - - V ) c  valid for L > L  C  (C.ll)  Equation (C.5) and Equation ( C . l l ) therefore give the maximum warpage for parts with lengths less than, and greater than Lc respectively.  -168-  Appendix C Calculations  C.3  F I G U R E S  0.05  -0.3 J X Coordinate (m)  Figure C . l : Deformation of the instrumented-tool / part assembly due to autoclave pressure compared with the deformation due to the bi-material strip effect. Even 103 kPa of autoclave pressure is sufficient to force the tool-part assembly to remain flat.  -169-  APPENDIX D : INSTRUMENTED T O O L R E S U L T S  For the sake of clarity, most of the instrumented tool results presented in Chapter 4 only showed results from one side of the tool symmetry line. This appendix presents the complete strain versus time results for the instrumented tool tests in Figure D . l through Figure D.4. In Table D . l through Table D.4, the elastic constraint data referred to in Section 4.3 is presented. Finally in Table D.5 through Table D.14 the time/temperature/strain data required for the calculations in Section 4.3 is given in table form. In cases where data presented in this appendix corresponds directly to figures presented elsewhere, the particular figure is indicated in parentheses.  -170-  Appendix D Instrumented Tool Results  D.l  T A B L E S  Table D . l : Elastic constraint evolution for 586 kPa / release agent experimental conditions (Figure 4.21 and Figure 4.22).  lime (min)  Degree of C u r e  Gage A (u/°C)  GageB (u/°C)  Uage T (n/°c)  Gage C (n/°c)  Gage C (u/°C)  Gage I" (u/°C)  Gage B ' (n/°c)  Gage A ' (n/°c)  61.8 84.3 103.8 146.3 176.3 206.3  0.07 0.15 0.39 0.84 0.87 0.89  -9.0 -9.3 -6.5 -19.2 -19.7 -19.6  -11.9 -8.0 -13.0 -21.0 -18.6 -19.0  0.0 4.0  -11.3 -10.2  -2.0 2.4  8.1 10.3 7.3 7.7  -13.7 -10.0 -13.3  236.3  0.89  -19.4  -19.9  8.2  -13.8 -17.0 -14.0 -16.7 -16.0  5.1 9.4 7.0 5.9 4.9  -9.5 -8.8 -12.2 -16.0 -14.3 -14.7 -14.1  -8.9 -10.1 -7.4 -15.2 -16.5 -18.1 -17.9  -19.8 -19.2 -18.8 -18.8  Table D.2: Elastic constraint evolution for 103 kPa / release agent experimental conditions (Figure 4.33).  Time (min)  Degree of Cure  Gage A (u/°C)  Gage B (u/°C)  Gage T (u/°C)  Gage C (u/°C)  Gage t " (u/°C)  Gage 1" (u/°C)  Gage B ' (u/°C)  Gage A ' (u/°C)  71.0 95.0 116.0 166.0 198.0 226.0 256.0  0.08 0.18 0.41 0.84 0.87 0.88 0.89  -8.2 -4.6 -1.8 -19.4 -21.0 -22.0 -22.6  -1.6 -2.8 -11.3 -21.1 -21.2 -22.1 -22.7  0.0 0.6 8.9 14.8 14.7 15.5 12.7  -7.8 -8.3 -9.7 -20.2 -19.8 -19.9 -20.8  -4.2 -4.0 -9.5 -19.8 -19.2 -19.0 -20.0  0.7 1.5 7.8 12.2 12.7 11.8 9.7  -2.2 -2.0 -6.5 -15.5 -17.2 -18.1 -19.8  -7.9 -6.8 -1.9 -16.3 -15.9 -15.6 -16.6  Table D.3: Elastic constraint evolution for 586 kPa / F E P experimental conditions (Figure 4.34).  lime (min)  Degree of Cure  Gage A (u / °C)  GageB (n/°c)  Gage T (u/°C)  GageC (n/°c)  59.0  O.07  -4.6  -6.0  0.15  -5.6  -5.4  -5.7 3.7  -8.5  80.0 98.0 140.0  0.39 0.83  0.4 -14.2  -5.3 -15.7  170.0 200.0 230.0  0.86 0.88 0.89  -16.0 -18.4 -16.7  -15.2 -18.1 -17.0  8.6 8.9 8.3 6.0 5.0  -171-  -6.1 -6.7 -15.3  Gage C (u/°C) -7.8 -6.1 -7.3 -12.0  -14.7 -17.0 -16.1  -13.1 -15.9 -14.9  Gage ! ' (n/°c)  Gage B ' (u/°C)  Gage A ' (u/°C)  -6.5 2.1  -9.4  -2.1  -5.9 -5.9 -14.5  -1.0 -3.3 -9.8  -14.8 -17.0 -16.0  -11.9 -15.7 -15.3  7.0 7.9 6.4 4.7 3.1  Appendix D Instrumented Tool Results  Table D.4: Elastic constraint evolution for 586 kPa / F E P experimental conditions (Figure 4.35).  Time (min)  Degree of Cure  66.4 94.9 113.9 163.9 195.4 225.4 252.9  0.08 0.25 0.50 0.85 0.87 0.88 0.88  Gage A  Gage B  Cage T  Gage C  Gage C  Gage ! '  Gage B '  Gage A '  (n/°c)  (u/"C)  0i/*c) -2.7 -1.9 -7.6 -20.6 -16.1 -19.8 -18.3  (n / °c)  -1.3 -2.9 -6.5 -14.5 -13.2 -15.9 -15.5  (n/°c) -4.5 -6.0 -12.6 -21.0 -16.6 -21.2 -20.5  (n/°c)  -2.3 3.1 -2.3 -1.9 -0.5 -3.5 -2.3  (n/°c) 0.4 5.0 7.4 12.1 9.5 12.5 12.6  -0.4 3.6 5.1 7.1 6.4 9.4 10.3  -1.3  (n/*c) -5.9 -3.0 -2.5 -0.2 2.6 -1.9 -2.0  -0.6 -6.4 -15.2 -14.6 -15.9 -11.3  Table D.5: Temperature and strain data corresponding to instrumented tool - part debonding during cooldown. 586 kPa / release agent experimental conditions (Figure 4.18).  Gage  ll  1  152.4 129.8 127.5  101.6 121.5  D e b o n d F i n i s h T e p e r a t u r e (°C)  A 254.0 142.9 139.4  A T ("<_)  3.5  2.3  808  948  N/A  1243  341  465  709  467  482  N/A N/A  X C o o r d i n a t e (mm) D e b o n d Start T e p e r a t u r e (°C)  E'  (Ji)  As (n)  N/A  C 50.8 114.6 111.9  Average  2.8  2.8  534  495  Table D.6: Temperature and strain data corresponding to instrumented tool - part debonding during cooldown. 103 kPa / release agent experimental conditions (Figure 4.36).  Gage  A  1!  1  C  X C o o r d i n a t e (mm) D e b o n d Start Teperature ( C )  254.0 142.6  152.4 142.6  101.6 140.4  50.8 138.8  D e b o n d F i n i s h T e p e r a t u r e (°C)  N/A  141.8  N/A  0.8  N/A N/A  137.8  A ! ( C)  772  607  N/A  630  180  199  592  407  N/A N/A  373  U  U  AS (H)  -172-  1.0  Average  0.9  257 457  Appendix D Instrumented Tool Results  Table D.7: Strain reading versus location for various times during the cure cycle. 586 kPa / release agent interface (Figure 4.19 and Figure 4.24).  A 254  Ii 152.4  C 50.8  -5.2 36.0 17.5 392.0  -n.i  -17.4 -72.9 -149.0 730.1  Gage Designation Location (mm) 78 Minutes (LL) 1UU Minutes (U) 118 Minutes (p.) Cooldown  -69.7 -126.0 504.9  Table D.8: Strain reading versus location for various times during the cure cycle. 103 kPa / release agent interface (Figure 4.29).  Location (mm)  A 254.0  H 152.4  50.8  89 Minutes (u)  13.5  -59.0 -83.2  Gage Designation  C  110 Minutes (u)  34.2  -37.7 -54.1  140 Minutes (u) Cooldown (LI)  -37.5  -178.2  -204.8  116.7  107.9  176.5  Table D.9: Strain reading versus location for various times during the cure cycle. 586 kPa / F E P interface (Figure 4.30).  Gage Designation Location (mm) 96 Minutes (u.) 113 Minutes (u.) Initial Cooldown (u) Initial Cooldown (\x)  A 304.8  254.0  c 152.4  14.3 -20.0 52.8 110.7  -17.8 -95.0 301.2 428.8  -34.7 -120.0 502.6 704.0  -173-  Appendix D Instrumented Tool Results  Table D.10: Strain reading versus location for various times during the cure cycle. 103 kPa / F E P interface (Figure 4.31).  Gage Designation  A  B  Location (mm)  254.0  152.4  C 50.8  86 Minutes (u)  -11.6 8.4 30.0 75.0  -39.4 -63.5 -62.5 48.6  -62.1 -94.6 -94.0 73.0  108 Minutes (u) 132 Minutes (p.) Cooldown (u)  Table D . l l : Change in Tsuding with respect to part degree of cure for 586 kPa / release agent interface conditions (Figure 4.25)  Time (min) Degree of Cure  T  s.idin (kPa) g  64.0  0.07  0.0  78.0  0.11  5.3  100.3  0.32  118.0  0.63 0.90  16.1 33.2  N/A  166.7  Table D.12: Change in Tsuding with respect to part degree of cure for 103 kPa / release agent interface conditions (Figure 4.32).  lime (min) Degree of Cure 60.0  0.06  S.iding 0.0  88.5  0.13  12.2  110.0  0.31  16.3  140.0  0.71  47.9  N/A  0.90  39.7  -174-  T  W  Appendix D Instrumented Tool Results  Table D.13: Change in tsnding with respect to part degree of cure for 586 kPa / F E P interface conditions (Figure 4.32).  Time (min) Degree of Cure 72.0  0.10  Sliding (^a) 0.0  96.0  0.34  6.4  113.0  0.62  27.2  N / A  0.89  104.1  N/ A  0.90  147.5  Table D.14: Change in r mng with respect to part degree of cure for 103 kPa / F E P interface conditions (Figure 4.32). S  Time (min) Degree of Cure  x  s.idi„ 0.0 g  60.0  0.05  85.9  0.15  12.2  108.4  0.41  18.6  132.0  0.71  17.8  N / A  0.90  18.6  -175-  Appendix D Instrumented Tool Results  D.2  FIGURES  Figure D . l : Instrumented tool mechanical strain development for the entire cure cycle. 586 kPa / release agent interface condition.  Figure D.2: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / release agent interface condition.  -176-  Appendix D Instrumented Tool Results  Figure D.3: Instrumented tool mechanical strain development for the entire cure cycle. 586 kPa / F E P interface condition.  Figure D.4: Instrumented tool mechanical strain development for the entire cure cycle. 103 kPa / F E P interface condition.  -177-  

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