Abstract
Measurements of the distributions of crack spacings developed in the 90° ply of 0°/90°/0° glass fibre/epoxy resin laminates under tensile loading show that the ply has a variable strength. As a consequence the strain at which cracking begins is very dependent on the specimen length. The observed distributions of crack spacing are not consistent with the assumption of a uniform strength for the 90° ply. A statistical model provides a good description of the cracking behaviour particularly when the cracks are widely spaced. Magnification of the stress in the matrix between the relatively stiff glass fibres leads to debonding which is observed as a reversible “stress-whitening.” The distributions reveal a lower probability of crack formation in the under-stressed region close to the existing cracks and provide estimates of the size of this region. The method of analysis can be applied to many systems which exhibit multiple fracture.
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Abbreviations
- GBP:
-
Garrett, Bailey, Parvizi
- c.d.f.:
-
Cumulative distribution function
- i.i.d.:
-
Independent and identically distributed
- NMA:
-
Nadic methyl anhydride
- BDMA:
-
Benzyl di-methyl amine
- A :
-
Cross-sectional area of 90° ply
- L :
-
Crack spacing
- V :
-
Volume of 90° ply under consideration
- b :
-
0° ply thickness
- d :
-
90° ply half-thickness
- E 0,E 90 :
-
Young's modulus of 0° and 90° ply, respectively
- G 90 :
-
Shear modulus of 90° ply
- y :
-
Distance from plane of crack
- N :
-
Total number of crack spacings
- n :
-
Subset ofN
- σ,σ 90 :
-
Stress, stress in 90° ply
- σ a :
-
Average applied stress on laminate
- σ *,ε * :
-
Weibull scale parameter in terms of stress and strain
- w :
-
Weibull shape parameter
- Β :
-
Exponent in GBP stress function
- Μ :
-
Average number of cracks per unit length
- γ:
-
Gamma function
- S,S v :
-
c.d.f. for strength of 90° ply, (of volumeV)
- S 0 :
-
c.a.f. for strength of unit volume
- R,R v :
-
Risk of rupture of 90° ply, (of volumeV)
- Φ :
-
Risk of rupture per unit volume
- u,v,z :
-
Displacement in shear lag analysis
- δσ90 :
-
Difference between 90° ply stress in presence of cracks and the expected stress in the absence of cracks
- Τ :
-
Interfacial shear stress between 0° and 90° plies
- ε 0,ε 90,ε a :
-
Tensile strains in 0°, 90° plies and applied strain
References
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Manders, P.W., Chou, TW., Jones, F.R. et al. Statistical analysis of multiple fracture in 0°/90°/0° glass fibre/epoxy resin laminates. J Mater Sci 18, 2876–2889 (1983). https://doi.org/10.1007/BF00700768
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DOI: https://doi.org/10.1007/BF00700768