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Acoustic emission and mechanical properties of particle reinforced composites Godoy, Ana Esmeralda 1982

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ACOUSTIC OF  EMISSION PARTICLE  AND  MECHANICAL  REINFORCED  PROPERTIES  COMPOSITES  by ANA B.Sc. ,  THESIS THE  GODOY  (Metallurgical  University  A  ESMERALDA  Simon  SUBMITTED  Bolivar,  IN  REQUIREMENTS MASTER  OF  Engineering), Venezuela,  PARTIAL FOR  THE  APPLIED  1979  FULFILMENT DEGREE  OF  SCIENCE  i n THE  FACULTY  Department  We  of  accept to  THE  GRADUATE  Metal 1urgical  this  the  OF  thesis  required  UNIVERSITY  OF  August, (c)  Ana  Esmeralda  as  STUDIES Engineering  conforming  standard  BRITISH  COLUMBIA  1982 Godoy,  1982  OF  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree at the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e for reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may department or by h i s or her  be granted by  the head o f  representatives.  my  It i s  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department o f  1  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date /  DE-6  (3/81)  written  ABSTRACT  Fracture on  alumina  and  acoustic  p a r t i c l e - f i l l e d  martensitic  steel  was  measure  used  to  steel  fracture  test.  on  the  AE  The  modulus  and  dependent modulus the  AE  of  epoxy  the  tests  alumina  ring-down  were  performed  particle-fi11ed counting  method  were  AE was  with  out  recorded  appeared  and  AE  to  have  attenuation  composites  average  carried  for  the  during  mar-  the  l i t t l e  effect  of  alumina  steel.  attenuation  attenuation  of  were  the  alumina  decreased  analyzed.  epoxy  alumina  slightly  The  composites  particle  increasing  the  with  elastic  were  size.  The  volume  fraction  in-  elastic  increasing  and  alumina  fraction.  Double fracture  The  alumina  modulus  increased  volume  epoxy  AE  and  martensitic  p a r t i c l e - f i l l e d  and  The  tests  composites  elastic  (AE)  AE.  bending  The  from  epoxy  composites.  Three-point tensitic  emission  torsion,  tests  were  composites.  fracture  creasing  energy  volume  wedge-1oading  carried AE was and  fraction  out  for  recorded  toughness and  were  i i  and  three-point  the during  bending  alumina-reinforced each  fracture  values-increased with independent  of  the  test. in-  particle  size. of  The  increase  particles  fracture  accounted  epoxy.  seemed  During  increasing at  about  AE  occurs  volume  fracture for  surface  about  60%  of  due  to  the  presence  the  increase  in  of  pure  energy.  Crazing  alumina  in  failure  particle  40  ym  with  to  be of  fractions  fraction  curves.  due  to  the  major  contributing  A  to  major  a  cut-off  of  the  value  below  was  pinning  presence  of  hard  factor  to  the  no  For  release  particles the  in  increased  particle  observed  and  AE o f  AE  AE  in  which  particles.  maximum  The  source  composites  exist,  addition  volume  front  the  size.  appears the  the  size  increase  in  intermediate in  AE  of  appeared epoxy  with  versus  the to  crack be  the  composites.  TABLE  OF  CONTENTS  Page TITLE  PAGE  . . .  1  ABSTRACT TABLE  OF  ii CONTENTS  LIST  OF  TABLES.  LIST  OF  FIGURES  iv vii .'  v i i i  NOMENCLATURE  xi i  ACKNOWLEDGEMENT  1.  xvii  INTRODUCTION 1.1.  1  Measurement 1.1.1.  1.1.2.  of  Acoustic  Parameters  Used  for  Emission  3  Ring-Down  Count  Root  Square  Amplitude  Distribution  Frequency  Analysis  1.2.  Sources  of  1.3.  Current  Research  Mean  Acoustic on  Method (RMS)  3 Method  Selection  of  2.2.  Fabrication  7  9 Emission  10 12  Materials of  ..  6  8  Emission Acoustic  ....  Analysis  PROCEDURE  2.1.  2  Measuring  EXPERIMENTAL  2  Instruments Required for the Detection of A c o u s t i c Emission  Acoustic  2.  Emission  Composites  13 ..'..*.  15  ^ O —  i v  Page  2.3.  2.2.1.  Fabrication  of  Epoxy  Composites  2.2.2.  Fabrication  of  Steel  Composites  Tests  on  2.3.1.  Epoxy  Composites  Material  and  Fraction  3.1.  Particle  Volume  Determination  19  Constants  21  Elastic  Wave  23  Fracture  Attenuation  Tests  26  Double  Wedge-Loading  Three-Point  Compliance  Torsion  Specimens Specimens  Bending  34  Wedge-Loading  Steel  Emission  Fracture  Tests  2.4.2.  Acoustic  Emission  Tests 3.1.1.  Specimens Specimens  Tests  Composites  2.4.1.  AND  32  Torsion  on  30  34  Double  Acoustic  Tests  26  Calibration  Tests  RESULTS  19  Elastic  2.3.3.  3.  18  2.3.2.  2.4.  . . . . . .  19  Characterization  Density  15  35 36 37 37  Tests  38  CALCULATIONS  41  on  41  Epoxy Material  Composites Characterization  41  Density and P a r t i c l e Volume Fraction Determination  42  Elastic  Constants  43  Elastic  Wave  47  v  Attenuation  Page 3.1.2.  Fracture  Double  Wedge-Loading  Three-Point  Compliance  Tests  Bending  Wedge-Loading  3.1.4.  Tests  Emission  Tests  61  Specimens  of  from  Wedge70 Three77  Alumina-Filled  Epoxy 78  Composites  82  Fracture  Tests  3.2.2.  Acoustic  Emission  3.2.3.  Fractography of Alumina-Fi11ed Martensitic Steel Composites  82 Tests  A N A L Y S I S OF R E S U L T S A N D D I S C U S S I O N F O R R E I N F O R C E D EPOXY COMPOSITES . . . . . . . . 4.1.  Elastic  4.2.  Attenuation  4.3.  Fracture  Energy  4.4.  Acoustic  Emission  CONCLUDING  66 69  3.2.1.  88  88  ALUMINA 94  Constants of  61  Specimens  Acoustic Emission from Point Bending Tests  Steel  55  Tests  Acoustic Emission Loading Tests  Fractography Composites on  55  Calibration Acoustic  53  Tests  Double-Torsion  5.  Torsion  4.  53  3.1.3.  3.2.  Tests  94  Elastic and  Waves  97  Toughness  during  100  Fracture  114  REMARKS  119  APPENDIX  120  REFERENCES  121  vi  —-.  LIST  OF  TABLES  TABLE I.  II.  III.  IV.  V.  VI.  VII.  Page D e n s i t i e s and Volume Epoxy Composites  Fractions  E l a s t i c Constants Specimens  Alumina-Fi11ed  of  of  Alumina-Fi11ed 42 Epoxy 45  Linear Equations for Counts Versus Distance P u l s e r T e s t s and R e s u l t s from Front-to-Front Attenuation Tests  49  F r a c t u r e Toughness of Double T o r s i o n Tests  Epoxy  54  Experimental Fracture Fracture Toughness of  Energy and Experimental Wedge-Loading Tests  F r a c t u r e Toughness of Epoxy Three-Point Bending Tests Summary Double  of  Compliance  Torsion  Composites.  Composites. 60  Calibration  Results  64  Summary  of  AE  Results  from  Wedge-Loading  IX.  Summary Tests  of  AE  Results  from  Three-Point :  XI.  XII.  for  Specimens  VIII.  X.  Fracture Steels.  Toughness of A l u m i n a - F i l l e d Three-Point Bending Tests  Acoustic Steels.  E m i s s i o n of Three-Point  Fracture Constants and of A l u m i n a  Alumina-Fi11ed Bending Tests  and  57  Elastic  Moduli  Tests  72  Bending 79 Martensitic 87  Martensitic 89 of  Epoxy 105  vii  LIST  OF  FIGURES  Fi gure  Page  1  Acoustic  2  Ring-down voltage  3  Epoxy (a) (b)  4  count  (b) (c)  (AE)  monitoring  method;  V.  is  composites  and (c) Silicon  the  Aluminum plates rubber gasket apparatus  and  16 specimen.  attenuation  (a)  Test  for  (b)  Front-to-front  specimen  22.  tests.  attenuation  versus  attenuation  F i x t u r e used for a t t a c h i n g t r a n s d u c e r martensitic steel composite specimens  13  specimen  loading  24  8  bending  and  test  Three-point points  12  specimen  distance.  7  11  torsion  and  Double  10  and  to  pulser  39  46 distance 48  volume f r a c t i o n and of a t t e n u a t i o n lines  volume f r a c t i o n front-to-front  to  epoxy  E f f e c t of alumina volume f r a c t i o n and s i z e on t h e y i n t e r c e p t of attenuation E f f e c t of alumina s i z e on c o u n t s i n tests  27  33  versus transducer and g l a s s  E f f e c t of alumina s i z e on t h e s l o p e  points  loading  E l a s t i c c o n s t a n t s of a l u m i n a - f i 1 1 e d compared to t h e o r e t i c a l predictions AE c o u n t s for epoxy  4  threshold  6  9  . . . . . . . .  mould  Loading f i x t u r e , transducer front-view. Specimen back-view. Specimen side-view  Pulser  system  5  Wedge-1oading (a)  5  emission  particle 50 particle lines . . . . .  51  and particle attenuation 52  vi i i  Fi gure 14  15  16  17  18  Page Load versus time curve during wedge-1oading tests of specimens of d i f f e r e n t compositions  . . . .  E f f e c t of alumina volume f r a c t i o n and particle s i z e on f r a c t u r e toughness. Wedge-1oading tests. (a)  Average  particle  sizes:  50  ym  and  65  (b)  Average  particle  sizes:  90  ym  and  137  ym ym  ....  58  ...  59  Fracture toughness versus volume fraction. W e d g e - 1 o a d i n g and t h r e e - p o i n t bending tests  62  Fracture toughness versus volume fraction. Double t o r s i o n , w e d g e - 1 o a d i n g and three-point bending tests  63  Compliance versus machined notch length of double torsion specimen. Average particle size: 65 y m . V = 0.12  a .  f  19  56  Compliance specimen. V = 0.23  versus crack length for Average p a r t i c l e size:  a wedge-1oading 90 ym. 68  f  20  21  22  23 24,  AE of  versus time curve during wedge-1oading specimens of d i f f e r e n t compositions  E f f e c t of volume AE p e r u n i t a r e a p a r t i c l e s i z e . Average  particle  sizes:  50  ym  and  65  (b)  Average  particle  sizes:  90  ym  and  137  E f f e c t of volume AE p e r u n i t a r e a p a r t i c l e s i z e . Average  particle  sizes:  50  ym  and  65  (b)  Average  p a r t i c l e ' s i z e s :  70  ym  and  137  Enlargement epoxy  71  ym ym  ....  73  ...  74  fraction o f a l u m i n a on average for composites of differing  (a)  electron  tests  fraction o f a l u m i n a on total for composites of differing  (a)  Scanning epoxy  65  micrographs  (SEM)  of  ym ym  ....  75  ...  76  unfilled 80  of  Section  i x  A  in  Figure  23. ,  Unfilled 80  Figure 25  26  27  Page Enlargement of U n f i l l e d epoxy SEM o f  Section  B in  Figure  23. 81  alumina-fi11ed  epoxy.  (a)  Average  particle  size:  50  ym.  V  f  =  0.013  (b)  Average  particle  size:  65  ym.  V  f  =  0.194  (c)  Average  particle  size:  137  ym.  =  0.186  ..  84  (d)  Average  particle  size:  137  ym.  =  0.444  ..  84  SEM o f a l u m i n a - f i l l e d e p o x y pull-out. Average p a r t i c l e V = 0.013  V  f  ..  83  exhibiting particle size: 50 y m . 85  f  28  SEM o f a l u m i n a - f i l l e d e p o x y e x h i b i t i n g particle pull-out and embedded p a r t i c l e s . Average particle size: 137 ym. V = 0.186  85  SEM o f a l u m i n a - f i 1 1 e d e p o x y . on t h e s u r f a c e o f t h e a l u m i n a particle size: 137 ym. =  86  f  29  30  83  SEM s h o w i n g a particle size V = 0.186  Epoxy can particle. 0.186  be s e e n Average  small alumina p a r t i c l e . Average of the c o m p o s i t e : 137 ym. 86  f  31  SEM o f  iron  powders  Atomet  28  90  32  SEM o f m a r t e n s i t i c steel composite' exhibiting intergranular failure. Average particle size: 5 0 ym V = 0.01  90  SEM o f m a r t e n s i t i c at l i q u i d n i t r o g e n  92  f  33  34  steel composite temperature.  fractured = 0.000  SEM o f m a r t e n s i t i c steel composite exhibiting a region of p a r t i c l e decohesion. Average particle size: 40 ym. V = 0.01  92  SEM o f m a r t e n s i t i c steel composite exhibiting dimples. Average p a r t i c l e s i z e : 40 ym. V = 0.01  93  f  35  f  36  F r a c t u r e e n e r g y v e r s u s mean f r e e composites of d i f f e r i n g p a r t i c l e (a)  Average  particle  sizes: x  50  path for size. ym  and  65  ym  . . . .  109  Figure 36  37  Page (b)  Average 1 3 7 ym  particle  sizes:  90  ym  and 110  F r a c t u r e e n e r g y v e r s u s mean f r e e p a t h o f alumina trihydrate-epoxy composite^ ..  xi  an 112  NOMENCLATURE  crack  length  amolitude total  of  area  acoustic  of  wave  intersected  particles  Parameter in equations for calculating the t h e o r e t i c a l e l a s t i c modulus of particl f i l l e d composites AE a t a z e r o transducer Beam  between  source  and  thickness  Constant slab  distance  dependent  thickness  in  on  the  the  elastic  plane  of  modulus  the  crack  p a r a m e t e r i,n e q u a t i o n s for calculating the t h e o r e t i c a l e l a s t i c modulus of particl f i l l e d composites compliance c o n s t a n t d e p e n d e n t on t h e double torsion specimens interparticle  dimensions  distance  average  f i l l e r  particle  modulus  of  elastic  modulus  of  elastic  modulus  of  a  elastic  modulus  of  epoxy  elastic  modulus  of  glass  size  elasticity  xi i  alumina composite  of  Symbol  'AE F " F F  G G  co  G  o  !  emission  fraction  of  energy  acoustic  f r i c t i o n  force  fracture  energy  corrected  fracture  emission  beam  P sg  width  in  wedge-1oading of  a  non-grooved  moment  of  inertia  of  a  grooved  total  specimen  weight  a 1umi na  m  weight  of  alumina  weight  of  epoxy  weight  of  porcelain  weight  of  curing  agent  weight  of  liquid  epoxy  weight  of  epoxy  weight  of  a  sample  weight  of  a  sample  m m  curing LE resin  m. ( s>w m  n(A)  agent  points  in  three-  lenght  of  m  sample  ,  wei ght  B  sample  intensity  m A  m  tests  inertia  d i s t a n c e between loading point bending tests  accelerator  form  of  L/2  A+B  to  moment  stress  LT w  population  energy  K  m  wave  energy per u n i t area r e q u i r e d a new f r a c t u r e surface  H  !  acoustic  powder  and  porcelain  accelerator boat  resin  immersed  in  fraction o f t h e emi s s i on' wi t h amplitude greater than A  water a  peak  boat  Symbol  N  number  N  ring-down  counts  a v e r a g e number of p a r t i c l e intersections per unit area of s e c t i o n i n g plane  s  N  of  number  v  of  p a r t i c l e s per  N(t)  ring-down  p  probability a  applied  s  groove ,  of  slope  half  fracture  of  pulser  surface  of  a  c r i t i c a l line crack front highest  of  energy  curing  ambient work  counts  versus  distance  particle  T  per  temperature  temperature f r i c t i o n  volume  of  volume  fraction  V^£  volume  of  V  maximum  V  intersecting  lines  time  o  plane  length  t  Tp  rate  load  calculated Sp  volume  particle  P  SLO  count  unit  forces  alumina of  liquid  i n i t i a l  volume  of  a  V<.£  volume  of  solid  V^  threshold  f i l l e r epoxy  voltage  particle  P epoxy  voltage  xi v  unit  length  of  total RMS  volume  voltage  moment bar  arm  width  width  of  at in  in  a  time  t  double double  torsion torsion  three-point  tests tests  bending  specimens t h  crack  length  deflection  elevated  of  y intercept calculated  to  the  n  power  beams  of p u l s e r lines  counts  versus  parameter in the s t r e s s i n t e n s i t y of t h r e e - p o i n t bending specimens  distance  equation  thermal  contraction  thermal  contraction  coefficient  of  alumina  thermal  contraction  coefficient  of  epoxy  f i t t i n g  parameter  logarithmic wedge  half  Poisson's  coefficient  in  voltage  compliance.equations decrement  angle ratio  Poisson's  ratio  of  alumina  Poisson's  ratio  of  epoxy  transducer  resonant  frequency  dens i ty dens i t y  of  a 1umi na  d ens i ty  of  e p o xy  density  of  bubble-free  epoxy  composites  dens  ity  of  liquid  dens i ty  of  a  dens i ty  of  water  thermal  stress  epoxy  composite  xvi  ACKNOWLEDGEMENT  The Bennett, and  author Mrs.  D.  encouragement  wishes Benz  the  National  and  with  Acknowledgement Science  to  thank Mrs.  this  is and  E.  Dr.  J . S .  Nadeau  Nadeau, for  their  Mr.  Roger  guidance  work.  made  of  financial  Engineering  Canada.  xvi i  assistance  Research  Council  from of  1  1.  Ac oustic  emission  (  waves and to  generated  strain the  emission insight in  fields  many has  quality  used  sources,  emission  are  not  acoustic  emission  the  mental  of  this  specific  (i)  objectives  to  detection  is  as  the  obtained. to  gain  acoustic were  the  the  It  emission  of  of  for  the the  into  acoustic  advantage  realized  was  insight  the  of  generation overall  some  generation.  on  and  acoustic  emission  particle  mechanical during  composites.  the  of  until  fundaThe  following:  effect  particle-fi11ed  be  tool  prevention.  Full  nature  fraction  of  a  and  volume on  as  propagation  not  greater  processes  failure  will  applied  acoustic  a  and  such  determine  obtain  understood.  also  years  used  stress  waves.  fracture  been  local is  analysis  study of  to  elastic  the  term  twenty  and  has  in  the  elastic  order  failure  to  The  such  last  in  techniques  waves  mechanisms  the  clearly  knowledge  acoustic  objective  yet  given  changes  detect  over  failure  the  of  to  technique  However,  name  material.  monitored  This  control,  fundamental  a  deformation,  materials.  the  transient  within  studies been  into  is  during  techniques  In  INTRODUCTION  size  and  properties fracture  2  (ii)  to  relate  to  the  fundamental  acoustic  fracture  emission  of  mechanisms  particle-fi11ed  composites.  First, of  a  knowledge  1.1.  brief  on  testing  mation  phase  The  which  generated  the in  surface  response  of  the  transducer  processed.  which,  in  harmonics  addition of  system to  fying.  the  noise^.  a minimum The  signal  with  processes  of  the to  a  It  is  through  to  amplifying and  and  is  then  the  followed is  the  f i r s t by  analyzed  wave is  f i r s t  great  a  defor-  structure. to  detect  (event) electroniamplifier  produces deal  of  amplification  f i l t e r i n g in  are  structure.  signals, a  a  used  which  contributes  Therefore,  failure,  are  a  active  signals  within  strain  signal  passed  are  monitored  emission"  signal  state  Detection  emission  transducers  the  cally  the  conjunction  on  "acoustic  present  techniques  acoustic  transformation  electromechanical  the  for  monitoring  waves  becomes  kept  Acoustic  in  the  Emission  Emission  and  strain  Acoustic  emission  of  emission.  of  transient  Sensitive  given  Required  methods  or  of  is  Instruments  Acoustic  the  acoustic  Measurement 1.1.1.  summary  and  processing  is  reampliunit.  3  This  step  output chart  is  will  be  shown  (Fig.  explained  on  a  in  digital  Section  display  1.1.2.  and/or  The  final  plotted  on  . a  1) .  1.1.2.  Parameters  Used  for  Measuring  Acoustic  Emi s s i on  The  number  (amplitude) old  value  event  in is  (Fig.  damped  an  Ring-Down  of  times  2).  sinusoids  the  acoustic  defined  as  Count  Method  magnitude  emission  the  The  signals  and  the  event  ring-down are  number  of  voltage  exceeds  count  usually of  the  a  number  in  the  ring-down  threshfor  form  that of  counts,  N,  for  2 event  detected  by  the  transducer  N  where  v  V  R  o  The,count time  the  transducer  is  the  logarithmic  is  the  maximum  is  the  threshold  rate  during  is  which  the they  take  shown  to  be  :  CD  resonant  frequency,  voltage  decrement,  i n i t i a l  ratio  been  In  3  is  has  voltage,  and  voltage.  of  the  place.  number  of  counts  to  the  an  4  TRANSDUCER AMPLIFIER  FILTER SAMPLE  PREAMPLIFIER  SIGNAL PROCESSOR  PLOTTER  Figure  1.  Acoustic  emission  monitoring  system.  NUMERICAL DISPLAY  5  6  The facto  number  geometry  gain  (ii;  selected  (iv;  is  the  of  of the  amplifiers  threshold  following  specimen  ( vi i [  transducer  to  source  transducer  number  of  of  and  the  signal),  f i l t e r s ,  voltage,  to  The  the  range,  transducer  i  by  specimen.  (vi;  ( vi i  influenced  amplification  frequency  detection  (v;  of  (magnitude  performance  ( i i i  counts  rs:  the  (i:  of  bond,  distance,  properties.  counts  is  not  a measure  of  a  fundamental  property.  This  Root  technique  amplitude  of  threshold  voltage.  intensity  of  dication process. studying  of  the  acoustic Used  acoustic  the  signals alone  it  emission,  strain  Therefore,  Square  measures  acoustic the  Mean  energy  the  (RMS)  root and  it  released  RMS m e t h o d  emission  mean is  yields  but  is  intensity.  Method  not  of  not  the  more  the  dependent  information  does in  square  give  total  suitable  on  on  the  an  in-  fracture for  7  Energy equipment  analysis  and  can  of  (i)  the  sum  (ii)  the  area  voltage  mean  The same the  squared  voltages  time  sive  A  the  count  V(t)  is  the  RMS v o l t a g e  analysis affect  the  on  the  voltages,  squared  (2)  energy,  rate, at  methods  a  are  time  t.  influenced  the  ring-down  detection  threshold  voltage.  Distribution  Analysis  Amplitude  analyzed.  emission  2  is  of  peak  EN(t)V (t)  measured  to  ring-downs  =  £  the  that  sophisticated  curve,  is  distribution  only  the  o N(t)  energy  more  following:  under  are  the  E ^  exception  events  of  using  of  vs.  variables  The  one  by  squares  E  RMS a n d  possible  the  (iii)  where  is  of An  amplitudes amplitude  the  peak  amplitude  which  tend  to  the  the  method  acoustic  sorter,  of  obscure  of  count  by  which  signal,  with  emission is  not  essential  the  responto  data,  the has  3 been  employed  .  The  different  amplitude  amplitude  sorter  ranges:  0.05  -  sorter ranges.  separates 0.5,  0.5  -  separates For  the  example,  the  signals  50,  50  -  amplitudes the  into  500,  500  into  Dunegan  the -  Endevco  following 5000  and  8  >  5000  mV .  The  J  amplitude  f a l l s  fraction between  A  of  the  and  A  emission +  6A,  population  where  A  is  whose  the  peak  3 amplitude,  is  given  F.  where peak  n(A)  is  the  amplitude  in  the  This  yielding  RMS  the  of  the  -  :  n(A)  (3)  emission  population  analysis  is  useful  processes  in  the  also  detect  deformation very  different failure  analysis  whose  can  or  significant  failure  of  changes  mechanism.  for  failure  processes  example,  Therefore,  complement  recog-  presence  useful,  occur.  for  ring-down  in  such  fibre as  matrix  amplitude count  and  measurements.  where cessing the  6A)  relation  A.  can  becomes  fibre  distribution  +  It  where  and  n(A  deformation  of  technique  composites,  =  fraction  noise.  nature  following  distribution  specific  background  the  exceeds  Amplitude nizing  by  Frequency  The  emission  the  waves  by  data  a as  frequency . 2  are  signal  is  Analysis  passed  translated  into  into  digital  computer.  Fourier  transform  a  between  peak  relation  a  transient form  for  programs  amplitudes  recorder  and  pro-  interpret wave  9  This  technique  i s t i c  of  major  amplitude  can  particular  For  example,  and  matrix  in  acoustic should  fibre  reinforced  wave  frequencies.  does  not  should It  have  occur  frequencies  such  pronounced  fibre  different the  Ideally,  frequencies.  composites,  that  character-  sources.  for  exhibit  appears a  wave  emission  peaks  yielding  always  reveal  characteristic  geometry  influence  failure  on  of the  the  sample  frequency  2 a n a l y s i s .  This and  the  it  is  1.2.  requires  interpretation  not  as  commonly  Sources  At as  method  of  present,  acoustic  of  emission  used  (ii)  dislocation release  of  as  deal is  the  of  instrumentation  complex.  other  Therefore,  methods.  Emission  following  processes  have  been  sources:  4 (i)  great  results  Acoustic  the  a  glide  5 '  ,  dislocation  pile-ups  from  pinning  A ( i i i )  points', decohesion  and  fracture  of  second  phases  fi -1 ? of  inclus ions  "  ,  13 (iv) (v)  release phase  of  cracks  from pinning 14 15 transformations '  points  ,  and  identified  10  1.3.  Current  The to  its  Research  major  of  have  strain  2 waves stress  . and  strain  of  with  waves  to  characterize  on  are  related  detection.  parameters, the  the  effect  such  as  generation  loss  attenuation^.  of  into  of  the  The  wave  Attenuation  dispersion  through  of  bulk  acoustic  sound  in has  waves  m a t e r i a l ^ .  involved,  very  causes decrease  space been and  also  work  has  the  resonances  effects,  second  inter-  phases  attenuation of  of  amplitude  due  contributes  the of  local  by  system  expressed of  of  influenced  with  Because  l i t t l e  change  thermal  interaction  wave.  the  are  the  boundaries,  discontinuities  stress  spreading  variables  structural  dislocations,  propagating  waves  at  analyzed 2 13 time ' .  measurements  Energy  the  the  and  emission  have  with  emission  microstructural  the  studies  fields  and  of  acoustic  macroscopic  toughness,  Other  attenuation.  the  made  Emission  4-12 '  scattering  to  about  been  and  and  Acoustic  action  Acoustic  propagation  microstructure  stress,  and  concerns  generation,  Attempts  on  as  a  to  function  absorption the  been  of  numerous done  on  attenuation.  Attempts measurements  are so  being  that  made  results  to  standardize  obtained  using  acoustic different  emission testing  techniques for  .become  instance, 2  gains  to  comparable. compare  It  then  experiments  18 '  ,  materials  and  equipment.  becomes  done  with  possible, different  12  2.  In been  this  given  cation,  f i l l e d  of  the  The  rationale  selection  of  and  The  on  epoxy  description  tests,  materials  alumina-fi11ed  experiments  a  materials,  characterization  and  have  composite fracture  selected  martensitic  composites  1)  material  characterization  2)  fracture  tests  3)  acoustic  the  section  the  purpose  and  attenuation  essential acoustic  and  to  procedure were  emission  fabri-  and  were  acoustic  alumina-  steel.  were  divided  into  •However, this  for  these  given; the  with  material  measuring the  data  results  consist  bending studying tests  chapter.  of  tests  the  from  from  characterization, density, these  the  e l a s t i c i t y  tests  fracture  were and  experiments.  tests  three-point  undertaken  emission  dealing  interpret  Fracture  in  PROCEDURE  categories:  In  and  a  experiments.  epoxy  three  chapter  material  emission  EXPERIMENTAL  To  of  tests. fracture  were  double  torsion,  Double  torsion  and  abandoned  confirm  acoustic for  wedge tests  were  emission.  reasons  wedge-loading  loading,  tests,  explained three-point  13  bending  tests  were  Acoustic test  emission  bending  2.1.  tests  were  Selection  were  as  (i)  monitored  during  every  fracture  because  of  only  three-point  experimental  . d i f f i c u l t i  for  selecting  the  material  to  be  number  of  tested  fol1ows :  materials  the  of  had  to  easy  In  order  composites  to  were  f i l l e r  e m i s s i o n , such  control  to  as  fracture  have  acoustic  micro structure  be  the  steel  Materials  c r i t e r i a  the  hard  martensitic  conducted  of  mechanisms  and  was  alumina-fi11ed  The  and  out.  performed.  For  (ii)  carried  of  chosen  and  particles  the  the was  particles  during  material  fracture,  chosen  had  to  reproduce.  these  dislocation of  minimum  emission  and  f u l f i l l  a  requirements, selection  made. glide, were  of  a  Sources dimple thus  particle-fi11ed b r i t t l e of  acoustic  formation,  avoided.  matrix  y i e l d i n g ,  14  The which  is  material very  hard  particle  sizes.  abrasive  grain  separated 75-105  Zinc  was  steel  To  of  Fe  The of  and  The  (Shell)  thus  not  suitable  that  martensitic  Mn:  0.01  wt.%  Si :  0.10  wt.%  carbon  was It  range  oxide, of  technical was  sieved  36-44  ym,  in  favour  the  for  zinc  of  and  55-74  ym  martensitic was  fracture  matrix was  matrices.  composite  b r i t t l e  composition  0.105  28:  wide  ranges:  steel  Carbon:  aluminum  ym.  discarded  following  a  used  i n i t i a l l y  found  of  from  very  tests.  powder,  iron  used:  wt.%  balance  was  Fisher  S c i e n t i f i c  technical  grade  powder.  epoxy  anhydride and  size  125-149  were  in  was  Carborundum.  was  the  f i l l e r  oxide  following  epoxy  Atomet  graphite  methyl  W from  ym,  a  available  it  the  source  is  as  aluminum  subsequently  fabricate  powder  the  and  because  ductile  The  106-124  Zinc  and  type  into  ym,  selected  the  was  fabricated  (Ciba  Geigy  accelerator  using  906),  the  the  hardener  epoxy  t r i e t h y l amine  resin  (Ciba  nadic EP0N  Geigy  828  6010).  15  2.2.  Fabrication 2.2.1.  The  of  Composites  Fabrication  cycle  of  of  mixing  Epoxy  and  Composites  curing  used  was  described  by  19 R.J. the  Crowson  and  following  R.G.C.  Arridge  .  The  matrix  material  had  composition:  100  parts  by  weight  -  Resin  Epon  90  parts  by  weight  -  curing  828  agent  nadic  methyl  a n h y d r i de 2  parts  by  The  alumina  powder  The  mixture  was  The  epoxy  and  stirred  in  a  it  from  mixture cast 3.5  vacuum  20  to  then  =  added 40°C  added  minutes.  and  and  The  to  the  accelerator  was  heated  for  five  heated  mould  the  for  of  hours  temperature to  aluminum  type  sixteen  200°C  for  plates  mould  and  was half  and  allowed  a  minutes.  at  hour.  silicone  heat,  a  100°C.  increased an  was  and  The  minutes. heated  left  standing removing  added  and  the  mixture  frequency To  to  20  was  After  minutes.  rotated at  was  agent.  for  mixture  mixture  the  a  curing  stirred  dessicator  more  t r i e t h y l amine  the  the  finally  This  was  f i r s t  five  into  two  heated  accelerator  for  rev/min  and  for  was  -  dessicator  process,  of  resin  weight  end  the  150°C  for  The  mould  was  of curing one  hour  consisted  rubber  frame  (Fig.  trapped  gases  to  be  3).  16  17  released  while  rectangular formulas agent,  slabs  used  to  epoxy  volume  cured.  measuring calculate  accelerator,  particular as  the  and  22  The cm x  the  7.6  amounts  alumina  fraction  samples  of  cm x of  were  1.3  The  cm.  resin,  necessary  f i l l e r ,  obtained  for  V^,  were  curing  achieving  a  developed  fol1ows  V  V  where  •  f  ^  =  f  (4)  ^  (5)  is  the  volume  of  aluminum  V<~£  is  the  volume  of  solid  V  is  the  volume  of  the  T  Epoxy  shrinks  5% o f  the  during  volume  of  curing. liquid  epoxy,  Substituting  volume  - V  The  shrinkage  epoxy  -  f  V with  ( V ^ ) .  m  A  —  mass  "  and  composite.  0.95 1  oxide,  V.  is  approximately  Thus,  c  ^  density  V A  V  f  (6)  ratio,  m/p:  (7)  18  LE  M  P/\  where  =  3  •  9 0  9  r  /  P  le  =  1.17  V  T  =  226  cc  1%  loss  Considering  a  (T95  '  c  c  of  the  this  the  m  m  material  =  A  =  of  V  281(1  -  the  curing  =  Fabrication  Particle-fi11ed mixture  of  graphite,  iron  V )  (described  Steel  was  can  at be  the  beginning  obtained:  m. LE  (11 )  r  0.469  ° -  "  and  (10)  f  equations  =  of  steel  (.9)  0.521  . agent  casting:  f  matrix  following  . resin  during  890  "accelerator  2.2.2.  8  ±  of  L E  composition section)  <>  ±  m  From  " V  ±  gr/cc  m  VLE<'  0  1  0  m, LE  (12)  c  ™ L E  (  1  3  Composites  obtained  alumina  by  hot  powders.'  forging The  a  graphite  )  19  content was  was  1 wt.%  enclosed  cups  to  a  prevent  15  minutes.  hot  worked  forging  in  steel  was  steel 40  a  1.55  The was  by  approximately  The particles but were  2.3.  samples from  0  containing also  hardness the  a  with  heated  a  at  forging  50  R^.  rate  1100  C  for  made  of  loadused  50 of  powder  graphite  die  The  was  diameter  This  KN/sec. 5.70  for The  cm.and  was  then  hot  during  to  0.05.  alumina  of  at  heating.  mm r e d u c t i o n  contained  rolled  in  1100°C. Six  thickness,  volume Samples  different  fractions of  passes, were  of  similar  grain  The  steel  each  of  used.  alumina  volume  sizes,  fractions  Section  2 . 1 . ,  made.  Tests 2.3.1.  on  Epoxy  Composites  Material  Characterization  Density Determi  After was  in  loading had  covered  and  of  mixture.  cm.  graphite 1.5  placed  product  material  covered  a  KN a n d  forged  of  iron-graphite  container,  then  of  cylindrical height  the  decarbonization,  It  was  in  unknown  casting, because  the  and  Particle  Volume  Fraction  nation  actual  particle  volume  fraction  segregation  of  occurred  alumina during  .  20  this in  process.  order  to  The  calculate  the  particles.  the  volume  the  a  the  nylon  thread  it  an  'on  using  in  the  were  was  measured  introduced  essential  a  piece  density  of  method.  to  and  following  percentage  broken,  the  balance.  water,  composites  to  by  measure  f i l l e r .  The  glued  analytical  immersed  was  immersion  were  the  void  the  faces.  water  of  values  of  sample  fracture  using  the  Density  fraction  After of  density  the  Small  specimen The  weighed  was  again.  piece  strings in  sample  cut. from  order  was  was  measured  of  thin  to  suspend  dried,  Density  one  was  weighed, determined  equation:  (14)  5  P  "  s  s  m  ~  (  p  is  g  m. (m  s  )  w  D w  p  Next by  the  the  sample  s  the  weight  of  the  sample,  is  the  weight  of  the  sample  in  water,  is  the  the  following  The  epoxy  and  weighed  V w  w  p  where  t  density,  immersed  and  density  amount  of  of  water.  alumina  in  the  sample  was  determined  procedure:  composite  sample  separately.  and  The  a  boat  porcelain was  boat  were  again.weighed  dried with  21  the an  specimen hour.  weight  of  inside,  and  Only  alumina  boat  and  placed  in  the  furnace  in  the  container  together  was  measured.  was  powder  left  (ra. A+B R  v  =  f  where and  The  m  /\ 3  the  s  +  m  is  g  density  of  Elastic equations in  wedge  loading  e l a s t i c i t y  data were  were  the  developed  for  obtained  specimens.  is  described  Section  deflection  powder  using  to  and  a  1  5  )  boat  pycnometer.  verify  for  calculating  the  the  calibrating  The  the stress  analytical intensity  procedure  modulus the  of  of  compliance  this  +  experiment  ^ H  Specimen  (  4).  while  wedge-loaded  +  f l  boat  needed  (Fig.  required  the  Constants tests  and  for  s  measured  Elastic  of  in  R  alumina  of  was  constants  (Sect.  The  weight  alumina  of  550°C  m )/p — B A m /p s  weight  the  -  at  per  unit  (.16) By  load  (a)  (b)  + B n l B (c)  4-  Figure  4.  Wedge-loading (a) (b) (c)  apparatus  and  specimen.  Loading f i x t u r e , transducer front-view. Specimen back-view. Specimen side-view.  and  specimen  23  where  E  is  the  modulus  P  is  the  load  the  y^,  to  the  (Figure  a  is  the  crack  H  i s  the  beam  width,  B  is  the  beam  thickness,  y  is  the  deflection  In  order  composites  necessary  to  to of  attenuation.  attenuation  Wave  compare  the  the  epoxy  the  in  4),  two  (Figure  Elastic  The  of  of  y-j ,  different  know  sample  length,  direction  on  e l a s t i c i t y ,  applied  direction  the  of  of  either  4).  acoustic  of  alumina  emission  content particle  particles by  in  Attenuation  f i l l e r  effect  beams  and  generation  sizes, it  volume  might  increasing  fraction  change  the  was  the  scatter  of  * the  waves  or  Therefore, on  every  In end  of  by  the  improving measurement  sample,  some  prior  tests  an  the  propagation  of  of  attenuation  was  to  the  AE  source  an  epoxy  composite  cm,  while  a  fracture  x  1.3  transducer  was  *  D u r i n g t h e s e e x p e r i m e n t s i t was g l a s s had much l e s s a t t e n u a t i o n  carried  was  measuring  placed  waves  . out  test.  (pulser)  specimen  the  at  fixed 22.0  the  found that than epoxy  at  cm'x  other  one 3.7  end  cm (Fig.  Figure  5.  Pulser (a) (b)  attenuation  tests.  Test for attenuation versus distance, test. Front-to- front attenuation  25  AE  counts  pulsing. the  in  22.0  accumulated  Then,  pulser  were of  were  the  was  cm  x  distance  reduced  contact.  The  3.7  for  cm  in  x  between  2.5  same  periods  cm  test  0.6  cm  for  of  the  one  a  done  of  transducer  decrements was  minute  until  for  pulsing  a  and  the  glass  period  two sample  of  five  minutes.  A  second  and  the  the  sample  type  transducer  The  of  placed  thickness  Wide  -  908  band  range  used  0.2  Preampli fi  was  front  (Fig.  equipment  Pulser  test  conducted  with  to  separated  front,  the  pulser. by  5b).  for  the  attenuation  tests  was  Dunegan/Endevco  transducer,  sensitive  -  D 9201  0.8  MHz  -  in  the  frequency  D/E  er  Filter Post-amplifier Ring-down  counter  Plotter  Items 301  Test  pulse  (iv)  through  Totalizer.  generator  (vi)  Item  were  ( v i i i )  contained was  in  contained  the in  Dunegan the  Endevco  Dunegan  26  Endevco (ii)  920  through  generator into in  distribution  a  gives  burst  i t s e l f  A not  In  is  the  a  pulse  -  one  acoustic  intensity  in  crack  slow  length  through  the  was  were  of  1,1,  is  items  The'test  transformed  pulser.  The  pulser  kept  crack  this  which  f i l t e r e d .  gain,  A  were  threshold  frequency  range,  constant.  Torsion  the  Specimens  objectives rates  growth their  to  of  this  geometry  The  study  values  Double  stress  sample.  of  the  tests.  simple  independence  for  were  Signals  Tests  of  of  used,  The  emission  because the  Section which  range  Double  correlate  of  in  functions  volts  fixed.  Fracture  I n i t i a l l y ,  because  dB  MHz  was  chosen  +5  waves  95  voltage  2.3.2,  were  of  0.3  volt  threshold  of  The  transducer,  gain  1  explained  stress  0.1  of  were  a  of  total  voltage and  (vi)  analyzer,  (Fig, (K)  stress  to  stress  torsion  intensity  standard  of  was  6) on  tests and the  intensity  20 equation  is  the  foil  K  o w i n g :  =  Pw m  m  (  3  (  1  +  v  3  WB B J  n  )  )  V  2  (17  Figure  6.  Double  torsion  specimen  and  loadi  28  s  the  total  W/2  s  the  bar  width,  B  s  the  bar  thickness,  s  the  slab  of  the  crack,  is  Pois son's  where  P/2 w  B  applied  to  one  bar,  m  n  V  Two torsion  (i)  load  methods  were  thickness  in  the  plane  ratio.  used  to  measure  crack  speeds  in  double  tests:  The  load  relaxation  displacement  is  method,  kept  where  constant  the  while  crosshead  the  crack  is  propagating. (ii)  The  constant  speed  is  load  kept  method,  constant  where  while  the  the  crosshead  crack  is  propagating.  The  compliance  of  double  torsion  specimens  can  be  expressed  21 with  the  following  equation  y  where  B  modulus  c  and of  C  the  c  are test  =  :  P(B a  constants material  c  +  c  that and  (.18)  C )  depend  the  on  the  dimensions  elastic of  the  specimen  29  and  test  device.  the  following  Differentiating  for  the  expressed  as:  where  a.  is  given  _ "  load  the  relaxation. is  the  (B  a  +  relaxation  length  the  constant  following  Procedure:  thin the A  cm  x  1.3  diamond diamond  small  bottom  5.08  x  time  yields  same  was  initiated  notch. Figure  is  crack  the  speed  Toad  method,  the  at  can  the  crack  be  onset  of  speed  (21)  epoxy  through  by  2.5  cm  slabs  the  half  depth  direction pressing  The  double  6.  The  cm/min.  P.  the  (19)  c  the  along  da dt  c  dy_ _ J dt B P  of  in 10  _  notch  _3 was  to  equation:  Particle-fi11ed  A  B P  load  saw.  the  illustrated  and  grooved  saw  dP dt  method,  cm w e r e  crack of  )  c  d_a dt  7.6  C  c  crack  For  by  respect  equation:  dX dt  Thus,  with  torsion  crosshead  22.0  width  was  as a  of  also  the  razor  with cut  groove  used  is  the  a  (Fig. to  for  x  with  blade  fixture speed  cm  6).  the  experiments  30  Several double the  problems  torsion  crack  cracks  tests.  along  transparent.  the  A  for  Because  of  abandoned  and  a  load The  and  cell  a  the  stress  supporting  moved  in  the  into  method  in  locating was  this  could  was  not  when  the  case  the  not  torsion  out  be  tests  applied.  were  adopted.  Specimens  specimen  Instron notch  in  material  grooves;  rod, which  the  carrying  encountered  double  beam  an  the  intensity  Wedge-Loading  cantilever  while  difficulty  was  guiding  problems,  contained  wedge  the since  a wedge-1oading  double  wedge  was  difficulty  calculating these  encountered  specimen,  from  A  One  second  wandered  formula  were  was  was  attached  testing  during  placed to  machine  the  test.  between a  compression  (Fig.  4).  A wedge  of 22  30°  was  The  specimens  for  double  x  3.7  The of 3.5  cm  x  groove the  of  sides  contact  as  here  torsion 1.3  suggested were  cm w e r e  cut the of  one  by- t h e  Epoxy  thin  end  of  2/3  thick  diamond  notch  a  crack  was  with.the  wedge.  were  Hoagland of  their  saw  groove  a  notch  arms  of  diamond the  of  rectangular  with  the  work  uncracked  grooved  a  -  At  the  tests.  made with  beam.  cm w a s  bottom The  chosen,  ran a  saw  initiated  levelled  in  samples slabs  total along  notch (Fig. with order  et  of 4). a to  of  al  used 22.0  cm  thickness. the  axis  approximately At  the  razor  blade.  allow  better  31  The of  wedge  analytical loading  expression  tests  was  for  the  developed  fracture  as  toughness  follows:  8a P 3  (16)  H By 3  and (22)  P  Fracture  energy,  G  ,  is  given  2  Substituting  (16)  and  (22)  by  p  equation  ( 8 4 Ar )  2  in  (23)  H  the  it  is  assumed  stress  s  Therefo re,  that  intensity,  the K,  2  K  3  B  B  a  n  factor is  2 (24)  /GE  -1/2  E 2  (1-v  related  -  (23)  V  12P  If  (23)  to  )  is G by  approximately equation  one  (25)  (25)  32  Since  the  careful  stress  intensity  measurement  locate  the  crack  groove  was  coated  The  of  in  sample  the  the  a  function  crack  a  layer  loaded  of  as  of  length  specimen,the  with  was  is  was  side  black,  the  crack  length,  required.  opposite  To  the  water-proof  wedge  travelled  ink.  at  a  -3 constant  speed  vs.  time  was  recorded.  dropped;  the  position  local  maximum  propagation until data  the  of  5.08  load  of  50%  a  the  chart  these  number  tests  Three-Point  tests  were  in  done  the  in  from  epoxy  slabs  the  total  thickness  of  notch.  by  pressing A  compressive  a  cell  with  razor  three-point load  The  broken. in  Bending  of a was  bending on  the  the  load  and  the  crack  testing  A  sample  continued of  the  I.  Tests  to  confirm  the  toughness  experiments.  10.5  cm x  thin  diamond  made  blade  load  after  Appendix  order  of  specimen  labelled  wedge-1oading  samples  the  (i).  is  graph  propagated,  on  were  completely  for  The  crack  crack  was  rectangular  initiated the  the  sample  obtained  cut  the  same  These  were  When of  on  cm/min.  the  The  10  with  obtained  values  x  and  into  fixture  Instron  1.4  a  the was  (Fig.  cm x saw.  crack bottom  1.3 A  notch  was of  attached 7).  cm  to  33  gure  7.  Three-point  bending  specimen  and  loading  points.  34  Some  of  the  these  tests  whole  specimen).  The  (the  toughness  samples crack In  for  exhibited  stopped  these  these  slow  before  cases,  samples  growth  propagating  the  is  crack  maximum  given  by  through  load  the  during  was  the  recorded  following  23 equations  : K  -  2 ^ V l * 2  Y(L/W  B  =  8)  =  1.107 -  where  the  distance  Wg  is  the  sample  Y  is  a  and It  per  applicable Once  the  fracture Equations  for  for  specimen  load  the  performed  analytically  the  unit  comparing was  a  to  double  the  crack to  torsion  toughness  calculation  of  of  specimen  had  could  relating  length  of  dimensions.  (Section out  been be  in  for  the  sample  developed this  completed,  calculated  these  de-  equation.  equations  calibration  velocities  the  standard  the  tests  Compliance  crack  the  carried  energy  25.  points,  Specimens  the  whether  calibration  and  (28)  4  B  consists  compliance  23  2  B  14.25(a/W )  on  Torsion  experiments  and  )  Calibration  the  verify  7  and  measurements to  7.71(a/W )  loading  dependent  Compliance  Calibrating  +  3  between  Double  +  B  width  parameter  flection  2.120(a/W )  B  is  2  VB  13.5(a/W )  L/2  -  (  also  study. the using permits  samples.  were  35  In  order  ("cracked") vs.  time  crack  to  perform  sample  and  load  length.  was vs.  loaded time  Then,  the  this  was  2/3  the  compliance  for  was  considered  calibrated.  load the  the  was  function  The  loads  the  length.  voltage  six  the  crack  deflection  to  534  were  of  tested.  until  The  length  crack  the  relation  with  the  notch obtaining  the  sample  length,  of  sample  the  After  using  deflection  function.  the  made  notch  increased  of  lengths,  each  notched  particular  was  specimen.  a  deflection  a  notch  For  of  of  for  the  the  The for  and  slope  the  of  particular  compliance  plotted  as  length.  the  sample  transducer  N were  the  linear  compliance  Graphs  of  a  graphs  recorded  different  as  measurements,  the  of  of  analysis,  differential  up  lengths  length  approximated  line  were  repeated  total  regression  was  notch a  of  was  and  length  and  linear  process  compliance  measured  (LVDT).  recorded  notches  was  for  were  the  made  with  a  Deflections different with  a  linear  of  notch  thin  diamond  s aw.  Compliance performed torsion bration  for  the  samples. of  Wedge-Loading  calibration same The  grooved  of  reasons  wedge-1oading it  compliance  specimens  Specimens  was test  when  the  carried made  specimens out  for  possible  analytical  the  was double cali-  solution  was  d i f f i c u l t .  elastic  Once  modulus  of  the  the  calibration  material,  was  done,  fracture  using  toughness  the was  calculated.  Procedure: with  a  razor  Two  blade.  ducted'  and  of  cross-marks  the  scope. men,  After  the  the  were  crack  effects  recorded.  of  2.3.3.  while tape there A  Acoustic  A D/E  gain  of  95  between dB  was  as  on  the  a  load  to  speci  and  de-  compliance  length  groove  micro-  the  Section  crack  con-  deflections  travelling  in  a  sample  being  obtaining  the  of  measure  c a l i b r a t i o n .  Tests  was  attached  (Figs.  samples  to  bending 4,  6  and/or  specimens  used.  was  the  and  three-point  the  the  marked  of  with  on  tests  the  a  and  without  groove  and  notch,  same  sample  transducer  around  contact  the  and  fracture  wrapped  was  a  method  on  test  stopped  Emission  wedge-1oading,  performing  total  side  was  was  made  using  located  The  graphs  the  D 9201  was  was  with  the  torsion,  crack  obtained  was  the  measured  of  cm  A  were  were  fracture  penetrated  compliance  2.5  the  crosshead  length  The  While  wedge  Instron  flection vs.  the  cross-marks  Signals  and  and  the  specimens 7).  fixture the  which  double  Teflon where  fixture. were  not  37  in  the  0.1  voltage and  -  0.3  1  volt  of  threshold  MHz  range  was  fixed.  voltage  were  test.  Graphs  of  on  the  charts  attached  In  the  wedge-1oading  same  (i)  a)  the  AE c o u n t s  b)  the  local  c)  2.4.  the  Tests  to  the  used  on  for  threshold  were  fracture recorded  emission  crack  range,  every  time  acoustic  equipment.  propagation  the  designate:  the  maximum  vs.  A  frequency  constant  after  to  out.  gain,  emission  AE  load  vs. on  time  the  chart,  load  vs.  chart, position  of  on  Composites  Steel  the  crack  Fracture  Tests  Milling  machines  could  material  steel  composite  caused  specimens  were  involving  a  slabs  kept  2.4.1.  the  f i l t e r e d  The  tests,  number  time  from  acoustic  was  were  severe chosen  minimum  yielded  not  slabs  tool  a maximum  be  of  the  used  because  wear.  because  amount  on  of  specimen.  for  the  producing  alumina  Three-point their  simple  cutting.  Also,  number  used.  The  samples  were  cut  x  cm,  using  thin  diamond  of  into  specimens pieces  of  the  bending preparation, the  when 7.5  in  samples  hot-rolled beams  cm  x  of  10  0.6  were cm  _3 0.25  a  saw  at  a  speed  m/min.  38  In the  order  to  composite,  Leco  its  Analyzer.  range  0.52  eliminate matrix,  -  estimate  Carbon  0.66.  surface  the  carbon  (Fig.  A three-point load  of  determined  samples  were  surface-ground  To  get  depth  the  be  in  homogeneous  austenized were  bending  on  a  to  at  860°C  made  on  fixture,  Instron,  was  of  using  found  50%  cell  was  were  were  Grooves  compressive  content  scales.  specimens  austenizing' temperature  contents  The  quenched. 7).  the  a  the to  martensitic and  the  water-  sample  attached  to  used.  cross-  A  a  - 3 head the 27  speed  and  28  The  were  hot  broken  by  Some  to  impact  of  and  to  test  Equations  fracture  nitrogen  X-ray  B  7)  recorded.  liquid  fracture  D/E  the  to  r o l l i n g ,  A  (Fig.  calculate  specimens  the  were  maintained  hot  Acoustic  sample  loads  was  consolidation  2.4.2.  D 140  cm/min  the  and  at  the the  10  maximum  forging  examining  Microscope  x  used  order  during  the  5.08  samples.  In  in  of  were  Emission  transducer using  the  of  toughness.  the the  iron  powders  samples  was  temperatures.  coated  surface energy  one  of  break  using  with the  dispersive  gold  to  Scanning  ai d Electron  analyzer.  Tests  was  fastened  device  shown  to in  one Fig.  side 8.  of The  Figure  8.  F i x t u r e used f o r a t t a c h i n g transducer to martensitic steel composite specimens.  gain, the  frequency  same  as  range,  described  and in  threshold  Section  voltage  2.3.3.  used  were  41  3.  The  RESULTS  results  and  the  tests  conducted  The  order  followed  followed  for  The epoxy  the  in  composites  were  study  the  three  Fracture  data.  3)  Acoustic  emission  3.1.  on  Tests 3.1.1.  and  in  is  from  this  chapter.  similar  to  the  experiments  on  categories:  data.  AE  results  were  presented  for  the  Composites  Material  Characterization  Density  and  Particle  Volume  Fraction  D e t e r m i n a t i on The fractured  densities samples  and  are  particle  listed  in  volume Table  I,  fractions The  of  density  the of  3 alumina  was  determined  that  procedure.  composites.  Epoxy  data  divided  2)  steel  the  into  obtained  reported  from  characterization.  martensitic  are  data  calculations  Material  fracture  the  experimental  1)  Only  of  presenting  describing  and  CALCULATIONS  trends  the  for  results  AND  as  3,990  g/cm  using  pycnometers.  TABLE I Densities and Volume Fractions of AluminaFilled Epoxy Specimens  Average Alumina Particle Size (pm)  -  40 II  II  50 II  11 II It II  65 II II II II II II II II II II II II II  11 II II  90 II II II II II II II  115 II II II  128 II  137 II II II II II II II II II II II II  Density (gr/cnw)  1.22 1.22 1.24 1.48 1.76 1.26 .1.29 1.32 1.45 1.58 1.61 1.33 1.34 1.35 1.44 1.45 1.48 1.55 1.56 1.58 1.75 1.76 1.77 2.00 2.01 2.01 2.14 2.14 1.24 1.34 1.58 1.74 1.75 1.85 2.08 2.17 1.27 1.30 1.44 1.47 1.44 1.51 1.23 1.23 1.28 1.29 1.31 1.32 1.73 1.93 1.93 2.00 2.07 2.44 2.59  Alumina Volume Fraction  0.000 0.000 0.006 0.090 0.128 0.013 0.025 0.037 0.087 0.132 0.140 0.038 0.042 0.045 0.077 0.083 0.093 0.121 0.124 1.130 0.191 0.194 0.200 0.288 0.288 0.287 0.337 0.336 0.007 0.042 0.134 0.189 0.195 0.230 0.314 0.378 0.096 0.025 0.076 0.093 0.078 0.106 0.001 0.003 0.021 0.025 0.031 0.034 0.186 0.258 0.260 0.281 0.309 0.444 0.499  + The average alumina particle size was obtained by averaging the highest and lowest particle size in a determined range.  43  The with  density  increasing  bubble-free  and  was  the  second  firmed  to  was  function  =  be  in  V p f  A  as  then  +  (1  agreement  The  calculated  -  V ) p f  with  Therefore,  bubble-free.  expected,  fraction.  was  place.  Fracture  density  of  according  to:  (29)  E  the it  increased  measured appears  surface  values  that  to  the  analysis  con-  observation.  Elastic  compliance of  volume  (pj)  Pj,  The  composites,  alumina  decimal  this  the  material  found  material  of  the  (C)  crack  Constants  of  wedge-loaded  length  y. P  specimens  is  a  cubic  (a):  -  8a 3 BH^E 3  Y  (16)  and £ P  =  C  Therefore,  o C  The  program  which  (22)  u  P:2R  utilizes  of  the  linear  -  -M-  (30)  3 BhTE  Biomedical  regression  Computer  analysis,  Programs was  used  P-series, in  order  44  to  obtain  and  a  3  a  linear  function  between  compliance  + b  3  4  values  of  b were  negligible,  C  it  measured  .  a a  The  the  follows  =  (31 )  thus  a a  (32)  3  4  that (.33)  8  H Bcx 3  The  elastic  posites are  of  listed  theoretical be  dealt  The fraction,  moduli  (as  different in  Table  particle II,  predictions  with  in  detail  elastic but  it  calculated  for in  modulus was  from  sizes  Figure  9  Equation  and  f i l l e r  compares  these  33)  for  volume  these  composites.  Chapter  comfractions  results  This  topic  with will  4.  increased  independent  4  of  with  the  particle  alumina size  volume  (Fig.  9). 24  The A  same  scatter  (Fig.  9).  trends band  have of  been  elastic  observed modulus  by  other  values  can  investigators be  observed  25 '  26 '  TABLE Elastic  Constants of  Average Alumina P a r t i c l e S i z e (ym)  -  50 II II II  n n 65 II  n II  H H  90 II  n n H II II  n 115 n H  n 128 II  137 II II  M II II  n  II  A l u m i n a - F i l l e d Epoxy Specimens  Volume F r a c t i o n o f Alumina  E l a s t i c Modulus (GPa)  0.000  4.344  0.013  4.409  0.025  5.428  0.037  3.677  0.087  3.726  0.132  5.345  0.140  8.975  0.038  2.568  0.083  5.740  0.121  6.995  0.194  4.539  0.287  11.649  0.337  10.775  0.007  4.762  0.042  2.320  0.134  4.720  0.189  4.628  0.195  5.842  0.230  6.738  0.314  8.744  0.378  9.733  0.010  3.873  0.025  4.397  0.076  4.090  0.093  5.707  0.078  4.324  0.106  3.502  0.003  4.153  0.021  5.739  0.025  4.305  0.186  6.487  0.258  7.337  0.260  7.831  0.444  12.559  46  i  14  r  PAULS UPPER  BOUND  KERNER'S SOLUTION O LLCS  GO  Z>  10  _j  Z> Q O ISHAl's SOLUTION  O GO  <  — PURE EPOXY  — 50^tm  LLI  — 65/i.rn A o •  0  01  0-2  — 90/J.m — 115/un — 128/irn — 137/im  1  0-3  1  0-4  1  V O L U M E FRACTION , ALUMINA Figure  9.  E l a s t i c constants of a l u m i n a - f i l l e d to t h e o r e t i c a l predictions.  epoxy  compared  0-5  47  3.1,1.3,  The  graph  distance has  for  a much  both  to  the  graph  shape was  The  is  glass  inherent  of  other  the  Figure  10,  effect  on  the  in  Figures  in  the  of  The the  calculated 11  slope  and of  tests  to  a  slope 12,  on  lines  was  However,  particle  size  slope,  the  of  volume  the  the  y  about  that  it  is  the  in  significant the  there  no  apparent  fraction  intercept  and  the  linear illustrated  of  alumina  decrease  alumina  seems  particle  III.  illustrated  as  y  the  Table  size is  same  sensitive  is  observed  The  the  results,  function listed  the between  applying  intercept  is  but  distance  particle  A  Epoxy  is  are  pulser  10.  curve  a  and  to  glass,  function,  such  fraction and  than  interpret  equations  increased.  of  To  Figure  to  the  linear  fraction  dependent  of  respectively.  the  in  indicated  A graph  volume  transducer  attenuation  shape  linear  the  on  shown  specimen.  analysis.  the  insensitive  The  approximated  regression in  and  relatively  and  Attenuation  versus  detector,  cases  Wave  AE c o u n t s  epoxy  is  and  in  of  greater  attenuation source  Elastic  volume  effect to size  be of  of inthe  alumina.  The summarized these of  the  results in  tests, volume  of  Table the  front-to-front III  number  fraction  and of and  attenuation  illustrated counts the  in  appears  particle  tests'are  Figure to  be  size  of  13,  In  independent alumina.  The  48  120  T R A N S D U C E R TO P U L S E R DISTANCE , Ixl0~ m. 2  Figure  10.  AE c o u n t s for epoxy  versus transducer and glass.  to  pulser  distance  49 TABLE Linear  Equations  and R e s u l t s  Average Alumina Particle Size (ym)  50 II  H II II II  65 II II II  n II  90 n  II II II II  M II  115 II II II  128 n  137 H  n H  n H -  for  III  Counts Versus  Distance  Pulser  from F r o n t - t o - F r o n t A t t e n u a t i o n  Volume Fraction of Alumina  Linear Regression Analysis Equations AE = S L 0 • d + y INI ( c o u n t s ]|  0.000 0.013 0.025 0.037 . 0.087 0.132 0.140 0.038 0.083 0.121 0.194 0.287 0.337 0.007 0.042 0.134 0.189 0.195 0.230 0.314 0.378 0.010 0.025 0.076 0.093 0.078 0.106 0.003 0.021 0.025 .0.186 0.258 0.260 0.444  -22140 -21280 -18240 -20470 -26780 -19280 -13890 -19660 -28840 -24860 -11090 -15150 -12700 -22430 -22350 -21620 -13340 -12160 -15420 -15570 - 8070 -26790 -25740 -18750 -23290 -21030 -19210 -17890 -18880 -20080 -15370 -13580 -18580 -11640  T  X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X d + X X X X  d + d + d + d +  X d + X d + X d + X d + X d + X d + X d + X d + X d +  .1  3500. 3700. 2860. 3470, 3560. 3250. 3430. 3640. 4420. 3630. 2900. 3830. 3100. 3650. 3460. 3360. 3510. 3030. 3510. 3150. 3100. 3970. 4190. 3150. 3590. 3560. 3050. 3690. 3010. 3370. 3900. 3340. 3620. 3520.  Correlation Coefficient r  T  .  0.96 0.98 0.99 0.95 0.97 0.99 0.98 0.92 0.88 0.98 0.95. 0.99 0.91 0.98 0.98 0.98 0.93 0.88 0.92 0.96 0.86 0.94 0.96 0.97 0.97 0.98 0.96 0.88 0.95 0.99 0.90 0.96 0.94 0.85  Tests  Tests  Results of Front to Front Attenuation Tests (counts) 3500. 3260. 3820. 2800. 3000. 3550. 3900. 3000, 3630. 3860. 3280. 3260. 3220. 3100. 2790, 3210. 4410. 3870. 4130. 2640. 3280. 3390. 3280. 3690. 3580. 3530. 3100. 3260. 3470. 2780. 3360. 4070. 3530. 3420.  50  (f)  H  O O o  UJ CL O _J  (f)  z g  < LLI  <  O  -10 h-  C/)  o h</)  3 O O <  V O L U M E FRACTION . A L U M I N A Figure  11.  E f f e c t of alumina s i z e on t h e s l o p e  volume f r a c t i o n of attenuation  and particle l i n e s .  51  CO H  z  D O O ro  o  z o (f)  CO  O H CO D O O <  VOLUME Figure  12.  FRACTION, ALUMINA  E f f e c t of alumina volume f r a c t i o n and s i z e on t h e y i n t e r c e p t of attenuation  particle lines.  52  1—r  i—r  i—r  CO • •  3 O O  o  4-9  o CO CO UJ  o h-  CO 3 O O  ® - PURE EPOXY • - 50^tm A - 65fj,m  <  •  -  90/i.m  o  -  l28^Lm  • - 137/im 0  1  i  0  01  VOLUME Fiaure  13  Effect of alumina s i z e on c o u n t s i n  1 0-2  0-3  0-4  FRACTION , A L U M I N A volume f r a c t i o n and p a r t i c l e front-to-front attenuation tests.  0-5  53  number same  counts  range  seems in  of  to  of  indicate  to  be  that  for  in  epoxy  crack  the  d i f f i c u l t i e s summary drawn and  the  which  were  in  from  these  tests  toughness  fraction values  obtained  from  ment  found.  was  from  other The  the  the This  III.  differences  are  not  large  equipment,  Tests  composites few  tested  toughness because  of  encountered  Table  on  testing  within  Table  microstructures  the  tests  given  in  distances  Torsion  Very  torsion  fell  Tests  Double  and  tests  intercept  short  with  is  volume  y  different  growth.  double  the for  Fracture  slow  as  detected  3.1.2,  The  front-to-front  values  attenuation  enough  in  IV.  fracture the  tests  the  no  the  fracture  tests  double  torsion  were  of  A  can  be  particle  However,  compared  with  generally  values  obtained  conclusion  effect  and  exhibit  experimental  toughness, were  not  values  (Section  Thus,  regarding  did  were  size  the  those  good also  agreein  good  27 agreement low  with  volume  torsion  results  fraction  tests.  published  si1ica-fi11ed  by  Beaumont  epoxy  and  fractured  Young in  for  double  TABLE Fracture  Toughness of  IV Epoxy C o m p o s i t e s .  Double T o r s i o n  Average Alumina Particle Size • (ym)  Tests  Volume Fraction of Alumina  Fracture Toughness (MPa/m)  50  0.014  0.84  50  0.025  0.90  90  0.035  1.18  90  0.101  1.23  137  .0.014  0.69  137  0.022  0.78  55  Figure  14  Wedge-Loading  shows  the  load  to  wedge-loading  tests,  for  posites.  of  composites  0.45  One  andan  composite ticle  (G^)  in  alumina  size  seem of  15  V  on  the  be  different  of  the  affected  two  volume 137  ym. and  failure  time* epoxy  The an  during com-  fraction  of  second  average  increased  experimental toughness  the  par-  with  Both  (K^)  for  of  of  energy  the  volume  composites  fracture  alumina  fracture  different  testing.  effect  toughness  size.  for  0.34  wedge-load  increasing  energy  volume  significantly  and  fraction  by  the  fraction of  differing toughness but  did  average  particle  alumina.  Table  of  to  fracture  fracture  with to  are  in  a  versus  fraction,  illustrates  particle  increased not  Table  and  had  size  load  volume  failure  epoxy  fraction The  fractured  Figure  average  ym.  experimental  composites  of  65  pure  particle  volume  alumina  Listed and  a  of  increasing  -  average  had  size  the  Tests  VI  Three-Point  contains  specimens  used  values in  Bending  of  Tests  fracture  three-point  toughness  bending  for  tests.  the These  56  250  V - 0-446 f  PARTICLE SIZE , 137/u.m.  200  A  ^  w  A  r  A  PARTICLE SIZE , 6 5 / i m .  •o °b-°.o  o. . 0  80  100  TIME , MINUTES. Figure  14.  Load test  versus time curve during of specimens of d i f f e r e n t  wedge-loading compositions.  120  TABLE V Experimental Fracture  Average Alumina Particle Size (ym)  -5 0 II II II H  65 M  II  n n n 90 H H  u II II  n II  115  Fracture  E n e r g y and  Toughness of  Alumina Volume Fraction  Wedge-Loading  Average Experimental Fracture Toughness (MPa/m)  0.000  0.97  0.013  1.04  0.025  1.54  0.037  0.97  0.087  1.15  0.132  1.48  0.140  2.33  0.038  0.75  0.083  1.37  0.121  1.89  0.194  1.40  0.287  3.09  0.337  2.83  0.007  1.02  0.042  0.70  0.134  1.31  0.189  1.45  0.195  1.72  0.230  1.66  0.314  2.38  0.378  2.58  0.010  0.79  0.025  0.92  0.076  1.04  n  0,093  1.36  128  0.078  1.10  0.106  1.09  0.003  0.69  0.021  1.19  0.025  0.91  0.186  1.50  0.258  2.15  0.260  1.85  0.444  3.72  H  n  H  137 n II II - II  II II  Experimental  + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +  Tests  Average Fracture Energy G (N/m)  0.1  220.  ±  30.  0.1  250.  ±  50.  0.1  470.  ±  200.  0.1  260.  ±  70.  0.1  360.  ±  90.  0.1  410.  ±  40.  0.4  620.  ±  200.  0.2  230  ±  100.  0.1  330.  ±  40.  0.1  590.  ±  50.  0.1  430.  ±  70.  0.2  820.  ±  180.  0.3  750.  ±  180.  0.1  220.  ±  50.  0.1  210.  ±  30.  0.1  370.  ±  70.  0.2  460.  ±  70.  0.1  510.  ±  100.  0.2  410.  ±  80.  0.1  650.  ±  90.  0.2  690.  ±  60.  0.1  160.  ±  20.  0.1  200.  ±  70.  0.1  270.  ±  40. 30.  0.1  330.  ±  0.1  280.  ±  50.  0.1  340,  ±  80. 50.  0.1  120.  ±  0.2  260.  ±.100.  0.1  200.  ±  50.  0.2  350.  ±  90.  0.2  630.  ±  160  0.2  440.  ±  90.  ±  90.  0.3  mo.  58  Fi gure  15a.  E f f e c t of alumina volume f r a c t i o n and particle s i z e on f r a c t u r e t o u g h n e s s . Wedge-1oading tests.  59  VOLUME FRACTION , A L U M I N A Figure  15b.  E f f e c t of alumina volume f r a c t i o n and particle s i z e on f r a c t u r e toughness. Wedge-1oading tests.  TABLE F r a c t u r e Toughness of Three-Point  Average Alumina Particle Size (pm)  -  VI Epoxy Composites.  Bending  Volume F r a c t i o n of Alumina  Tests  Fracture Toughness (MPa/m)  0.000  0.43  0.000  1.03  0.042  0.71  0.045  1.35  II  0.077  1.12  M  0.093  1.12  H  0.124  1.01  II  0.130  1.54  II  0.201  1.56  II  0.289  1.63  II  0.289  1.42  0.333  1.79  0.001  0.50  0.001  0.89  0.031  1.19  65  137 n n n  0.034  0.73  M  0.282  1.35  H  0.310  1.38  II  0.500  1.91  61  tests,  like  increased  the  with  alumina  significantly versus point an  sult  bending  for  double The  different  yielded  in  found  resulting  of  the  from  summary torsion  disagreement  Compliance  Double  the  is  illustrated  Figure  expected  values for  a  are  18.  linear  constant  for  No  size  toughness  and  of  very  volume crack  three-  satisfactory  with the  137  ym  refor  tests.  similar fractions. growth  wedge-loading  the  not  bending  yielded  between  and  was  presents  three-point  alumina  toughness  specimens  17  particle  tests,  was  tests  explanation  toughness  values  bending  tests.  three-point  Calibration  Torsion  compliance  specimens  16  subcritical  values.  compliance  pliance  low  it  Fracture  Figure  tests  for  wedge-1oading  of  and  bending  and> c a 1 c u 1 a t e d in  ym.  average  that  the  wedge-1oading  Figure  where  toughness  for  64  loading  values  double  an  three-point  A  of  fractions,  higher  in  that  and  size.  for  wedge-1oading  types  volume  particle  shown  size  showed  fraction  fraction  with  toughness  hi g h  by  is  particle  torsion,  observed  was  tests  material  fracture At  volume  tests,  volume  affected  alumina  average  wedge-1oading  given  values  Specimens  calibration in  Table  versus  moment  of  VII.  notch  Experimental functions  results  and  Experimental length  are  calculated  notch  specimen.  for  The  length,  com-  as  calculated  62  1  1  ~T  • - T H R E E - P O I N T BENDING  f  0  PARTICLE  01  VOLUME Figure  16.  TESTS  0-2  0-3  SIZE,65/xm.  0-4  FRACTION, ALUMINA  Fracture toughness versus volume fraction. W e d g e - l o a d i n g and t h r e e - p o i n t bending tests.  0-5  63  h A-DOUBLE-TORSION A-THREE-POINT  1 D  BENDING  • -WEDGE-LOADING  CL  TESTS TESTS  TESTS  CO CO LU  z: x  =) o LU  cr z>  H O < o r  PARTICLE SIZE,l37^.m  0  0  0-2  0-3  0-4  VOLUME FRACTION, ALUMINA Figure  17.  Fracture toughness versus volume Double t o r s i o n , wedge-loading and bendingtests.  fraction. three-point  0-5  TABLE Summary o f  V  f  Compliance C a l i b r a t i o n  Linear Regression Analysis Equations:  Results for  = 0.003  Average P a r t i c l e 137 ym  VII  V Size:  f  Double T o r s i o n  Specimens  = 0.122  Average P a r t i c l e 65 ym  V Size:  = 0.340  f  Average P a r t i c l e 65 ym  Size:  _  fi  6.53 x 10"°a  + 3.8 x 1 0  _ /  5.06  x 10"°a  + 3.3 x 1 0  - /  2.77  x 10"V+  1.19  x  10"  C = £ = Ba + D  No.  of  data  Points Correlation Coefficient r  6  0.99  6  0.99  6  '  0.98  cn -p.  Figure  18.  Compliance versus machined notch length of double torsion specimen. Average particle size: 65 ym. V, = 0.12.  a  66  c o m p l i a n c e was  obtained  using  the  following  w 2a(l  +  m  equation  20  v)  C  where  v  =  the  Poisson's  E  =  the  elastic  loading was  relation  loading  for  crepancy  between  probably  due  to  in  a  express  empirical function  curve was  First,  the  sample  i s :  that  as  0.3,  wedgeof  that  the of  sample the  calibration).  is  no  displacement  equal  empirical  to  zero.  at  the  The  compliance  Wedge-Loading  dis-  is  compliance  f i t t i n g  selected  was  for  done  curve  equation  for  as  Specimens  a  by  function a  of  computer . +  f i t t i n g  for  compliance  two in  C  crack A  length,  cubic  reasons. a  non-grooved  (30) BH  +  to  assumption.  the  analytic  same  length) and  in  composition  the  there  approximated  determined  compliance  calculated this  was  (The  (crack  To  modulus  tests.  assumes  points  ratio,  approximately  sample  This  (34)  E  The p r o g r a m P : 2 R o f t h e B i o m e d i c a l P r o g r a m s P - s e r i e s was used.  Computer  67  and  second,  after  correlation pliance  a  trial  coefficient  values,  The  run,  of  the  .99  empirical  with  empirical  the  values  had  experimental  equation  for  a  com-  compliance  became:  C  where  In  a  most  n  =  of  the  In  is  +  O Q  f i t t i n g  a-|X.|  19,  the  The  and  and  are  of  x  a  the  the  3  x  =  n  were  graphed,  agreement  +  0 2 X 2  empirical,  compliance  length.  +  parameters  equations  Figure  experimental crack  =  3  a  (35)  n  .  equal  to  zero.  analytical  each  as  three  a  and  the  function  compliance  of  curves  significant.  Since  the  analytic  compliance  is  calculated  for  a  non-  28 grooved factor This of  for  factor  the  where  sample,  calculating accounts  presence I  Hoagland  of  the  for  the  suggests fracture  the  changed  groove.  The  the  use  energy moment  of  of of  correction  a  correction  grooved inertia factor  is  the  moment  of  inertia  of  a  grooved  I  is  the  moment  of  inertia  of  a  non-grooved  s  is  one  half  sg  of  the  groove  depth.  samples. because is  (y^ ) sg  sample, sample  68  / A — EMPIRICAL COMPLIANCE • — CALCULATED COMPLIANCE • — EXPERIMENTAL COMPLIANCE  0-05  0  CRACK Figure  19.  Compliance specimen.  0-15  010 LENGTH , METRES.  versus crack length for Average p a r t i c l e size:  a wedge-loaded 90 ym. = 0.23.  69  ^L£  =  s  t  tan  .  6 ^ ^  ^  +  4  .  n  tan  s  _  3 0  ]  u  P (1 I  _  1  "  2  t  a  n  H  3  "  1  e  Thus,  is  the  the  wedge  corrected  to  correction be  <  2%.  between  3.1.3.  AE counts In  per  area on  torsion  Therefore, and  the  G  angle.  G(I x  p  /'I  sg  )  1  /  c  ,  Q  i s :  3 v  wedge-loading  length the  factor  groove the  Acoustic  depends  double  loading  of  correction  agreement  energy,  e  samples  is  thickness  and  apparent  on  the  compliance and  Emission  Tests  size  of  here, the  the  presented  three-point  no  calculated  specimens  data  cm,  sample  reported  the  2.5  bending  since  was  crack are  tests.  was  the  of  explains  broken  same  the the  values.  number  of  in  specimen.  hardly  only  found  introduced.  effect  the  (37) '  non-grooved  experimental  area  here  a  was  remained  2/3  the  (36)  of  groove  of  ]  notch  after  existence  -  of  a  low  for  2  6j  compliance  having  The  *  tan  =  co  2  tan  experimental  sample, a  s_ BH  half  factor  The  2  B H  fracture  G  The  s  2 1  where.,  L  +  9  from  the  AE  v i s i b l e . wedge-  70  3,1.3,1.  Acoustic  Emission  from  Wedge-Loading  Tests  The (".Figure paring the  AE  14) the  of  are two  loading  magnitude  counts  Table  the  during the unit  average  the  fracture  22  shows  volume  fraction AE  per  i n i t i a l l y  as  at  a  higher  average of For AE  137 any per  AE ym  unit the  of  particle  volume  the  the  in  Figure  that  each  with size  the  an  tests  20.  By  com-  inflection AE  and  and  size  was  crack  sample,  burst.  volume  of  per  on The  fraction  unit  AE  per  fraction  total  dropped,  as  differing  average  volume  21  on  AE  per  except  total  a  unit  unit  to  total  AE  per  area  larger  per  particle  size.  function  of size.  area  increased  and  composites  reach  particle  Then,  area  the  appeared  for  AE  increased.  it  increased  occurred  particle  for  averaging  illustrates  where  unit  by  which  average area  wedge-loading  calculated  jumps,  alumina  of  from  Figure  differing  fraction, area  results  area  the  of AE  AE  unit  composites  fraction  area  with  all  alumina  unit  found  fraction  area  volume per  unit  of  average for  wedge-loading  time  associated  per  composites  Figure  Total  area  the  20).  AE  volume  for  is  summarizes  unit  area  be  (Figure  of  it  can  per  effect  versus  increases  VIII  The  AE  figures  AE  particles  tests.  plotted  curve  of  accompanying  and  a  plateau.  average  sizes.  71  60  T  00  h-  z  /  D  50  o *  40  O wO  T  T  V, = 0-446 ^ PARTICLE SIZE, 137/xm.  o CO CO  30 V « 0-340  LLI  f  o H  CO D  o o <  PARTICLE SIZE 65/xm. t  20  10 P U R E EPOXY  co-o  0  n-mnrc  20  40  60  n-on-n— " I n  J  80  a  100  TIME , M I N U T E S . Figure  20.  AE v e r s u s t i m e c u r v e d u r i n g w e d g e - l o a d i n g of specimens of d i f f e r e n t compositions.  tests  120  TABLE Summary o f AE R e s u l t s  Average A l u m i na Particle Size (ym)  VIII  f r o m Wedge L o a d i n g T e s t s  Total Acoustic Emission per Unit Fractured Area  Volume Fraction of Alumina  (10  7  x counts/m  7  )  Average A c o u s t i c Emission per Unit Fractured Area  (10  7  2  x counts/m )  >  40 it n  0.000  0.4496  0.4237  0.006  0.2710  0.5930  0.091  0.9043  1.8730  0.129  1.7069  2.0775  0.8529  0.8671  50  0.013  H  0.025  0.2061  0.5600  0.037  1.4261  2.2160  II II  n II  65 II II II II  H  90  .  0.087  3.5355  3.4724  0.132  0.5936  0.7129  0.140  1.3424  2.1261  0.038  7.0536  7.4424  0.083  4.6024  6.2435  0.121  7.9932  8.6685  0.194  4.2072  4.6237  0.287  2.0314  2.1154  0.337  3.0960  1.8655  0.007  0.3820  0.5697  0.042  0.1575  0.1765  0.134  3.5319  3.2585  0.189  7.8488  7.8110  0.195  8.3210  9.0380  0.230  12.4906  11.6548  0.314  4.0795  2.8995  0.378  4.3055  2.3474  0.010  3.2374  3,3200  0.025  2.1288  2.7618  0.076  8.6490  7.9142  0.093  9.1538  9.6891  128 n  0.078  5.5108  5.7799  0.106  7.7890  8.9662  137  0.003  0.6103  0.8192  0.021  0.8937  1.0541  0.025  5.7702  5.4341  0.186  16.4538  17.8205  0.258  21.7427  22.0946  0.260  14.7361  16.2253  0.444  14.5145  14.0995  II  II II  n 115 M II II  II II H  n II II  73  25  • — 50^x.m  20  A — 65/xm  15  10  A •  0 01  0  0-2  0-3  0-4  V O L U M E FRACTION , ALUMINA Figure  21a.  E f f e c t of volume AE p e r u n i t area particle size.  fraction of a l u m i n a on total for composites of differing  0-5  74  VOLUME Figure  21b.  F R A C T I O N , ALUMINA  E f f e c t of volume AE p e r u n i t a r e a particle size.  fraction o f a l u m i n a on total f o r composites of differing  75  VOLUME Figure  22a.  FRACTION, ALUMINA  Effect of volume f r a c t i o n of a v e r a g e AE p e r u n i t a r e a f o r of d i f f e r i n g p a r t i c l e size.  alumina on composites  76  VOLUME Figure  22b.  FRACTION, ALUMINA  Effect of volume f r a c t i o n of a v e r a g e AE p e r u n i t a r e a f o r of d i f f e r i n g p a r t i c l e size.  alumina on composites  77  In  most  wedge-loading  groove.  However,  from  groove  was of  the  stopped the  test  corded. to  the  count  AE  for  for  M  Q  D  =  AE(.l  at  is  the  crack  are  the  y  the  AE  is  the  length  graphs  AE^Qp  were  curves in  of  tests  the  most  of  crack  crack  the  notch.  only  the  AE  the  the  the deviated The  test  of  the  part  groove  was  re-  dependent was  crack.  on  made The  the to  AE correct  following  -^-  -  (lj  Y  zero  -  distance  a))  from  (38)  the  transducer,  length, and  of A E  lines  the  M  21  Q  D  slope,  respectively,  (Section  Acoustic  the  not  22.  Emission  differ  significantly  Therefore,  the  data  propagated  from  Three-Point  Tests  specimens in  used one  and  specimen.  did  and  the  included.  Bending  In  of  the  from  attempt  attenuation  Figures  not  an  intercept  of  the  and  followed  used:  a  the  specimens  somewhat  position  AE  of  is  crack  followed  distance,  the  shape  the  distance  crack  is  SLO  of  happened,  AE^gp  and  from  short  the  the  was  Lj The  number  attenuation  A E  y-r^j  a  this  transducer  approximation  where,  a  which  Since  source  at  when in  in  tests,  in  three-point  jump.  Therefore,  bending only  78  total the  AE  AE  these  per  per  jumps  that  data  the  have  a  an the  during  average AE  the  large  AE  the  AE  per  AE  per  unit  used  of  per  unit  was  analyzed, area  unit  area  fracture  unit  contains in  scatter.  variations  burst  AE  per  IX  specimens  average  standard  one  Table  different  tests  tests  tests,  3.1.4.  the  occurred  only  smaller  calculated.  averaging  as  When  bending  much  for  AE  by  magnitude  point  was  wedge-loading  culated,  a  The  wedge-loading  same  area  area  calculated  crack In  unit  tests.  In was  unit  of  of  the  up  to  area  area all  were as  the  sample, the cal-  in  calculated  threerepresents  sample.  Fractography  of  Alumina-Fi11ed  Epoxy  Compos i t e s  Sections covered crack the  with  had  crack  Figure  higher  Small  The  24  shows  magnification  25).  ym  The  a  which seemed  wide,  in  f i b r i l s  (parallel  regions  1  surface  particularly  marks  Figure  cavities,  (Figure  fracture  arrested.  arrest  23.  the  f i b r i l s ,  been  initiated. at  of  to  appeared  could  have be  pure  epoxy  were  the  sites  ran  perpendicular  direction  section  to  of  where  of the  where  crack f i b r i l  macroscopically an  seen  uneven in  the  the to advance), was smooth,  texture. f i b r i l s ,  79  TABLE Summary o f  IX  AE R e s u l t s f r o m T h r e e - P o i n t Bending Tests  Average Alumina Particle Size (ym)  Volume Fraction of Alumina  Total  T o t a l A c o u s t i c Emmission per Unit Fractured Area  Acoustic Emission  (10  (counts)  7  2  x counts/m )  0.000  880.  1.0672  -  0.000  330.  0.2672  90  0.042  425.  0.4522  II  0.045  317.  0.3563  n  0.077  949.  1.1152  II  0.093  500.  0.5512  II  0.124  230.  0.2849  220.  0.2398  n n  0.130  •  0.201  709.  0.8083  H  0.289  1173.  1.2468  II  0.289  900.  0.9119  H  0.333  1200.  1.4215  137  0.001  581.  0.6569  II  0.001  564.  II  0.031  310.  0.3389  •  0.6153  0.034  550.  0.6099  II  0.282  5500.  6.6951  II  0.310  +  -  H  0.500  39900.  46.5686  + Out o f  scale  120 Figure  23.  m  u  Scanning-electron micrograph of u n f i l l e d epoxy.  (SEM)  5 ym  Figure  24.  Enlargement of Section Unfilled epoxy.  A  in  Figure  23.  81  10 ym Figure  25.  Enlargement of Section Unfilled epoxy.  B  in  Figure  23.  82  Figures size  and  26a,  b  volume  and  c,  present. not  be  For  seen  exhibit  epoxy  from  Table different  appeared  of  the  effect  fracture  of  fraction,  even  at  0.44, of  low  particle  surface.  crack-particle  Composites  on  X  to  the  the  of  In  Figures  interaction such  large  marks  particle  volume  it  was  of  are can size  fractions  was  Figure  alumina  were  found  present  29.  that  imprinted 28  shows  particles on  Using pieces  wedge-loading  the  surface  X-ray of  cavities  from  the  in  energy  alumina  tests  (Figure  30).  Composites  Fracture  Tests  contains  values  used  fraction with  volume this  28).  Figure  during  Steel  particles  and  epoxy  particles,  decrease  follow  27  separation  Pieces  volume  alumina  alumina  (Figures  specimens  alumina  not  26d).  fractured  3.2.1.  did  the  volume  cracking  analysis,  Tests  an  large  matrix  particles  for  on  show  indicating  (Figure  alumina  spectral  an  a  matrix.  some  3.2.  marks  surface  resulting  of  fraction  26d  26b).  The  epoxy  through.  secondary  (Figure  the  26a  in  fracture  three-point of  0.01,  of  the  the  for  tests.  fracture  particle  0.05,  Therefore,  toughness bending  the  increasing  fraction  trend.  of  the For  toughness  size.  However,  toughness  values  lack  of  a  distinct  t 0k  V  r  >»  - —  NO  170 pm Figure  26.  SEM o f a l u m i n a - f i l l e d epoxy. a. Average p a r t i c l e size: 50 Vf = 0.013  | 4 2 0 pm Figure  26.  |  SEM o f a l u m i n a - f i l l e d epoxy. b. A v e r a g e p a r t i c l e size: 65 V = 0.194 f  ym  pm  420 ym Figure  26.  SEM o f a 1 u m i n a - f i 1 1 e d epoxy. c. Average p a r t i c l e size: 137 V = 0.186  ym.  f  420 ym Figure  26.  SEM o f a 1 u m i n a - f i 1 1 e d epoxy. d. Average p a r t i c l e size: 137 V 0.444 f  ym.  8 5 ym Figure  28.  SEM o f a l u m i n a - f i l l e d e p o x y exhibiting particle pull-out and embedded p a r t i c l e s . Average p a r t i c l e size: 137 ym. V = 0.186. f  20 ym Figure  29.  SEM o f alumina-filled epoxy. Epoxy can be s e e n on t h e surface of the alumina p a r t i c l e . Average p a r t i c l e size: 137 V' = 0.186.  10 ym Figure  30.  SEM s h o w i n g a s m a l l alumina Average particle s i z e cf the 137 ym. V . = 0 . 1 8 6 .  p a r t i c l e . composite:  TABLE X Fracture  Toughness o f  Alumina-Filled Martensitic  Three-Point  Average Alumina P a r t i c l e S i z e (ym)  Steels.  Bending Tests  Volume F r a c t i o n of Alumina  F r a c t u r e Toughness (MPa/m)  -  0.000  36.16  0.000  49.29  50  0.01  21.52  0.01  38.53  0.01  38.37  0.01  44.58  0.01  43.37  0.01  25.90  0.01  32.88  0.01  34.65  0.01  29.64  90  0.01  23.88  II  0.01  23.95  II  0.01  24.57  0.01  20.08  0.01  25.15  0.01  25.79  II  ti H  65 II  II  II  n II  n n  0.01  25.13  H  0.01  28.93  137  0.05  34.07  H  0.05  26.16  n  0.05  31.05  II  0.05  24.71  II  0.05  27.05  88  pattern The  for  bluntness  position  and  specimens in  all  the  of  could  crack  changing all  have  does in  not  the  allow  for  conclusions.  samples,  the  varying  microstructure contributed  of  to  the  the  com-  fabricated  large  scatter  results.  Table for'the  Acoustic  XI  be  different  made  AE  test  measured  of  the  AE  controlled.  AE  per  used  the  in  area  does  not  permit  cracking  bending a  tests.  correlation  microstructure.  one  the  could  during  three-point  only  and  factors  unit  composite  because  Both  Tests  results  and  unreliable  (Section  the  specimens  between  was  Emission  contains  -inconsistency  to  be  results  the  the  3.2.2.  The  the  AE  burst  composition have  The  was could  contributed  not  to  the  scatter.  3.2.3.  Fractography Steel  The the  original  surface  Figure grain  32.  of  a  From  size  of  the  Therefore,  it  is  of  Alumina-Filled  Martensitic  Composites  iron  powders  fractured the  are  shown  composite  electron  steel  matrix  evident  that  is  scanning was the  in  Figure  31  represented  in  micrographs,  estimated cracks  to  be  propagated  and  the 4-13  ym.  through  TABLE Acoustic  Emission of  XI  Alumina-Filled Martensitic  Three-Point  Bending  Steels.  Tests  Average Alumina P a r t i c l e S i z e (ym)  Volume F r a c t i o n of Alumina  Acoustic Emission per Fractured A r e a (109 c o u n t s / m )  -  0.000  1.179  -  0.000  3.004  50  0.010  14.246  0.010  3.292  0.010  10.675  0.010  4.163  0.010  3.729  0.010  7.331  0.010  4.002  0.010  6.090  0.010  2.194  0.010  1.654  0.010  7.722  0.010  8.409  0.010  11.593  0.010  4.443  0.010  2.707  0.010  3.939  0.010  3.200  0.050  5.706  0.050  9.187  0.050  6.905  0.050  9.039  0.050  10.580  II  65 II  II  II  90 II  II  n n II  n  137 n II  II  II  2  165 pm  Figure  31.  SEM o f  iron  powders  Atomet  28.  15 pm Figure  32.  SEM o f m a r t e n s i t i c s t e e l composite exhibiting intergranular failure. Average p a r t i c l e s i z e : 50 p m . V , = 0.01  91  the at  original liquid  and  steel  nitrogen  tntergranular  test  further  during  hot  travelled  forging  some- o f  particle to  have  (Figure  the  point have  the  contact  (Figure taken  and  34).  place  composite~which  exhibited  (Figure  that hot  the  33).  iron  rolling  steel  decohesion  from  zones  the  over  powders  had  consolidated  that  the  therefore than  matrix  entire  particle  the  fracture  the  around  seemed  bonding  the  ar  temperature  matrix  Nevertheless,  transgranul low  rather  between  fractured  This  and  powders  both  was  to  occur  and  the  appeared surface  (Figure  bending masked  areas  of  35).  After  tests  the  were  effect  of  observing  abandoned the  surface dimple  not area  since  alumina  the  exhibited zones,  three-  dimples  particles  on  could  AE.  cracks  them.  34).  Extensive dimples  failure  through  The  temperature  confirmed  Particle in  powders.  92  5 ym Figure  33.  Figure  34.  SEM o f m a r t e n s i t i c steel composite fractured at l i q u i d nitrogen temperature. V# = 0 . 0 0 0  93  Figure  35.  SEM o f m a r t e n s i t i c steel composite exhibiting dimples. Average particle size: 40 p m . V , = 0.01  94  4,  ANALYSIS ALUMINA  In epoxy  this  are  martens i ti c  explained posites  in  are  steels  Section  3.2.  discussed  in  2.  acoustic  wave  3.  fracture  energy  4.  acoustic  emission  Elastic  (Figure  of  fabricated  their  some  could  have  in  properties  not  The the  The  of  alumina  results  dealt  following  from  with  properties  and  of  reinforced  particle-  for  reasons  the  epoxy  com-  order:  toughness.  during  fracture.  observed  in  could  attributed  the  be  samples. of  the  During  changed  are  COMPOSITES  attenuation.  composition.  occurred, have  9)  batches  changes  EPOXY  FOR  Constants  scatter  different  the  DISCUSSION  constants.  stants the  AND  discussed,  elastic  The  in  only  1.  4.1.  RESULTS  REINFORCED  chapter  composites  f i l l ed  OF  The  values  and  curing  The  age  of  batch,  moisture The  such  to  samples  resin  frequent  occurred.  the  as  the  the  elastic  prepared varying  materials  temperature  exposure  to  the  and  bulk  fluctuations  from slightly  varied  polymerization,  of  con-  characteristics  were  agent  these  sampling, content  of  could  air  and have  could  contamination in  the  furnace,  95  during batch  17 of  sample  1/2  samples  did  pliance  not  and  the  29  ,  next,  The  the  apparent  9  illustrates 30  ,  and  modulus and  for  elastic elastic  the  Ishai  are  in  in  but  ,  The  the  did  elastic  vicinity  of  the  com-  define  to  matrix  elastic  .  This  is  the  an  averaging  of  predicted  narrow  which  of  values  these  ,  f  affect  predictions  in  E  one  modulus.  composites,  modulus,  from  finished  experimental  equations  of  varied  theoretical  the  Ishai's  moduli  31  have  holes  therefore  Paul's  f i l l e r  the  could  toughness,  curves. the  curing,  the  Paul  elastic  to  of  affect  Figure Kerner  hours  boundaries  the  ratio  modulus,  of  E^,  32 is  greater  epoxy.  than  Kerner  elongations derive used  used  and  formulas  the  20  energy  stresses for  the  within  of  for  procedure the  elastic  theorems  case  alumina-filled to  composite  modulus.  e l a s t i c i t y  to  Paul  determine in  order  and  obtain  to  Ishai their  equations. 1  =  +  A  ( 1 -  A  cV t T_\ cV  E  =  the  e l a s t i c  (39)  (40)  t  V E E  where  c ;  f  E  c  f  A  /  E  modulus  E  +  of  1  (41) A  t  the  composite,  96  E. V  f  v  £  =  393,  is  the  GPa  2  is  6  volume  the  elastic  fraction  of  modulus  alumina,  of  alumina,  and 19  =  0.352  Paul's modulus  is  the  equation  Poisson's  for  ratio  the  upper-bound  (E.  -  of  epoxy  values  .  of  the  elastic  is 2/3 Er  E  =  r  Ep [  E E  Ishai's  +  E  +  (  E  *  A  equation  E  •  E  E  F  ) V  f  2 T 3 )  V  f  defines  (  the  1  -  T73-  "  1  f  V  J  (  4  2  )  '  lower-bound  values  of  the  31 elastic  modulus  : V ( E  c  Even though concentrations, centrations  E 4.34  is  the  of  the  this  values.  by  possible  for  ) / ( E  and  if  in  -  E  1)  -  refers  this  (.43)  f  only  to  l o w - f i l l e r for  high  agreement  with  Kerner's  of  epoxy,  was  determined  in  calculations  used  the  experimental  the  /V  experiment  was  volume  Ishai's  the  / E  from  modulus  of  A  •]  equation  be  large  outside  that,  to  value  Most  Paul's  points  E  results  elastic  composites  bounded set  >  / E  Kerner's  appeared  GPa and  dicted the  E  A  F  the  fractions  curves.  boundaries values  elastic  of  E  in  However, of  F  are  these  between  curve.  to  of  moduli the there  regions. 3  GPa -  con-  be  preof  region is  one It  4 GPa  97  were  used  would  be  for  Kerner's  within  the  and  Ishai's  boundaries.  equations,  Values  of  3  these  points  GPa h a v e  been  19  published  Summary The alumina of  the  elastic  volume  Paul  reinforced  was  and  Ishai  values  Attenuation  The in  particle  composites  experimental 4,2.  fraction.  alumina  Kerner,  modulus  With  not  possible  pulser which  tests was  a  the  on  elastic  of  in  a  relative  to  this  increasing  constants  were  independent  predictions  modulus  of  of  particle  agreement  with  the  study.  Waves  is  equipment  generally  used  attenuation measure  with  reasonable  material  of  increase  theoretical  elastic  in  measure  (Section  The  the  Elastic  type  to  The  were  attenuation  dB/m.  found  size.  found  of  was  of  in  in  expressed changes  expressed  this  dB/m.  study, However,  attenuation  in  the  it  in  magnitude  the  counts/m, of  attenuation.  A During the  pulser fracture,  surface  of  introduces AE the  is  AE  through  generated  material.  AE  the  both is  in  surface the  measured  of  a  interior in  all  material. and  on  cases  by  98  a  transducer  assume  that  transducer similar  placed the  and  the  produced elastic  could  that  was  agent  For  AE  in  fractured  in  and  the  longitudinal  to  the  waves  to  between  would  the  follow  a  shape  of  the  sample  cavities  in  the  specimens,  the  as  in  testing  properties  affecting  the  been  the  as  the  scatter  attenuation  has  distance epoxy  Just  4.1.),  reasonable  tests,  by  such  seemed  the  pulsing  factors  contributed  metals,  and  results.  (Section  It  of  influenced  unpredictable  have  surface.  Imperfections,  modulus  curing  source  to  Attenuation 10).  the  relations  pattern  (Figure  on  of  related  in  the  the  the  sample  the resin,  fabrications  results.  elastic to  of  for  shear  waves  inverse  of  and  the  33 velocity  of  the  wave  .  Since  the  velocity  of  the  wave  ln-  34 creases  with  attenuation Therefore, glass  the  decreases the  (Figure  elastic  elastic  modulus  with  difference 10)  moduli,  is  a  the of  any  solid  increase  of  attenuation  result  Eg/E^ ~  of  of  the  material  the  ,  e l a s t i c  between  difference  modulus.  epoxy in  and  their  23.  34 Mun'son f i l l e d  epoxy  et  found  increased  Assuming  that  epoxy  similar  is  al  the  wave to  with  that  the  increasing  propagation  that  in  wave  metals,  velocity  alumina  phenomenon the  of  volume in  decrease  aluminafraction.  alumina-filled in  attenuation  99  with be  the  increase  mainly  that in  of  alumina  attributed  particle  agreement  independent suggested  size  the  no  the  discontinuities  influence that  size  scatter  in  the  of  waves in  the  attenuation  (.Figure  modulus.  on  to  the  material the  can  was  observed  This  modulus  due  since  It  11)  attenuation.  elastic  (Section  (interfaces)  factor  fraction  increasing  fact  particle  that  important  the  had  with of  to  volume  is  It  also  also  presence  was  not  amount  is  of  an  of  inter35  face  increases  studying  the  composites,  as  have  where  sample  thickness  were  5  10).  In  volume cepts  higher  fraction, on  volume  satisfactory  the  distance  testing  shock  that  and  size  the  a  than y  waves  was  in  intercepts calculated  dependence  through  of for  epoxy of  the  In  linear and  was  observed  explanation  was  found  for  the  in  12  the  glass relation  functions epoxy  composites  (Figure  attenuation by  same  front-to-front  fraction  of  of  (Figure varying  and  y  inter-  and  13).  No  latter.  S u m m a r.y  The source  and  attenuation detector  of in  acoustic  the  epoxy  waves  due  composites  to was  ,  phase  the  counts The  glass  of  separated  the  epoxy.  workers  fibre-reinforced  effect  were  tests),  those  Other  negligible.  transducer  a1umina-fi11ed no  decreases.  dispersive  (front-to-front  between  versus  of  attenuation  pulser  times  found  counts  a  found on  tests,  was  particle  propagation  discontinuities  ^  the  distance found  to  between be  100  dependent be  volume  of  the  4.3.  but  decreased  the  effect  fracture  energy  Energy  attempt  and  existing  is  theories.  Surface  alumina.  particle  slightly  was  and  made  toughness  increase  of  too  It  size.  with  small  appeared  The  acoustic  increasing  to  be  of  to  elastic  significance  studies.  Fracture  An  fraction  the^alumina  attenuation  modulus,  to  the  independent  wave  in  on  the  Toughness  here  results Some  fracture  of  to  analyze  from the  this  are  compare  the  study  with  the  that  have  been  factors  energy  and  fracture  already suggested  discussed.  Roughness  Fracture  energy  values  are  calculated  for  a  smooth  surface.  25 Lange  estimated  composite  of  surface  of  in  due  area  particle the  in  determine  area.  to  The  surface  fraction  to  unfilled  material.  surface  roughness  In  this 28)  The  surface the  fracture  volume  (Figure  observed.  crease  here.  an  size.  matrix  were  0.5  the  study and  two  surface  following  area model  is  be  =  2  particle times  independent  of  particle cracking  reinforced  the  that  factors  (because  a  suggested  partial  secondary  latter  roughness  He  of  fracture the  the  f i l l e r  separation (Figure  together  with  the  the  presence  increase  for  the  composites  was  to  calculate -a-  the  from  '25c)  of  used  increase  of  inparticles) tested  total  surface  101  Assumption:  The are  interfaces  completely  of  all  to  =  v  p  crack  3  =  s  average unit  N  the  Fullman ^,  N  g  by  Development:  According  N  intersected  fractured.  Mathematical  where  particles  N p  number  area of  of  =  number  =  probability  (44)  y  of  intersections  sectioning  particles/unit of  plane  per  plane. vol.  intersecting  a  particle, and  D  where  The  D is  volume  f o l 1 o w i ng  the  average  fraction relati  of  =•  D  (45)  particle  f i l l e r  can  size.  be  calculated  using  the  on:  N V V  f  =  (46)  102  where V  =  T  Vp  Thus ,  i t  1 is  is  a  the  fol1ows  unit  volume  volume  of  a  and particle  that  ,3 V  Substituting  V  in  p  n  P  =  equation  (47)  (46)  6 V  F  (48) TT  D  Thus , 6V  f  (49)  TTD2  The  surface  area  of  a  single  S  The  total  area  of  P  =  intersected  A  s  particle  TTD  is  (50)  2  particles  =  A  =  6V. f  N  p  x  N s  is  (51)  Thus , A  p  s  (52)  103  The epoxy  composites  particle to  size  notice  addition this of  increase  a  study,  the  with  the  for  a  For  that  fractured of  in  the  fracture  energy  some  distance  occurred  as  be  greater  in  this  study  distance  Energy  than  from  than  f i l l e r  the  spectral small for  alumina  the  as  chips  following  not  reasons:  predicts  times  the  appear  for  that  about  60%  considered  particle  in  the  that  decohesion  fractured  of  of  area  data  would  was  particles  at  obtained a  Particle  presence  did  3  energy  of  model  experimental  microscope  alumina  fracture  would  decohesion  F i l l e r  In  is  were  plane  no  the  particles.  analysis  it  caused  energy  account  increase  crack.  the  If  crack  main  electron  revealed  can  important  independent.  this  it  is  the  fracture 0.5,  It  was  by  the  composite  area  the  size  fraction  V.  area  0.5  Thus,  However,  by  surfaces  the  the  regarding  Absorbed  Scanning  the  then  3.  the  of  increase.  from  w e l l ,  the  matrix.  fractured  ^  alumina-filled  volume  Table  particle  times  of  in  the  fractured  fraction  the  increase  shown in  of  f i l l e r  fraction  5  area  the  at  ^  volume  area  as  also  volume  matrix.  fractured  a  is  was  energy  increasing  increase  f i l l e r  composite  the  fracture  independent  that of  in  of  These  observations particles were  to  much  fracture smaller  indentified  particles. appear  of  be  The a  by  fracture  frequent  X-ray of  event  104  i)  Scanning  electron  microscopy  of  sections  of  large  particles size  of  of  the  the  disclosed  fracture  the  surface,  same  size  as  the  composite  were  observed  existence  where  average  embedded  particle  (Figures  26  and  28). ii)  The  fracture  greater  than  XII). tip  reaches  the  the  matrix  of  Epoxy  and  on  Parting  alumina  (Ref.  19).  which  had  stresses  (o)  of  epoxy  intensity  necessary  to  is  (Table  in  the  crack  fracture  the  alumina  occurs.  particles  the  total  Fracture  have =  8  °C  particles  very  likely  fracture  had  energy  of  a the  composites.  (a);  10  alumina  toughness  failure  contractions x  the  stress  alumina  epoxy  Between  the  value  contribution  a 1umina-fi11ed  of  fracture  before  fracture  negligible  Friction  the  Thus,  particles,  Thus,  toughness  a  70  This to  be  Surfaces  different x  coefficients' (Ref.  10  would  have  overcome  to  26),  created pull  the  of a  thermal  epoxy  residual particles  38 out  of  the  matrix  (  a  A l  2  :  0  3  "  a  epoxy)(T h  T ) p  (53)  105  TABLE Fracture of  Constants  XII and E l a s t i c  Epoxy and o f  Moduli  Alumina  Epoxy  Alumina  Young's Modulus (GPa)  4.0  393*  F r a c t u r e Toughness (MPa/m)  1-0  5.2  F r a c t u r e Energy (N/m)  250  20  +  * Reference + Reference x Reference  26. 37. 38.  x  106  where T"  h  is  the  highest  Tp  is  the  ambient  Examining  the  particles  partially  observed was  friction of  the  as  to  28).  between energy  surface  pulled  pull the  temperature  =  200°C  and  temperature  fracture  (Figure  expended  curing  out  Thus, out  with of  it  the  for  scanning  microscope,  the  matrix  were  would  appear  that  particles  particles  required  a  in  order  frequently some  to  and  the  matrix.  pulling  out  particles  energy  overcome  The  magnitude  can  be  estimated  follows:  Work  of  Pull-Out  The  work  of  friction  (Up)  for  pulling  out  a  square  particle  is:  U  where  When force  Fp  the is  Although in  this  is  the  pull-out at a  friction  of  maximum friction  case  the  =  F  a  F  x  D  (54)  force.  particle  because force  normal  F  the  is  force  is  i n i t i a t e d ,  friction  normally depends  area  the is  independent upon  the  friction largest. of  area  area, of  particle  107  exposed  to  the  completely  residual  pulled  out,  stress. the  When  friction  force  particle is  is  zero.  almost  Thus,  aS ' - J *  r  F  the  =  (55)  where a S  The  P  is  the  thermal  stress  is  the  surface  area  area  exposed  total  and  of  a  particle  =  6V  is  A  s  (52)  f  Thus , a6 U  This size  model  composites Thus,  it  particles  was  Interaction Phase  The  tested  would  not  in  the  a  that  fracture this  appear  of  D  predicts  dependent.  that  major  Crack  the  the  was  of not  energy  reinforcing  Front  (56)  pull-out  energy  study  with  the  energy  particle  alumina-filled  particle  required factor  the  is  size  for  in  pulling  this  According  to  where  second  the  Lange  32 '  phase  ,  the  Second  exists  pinning  increases  of the  the  out  instance.  40 '  epoxy  dependent.  Dispersion  25  front  V.  =  F  crack-  fracture  108  energy pair  of  breaks for  considerably. pinning away  Since  the  positions,  from  the  the  increase  in  Lange's  equation  for  crack  its  pinning  front  length  increases  points.  crack  length  the  fracture  The  is  bows  between before  energy  called  energy  the  of  each it  required  line  the  energy.  composite  .25.  1s  G  where  G  is  0  the  a T  new  is  fracture  the  the d  energy/unit  is  the  action the  57  inverse  there  are  composite should spacing Figure  so  many  becomes  drop. of 36.  the  The  the  2D 3  =  that  <'  when  form  length  relation  composites no  of  of  f>  (58)  front  is  a  of  fracture in  particle  linear  the  system,  in  positions:  distance.  examined  drop  V  crack  ahead  "uniform",  pinning  " V.  energy  particles  However,  to  energy/unit  interparticle  a  required  between  pi a c e , f r a c t u r e of  area  line  distance  indicates  takes  (57)  front,  d  Equation  I d  surface,  c r i t i c a l  crack  +  o  function  However,  crack  the  front  fracture  energy this  fracture  inter-  energy  when that  the  energy  and  study  of  interparticle is  was  linear observed  see  109  1200  1000  >  T e — ©  50/zm.  O  65fJLTT\.  •  800  CD CC LU  600  8  INVERSE Figure  36a.  10 3 _-|  MEAN FREE PATH , 10 m  F r a c t u r e e n e r g y v e r s u s mean f r e e composites of d i f f e r i n g particle  path for size.  12  110  0  2  4  6  8  10  INVERSE MEAN FREE P A T H , Figure  36b.  F r a c t u r e e n e r g y v e r s u s mean f r e e composites of d i f f e r i n g p a r t i c l e  ICrV  path for size.  12 1  Ill  at  large  volume  fractions  fracture  energy  of  an  epoxy  evidence  of  diminished  . by  of  particles. A ^ O ^  •  Figure  3 ^ 0  37  shows  composite  the  studied  • 40 Lange  The action  for  volume  fractions  and  from  behind  higher  AE  the  of  marks  accompanied small  to  Comet (see  by  at  high  a  than  in  they  also  observed  Evans observed of  the  et  when  crack  a l  by  26a,  26b,  volume  marks  4  have  1  adding  a  crack  and The  27)  disappearance  Figure For  at  were  26d)  is  composites  lower  volume  particle  sizes.  This  that  toughness  trend  40 '  .  proposed  dispersed  deflection  main  21).  ceased  surface  26c  (see  Figure  large  the  fractions.  fractions  (see  for  Lange  fracture  Figures  25 was  the  inter-  intermediate  by  the  did  for  left  AE  sizes,  than  from  volume  drop  front-particle  marks  intermediate  particle  fractions  fractions  obtained  particles  up  of  was  studies.  observed comet  volume  crack  around  the  second  the  phase  is  increase  a  consequence  particles.  For  sphere-like  an  in  41 dispersions, energy  with  due  crack  a  to  volume  Evans  al  increasing deflection  fraction  posite  is  of  matrix.  the  et  of  predicted The  predict  volume is  0.5, to  be  fraction.  particle the  The  size  fracture  1.8  toughness  increase  times  increase  fracture  reinforcement  independent.  energy the due  of  the  fracture to  crack  For com-  energy deflection  Figure  37.  F r a c t u r e e n e r g y v e r s u s mean f r e e path o f an a l u m i n a t r i h y d r a t e - e p o x y composite  113  could  have  made  alumina-filled  some  contribution  epoxy  Debonding  at  composites  crack  tips  to  the  tested  in  toughness  in  glass  this  of  the  study.  bead-filled  epoxy  42 has  been  observed  can  impede  crack  at semi-voids  This  process  to is  The  motion  around  contribution here.  .  presence  due  to  alumina  the  of  crack  such  blunting.  particles  fracture  energy  a  natural  extension  proposed  earlier  in  this  debonded  could of  of  the  Crack  have  the  zones blunting  made  some  composites  surface  used  roughening  section.  Summa r y  The fracture  i)  following energy  Surface  ii)  Crack  of  For  Crack  a  alumina  The  to  contribute  to  the  epoxy:  due  to  the  presence  of  a  phase,  blunting  alumina-filled matrix.  a1umina-fi11ed  deflection  volume  appear  roughness,  dispersed i i i )  factors  fraction  insemi-voids  of  composites increase  particles  was  in  ^  0.5, was  ^  surface  estimated  around  the 5  fracture  times area  here  particles.  the  due to  energy  be  of  toughness  to ^  the  the of  presence  6V . f  Thus,  the of for  114  a  volume  is  ^  3  fraction  times  roughness the  the  0.5,  the  fractured  seems  increase  of  to  in  be  fractured  area  of  area  epoxy.  of  the  composite  Consequently,  one  of  the  major  factors  toughness  of  the  composites  surface  controlling  used  in  this  study.  4.4.  Acoustic  In  the  acoustic  Emission  following  emission  in  During  Fracture  section  the  possible  alumina-reinforced  factors  epoxy  will  which be  affect  analyzed  anddiscussed.  Crazing  Crazing Using  ordinary  variations He  has  in  concluded  AE the  that  been  AE  more  probe)  was  required  23-25)  crazes They  in  found  dicular  to  to  the  AE  plastic from  to  detect  observed  be  various that  a  crazes. epoxy  the crack  be  in  arrest  source  of  AE  observed  when  crazing  crazing was  equipment  plastics "*' 4  no  was  masked  (laser  in  significant increased.  by  machine  displacement  it.  epoxy,  Lilley  resins  crazes  a  Peterlin  sophisticated  f i b r i l s  seem  of  the  and  The  to  equipment,  noises  .  found  and  in  this  Holloway  fractured  developed marks,  study,  in  just  by a as  45  (Figures  have  observed  wedge-1oading.  direction observed  perpenin  this  4  4  115  study.  No  epoxy.  AE was  pagation marks is  a  of  AE  AE was  was  generated  during  only  reinitiated.  where  crazes  source due  detected  of  to  AE  slow  at  the  Since  developed, the  unfilled  crazing  was  so  low  was  rapid  in  would  in  growth  moment  it  it  crack  the  appear  matrix.  that  it  in  crack  crack that  not  pro-  arrest  crazing  However,  was  pure  a  the  level  factor  in  f i l l e d c o m p o s i t e s .  Interaction Second  of  Phase  the  Crack  Front  with  the  Dispersion  1 3 Nadeau These  studied  plates  had  a  microstructure. pinning below  and  series  He  a threshold study,  alumina  particle  of  of  AE p e r  size  of  area  of  the  matrix.  particle  size  of  137  ym  50  times  study,  a  tinuity  strong  stress  produced.  of  the  had  grooves  to  resulted  area  was  AE  No  glass  of up  successive  AE was  ^  4  with  an  unit  area  Thus,  just  as  found  between  the  with  an  the  AE  times  per  detected In  composites to  plates.  represent  discontinuity.  Composites an  from  crack.  ym w a s  matrix.  dependence  of  average of  in  up  to  Nadeau's  AE a n d  discon-  size.  When load  that  main  unit  unit  ^  AE  surface  40  fracture  parallel  that the  value  the  AE d u r i n g of  found  breakaway  present  per  the  a  crack and  For  is  released  strain small  from  a  accumulations  particles  the  pinning are  point  released  pinning  action  and is  (particle), AE not  is very  116  large^ .  Consequently,  obstacles  is  5  in  pure  not  local  crack  significantly  epoxy.  Since  the  greater  amplitude 8  with  increasing  effect  on  crack  AE.  The  AE  The  per  converse  with  increasing  (see  Section  4.3.)  high  alumina  volume  material on  the  of  were  crack  that  the  discontinuities  and  AE  pinning is  a  emitted  small  true  crack  small  speed  pulses  particles  for  fraction in  the  front.  surpassing  the  large  alumina-fi11ed  present  fractions  than  of  ,  holds  of  for  increases  13 '  volume  decreases  appear  increased  when  fracture  composite  comet  a  Consequently,  the  per  unit  decreases.  and  breakaway  c r i t i c a l  factor  of  in  marks  surface.  becomes  area  l i t t l e  particles.  epoxy  only  the  have  pinning  the  the  main  For  "uniform" action It crack  generation  AE.  Decohesion  If  of  the  particles  drop  for 22.  account  Alumina  main  from  increasing  and  area  alumina  the  crack  would from  to  velocity  unit  speed  the  volume  high  for  source  the  the  of  matrix,  AE w o u l d  volume  decohesion  observed  from  AE w e r e  fraction.  alumina  Thus,  Particles  the  the  AE  fractions, the  behaviour.  decohesion  increase  However,  of  Matrix  per as  f i l l e r  of  alumina  monotonically unit  shown from  area in  values  Figures  epoxy  with  21  cannot  117  Fracture  of  The a  major  Alumina  fracture  AE  alumina  of  source  as  reason  decohesion  as  Surface  times  take  AE  per  that  into  would  Fracture  as  was  as  decohesion  of  Surfaces  parting  factor of  reasons  disregarded  fracture  contributing  surfaces  to  AE  for  was  the  same  alumina.  Roughness  The 50  major  was  matrix.  between  neglected  particles  same  the  Parting  f r i c t i o n a  the  from  between  The  alumina  for  particles  Friction  Particles  area  of  the  account  have  had  no  the  of  some  epoxy.  of  Using  surface  major  the a  composites  was  correction  factor  roughness  effect  on  the  of  AE  the  per  up  to to  composite  unit  area  values.  Summary  Crazing  appears  epoxy.  For  the  pinning  and  breakaway  to  be  the  major  to  be  the  major  a 1 u m i n a - f i 1 1 e d epoxy of  the  contributing  main  source  composites,  crack  factor  of  to  from the  AE  in'  the  pure successive  particles  generation  seems of  AE.  Even results, the  a  worst  found value.  to  though large  Such  AE  scatter  cases, have  the  the  the  standard  quantifying  information  the  wave  r e l i a b i l i t y  of  fracture  observed  yielded in  variation of  the of  magnitude were  not  toughness.  contained  propagation AE  study  variations  such  of  was  order  properties,  complexity  this  standard  same  as  in  in  as  AE  The  data.  per the  found  elastic  phenomena  techniques.  AE  consistent  area  In was  average in  other  d i f f i c u l t y waves  seriously  and  in the  limits  119  CONCLUDING  The  fracture  toughness  and  studied  increased  with  composites and in  were  independent  fracture  ticles  surface  accounted  The  AE  for  per  f i l l e d  composites  size.  A  below AE  maximum and  cut-off  which  per  no  unit at  f i l l e d  to  of  alumina  due  to  about  unit  be  particle  versus  major  composites.  increasing  the  during  of  fracture  about with  fraction volume due  contributing  to  the  increase.  alumina ym  particle  appears  addition  to  of  the  The of AE o f  exist, particles.  exhibited  presence to  par-  alumina-  fractions.  factor  increase  alumina  the  curves  the  fraction  energy  of  40  the  The  the  increasing  occurs  front  of  of  volume  size.  failure  with  alumina  energy  particle  of  volume  crack  fracture  presence  size  increase  the  the  60%  area  intermediate of  the  increased  AE  area  release  seemed  REMARKS  a pinning  particles alumina-  APPENDIX  APPENDIX 1 Sample T a b l e o f . t h e  Data C o l l e c t e d  During  a Wedge L o a d i n g T e s t  Sample Width H ( 1 0  -  2  Plate Thickness i n the plane o f t h e C r a c k , Bn  x m)  ,860  (10*  2  Critical Load, *l (lbs) P +  x m)  0.440  II  II  n II  n n II  n n II II  it II  n n II  n II II  M  1  320  2  0.460 it  16.6  3.0  400  3  14.8  3.3  570  4  0.490  14.6  3.8  780  5  0.450  14.4  4.1  450  6  0.480  14.0  4.4  610  7  0.460  14.5  4.7  2120  8  0.420 n  13.9  5.8  210  9  10.2  6.0  2460  10  0.440  8.8  7.1  1020  11  0.460  8.8  7.7  1540  12  0.440  8.3  8.0  1290  13  0.430  7.9  8.6  2170  14  0.430  7.4  8.9  1150  15  0.440  6.8  9.3  1320  16  0.430  6.7  9.7  3460  17 18  6.9  10.3  1330  0.460  6.2  10.9  410  19  0.410  6.4  11.2  610  20  0.400  6.1  12.1  2190  21  0.410  5.3  13.6  980  22  0.430  5.7  14.0  1810  23  5.7  14.4  2120  24  9.4  15.2  1550  25  0.440  9.6  15.5  1450  26  0.460  4.8  16.3  14360  27  -  2  2  P =  \ 2  tan e  (counts)  140  Alumina volume f r a c t i o n : 0.076 Average alumina p a r t i c l e s i z e : 1 2 9 ym Sample t h i c k n e s s : 1.27 x 1 0 m. Sample l e n g t h : 1 8 . 0 x 1 0 ~ m. +  x m)  2.5  0.430  n  2  2.1  II II  -  Step number, i  18.9  II  II  ( 1 0  AE  20.8  II  M  Crack Length, a  121  REFERENCES  1.  Dunegan/Endevco, " S y s t e m D e s i g n " , S h o r t C o u r s e on Acoustic E m i s s i o n , San Juan C a p i s t r a n o , C a l i f o r n i a , June 17-21, 1974, p. 1 .  2.  H.N.6. W a d l e y , C . B . Scruby and J . H . S p e a k e , "Acoustic Emission for Physical Examination of M e t a l s " , I nternati Metals R e v i e w s 25 ( 1 9 8 0 ) 41.  onal  3.  A.A. Pollock, "Acoustic Emission-2. Acoustic Emission Amplitudes", Non-Destructive Testing 6 (1973) 264.  4.  C R . Heiple, S . H . C a r p e n t e r and M . J . C a r r , "Acoustic Emission from D i s l o c a t i o n Motion in Precipitation-Strengthened A l l o y s " , Metal S c i e n c e 15 ( 1 9 8 1 ) 587.  5.  C.B. Scruby, H.N.G. Wadley, K. R u s b r i d g e a n d D. 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