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Stress and deformation build-up in bonded composite patch repair Curiel, Tomer Maurice 2006

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Stress and deformation build-up in bonded composite patch repair by Tomer Maurice Curiel B . E n g . (Mechanical Engineering), Concordia University, 2002  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF A P P L I E D SCIENCE in F A C U L T Y OF G R A D U A T E STUDIES (Metals and Materials Engineering)  T H E U N I V E R S I T Y OF BRITISH C O L U M B I A February 2006  © Tomer Maurice Curiel, 2006  Abstract  Abstract Bonded composite patch repairs have many advantages over traditional riveted doubler repairs and have been used successfully in a number o f repair programs. A mismatch in the coefficients o f thermal expansions o f the patch and substrate causes thermally induced residual stresses, which are detrimental to the long-term service life o f the repair. A dynamic mechanical thermal analyzer bimaterial beam technique is developed that can be used in a variety o f different configurations and loading conditions for innovative and versatile characterization o f time, temperature, and cure dependant material properties.  The technique is first used to determine the stress relaxation modulus o f a viscoelastic material bonded to an elastic substrate. The relaxation modulus o f Lexan specimens are characterized, first as monolithic beams and then bonded to an elastic substrate. Results show that the relaxation modulus o f Lexan can be determined from bimaterial beam relaxation tests. The temperature and cure dependant modulus o f F M 3 0 0 adhesive is then characterized by subjecting a bimaterial beam to a dynamic displacement while curing isothermally at a variety o f temperatures. The results are fit to a model that defines the instantaneous modulus as a function o f two variables - the instantaneous temperature and the instantaneous glass transition temperature.  The technique is then extended to quantify the development o f  process induced residual stresses in beam specimens designed to simulate a bonded composite patch repair. In these beam specimens, residual stresses correspond to an out o f plane deflection that can be monitored in-situ throughout a complete cure cycle. Specimens, consisting o f a steel shim, an F M 3 0 0 adhesive layer, and an AS4/3501-6 [0°]2 composite patch, are subjected to a variety o f cure cycles to determine the effects o f cure time and temperature on the out o f plane deflection in single- and multi-hold cycles. The experimental results are then compared to those obtained from a cure hardening instantaneously linear elastic ( C H I L E ) model modified to include thermal softening. Results show that a reduction in thermally induced residual stresses is possible by modifying the cure cycle. Model sensitivities, cycle times, real versus idealized cycles, and the effects o f thermal softening are also investigated.  n  Abstract The D M A beam technique is shown to be an effective means o f material characterization, as well as monitoring the out o f plane deflection o f bonded composite patch repair specimens throughout a cure cycle. Insight gained from these measurements can be used to optimize cure cycles so as to reduce the thermally induced residual stresses in real applications o f bonded composite patch repairs.  111  Table of Contents  Table of Contents Abstract  ii  Table o f Contents  iv  List o f Tables  vii  List o f Figures  viii  Nomenclature..  x  n  Acknowledgments  x  v  1.  2.  Introduction 1.1  Background  1  1.2  Objective  4  Literature Review  5  2.1  Historical Overview  5  2.2  Material M o d e l i n g  5  2.2.1  Cure Kinetics  6  2.2.2  Glass Transition Temperature  7  2.2.3  Viscoelasticity  8  2.2.4  Pseudo-Viscoelastic ( P V E ) Models  2.3  13  Bonded Composite Repair Modeling  2.3.1  Finite Element Modeling  2.3.2  Analytic M o d e l i n g  2.3.3  Closed F o r m Beam Theory  2.4  3.  1  14 :  15 16  ;  Optimization  17 19  2.4.1  Stress Measurement Techniques  20  2.4.2  Process Induced Residual Stresses  21  2.4.3  Patch Repair Optimization  24  Models and Analysis  29  3.1  Introduction  29  3.2  Bimaterial beam stress relaxation  29  3.3  F M 3 00 Cure Kinetics M o d e l  31  3.4  F M 3 0 0 Glass Transition Temperature Development M o d e l  32  iv  Table of Contents  4.  3.5  F M 3 0 0 Modulus Development Analysis  33  3.6  Bonded Composite Patch Repair Specimen  35  3.6.1  Thermo-elastic Deflection  35  3.6.2  Constitutive M o d e l  38  3.6.3  Thermal Residual Stresses  40  Methods 4.1  Introduction  45  4.2  Rheometric Scientific Inc. D M T A V  45  4.3  Temperature Control  48  4.4  Bimaterial beam stress relaxation  49  4.4.1  Objective  49  4.4.2  Specimen Preparation  49  4.4.3  Experimental Details  50  F M 3 0 0 Modulus Development  51  4.5 4.5.1  Objective  51  4.5.2  Specimen Preparation  51  4.5.3  Experimental Details  51  4.6  5.  45  Bonded Composite Patch Repair  53  4.6.1  Objective  53  4.6.2  Specimen Preparation  53  4.6.3  Experimental Details  53  Results and Discussion 5.1  56  Bimaterial beam stress relaxation  56  5.1.1  Effect o f the Adhesive layer  56  5.1.2  Bimaterial beam stress relaxation results  59  5.1.3  Sources o f error  61  5.2  Modulus Development  :  62  5.2.1  F M 3 0 0 Modulus Development  62  5.2.2  Sources o f Error  66  5.3 5.3.1  Bonded Composite Patch Repair  67  Presentation o f Results  67  Table of Contents 5.3.2  M o d e l Implementation  5.3.3.-  One-step cycle  72  5.3.4  Post-cure cycles  78  5.3.5  Two-step cycles  82  5.3.6  Summary  88  5.3.7  Sources o f Error  89  Idealized cycles - Warpage  91  5.4.1  One-Step Cycles  92  5.4.2  Post Cure Cycles  92  5.4.3  Two-Step Cycles  93  5.4.4  Summary o f idealized results  94  5.4.5  Comparison to experimental results  96  5.5  Idealized cycles - Thermal Residual Stresses  98  5.6  Effects o f thermal softening on the C H I L E model  100  5.7  Cycle Times  104  5.8  M o d e l Sensitivities  106  5.4  •••••  70  5.8.1  Sensitivity o f idealized cycles to the adhesive layer thickness  106  5.8.2  Sensitivity o f idealized cycles to the maximum temperature  109  5.8.3  Sensitivity o f idealized cycles to the ramp rate  113  6.  Conclusions  116  7.  Future W o r k  119  8.  References  121  Appendix A - Additional Bonded Composite Patch Repair Experimental Results  vi  128  List of Tables  List of Tables Table 2.1 - Summary o f Cho & Sun patch repair tests  :  25  Table 2.2 - Summary o f Djokic et al. F M 7 3 patch repair tests  26  Table 2.3 - Summary o f Djokic et al. F M 3 0 0 patch repair tests  28  Table 3.1 - Cure kinetics model constants  31  Table 3.2 - F M 3 0 0 Glass transition temperature model constants  32  Table 4.1 - Summary o f D M A beam techniques  48  Table 4.2 - Test Temperatures, Durations, and M a x i m u m Degree o f Cure  52  Table 4.3 - Cycles specifications  55  '.  Table 5.1 -Stress relaxation o f Lexan - monolithic versus system response  61  Table 5.2 - Modulus model constants  65  Table 5.3 - One-step cure cycles  72  Table 5.4 - Experimental Results - One-step cure cycles  76  Table 5.5 - Specimen geometries - One-step 177 ° C cycles  77  Table 5.6 - Post-cure cycles  79  Table 5.7 - Experimental Results - Post-cure cycles  81  Table 5.8 - Two-step cure cycles  83  Table 5.9 - Experimental Results - Two-step cycles  87  Table 5.10 - Experimental deflections  88  Table 5.11 - Virtual specimen geometry and properties  91  Table 5.12 - Idealized cycle deflections  95  Table 5.13 - Comparing averaged experimental, scaled experimental, and idealized deflections  97  Table 5.14 - M a x i m u m Stresses  98  Table 5 . 1 5 - Percent reductions o f maximum stresses  100  Table 5.16 - Comparing C H I L E with thermal hardening  101  Table 5 . 1 7 - C y c l e Times  105  Table 5.18 - Sensitivity to adhesive layer thickness  108  Table 5.19 - Sensitivity to maximum temperature  112  Table 5.20 - Sensititvity to ramp rate  •  vii  114  List of Figures List of Figures Figure 1 . 1 - Schematic o f (a) a riveted doubler repair and (b) a bonded composite patch repair  2  Figure 1.2 - Schematic o f thermal residual stress problem  3  Figure 2.1 - Schematic o f material models: elastic (a), viscous (b), K e l v i n (c), M a x w e l l (e), and Zener (e and f)  9  Figure 2.2 - Dynamic response o f a viscoelastic material  11  Figure 2.3 - Geometry o f double sided bonded composite patch repair  17  Figure 2.4 - Geometry o f single sided bonded composite patch repair  18  Figure 3.1 - Schematic o f bimaterial beam specimen  30  Figure 3.2 - Development o f the glass transition temperature o f F M 3 0 0 with cure  32  Figure 3.3 - Modulus development specimen geometry and loading conditions  33  Figure 3.4 - Modulus versus T - T g model  35  Figure 3.5 - Schematic o f bonded composite patch repair specimen  36  Figure 3.6 - Effect of the adhesive's shear modulus, Ga, on the coupling factor, f{Ga), for the geometry shown i n the insert  37  Figure 3.7 - Schematic illustrating the difference between cure hardening (a) and thermal softening (b)  39  Figure 3.8 - Effect o f the adhesive's shear modulus, G , on the coupling factor, g(G ), for a  a  the geometry shown i n the insert  42  Figure 3.9 - Effect o f the adhesive's shear modulus, G , on the coupling factor, h(G ,z), for a  a  the geometry shown in the insert  43  Figure 3.10 - Coupling factor, h(G ,z), as a function o f natural coordinate system o f the a  beam, for the geometry shown in the insert  43  Figure 4.1 - R S I D M T A V  46  Figure 4.2 - D M T A three-point bend set-up  46  Figure 4.3 - Generic Schematic o f D M A beam specimen  47  Figure 4.4 - D M A multi-frequency - strain mode  52  Figure 4.5 - Schematic o f Specimen Geometry and Loading Conditions  54  Figure 5.1 - Steel Specimen - Relaxation Modulus  57  viii  :  List of Figures Figure 5.2 - Dynamic testing for Steel/EA9392/Steel (Frequency = 0.1 H z )  57  Figure 5.3 - Steel/EA9392/Steel Average System Relaxation Modulus  58  Figure 5.4 - Lexan Specimens - Average Relaxation Modulus  59  Figure 5.5 - Steel/EA9392/Lexan Specimens - Average  System Relaxation Modulus  60  Figure 5.6 - Steel/EA9392/Lexan Specimens - Average Lexan Relaxation Modulus  60  Figure 5.7 - Typical Modulus development as a function of time  63  Figure 5.8 - Typical T g development versus time  64  Figure 5.9 - Typical F M 3 0 0 modulus versus T - T g  64  Figure 5.10 - Modulus versus T - T g for F M 3 0 0  65  Figure 5.11 - Modulus development specimens - with and without peel-ply  66  Figure 5.12 - Characteristic time domain 1-step cure cycle response  68  Figure 5.13 - Characteristic temperature domain 1-step cure cycle response  68  Figure 5.14 - Characteristic time domain 2-step cure cycle response  69  Figure 5.15 - Characteristic temperature domain 2-step cure cycle response  70  Figure 5.16 - Representative time domain experimental results for one-step cycles  73  Figure 5.17 - Representative temperature domain experimental results for one-step cycles . 73 Figure 5.18 - Bonded composite patch repair specimen - post-cure, showing adhesive layer squeeze out  74  Figure 5.19 - Representative time domain results for one-step cycles  75  Figure 5.20 - Representative temperature domain results for one-step cycles  75.  Figure 5.21 - Experimental results - One-step cycles  77  Figure 5.22 - Scaled results for 177°C cycle  78  Figure 5.23 - Representative time domain results for post-cure cycles  80  Figure 5.24 - Representative temperature domain results for post-cure cycles  80  Figure 5.25 - Experimental Results - post-cure cycles  82  Figure 5.26 - Representative time domain results for two-step cycles  84  Figure 5.27 - Representative temperature domain results for two-step cycles  84  Figure 5.28 - Representative time domain results for two-step cycles  85  Figure 5.29 - Representative temperature domain results for two-step cycles  85  Figure 5.30 - Experimental Results - two-step cycles  86  Figure 5.31 - Experimental deflections.....  89  :  ix  List of Figures Figure 5.32 - Time domain results for a thickness test  90  Figure 5.33 - Idealized one-step cure cycles: deflection (a) and shear modulus (b) versus temperature  92  Figure 5.34 - Idealized post-cure cycles: deflection (a) and shear modulus (b) versus temperature  92  Figure 5.35 - Idealized two-step 155/177°C cycles: deflection (a) and shear modulus (b) versus temperature  94  Figure 5.36 - Idealized two-step 120/177°C cycles: deflection (a) and shear modulus (b) versus temperature  94  Figure 5.37 - Idealized cycle deflections  96  Figure 5.38 - Averaged experimental (left bars), scaled experimental (centre bars), and idealized (right bars) deflections  97  Figure 5.39 - M a x i m u m normal stresses in the x-direction i n the patch and the substrate  99  Figure 5.40 - M a x i m u m shear stresses in the adhesive layer  99  Figure 5.41 - Comparing the standard C H I L E model with the modified, thermal softening C H I L E model  101  Figure 5.42 - Effect of thermal softening on a post cured 120°C idealized cure cycle  102  Figure 5.43 - Effect o f thermal softening on a 2-step 155°C/177°C idealized cure cycle.... 102 Figure 5.44 - Effect o f thermal softening on a 2-step 120°C/177°C idealized cure cycle.... 103 Figure 5.45 - Effect o f thermal softening on a 2-step 120°C/177°C idealized cure cycle.... 103 Figure 5.46 - Increase i n cycle time and reduction in warpage comparison  106  Figure 5.47 - Time domain results for thickness sensitivity o f an idealized two-step cycle 107 Figure 5.48 - Temperature domain results for thickness sensitivity o f an idealized two-step cycle  ;  Figure 5.49 - Sensitivity o f an idealized two-step cycle to the adhesive layer thickness  107 108  Figure 5.50 - Time domain results for temperature sensitivity o f an idealized two-step cycle 109 Figure 5.51 - Temperature domain results for temperature sensitivity of an idealized two-step cycle  110  Figure 5.52 - Time domain results for temperature sensitivity o f an idealized two-step cycle 110  x  List of Figures Figure 5.53 - Temperature domain results for temperature sensitivity o f an idealized two-step cycle  Ill  Figure 5.54 - Sensitivity o f an idealized two-step cycle to the maximum cycle temperature 112 Figure 5.55 - Time domain results for ramp rate sensitivity o f an idealized two-step cycle 113 Figure 5.56 - Temperature domain results for ramp rate sensitivity o f an idealized two-step cycle  114  Figure 5.57 - Sensitivity o f an idealized two-step cycle to the ramp rate  xi  115  Nomenclature  Nomenclature a  Degree o f cure  a  Cross-over point between kinetic and diffusion controlled curing  c  a i  Degree o f cure at which gelation occurs  cc  Glass transition temperature model constant  ge  Tg  a =  Rate o f cure  dt  8  Phase angle  s  Strain Bonded composite patch repair specimen constant for deflection,  K ,K ,K W  A  T  stress, and shear stress v  Poisson's ratio  cr(Ga)  Thermally induced residual stresses i n the patch and substrate layers  r(Ga, x)  Thermally induced shear in the adhesive layer  X  Natural coordinate system o f a beam  cx>  Angular frequency  A  R  C  Glass transition temperature model constants  4  Arrhenius pre-exponential constant  A*  Modulus model pre-exponential constant  b  Specimen width  r  Diffusion control constant  ^DOC  CTE  Coefficient o f thermal expansion  E  Elastic modulus  E'  Storage modulus  E"  Loss modulus  E'  Complex modulus  E \' Erf' c  -^c3  Elastic moduli fit to modulus development model  xii  Nomenclature  (E -I) ff  Complex bending stiffness o f a beam  (El)  Equivalent beam stiffness  AEj  Arrhenius activation energy  F  A p p l i e d force  E  eq  f(G ),g(G ), a  h(G )  a  a  Adhesive coupling factor for deflection, stress, and shear stress in a bonded composite patch repair  G  Adhesive shear modulus  I  Second moment o f inertia  a  K  Kinetic rate constant  K*  Modulus model constant  L  Specimen length  t  L  Length between the span support and the end o f the prepreg material  c  m  Kinetic exponent controlling n order reaction th  i  Kinetic exponent controlling autocatalytic reaction  R  Universal gas constant  T  Temperature  T*  Difference between a specimen temperature and it's glass transition temperature  T , T, T  Transition temperatures fitted to modulus development model  T  Glass transition temperature  cX  g  c2  c3  Time a  Adhesive thickness  p  Patch thickness  v  Steel shim thickness  7  .  Total specimen thickness  Ar  Time step  w  Central deflection o f a beam specimen  x  Beam coordinate system along the length o f the beam  Xlll  Nomenclature  y .  Beam coordinate system through the thickness o f the beam  y  Distance to the neutral axis o f a beam  eq  xiv  Acknowledgments  Acknowledgments  I would like to take this opportunity to acknowledge the help o f those without whom I could not have finished this work. Firstly, I would like to thank my supervisor D r . Goran Fernlund for his invaluable advice, expertise, and patience. In addition, D r . Anoush Poursartip, Dr. Reza V a z i r i , and the members o f the composites group at U B C (both past and present) have been enormously helpful; Sharing experience and knowledge, as well as a heartfelt laugh and a good time. M a n y people have passed through the office i n Frank Forward 105 and I appreciate the camaraderie. Roger Bennett's technical expertise and help with specimen preparation was especially appreciated. I would also like to thank D r . Andrew Johnston and Lucy Bordovsky o f the Institute for Aerospace Research o f the National Research Council o f Canada in Ottawa for technical expertise and materials.  I would like to thank all my friends who have helped make my time Vancouver so enjoyable. It has been a wonderful experience and I appreciate their company and support. Many have been ready with an open ear and an outstretched hand whenever I needed help.  Finally, I would like to thank my family. Although they are far away, they have always been a constant source o f inspiration. Without their support and fostering I could not have achieved as much.  Financial support for this research was provided by the National Sciences and Engineering Research Council ( N S E R C ) .  xv  Chapter 1 Introduction  1. Introduction  1.1  Background  During its service life, an airframe w i l l be subjected to thousands o f load cycles in a wide range o f environmental conditions involving both temperature  and humidity. Although  engineers go to great lengths to design and test for fatigue damage, such occurrences are inevitable. Inspection schedules are thus designed to ensure that damage is detected and monitored before it becomes hazardous to the safety o f the airframe, passengers, crew, and cargo. Once damage is deemed critical to the structural integrity o f the airframe, the damaged part must be retired and replaced or it can be repaired. The high costs associated with retiring components from service, due i n part to limited production and availability o f replacement parts, and loss o f revenue due to downtime, has created the need to develop repair techniques that can extend service life.  Two main repair schemes exist for airframe components: riveted doubler repairs and bonded composite patch repairs. In a riveted doubler repair, shown in  Figure 1.1-a, a metallic  doubler is fabricated to the same contour as the original structure. The surface is then prepared, rivet holes are drilled through both the doubler and the original structure and rivets are installed. Rivet patterns are engineered following rules o f thumb that define features such as edge distances, pitch, etc.  In a bonded composite patch repair, shown in Figure  \ .\-b, a unidirectional composite patch  is designed and fabricated with fibres running perpendicular to the crack direction. The patch is then adhesively bonded to the original structure by applying an aerospace grade adhesive and cured in-situ at an elevated temperature using a heating blanket. The patch is tapered to reduce peel stresses and is designed to restore the strength o f the underlying structure without over-stiffening the repaired area.  1  Chapter 1 Introduction (a)  (b)  Riveted Doubler  Composite Patch  Doubler—H  Skin-  Figure 1.1 - Schematic of (a) a riveted doubler repair and (b) a bonded composite patch repair  Composite reinforcements offer many benefits, such as: •  Stiffening under-designed regions  •  Restoring strength or stiffness  •  Reducing the stress intensity factor  •  Improving damage tolerance  Composite patches also offer a number o f advantages when compared to conventional riveted doubler repairs: •  In-situ repair leads to reduced downtime  •  Sealed interface eliminates corrosion problems  •  Does not cause additional damage  to the  structure  countersinks, etc. •  Reduces the chances o f accidental damage during repair  •  Easily contoured to mate with curved surfaces  •  Produces a low aerodynamic footprint  2  i n terms of rivet holes,  Chapter 1 Introduction Chester et al. [1] showed that in a repair to the lower wing skin o f an F - l l l , fatigue life increased from 15.8 flight hours for an unpatched specimen, to over 2000 hours for a boron/epoxy patched specimen. Ong & Shen [2] observed that adhesively bonded repairs could enhance the fatigue life o f a cracked aluminium substrate by 60-100 times.  One o f the disadvantages o f composite repair patches arises from the mismatch in the coefficients o f thermal expansion between the repair patch and the underlying metallic repair area. Repair patches are generally designed with the 0° direction perpendicular to the crack growth direction and thus the patch properties are governed by the fibres. Coefficients o f thermal expansion for typical fibre materials can range from -1 to 7 \\xnlm°C [3], while the coefficient o f thermal expansion for aluminium is 23 u m / m ° C and that o f steel is 11.3-17.8 [4]. Thus as the patch is subjected to the adhesive's cure cycle, thermally induced residual stresses are created, shown schematically in  Figure 1.2, which can limit the effectiveness o f  the repair in terms o f fatigue life.  Cool-down  Heat-up  • Patch is applied at room temperature  • Substrate expands • Adhesive cures • System couples  Substrate contracts Stresses are produced Out o f plane deflection in bi-material beam  Figure 1.2 - Schematic of thermal residual stress problem  A number o f attempts have been made to reduce the detrimental effect produced by this difference in coefficient o f thermal expansion. These include prestressing the patch, using materials for the patch, such as boron fibres, whose coefficient o f thermal expansion approach that o f the underlying structure and, most notably, optimizing the cure cycle to reduce the process induced residual stresses. Cho and Sun showed that by judiciously engineering the cure cycle used to bond a repair patch, an improvement in fatigue life o f up to 5 times over the manufacturer's recommended cycle can be achieved [5].  3  Chapter 1 Introduction Thus there exists a need to understand the development o f thermally induced residual stresses in bonded composite patch repairs: where in the repair process they develop, what factors most influence their development, how systems properties develop as a function o f the constituent properties, and how the residual stresses affect the system. Experimental methods are needed that are flexible enough to characterize important material properties throughout a cure cycle. A method is also required to simulate bonded composite patch repairs in a controlled laboratory setting that allows for in-situ measurement o f the development o f residual stresses throughout a cure cycle. Simultaneously, there is the need to develop simple models to aid i n the accurate prediction of the development o f residual stresses. Once combined, these tools w i l l help acquire a deeper understanding o f the mechanisms through which residual stresses are generated, their effect on the system response, and offer insight into novel methods to reduce the residual stresses produced during the bonding process.  1.2 Objective The objective o f this body o f work is to develop and validate a simple and efficient technique for cure cycle optimization o f bonded composite patch repair using a Dynamic Mechanical Analyzer ( D M A ) .  4  Chapter 2 Literature Review  2. Literature Review  2.1  Historical Overview  Composites began to see use as repair patches for aerospace applications in the early 70's with the pioneering work o f A l a n Baker at the Aeronautical and Marine Research Laboratories ( A M R L ) in Australia [6]. A M R L has since attempted to standardize the repair certification process. Davis and Bond [7] have outlined the principles involved in designing and implementing repairs that should produce durable, reliable bonds. These include design principles for both static and fatigue loadings, fabrication principles including surface preparation and inspection methods, and bonding procedures such as proper thermocouple placement.  A number o f military and commercial repair programs have since shown the benefits o f bonded composite repairs. These include the repair o f a Boeing 727 fuselage lap joint, a Boeing 767 keel beam [8], F-16 FS479 bulkhead vertical attach bosses [9], and an F/A-18 Y470.5 bulkhead crotch area [10]. Baker et al. [11] and Chester et al. [1] reported on an extensive validation program for the bonded composite repair o f a fatigue crack on the lower wing skin o f an F - l l l aircraft. In conjunction with a detailed F E analysis validated by a strain survey on a full scale wing, three levels of structural testing were conducted: coupon specimens to evaluate the repair under various environmental conditions using double overhead fatigue specimens, panel specimens to simulate the local geometry o f the wing skin, and box specimens to simulate the wing structure as a quasi-full scale test. Jones et al. [12] found that bonded repairs can extend the service life o f fuselage lap joints containing multi-site damage, even when subjected to adverse environmental factors. Their findings were validated on an Airbus A330/340 full-scale fatigue specimen.  2.2  Material Modeling  One o f the main differences between a thermoset polymeric material and a simple elastic material is that the polymeric material's properties are highly dependant on its state; during  5  Chapter 2 Literature Review processing the material undergoes a dramatic change in state, beginning as a viscous liquid and progressing to a viscoelastic solid. A number of models have been developed to account for these effects and are presented herein.  2.2.1  Cure Kinetics  The first step in the material characterization of thermoset polymers is the determination o f the cure kinetics o f the resin. During cure, the underlying structure o f a polymer is altered irreversibly. Single monomer units combine chemically to produce polymers - long chains o f repeating units, known as mers - and crosslink.  Generally, cure kinetics models focus on defining the rate o f cure. The degree of cure is then found by integrating the rate equation. Two general classes o f models are used to describe the rate of cure behaviour. The first class of models, known as mechanistic models, is based on a detailed understanding o f the underlying chemical reactions o f the system. These models take into account the main chemical reactions and explicitly relate the concentrations of species present in the system to a rate o f generation of products in a set o f kinetic expressions that describe the overall curing dynamics. While these models are comprehensive, they are difficult and time consuming to create and are generally not o f practical use due to the complexity o f the system, as well as the proprietary nature o f most resin formulations.  The second class o f models, known as phenomenological models, captures the main characteristics o f the underlying chemical reactions by fitting cure rate equations  to  experimental data. These are used nearly exclusively and are traditionally reported in the engineering literature. Although several forms o f reaction rate equations are used, their general form is ^ = Kf(a) at where a represents the degree o f cure, K is a reaction rate constant and f(a)  (1) represent a  function o f degree o f cure. The reaction rate constant is generally taken to be an Arrhenius temperature dependant constant o f the form  6  Chapter 2 Literature Review  K = A exp  AE RT.  (2)  where A is a pre-exponential, AE is the activation energy, R is the universal gas constant and T is the temperature (in Kelvin).  2.2.2  Glass Transition Temperature  During cure, as the polymer chains grow in length and cross-links develop, the resin's material properties begin to evolve. The material changes from a viscous-liquid to a viscoelastic solid. The system undergoes two major transitions - gelation and vitrification.  Gelation corresponds to the formation o f an infinite network, where the system passes from a liquid to a gel and acquires an equilibrium modulus [13]. Gelation occurs at a characteristic degree o f cure, which is dependant on the chemistry of the resin.  Vitrification corresponds to a reversible transition from a rubbery gel to a glassy solid. It relates to the freezing o f cooperative motion o f the kinetic segment o f the main chain, transitioning the system from viscoelastic behaviour to essentially elastic behaviour. A system is said to have vitrified i f the system's temperature drops below its glass transition temperature, T . The system's glass transition temperature increases with advancing degree g  of cure; as more bonds form, more input energy is required to shift between the glassy and rubbery regime and thus its onset is retarded [14,15].  Many material properties show a drastic change as the glass transition temperature is approached. A number o f experimental techniques have been used to quantify this change. Dynamic scanning calorimetry ( D S C ) techniques typically determine T  g  as a change in  specific heat capacity [16], as well as the inflection point o f the endotherm [17]. Thermal mechanical analysis ( T M A ) techniques determine T as a change in the coefficient of thermal g  expansion [18,19,19]. Dynamic mechanical thermal analysis ( D M A ) techniques determine T  g  by monitoring the change in a material's modulus [19]. The glass transition temperature defines the material's useful thermal operating envelop for many applications.  7  Chapter 2 Literature Review  The glass transition temperature as measured in a D M A has been defined in a number o f ways [19,20,20]: 1. The temperature at which the storage modulus, E', has fallen below a threshold value. The German standard D I N 53665 sets this threshold at the half height o f the step change. 2. The temperature at which the phase angle, tan(<5), has its maximum value. 3. The temperature at which the loss modulus, E", has its maximum value.  Traditionally, the most common definition used for T is the temperature at which the phase g  angle is a maximum. The glass transition temperature has been found to exhibit a one-to-one relationship with degree o f cure and is most commonly described using a DeBenedetto type relationship o f the form T (a)-T g  .  where T  Q  .  g0  T  >!/:  -7;  =  ( !  Xa \-(\~A)a  {  is the glass transition temperature o f the uncured resin, T  gco  }  is the glass transition  temperature o f the fully cured material, and A is a material constant. Chern and Poehlein [21] used the DeBenedetto equation to characterize an epoxy resin and Hojjati and Johnston [22] used it to characterize F M 7 3 adhesive. Other models include a piecewise quadratic fit, used by Djokic et al. [17] to model F M 3 0 0 and by K i m and White [23] for the neat resin 3501-6, and a logarithmic fit used by Sourour and Kamal [14] to characterize D G E B P A . Studying the development o f glass transition temperature o f the prepreg AS4/3501-6, K i m et al. [24] noted that the relationship between glass transition temperature and degree o f cure was similar to that found by K i m and White [23] for the neat resin 3501-6.  2.2.3  Viscoelasticity'  Polymeric materials differ from many other engineering materials as they can exhibit time or temperature dependant response to an applied stimulus and can be modeled using a viscoelastic constitutive model. Viscoelasticity arises as chain segments undergo Brownian motion, moving i n discrete diffusional jumps, yet continuing to cohere as a solid. A s mobile  8  Chapter 2 Literature  Review  molecular segments flow due to the applied stimulus, a back stress is developed that may stop the flow after a long time period and leads to complete recovery when the stimulus is removed [25].  Viscoelastic Constitutive M o d e l s A l l linear viscoelastic models are governed by a particular case o f the following equation.  a c> +fl,cr+ a a + a cr + 0  2  + a <j = b s + b^e + b s + b e + {n)  3  n  Q  where a, and b are constants, and cr " and s " (  )  {  i  }  2  3  +bs  {n)  n  represent time derivatives o f stress and  strain.  Figure 2.1 - Schematic of material models: elastic (a), viscous (b), Kelvin (c), Maxwell (e), and Zener (e and f)  These models, shown schematically in Figure 2.1, include: •  The elastic solid model, consisting o f a single spring element  •  The simple viscous model, consisting o f a single dashpot element  •  The K e l v i n model, consisting of a spring and dashpot in parallel  •  The M a x w e l l model, consisting of a spring and dashpot i n series  •  The Zener model, consisting of a spring i n series with a K e l v i n model, or equivalently, a spring in parallel with a M a x w e l l model  9  (3)  Chapter 2 Literature Review Stress Relaxation When a constant strain level is applied to a viscoelastic material, a time-varying stress results [25]. B y running relaxation tests at various constant strain levels, a family o f stress relaxation curves can be created. Plotting the stresses produced at a given time against the applied strain level and then connecting them with a curve, isochronous stress-strain curves can be produced. For a linearly viscoelastic material, this curve w i l l be linear and the slope is defined as the relaxation modulus. The relaxation modulus can then be plotted versus time and the material's stress relaxation function can be determined. The stress relaxation w i l l generally exhibit three distinct regions: •  A n initial maximum plateau, known as the "glassy" modulus, where the material exhibits an initial, essentially elastic response.  •  A n intermediate, transition zone  •  A final minimum plateau, known as the "rubbery" or equilibrium modulus  The point o f inflection o f the curve is defined as the characteristic relaxation time [26].  Creep Compliance Similarly, when a constant stress level is applied to a viscoelastic material, a time-varying strain results. B y running creep tests at various constant stress levels, a family of creep curves can be created. Plotting creep strains produced at a given time against the applied stress level and then connecting them with a curve once again produces isochronous stressstrain curves. For a linearly viscoelastic material, this curve w i l l be linear and the slope is defined as the creep compliance. Creep compliances can then be plotted versus time and the material's  creep compliance function can be determined. The creep compliance w i l l  generally exhibit three distinct regions, much like the stress relaxation, beginning with a low plateau and then transitions to a higher plateau.  Dynamic Response When a viscoelastic material is subjected to a cyclic excitation o f the form s(t) = e sm(cot), 0  the force required to produce this deflection is proportional, but out o f phase with the deflection as shown i n Figure 2.2, and can be defined as a = <J sin(<z> t + 8) . 0  10  Chapter 2 Literature Review  The stress can then be expressed as  cr(t) = <7  0  cos(#)- s i n ( t i ) t)+ <r0  <y{f) = s  0  [E'sin(«  sin(c?)-  cos(o  t)  (4)  t)+E" • cos(a> t)]  (5)  E' = ^cos(3)  (6)  £" = ^sin(c?)  (7)  Phase Shift  -Displacement  Time  Figure 2.2 - Dynamic response of a viscoelastic material  A n electrical analog may be used to replace the time dependant variables with their complex equivalents. Thus the instantaneous modulus can be replaced with an equivalent complex modulus, E *. This leads to the definition of an in-phase and an out-of-phase component for the modulus, known respectively as the storage modulus, E', and the loss modulus, E", as well as a phase angle, 8, where  E* = E'+iE" tan  8 -  (8)  £ * s i n £ _ E" E* cos 8  11  K  (9)  Chapter 2 Literature Review Correspondence Principle In a viscoelastic analysis, the boundary and equilibrium conditions remain similar to those o f an elastic analysis. The difference manifests itself through the constitutive equation. The correspondence principle is thus used to transform the solution for an elastic material into one for a viscoelastic material. The correspondence principle states i f the elastic solution to a problem is known, the corresponding solution to a viscoelastic problem can be obtained by replacing the elastic modulus with its viscoelastic equivalent [27]. Since viscoelastic functions are generally time-dependant, a transformation into the Laplace domain may also be necessary.  Superposition Principle Temperature  has  a very pronounced  effect  on viscoelastic materials.  For  thermo-  rheologically simple materials, experiments have shown that lowering the temperature has the effect o f shifting the response towards longer times, while increasing the temperature has the opposite effect, without affecting the shape o f the response. A time-temperature shift factor, a , r  master  can be used to collapse a series o f tests run at varying temperatures into a single  curve. Experimentally this phenomenon  can be very useful, as reducing the  temperature can slow down transitions that occur too rapidly for the test method, or temperature can be increased to speed up experiments whose duration would be otherwise prohibitive. The shift factor corresponds to a horizontal shift along the time axis, based on a reference temperature. The shift factor can take on a number o f forms, including Arrhenius behaviour [25] and  W - L - F behaviour [28]. The superposition concept has also been  extended to include applied stress [29-32] and degree o f cure [22,23,33].  Modulus The relaxation modulus o f polymeric materials has been found to be dependent on factors such as degree o f cure, temperature, and time of load application. Using M a x w e l l elements to model the behaviour o f material, the relaxation modulus can be defined as  E( S)=E„+(E -Ej).fw -&v ai  H  a  12  (10)  Chapter 2 Literature Review where E  u  is the unrelaxed or glassy modulus, E  m  relaxation time, £ is the reduced time, and W  a  is the rubbery modulus, r is the stress  is a set o f weight factors and x  a  is as set o f  discrete relaxation times [23,34,35]. W i t h this model, the glassy modulus corresponds to the initial instantaneous response, which then decays over time to the rubbery modulus.  Although this model may be used to accurately represent the relaxation phenomenon encountered, a large number o f parameters are required and difficulties arise in the use of curve fittings techniques to determine the parameters. Hojjati and Johnston [22] used a simple, three-parameter stretched exponential model to represent the relaxation modulus as  E{£,a)=E +(E -E )-exp x  u  x  (11)  where b is a material constant. This equation can be modified slightly to include cure and temperature effects as  E(C,a,T)=E +(E -E )-exp x  2.2.4  u  x  (12)  Pseudo-Viscoelastic ( P V E ) M o d e l s  Pseudo-viscoelastic ( P V E ) models are a class o f models where simplifying assumptions are used to disregard the processing or load history o f the material. The material is generally characterized using dynamic tests at an arbitrary, but low frequency [36]. Ferry [28] defines the relaxation modulus as a function o f the storage and loss moduli at a specified frequency G(/ = l/ffl)=G'(fi))-0.40G"(0.40ffl)-i-0.014G"(l0ffl)  (13)  O ' B r i e n et al. [35] and Cook et al. [37] propose similar conversions between dynamic results and relaxation modulus. The constitutive equation can be written in an incremental form as  Aa = E(T,a)-As where E{r,a) is the instantaneous modulus.  13  (14)  Chapter 2 Literature Review One such model, known as the cure hardening instantaneously linear elastic, or C H I L E model, is essentially an elastic model where the modulus is assumed constant during each time-step, but may be defined as a function of the temperature and the degree o f cure [38]. Zobeiry et al. [36] studied the validity of the P V E formulation and discussed the regimes where the C H I L E simplifications are valid and the model can be expected to produce accurate results. Johnston et al. [38], using a pseudo-viscoelastic constitutive model, defined the resin modulus as a monotonically increasing function o f degree o f cure.  T  E ( T ' )  =  E  0  +  (  E  X  -  E  J  T  *  -  T2 C  T  « T  CX  j  <  T  C  T  C  L  2  < T  T,  < T  C  2  (15)  < T  where T* = T — T is defined as the difference between the current temperature, T, and the S  instantaneous glass transition temperature, T , E ( T * ) resin, while E  Q  ,E  X  ,T  C I  , and T  C 2  is the instantaneous modulus o f the  are material constants. Similarly, Svanberg and Holmerg  [39,40] develop a pseudoviscoelasitc model which represents the limiting case o f linearviscoelasticity. In their model, incremental stresses are developed with the  material's  modulus defined as either the glassy or rubbery modulus, with a softening component implemented above the material's glass transition temperature.  2.3  Bonded Composite Repair Modeling  Full three-dimensional analysis o f bonded patch repairs is inherently computationally inefficient, as it involves large aspect ratios, due to the relative size o f the thickness with respect to the other two dimensions. Furthermore, single-sided patches develop curvilinear crack fronts and generate a highly non-linear three-dimensional stress response [6]. Thus a number o f alternative methods have been developed including analytic models and closed form beam bending models.  14  Chapter 2 Literature Review 2.3.1  Finite Element M o d e l i n g  A s full three-dimensional finite element modeling is computationally inefficient, a number of simplified F E techniques have been proposed. Sun et al. [41] developed a technique whereby the patch and substrate are modeled as plates while the adhesive layer is modeled by three spring elements, representing the in-plane and out-of-plane stiffnesses o f the material. This technique was shown to be capable o f predicting the stress intensity factor for double-sided repairs, as well as calculating the strain energy release rate along the debond front, but showed appreciable discrepancies for single sided repairs. Modifying the model to account for variation in the stress intensity factor through the thickness o f single sided repairs, K l u g et al. [42] showed that linear and non-linear geometrical analyses produced similar results when thermal effects were superposed on mechanical loading. Their results also indicated that increasing the thickness o f single-sided repairs might not significantly affect fatigue life, due to increased thermal residual stresses. Using the same method, Lena et al. [43] investigated the use o f composite repair patches as crack arrestors. W i t h the aim of hampering crack coalescence, they placed the repair patch between two edge cracks. Monitoring the crack growth, they noted that the patch had no effect until the crack grew into the patched area. They also confirmed that thermal effects  during processing could  significantly reduce the effectiveness o f repairs.  Naboulsi and M a l l [44] developed a similar three-layer technique, where the adhesive layer was modeled by an elastic continuum instead o f shear-spring elements. Their results showed better agreement to full three-dimensional analysis for both cohesive crack growth and adhesive failure. They proceeded to study the effect o f non-linear analysis on damage tolerance o f bonded patch repairs [45]. B y comparing results with geometric non-linearities (due to out o f plane deformation) to those from geometrically linear analysis, they noted that although both exhibited similar trends, non-linear analysis predicted lower stress intensity factors. It did not, however, affect the development o f thermal stresses during cure of the adhesive, AF-163-2. N o mention was made  o f the model used to characterize  the  development o f adhesive layer properties. The adhesive was then modeled as an elasticplastic material to capture  debond behaviour. In this case, the  15  difference  between  Chapter 2 Literature Review geometrically linear and non-linear analysis disappeared. Comparing different  stiffness  ratios, they found that higher stiffness ratios tended to reduce the stress intensity factor.  Umamaheswar and Singh [6] compared three different non-linear F E modeling strategies: A two-dimensional plate-beam model where the patch and substrate were modeled with shell elements and the adhesive is modeled as line springs or beams, a two/three-dimensional plate-brick model where the patch and substrate were modeled as shell elements and the adhesive is modeled as a brick element, and a three-dimensional single brick model where each layer was modeled as a single brick element. Results show that the single brick model matched the results obtained from a fully three-dimensional model to within 98%, and could thus be used as a good first order design tool.  Schubbe and M a l l [46] investigated the repair o f thick panels using bonded composite repairs. They found that for asymmetric repairs, the problem o f mismatch o f coefficient of thermal expansion caused the crack to open on the patched side and close on the unpatched side, leading to a non-linear crack front that complicates the analysis o f thick panel repairs significantly. Simple beam theory was unable to account for thermal effects and  2.3.2  Analytic Modeling  Rose [47] developed an analytic model to determine thermal residual stresses for an infinite isotropic plate reinforced with a circular orthotropic material using an inclusion analogy. Wang et al. [48] then proceeded to develop approximate solutions to correct for finite size. Daverschot et al. [49] compared the analytic Wang-Rose and V a n Barneveld-Fredell models and an F E model. The V a n Barneveld-Fredell model is similar to the Rose-Wang model, save that stresses i n the plate are calculated using an effective C T E , which is determined by the restraint o f the boundary conditions. They distinguished between "test specimens", which are free to contract during cooling, and "in-field specimens", whose thermal response is constrained by the surrounding structure. Experiments were performed on  specimens  consisting o f circular reinforcements applied to two substrates, whose dimensions simulated a test specimen and a much larger in-field specimen, to determine the stresses in the patch and the substrate post adhesive layer curing. Results suggest that while both models were  16  Chapter 2 Literature Review able to accurately model "test specimens", the V a n Barneveld-Fredell model was better able to model "in-field" specimens. The authors also noted that the actual specimen temperatures measured were lower than those predicted by the analytic models, as both models assumed adiabatic conditions.  2.3.3  Closed F o r m B e a m T h e o r y  Hojjati [50] developed a closed form elastic solution for the stresses in a double-sided bonded patch repair, as shown in Figure 2.3.  Patch .Substrate  t.  Patch 2L Figure 2.3 - Geometry of double sided bonded composite patch repair  Considering only thermal effects, the equations for adhesive layer shear stress, x , and the a  normal shear stress i n the patch, a , and substrate, cr , respectively are: p  v  («,-ftp)-?  1  2  E t  Et  7  x  sinh(^x) (16)  cos  ss  P P  cos h(/bt)' cosh(/lz)  \ s-a )-T  2 a  cos  p  ° " . v ( * )  =  t  cosh(/lZ) f ^ -  +  17  (17)  -  ^  (18)  Chapter 2 Literature Review where A is defined as 2  (  +  a  p  and a  2 E,t,  (19)  are the coefficients o f thermal expansion o f the patch and substrate respectively,  s  T is the temperature change, L is the half-length, x is the distance along the beam at which the deflection is calculated, and E  p  and E are the elastic moduli o f the patch and substrate s  respectively, and G is the shear modulus of the adhesive. a  Hojjati and Johnston [51] presented a closed form solution to the deflection o f a one-sided patch caused by mismatch o f the coefficient o f thermal expansion based on a threecomponent system, as shown in Figure 2.4: an elastic substrate, an elastic adhesive and an elastic substrate. The adhesive is assumed to carry only shear load as its thickness, t , a  much smaller than that o f the patch, t , p  and o f the substrate, t . s  is  Thus the system can be  analyzed using a standard shear lag approach that gives the central deflection o f a beam subjected strictly to thermal loads.  w(t)  y  Adhesive  x  2L  b  Figure 2.4 - Geometry of single sided bonded composite patch repair  w=  T-K-f{G ) a  18  (20)  Chapter 2 Literature Review  (a -a )-(t +2t +t )-L  2  p  K  s  p  a  =  AElX ,  J  x ;  2-(cosh(AZ)-l) A -I -cosh(AZ)  K  2  1 E t, p  2  1  ^(^,+2^+Q  E.t.  2EI  |  EI= \2\Ef t E t )  ,K  ptpEptp  p p+  K = 4 + 6-  (21)  x  (22)  (23)  (24)  p p  (25)  + 4-  / ( G ) can be conceptualized as the degree o f adhesive coupling between the patch and a  substrate. For an uncured adhesive, / ( G ) - > 0 , and the constituents acts as two separate a  beams. A s the adhesive's modulus increases /(G )—>1 and the system acts as a perfectly 0  bonded beam.  2.4  Optimization  During processing residual stresses are produced by a variety o f factors, including mismatch of coefficient o f thermal expansion, differential cure shrinkage and moisture desorption. Residual stresses are detrimental for a number o f reasons including development o f microcracks in the transverse direction and reduction i n efficiency o f patch repairs. A number of techniques have been developed to determine the residual stresses level o f the material. Researchers have mainly focused on reducing the level o f process-induced stresses by optimizing the cure cycle. In a similar vein, optimization strategies have been proposed to reduce the thermally induced residual stresses in bonded composite repairs.  19  Chapter 2 Literature Review 2.4.1  Stress Measurement Techniques  Typically, residual stress levels are either quoted as actual stress levels or in terms o f a change i n temperature, which correlates to a stress level using Laminate Plate Theory. The stress free temperature, T f, corresponds to the temperature to which the specimen must be s  raised to eliminate the existing residual stresses, while the effective temperature drop,  AT , eff  corresponds to the temperature drop that would produce thermal stresses in a stress free laminate equivalent to the measured residual stresses.  A number o f experimental techniques have been developed to determine process induced residual stresses. The first group o f techniques employ strain gauges to measure the surface strains o f a specimen and then use laminate plate theory to correlate this strain to residual stresses. White and Hahn [52] measured thermal shrinkage strains by bonding strain gauges to the surface o f laminates prior to cure and monitoring the development o f strain during intermittent cure. Crasto et al. [53] used embedded strain gauges to monitor the development of axial and transverse strains. Crasto and K i m [54] used a peel-ply technique to determine the residual stresses i n symmetric angle-ply specimens. In this technique, strain gauges are bonded to the outer ply o f a cured laminate and the strains that result when the outer layer is removed are used to determine the residual stresses. Similarly, C h o and Sun [5,55] bonded strain gauges to the substrate o f unsymmetric patch repair specimens post-cycle and dissolved the substrates in N a O H .  The second group o f techniques, suitable for asymmetric lay-ups, measures the deformation of the specimen due to processing. K i m and Hahn [56] measured the deflection produced during intermittent  cure cycles for graphite/epoxy laminates. White and Hahn [57]  investigated the effects o f cure cycle modification on the development o f deflection. Ramani and Zhao [58] bonded a thermoplastic to a steel substrate and measured the deflection during cool-down with a high-resolution camera. Cho and Sun [5,55] measured final deflections i n patch repair specimens and found that this technique gave similar results to those obtained through strain gauging. Djokic et al. [17] monitored the development o f residual stresses during a cure cycle by designing a j i g , consisting o f an instrumented cantilevered element i n  20  Chapter 2 Literature Review contact with a patch repair specimen spanning two uprights, to measure the out-of-plane deflection in a patch repair specimen in-situ.  Eliminating the need to correlate results with Laminate Plate Theory, Crasto and K i m [54], Findik et al. [59], and Djokic et al. [17] reheated specimens to produce a stress free condition, thus determining a stress-free temperature. Ochi et al. [60] measured the internal strains on an embedded steel ring surrounded by a curing resin, which they used to differentiate between cure shrinkage and thermal shrinkage. Schoch et al. [61] used a parallel plate fixture in a D M A to determine the shrinkage stresses o f a neat resin in-situ. Similarly, Lange et al. [13,62,63] used a parallel plate rheometer to determine the cure shrinkage o f epoxy and acrylate systems. Motahhari and Cameron [64] used the relative movement o f two guides implanted i n a neat resin as a measure o f cure shrinkage. They then measured the deflection o f a bimaterial specimen, consisting o f a layer o f the same neat resin and a layer o f fibres impregnated with the same resin, to determine the contribution o f resin shrinkage to the residual stress o f the system.  2.4.2  Process Induced Residual Stresses  K i m and Hahn [56] were one o f the first to study the effects o f residual stress development during processing. Intermittent curing was used to determine the development o f out o f plane deflection i n T300/301 -6 graphite/epoxy [04/904]T laminates as a function o f degree o f cure. They found that although an elastic solution predicted the development o f curvature relatively well, the stress free temperature was generally found to be below the cure temperature due to viscoelastic relaxation during cool down.  Crasto and K i m [54] studied the process-induced residual stresses in [04/904]T laminates and determined a stress free temperature by reheating specimens. Their results suggested that the stress free temperature was greater than the cure temperature, which they suggest may be caused by cure shrinkage and moisture desorption. Residual stresses i n various symmetric angle-ply lay-ups, with 0° outer layers, were also investigated using the peel-ply technique. Stress free temperatures determined by the peel ply technique lay in the vicinity o f the cure temperature and were lower than those from the reheat technique. The peel-ply technique  21  Chapter 2 Literature Review was found to be sensitive to the choice o f coefficient o f thermal expansion, as an analytical model is used to determine the stress free temperature  K i m and White [65] studied the stress relaxation behaviour o f a neat epoxy resin, 3501-6 produced by Hercules Inc., using a parallel arm D M A in stress relaxation mode. This technique eliminated many o f the difficulties incurred when transforming creep data in the Laplace domain (or dynamic data in the frequency domain) to stress relaxation data in the time domain. Using samples cured at various degrees o f cure, they developed a constitutive model, in the form o f a discrete exponential series, incorporating time- and cure-dependant effects. Using this model, they proceeded to extend laminate plate theory to viscoelastic materials  and then  investigated the  cool-down process-induced  stresses in terms o f  interlaminar normal stresses [66]. Comparing their results to the elastic response of Wang and Cross, a reduction o f up to 30% in interlaminar stresses is found due to viscoelastic relaxation. They proceeded to run the numerical model for an entire 2-step cure cycle, while neglecting cure  shrinkage. Results show that during the  ramp  to the  second  hold,  compressive interlaminar stresses were developed, which then proceeded to cancel out some of the thermal residual stresses produced during cool-down. The addition o f cure shrinkage to the model was found to increase the process-induced residual stresses. This effect is magnified i f cure shrinkage is assumed to occur later in the cure process.  White and Hahn [52,67] developed a comprehensive model to predict the development o f residual stresses during cure by modifying Laminate Plate Theory to account for time and cure varying parameters and viscoelastic relaxation. The residual stresses produced in interrupted cure cycles were shown to compare favourably to model results, except for the over prediction o f creep response at high degrees o f cure. They note that further investigation into the development o f some o f the material parameters was necessary. They concluded that cure shrinkage appears to account for approximately 5% o f the final process-induced residual stresses and that elastic models cannot properly predict the development o f residual stresses when viscoelastic effects are significant. They proceeded to study the effect o f varying the cure cycle on the process induced residual stresses in cross-ply [Gy904]T graphite/BMI specimens [57], by investigating the sensitivity o f the curvature to cure cycle parameters  22  Chapter 2 Literature Review including dwell times and temperatures, cool down rates, cool down pressure, and the effects of post-curing. Results showed that reducing the cure temperature and dwell times had the most profound effect on the curvature, however one must be conscientious in ensuring full cure as a reduction in degree o f cure correlates to a reduction in the mechanical properties. Slower cool down rates were shown to reduce final residual stresses, as relaxation processes were permitted longer times at higher temperatures. Post curing was shown to negate much of the perceived benefit o f low temperature one-step cycles, while varying pressure during cool-down did not affect the residual stresses. Finally, three step cycles, mimicking a twostep cycle immediately followed by a post-cure, without an intermediate cool-down, were investigated. These cycles showed a marked improvement over the one-step cycles. They did, however, highlight the need for a judicious selection o f the cycle and a matching o f the dwell times to the dwell temperatures. They also compared their results to those of a simple elastic model and found that such models over-predict the curvature. This was attributed to the inability o f the elastic model to capture relaxation phenomena, which tend to reduce the curvature.  Gopal et al. [68], using the model developed by White and Hahn, performed a numerical study to determine the effects o f heating/cooling rates on the process-induced stresses. Their results suggest that the optimum cure cycle requires an almost instantaneous temperature jump to the fist dwell as well as the second, while for cool-down, an optimum, cool down rate can be determined, which does not necessarily correspond to the minimum cool-down rate.  Crasto et al.  [53] endeavoured  to reduce  process-induced  stresses i n unidirectional  AS4/3501-6 laminates by matching thermal residual stresses to cure shrinkage stresses during heat up. Using an embedded strain gauge technique, they monitored the development of axial and transverse stresses in the laminates and found that the final process-induced residual strains could be significantly reduced by using a feedback-controlled heating rate that allowed matrix thermal expansion to compensate for cure shrinkage.  23  Chapter 2 Literature Review Bogetti and Gillespie [69] studied the evolution o f residual stresses i n thick thermoset laminates. They developed an elastic process model based on Laminate Plate Theory that calculated the lamina stresses based on a curing model for the resin that included cure kinetics, modulus development, cure shrinkage, and thermal effects. They found that the progression o f cure occurred very differently in thick section composites, when compared to thin composites. In thin composites, curing begins in the interior and progresses to the outside, while in thick section composites show a cure front that travels from the outside to the centre o f the material [70]. This cure front causes a reversal in the through thickness stress distribution. Due to the cure front, trends observed in thin section composites may not be applicable to thick composites. A s an example, slower ramp rates promote an inside to outside cure history, developing internal compressive stresses. They also note that the definition of a stress-free temperature isn't representative o f thick composites, as the stresses show a large variation through the thickness.  2.4.3  '  Patch Repair Optimization  Cho and Sun [5,55] studied the effects o f modifying the cure cycle on the residual stresses produced i n patch repairs consisting o f a Carbon(IM7)/Epoxy(954-2A) patch bonded to an aluminium substrate, using the aerospace grade adhesive Cytec F M 7 3 . A number of their conclusions were instrumental in the further development o f this area o f research. First they studied the effect o f modifying the cure temperature and hold time in 1-step cycles on the lap shear strength o f the adhesive at room temperature and at elevated temperatures (82°C and 110°C). R o o m temperature mechanical properties were found to be a required, but not sufficient, measure o f the extent o f cure, as evidenced by determination o f the glass transition temperatures o f the same cycle using A S T M E l 8 2 4 . Conversely, i f a specimen exhibits fully developed mechanical properties at elevated temperatures, they premise that it has reached full cure.  24  Chapter 2 Literature Review Table 2.1 - Summary of Cho & Sun patch repair tests [5]  Heating Test  Tcure  thold  [°C]  [min]  Cooling  Rate  Rate  [°C/min]  [°C/min]  AT  Percent eff  reduction  [°C]  in AT  1  121  60  -90  -  2  77/104  300/60  -61  32  3  77/104  360/60  -51  43  4  82/104  210/60  -57  37  5  82/104  240/60  -53  41  6  82/104  300/60  -53  41  7  88/104  210/60  -62  31  8  88/104  240/60  -62  31  3.3  1.1  eff  They then proceeded to modify both cure temperature and dwell times for 2-step cycles, as summarized in Table 2.1. Cycles were selected such that the first dwell temperature allowed for sufficient development o f mechanical properties without requiring inordinate dwell times. Their second dwell temperatures were chosen to ensure full cure as determined by their tests on 1-step cycles. Their results can be summarized by noting that " AT  eff  decreases as degree  of cure increases and cure temperature deceases i n the first-step cure," resulting i n a maximum reduction o f 40% in AT . Cho and Sun [71] then proceeded to develop a model eff  to predict the behaviour o f F M 7 3 when subjected to a multi-temperature bonding cycle. The viscoelastic response o f the adhesive was described by a M a x w e l l model and the effective temperature drop, AT , was found to compare favourably with previously determined eff  experimental results.  25  Chapter 2 Literature Review Table 2.2 - Summary of Djokic et al. F M 7 3 patch repair tests [72] DOC  Test  Tcure  thold  [°C]  [min]  Model  T  Tg  Exp.  s f  Model  Exp.  Model  Exp.  [°C]  [°C]  [°C]  [°C]  1  121  60  0.989  0.985  93.8  106  99.6  102.0  2  104  60  0.972  0.976  88.5  104  91.3  101.4  3  82  240  0.970  0.896  88.1  97  82  78.8  4  82  210  0.966  N/A  86.9  N/A  82  68.1  5  77  360  0.963  0.876  86  96  77  76.6  6  82/104  210/60  0.989  0.966  94  108  98  100  7  82/104  240/60  0.990  0.976  94  109  98  98  8  82/104  480/60  0.991  0.975  94  109  98  95  9  82/104  360/60  0.994  0.975  95  112  91  94  10  82/96  480/60  0.992  0.942  95  108  89  89  Djokic [73] extended the work o f Cho and Sun by designing a j i g to monitor the development of residual stresses in a patch repair specimen in-situ. Specimens consisted of 10 plies o f AS4/3501-6 carbon fibre/epoxy unidirectional laminate bonded to an aluminium substrate by F M 7 3 adhesive. Simultaneously, Djokic et al. [72] developed a viscoelastic model to describe the development o f warpage. The cure kinetics [73,74], glass transition temperature [22], and the development o f mechanical properties as a function time, temperature, and degree o f cure for F M 7 3 adhesive were characterized. The Boltzmann superposition principle was then used to model the development o f stresses throughout a cure cycle. Experimental results showed that the model accurately predicted the warpage produced in patch repair. Experimentally, T F was determined using the reheat technique, while numerically, an elastic S  model was used. The results are summarized in Table 2.2. Heating rates were 5 °C/min in all cases and cooling rates were 2.5 °C/min for tests 1 through 8 and for tests 9 and 10 a cooling rate o f 0.2 °C/min was used to 75 °C followed by a cooling rate o f 2.5 °C/min.  26  Chapter 2 Literature Review A number o f important observations can be drawn from the results. Focusing on one-step cure cycles (1-5), a reduction in T f with reduced cure temperature is evident. One must s  however be careful to ensure a sufficient degree o f cure. For two-step cycles (6-10), reductions in residual stresses over those found for a 1-step, 104°C cycle were observed. The reduction was not as pronounced as that found by Cho and Sun, as substantial reduction in residual stresses was only achieved by significantly extending the cure times at lower temperature. This was due to relaxation occurring during the ramp between first and second dwell temperatures as well as during the second hold, essentially negating the assumed benefit o f an initial, l o w temperature dwell. The results also suggest that although E  x  is  small, it is non-zero. The findings o f Findik et al. [59,75] support the results o f Djokic over those of Cho and Sun. Using an implanted strain gauge method on similar specimens, they found that using a 2-step cure cycle resulted in a maximum reduction o f thermal residual stresses of approximately 20%.  Using the same experimental set-up previously described, Djokic et al. [17] studied the effect of modifying the manufacturer's recommended cure cycle on the aerospace grade adhesive Cytec F M 3 0 0 (1 hour at 177°C) by: •  Changing the cure temperature, cure time, and cool down rate for 1-step processes  •  Investigating the effects o f post-curing  •  Changing the first hold temperature for 2-step processes  •  Introducing 3-step process to reduce processing times  Although they did not develop a viscoelastic model for F M 3 0 0 , they did characterize the cure kinetics and development o f glass transition temperature to guide their cycle design. From the results, summarized i n Table 2.3, a number o f the conclusions drawn from the study performed on F M 7 3 can be reiterated. First, a reduction in T f occurs with reduced cure S  temperature. Second, 2-step cycles can be used to reduce T f considerably. A number o f S  novel observations can also be made. First, post curing at 177°C to ensure full development of mechanical properties eliminated the benefits o f reducing the cure temperature. Second, cooling rate had little effect on the results, paralleling the results o f White and K i m [66]. Finally, their results suggest that it may be possible to develop a 3-step cure cycle that 27  Chapter 2 Literature Review minimizes residual stresses as well as cure time. This 3-step cycle would be comprised of an initial high temperature hold to promote initial cure, followed by a cool-down to a lower hold temperature at which vitrification occurs, before ramping to the final hold temperature to complete cure. The design of such a 3-step cure cycle is, however, very dependent on accurate cure kinetics and glass transition development models. Conversely, it would seem apparent that good temperature control is an absolute necessity to derive full benefits from such a cycle, and may thus be impractical in actual application.  Table 2.3 - Summary of Djokic et al. FM300 patch repair tests [17]  Test  Tcure  thold  [°C]  [min]  Heating Rate Cooling Rate [°C/min]  [°C/min]  AT  eff  [°C]  1  177-'  60  2  150  160  3  120  480  122  4  177  60  178  5  150  160  6  120  480  123  7  177/177  60/5  178  8  150/177  160/5  9  120/177  480/5  10  150/177  60/30  2.5 to 1 hold  11  120/177  330/30  1.0 to 2  12  150/ 130/ 177  28/40/38  13  150/ 1 3 0 / 177  28/40/38  2.5 to 1 hold  2.0 to 2  14  150/ 1 3 0 / 177  28 / 5 5 / 3 8  0.5 to 3  2.5 to R T  15  150/ 1 3 0 / 177  2 8 / 55 / 3 8  178 2.5  2.5-  150  0.5  2.5  152  2.5  2.5  172 169 165  st  n d  hold  2.5  167 168  st  rd  hold  n d  hold  158 153 151  28  Chapter 3 Theory  3. Models and Analysis  3.1 Introduction This chapter describes the theory behind the D M A beam technique that was developed to characterize material properties as a function of cure, time, and temperature, as well as to monitor the development o f thermally induced warpage in-situ i n bonded composite patch repair specimens.  First, equations are developed that describe the behaviour o f a composite beam when subjected to external mechanical loads. The behaviour is shown to be a function o f the geometry o f the beam and constituents and the mechanical properties o f the constituents. The equations are then modified i n order to determine the instantaneous modulus of a curing adhesive on a steel substrate.  A model for the modulus o f a curing resin as a function o f two variables - the instantaneous temperature and the instantaneous glass transition temperature is developed. Cure kinetics and glass transition temperature models for F M 3 0 0 adhesive are also presented.  The deflection o f bonded composite patch repair specimens when subjected to a variety o f cure cycles was then explored. A shear-lag model was used to describe the response o f an elastic specimen to thermal loads. A cure hardening instantaneously linear elastic ( C H I L E ) constitutive model, modified to account for thermal softening, was then developed to predict warpage, thermal stresses, and shear stresses in the adhesive layer i n a non-linear elastic system.  3.2  Bimaterial beam stress relaxation  The relationship between force, F, and displacement, w, for an elastic beam in three-point bending is  29  Chapter 3 Theory  w =—  (26)  A%E1  where E is the elastic modulus and I the moment o f inertia [76].  \u  H Figure 3.1 - Schematic of bimaterial beam specimen  For a bimaterial beam consisting o f two elastic materials as shown in  Figure 3.1, Equation  (26) is still valid i f the product El is replaced with the equivalent beam bending stiffness  {El) . Assuming perfect bonding and that the adhesive layer can be neglected (due to its cq  small thickness and l o w modulus), the system's bending stiffness,  (El) , can be expressed eq  as a function of the modulus o f the constituent materials and the specimen geometry as  {El) =E -I E -I =E eq  ]  ]+  2  2  (/,„ + r • A )+ E (l  + r •A)  2  ]  x  b • ?,  2  2o  2  2  b-t  ya  (6-0  e  ~12~  2  + E-,  2  (b-t )  y eq  t, -t +—+—' 2 E 2  (28)  7  2  yeq  (27)  2  x  t\ + — t E, 1  2  In the case where the modulus o f one o f the constituents is unknown, Equation (26) can be used to determine  \El)  from experimental force and displacement data.  (28) can then be used to solve for the unknown modulus (either E or x  Equations (27) and  E ). 2  In the case where one o f the constituents is viscoelastic, the system w i l l exhibit a time dependent response. In a time dependent mechanical test, either a load F(t)  30  is applied to the  Chapter 3 Theory specimen and the displacement w(t) is recorded, or vice-versa. For tests where a constant displacement is applied,  Equations (26)-(28) are still valid but the Y o u n g ' s modulus, E, is  replaced by the time dependant relaxation modulus,  3.3  E(t).  FM300 Cure Kinetics Model  Rogers and Lee-Sullivan developed a cure kinetics model for F M 3 0 0 incorporating autocatalytic/« order mechanisms as well as a diffusion-controlled denominator [7]. th  da _ K,a ' (l - af m  dt  + K a > (l - a)" m  2  2  l + exp[-C  o o c  (a-a )] c  where a represents the degree o f cure, m and n are exponents which control the n  th  i  and autocatalytic reactions respectively,  i  C  D0C  is a diffusion control constant,  order  a is the crossc  over point between kinetic and diffusion controlled curing for a given cure temperature, and K, is an Arrhenius form reaction rate constant.  ' K = A exp t  t  AE>  V RT  (30)  r  where A is a pre-exponential, A.E, is the activation energy, R is the universal gas constant t  (J/mol-K) and T is the temperature (in Kelvin). Table 3.1 lists the constants that were used in this model [77].  Table 3.1 - Cure kinetics model constants  A = 447.89 x l O  min"  9  1  = 1 0 5 . 5 6 x l O J/mol 3  A = 72.450 m i n " ' 2  AE = 1 8 . 3 5 2 x l O J/mol 3  2  m -= 0.3  m = 9 . 4 2 5 9 - 0.04853 xT  C  \ = 1.5  n  a  x  n  2  2  =4.9416-0.01791x7  31  c  D O C  =40  =0.003495 + 0 . 3 9 3 4 x 7  Chapter 3 Theory  3.4 FM300 Glass Transition Temperature Development Model Development o f F M 3 0 0 ' s glass transition temperature, T , was modelled as a quadratic function o f degree o f cure by Djokic et al. [17].  T(a) = \ [A  r  7g]  Tg2  where A , Ti  B ,  Tg2  C , and a  Tgj  Tgl  + B [a-a }a  r i  \  Tg  (  + C \a-a ) Tg2  \  (31)  s 2  Tg  a>  a  Tg  are fitting constants. The model constants, presented i n  Tg  Table 3.2, were modified slightly from those used by Djokic et al. to more appropriately model the development o f modulus. Figure 3.2 shows the resulting development o f the glass transition temperature o f F M 3 0 0 with cure.  Table 3.2 - FM300 Glass transition temperature model constants  Tgi  = 1.40xl0 °C  A  = 1.21xl0 °C  Tg\  = 5.46x10' °C  B  = 3 . 5 0 x l 0 °C  1  A  2  Tg2  B  2  Tg2  = 0.844  32  = 8 . 3 8 x 1 0 ' °C  c  = 8.38x10' °C  Chapter 3 Theory  3.5  FM300 Modulus Development Analysis  The general relationship between force, F, and the midspan deflection, w, for an elastic beam in three-point bending as shown in Figure 3.1 is given by Equation (26). When a dynamic deflection of the form w(t) = w sin(cot) is applied, the force required to produce the 0  deflection is proportional to, but out of phase with, the deflection and can be defined as F(t) - F sm(cot + 8). For a viscoelastic beam subjected to this dynamic load, the 0  correspondence principle states that the solution is equivalent to the elastic solution if the instantaneous modulus, E(t), is substituted for the elastic modulus [27].  E(t)  Jl_F(t)  (32)  48 • / w{t)  In order to determine the storage modulus of a neat resin from a system consisting of a steel shim and an initially uncured resin in the RSI DMTA V, a slight modification to the specimen geometry was necessary. To reduce the effect of the supports resting on the soft, low viscosity resin, the film adhesive was trimmed so as to only cover the metallic substrate between the supports, as shown in Figure 3.3.  l.  Figure 3.3 - Modulus development specimen geometry and loading conditions  To account for the change in geometry, Twigg [78] developed a modified beam equation  F • I • (EI) 3  Sted  + &• F • L • (EI) Steel  48-6-(£/)  33  c  S t e e /  -8-F-4  (33)  Chapter 3  Theory  where (E* I)  is the bending stiffness o f the beam, F and L are defined as previous, b is  Eff  the specimen thickness, (EI)  Sleel  inertia, and L  c  is the product o f the steel shim modulus and moment o f  is the length between the span support and the end o f the prepreg material.  Noting that the complex modulus and the storage modulus are related through the phase angle and that for slow test frequencies E « E'  [78], Equation  (33) can be rewritten to  represent the effective bending stiffness o f the bimaterial portion o f the beam as  F-L  •(EI) +%-F-L' -(EI) Steel  3  (E-I) *(E'-I) Eff  =  Eff  Steel  4S-w(EI) -S-F-L  c  • cosS  3  Sleel  Using test data for force and displacement, Equation  (34)  c  (34) can be equated to the classical  solution of Equation (28) to determine the modulus o f the resin, E , as a function o f time. In x  parallel, the degree o f cure o f the adhesive, and subsequently the glass transition temperature, can be calculated as functions o f the cure cycle using Equations (29) and (31).  Classically, a viscoelastic constitutive model is used to define the modulus o f a time, temperature, and cure dependant material. These models generally define a rubbery modulus, a glassy modulus and a time, temperature, and cure dependant transition [23,34,35,79]. A n alternate material model defines an instantaneous modulus for the resin as a function of the difference between the resin's temperature and its instantaneous glass transition temperature [38]. This model incorporates a relaxed and unrelaxed modulus and a piecewise defined transition regime, gel a < a,  0  E,•cl E(T)  cl  A* • exp(- K* • T*)  T , <f  <TCl  Ed+i  T <f  <T  r  c2  E,  34  r  C  (35)  Chapter 3  Theory  where T* =T-T  is defined as the difference between the current temperature, T, and the  instantaneous glass transition temperature, T . a is the instantaneous degree o f cure, a  gel  the degree o f cure at which gelation occurs (assumed as 0.5 for F M 3 0 0 ) , E(T*) instantaneous modulus o f the resin, and E , cX  E, c2  E, ci  T , cX  T, c2  T, ci  is  is the  A*, and K* are  constants fit to the data as shown in Figure 3.4.  The adhesive's instantaneous shear modulus is then determined using Hooke's law for an isotropic material. The Poisson's ratio was assigned a constant value o f 0.4 following Hojjati et al. [22], such that  1  C3  *C2  'Cl  Figure 3.4 - Modulus versus T - T g model  3.6 Bonded Composite Patch Repair Specimen  3.6.1  Thermo-elastic Deflection  Hojjati and Johnston [51] developed a closed form solution for the thermo-elastic deflection of a one-sided bonded composite patch repair geometry based on a three-component system as shown in Figure 3.5.  35  Chapter 3  Theory  QQ F Patch  s  Adhesive  t  Figure 3.5 - Schematic of bonded composite patch repair specimen  The system was modelled using an elastic shear lag approach by assuming that the adhesive layer carries only shear load. Modifying the definition of beam bending stiffness, E I , to account for the adhesive layer thickness, the central deflection, w, of an elastic beam subjected strictly to a thermal load, T, can be expressed as  •=  (37)  T-K -f(G ) w  a  (CTE -CTE ) (t 2t t )-(L/2)  2  p  s  :  p+  (38)  a+ s  4EIA  1 1 A  —  Et  1  Et  p p  E I  =  E  P  J {t +2t +t ) a  r -  p  +  -  2 P" P' t  +t  t  36  (39)  E.. •  12  y eq  ~  (40)  + E  eq  "  s  2EI  s s  +t  a  E  s p  p  2  (41)  Chapter 3 Theory  f{G )=\-  (42)  cos h(A(Gj),  a  A (  G  . ) = f J  G  (43)  . - {  where C r E and C T E , are the coefficients o f thermal expansion o f the patch and substrate respectively, T is the temperature change, L is the length o f the specimen, G  is the  a  instantaneous shear modulus o f the adhesive, and E  p  and E are the elastic moduli o f the s  patch and substrate respectively. 1.00  0.75  (TJ _ _ _  .1,-0-51)  O 0.50  1-Patch E (>135 CPa, CTEM1 ur.j-C ) -  t.=0.24 t,=0.16  iSnbilnitc (£-2»,CP»; CTE-15 H^C) .  0.25 -H (all measurements in mm)  0.00 0.2  0.4  0.6  0.8  Adhesive shear modulus (GPa)  F i g u r e 3.6 - Effect o f the adhesive's shear modulus,  G , on the c o u p l i n g a  factor,  f(G ),  f o r the  a  geometry shown i n the insert  / ( G ) i n Equation (37) can be conceptualized as the degree o f adhesive coupling between 0  the patch and substrate and is dependant on both the specimen geometry and the adhesive layer's shear modulus. A s can be seen in Figure 3.6, for an uncured adhesive f(G )->0 a  and  the constituents act as two separate beams. A s the adhesive's modulus increases, f(G )—> 1 a  and the system acts as a perfectly bonded beam.  37  Chapter 3 Theory 3.6.2  Constitutive M o d e l  The closed-form solution presented for thermal deflection, Equation (37), is only valid for linear elastic systems. A linear elastic constitutive model is path independent and defines increments in deflection as a function o f increments i n temperature and a constant that accounts for the geometry o f the specimen and the thermo-mechanical properties o f the constituents as  Aw = K • AT  (44)  Linear elastic constitutive models have generally been shown to be inadequate in describing the behaviour o f cure hardening materials [52,57,80]. A cure hardening, instantaneously linear elastic ( C H I L E ) constitutive model was thus investigated to describe the development of deflection observed during a cure cycle [36,38]. C H I L E models are path dependant and define a thermo-elastic component due to a step change in temperature occurring at an instantaneously defined modulus, which is assumed constant during each time-step, but may be defined as a function o f temperature and the degree o f cure, such that  , dw aw, = — •dT = K-f(G \-dT ' dT  (45)  a  where dw is an incremental deflection due to the temperature change t  dT.  The C H I L E constitutive model was found to be incapable o f completely describing the experimentally observed behaviour o f bonded composite patch repair specimens, as tested in a D M A with the adhesive F M 3 0 0 . The model was thus modified to include a thermal softening component, so that the deflection, w, is affected both by changes in temperature and by softening o f the adhesive. Changes in temperature are treated as a thermo-elastic deflection occurring with an instantaneously defined modulus. Softening o f the adhesive layer affects accumulated deflection, resulting in a relaxation o f accumulated thermally induced stresses. The difference i n these behaviours is shown schematically in Figure 3.7.  38  Chapter 3  Theory  (a)  (b)  Figure 3.7 - Schematic illustrating the difference between cure hardening (a) and thermal softening (b)  As the adhesive's modulus is a function o f the difference between the temperature and the instantaneous glass transition temperature o f the material, the deflection is a function o f two independent variables, T and T , and Equation (37) can be written in differential form as g  '  dT  d(G )  v  a  (46)  a )  d =^.dT 4^.J^Ld{r~r) Wi  dT  d(G ) d\T-T ) a  d =K.f{G ),dT+K. Af( ")} G  a  Wl  J X  (47)  +  '  a  h  T  /{GX,  g  v  s /  fPa) J _ ) T  3(Gj d{T-T ) g  (48)  T  (49)  V  A number o f conditions must be imposed on Equation (46). First, during a temperature hold, no changes in deflection occur. Cure is assumed to advance by the creation o f new, unstrained bonds and cross-links in the material. Thus advancement o f cure should not affect deflection until a further stimulus is applied. This marks one o f the major  differences  between C H I L E type models and viscoelastic models used to predict thermal residual stresses in patch repair systems. Second, thermal softening only occurs during a heat up i f the temperature increases at a faster rate than the development o f glass transition temperature. Thus the second term o f Equation (47) is only incorporated i f dT > 0 and d(T - T )> 0 . g  39  Chapter 3 Theory  Thermal softening results i n a reduction in the built-up deformation due to a drop in the modulus of the adhesive. This can be inferred by noting that from Figure 3.6  a[/(Gj] HG.)  > 0  and from Figure 3.4 (51)  <0  d(T-T ) g  Since dT > 0 and d(T - T )> 0, the second term in Equation (47) is opposite in sign to the g  first term and the net result is that the deflection during that time step is less than that predicted by an instantaneously elastic model.  3.6.3  T h e r m a l R e s i d u a l Stresses  In a real structure, a bonded composite patch repair is applied to a localized region o f a much larger structure. A s such the repair area's out-of-plane deflection is constrained, producing thermally induced residual stresses. A n expression for the thermo-elastic residual normal stresses o f a one-sided bonded composite patch repair geometry based on the threecomponent system shown in Figure 3.5, can be derived from the elastic shear lag model of Hojjati and Johnston [51] as  a{y) = E{y) • s  mech  tjy)  =  +  = E{y) • [s  bending  ~~EI  '^  +e  lensile  ~^  J  (52)  ( 5 3 )  P = ~P =P, P  (CTE -CTE )-L\T p  s  ( v  40  i  "I  1  1  cosh(2(G )) a  y  (54)  Chapter 3 Theory  M  (CTE -CTE )-(t +2t +t )-AT p  s  p  a  s  1  1  2X  (55)  cosh(A(Gj),  where a{y) is the stress at the centreline o f the specimen at a height o f y,  E(y) is the  modulus o f the constituent material at a height o f y, t(y) is the thickness o f the constituent located at the height y,  P is the thermally induced force i n the x-axis direction, M is the  thermally induced moment. Equation (53) can be simplified as  o(y) = (CTE  p  -CTE,)  (56)  TK {y)-g{G ) a  J_ t„  g(Gj = l  a  (t +2t +t ) p  V  a  s  •(ye  q  2EI  (57)  -y)  (58)  cos h(A(G a ))  In Equation (56), g(G ) can be conceptualized as the degree o f adhesive coupling between a  the patch and substrate. A s can be seen i n Figure 3.8, for an uncured adhesive g(G )^> :  a  0.  The constituents act as separate beams and no stresses are developed. A s the adhesive's modulus increases,  g(G )-+\ a  and the system acts as a perfectly bonded beam resulting i n  thermally induced residual stresses.  41  Chapter 3 Theory  1.00  t =0.50 p  I Patch (E=135 GPa, CTE=Q m/'C )  t=0.24  Adhesive  t =0.16  w =0.64  L=0.40  (all measurements in mm)  0.00  0.20  0.40  0.60  1.00  0.80  Adhesive shear modulus (GPa)  Figure 3.8 - Effect of the adhesive's shear modulus, G , on the coupling factor, g(G ), for the geometry a  a  shown in the insert  Similarly, an expression for the thermo-elastic shear stresses i n the adhesive can also be derived from the elastic shear lag model o f Hojjati and Johnston [51] as  T-K -h(G ,x)  T(x) =  T  2-(CTE  s  a  -CTE ) P  A -L h(G , ) a %  =  X{G )-smx{G )- {x)) a  a  X  cos h ( ^ ( G j )  (59) (60)  (61)  (62)  In Equation (59), h(G ,%) can be conceptualized as the degree o f adhesive coupling between a  the patch and substrate. A s can be seen in Figure 3.9 and Figure 3.10, the shear stress in the adhesive layer is zero at the centre o f the specimen and increases to a maximum at the edges. For an uncured adhesive, h(G ) -> 0, the constituents act as separate beams and no stresses a  42  Chapter 3 Theory are developed. A s the adhesive's modulus increases, g ( G ) - » l and the system acts as a a  •bonded beam resulting i n thermally induced shear stresses i n the adhesive layer.  12.00  Adhesive shear modulus (GPa)  Figure 3.9 - Effect of the adhesive's shear modulus, G , on the coupling factor, h(G ,%), for the a  a  geometry shown in the insert  12  — Fully cured  Natural co-ordinate, x  Figure 3.10 - Coupling factor, h(G ,x), as a function of natural coordinate system of the beam, for the a  geometry shown in the insert  43  Chapter 3 Theory A s shown for deflection, a C H I L E constitutive model modified to include thermal softening can be used to describe the experimentally observed behaviour o f bonded composite patch repair specimens as tested i n a D M A with the adhesive F M 3 0 0 . The stresses are once again a function o f two independent variables, T and T , and Equations (56) and (57) can be written g  in differential form as M y ) , ^  d  T  +  ^  g(G„)  dT  Y  4 G . )  cfc)  M  d(G )  (  d(T-T ) s  »'  6  3  )  (64)  (65)  a  The same conditions as those imposed on the deflection model, detailed i n section 3.6.2, are valid for the development o f thermally induced residual stresses i n the patch and substrate, as well as the thermally induced shear stresses i n the adhesive layer. First, during a temperature hold, no changes in residual stresses occur. Second, thermal softening only occurs during a heat up i f the temperature increases at a faster rate than the development o f glass transition temperature. Thus the second terms in Equation (63) and Equation (65) are only incorporated  if dT>0 and  d(T-T )>0. g  44  Chapter 4 Methods  4. Methods  4.1  Introduction  This chapter describes the experimental D M A beam technique that is used for material characterization and for the determination of thermally induced residual stresses in a bonded composite patch repair specimen. The D M A beam technique is used i n three different modes. First, the stress relaxation moduli o f monolithic and adhesively bonded bimaterial beam specimens are determined by applying a constant displacement and monitoring the time varying force at various temperatures. Second, the cure and temperature dependant modulus of a curing adhesive is determined by subjecting bimaterial (steel/adhesive) specimens to an offset fully reversing cyclic displacement while monitoring the required force under various thermal cycles. Finally, the D M A is used to measure the deflection o f bonded composite patch repair specimens in-situ throughout a variety o f cure cycles.  4.2  Rheometric Scientific Inc. D M T A V  The Rheometric Scientific Inc. D M T A V ( D M A ) is a mechanical spectrometer that controls and measures force environment.  A  and  variety  displacement of  fixtures  o f a load head can  be  installed  in a in  temperature-controlled  the  D M A to  facilitate  tensile/compressive, shear, or three-point bend testing o f rigid specimens. A D M A can be used to perform a number o f mechanical tests to determine a wide range o f mechanical material properties and examine how they vary with time, frequency, and temperature:  •  Static, constant displacement:  Stress relaxation  •  Static, constant force:  Creep compliance  •  Dynamic tests:  Storage modulus, loss modulus, phase angle, glass transition temperature  •  Coefficient  Thermal ramp tests:  o f thermal  induced warpage  45  expansion, thermally  Chapter 4 Methods Control Computer  DAQ  DMTA  Cryogenic Tank  DMTA Controller Figure 4.1 - RSI D M T A V  The D M A offers a number o f advantages over other mechanical test methodologies: •  Small sample size reduces material costs, preparation times, and thermal lag  •  Accurate, precise measurement o f force and displacement  •  Versatility allows for development o f novel test methods  •  Potential for rapid material characterization  Thermocouples  Rigid Fixture Specimen Load Head Figure 4.2 - D M T A three-point bend set-up  The RSI D M T A V s specifications allow for a maximum 125 micron deflection at an applied force o f 15 N [1]. The three-point bend fixture used required specimens having a 40 m m span  46  Chapter 4 Methods length  (L) and a nominal 6.4 m m width (b), as shown i n Figure 4.2. A schematic o f a  generic D M A beam specimen used is shown in Figure  QQ  4.3.  Q Q  Material 1  Material 2 Material 3  F(t), w (t)  b  Figure 4 . 3 - Generic Schematic of D M A beam specimen  The inherent flexibility o f the D M A beam technique allows for a variety o f tests to be conducted using a simple three-point bend specimen. These tests can be used to both assess a system's response to external stimulus and to characterize material properties. In this work, the D M A beam technique is used for three different tests, summarized in Table 4.1. First, stress relaxation tests are conducted on monolithic and bimaterial beam specimens. During these tests, temperature is held constant while a constant displacement is applied. The force required to produce the displacement can then be correlated to the time-dependant stress relaxation modulus o f the specimen. Second, modulus development tests are conducted on bimaterial beam specimens with a curing resin layer. In these test a dynamic displacement is applied to the specimen while temperature follows a pre-programmed cure cycle. The force required to produce the displacement can then be correlated to the cure and temperature dependant instantaneous modulus o f the specimen. Thirdly, bonded composite patch repairs are simulated using a trimaterial beam specimen. A nominal force is applied to ensure contact o f the load head, while a pre-programmed temperature cycle is applied. The resulting out o f plane deflection is measured by the load head and can be correlated to the thermal residual stresses generated in the specimen.  47  Chapter 4 Methods Table 4.1 - Summary of D M A beam techniques  Bimaterial St ress Relaxation  Modulus  Bonded Composite  Set-up 1  Set-up 2  Development  Patch Repair  Material 1  -  Steel, Lexan  -  AS4/3501-6 [0]  Material 2  -  Hysol E A 9 3 9 2  FM300  FM300  Material 3  Steel, Lexan  Steel  Steel  Steel  Stress  Stress  relaxation  relaxation  Dynamic  Thermal  Step  Step  Cure cycle  Cure cycle  Loading  Static applied  Static applied  Cyclic applied  Condition  strain  strain  strain  Relaxation  Relaxation  Instantaneous  modulus  modulus  modulus  Test Type Temperature Condition  Result  2  None  Deflection  4.3 Temperature Control Previous work on the R S I D M T A V by Graham Twigg [78] led to the discovery o f a large temperature gradient through the D M A ' s environmental chamber. A s the D M A ' s controlling platinum resistance thermometer device (P-RTD) is located approximately 25 m m from the specimen, three J-type thermocouples were placed at a distance o f approximately 2 m m from the specimen and logged externally using a data acquisition ( D A Q ) system and a L a b V I E W software applet. Temperature differences o f up to 20°C between the P - R T D and externally logged thermocouples were measured. Control temperatures were determined by calibrating D A Q temperature readings to D M A temperature readings. The D A Q readings o f the three thermocouples were averaged and linearly interpolated to match the D M A ' s sampling rate. Throughout this work temperature measurements from the D A Q were used instead o f the D M A ' s temperature readings.  48  Chapter 4 Methods  4.4 Bimaterial beam stress relaxation  4.4.1  Objective  The objective o f these tests was to ascertain whether it is possible to accurately determine the viscoelastic response o f a polymeric material from the system response o f bimaterial beams consisting o f an elastic substrate adhesively bonded to the viscoelastic polymeric material. To validate the approach, relaxation tests were performed on steel shims, Lexan beams, and bimaterial specimens o f Lexan adhesively bonded to a steel shim. Adhesively bonded steelsteel shims were also tested to ensure the test regime was below the glass transition temperature o f the adhesive and to show that the adhesive layer did not significantly affect the results.  4.4.2  Specimen P r e p a r a t i o n  Steel shims were nominally 45 m m long, 0.16 m m thick, and 6.4 m m wide, while the polymeric material used, G E Lexan (polycarbonate), was nominally 45 m m long, 1.8575 mm (1/16") thick, and 6.4 m m wide. Monolithic steel and Lexan specimens were prepared by the Materials Engineering machine shop and by the Composites group technician, Roger Bennett. For each specimen, thicknesses and widths were measured at three locations along the beam and averaged.  Bimaterial specimens were created by adhesively bonding Lexan specimens to steel substrates. Steel shims were prepared by sanding the surface with 320-grit sandpaper and then wiping them clean with acetone. The adhesive used was Hysol E A 9 3 9 2 , a two-part room temperature  cure epoxy paste adhesive with good mechanical strength at high  temperatures [81]. The adhesive was mixed as per the manufacturer's recommended ratio (100:32 by weight) and applied to the surface of the steel shim. The Lexan specimens were then placed over the adhesive, pressure was applied, and excess adhesive was cleaned off. The specimen was then allowed to cure for a minimum o f 7 days at room temperature with a constant pressure applied to the top surface. Thicknesses and widths o f both steel and Lexan beams were measured at three locations along the beam prior to being adhered. After the  49  Chapter 4 Methods adhesive cured, the total system thickness was measured at three locations along the beam. The adhesive layer thickness was found as the difference between the total specimen thickness and the thicknesses o f the steel and Lexan. Adhesive thicknesses were o f the order of 0.10 mm. The system width was taken as the average o f the Lexan and steel widths.  4.4.3  E x p e r i m e n t a l Details  Specimens were heated to the initial test temperature o f 30°C and held for 10 minutes to equilibrate thermally. A stress relaxation test was then run for 30 minutes by applying a constant strain to the specimen and monitoring the force required to maintain the strain. Specimens were heated to 40°C at a ramp rate o f 10°C/min and held at a constant temperature for 1 hour. This dwell period allowed for temperature equilibration and relaxation o f any residual stress from the previous test, which was performed at a lower temperature hold. Specimens were then subjected to a stress relaxation test before being heated by 10°C increments up to the final temperature o f 110°C, repeating the temperature hold and stress relaxation test at each increment. This final temperature was chosen to be below the glass transition temperature o f the adhesive. During temperature ramps and holds only a nominal force o f 0.05 N was applied to the'specimen to maintain contact between the load head and the specimen.  Specimens were designed to deflect 50 microns at their maximum stiffness under an applied force o f approximately 1 N to maximize measurement resolution. This resulted in the selection o f a specimen substrate thickness o f 0.16 m m and a patch thickness o f 1/16" or 1.8575 mm. The applied strain was approximately 375 pie, as calculated using Equation (67)  s = K* w =  L  V^ where t  T  w  2  J  is the total specimen thickness and w is the deflection [82].  50  (67)  Chapter 4 Methods 4.5 FM300 Modulus Development  4.5.1  Objective  The objective o f these tests was to determine the instantaneous modulus o f F M 3 0 0 as a function o f the instantaneous temperature and the material's instantaneous glass transition temperature. Bimaterial beams consisting o f F M 3 0 0 film adhesive adhered to a steel shim were dynamically tested in a Rheometric Scientific Inc. D M T A temperatures.  V at different cure  Test data was then used in conjunction with a cure kinetics model and glass  transition temperature model to plot the relation between modulus and T - T g . A piecewise defined model was then fit to the resulting data.  4.5.2  Specimen Preparation  Bimaterial beam specimens were prepared by adhering F M 3 0 0 to a metallic substrate. The substrate consisted o f steel shims, nominally 45 m m long, 0.16 m m thick, and 6.4 m m wide. Preparation consisted o f sanding the shims with 320-grit sandpaper, cleaning with acetone and wiping dry. The dimensions o f the shims (thickness and width) were then measured at three locations along the shim with a digital micrometer and recorded. The shims were then wiped clean with acetone once more to remove any contaminants that may have been deposited on the shims during measurement. One layer o f F M 3 0 0 film adhesive was then applied and excess adhesive was trimmed. The peel ply was then carefully removed on half the specimens, while the other half retained the peel ply throughout the experiment. The specimens were then wrapped lightly in F E P before being loaded into the D M T A .  4.5.3  Experimental Details  In order to determine F M 3 0 0 ' s modulus development as a function o f degree o f cure, threepoint bend specimens were tested in  Dynamic Temperature Ramp Mode. Specimens were  subjected to a cure cycle that consisted o f a 2.5°C/min ramp to a specified cure temperature and then a prescribed hold, before being allowed to cool to room temperature.  51  Chapter 4 Methods During the cure cycle a controlled cyclic displacement, w(t), was applied as an offset fully reversing cycle, as shown i n  Figure 4.4, with a frequency o f 0.1 H z and an amplitude o f 100  um. This corresponded to a strain amplitude (s)  of 2.0* 10" as found using Equation (67). 4  A n offset o f 125% o f the amplitude was used.  Phase Shift  Force Displacement  Amplitude  Figure 4.4 - DMA multi-frequency - strain mode  Tests were conducted at four isothermal cure temperatures. Each test was,run until the cure kinetics model predicted a cessation o f the cure process. T w o specimens were tested at each cure temperature: One specimen with the peel-ply removed and another with the peel ply on the adhesive. Test temperatures, durations, and maximum degrees o f cure are listed in Table  4.2.  Table 4.2 - Test Temperatures, Durations, and Maximum Degree of Cure  Specimen  Control  Hold Time  Final  Temperature (°C)  Temperature (°C)  (min)  DOC*  1  120  101.0  404  0.86  2  140  119.4  168  0.92  3  160  137.0  127  0.98  4  180  152.0  60  1.00  Test  '* as predicted by cure kinetics model  52  Chapter 4 Methods 4.6 Bonded Composite Patch Repair  4.6.1  Objective  The objective o f this set o f experiments was to develop and validate a simple and effective technique for cure cycle optimization o f bonded composite patch repairs.  A Rheometric  Scientific Inc. D M T A V was used to measure the deflection o f a bonded composite patch repair specimen in-situ during the entire cure cycle. The experimental data was then compared to the results o f a modified C H I L E model, which incorporates both cure and temperature dependant behaviour for the adhesive.  4.6.2 Bonded  Specimen Preparation composite patch  repair  specimens  were  created  by  adhesively bonding a  unidirectional composite patch to a metallic substrate using F M 3 0 0 adhesive. A [0]2 panel o f AS4/3501-6 was prepared at N R C - I A R according the manufacturer's recommended cure cycle and cut with a slow-speed diamond saw into specimens nominally 45 m m long, 6.4 m m wide, and approximately 0.5 m m thick. Steel shims nominally 45 m m long, 0.16 mm thick, and 6.4 m m wide were prepared by sanding the surface with 360-grit sand paper and then wiping them with acetone. One layer of F M 3 0 0 was then applied to the steel shim and trimmed to size. The AS4/3501-6 patch was then laid on the adhesive and pressed in place. Thicknesses and widths o f both the steel substrate and the AS4/3501-6 patch were measured at three locations along the beam. After cure, the total system thickness was measured at three locations. The adhesive layer thickness, on the order o f 0.20-0.30 m m , was found as the difference between the total specimen thickness and the sum o f the patch and substrate thicknesses. The system width was taken as the average o f the steel and patch widths.  4.6.3  Experimental Details  A schematic o f the bonded composite patch repair specimen is shown i n  Figure 4.5. The  specimen was placed in the three-point bend fixture o f the D M A , where the deflection generated by the thermal expansion mismatch between the patch and the substrate throughout a complete cure cycle was measured. To ensure that the load head maintained contact with 53  Chapter 4 Methods the specimen throughout the cure cycle, a constant nominal force o f 0.05 N was applied to the specimen.  Figure 4.5 - Schematic of Specimen Geometry and Loading Conditions  A series o f cure cycles were investigated, which fit broadly into three categories: one-step cycles, post-cure cycles, and two-step cycles. Three different one-step  cycles were  investigated, consisting o f a heat-up ramp to the dwell temperature and then a cool-down to room temperature. Similarly, three post-cure cycles were investigated. These consisted of a one-step cycle followed by a heat up to 177°C, a 5 minute hold and another cool-down to room temperature. T w o different two-step cycles were investigated, consisting o f a heat-up ramp to a first dwell temperature followed by a heat-up ramp to a second dwell temperature and then a cool-down to room temperature. These cycles were run with three different ramp rates between the first and second dwell, resulting in a total o f six permutations. The cure cycles investigated are summarized in Table 4.3.  54  Chapter 4 Methods Table 4.3 - Cycles specifications  Cycle Dwell Time  H e a t i n g Rate  C o o l i n g Rate  Description  T e m p (°C)  (min)  (°C/min)  (°C/min)  [1]  1 step - 177°C  177  60  2.50  2.50  [2]  1 step - 150°C  150  160  2.50  2.50  [3]  1 step - 120°C  120  480  2.50  2.50  177°C + Post Cure  177  60  2.50  2.50  [4]  177  5  2.50  2.50  150°C + Post Cure  150  160  2.50  2.50  [5]  177  5  2.50  2.50  120°C + Post Cure  120  480  2.50  2.50  [6]  177  5  2.50  2.50  2 step - 1 5 5 ° C / 1 7 7 ° C  155  60  2.50  (2.5°C/min)  177  30  2.50  2 step - 1 2 0 ° C / 1 7 7 ° C  120  330  2.50  (2.50°C/min)  177  30  2.50  2 step - 1 5 5 ° C / 1 7 7 ° C  155  60  2.50  (1.00°C/min)  177  30  1.00  2 step - 1 2 0 ° C / 1 7 7 ° C  120  330  2.50  (1.00°C/min)  177  30  1.00  2 step - 1 5 5 ° C / 1 7 7 ° C  155  60  2.50  (0.10°C/min)  177  30  0.10  2 step - 1 2 0 ° C / 1 7 7 ° C  120  330  2.50  (0.10°C/min)  177  30  0.10  [V]  [8]  [9]  [10]  [11]  [12]  55  2.50  2.50  2.50  2.50  2.50  2.50  Chapter 5 Results and Discussion  5. Results and Discussion This chapter presents the results and discussion o f the experimental program that was undertaken to validate the D M A beam technique. In the first section, results o f bimaterial beam stress relaxation tests conducted on monolithic steel and Lexan specimens, as well as bimaterial steel/Lexan specimens are presented. Test results show that the stress relaxation behaviour o f Lexan can be extracted from the stress relaxation behaviour o f a bimaterial beam. The second section presents modulus characterization tests conducted on bimaterial steel/FM300 specimens. Test results show that the instantaneous elastic modulus of F M 3 0 0 can be modeled as a function o f the difference between the material's  instantaneous  temperature and its instantaneous glass transition temperature. The third section presents results o f bonded composite patch repair specimens cured using a variety o f cure cycles and shows that the D M A can be used to obtain an in-depth look at the development o f warpage throughout a cure cycle. M o d e l results show that a modified C H I L E model can accurately predict the warpage. M o d e l Sensitivities, cycle times, real versus idealized cycles, and the effects o f thermal softening are also investigated.  5.1  5.1.1  Bimaterial beam stress relaxation  Effect of the A d h e s i v e layer  In order to ensure that the use o f a thin adhesive layer does not affect the behaviour o f bimaterial beam specimens, results o f steel/adhesive/steel samples were compared to those o f monolithic steel samples. Temperature ramp dynamic tests were conducted to ensure the system modulus corresponded to the monolithic steel modulus throughout the temperature range o f interest. Relaxation tests were also conducted to ensure that the adhesive layer did not cause time-dependant effects.  Figure 5.1 shows results o f 30 minute relaxation tests performed on monolithic steel specimens i n 10 °C increments from 30 °C to 110 °C, which correspond to expected values of 185-195 G P a . This modulus value can be compared to the results o f dynamic tests  56  Chapter 5 Results and Discussion performed on Steel/Adhesive/Steel samples with a temperature ramp to 110 °C, as shown i n  Figure 5.2.  -260-  Increasing Temperature  -160-  -1-2S•a o S  o It  -30"C  40°C  50"C  60°C  70°C  80"C  100  10  0.1  0.01  90°C  Time (min)  Figure 5.1 - Steel Specimen - Relaxation Modulus  200  200  150  -Storage Modulus (GPa) - Temperature °C  10  15  20  25  30  35  40  45  50  Time (min)  Figure 5.2 - Dynamic testing for Steel/EA9392/Steel (Frequency = 0.1 Hz)  57  Chapter 5 Results and Discussion The system's response throughout the temperature range shows a modulus whose magnitude is equivalent to that o f the stress relaxation tests o f monolithic steel specimens. From this we can also conclude that the system response is insensitive to the adhesive layer properties in this temperature range. Since the system's response remains relatively constant throughout the temperature range, we can also conclude that the adhesive's glass transition temperature is above 110°C, which agrees with the adhesive's recommended maximum operating temperature o f 177°C [81].  Thirty minute stress relaxation tests were then performed on steel/EA9392/steel specimens in 10°C increments from 30°C to 110°C. The results in  Figure 5.3 show a near constant  modulus throughout the temperature range with no time effects. A s the system modulus is once again consistent with that obtained for monolithic steel specimens, these tests confirm that under these conditions, the adhesive layer does not have a marked effect on the system results.  200 INCREASING I TEMPERATURE  160  120  80  40 —  30°C — 4 0 ° C  —50°C  —  60°C — 7 0 ° C 0  0.01  0.1  —80°C  —90°C  I  i  1  10  —110°C  Time Figure 5.3 - Steel/EA9392/Steel Average System Relaxation Modulus  58  100  Chapter 5 Results and Discussion 5.1.2  B i m a t e r i a l beam stress relaxation results  In order to validate the bimaterial beam technique for the characterization of the timedependent properties o f a viscoelastic material, three sets o f tests were performed. First, 30 minute stress relaxation tests on monolithic steel and Lexan specimens were performed in 10 °C increments from 30 ° C to 110 °C. Averaged results for steel were previously shown in  Figure 5.1, and the averaged results for Lexan are shown in Figure 5.4. While the results for steel show insensitivity to both temperature and time, Lexan results show the classic viscoelastic response, where the modulus decays with time and the rate o f decay accelerates as the temperature is increased. Bimaterial specimens consisting o f steel, Hysol E A 9 3 9 2 adhesive, and Lexan were then prepared and similar stress relaxation tests were performed. The system response, shown in  Figure 5.5, also shows a viscoelastic response. The  viscoelastic properties o f Lexan were then determined from the system response using  Equations (26)-(28) and are shown in Figure 5.6.  30°C — 4 0 ° C  0.01  0.1  50°C — 6 0 ° C  70°C  Time (min)  80°C  90°C — 1 0 0 ° C — 1 1 0 ° C  10  Figure 5.4 - Lexan Specimens - Average Relaxation Modulus (based on 3 tests)  59  100  Chapter 5 Results and Discussion  ro  a O  (A 3  O  0  ro x ro  30-C -^-40"C — 50-C ~ ^ 6 0 ° C  — 70"C ^ 8 0 ° C  9CTC — 1 0 0 ° C  0.1  0 . 0 1  -^110°cl  10  100  Time (min) Figure 5.5 - Steel/EA9392/Lexan Specimens - Average System Relaxation Modulus (based on 3 tests)  3 0 ° C  0 . 0 1  —  4  0  °  C  5 0 ° C  6 0 ° C  —  7  0  °  C  0 . 1  Time (min)  8 0 ° C  9  0  -  1 0 0 ° C  —  1  1  0  °  10  Figure 5.6 - Steel/EA9392/Lexan Specimens - Average Lexan Relaxation Modulus (based on 3 test)  60  C  1 0 0  Chapter 5 Results and Discussion Table 5.1 -Stress relaxation of Lexan - monolithic versus system response  Lexan Modulus (GPa)  TIME  110°C  80°C  50°C  (min) Monolithic  System  %  Monolithic  System  %  Monolithic  System  %  0.08  2.04  2.08  1.77  1.93  2.01  4.15  1.81  1.92  5.95  2.91  2.00  2.01  0.54  1.85  1.94  4.97  1.65  1.73  447  5.91  1.98  1.98  0.02  1.83  1.91  4.35  1.59  1.65  4.32  8.91  1.97  1.97  0.26  1.81  1.88  4.08  1.54  1.60  4.26  11.91  1.96  1.95  0.44  1.79  1.87  4.09  1.50  1.57  4 77  14.91  1.96  1.95  0.45  1.78  1.85  3.83  1.47  1.54  5.07  17.91  1.95  1.94  0.68  1.77  1.84  3.84  1.43  1.52  5.55  20.91  1.95  1.93  0.83  1.76  1.83  3.70  1.41  1.50  6.42  23.91  1.94  1.92  0.93  1.75  1.82  3.77  1.38  1.48  7.16  26.91  1.94  1.92  0.83  1.75  1.81  3.69  1.36  1.47  7.73  29.91  1.93  1.92  0.86  1.74  1.81  5.56"  1.34  1.45  8.43  From the data presented in Table 5.1, we see good correlation between the stress relaxation data for the monolithic Lexan specimen tested bonded to the steel substrate  (Figure 5.4) and the reduced data for Lexan when  (Figure 5.6). Error bars for both the monolithic Lexan  and the reduced Lexan data from the bi-material system were included i n the figures for data at 50°C and for 110°C. The data shows a scatter o f less than ± 5 % . The error bars are representative o f the scatter seen at all temperatures. A n anomaly appears at the lowest test temperature (30°C) for the system response, where the modulus is seen to increase slightly with time. N o explanation for this is given, however we note that this increase represents less than a 1% increase over the minimum modulus value for this temperature.  5.1.3  Sources of e r r o r  The major source o f error in this experiment is machine compliance. Although many newer D M A models (such as the T A D M A Q800) include a machine compliance calibration, the calibration procedure used for the R S I D M T A V does not include a calibration to determine  61  Chapter 5 Results and Discussion the stiffness o f the fixtures. Thus the force/displacement data collected by the D M A is result of a fixture response superposed on the specimen response. N o attempt was made to characterize the stiffness response o f the fixtures.  A second source o f error is the unknown initial state o f the material. The Lexan specimens were not pre-conditioned and so any residual stresses present in the specimen before testing may affect the relaxation response slightly and may account for some o f the observed variability.  5.2  5.2.1  Modulus Development  F M 3 0 0 M o d u l u s Development  The bimaterial beam development  method  can be used to explore the  o f mechanical properties  and the  advancement  relationship between  the  o f chemical cure. The  development o f the system storage modulus o f a bimaterial beam specimen is monitored as samples are cured with a series o f different temperature cycles. The modulus of the curing resin layer can then be extracted from the system response using the bimaterial beam analysis presented i n Section 3.5.  Results obtained with this method, while agreeing qualitatively with expected trends, did not correspond quantitatively to values in the literature. Cytec lists the room temperature shear modulus o f F M 3 0 0 as 908 M P a [83]. Using Hooke's law for an isotropic material, Equation (36) with a Poisson's ratio o f 0.4 yields an unrelaxed modulus o f 2.54GPa. LaPlante and LeeSullivan [84], investigating fully cured neat F M 3 0 0 adhesive specimens, found the unrelaxed modulus,  E, u  to be 2.69 G P a and the fully relaxed modulus,  E, x  to be 18 kPa.  Experimentally determined values for the unrelaxed modulus i n the current study were, however, found to be nearly twice the value quoted in the literature. This is believed to be an experimental artefact, as the experimental method offers no means o f controlling the thickness o f the resin layer, to which the calculation o f the modulus is very sensitive. The experimentally determined instantaneous modulus, E  ,  mcal  62  was thus calibrated by scaling the  Chapter 5 Results and Discussion experimentally determined moduli between the known limits. The experimental unrelaxed modulus, £ modulus,  m a x  E  , was defined as the maximum  ,  a=0i  was defined as  instantaneous modulus,  E ,  uncal  and the experimental fully relaxed  uncal  at gelation (degree o f cure o f 0.5). The calibrated  was then found as  cal  E  = E„ + (E. - E^JT  5  cal  Figure 5.7 shows  E  E  (68)  representative results for a cure cycle o f 160°C for 127 minutes. The cure  cycle temperature, system storage modulus, uncalibrated and calibrated resin modulus are shown.  Figure 5.7 - Typical Modulus development as a function of time  Simultaneously, using the cure kinetics model o f section 3.3 and the glass transition temperature model o f section 3.4, the development o f glass transition temperature through the same temperature cycle can be calculated. Figure 5.8 shows the development o f glass transition temperature for the same 160°C cycle.  63  Chapter 5 Results and Discussion  Figure 5.8 - Typical Tg development versus time  A s both modulus and glass transition temperatures are functions o f the cure cycle, the resin's modulus can then be plotted against T -T . g  Figure 5.9 shows a typical resin instantaneous  modulus versus T - T curve for the 160°C cycle. g  0_  •a o S  Figure 5.9 - Typical FM300 modulus versus T-Tg  64  Chapter 5 Results and Discussion The results o f a series o f cure cycles can then be plotted on the same graph. Figure 5.10 shows results obtained for the adhesive FM300. A l l four cycles studied show a similar response. F o r the purposes o f this analysis, all data collected pre-gelation is ignored and is not shown in the graphs. In the pre-gelation regime, the resin's viscosity drops and the resin may flow. A s this method offers no dimensional control, any data collected in this regime is unreliable due to variations in the system's geometry.  3.00  -200  -150  -100  0  -50  50  100  150  200  T-Tg  Figure 5.10 - Modulus versus T-Tg for FM300  Superimposed over the test data, Figure 5.10 also shows the modulus model for F M 3 0 0 as presented in  Section 3.5. The model constants o f Equation (35), which were selected to  provide a best fit to the experimental data, are summarized in fable 5.2.  Table 5.2 - Modulus model constants  T  A  = 30°C  7/ =-10°C c 2  E =0.02GPa  E =\.\GPa  cc =0.5  A* =0.40393 GPa  c]  gel  c2  65  T = -90°C c3  = 2.69 GPa  K* = - 0 . 1 0 0 1 8 ° C  Chapter 5 Results and Discussion 5.2.2  Sources of Error  The major source o f error i n this test methodology relates to dimensional stability. Initially the adhesive is uncured and very soft, and accurate pre-test measurement o f the thickness is not feasible. During the experiment, the adhesive is unconstrained and changes to the thickness may occur. A s the neat adhesive cures and the viscosity drops, the adhesive may flow causing an uneven, cratered surface, as seen in  Figure 5.11, which shows a typical  specimen post-test. Since vacuum bagging cannot be used i n this method, out gassing adds to the creation o f a pockmarked, uneven surface. In an effort to reduce flow, half the specimens were tested without removing the peel-ply. Visual inspection shows that while this attempt did improve the surface, experimental results were comparable to specimens that were tested without the peel ply.  Figure 5.11 - Modulus development specimens - with and without peel-ply  Another thickness related issue is that the model does not take cure shrinkage into account, nor does it incorporate thermal expansion. A s neat resins have relatively high coefficients o f thermal expansion and may shrink by as much as 2-6% during cure [57,64,69] these phenomena may have an effect on the results.  These errors justify the need to calibrate the modulus values between known relaxed and unrelaxed moduli from monolithic resin specimens, which can be determined with much better accuracy. 66  Chapter 5 Results and Discussion 5.3 Bonded Composite Patch Repair  5.3.1  Presentation of Results  Throughout this work, results from representative cycles o f bonded composite patch repair specimens cured under a variety o f cure cycles are presented. Results show experimental deflections, model predictions and the difference between them. The development o f glass transition temperature and the instantaneous shear modulus are also shown, to aid in obtaining a better understanding of the factors that affect the development o f thermal residual stresses and warpage.  Although results o f thermal residual deflection tests can be displayed in the classical time domain, a number o f important phenomena are more apparent temperature  domain. Firstly,  the  temperature  domain  when viewed in the  linearizes temperature  ramps,  eliminating artefacts in the time domain response caused by loose control o f ramp rates, overshoots, etc. Thus it allows one to easily distinguish between linear elastic and non-linear elastic  temperature-deflection  response.  Second,  the  temperature  domain  contracts  temperature dwells, magnifying phenomena occurring at a constant temperature; Phenomena such as creep and relaxation are displayed as vertical lines occurring at a constant temperature instead o f slow drifts. Throughout this chapter, results are presented in both the time and temperature domain.  Figure 5.12 shows a representative profile for a one-step cycle in the time domain, while Figure 5.13 shows the profile in the temperature domain. A number o f characteristic features can be observed. First, during heat up to the first hold, no warpage is measured. This is expected, as during this stage, the adhesive is uncured and the system is uncoupled. Second, during the first isothermal hold, no response is noted; the system is held isothermally and no stresses have been introduced. Third, during cool down, the resulting warpage for non-linear elastic materials differs from that o f linear elastic materials. While linear elastic materials show warpage that is linearly proportional to the change i n temperature, non-linear elastic materials may show different results.  67  Chapter 5 Results and Discussion  Vitrification  * Temperature Cycle * Glass Transition Temperature * Degree of Cure  Gelation*  * Deflection - Linear Elastic Response • Deflection - Non-Linear Elastic Response  Time Figure 5.12 - Characteristic time domain 1-step cure cycle response  Cure Temperature Figure 5.13 - Characteristic temperature domain 1-step cure cycle response  Two-step cycles show distinctly different characteristics, as shown in domain) and  Figure 5.15 (temperature domain).  Figure 5.14 (time  The response during the ramp to the first  hold and during the first hold is similar to that o f the one-step cycles. During the second heat up, linear elastic and non-linear elastic materials once again show differing responses. Elastic materials  show a "negative" warpage  that is linearly proportional to the change in  temperature. They show no response during the second hold and then follow the same slope during cool down in the "positive" warpage direction until the specimen has cooled to room temperature.  68  Chapter 5 Results and Discussion Non-linear elastic materials, on the other hand, show a more complex response. Although during heat up to the second hold they also exhibit a "negative" warpage that increases with temperature, the magnitude o f the warpage may be less than that o f a linear elastic material due to thermal softening. Proper characterization o f the material's intrinsic properties (degree of cure, glass transition temperature, etc.) in this region is vital to accurately capture the response o f the specimens. The development o f T up to this point is limited by the g  temperature o f the first hold, which retards the cure process due to diffusion. This region thus corresponds to a state where the material's behaviour is highly dependant on these properties.  During the second temperature hold no change in deflection is seen. Finally, during cooldown, the system exhibits behaviour similar to that seen in the one-step cycles.  s £ <— a *; o o g  ^Vitrification  • Glass Transition Temperature * Degree of Cure  • Gelation  Temperature Cycle * Deflection - Non-Linear Elastic Response * Deflection - Linear Elastic Response  Figure 5.14 - Characteristic time domain 2-step cure cycle response  69  Chapter 5 Results and Discussion  • Non-Linear Elastic Response - Cool Down » Second Isothermal Hold Cure Temperature  Linear Elastic Response 2" Heat up and Cool Down • Non-Linear Elastic Response • - 2 Heat-up d  nd  Figure 5.15 - Characteristic temperature domain 2-step cure cycle response  5.3.2  Model Implementation  Material Constants The material constants for the patch and substrate where taken from the literature, as no characterization tests were performed. A modulus o f 200 G P a and a coefficient o f thermal expansion o f 11-17  \iz/°C are listed for the steel substrate [4], while a modulus o f 140 G P a  and a coefficient o f thermal expansion o f - 0 . 5 u.e/°C are listed for the AS4/3501-6 patch in the 0° direction [85]. Characterization tests were performed on the adhesive to determine its instantaneous modulus and the results are presented in  section 5.2. The modulus is shown to  be a function o f the adhesive's instantaneous temperature and glass transition temperature.  Geometry The specimen length o f 40 mm is based on the manufacturer specified distance between the supports o f the three-point bend fixture used in the experimental technique. The patch and substrate thicknesses are measured before the specimen is assembled. The adhesive thickness  70  Chapter 5 Results and Discussion is determined as the difference between the total specimen thickness (as measured post-test) and the sum o f the patch and substrate thicknesses. A slight non-uniform thickness was found, with the adhesive layer being thicker at the ends and thinner in the middle o f the specimen. The adhesive layer thickness used in the model was thus taken to be slightly less than the average thickness, as the deflection is a strong function o f the thickness and the average is not a true representation o f the specimen thickness.  W a r p a g e Prediction Using the D A Q temperature profile, the cure cycle is stepped through using a spreadsheet application and an associated macro language. For each time-step, the degree o f cure is calculated using the cure kinetics model o f Rogers and Lee-Sullivan presented in section  3.3.  The glass transition temperature is then calculated using the glass transition temperature development model presented in  section 3.4. The instantaneous modulus can then be  determined using the temperature and glass transition temperature corresponding to that time-step and the modulus development model presented in section  The warpage model presented in  3.5.  section 3.6 is used to predict the out o f plane deflection of  the bonded composite patch repair specimens. The deflection is assumed to be zero until the end of the first temperature hold: during the ramp to the first temperature hold the adhesive is a viscous liquid that cannot develop stresses and during the first isothermal hold no thermally induced effects occur. A s the cycle progresses, the adhesive's instantaneous modulus is compared to that o f the previous time-step. I f the modulus has dropped, then thermal softening is assumed to have occurred. Equation (46) is then used to predict the warpage at that time-step. Since the modulus history o f the specimen is known, ^ treated as AG = (G ) - (G ),_,. a  a  (  a  ^d{r-T ) s  is  I f the modulus increases or remains the same, thermal  softening does not occur, Equation (46) simplifies to Equation (45), and basic C H I L E is used to predict the warpage at that time-step.  Two model calibrations were performed due to some uncertainty i n the model input. First, coefficients o f thermal expansion were chosen that matched the experimentally determined  71  Chapter 5 Results and Discussion slope of deflection versus temperature during cool down. This resulted i n the selection of a ACTE o f 15±1 p,e/°C, which agrees well with literature values for the coefficient o f thermal expansion o f steel and AS4/3501-6.  Second, the average adhesive layer thickness was  reduced by 10% to account for the non-uniform adhesive layer exhibited by the specimens (thinner at the middle o f the specimen and thicker at the ends). While this allowed for better predictions o f the  experimental deflections during post-cure  or at the  second  hold  temperature, it did not have a considerable effect on final deflections. The sensitivity o f the model to adhesive layer thickness is discussed further in section  5.3.3  5.8.1.  One-step cycle  The first method o f cure cycle optimization investigated was reduction o f the temperature.  Three  one-step cycles were  examined  (177°C,  150°C,  and  cure  120°C)  as  summarized i n Table 5.3. The 177°C cycle is used as the baseline, standard cycle for warpage comparisons.  Table 5.3 - One-step cure cycles  (Itycle Description  Temp  Dwell Time  (°Q  (min)  Heating Rate  Cooling Rate  (°C/min)  (°C/min)  [1]  lstep-177°C  177  60  2.50  2.50  [2]  lstep-150°C  150  160  2.50  2.50  [3]  1 step - 120°C  120  480  2.50  2.50  The results o f a representative 177°C cycle are shown in Figure 5.16 (in the time domain) and  Figure 5.17 (in the temperature domain). The time domain graph shows the cure cycle  temperature, the deflection measured by the D M A , the predicted degree o f cure, and the predicted glass transition temperature. The temperature domain graph shows the deflection measured by the D M A , the degree o f cure, and the glass transition temperature.  72  Chapter 5 Results and Discussion  One-step cycle - 177°C Deflection: 0.458  200  250  300  350  400  450  Time (min) • Deflection  DOC  - Temperature  "Tg  Figure 5.16 - Representative time domain experimental results for one-step cycles  One-step cycle - 177°C Deflection: 0.458  60  80  100  120  140  160  180  200  Cure Temperature (C) —  Deflect io n  —  DOC  Temperature  — T g  Figure 5.17 - Representative temperature domain experimental results for one-step cycles  73  Chapter 5 Results and Discussion These graphs illustrate a number o f important observations. First, an initial deflection is observed during heat up with a magnitude of approximately 0.20 m m . Post-test thickness measurements show a reduction in the adhesive layer thickness o f approximately the same magnitude. Post-test visual inspections of the test specimens shows that some o f the adhesive squeezed out o f the samples during the test, as can be seen in  Figure 5.18. The initial  displacement o f the load head is thus assumed to be due to a thinning o f the adhesive layer caused by an initial drop in the adhesive's viscosity during heat-up. A s this initial displacement is an experimental artefact due to the sample size and geometry, the deflections are zeroed at the end o f the first hold. The zeroed results for this cycle, along with the model deflections and the difference between the experimental and model deflection, are shown again in  Figure 5.19 (in the time domain) and Figure 5.20 (in the temperature domain).  Second, the deflection increases monotonically with temperature drop during cool-down. When viewed i n the temperature domain, a linear relationship between deflection and temperature is easily observed at low temperatures, while a slightly non-linear relationship is seen at high temperatures.  10  20  30  40  50  Figure 5.18 - Bonded composite patch repair specimen - post-cure, showing adhesive layer squeeze out  74  Chapter 5 Results and Discussion  Figure 5.19 - Representative time domain results for one-step cycles  One-step cycle - 177°C Deflection: 0.458  Cure Temperature (°C) —  Experiment  Difference  Model  — S h e a r Modulus  Figure 5.20 - Representative temperature domain results for one-step cycles  75  Chapter 5 Results and Discussion The results for the one-step cure cycles examined are listed in Table 5.4. For each specimen, the experimental deflection at the end o f the cycle, the model deflection at the end o f the cycle, the relative difference, and the degree o f cure as predicted by the model are listed. The deflections and degrees o f cure are then averaged for all specimens cured using the same cycle. The standard deviations are also shown for deflection values. Results show very good agreement between experiments and the model.  The experimental deflection results are also shown graphically i n Figure 5.21, along with the calculated degrees o f cure. Results show that a considerable reduction i n deflection can be achieved by curing at a lower temperature, however this results in a lower final degree of cure. A s mechanical properties at elevated temperatures have been shown to be directly affected by degree o f cure, the drop in degree o f cure is unacceptable for most applications. This illustrates the competing requirements placed on an optimized cure cycle: reduce the final thermally induced stresses, but ensure complete cure. This trend is consistent with that found by Cho and Sun [5] and Djokic et al. for F M 7 3 and F M 3 0 0 [17,72].  Table 5.4 - Experimental Results - One-step cure cycles  Cycle [1] 1 s t e p - 1 7 7 ° C  Deflection  Model  Experiment (mm) Model (mm) Difference (%)  DOC  (a)  0.458  0.458  0.13  0.996  (b)  0.502  0.510  -1.53  0.998  •(c)  0.486  0.506  -4.20  0.997  (d)  0.469  0.480  -2.43  0.997  0.416  0.414  0.62  0.998  0.466  0.473  -1.56  0.997  0.035 (7.48%)  1.75  (e) Average  Standard Deviation 0.029 (6.26%) [2] 1 step- 150°C  (a)  0.406  0.405  0.37  0.966  [3] 1 step - 120°C  (a)  0.335  0.337  -0.63  0.861  (b) Average  0.338  0.338  -0.03  0.868  0.336  0.337  -0.33  0.865  0.001 (0.22%)  0.30  Standard Deviation 0.002 (0.52%)  76  Chapter 5 Results and Discussion  0.55  1.00  • Deflection • Final Degree of Cure 0.00  0.00  o  o o  o  8  CM  Figure 5.21 - Experimental results - One-step cycles  The scatter in the experimental data can largely be explained by variations in the actual specimen geometries. Table 5.5 lists the geometries for the specimens used in the one-step 177°C cycles.  Table 5.5 - Specimen geometries - One-step 177 °C cycles  Substrate  Patch  Adhesive  Total  (mm)  (mm)  (mm)  (mm)  (a)  0.154  0.508  0.266  0.928  (b) (c) (d)  0.155  0.526  0.192  0.873  0.154  0.522  0.207  0.883  0.152  0.535  0.229  0.916  (e)  0.150  0.523  0.287  0.960  Cycle [1] 1 step - 177°C  Figure 5.22 shows the deflection values, both experiment and model, for the 1 step 177°C cure cycles plotted versus adhesive layer thickness. Using the geometry and the cure temperature history o f the 1 step - 177°C (d) specimen, the model was run with adhesive layer thickness o f 0.200, 0.225, 0.250, 0.275, and 0.300 mm. These results are also plotted in  77  Chapter 5 Results and Discussion Figure 5.22 to show the effect o f the adhesive layer thickness. A l l the experimentally determined deflection for this cycle fall very close to this line, highlighting the sensitivity of the experiment to the adhesive layer thickness! Thus the variability i n measured deflection for the 1-step 177°C cured specimens, as shown in Figure 5.21 and Table 5.4, is found to be due to variability in the thickness o f the adhesive layer o f the specimens. The model shows that the results are sensitive to the thickness o f the adhesive layer and is discussed further in  section 5.8.1.  0.600  0.500  -~  0.400  E 0.300  o <D IS a Q  0.200  0.100 +  0.000 0.200  0.225  0.250  0.275  0.300  Adhesive Layer Thickness (mm) I  x Experimental Deflections  o Model Deflections  — Effect of thickness  |  Figure 5.22 - Scaled results for 177°C cycle  5.3.4  Post-cure cycles  Post-curing following l o w temperature cure cycles was examined as a method o f attaining complete cure while reducing the process induced residual stresses. Three post-cure cycles were studied, as summarized i n Table 5.6. These cycles consisted o f the one-step cycles previously investigated followed by a five-minute post-cure at 177 °C.  The results o f a representative 120°C post-cure cycle are shown i n domain) and  Figure 5.23 (in the time  Figure 5.24 (in the temperature domain). The model agrees with experimental  78  Chapter 5 Results and Discussion results at key points in the cycle: the end o f the cool-down from the cure temperature, the end of the post cure hold, and the end o f the cool-down from the post-cure temperature. In the time domain, the model results track the experimental results well. When viewed in the temperature domain, however, the model is seen to deviate from the experimental results during ramps. This is likely caused by small differences between measured temperature and actual temperature in the specimen during temperature ramps, which eventually equilibrate during holds. These types o f effects are magnified in the temperature domain.  Table 5.6 - Post-cure cycles  Cycle Description  [4] 177°C +Post Cure  [5] 150°C + Post Cure  [6] 120°C + Post Cure  Temp  Dwell Time  Heating Rate  Cooling Rate  (°Q  (min)  (°C/min)  (°C/min)  177  60  2.50  2.50  177  5  2.50  2.50  150  160  2.50  2.50  177  5  2.50  2.50  120  480  2.50  2.50  177  5  2.50  2.50  79  Chapter 5 Results and Discussion  Post-cured cycle - 120°C Initial Deflection: 0.338 Post-cured Deflection : 0.451  Time (min) |  ExperimentaI  Model  Difference  Temperature  Tg  Figure 5.23 - Representative time domain results for post-cure cycles  Post-cured cycle - 120°C Initial Deflection:  0.338  Post-cured Deflection .-  0.45?  E _£  c o  8 •&  Q  -0.1  -0.2  Cure Temperature (C) —  Experiment  Model  Difference  — Shear Modulus  Figure 5.24 - Representative temperature domain results for post-cure cycles  80  Chapter 5 Results and Discussion The results for the post-cure cycles examined are listed i n  Table 5.7. In Figure 5.25 the post-  cure results are shown, along with the matching one-step cure cycles for comparison. These help illustrate a number o f observations. Firstly, the final degree o f cure is increased to near 100% by the post-cure, ensuring fully developed mechanical properties. Second, the results dispute the effectiveness o f this approach. Although cure is advanced sufficiently, this is accompanied by a large increase in warpage during the cool-down from the post-cure temperature. These findings agree with those o f Djokic [17]. Although the 120°C post-cured cycle seems to exhibit a larger final deflection than the 150°C post-cured cycle this is due to variability in specimen geometry, as only one specimen at each temperature was tested. Scaled results, similar to those produced for the one-step 177°C cycle, are presented in  Section 5.3.6. Examining Figure 5.24 for some additional insight into the results, we note that during the ramp to the post-cure temperature the adhesive's modulus drops to its minimum value and softening occurs. The softening causes a reduction in the "negative" warpage that is used to counteract the warpage generated during cool-down from the postcure. The 177°C post-cured cycles show that post-curing does not affect the results i f the adhesive is fully cured prior to the post-cure. The thermal softening model is thus shown to accurately predict the development o f warpage through a cure cycle that shows considerable thermal softening.  Table 5.7 - Experimental Results - Post-cure cycles  Model  Deflection Cycle [4] 177°C +post-cure  Difference (%) DOC  Experimental (mm)  Model (mm)  (a)  0.506  0.508  -0.45  0.998  (b)  0.417  0.412  1.20  0.998  0.461  0.460  0.29  0.998  0.044 (9.61%)  0.048 (10.43%)  0.83  Average Standard Deviation [5] 155°C +post-cure  (a)  0.440  0.436  0.86  0.989  [6] 120°C +post-cure  (a)  0.451  0.453  -0.44  0.984  81  Chapter 5 Results and Discussion  0.55  • One-step cycles  0.50 +  £  E. c .2  • Post-cure cycles  • • •  0.45  5'  040  o  £  0.35  0.30  0.00 O  O CL  t  O  CL  +  o  o  o  o  O  O CN  in  Figure 5.25 - Experimental Results - post-cure cycles  5.3.5  Two-step cycles  Another optimization method involves curing the adhesive in two steps - first at a lower cure temperature and then ramping to a higher cure temperature to complete the process. This method presupposes that i f cure can be advanced sufficiently during the first hold such that an increase in modulus occurs, subsequent increases in temperature will create a "negative" thermal residual stress that will then counteract a portion o f the cool-down residual stresses, effectively reducing the final warpage value. T w o two-step cycles were examined, along with three ramp rates between the first and second dwell, resulting in six cycle permutations. These cycles are summarized in Table 5.8.  82  Chapter 5 Results and Discussion Table 5.8 - Two-step cure cycles  Cycle Temp  Dwell Time  Heating Rate  Cooling Rate  (°C)  (min)  (°C/min)  (°C/min)  2 step - 1 5 5 ° C / 1 7 7 ° C  155  60  2.50  (2.50 °C/min)  177  30  2.50  2 step - 1 2 0 ° C / 1 7 7 ° C  120  330  2.50  (2.50 °C/min)  177  30  2.50  2 step - 1 5 5 ° C / 1 7 7 ° C  155  60  2.50  (1.00 °C/min)  177  30  1.00  2 step - 1 2 0 ° C / 1 7 7 ° C  120  330  2.50  (1.00 °C/min)  177  30  1.00  2 step - 1 5 5 ° C / 1 7 7 ° C  155  60  2.50  (0.10°C/min)  177  30  0.10  2 step - 1 2 0 ° C / 1 7 7 ° C  120  330  2.50  (0.10°C/min)  177  30  0.10  Description  [7]  [8]  [9]  [10]  [11]  [12]  2.50  2.50  2.50  2.50  2.50  2.50  The results o f a representative 120/177°C cycle with a 2.5°C/min ramp rate are shown in  Figure 5.26 (in the time domain) and Figure 5.27 (in the temperature domain). The results o f a representative 120/177°C cycle with a 0.1°C/min ramp rate are shown i n Figure time domain) and  5.28 (in the  Figure 5.29 (in the temperature domain).  The model agrees well with the experimental results for two-step cycles. A small offset between the experimental and model deflection is seen at the second hold temperature, which is then carried through the final cool-down. This observation is once again more easily noticed in the temperature domain than in the time domain. The offset is likely due to inherent limitations o f the modulus development model. A s temperature ramps to the second hold, considerable time is spent in the region o f the modulus development curve where errors in the warpage model, in terms o f degree o f cure, glass transition temperature, and modulus development modeling, are most likely to affect results.  83  Chapter 5 Results and Discussion  Two-step c y c l e - 120/177"C  ramp rate = 2.50°C/min Deflection: 0.454  -0.2  I o  Time (min) |  Experimental  Model  — Difference  Temperature  Tg I  Figure 5.26 - Representative time domain results for two-step cycles with a 2.50°C/min ramp rate  Two-step cycle - 120/177"C  '  _O. J 2  I n  Cure Temperature (°C) |  —  Experiment  Model  —Difference  — S h e a r Modulus  Figure 5.27 - Representative temperature domain results for two-step cycles with a 2.50°C/min ramp rate  84  Chapter 5 Results and Discussion  Two-step cycle -120/177°C ramp rate = 0.10°C/min  Deflection:  -0 2  0.416  L„  I  Time (min) |  Experimental  — Model  Difference  Temperature  Tg ]  Figure 5.28 - Representative time domain results for two-step cycles with a 0.10°C/min ramp rate  Two-step cycle - 120/177*C  -0.2  —  —  '  J 0  —  Cure Temperature (°C) I  —  Experiment  Model  — Difference  — Shear Modulus I  Figure 5.29 - Representative temperature domain results for two-step cycles with a 0.10°C/min ramp rate  85  Chapter 5 Results and Discussion The results for the two-step cycles are listed in  Table 5.9. In Figure 5.30 the two-step cycle  results are shown, along with the one-step 177°C cycles for comparison. Looking at the results we note a large degree o f scatter. Once again, this is due to sensitivity o f the results to geometry. Scaled results, similar to those produced for the one-step 177°C cycle, are presented later in  Section 5.3.6. A slight trend to lower deflection values is evident for slow  ramp rate cycles. A t the fast ramp rate (2.5°C/min) the adhesive's shear modulus drops to its minimum value during the ramp to the second hold and thermal softening eliminates the advantages anticipated from the lower dwell cure. A t slower ramp rates, however, the adhesive's modulus remains above the minimum and thus more o f the deflection on heat up is maintained. Two-step 155/177°C cycles with 1.0 and 0.1°C/min ramp rates seem to show a higher warpage value than equivalent two-step 120/177°C cycles, however this is attributed to geometrical differences. The C H I L E model modified to include thermal softening is once again shown to predict the softening response o f a curing adhesive in a complicated cure cycle.  0.55  0.50  E E  0  45  0 0 40 O  1„  Q  35  • 1 Step C y c l e - 1 7 7 C  0  • 2 Step - Ramp = 2.50 C/min • 2 Step - Ramp = 1.00 C/min  0.30  . 2 Step - Ramp = 0.10 C/min  0.00  Figure 5.30 - Experimental Results - two-step cycles  A n important observation is that there are no observable changes in deflection during the holds. This observation suggests that the system does not exhibit viscoelastic behaviour. In the Djokic study o f F M 3 0 0 [17], only the final deflection values for the two-step cycles are 86  Chapter 5 Results and Discussion quoted and thus no comparison o f the development o f warpage can be made. Conversely, i n the Djokic study o f F M 7 3 [72], viscoelastic creep during the second hold is noted and a modulus defined by a power law and the Boltzmann superposition principal are used to model the development o f defection. N o attempt is made in this study to determine the underlying reasons for the fundamental difference in behaviour between F M 7 3 and F M 3 0 0 .  Table 5.9 - Experimental Results - Two-step cycles  Cycle [7] 2 step- 155°C/177°C  Model  Experimental (mm) Model (mm) Difference (%)  DOC  (a)  0.430  0.440  -2.16  0.993  (b)  0.464  0.443  4.52  0.994  0.447  0.442  1.31  0.994  0.017(3.71%)  0.002 (0.49%)  3.34  (a)  0.462  0.473  -2.40  0.994  (b)  0.454  0.465  -2.35  0.995  (c)  0.476  0.472  0.84  0.955  0.464  0.470  -1.28  0.995  0.009(1.96%)  0.004 (0.77%)  1.52  Average Standard Deviation [8] 2 step- 120°C/177°C  Deflection  Average Standard Deviation [9] 2 step- 155°C/177°C  (a)  0.470  0.452  3.79  0.995  [10] 2 step - 120°C/177°C  (a)  0.439  0.418  4.78  0.994  (b)  0.404  0.415  -2.65  0.994  0.422  0.416  1.22  0.994  0.018(4.15%)  0.002 (0.40%)  3.72  Average Standard Deviation [11] 2 step- 155°C/177°C  (a)  0.483  0.470  2.67  0.998  [12] 2 step- 120°C/177°C  (a)  0.416  0.434  -4.33  0.998  (b)  0.421  0.425  -1.07  0.998  (c)  0.417  0.411  1.30  0.998  0.418  0.423  -1.36  0.998  0.002 (0.48%)  0.009 (2.19%)  2.31  Average Standard Deviation  87  Chapter 5 Results and Discussion 5.3.6 Summary A s variations i n specimen geometry were found to contribute to a large scatter i n the experimental results, results were scaled to a standard adhesive layer thickness o f 0.24 m m by running the model using the experimental temperature cycle. Table 5.10 and Figure 5.31 summarize the average deflection values, both experimentally and scaled to account for variations i n the thickness o f the adhesive layer, along with the degree o f cure and the percent reduction i n deflection based on the scaled results with the 1 step 177° cycle used as the baseline. Comparing the experimental results to those scaled to a standard adhesive layer thickness, we note that the thickness o f the adhesive layer can have a large effect on the experimental results. Table 5.10 - Experimental deflections  Cycle  Deflectioil (mm) Scaled Experimental  DOC  Reduction in deflection (%)  [1]  lstep-177°C  0.466  0.489  0.997  -  [2]  lstep-150°C  0.406  0.401  0.966  18  [3]  lstep-120°C  0.336  0.311  0.865  36  [4]  177°C + post-cure  0.461  0.478  0.998  2  [5]  155°C + post-cure  0.440  0.432  0.989  12  [6]  120°C + post-cure  0.451  0.425  0.984  13  0.447  0.439  0.994  10  0.464  0.432  0.995  12  0.470  0.428  0.995  12  0.422  0.400  0.994  18  0.483  0.425  0.998  13  0.418  0.402  0.998  18  [7]  [8]  [9]  [10]  [11]  [12]  2 step - 1 5 5 ° C / 1 7 7 ° C F  (2.5 °C/min) 2 step - 1 2 0 ° C / 1 7 7 ° C F  (2.5 °C/min) 2 step - 1 5 5 ° C / 1 7 7 ° C V  (1.0°C/min) 2 step - 1 2 0 ° C / 1 7 7 ° C v  (1.0°C/min) 2 step - 1 5 5 ° C / 1 7 7 ° C V  (0.1°C/min) 2 step - 1 2 0 ° C / 1 7 7 ° C F  (0.1°C/min)  88  Chapter 5 Results and Discussion  0.60  I Averaged Experimental 0.50  £  0  • Scaled Experimental  4  40  E  c .2  0.30  Tj  % Q  0.20  0.10  0.00  V  In .£  «  *; E  1o  J N  to CN  7  E 3 o  in c  T  E  T  E  Q-D  5T  Figure 5.31 - Experimental deflections  Examining the scaled results we first note that for the one-step cycles, although a reduction in the cure temperature produces a reduction in deflection, a marked drop in the final degree o f cure also occurs. A s many mechanical properties are functions o f the degree o f cure, this drop is unacceptable for most applications. Post-curing the specimens, although increasing the final degree o f cure, negates some o f the benefit o f a lower initial cure temperature. The two-step cycles show that reducing the first hold temperature can result in a reduction in the final deflections. This improvement is more pronounced for slower heating rates between the dwell temperatures, as fast heating rates result in a lag between the temperature increase and the development glass transition temperature.  5.3.7  Sources of Error  The test methodology incorporates a number o f systemic errors. The first source o f error is that the temperature o f the specimens is not measured directly. Although thermocouples are placed approximately 2 mm from the specimens, it is still possible that a small difference in temperature exists between the specimen and the environment. A small temperature lag in the  89  Chapter 5 Results and Discussion specimens during ramps, which equilibrates during holds, may explain the  difference  between experimental and model results during ramps.  Second, due to the small specimen size, a significant amount o f adhesive squeeze out was observed  (Figure 5.18). This resulted in an initial change in total specimen thickness during  the test, which was evident in the displacement o f the load head  (Figure 5.16 and Figure  5.17). A s this occurs early in the cure cycle when the adhesive viscosity drops, the deflection measurements are zeroed to the deflection values at the end o f the first temperature dwell. T o further prove the assumption that this initial deflection is an experimental artefact, a cycle was run where the temperature was ramped to 110°C, cooled to room temperature, ramped once more to 110°C, and cooled to room temperature before a standard 177°C cure cycle was applied. The time domain results o f this test, shown in  Figure 5.32, illustrate the effect o f  adhesive layer thinning. Initially an approximate 0.2 mm deflection is observed which corresponds to a physical change in the geometry o f the specimen and not a thermal effect. This deflection is carried through the remainder o f the experiment, before the expected thermally induced behaviour o f the 177°C cure cycle is observed.  Figure 5.32 - Time domain results for a thickness test  90  Chapter 5 Results and Discussion 5.4  Idealized cycles - Warpage  The experimental results did not exhibit some o f the trends reported by other researchers. Temperature control, which was found to be a major source o f consternation, affects the cycles in three major ways. First, although the temperatures were externally logged with three thermocouples, there is still the distinct possibility that the specimen temperatures differed slightly from the recorded temperatures, most notably during temperature ramps. These differences in temperature affect the specimen's cure history, and thus its shear modulus during the most important portion o f the cycle. Second, loose temperature control creates overshoots when transitioning from ramps to holds. During these overshoots, the adhesive's shear modulus may drop below the intended minimum, causing a softening response which results in a larger than expected final deflection. Third, even though a smooth temperature ramp is programmed, the environmental temperature fluctuates about the target temperature. These oscillations can cause a small drop in modulus, resulting in additional thermal softening and an increase in final warpage.  The effect o f poor temperature control was investigated by running the analytical model for idealized temperature cycles, following the same cycles outlined for the experimental program in Table 4.3. Temperature histories for idealized cure cycles were created such that the ramp rates and hold temperature exactly matched those stipulated i n the cure cycle summary. The experimental cure cycles were simulated on a virtual specimen, with dimensions and properties shown Table 5.11.  Table 5.11 - Virtual specimen geometry and properties  Geometry  M a t e r i a l Properties  Substrate Thickness  0.16  (mm)  Substrate Modulus  200  (GPa)  Patch Thickness  0.50  (mm)  Patch Modulus  140  (GPa)  Total Thickness  0.90  (mm)  Adhesive Thickness  0.24  (mm)  Substrate C T E  15  (pe/°C)  Width  6.40  (mm)  Patch C T E  0  (ps/°C)  40.00  (mm)  Length  '  91  Chapter 5  5.4.1  Results and Discussion  One-Step Cycles  The ideal deflections for the three one-step cycles are shown in Figure 5.33 (a), along with the corresponding shear moduli in Figure 5.33 (b). Results are summarized in section 5.4.4. A near linear slope is observed, which is similar for all of the cycles, and thefinaldeflection value is a function of the cure temperature.  T e m p e r a t u r e (C)  (a)  (b)  Figure 5 . 3 3 - Idealized one-step cure cycles: deflection (a) and shear modulus (b) versus temperature  5.4.2 Post Cure Cycles The ideal deflections for the three post-cure cycles investigated are shown in Figure 5.34 (a), along with the corresponding shear moduli in Figure 5.34 (b).  200  T e m p e r a t u r e (C)  T e m p e r a t u r e (C)  (a)  (b)  Figure 5 . 3 4 - Idealized post-cure cycles: deflection (a) and shear modulus (b) versus temperature  92  Chapter 5 Results and Discussion Results are summarized i n section  5.4.4. The results for the initial heat-up and cool-down  mirror those o f the one-step cycles. During heat-up to the post-cure temperature, a slight softening response is observed, which begins slightly before the initial cure temperature is reached. This effect is most pronounced for the 120°C post-cure cycle, both i n terms o f absolute change i n deflection and relative change i n deflection. The absolute changes i n deflection are due to the increase i n temperature between the first dwell and the post-cure dwell. The relative change i n deflection i n the 120°C post-cure cycle is larger than for the other cycles due to the larger drop i n shear modulus for this cycle, as evidenced i n  Figure  5.34(b).  5.4.3 Two-Step Cycles The ideal deflections for the 155°C/177°C two-step cycles with different heating rates are shown i n Figure 5.35 (a), along with the corresponding shear moduli i n Figure 5.35 (b), while those for the 120°C/177°C two-step cycles with different heating rates are shown i n Figure 5.36 (a), along with the corresponding shear moduli i n Figure 5.36 (b). Results are summarized in  section 5.4.4. From these results a number o f important observations can be  made. First we see that as the heat-up rate decreases, the behaviour o f the adhesive's shear modulus development changes dramatically. For fast heat up rates, the adhesive's shear modulus drops to the fully relaxed value and thus the benefits o f a two-step cure cycle are dramatically reduced. A t slower heat-up rates, however, the minimum adhesive modulus reached is above the fully relaxed value, and thus the benefits o f a two-step cycle are more pronounced. W e also note that even though the heating rate is constant, the development o f adhesive modulus may not be monotonic. This suggests that a non-constant heating rate may produce a more optimized cycle, both i n terms o f thermal residual stresses and i n terms o f cycle time.  93  Chapter 5 Results and  5.4.4  Discussion  Summary of idealized results  Idealized results, summarized in Table 5.12 and Figure 5.37, show that a large reduction in warpage is possible by modifying the cure cycle. Results for idealized one-step cycles mirror those found experimentally; lowering the cure temperature results in a reduction in the induced warpage. A s previously commented, this is generally accompanied by a reduction in the final degree o f cure that may be unacceptable.  94  Chapter 5 Results and Discussion  Idealized results for post-cured cycles also show similar trends to those determined experimentally. While post-curing does increase the final degree o f cure, this is accompanied by a lessening i n the reduction o f warpage. For two-step cycles, however, trends shown by the idealized cycles are more pronounced than those found experimentally. The two-step idealized cycles show that reducing the temperature o f the first dwell can result in an appreciable reduction i n warpage that becomes more pronounced for slower ramp rates between the dwell temperatures. The maximum attainable percent reduction i n deflection for the idealized cycles is shown to be 32% for a two-step 120°C/177°C cycle with a ramp rate of0.1°C/min.  Table 5.12 - Idealized cycle deflections  Deflection  Percent  (mm)  Reduction  DOC  [1] 1 step - 177  0.474  0  0.994  [2] 1 s t e p - 1 5 0  0.388  18  0.915  [3] 1 step - 120  0.294  38  0.839  [4] 177 + post-cure  0.470  [5] 150 + post-cure  0.420  11  0.974  [6] 120 + post-cure  0.399  16  0.970  [7] 2 step - 155/177 (2.5C/min)  0.437  8  0.990  [8] 2 step - 120/177 (2.5C/min)  0.420  11  0.989  [9] 2 step - 155/177 (l.OC/min)  0.429  9  0.992  [10] 2 step - 120/177 (l.OC/min)  0.370  22  0.991  [11] 2 step - 155/177 (O.lC/min)  0.416  12  0.997  [12] 2 step - 120/177 (O.lC/min)  0.322  32  0.997  Cycle  95  1'  0.995  Chapter 5 Results and  Discussion  Figure 5.37 - Idealized cycle deflections  5.4.5  C o m p a r i s o n to experimental results  The results o f the idealized cycles are listed (along with averaged and scaled experimental results) in Table 5.13 and are compared to the scaled experimental results for each cycle studied. Figure 5.38 also shows a graphical representation o f the averaged experimental, scaled experimental, and idealized results.  Results show a large discrepancy between experimental and idealized results for a number o f the cases investigated. Some o f these are corrected by scaling the experimental results to account for variations in the adhesive layer thickness. However, taking variations in the adhesive layer thickness into account did not account all o f the discrepancies.  These  discrepancies are believed to be caused by poor temperature control in the D M A during experimentation, both in terms o f temperature control during ramps and overshoots when transitioning between ramps and holds. The results suggest that the cycles with the lowest hold temperature (120°C) are most sensitive to temperature variations. This may be due to the sensitivity o f the cure kinetics to these lower temperatures, where cure rates are high and small variations impact the development o f warpage.  The relatively long ramps to the  maximum cycle temperature (177°C) may also accentuate these discrepancies.  96  Chapter 5 Results and Discussion  Figure 5.38 - Averaged experimental (left bars), scaled experimental (centre bars), and idealized (right bars) deflections  Table 5.13 - Comparing averaged experimental, scaled experimental, and idealized deflections  Cycles  Deflection s  Percent Difference  Averaged  Scaled  [1] 1 step - 177  0.466  0.489  0.474  3  [2] 1 step - 150  0.406  0.401  0.388  3  [3] 1 step - 120  0.336  0.311  0.294  6  [4] 177 +post-cure  0.461  0.478  0.470  2  [5] 150 + post-cure  0.440  0.432  0.420  3  [6] 120 + post-cure  0.451  0.425  0.399  7  [7] 2 step - 155/177 (2.5C/min)  0.447  0.439  0.437  0  [8] 2 step - 120/177 (2.5C/min)  0.464  0.432  0.420  3  [9] 2 step - 155/177 (l.OC/min)  0.470  0.428  0.429  0  [10]2 step - 120/177 (l.OC/min)  0.422  0.400  0.370  8  [ l l ] 2 s t e p - 155/177 (O.lC/min)  0.483  0.425  0.416  2  [12]2 step - 120/177 (O.lC/min)  0.418  0.402  0.322  25  97  Idealized (Scaled vs. idealized)  Chapter 5 Results and Discussion 5.5 Idealized cycles - Thermal Residual Stresses The purpose o f modifying the cure cycle is to reduce the thermally induced residual stresses in the substrate layer o f a bonded composite patch repair. In the D M A beam technique, warpage is used as a measure o f the residual stresses. A reduction i n warpage thus corresponds to a reduction i n thermally induced residual stresses. Table 5.14 lists the maximum thermally induced normal stresses in the patch and the substrate, as well as the maximum shear stresses i n the adhesive layer for the idealized cycles. These results are shown graphically, along with the warpage for each cycle, i n Figure 5.39 and Figure 5.40. Table 5.15 lists the percent reductions i n warpage and stresses for each cycle'using the onestep 177°C cycle as the baseline. The results show that the percent reduction i n warpage corresponds to a similar reduction i n normal stresses. Shear stresses i n the adhesive, while following the same trends as the normal stresses, do not show the same percent reductions. Table 5.14 - Maximum Stresses  Idealized Cycle  Maxi mum Stress (MPa)  Deflection (mm) Patch,rj Substrate,rr Adhesive,x  [1] 1 step - 177  0.4740  -221  462  16.1  [2] 1 step - 150  0.3878  -181  379  12.6  [3] 1 step - 120  0.2944  -138  288  9.2  [4] 177 + post-cure  0.4695  -220  461  15.3  [5] 150 + post-cure  0.4198  -195  407  14.5  [6] 120 + post-cure  0.3988  -183  383  14.4  [7] 2 step - 155/177 (2.5C/min)  0.4374  -202  422  15.6  [8] 2 step - 120/177 (2.5C/min)  0.4200  -192  402  15.4  [9] 2 step - 155/177 (l.OC/min)  0.4290  -197  413  15.5  [10] 2 step - 120/177 (l.OC/min)  0.3700  -166  347  14.8  [11] 2 step - 155/177 (O.lC/min)  0.4160  -191  400  15.3  [12] 2 step - 120/177 (O.lC/min)  0.3218  -144  300  13.9  98  Chapter 5  Results and  Discussion  NOTE:  500  W  - Patch stresses are compressive - Substrate stresses are tensile  n_  400  m —. 0 re Vi S  n_  0.40  n  re » 300  0.30  11 E  "3  g 200  1* xi  0.20  10  re  ?  E. c  100 4  ^  to •  0.10  f-  h-  >st-c  K  a +  o  CN  in c in E a  a>  in  o CO CN  r-j  I Patch,a  O IN  C  E  O  a . in  CD CN  cn  0.00  t—  h-  K.  in c CO E  o  Q. 0) CN  3 Substrate,a  c  E  C  in  CO  F  o CD  CL a> d  in  cn  CL  cn  CN  CN  CN  CN  o  CN  C  0)  c  F  o d  CN  • Deflection (mm)  Figure 5.39 - Maximum normal stresses in the ^-direction in the patch and the substrate  20  0-  0.50  JI  JI  15  JI  0.40  U)  E  £ k. ra 10 X:  0.30 E  co  cu CO  + 0.20  E  o ai  o  a  £  X Rl  0.10  II II cn  +  ill E  . o  + o  CD CN  I Adhesive,?  o  CN  .t g  o  d  5  CN  i E  co fc co E  in CN  • Deflection (mm)  Figure 5.40 - Maximum shear stresses in the adhesive layer  99  o.oo o CN  E  o  Chapter 5 Results and Discussion Table 5.15 - Percent reductions of maximum stresses  Percent Reduction Cycle  Deflection (mm) Patch,a Substrate,o Adhesive,x  [1] 1 step - 177  -  -  -  -  [2] 1 step - 150  18  18  18  0.22  [3] 1 step - 120  38  38  38  0.43  [4] 177 +post-cure  1  0  0  0.05  [5] 150 + post-cure  11  12  12  0.10  [6] 120 + post-cure  16  17  17  0.11  [7] 2 step - 155/177 (2.5C/min)  08  9  9  0.03  [8] 2 step - 120/177 (2.5C/min)  11  13  13  0.04  [9] 2 step - 155/177 (l.OC/min)  9  11  11  0.04  [10]2 step - 120/177 (l.OC/min)  22  25  25  0.08  [11]2 step - 155/177 (O.lC/min)  12  14  13  0.05  [12]2 step - 120/177 (O.lC/min)  32  35  35  0.14  5.6  Effects of thermal softening on the C H I L E model  The effect o f thermal softening on C H I L E model predictions is investigated by running the C H I L E model, both with and without the thermal softening component, on the scaled experimental cycles presented i n section  5.3.6. Table 5.16 and Figure 5.41 show the resulting  model deflections for both the C H I L E model with thermal softening ( C H I L E w/TS) and the standard C H I L E model ( C H I L E ) , as well as the percent difference between the two models.  From these results we note that the introduction o f a thermal softening component can only result in an increase in predicted deflections. For the 1-step cycles, no difference between the two variations o f the model is observed. This is expected since the thermal softening component o f the C H I L E model only affects the deflection during heat-ups and in the 1 -step cycles the only heat up occurs prior to gelation o f the adhesive.  100  Chapter 5 Results and Discussion  Table 5.16 - Comparing CHILE with thermal hardening  Cycle  C H I L E w/TS  CHILE  Difference  (mm)  (mm)  (%)  [1]  1 step - 1 7 7  0.489  0.489  0.00  [2]  1 step-150  0.401  0.401  0.00  [3]  1 step - 120  0.311  0.311  0.00  [4]  177 + post-cure  0.478  0.483  -1.05  [5]  155 + post-cure  0.433  0.412  4.85  [6]  120 +post-cure  0.425  0.383  9.88  [7] : step - 155°C / 1 7 7 ° C (2.5 °C/min)  0.439  0.424  3.42  [8] : step - 120°C /177°C (2.5 °C/min)  0.432  0.394  8.80  [9] : step - 155°C /177°C (1.0 °C/min)  0.429  0.418  2.56  [10] : step - 120°C /177°C (1.0 °C/min)  0.400  0.363  9.25  [11] : step - 155°C /177°C (0.1 °C/min)  0.425  0.407  4.24  [12] : step - 155°C /177°C (2.5 °C/min)  0.402  0.318  20.90  0.50  -i  Figure 5.41 - Comparing the standard CHILE model with the modified, thermal softening CHILE model  101  Chapter 5 Results and Discussion  Figure 5.42 - Effect of thermal softening on a post cured 120°C idealized cure cycle  Figure 5.43 - Effect of thermal softening on a 2-step 155°C/177°C idealized cure cycle  102  Chapter 5 Results and Discussion with a 2.50°C/inin ramp rate Two-step cycle -1 20/177»C r a m p r a t e = 2 . 5 0 °C / m i n  CHILE CHILE  deflection. 0.432  w/TS  deflection Difference.  mm  0.394 mm 8.80%  Cure Temperature (°C) CHILE with Thermal Softening  -CHILE  Difference  Shear Modulus  Figure 5.44 - Effect of thermal softening on a 2-step 120°C/177°C idealized cure cycle with a 2.50°C/min ramp rate Two-step cycle - 120/177"C ramp rate = 0.10"C/min  CHILE CHILE  deflection:  w/TS deflection. Difference:  0.402  mm  0.318 mm 20.90%  Cure Temperature (°C) -CHILE with Thermal Softening  CHILE  Difference  Shear Modulus  Figure 5.45 - Effect of thermal softening on a 2-step 120°C/177°C idealized cure cycle with a 0.10°C/min ramp rate  103  Chapter 5 Results and  Discussion  For post-cure cycles, the effect o f thermal softening increases as the initial cure temperature decreases. The results o f an idealized 120°C post cured cycle are shown in Figure 5.42, for models run with and without thermal softening. Thermal softening occurs during the reheat portion o f the cycle since the modulus drops as the rate o f development o f the glass transition temperature lags the temperature ramp. Thermal softening causes a reduction in "negative" warpage on the reheat portion o f the cycle, resulting i n a larger final deflection than that obtained with a simple C H I L E model. The slope on cool-down is unaffected by thermal softening.  Similarly, the results for the two-step cycles show that the effect o f thermal softening increases as the first dwell temperature decreases. The results for a two-step 155°C/177°C cure cycle with a ramp rate o f 2.5°C/min are shown i n Figure 5.43, while those for a twostep 120°C/177°C cure cycle with a ramp rate of 2.5°C/min are shown in Figure 5.44. These figures present the model results, both with and without thermal softening. The results for the two-step cycles also show that the effect o f thermal softening becomes more pronounced as the heating rate between first and second dwells is increased. The results o f a two-step 120°C/177°C cure cycle with a ramp rate o f 0.1°C/min are shown in Figure 5.45, for model predictions with and without thermal softening. A slow ramp rate between the first and second dwell allows the development o f glass transition temperature to keep pace with the increase in temperature. Increasing the ramp rate causes the development o f glass transition temperature to lag behind the temperature, resulting in a drop i n modulus and consequently an increased in the effect o f thermal softening.  5.7 Cycle Times While reducing thermal residual stresses is important to the long-term durability and fatigue life o f bonded composite patch repairs, the cycle time is also a concern. A s modified cycles may require more sophisticated heating and temperature control technologies and increased cycle times result in longer downtimes, a compromise between reduced thermal residual stresses and increased cycle times is often required. Table 5.17 lists the cycle times for the idealized cycles investigated, as well as the percent increase i n cycle time over the  104  Chapter 5 Results and Discussion idealized cycles investigated, as well as the percent increase i n cycle time over the manufacturer recommended one-step 177°C cycle. A l s o shown are the idealized warpage values and the corresponding percent decreases i n warpage. A comparison between percent increase i n cycle time and percent reduction i n warpage is shown i n  Figure 5.46. These  values can help determine an acceptable trade off between increased cycle time and reduction in warpage.  Table 5.17 - Cycle Times  Cycles  Cycle Time Percent (minutes)  Idealized  Percent  increase warpage (mm) decrease  [1] 1 step - 177  191  -  0.474  -  [2] 1 step - 150  269  41  0.388  18.2  [3] 1 step - 120  565  196  0.294  37.9  [4] 177 + post-cure  317  66  0.470  0.9  [5] 150 +post-cure  396  108  0.420  11.4  [6] 120 + post-cure  692  263  0.399  15.9  [7] 2 step - 155/177 (2.5C/min)  221  16  0.437  7.7  [8] 2 step - 120/177 (2.5C/min)  491  157  0.420  11.4  [9] 2 step - 155/177 (l.OC/min)  234  23  0.429  9.5  [10]2 step - 120/177 (l.OC/min)  525  175  0.370  21.9  [11]2 step - 155/177 (O.lC/min)  432  127  0.416  12.2  [12]2 step - 120/177 (O.lC/min)  1038  444  0.322  32.1  105  Chapter 5 Results and Discussion  Figure 5.46 - Increase in cycle time and reduction in warpage comparison 1 7 7 ° C  5.8  cycle used as a baseline  Model Sensitivities  The sensitivity o f the cure hardening, instantaneously linear elastic model (modified to include thermal softening effects) to variations in geometry and cure conditions was investigated by running the model under idealized cycle conditions. The sensitivity o f the model to specimen geometry was investigated by modifying the adhesive layer thickness. The sensitivity o f the model to cure conditions was investigated by modifying an idealized two-step cure cycle's ramp rate between the first and second temperature dwells, as well as the maximum cure cycle temperature.  5.8.1  Sensitivity of idealized cycles to the adhesive layer thickness  To determine the sensitivity o f the model to the adhesive layer thickness, a two-step cycle was simulated on the virtual specimen o f section 5.5 with different adhesive thicknesses. The two-step cycle consisted o f a 120°C dwell for 330 minutes followed by a ramp to 177°C at 0.1°C/min and a hold for 30 minutes. The adhesive thicknesses ranged from 0.15 mm to 0.35  106  Chapter 5 Results and Discussion  mm to span the variation in experimentally observed thicknesses. The virtual specimen with an adhesive layer thickness o f 0.24 mm was used as the baseline for comparison.  Two-step cycle - 120/177°C R a m p rate = 0.1  200  "C/min  Time (min) —ta=0.15  ta=0.20  —ta=0.24  —ta=0.30  —ta=0.35  —Temperature  Figure 5.47 - Time domain results for thickness sensitivity of an idealized two-step cycle 0.4  Two-step cycle - 120/177"C Ramp  rate  = 0.1  "C/min  0.8  TO Q-  0.6 O  o 0.4  _  TO 200  in  0.2  -0.2  Temperature (°C) -ta=0.15  ta=0.20  ta=0.24  —ta=0.30  —ta=0.35  —-Shear Modulus  Figure 5.48 - Temperature domain results for thickness sensitivity of an idealized two-step cycle  107  Chapter 5 Results and Discussion Figure 5.47 shows the temperature cycle and the resulting deflections for the different adhesive layer thicknesses in the time domain. Similarly,  Figure 5.48 shows the modulus  development, which is the same for all the cycles, and resulting deflections for the different adhesive layer thicknesses in the temperature domain.  Table 5.18 - Sensitivity to adhesive layer thickness  Thickness  Deflection  Difference  (mm)  (mm)  (%)  0.15  0.3818  18.6503  0.20  0.3463  7.6240  0.24  0.3218  0.0000  0.30  0.2903  -9.7826  0.35  0.2681  -16.6891  The results o f the thickness sensitivity study and the relative differences are tabulated in  Table 5.18 and presented graphically in Figure 5.49. These results illustrate the importance o f accurately measuring thickness. From the results we note that increasing the adhesive layer thickness results in a more compliant system, which corresponds to less warpage at the end o f the cycle. Two-step cycle - 120/177C Ramp  rate = 0.1 C/min  Ramp rate (°C/min) |  • Deflection (mm)  • Relative Difference  |  Figure 5.49 - Sensitivity of an idealized two-step cycle to the adhesive layer thickness  108  Chapter 5 Results and Discussion . 5.8.2 Sensitivity of idealized cycles to the maximum temperature To determine the sensitivity o f the model to temperature overshoots, two-step cycles with different second dwell temperatures were simulated on virtual specimens.  The two-step  cycles consisted o f a 120°C dwell for 330 minutes followed by a ramp to the maximum cure temperature and a hold for 30 minutes. Ramp rates o f 0.1°C/min and 2.5 °C/min were investigated. The second dwell temperature was varied between 170 and 185°C to determine the effect on the final deflection, with a maximum cycle temperature o f 177°C chosen as the baseline for relative difference calculations.  Two-step cycle - 120/177"C  -0.2  J  Time (min) 175  176  177  178  180  185  Rampto175  Rampto185  Figure 5.50 - Time domain results for temperature sensitivity of an idealized two-step cycle with a 0.10 °C/min ramp rate  109  Chapter 5 Results and Discussion  OA  Two-step cycle - 120/177°C Ramp rate = 0.1 "C/min  4  0.3  0.2  ? c .2  0.1  -0 1  -0.2  Temperature (°C) -175  176  -177  178  -180  -185  Figure 5.51 - Temperature domain results for temperature sensitivity of an idealized two-step cycle with a 0.10 °C/min ramp rate Two-step cycle - 120/177°C Ramp rate = 2.5 "C/min  200  0.4  E £  0  3  c  .2 o  i  0.2 INCREASING TEMPERATURE 0.1  0  50  100  150  200  250  300  350  -0.1  Time (min) T=175  T=176  —T=177  T=178  —T=180  —T=185  R a m p to 170  - - R a m p to 1 8 5  Figure 5.52 - Time domain results for temperature sensitivity of an idealized two-step cycle with a 2.50 °C/min ramp rate  110  Chapter 5 Results and Discussion  Cure Temperature (°C) |  T=175  T-176  -—T=177  T=178  T=180  T=185  Figure S.S3 - Temperature domain results for temperature sensitivity of an idealized two-step cycle with a 2.50 °C/min ramp rate  Figure 5.50 and Figure 5.52 show the results in the time domain for cycles with a 0.1°C/min and a 2.5°C/min ramp rate respectively. These figures show the temperature cycles for the 175°C and 185°C maximum temperatures and the deflection values for varying maximum cycle temperatures. Figure 5.51 and Figure 5.53 show the results in the temperature domain for cycles with a 0.1°C/min and a 2.5°C/min ramp rate respectively. These figures show the deflection values for varying maximum cycle temperatures and the adhesive's shear modulus throughout the various cycles.  The results o f the maximum cure cycle temperature study and the relative differences are tabulated in  Table 5.19 and presented graphically in Figure 5.54. These results show that for  slow heating rates, variations in the maximum temperature achieved during the cure cycle had a more profound effect on the final deflection value than for fast heating rates. Since fast heating rates cause the modulus to drop to the fully relaxed modulus, temperature overshoots result in a slightly larger warpage due to the magnitude o f the overshoot. For slow heating rates, the overshoot not only increases the warpage due to a slightly higher temperature, but  111  Chapter 5 Results and Discussion  also causes a reduction in the modulus, resulting in an increase in warpage due to thermal softening.  Table 5.19 - Sensitivity to maximum temperature  0.10° C/min Temperature (  2.50° C/min  Deflection  Difference  Deflection  Difference  (mm)  (%)  (mm)  (%)  185  0.3436  6.77  0.4320  2.86  180  0.3281  1.97  0.4249  1.17  178  0.3237  0.59  0.4217  0.40  177  0.3218  0.00  0.4200  0.00  176  0.3201  -0.53  0.4183  -0.41  175  0.3185  -1.01  0.4165  -0.83  °  C  )  0.50 -, 0.416  HI  -0.01  a  -0.01  0.418  -001  175  0.420  0.01  0.00  176  0.422  177  000  0.425  0.02  178  0.01  180  0432  0.07  0.03  185  -0.10  Maximum Cycle Temperature (°C) I O . 1 0 C / m i n - Deflection  • O . I O C / m i n - Difference  • 2 . 5 0 C / m i n - Deflection  O 2 . 5 0 C / m i n - Difference  Figure 5.54 - Sensitivity of an idealized two-step cycle to the maximum cycle temperature  112  Chapter 5 Results and Discussion  5.8.3  Sensitivity o f idealized cycles to the ramp rate  To determine the sensitivity o f the idealized cycle to the ramp rate, a two-step cycle was simulated on virtual specimens with different ramp rates between the first and second dwell temperatures.  The two-step cycle consisting o f a 120°C dwell for 330 minutes followed by a  ramp to 177°C at 2.5°C/min and a hold for 30 minutes was chosen as the baseline for relative difference calculations. The ramp rate was then varied between 0 l°C/min and 10.0°C/min to determine the effect on the final deflection.  Figure 5.55 shows the temperature profiles for two-step cycles with ramp rates o f 0.1 °C/min and 10.0 °C/min and the resulting deflections for the different ramp rates in the time domain. Similarly Figure 5.56 shows the development o f the adhesive layer's shear modulus and the resulting deflections for the different ramp rates in the temperature domain.  Two-step cycle - 120/177"C Ramp rate sensitivity CC/rnin)  Time (min) -Ramp=0.1  —Ramp=0.5  Ramp=1.0  Ramp=2.5  Ramp=5.0  Ramp=10.0  Figure 5.55 - Time domain results for ramp rate sensitivity of an idealized two-step cycle  113  Chapter 5 Results and Discussion  Two-step cycle - 120/177°C  Cure Temperature (°C) Ramp=0.1  Ramp=0.5  Ramp=2.5  Ramp=1.0  —-Ramp=5.0  Ramp=10.0  Figure 5.56 - Temperature domain results for ramp rate sensitivity of an idealized two-step cycle  Table 5.20 - Sensititvity to ramp rate  R a m p rate  Deflection  Difference  (°C/min)  (mm)  (%)  0.1  0.3220  -23.33  0.5  0.3450  -17.86  1.0  0.3700  -11.90  2.5  0.4200  0.00  5.0  0.4300  2.38  10.0  0.4300  2.38  114  Chapter 5 Results and Discussion  0.50  I II I I I 0.420  o c  01  0.40 0.30  5 41  > 01  0£ 0.10 ?  E.  0.00  o -0.10 «i  0.370  0 1  0  5  0.430  •  2.5  5.0  10.0  -0.12  01 Q  1 0  0.430  -0.20  -0.18 -0.23  -0.30  Ramp rate (°C/min) r • Deflection (mm)  • Relative Difference  |  Figure 5.57 - Sensitivity of an idealized two-step cycle to the ramp rate  The results o f the ramp rate sensitivity study and the relative differences are tabulated in  Table 5.20 and presented graphically Figure 5.57. These results show how important accurate temperature control is during the ramp. In Figure 5.56 we see that when slower ramp rates are used the shear modulus during the ramp can remain considerably higher than the fully relaxed shear modulus. For faster heating rate, however, the effect o f two-step curing is largely negated due to thermal softening during heat-up as the adhesive's shear modulus drops towards the fully relaxed value. For the two fastest heating rates investigated, the final deflection values are equal, as the adhesive's shear modulus dropped to the fully relaxed modulus in both cycles.  115  Chapter 6 Conclusions  6. Conclusions The objective o f this thesis was to develop and validate a simple and efficient technique for cure cycle optimization o f bonded composite patch repair using a Dynamic Mechanical Analyzer ( D M A ) . Thus the D M A beam technique was shown to be an effective, versatile method o f characterizing materials, as well as monitoring the out o f plane deflection o f bonded composite patch repair specimens throughout a cure cycle. Insight gained from these measurements can be used to optimize cure cycles so as to reduce the thermally induced residual stresses in real applications o f bonded composite patch repairs.  Bimaterial beam technique A bimaterial beam technique was used to extract unknown viscoelastic material properties o f a polymeric material from the system's material properties. Relaxation tests were performed in a D M A on both monolithic Lexan specimens and bimaterial steel/Lexan specimens. The viscoelastic response o f Lexan was then extracted from the bimaterial system response and compared to the monolithic response. Tests were conducted well below the glass transition temperature o f Lexan and results showed good agreement between the relaxation modulus o f Lexan as extracted from the bimaterial system response and the monolithic Lexan response, with an error o f less than 8% for the highest temperatures tested and better agreement at lower temperatures.  Material Characterization The modulus o f an aerospace grade adhesive, F M 3 0 0 , was characterized using a D M A bimaterial beam technique. Bimaterial beams consisting o f an elastic shim and an uncured layer o f F M 3 0 0 were cured i n the D M A at a variety o f isothermal temperatures, while a cyclic deflection was applied. Using a cure kinetics model and a glass transition temperature model, the modulus was shown to be an instantaneous function o f the difference between the temperature and the glass transition temperature.  116  Chapter 6 Conclusions Bonded Composite Patch Repair Specimens The development o f deflection i n bonded composite patch repair specimens consisting o f an elastic substrate (steel), a curing adhesive (FM300), and a composite patch (AS4/3501-6), throughout a cure cycle were measured in-situ using a D M A . The effect o f modifying the cure cycle on the development o f thermally induced warpage was investigated. For one-step cycles, although a reduction in the cure cycle temperature results i n a reduction in the final deflection values, a marked drop in the final degree o f cure also occurs that may be unacceptable for some applications. Post-curing the specimens increases the final degree o f cure but negates some o f the benefits o f a lower initial cure temperature. For the two-step cycles, reducing the first dwell temperature results i n a reduction i n warpage. The ramp rate between the first and second dwell was found to be an important factor in the generation o f warpage. Slow ramp rates allow the glass transition temperature to develop and keep pace with the increase in temperature. For faster rates, the temperature increase outpaces the development o f glass transition temperature resulting i n thermal softening, which adversely affects warpage. Thus slow rates result in a reduction i n warpage when compared to faster rates.  A wide scatter i n experimental results was noted. Due to the small specimen size the experimental method is sensitive to variations in geometry, most notably in the adhesive layer thickness. Scaling the results to a standard adhesive layer thickness reduced the degree of scatter considerably.  Bonded Composite Patch Repair Model A modified C H I L E model, which incorporates both cure hardening and thermal softening behaviour for the adhesive layer, was shown to accurately predict the development o f warpage in bonded composite patch repair specimens. M o d e l results agree well with experimental values for a wide range o f cure cycles. The addition o f a thermal softening term has the potential to expand the applicability of pseudo-viscoelastic models.  The modified C H I L E model was then used to study the response o f a virtual specimen subjected to idealized cycles. Results showed a number o f differences between the idealized 117  Chapter 6 Conclusions cycles and the actual D M A cycles. These differences are attributed to temperature control problems in the D M A , both due to poor control during temperature ramps, which result a temperature profile that oscillates about the desired ramp rate, and overshoots when transitioning from a ramp to a hold. The results indicate that improved temperature control could improve the effectiveness o f cure cycle optimization by as much as 25%.  In an attempt to quantify the effects o f variation in specimen geometry and poor temperature control, the sensitivity o f the model to changes in adhesive layer thickness, ramp rate, and maximum cycle temperature were examined. Results show that considerable variations in deflection occur as a result o f changes to the adhesive layer thickness or ramp rate, while the maximum cure cycle temperature was not found to affect deflections significantly.  118  Chapter 7 Future Work  7. Future Work A s the main impetus for the design o f an optimized cure cycle is an increase in the fatigue life o f the repair, it is important to correlate reductions in thermally induced residual stresses (or conversely warpage) with increases in fatigue life. While other researchers have studied the long-term effects o f cure cycle optimization, no such attempt has been made herein. Long-term fatigue tests o f the cure cycles investigated i n this work should be performed to determine how reductions i n warpage affect the patch repair's fatigue life. Such a study would help designers determine what trade-offs, i n terms o f costs associated with processing time and sophistication o f heating and temperature control systems versus increased fatigue life, are acceptable for specific repair applications.  Although the developed C H I L E with thermal softening model agrees well with experimental results for F M 3 0 0 , results from other researchers into the behaviour o f similar adhesives show very different constitutive responses. Work by Djokic [73] on F M 7 3 shows significant stress relaxation throughout the cure cycle. Stress relaxation, much like thermal softening, results in a lessening o f the benefits o f cure cycle optimization. N o attempt was made in this work to determine the causes o f the difference in behaviour between these adhesive systems. It may therefore prove fruitful to test bonded composite patch repair specimens with F M 7 3 adhesive. Results could help determine whether the thermal softening phenomena is an artefact o f the experimental method and/or specimen size. Should F M 7 3 exhibit behaviour similar to that reported for F M 3 0 0 , experiments could be undertaken to determine i f F M 3 0 0 exhibits viscoelastic behaviour in larger sized bonded composite patch repair specimens. These results could help quantify the effect o f size on the analysis method proposed herein.  Cocuring o f the adhesive layer has been proposed as a method o f decreasing the downtime associated with structural repair. Patches could easily be designed to mate with complex aerodynamic surfaces and cured in-situ without the need for a tool or an autoclave. To the best o f the author's knowledge, no studies have focused on the effects o f cocuring the patch. Cocuring may also negate the need for an adhesive layer, as it may be possible to design the curing patch's material such that adhesion with the substrate is assured.  119  Chapter 7 Future Work  Newer D M A models such as the T A Instruments Q800 D M A may allow the operator to measure  the  out  o f plane  deflection caused  by thermally induced stresses,  while  simultaneously applying a small dynamic disturbance. This would allow measurement o f both thermally induced deflection and instantaneous modulus in-situ throughout the entire cure cycle. This test methodology would eliminate a number o f the intermediate steps necessary for model predictions and the associated error. It would also effectively combine characterization o f the adhesive layer's instantaneous modulus and development o f deflection in bonded composite patch repairs. Characterizing the adhesive layer's modulus in this type of test would also improve dimensional stability, a major source o f error for the modulus characterization test; Having the patch layer on top o f the adhesive minimizes adhesive flow and creates a more consistent adhesive layer thickness.  Slowing the ramp rate between the first and second dwell temperatures has been shown to be an effective method o f optimization. This method has however been shown to have a practical limitation, as the model predicts a maximum achievable modulus at the end o f the ramp, G (T* =T a  mm  - T  ). In some cases, constant ramp rates allow the modulus to increase  above this value during the ramp, indicating a ramp rate that is slower than necessary. Conversely, i f the modulus drops below this value thermal softening w i l l occur, adversely affecting warpage and indicating that the ramp rate that is too fast. Building on this technique further, a feedback control scheme could be developed whereby the rate o f temperature increase could be controlled using a measurement o f the material's instantaneous modulus; should the modulus drop below a preset threshold, the thermal ramp rate would be slowed, while i f it rises above the theoretical maximum achievable modulus, the ramp rate could be increased.  120  Chapter 8 References  8. References [1]  Chester,R.J., Walker,K.F., and Chalkley,P.D., "Adhesively Bonded Repairs to Primary Aircraft Structure", International Journal of Adhesion and Adhesives, V o l . 1 9 , N o . l , p p . 1-8, 1999.  [2]  Ong,C.L. and Shen,S.B., "The Reinforcing Effect o f Composite Patch Repairs on Metallic Aircraft Structures", International Journal of Adhesion and Adhesives, V o l . 12, N o . 1, pp. 19-26, 1992.  [3]  H y e r , M . W . , "Stress Analysis of Fiber-Reinforced Composite Materials", 1998.  [4]  Canadian Institute of Steel Construction, "Handbook o f Steel Construction", V o l . 4th, 1985.  [5]  Cho,J. and Sun,C.T., "Lowering Thermal Residual Stresses i n Composite Patch Repairs in Metallic Aircraft Structure", A I A A Journal, V o l . 39, N o . 10, pp. 20132018, 2001.  [6]  Umamaheswar,T.V.R.S. and Singh,R., "Modelling of a Patch Repair to a T h i n Cracked Sheet", Engineering Fracture Mechanics, V o l . 62, N o . 2-3, pp. 267-289, 1999.  [7]  D a v i s , M . and Bond,D., "Principles and Practices o f Adhesive Bonded Structural Joints and Repairs", International Journal of Adhesion and Adhesives, V o l . 19, N o . 23, pp. 91-105, 1999.  [8]  B a k e r , A . A . and Chester,R.J., "Recent Advances in Bonded Composite Repair Technology for Metallic Aircraft Components", pp. 45-49, 1993.  [9]  K e r r , A . and Ruddy,J., "Development of a Bonded Repair for the F-16FS479 Bulkhead Vertical Tail Attach Bosses", Applied Composite Materials, V o l . 6, N o . 4, pp. 239-249, 1999.  [10]  Bartholomeusz,R.A., Baker,A.A., Chester,R.J., and Searl,A., "Bonded Joints With Through-Thickness Adhesive Stresses - Reinforcing the F / A - 1 8 Y470.5 Bulkhead", International Journal of Adhesion and Adhesives, V o l . 19, N o . 2-3, pp. 173-180, 1999.  [11]  Baker,A.A., Rose,L.R.F., Walker,K.F., and Wilson,E.S., "Repair Substantiation for a Bonded Composite Repair to F l 11 Lower W i n g Skin", A p p l i e d Composite Materials, V o l . 6, N o . 4, pp. 251-267, 1999.  [12]  Jones,R., Molent,L., and Pitt,S., "Study of Multi-Site Damage o f Fuselage Lap Joints", Theoretical and Applied Fracture Mechanics, V o l . 32, N o . 2, pp. 81-100, 1999.  121  Chapter 8 References [13]  Lange,J., Toll,S., Manson,J.A.E., and Hult,A., "Residual Stress B u i l d - U p in Thermoset Films Cured B e l o w Their Ultimate Glass Transition Temperature", Polymer, V o l . 38, N o . 4, pp. 809-815, 1997.  [14]  Sourour,S. and K a m a L M . R . , "Differential Scanning Calorimetry o f Epoxy Cure Isothermal Cure Kinetics", Thermochimica Acta, V o l . 14, N o . 1-2, pp. 41-59, 1976.  [15]  Shutilin,Y.F., "On Application of Williams-Landel-Ferry and Arrhenius Equations to Description of Relaxational Properties of Polymers and Polymer Homologs", Vysokomolekulyarnye Soedineniya Seriya A , V o l . 33, N o . 1, pp. 120-127, 1991.  [16]  HutchinsomJ.M. and Montserrat,S., " A Theoretical M o d e l o f Temperature-Modulated Differential Scanning Calorimetry in the Glass Transition Region", Thermochimica Acta, V o l . 305, pp. 257-265, 1997.  [17]  Djokic,D., Johnston,A., Rogers,A., Lee-Sullivan,P., and M r a d , N . , "Residual Stress Development During the Composite Patch Bonding Process: Measurement and Modeling", Composites Part A - A p p l i e d Science and Manufacturing, V o l . 33, N o . 2, pp. 277-288, 2002.  [18]  Sideridou,I., Achilias,D.S., and Kyrikou,E., "Thermal Expansion Characteristics of Light-Cured Dental Resins and Resin Composites", Biomaterials, V o l . 25, N o . 15, pp. 3087-3097, 2004.  [19]  Ramis,X., Cadenato,A., Morancho,J.M., and Salla,J.M., "Curing of a Thermosetting Powder Coating by Means of D M T A , T M A and D S C " , Polymer, V o l . 44, N o . 7, pp. 2067-2079, 2003.  [20]  Rieger,J., "The Glass Transition Temperature T-g o f Polymers - Comparison of the Values From Differential Thermal Analysis ( D T A , D S C ) and Dynamic Mechanical Measurements (Torsion Pendulum)", Polymer Testing, V o l . 20, N o . 2, pp. 199-204, 2001.  [21]  Chern,C.S. and Poehlein,G.W., " A Kinetic-Model for Curing Reactions of Epoxides W i t h Amines", Polymer Engineering and Science, V o l . 27, N o . 11, pp. 788-795, 1987.  [22]  Hojjati,M. and Johnson,A.F., "Stress Relaxation Behaviour of Cytec F M 7 3 Adhesive During Cure", 2002.  [23]  K i m , Y . K . and White,S.R., "Stress Relaxation Behavior of 3501-6 Epoxy Resin During Cure", Polymer Engineering and Science, V o l . 36, N o . 23, pp. 2852-2862, 1996.  [24]  K i m , J . , Moori,T.J., and Howell,J.R., "Cure Kinetic M o d e l , Heat o f Reaction, and Glass Transition Temperature of AS4/3501-6 Graphite-Epoxy Prepregs", Journal of Composite Materials, V o l . 36, N o . 21, pp. 2479-2498, 2002.  122  Chapter 8 References [25]  M c C r u m , N . G . , B u c k l e y , C . P . , and Bucknall,C.B., "Principles of Polymer Engineering", V o l . 2nd, 1997.  [26]  Roylance,D., "Engineering Viscoelasticity", 2001.  [27]  Fliigge.W., "Viscoelasticity", V o l . 7th, 1967.  [28]  Ferry,J.D., "Viscoelastic Properties of Polymers", V o l . 3rd, 1980.  [29]  Brostow,W., "Temperature Shift Factor - Polymer Mechanical-Properties Above and B e l o w Glass-Transition", Materials Chemistry and Physics, V o l . 13, N o . 1, pp. 47-57, 1985.  [30]  Brostow,W., "Time-Stress Correspondence in Viscoelastic Materials: an Equation for the Stress and Temperature Shift Factor", Materials Research Innovations, V o l . 3, N o . 6, pp. 347-351,2000.  [31]  A k i n a y , A . E . , Brostow,W., Castano,V.M., Maksimov,R., and 01szynski,P., "TimeTemperature Correspondence Prediction o f Stress Relaxation o f Polymeric Materials From a M i n i m u m o f Data", Polymer, V o l . 43, N o . 13, pp. 3593-3600, 2002.  [32]  A k i n a y , A . E . and Brostow,W., "Long-Term Service Performance o f Polymeric Materials From Short-Term Tests: Prediction of the Stress Shift Factor From a M i n i m u m o f Data", Polymer, V o l . 42, N o . 10, pp. 4527-4532, 2001.  [33]  Simon,S.L., M c K e n n a , G . B . , and Sindt,0., "Modeling o f the Evolution of the Dynamic Mechanical Properties o f a Commercial Epoxy During Cure After Gelation", Journal o f Applied Polymer Science, V o l . 76, pp. 495-508, 2000.  - [34]  E o m , Y . , Boogh,L., M i c h a u d , V . , Sunderland,P., and Manson,J.A., "Time-CureTemperature Superposition for the Prediction of Instantaneous Viscoelastic Properties During Cure", Polymer Engineering and Science, V o l . 40, N o . 6, pp. 1281-1292, 2000.  [35]  0'Brien,D.J., Mather,P.T., and White,S.R., "Viscoelastic Properties o f an Epoxy Resin During Cure", Journal of Composite Materials, V o l . 35, N o . 10, pp. 883-904, 2001.  [36]  Zobeiry,N., V a z i r i R., and Poursartip A . , "Computationally Efficient PseudoViscoelastic Models for Evaluation of Residual Stresses i n Thermoset Polymer Composites During Cure", to be published in Composites: Part A , 2005.  [37]  C o o k , W . D . , Scott,T.F., Quay-Thevenon,S., and Forsythe,J.S., "Dynamic Mechanical Thermal Analysis o f Thermally Stable and Thermally Reactive Network Polymers", Journal o f A p p l i e d Polymer Science, V o l . 93, N o . 3, pp. 1348-1359, 2004.  [38]  Johnston,A., Vaziri,R., and Poursartip,A., " A Plane Strain M o d e l for Process-Induced Deformation of Composite Structures", Journal o f Composite Materials, 2001.  123  Chapter 8 References [39]  Svanberg,J.M. and Holmberg,J.A., "Prediction o f Shape Distortions Part I. F E Implementation o f a Path Dependent Constitutive M o d e l " , Composites Part A Applied Science and Manufacturing, V o l . 35, N o . 6, pp. 711-721, 2004.  [40]  Svanberg,J.M. and H o l m b e r g J . A . , "Prediction o f Shape Distortions. Part II. Experimental Validation and Analysis o f Boundary Conditions", Composites Part A Applied Science and Manufacturing, V o l . 35, N o . 6, pp. 723-734, 2004.  [41]  Sun,C.T., K l u g , J . , and A r e n d t , C , "Analysis o f Cracked A l u m i n u m Plates Repaired With Bonded Composite Patches", A I A A Journal, V o l . 34, N o . 2, pp. 369-374, 1996.  [42]  Klug,J., Maley,S., and Sun,C.T., "Characterization o f Fatigue Behavior o f Bonded Composite Repairs", Journal o f Aircraft, V o l . 36, N o . 6, pp. 1016-1022, 1999.  [43]  Lena,M.R., K l u g , J . C , and S u ^ C . T . , , "Composite Patches A s Reinforcements and Crack Arrestors in Aircraft Structures", Journal o f Aircraft, V o l . 35, N o . 2, pp. 318323, 1998.  [44] Naboulsi,S. and M a l l , S . , "Modeling o f a Cracked Metallic Structure W i t h Bonded Composite Patch Using the Three Layer Technique", Composite Structures, V o l . 35, N o . 3, pp. 295-308, 1996. [45] Naboulsi,S. and M a l l , S . , "Nonlinear Analysis o f Bonded Composite Patch Repair o f Cracked A l u m i n u m Panels", Composite Structures, V o l . 41, N o . 3-4, pp. 303-313, 1998. [46]  Schubbe,J.J. and M a l l , S . , "Investigation o f a Cracked Thick A l u m i n u m Panel Repaired W i t h a Bonded Composite Patch", Engineering Fracture Mechanics, V o l . 63, N o . 3, pp. 305-323, 1999.  [47] Rose,L.R.F., " A n Application o f the Inclusion Analogy for Bonded Reinforcements", International Journal o f Solids and Structures, V o l . 17, N o . 8, pp. 827-838, 1981. [48]  Wang,C.H., Rose,L.R.F., Callinan,R., and Baker,A.A., "Thermal Stresses in a Plate W i t h a Circular Reinforcement", International Journal o f Solids and Structures, V o l . 37, N o . 33, pp. 4577-4599, 2000.  [49]  Daverschot,D.R., V l o t , A . , and Woerden,H.J.M., "Thermal Residual Stresses in Bonded Repairs", Applied Composite Materials, V o l . 9, N o . 3, pp. 179-197, 2002.  [50]  Hojjati,M., X i a o , X . , and Johnson,A.F., "Modelling o f Residual Stress Development During Composite Patch Repair o f Metallic Structures: a Litterature Review", 2000.  [51]  Hojjati,M. and Johnson,A.F., "Closed-Form Solution for Residual Stress Development i n a Simple Single-Sided Bonded Patch Repair", 2002.  124  Chapter 8 References [52]  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, V o l . 26, N o . 16, pp. 2423-2453, 1992.  [53]  Crasto,A., K i m , R . Y . , and RussellJ.D., "In Situ Monitoring of Residual Strain Development During Composite Cure", 44th International S A M P E Symposium, pp. 1706-1717, 1999.  [54]  Crasto,A.S. and K i m , R . Y . , "On the Determination of Residual-Stresses in FiberReinforced Thermoset Composites", Journal of Reinforced Plastics and Composites, V o l . 12, N o . 5, pp. 545-558, 1993.  [55]  Cho,J. and Sun,C.T., "Lowering Thermal Residual Stresses i n Bonded Composite Patch Repairs", Technical Conference, V o l . 14, 1999.  [56]  K i m , K . S . and Hahn,H.T., "Residual Stress Development During Processing o f Graphite/Epoxy Composites", Composite Science and Technology, V o l . 36, pp. 121132, 1989.  [57]  White,S.R. and Hahn,H.T., "Cure Cycle Optimization for the Reduction of Processing-Induced Residual-Stresses in Composite-Materials", Journal o f Composite Materials, V o l . 27, N o . 14, pp. 1352-1378, 1993.  [58]  Ramani,K. and Zhao,W.P., "The Evolution of Residual Stresses i n Thermoplastic Bonding to Metals", International Journal of Adhesion and Adhesives, V o l . 17, N o . 4, pp. 353-357, 1997.  [59]  Findik,F., M r a d , N . , and Johnston,A., "Strain Monitoring i n Composite Patched Structures", Composite Structures, V o l . 49, N o . 3, pp. 331-338, 2000.  [60]  O c h i , M . , Yamashita,K., and Shimbo,M., "The Mechanism for Occurrence of InternalStress During Curing Epoxide-Resins", Journal o f Applied Polymer Science, V o l . 43, N o . 11, pp. 2013-2019, 1991.  [61]  Schoch,K.F., Panackal,P.A., and Frank,P.P., "Real-Time Measurement of Resin Shrinkage During Cure", Thermochimica Acta, V o l . 417, N o . 1, pp. 115-118, 2004.  [62]  Lange,J., Manson,J.A.E., and Hult,A., "Build-Up o f Structure and Viscoelastic Properties in Epoxy and Acrylate Resins Cured B e l o w Their Ultimate Glass Transition Temperature", Polymer, V o l . 37, N o . 26, pp. 5859-5868, 1996.  [63]  LangeJ., Toll,S., Manson,J.A.E., and Hult,A., "Residual-Stress Buildup i n Thermoset Films Cured Above Their Ultimate Glass-Transition Temperature", Polymer, V o l . 36, N o . 16, pp. 3135-3141, 1995.  [64]  Motahhari,S. and Cameron,J., "The Contribution to Residual Stress by Differential Resin Shrinkage", Journal o f Reinforced Plastics and Composites, V o l . 18, N o . 11, pp. 1011-1020, 1999.  125  Chapter 8 References [65]  K i m , Y . K . and White,S.R., "Stress Relaxation Behavior o f 3501-6 Epoxy Resin During Cure", Polymer Engineering and Science, V o l . 36, N o . 23, pp. 2852-2862, 1996.  [66]  White,S.R. and K i m , Y . K . , "Process-Induced Residual Stress Analysis o f AS4/3501-6 Composite Material", Mechanics o f Composite Materials and Structures, V o l . 5, N o . 2, pp. 153-186, 1998.  [67]  White,S.R. and Hahn,H.T., "Process Modeling o f Composite Materials: Residual Stress Development During Cure. Part I. M o d e l Formation", Journal o f Composite Materials, V o l . 26, N o . 16, pp. 2402-2422, 1992.  [68]  G o p a l , A . K . , Adali,S., and Verijenko,V.E., "Optimal Temperature Profiles for M i n i m u m Residual Stress in the Cure Process o f Polymer Composites", Composite Structures, V o l . 48, N o . 1-3, pp. 99-106, 2000.  [69]  Bogetti,T.A. and Gillespie,J.W., Jr., "Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates", Journal o f Composite Materials, V o l . 26, N o . 5, pp. 626-659, 1992.  [70]  Bogetti,T.A., Gillespie,J.W., and McCullough,R.L., "Influence o f Processing on the Development o f Residual Stresses in Thick Section Thermoset Composites", International Journal o f Materials & Product Technology, V o l . 9, N o . 1-3, pp. 170182, 1994.  [71]  Cho,J. and Sun,C.T., "Modeling Thermal Residual Stresses in Composite Patch Repairs During Multitemperature Bonding Cycles", Journal o f Aircraft, V o l . 40, N o . 6, pp. 1200-1205,2003.  [72]  Djokic,D., Hojjati,M., Johnston,A., and Lee-Sullivan,P., "Process Optimization for Reduction o f Composite Patch Repair Residual Stresses", International S A M P E Technical Conference, V o l . 33, pp. 356-368, 2001.  [73]  Djokic, D . , (2002). "Reduction o f residual thermal stresses during bonded composite patch repair", M . S . E n g . , University o f N e w Brunswick,  [74]  Hojjati,M., Johnson,A.F., and C o l e , K . C , "Cure Kinetics o f Cytec F M 7 3 Epoxy Adhesive", 2001.  [75]  Findik,F. and U n a l , H . , "Development o f Thermal Residual Strains in a Single Sided Composite Patch", Composites Part B-Engineering, V o l . 32, N o . 4, pp. 379-383, 2001.  [76]  H i b b e l e r , R . C , "Mechanics o f Materials", V o l . 4th, 1999.  [77]  Rogers,A.D. and Lee-Sullivan,P., " A n Alternative M o d e l for Predicting the Cure Kinetics o f a H i g h Temperature Cure Epoxy Adhesive", Polymer Engineering and Science, V o l . 43, N o . 1, pp. 14-25, 2003.  126  Chapter 8 References [78]  T w i g g , G . A . and Poursartip A . , 2005.  [79]  Hojjati,M., Johnston,A., Hoa,S.V., and Denault,J., "Viscoelastic Behavior o f Cytec F M 7 3 Adhesive During Cure", Journal o f Applied Polymer Science, V o l . 91, N o . 4, pp. 2548-2557, 2004.  [80]  K i m , K . S . and Hahn,H.T., "Residual-Stress Development During Processing o f Graphite Epoxy Composites", Composites Science and Technology, V o l . 36, N o . 2, pp. 121-132, 1989.  [81]  Loctite Corporation, "Hysol 9392 Epoxy Paste Adhesive", V o l . Rev 1, 2001.  [82]  Rheometric Scientific Incorporated, "Dynamic Mechanical Analyzer D M T A V , Document Manual 925-50010", N o . Rev A , 1999.  [83]  Cytec Engineered Materials, "FM300 High Shear Strength Modified Epoxy F i l m Adhesive", 2005.  [84]  LaPlante,G. and Lee-Sullivan,P., "Moisture Effects on F M 3 0 0 Structural F i l m Adhesive: Stress Relaxation, Fracture Toughness, and Dynamic Mechanical Analysis", Journal o f Applied Polymer Science, V o l . 95, N o . 5, pp. 1285-1294, 2005.  [85]  R o y , A . K . and K i m , R . Y . , "Measurements for Determining the Thermal-Expansion Coefficient ( C T E ) o f Laminated Orthotropic Rings", Journal o f Reinforced Plastics and Composites, V o l . 12, N o . 4, pp. 378-385, 1993.  127  Appendix A Additional Bonded Composite Patch Repair Graphs  Appendix A Additional Bonded Composite Patch Repair Experimental Results  128  Appendix A Additional Bonded Composite Patch Repair Graphs One-step cycle - 177°C Deflection: 0.458  E E +3  O  01  Q O  -0 2  Time (min) • Experimental  - - Model  -Difference  Temperature  Tg  One-step cycle - 177°C Deflection:  0.458  Cure Temperature (°C) —  Experiment  Model  Difference  •Shear Modulus [  Figure A.1 - One-step cycle - 177°C - Specimen 1(a) Experimental and model results in the time and temperature domains  129  Appendix A Additional Bonded Composite Patch Repair Graphs  Figure A.2 - One-step cycle - 177°C - Specimen 1(b) Experimental and model results in the time and temperature domains  130  Appendix A Additional Bonded Composite Patch Repair Graphs  One-step cycle - 177"C Deflection: 0.486  Cure Temperature (°C) Experiment  Model  Difference  — S h e a r Modulus  Figure A.3 - One-step cycle - 177°C - Specimen 1(c) Experimental and model results in the time and temperature domains  131  Appendix A Additional Bonded Composite Patch Repair Graphs  One-step cycle - 177°C Deflection:  0.469  Cure Temperature (°C) —  Experiment  Model  Difference  — S h e a r Modulus  Figure A.4 - One-step cycle - 177°C - Specimen 1(d) Experimental and model results in the time and temperature domains  132  Appendix A Additional Bonded Composite Patch Repair Graphs  1 Step cycle - 177»C Initial Deflection:  0.416  Time (min) •Experimental  Model  Difference  Temperature  "Tg  1 Step cycle - 177°C Initial Deflection:  0.416  Cure Temperature (°C) —  Experiment  Model  - Difference  — S h e a r Modulus  Figure A.5 - One-step cycle - 177°C - Specimen 1(e) Experimental and model results in the time and temperature domains  133  Appendix A Additional Bonded Composite Patch Repair Graphs  Post-cured cycle - 150°C Initial Deflection:  0.406  -0.2  Lo  Time (min) Experimental  Model  Difference  Temperature  Tg j  Figure A.6 - One-step cycle - 150°C - Specimen 2(a) Experimental and model results in the time and temperature domains  134  Appendix A Additional Bonded Composite Patch Repair Graphs  Time (min) •Experimental  —- Model  Difference  Temperature  Tg  One-step cycle - 120°C 0.5 -  Deflection:  0 335  04  0 3  E 0.2  o o 01 «=  0 1  01  Q  -0.1  -0.2 Cure Temperature (°C) —  Experiment  Model  -Difference  — S h e a r Modulus  Figure A.7 - One-step cycle - 120°C - Specimen 3(a) Experimental and model results in the time and temperature domains  135  Appendix A Additional Bonded Composite Patch Repair Graphs  Post-cured cycle Initial Deflection:  120»C 0.338  Time (min) •Experimental  Model  —Difference  Temperature  Tg  Post-cured cycle - 120°C  05  Initial Deflection:  0.338  04  03  E 0.2  O  01 IP  &  -0 1  -0  2  Cure Temperature (C) • Experiment  Model  Difference  Shear Modulus  Figure A.8 - One-step cycle - 120°C - Specimen 3(b) Experimental and model results in the time and temperature domains  136  Appendix A Additional Bonded Composite Patch Repair Graphs  Post-cured cycle - 177°C Initial Deflection:  0.502  Post-cured Deflection:  0.506  Time (min) Experimental  - - Model  -Difference  Temperature  Tg  Figure A.9 - Post cure cycle - 177/177°C - Specimen 4(a) Experimental and model results in the time and temperature domains  137  Appendix A Additional Bonded Composite Patch Repair Graphs  Figure A.10 - Post cure cycle - 177/177°C - Specimen 4(b) Experimental and model results in the time and temperature domains  138  Appendix A Additional Bonded Composite Patch Repair Graphs  Post-cured cycle - 150°C Initial Deflection: 0.406 Post-cured Deflection : 0.440 0 4  0  0.2  1 |  01  o 900  -oi 4  -0.2  Time (min) •Experimental  Model  —Difference  Temperature  Tg  Figure A . l l - Post cure cycle - 150/177°C - Specimen 5(a) Experimental and model results in the time and temperature domains  139  Appendix A Additional Bonded Composite Patch Repair Graphs  Cure Temperature (C) —  Experiment  Model  Difference  — S h e a r Modulus  Figure A. 12 - Post cure cycle - 120/177°C - Specimen 6(a) Experimental and model results in the time and temperature domains  140  Appendix A Additional Bonded Composite Patch Repair Graphs  Two-step cycle - 155/177'C r a m p rate = 2.5CrC/min Deflection:  -0.2 -  1  0.430  —  L o  Time (min) |  Experimental  -Model  — Difference  Temperature  Tg |  Two-step cycle - 155/177°C  Cure Temperature (°C) —  Experiment  Model  Difference  —  Shear Modulus  Figure A.13 - Two-step cycle - 155/177°C, 2.5°C/min - Specimen 7(a) Experimental and model results in the time and temperature domains  141  Appendix A Additional Bonded Composite Patch Repair Graphs Two-step cycle - 155/i77"C r a m p rate = 2 . 5 0 ° C / m i n  Deflection:  0.464  Time (min) Experimental  Model  Difference  Temperature  Tg  Cure Temperature (°C) Experiment  Model  Difference  —  Shear Modulus  Figure A.14 - Two-step cycle - 155/177°C, 2.5°C/min - Specimen 7(b) Experimental and model results in the time and temperature domains  142  Appendix A Additional Bonded Composite Patch Repair Graphs  Two-step cycle - 1207177°C  -0.2  !• 0  J  Time (min) |  Experimental  —Model  —Difference  Temperature  Tg~]  Two-step cycle - 120/177°C  Cure Temperature (°C) Experiment  Model  Difference  — S h e a r Modulus  Figure A. 15 - Two-step cycle - 120/177°C, 2.5°C/min - Specimen 8(a) Experimental and model results in the time and temperature domains  143  Appendix A Additional Bonded Composite Patch Repair Graphs  -0.2  Time (min) -Experimental  Model  Difference  Temperature  Tg  Figure A.16 - Two-step cycle - 120/177°C, 2.5°C/min - Specimen 8(b) Experimental and model results in the time and temperature domains  144  Appendix A Additional Bonded Composite Patch Repair Graphs Two-step cycle - 120/177°C  -0.2  J  Time (min) |  Experimental  Model  —Difference  Temperature  Tg  Cure Temperature (°C) —  Experiment  Model  Difference  — S h e a r Modulus  Figure A.17 - Two-step cycle - 120/177°C, 2.5°C/min - Specimen 8(c) Experimental and model results in the time and temperature domains  145  Appendix A Additional Bonded Composite Patch Repair Graphs Two-step cycle - 155/177"C r a m p r a t e = 1,00°C/min Deflection:  0.470  Time (min) Experimental  Model  —Difference  Temperature  Tg  Two-step cycle - 155/177"C  -0.2  —  --  1  10  Cure Temperature (°C) —  Experiment  Model  Difference  — S h e a r Modulus  Figure A.18 - Two-step cycle 155/177°C, 1.0°C/min - Specimen 9(a) Experimental and model results in the time and temperature domains  146  Appendix A Additional Bonded Composite Patch Repair Graphs  Two-step cycle - 120/177°C r a m p rate = 1 . 0 0 ° C / m i n Deflection:  0.439  -0.2  Lo  Time (min) j  Experimental  Model  —Difference  Temperature  Jg7\  Figure A.19 - Two-step cycle 120/177°C, 1.0°C/min - Specimen 10(a) Experimental and model results in the time and temperature domains  147  Appendix A Additional Bonded Composite Patch Repair Graphs  Figure A.20 - Two-step cycle 120/177°C, 1.0°C/min - Specimen 10(b) Experimental and model results in the time and temperature domains  148  Appendix A Additional Bonded Composite Patch Repair Graphs Two-step cycle -  ^S&mTC  r a m p rate = 0 . 1 0 ° C / m i n  Time (min) Experimental  — Model  —Difference  Temperature  Tg j  Cure Temperature (°C) —  Experiment  Model  Difference  — S h e a r Modulus  Figure A.21 - Two-step cycle - 155/177°C, O.rc/min - Specimen 11(a) Experimental and model results in the time and temperature domains  149  Appendix A Additional Bonded Composite Patch Repair Graphs Two-step cycle -120/177°C ramp rate = 0 . 1 0 C / m i n o  Deflection:  -0.2  0.416  Lo  J  Time (min) |j  Experimental  Model  Difference  Temperature  Tg I  Figure A.22 - Two-step cycle - 120/177°C, 0.1°C/min - Specimen 12(a) Experimental and model results in the time and temperature domains  150  Appendix A Additional Bonded Composite Patch Repair Graphs Two-step cycle - 120/177*C r a m p rate = 0.10°C/min Deflection: 0.421  _0 2  J  L  Time (min) |  Experimental  Model  -Difference  Temperature  Tg  Figure A.23 - Two-step cycle - 120/177°C, 0.1°C/min - Specimen 12(b) Experimental and model results in the time and temperature domains  151  o  Appendix A Additional Bonded Composite Patch Repair Graphs  Two-step cycle - 120/177°C  Cure Temperature (°C) —  Experiment  Model  Difference  — S h e a r Modulus  Figure A.24 - Two-step cycle - 120/177°C, 0.1°C/min - Specimen 12(c) Experimental and model results in the time and temperature domains  152  

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