Photoelastic Characterisation of the Stress Transfer at...
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Photoelastic Characterisation of the Stress Transfer at Fibre- break in Model Composites Fangming Zhao and Frank Jones Ceramics and Composites Laboratory Department of Engineering Materials The University of Sheffield CompTest 2006, 10-12 April 2006, Porto, Portugal
Transcript of Photoelastic Characterisation of the Stress Transfer at...
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Photoelastic Characterisation of the Stress Transfer at Fibre-break in Model Composites
Fangming Zhao and Frank Jones
Ceramics and Composites LaboratoryDepartment of Engineering Materials
The University of Sheffield
CompTest 2006, 10-12 April 2006, Porto, Portugal
-
Outline• Background
– Micro-mechanical methods to evaluate fibre surface treatment and composite interface
• Phase-stepping photoelasticity– Phase-stepping polariscope – Experimental system
• Photoelastic analysis and Finite Element Analysis– Stress transfer at the end of fibre-break – Results from photoelastic analysis– Results from FEA
• Conclusions• Acknowledgements
-
Background Current approaches for quantifying interfacial response in a fibre composite
Fragmentation testPull-out testMicro-bond test
Interfacial shear strength(shear stress)
c
fufi L
r στ =
Raman or fluorescencespectroscopy
Strain or stress in fibre Inferring τi
dxdr fx
ixσ
τ2
=
How to quantify the effect of debonding and matrix crack onStress transfer
Carbon and polymer fibres (high modules)
-
Phase-stepping photoelasticity
• Stress field in matrix• Interfacial shear stress
Phase-stepping Photoelasticity
Direct measurement
Recording birefringent images at the instantaneous moment that failure events occur
-
Principle of phase-stepping photoelasticity• Four CCD cameras are used for
collecting photoelastic images simultaneously
• Cubic beam-splitters provide four elliptically polarized light beam
• The pairs of quarter-wave plates and analysers are orientated so as to generate four phase-steps in photoelastic data
Image number
Orientation of quarter-wave plate
Orientation of analyser
1 π/4 π/42 0 03 π/2 π/24 0 π/4
An arrangement of optical device and light path
-
Theoretical model for the instrument
)sin2sin1(2
2
3 δθ−=aE
)sin2sin1(2
2
2 δθ+=aE
)cos1(2
2
4 δ−=aE
)sin2cos1(2
2
1 δθ−=aE
E.A. Patterson & Z.F. Wang J Strain Analysis 33 (1998) 1-15
Isoclinic angle
Relative retardation
⎟⎟⎠
⎞⎜⎜⎝
⎛−+
−= −132
321
2tan
21
EEEEEθ
⎟⎟⎠
⎞⎜⎜⎝
⎛−+
−= −)2(2
tan21
432
321
EEESinEE
θδ
-
Experimental system
hNf2
)(21
21maxσσστ =−=
αττ 2sinmax=i
A filter (wavelength: 542±5 nm)produces an essentially mono-chromatic green sourceA multiplex combines four signals into a single compositeimageThe composite image is re-divided into four phase-steepingimages and processed by a software operation
Mini-tester
Phase-steppingpolariscope
Microscope
πδ2
=N
-
Single fibre model composites (SFC)
• Araldite LY5052/HY5052 cold cured epoxy resinCold-cured
Young’s modulus (GPa): 3.20Tensile strength (MPa) : 72Stress-fringe constant fσ (MPa/fringe/mm): 20.23
Cold-curing: 7 days at room temperature
• E-glass and Al2O3 fibresE-glass Al2O3
Young’s modulus 72 GPa 414 GPaDiameter 80 μm 125 μm
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Fragmentation test of SFC and photoelasticmeasurement
Measured area
Fibre Strain gauge
F F
Increasing matrix stress/strain
Fibre end
Fibre break& matrix crack
-
Effect of a soft interphase on matrix crackfor glass fibre
Resin Em(MPa)
σuts(MPa)
Cold-draw strength (MPa)
Matrix resin 3200 72
Coating epoxy 2100 41 31
LY 1556 GY 298 NMA Capcure 3-80050 50 55.9 20.9
The resin cured at 80 ºC for 4 hours and 130 ºC for 3 hours
Epoxy resin for coating
Mechanical properties of matrix and coating epoxy resins
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Uncoated glass fibre Contour maps of fringe order at fibre-break
(b) σapp = 17.45 MPa, Lf = 3.35 mm
End of broken fibreTip of matrix crack
(a) σapp = 14.37 MPa, Lf = 11.26 mm
0.89 mm
0.52 mm
Matrix
• A zone of higher fringe order appears initially at the tip of the matrix crack
• At higher applied stress, the zone of higher fringe order extends along the fragment
• The matrix crack disturbs the stress field inthe matrix close to the interface
d = 88.65 μm
Fibre
Crack
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Epoxy-coated fibre: Contour maps of fringe order in matrix at fibre-break
(b) σapp = 12.42 MPa, Lf = 11.03 mm
(c) σapp = 17.63 MPa, Lf = 0.92 mm
d = 91.71 μm
Smaller transverse matrix cracksNo debonding
(a) σapp = 8.56 MPa, Lf = 11.03 mm
Crack tip Fibre
Matrix
FM Zhao, EA Patterson, FR Jones, Materials Sci Eng A 412 (2005) 83–87
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0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1 1.2
Distance from fibre break (mm)
Inte
rfac
ial s
hear
stre
ss (M
Pa)
14.37 MPa17.45 MPa
Role of interphase on shear stress profiles
0
5
10
15
20
25
30
0 0.2 0.4 0.6 0.8 1 1.2
Distance from fibre break (mm)
Inte
rfac
ial s
hear
stre
ss (M
Pa)
8.56 MPa12.42 MPa17.63 MPa
Uncoated fibre Epoxy-coated fibre
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Effect of the size of transverse matrix crackContour maps of fringe order around the cracks with different sizes
Crack size: less than 2 μmLf = 3.77 mm, σm = 9.17 MPa
Crack size: 98.72 μmLf = 1.80 mm, σm = 13.65 MPa
Crack tip
Crack size: 62.02 μmLf = 6.37 mm, σm = 9.17 MPa
Crack tip
Crack tip
Matrix
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Effect of the size of transverse matrix crackDistribution of fringe order at interface
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2
Distance from fibre-break (mm)
Inte
rfaci
al fr
inge
ord
er
B1, crack length: ~ 2 μm
B2, crack length: 63 μm
σm = 9.04 MPa1
1.1
1.2
1.3
1.4
0 0.5 1 1.5 2
Distance from fibre-break (mm)
Inte
rfaci
al fr
inge
ord
er
B3, crack length: 99 μm
σm = 13.65 MPa
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FEA results for different sizes of crack
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6Distance from the fibre end (mm)
Tens
ile s
tres
s in
the
fibre
(MP
a)
No matrix crack0.1 mm matrix crack0.2 mm matrix crack0.4 mm matrix crack
0 0.1 mm0.2 mm0.4 mm
0
5
10
15
20
25
30
35
40
45
0 0.2 0.4 0.6 0.8 1Distance from the fibre end (mm)
Shea
r stre
ss a
t fib
re/m
atri
x in
terfa
ce
(MPa
)
No matrix crack0.1 mm matrix crack0.2 mm matrix crack0.4 mm matrix crack
Maximum
AC. Johnson, FM. Zhao, SA. Hayes, F. R. Jones Composites Sci and Technol., on-line available
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Comparison of FEA and experimental results
0
5
10
15
20
25
30
35
0 0.25 0.5 0.75 1 1.25 1.5Distance from the fibre break (mm)
shea
r st
ress
at t
he fi
bre/
mat
rix
inte
rface
(MP
a)Determined by photoelasticity
Finite element prediction
Transverse crack length = 0.2 mm
-
Effect of a transverse matrix crack on shear stress transfer
0
4
8
12
16
20
0.0 0.5 1.0 1.5
Distance from fibre break (mm)
Inte
rfaci
al sh
ear s
tress
(MPa
)
εapp = 0.188%σapp = 6.36 MPa
εapp = 0.188%, σapp = 6.36 MPaLf = 13.32 mm
Al2O3 fibre
Matrix crackFibre
Matrix
F.M. Zhao et al Composites Part A, 36 (2005) 229-244
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Combined effect of transverse matrix crack and debonding at fibre-break (Al2O3 fibre)
Crack tip
Crack
σapp = 16.08 MPa, εapp = 0.48%
Debonded interface
Bonded area
FM Zhao, FR Jones et al., Composites Part A 36 (2005) 229-244
Crack tip
σapp = 13.10 MPa, εapp = 0.388%
Crack
Matrix
1.67 mm
1.00
mm
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Conclusions
• Automated phase-stepping polariscope has been used to measure the micro stress field in the matrix near a fibre-break and the interfacial shear stress for Al2O3 and E-glass fibre epoxy model composites
• Effect of a transverse matrix crack on stress transfer has been investigated by photoelasticity
• It has been found that the matrix crack can delay significantly stress transfer
• A soft interphase can be created, which controls the propagation of a transverse matrix crack
• The debonding at the fibre break can be detected accurately by photoelasticity
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Acknowledgements
• EPSRC for funding the research
• Photran Inc. (USA) for the supply of sapphire fibre and The Advanced Composites Group (UK) for supplying epoxy resins
• Prof K Schulte (Germany) for supplying E-glass fibre made by The Institute of Polymer Research Dresden.
• Prof EA Patterson for introducing the phase-stepping photoelastictechnique
• Dr C Johnson,Mr H Sugihara and Mr Z Liu for coating E-glass fibres
• Dr Z Wang for technique support
Photoelastic Characterisation of the Stress Transfer at Fibre-break in Model Composites OutlineBackground Current approaches for quantifying interfacial response in a fibre compositePhase-stepping photoelasticityPrinciple of phase-stepping photoelasticityTheoretical model for the instrumentExperimental systemSingle fibre model composites (SFC)Fragmentation test of SFC and photoelastic measurementEffect of a soft interphase on matrix crack�for glass fibreUncoated glass fibre Contour maps of fringe order at fibre-breakEpoxy-coated fibre: Contour maps of fringe order in matrix at fibre-breakRole of interphase on shear stress profilesEffect of the size of transverse matrix crack�Contour maps of fringe order around the cracks with different sizesEffect of the size of transverse matrix crack�Distribution of fringe order at interfaceFEA results for different sizes of crackComparison of FEA and experimental resultsEffect of a transverse matrix crack on shear stress transferCombined effect of transverse matrix crack and debonding at fibre-break (Al2O3 fibre)Conclusions Acknowledgements
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Photoelastic Characterisation of the Stress Transfer at Fibre-break in Model Composites
Fangming Zhao and Frank Jones
Ceramics and Composites Laboratory
Department of Engineering Materials
The University of Sheffield
CompTest 2006, 10-12 April 2006, Porto, Portugal
Outline
Background
Micro-mechanical methods to evaluate fibre surface treatment and composite interface
Phase-stepping photoelasticity
Phase-stepping polariscope
Experimental system
Photoelastic analysis and Finite Element Analysis
Stress transfer at the end of fibre-break
Results from photoelastic analysis
Results from FEA
Conclusions
Acknowledgements
Background Current approaches for quantifying interfacial response in a fibre composite
Fragmentation test
Pull-out test
Micro-bond test
Interfacial shear strength
(shear stress)
Raman or fluorescence
spectroscopy
Strain or stress
in fibre
Inferring ti
How to quantify the effect of
debonding and matrix crack on
Stress transfer
Carbon and polymer fibres
(high modules)
Phase-stepping photoelasticity
Stress field in matrix
Interfacial shear stress
Phase-stepping Photoelasticity
Direct measurement
Recording birefringent images
at the instantaneous moment that failure events occur
Principle of phase-stepping photoelasticity
Four CCD cameras are used for collecting photoelastic images simultaneously
Cubic beam-splitters provide four elliptically polarized light beam
The pairs of quarter-wave plates and analysers are orientated so as to generate four phase-steps in photoelastic data
An arrangement of optical device
and light path
Image numberOrientation of quarter-wave plateOrientation of analyser
1/4/4
200
3/2/2
40/4
142.psd
Theoretical model for the instrument
E.A. Patterson & Z.F. Wang J Strain Analysis 33 (1998) 1-15
Isoclinic angle
Relative retardation
Experimental system
A filter (wavelength: 5425 nm)
produces an essentially mono-
chromatic green source
A multiplex combines four
signals into a single composite
image
The composite image is re-
divided into four phase-steeping
images and processed by a
software operation
Mini-tester
Phase-stepping
polariscope
Microscope
Single fibre model composites (SFC)
Araldite LY5052/HY5052 cold cured epoxy resin
Cold-cured
Young’s modulus (GPa): 3.20
Tensile strength (MPa) : 72
Stress-fringe constant fs (MPa/fringe/mm): 20.23
Cold-curing: 7 days at room temperature
E-glass and Al2O3 fibres
E-glass Al2O3
Young’s modulus 72 GPa 414 GPa
Diameter 80 mm 125 mm
Fragmentation test of SFC and photoelastic measurement
Measured area
Fibre
Strain gauge
F
F
Increasing
matrix stress/strain
Fibre end
Fibre break
& matrix crack
Effect of a soft interphase on matrix crack
for glass fibre
The resin cured at 80 ºC for 4 hours and 130 ºC for 3 hours
Epoxy resin for coating
Mechanical properties of matrix and coating epoxy resins
ResinEm (MPa)suts (MPa)Cold-draw strength (MPa)
Matrix resin320072
Coating epoxy21004131
LY 1556GY 298NMACapcure 3-800
505055.920.9
Uncoated glass fibre Contour maps of fringe order at fibre-break
A zone of higher fringe order appears
initially at the tip of the matrix crack
At higher applied stress, the zone of higher
fringe order extends along the fragment
The matrix crack disturbs the stress field in
the matrix close to the interface
(b) sapp = 17.45 MPa, Lf = 3.35 mm
End of broken fibre
Tip of matrix crack
(a) sapp = 14.37 MPa, Lf = 11.26 mm
0.89 mm
0.52 mm
Matrix
d = 88.65 mm
Fibre
Crack
Epoxy-coated fibre: Contour maps of fringe order in matrix at fibre-break
d = 91.71 mm
Smaller transverse matrix cracks
No debonding
FM Zhao, EA Patterson, FR Jones, Materials Sci Eng A 412 (2005) 83–87
(b) sapp = 12.42 MPa, Lf = 11.03 mm
(c) sapp = 17.63 MPa, Lf = 0.92 mm
Crack tip
Fibre
Matrix
(a) sapp = 8.56 MPa, Lf = 11.03 mm
162.psd
Role of interphase on shear stress profiles
Uncoated fibre
Epoxy-coated fibre
Effect of the size of transverse matrix crack
Contour maps of fringe order around the cracks with different sizes
Crack size: less than 2 mm
Lf = 3.77 mm, sm = 9.17 MPa
Crack size: 98.72 mm
Lf = 1.80 mm, sm = 13.65 MPa
Crack tip
Crack size: 62.02 mm
Lf = 6.37 mm, sm = 9.17 MPa
Crack tip
Crack tip
Matrix
Effect of the size of transverse matrix crack
Distribution of fringe order at interface
B1, crack length: ~ 2 mm
B2, crack length: 63 mm
sm = 9.04 MPa
B3, crack length: 99 mm
sm = 13.65 MPa
FEA results for different sizes of crack
AC. Johnson, FM. Zhao, SA. Hayes, F. R. Jones
Composites Sci and Technol., on-line available
Maximum
Comparison of FEA and experimental results
Transverse crack length = 0.2 mm
Effect of a transverse matrix crack on shear stress transfer
eapp = 0.188%
sapp = 6.36 MPa
F.M. Zhao et al Composites Part A, 36 (2005) 229-244
eapp = 0.188%,
sapp = 6.36 MPa
Lf = 13.32 mm
Al2O3 fibre
Matrix crack
Fibre
Matrix
Chart3
0.007196
0.014392
0.021588
0.028784
0.03598
0.043176
0.050372
0.057568
0.064764
0.07196
0.079156
0.086352
0.093548
0.100744
0.10794
0.115136
0.122332
0.129528
0.136724
0.14392
0.151116
0.158312
0.165508
0.172704
0.1799
0.187096
0.194292
0.201488
0.208684
0.21588
0.223076
0.230272
0.237468
0.244664
0.25186
0.259056
0.266252
0.273448
0.280644
0.28784
0.295036
0.302232
0.309428
0.316624
0.32382
0.331016
0.338212
0.345408
0.352604
0.3598
0.366996
0.374192
0.381388
0.388584
0.39578
0.402976
0.410172
0.417368
0.424564
0.43176
0.438956
0.446152
0.453348
0.460544
0.46774
0.474936
0.482132
0.489328
0.496524
0.50372
0.510916
0.518112
0.525308
0.532504
0.5397
0.546896
0.554092
0.561288
0.568484
0.57568
0.582876
0.590072
0.597268
0.604464
0.61166
0.618856
0.626052
0.633248
0.640444
0.64764
0.654836
0.662032
0.669228
0.676424
0.68362
0.690816
0.698012
0.705208
0.712404
0.7196
0.726796
0.733992
0.741188
0.748384
0.75558
0.762776
0.769972
0.777168
0.784364
0.79156
0.798756
0.805952
0.813148
0.820344
0.82754
0.834736
0.841932
0.849128
0.856324
0.86352
0.870716
0.877912
0.885108
0.892304
0.8995
0.906696
0.913892
0.921088
0.928284
0.93548
0.942676
0.949872
0.957068
0.964264
0.97146
0.978656
0.985852
0.993048
1.000244
1.00744
1.014636
1.021832
1.029028
1.036224
1.04342
1.050616
1.057812
1.065008
1.072204
1.0794
1.086596
1.093792
1.100988
1.108184
1.11538
1.122576
1.129772
1.136968
1.144164
1.15136
1.158556
1.165752
1.172948
1.180144
1.18734
1.194536
1.201732
1.208928
1.216124
1.22332
1.230516
1.237712
1.244908
1.252104
1.2593
1.266496
1.273692
1.280888
1.288084
1.29528
1.302476
1.309672
1.316868
1.324064
1.33126
1.338456
1.345652
1.352848
1.360044
1.36724
1.374436
1.381632
1.388828
1.396024
1.40322
1.410416
1.417612
1.424808
Left end of F2
Distance from fibre break (mm)
Interfacial shear stress (MPa)
17.8137669948
20.0987265496
18.8341403649
14.4426665422
10.4192118281
7.9026922007
6.3902585892
5.1190847294
3.9519989271
3.276674982
2.5448879222
1.9744761267
1.6669316785
1.3116060747
0.9201926538
0.5341895007
0.2476468525
0.172571924
0.1770517694
0.178569812
0.0456755991
0.2700959246
0.4779870602
0.6008421138
0.6008421138
0.8213796678
0.8369863033
0.8438696458
0.9807260921
1.3293383437
1.4511498858
1.6917336585
1.5730203617
1.5572237747
1.8837944762
1.8837944762
2.1547456379
2.316918968
2.5621156316
2.5426354894
2.6638081318
2.7635031021
3.0083295824
3.2782053949
3.4717545553
3.7139253696
4.0527364063
4.2186767129
4.1415807025
4.3288439965
4.3420310219
4.5144743402
4.7228659954
4.8741088778
4.8266732391
4.8266732391
4.8725112305
4.9932862661
5.1073691108
5.4496161668
5.5388729499
5.3730280448
5.4515108886
5.5957036688
5.6719200278
5.7790907715
5.8125240975
5.9934570768
6.0655601861
6.2516631995
6.1278353088
5.9695484131
5.8126812944
5.8507862143
5.9463778929
5.8629074806
6.0574195407
6.2233644786
6.5289226238
6.4785157626
6.2770049473
6.1358686789
6.1358686789
6.1977696454
6.2281659649
6.2894229566
6.2211058485
6.1648755103
6.1648755103
6.0783126813
6.1352529288
6.2352509402
6.0859976042
6.2594786117
6.1520661038
6.0448283295
6.1315258823
6.0963081272
6.1040542877
6.2209743265
6.2209743265
6.0880461274
5.9892460739
5.9399907493
5.8217281964
5.7199817632
5.5878639986
5.5878639986
5.5454606449
5.547155918
5.6266032908
5.5262058269
5.5764650394
5.6558453149
5.4535641442
5.3818135795
5.2775917235
5.2319503023
5.2857159771
5.2319503023
4.9729569291
4.8992601337
4.7322286765
4.982704777
5.0676054499
5.0676054499
5.0893275542
4.9936753599
4.7934939732
4.6639065957
4.5931753143
4.4952611772
4.4384475643
4.5656996214
4.6683126239
4.6998047238
4.5691087592
4.3668457622
4.2691403747
4.2377945138
4.3959292321
4.270778823
4.081732479
3.9848541879
4.0445718623
3.9755811907
3.8398353175
3.7381557239
3.6783602526
3.7772340054
3.6783602526
3.638256164
3.7037665976
3.7293071815
3.6913930377
3.6265903708
3.5992181207
3.7017590778
3.5648543586
3.5236812848
3.4488579813
3.5368530638
3.6005622886
3.6005622886
3.329225885
3.2848529265
3.301493876
3.4063668624
3.4763215361
3.4763215361
3.344011994
3.2090160978
3.2090160978
3.3146194549
3.3028646889
3.0893488597
3.1645160038
3.0871699767
3.1607208189
3.0420566342
3.0420566342
2.996099234
2.8540000441
2.883576627
2.7969293666
2.714614474
2.608834315
2.5300684194
2.4478425046
2.6624601407
2.6624601407
2.7148689414
2.5033828044
2.4478425046
2.3655616199
2.2381215852
2.0931669844
2.052037904
Sheet1
Sheet1
00
0.0071960.007196
0.0143920.014392
0.0215880.021588
0.0287840.028784
0.035980.03598
0.0431760.043176
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0.0791560.079156
0.0863520.086352
0.0935480.093548
0.1007440.100744
0.107940.10794
0.1151360.115136
0.1223320.122332
0.1295280.129528
0.1367240.136724
0.143920.14392
0.1511160.151116
0.1583120.158312
0.1655080.165508
0.1727040.172704
0.17990.1799
0.1870960.187096
0.1942920.194292
0.2014880.201488
0.2086840.208684
0.215880.21588
0.2230760.223076
0.2302720.230272
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0.2590560.259056
0.2662520.266252
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0.3526040.352604
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0.3669960.366996
0.3741920.374192
0.3813880.381388
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0.5253080.525308
0.5325040.532504
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0.5540920.554092
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0.7124040.712404
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0.7267960.726796
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0.7627760.762776
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0.7987560.798756
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0.8419320.841932
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0.8779120.877912
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0.8923040.892304
0.89950.8995
0.9066960.906696
0.9138920.913892
0.9210880.921088
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0.93548
0.942676
0.949872
0.957068
0.964264
0.97146
0.978656
0.985852
0.993048
1.000244
1.00744
1.014636
1.021832
1.029028
1.036224
1.04342
1.050616
1.057812
1.065008
1.072204
1.0794
1.086596
1.093792
1.100988
1.108184
1.11538
1.122576
1.129772
1.136968
1.144164
1.15136
1.158556
1.165752
1.172948
1.180144
1.18734
1.194536
1.201732
1.208928
1.216124
Left end of F1
Right end of F2
Distance from fibre end (mm)
Interfacial shear stress (MPa)
11.8525224155
10.1460931241
12.4653381267
10.4743563779
12.2540195349
10.2619192049
10.7438775701
9.5694559099
8.1782462701
9.7042918756
6.1101760989
10.3494542986
4.7153212115
10.7150360796
3.9565258707
10.3672389512
3.405370528
9.4339850578
2.690572914
8.4411729791
1.8261944543
8.2150973034
1.5460827076
8.3205434314
1.490927626
8.1898135668
1.1281145957
7.86892449
1.1205626991
7.2312048129
1.1130108025
6.5907734975
1.3150129724
5.6394771015
1.8586062934
5.0160670585
2.3459832714
4.5859824594
2.4218268035
4.5070695276
2.6236055029
4.4651675906
2.31012279
4.6426870558
1.9693417258
4.8897534639
1.1708659319
5.0932435261
0.518990233
4.9505004688
0.3299611029
4.5055608359
0.5541655627
4.1384015207
1.6339950532
4.0326626857
2.6086774019
3.9651822172
3.418396805
3.8610116553
4.3098062215
3.6017834796
4.9857031324
3.378950272
5.8626899103
3.2661147137
6.7162106762
2.9817795595
7.6704298416
2.6115847543
7.8343440038
2.0830101006
8.6535019052
1.9924968615
9.1512146014
2.074943263
9.5338366229
2.2730271215
9.5760881675
2.2908513626
9.6655671593
2.2199103519
9.9397459165
1.4733513659
10.3297326493
0.8225086341
10.6911275573
0.2199911017
11.1580689563
0.0269529076
11.3559619998
0.0455716568
11.7281815906
0.2863769739
11.3641457298
0.5296085694
11.4714045622
0.9355267623
11.4284617623
1.5921071699
11.9617570085
2.097208371
12.283422603
2.763301319
12.2239294269
3.2585288778
12.1007645611
3.8824396718
11.9908359168
4.3908183142
12.0383193248
4.7182392441
12.6040133307
5.1720617392
12.5179095367
5.2192925623
12.2979012913
5.3020989231
12.0014852082
5.5177688093
11.8384743963
5.8646057273
12.0830498134
6.0581210661
11.7467097174
6.3238985321
11.452822632
6.4261997352
11.8247091488
6.4910189358
12.2065913353
6.8520240162
12.4226649563
7.0998620052
12.4006625221
7.2111991636
12.1547601906
7.2286590692
11.9383568907
7.2995586991
11.9383568907
7.4233552995
11.6917967063
7.6420710008
11.7302866513
7.6922231597
11.9119728008
7.6264505989
11.8817250557
7.6725958521
12.071975494
7.9786251205
11.9873204925
8.1425509576
11.7005499967
8.1380072631
11.7436948262
8.0045974031
11.6446622206
8.0063147482
11.3969162414
8.0484477357
11.21573492
7.9291210101
11.2404616881
7.8777056836
11.3749489648
7.9241290023
11.5757413107
8.1521418504
11.5654059139
8.252220181
11.1893808027
8.3060296934
11.0069897451
7.9506193236
11.0069897451
7.8484866638
10.9836608499
8.0790988092
10.7953129503
8.2218433408
11.0416705499
8.1957751785
10.8073358877
7.9556230477
10.9475576562
7.8430000987
10.819670851
7.8560494477
10.6639198502
7.9171758689
10.7825880701
7.9171758689
11.008425019
7.9556230477
11.134787562
7.8044345942
11.0806739707
7.7030130406
11.1181415449
7.5876202107
11.0995296293
7.8136030475
11.035275047
7.812219886
10.6360740713
7.8136030475
10.2471008283
7.6388093444
10.5953602868
7.6891431751
10.673281808
7.6891431751
10.836142148
7.7435651345
10.5139619585
7.6277852295
10.3630228548
7.5141806711
10.0033864915
7.4129712997
10.1133314013
7.6025192465
10.1531908704
7.7226485504
10.3774891694
7.5386224846
10.4082941744
7.3560499624
10.4996170283
7.4357167294
10.619502387
7.492258622
10.2188675437
7.4313401816
10.1063818258
7.3493460143
9.8829372402
7.2855851351
9.6218414357
7.0798868253
9.7146292768
6.7353403205
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6.5080822216
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6.6781845435
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6.603926474
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6.392612301
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6.694272926
9.6581515913
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9.758215145
9.9441369198
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9.5515310397
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9.1013086465
9.131085008
9.0032800107
9.1363611681
8.8707596683
8.6540853957
8.5720679242
8.5720679242
8.5899235758
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8.7403722574
8.6054456409
8.4237102464
8.3672516607
8.2069782602
8.4995709891
8.3696136588
8.3696136588
8.3696136588
8.369614281
Sheet2
0.0071960.007196
0.0143920.014392
0.0215880.021588
0.0287840.028784
0.035980.03598
0.0431760.043176
0.0503720.050372
0.0575680.057568
0.0647640.064764
0.071960.07196
0.0791560.079156
0.0863520.086352
0.0935480.093548
0.1007440.100744
0.107940.10794
0.1151360.115136
0.1223320.122332
0.1295280.129528
0.1367240.136724
0.143920.14392
0.1511160.151116
0.1583120.158312
0.1655080.165508
0.1727040.172704
0.17990.1799
0.1870960.187096
0.1942920.194292
0.2014880.201488
0.2086840.208684
0.215880.21588
0.2230760.223076
0.2302720.230272
0.2374680.237468
0.2446640.244664
0.251860.25186
0.2590560.259056
0.2662520.266252
0.2734480.273448
0.2806440.280644
0.287840.28784
0.2950360.295036
0.3022320.302232
0.3094280.309428
0.3166240.316624
0.323820.32382
0.3310160.331016
0.3382120.338212
0.3454080.345408
0.3526040.352604
0.35980.3598
0.3669960.366996
0.3741920.374192
0.3813880.381388
0.3885840.388584
0.395780.39578
0.4029760.402976
0.4101720.410172
0.4173680.417368
0.4245640.424564
0.431760.43176
0.4389560.438956
0.4461520.446152
0.4533480.453348
0.4605440.460544
0.467740.46774
0.4749360.474936
0.4821320.482132
0.4893280.489328
0.4965240.496524
0.503720.50372
0.5109160.510916
0.5181120.518112
0.5253080.525308
0.5325040.532504
0.53970.5397
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0.7627760.762776
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0.7771680.777168
0.7843640.784364
0.791560.79156
0.7987560.798756
0.8059520.805952
0.8131480.813148
0.8203440.820344
0.827540.82754
0.8347360.834736
0.8419320.841932
0.8491280.849128
0.8563240.856324
0.863520.86352
0.8707160.870716
0.8779120.877912
0.8851080.885108
0.8923040.892304
0.89950.8995
0.9066960.906696
0.9138920.913892
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0.935480.93548
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0.9570680.957068
0.9642640.964264
0.971460.97146
0.9786560.978656
0.9858520.985852
0.9930480.993048
1.0002441.000244
1.007441.00744
1.0146361.014636
1.0218321.021832
1.0290281.029028
1.0362241.036224
1.043421.04342
1.0506161.050616
1.0578121.057812
1.0650081.065008
1.0722041.072204
1.07941.0794
1.0865961.086596
1.0937921.093792
1.1009881.100988
1.1081841.108184
1.115381.11538
1.1225761.122576
1.1297721.129772
1.1369681.136968
1.1441641.144164
1.151361.15136
1.1585561.158556
1.1657521.165752
1.1729481.172948
1.1801441.180144
1.187341.18734
1.1945361.194536
1.2017321.201732
1.2089281.208928
1.2161241.216124
1.223321.22332
1.2305161.230516
1.2377121.237712
1.2449081.244908
1.2521041.252104
1.25931.2593
1.2664961.266496
1.2736921.273692
1.2808881.280888
1.2880841.288084
1.295281.29528
1.3024761.302476
1.3096721.309672
1.3168681.316868
1.3240641.324064
1.331261.33126
1.3384561.338456
1.3456521.345652
1.3528481.352848
1.3600441.360044
1.367241.36724
1.3744361.374436
1.3816321.381632
1.3888281.388828
1.3960241.396024
1.403221.40322
1.4104161.410416
1.4176121.417612
1.4248081.424808
1.432004
1.4392
1.446396
1.453592
1.460788
1.467984
Right end of F1
Left end of F2
Distance from fibre break (mm)
Interfacial shear stress (MPa)
14.947664224
17.8137669948
15.420881365
20.0987265496
14.1760504122
18.8341403649
12.2513823809
14.4426665422
10.0192775612
10.4192118281
7.6515046905
7.9026922007
6.2687136118
6.3902585892
5.3299685951
5.1190847294
4.681935587
3.9519989271
4.1468688226
3.276674982
3.5631288343
2.5448879222
2.8903196717
1.9744761267
2.2285978192
1.6669316785
1.9420871601
1.3116060747
1.7488305662
0.9201926538
1.4417005655
0.5341895007
1.4656101749
0.2476468525
1.2501667055
0.172571924
1.1806930847
0.1770517694
0.8667238983
0.178569812
0.7760823827
0.0456755991
0.6909429733
0.2700959246
0.3478170286
0.4779870602
0.1153126959
0.6008421138
0.2491654543
0.6008421138
0.4890657035
0.8213796678
0.7442055825
0.8369863033
0.7649982461
0.8438696458
0.7709044518
0.9807260921
0.9947739741
1.3293383437
1.3427708447
1.4511498858
1.7009174595
1.6917336585
1.9411797642
1.5730203617
2.1747981894
1.5572237747
2.3412253176
1.8837944762
2.4661915201
1.8837944762
2.6147222746
2.1547456379
2.8294468648
2.316918968
2.9328251802
2.5621156316
3.0815227604
2.5426354894
3.2393686851
2.6638081318
3.5571237935
2.7635031021
3.8983880119
3.0083295824
3.9255647455
3.2782053949
4.1091035348
3.4717545553
4.2303867493
3.7139253696
4.1312090145
4.0527364063
4.448249117
4.2186767129
4.7922546407
4.1415807025
5.0856115548
4.3288439965
5.2546118146
4.3420310219
5.3428093678
4.5144743402
5.5021166719
4.7228659954
5.5449073976
4.8741088778
5.5449073976
4.8266732391
5.657237503
4.8266732391
5.657237503
4.8725112305
5.8099821555
4.9932862661
5.7667816546
5.1073691108
5.8150802439
5.4496161668
5.8727513835
5.5388729499
6.1632269242
5.3730280448
6.2569445292
5.4515108886
6.5399674348
5.5957036688
6.6496185406
5.6719200278
6.4270954731
5.7790907715
6.599804473
5.8125240975
6.5588793776
5.9934570768
6.7347852763
6.0655601861
6.9416467231
6.2516631995
6.8203798081
6.1278353088
6.8709031976
5.9695484131
6.7665913453
5.8126812944
6.6655608107
5.8507862143
6.7401945716
5.9463778929
6.7802150946
5.8629074806
6.8958537484
6.0574195407
6.7495196855
6.2233644786
7.0233790979
6.5289226238
7.1863573686
6.4785157626
7.2786515895
6.2770049473
7.1659556542
6.1358686789
7.0180259033
6.1358686789
7.0316460848
6.1977696454
6.9773579229
6.2281659649
7.0238314305
6.2894229566
6.914292036
6.2211058485
6.8194386314
6.1648755103
6.9278276966
6.1648755103
6.9278276966
6.0783126813
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6.1352529288
6.8604945657
6.2352509402
6.8043316353
6.0859976042
6.7463445716
6.2594786117
6.8530450665
6.1520661038
6.9101030708
6.0448283295
6.9992390023
6.1315258823
7.2096605121
6.0963081272
7.1009257457
6.1040542877
6.9996826614
6.2209743265
6.9563889747
6.2209743265
6.8579784491
6.0880461274
6.7621441383
5.9892460739
6.7621441383
5.9399907493
6.5637497641
5.8217281964
6.5102100522
5.7199817632
6.3603683192
5.5878639986
6.3549824885
5.5878639986
6.4602647121
5.5454606449
6.5429424729
5.547155918
6.4425709524
5.6266032908
6.6901803062
5.5262058269
6.6791454952
5.5764650394
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5.6558453149
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5.4535641442
6.2456033217
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5.2775917235
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5.2319503023
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5.2857159771
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4.7322286765
5.9466781672
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4.9936753599
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4.7934939732
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4.6639065957
5.6473915178
4.5931753143
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2.2381215852
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Sheet3
Combined effect of transverse matrix crack and debonding at fibre-break (Al2O3 fibre)
FM Zhao, FR Jones et al., Composites Part A 36 (2005) 229-244
Crack tip
Crack
sapp = 16.08 MPa, eapp = 0.48%
Debonded interface
Bonded area
Crack tip
sapp = 13.10 MPa, eapp = 0.388%
Crack
Matrix
1.67 mm
1.00 mm
Conclusions
Automated phase-stepping polariscope has been used to measure the micro stress field in the matrix near a fibre-break and the interfacial shear stress for Al2O3 and E-glass fibre epoxy model composites
Effect of a transverse matrix crack on stress transfer has been investigated by photoelasticity
It has been found that the matrix crack can delay significantly stress transfer
A soft interphase can be created, which controls the propagation of a transverse matrix crack
The debonding at the fibre break can be detected accurately by photoelasticity
Acknowledgements
EPSRC for funding the research
Photran Inc. (USA) for the supply of sapphire fibre and The Advanced Composites Group (UK) for supplying epoxy resins
Prof K Schulte (Germany) for supplying E-glass fibre made by The Institute of Polymer Research Dresden.
Prof EA Patterson for introducing the phase-stepping photoelastic technique
Dr C Johnson,Mr H Sugihara and Mr Z Liu for coating E-glass fibres
Dr Z Wang for technique support
0
10
20
30
40
50
00.20.40.60.811.2
Distance from fibre break (mm)
Interfacial shear stress (MPa)
14.37 MPa
17.45 MPa
0
5
10
15
20
25
30
00.20.40.60.811.2
Distance from fibre break (mm)
Interfacial shear stress (MPa)
8.56 MPa
12.42 MPa
17.63 MPa
0
4
8
12
16
20
0.00.51.01.5
Distance from fibre break (mm)
Interfacial shear stress (MPa)
0.5
0.6
0.7
0.8
0.9
00.511.52
Distance from fibre-break (mm)
Interfacial fringe order
1
1.1
1.2
1.3
1.4
00.511.52
Distance from fibre-break (mm)
Interfacial fringe order
0
100
200
300
400
500
600
700
800
900
0123456
Distance from the fibre end (mm)
Tensile stress in the fibre (MPa)
No matrix crack
0.1 mm matrix crack
0.2 mm matrix crack
0.4 mm matrix crack
0
0.1 mm
0.2 mm
0.4 mm
0
5
10
15
20
25
30
35
40
45
00.20.40.60.81
Distance from the fibre end (mm)
Shear stress at fibre/matrix interface
(MPa)
No matrix crack
0.1 mm matrix crack
0.2 mm matrix crack
0.4 mm matrix crack
0
5
10
15
20
25
30
35
00.250.50.7511.251.5
Distance from the fibre break (mm)
shear stress at the fibre/matrix
interface (MPa)
Determined by photoelasticity
Finite element prediction
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