International Journal of Fracture

, Volume 211, Issue 1–2, pp 61–74 | Cite as

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

  • I. G. García
  • V. Mantič
  • A. Blázquez
Original Paper


A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.


Transverse cracking Coupled criterion Residual thermal stresses Finite fracture mechanics 



The authors are indebted to Professor Federico París (University of Seville) for inspiring discussions. This investigation was supported by the Spanish Ministry of Education (FPU Grant 2009/3968), the Spanish Ministry of Science and Innovation (Project MAT2009-14022), the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (Projects MAT2012-37387 and MAT2015-71036-P), the Junta de Andalucía and the European Social Fund (Project P08-TEP-4051).


  1. Bailey J, Parvizi A (1981) On fibre debonding effects and the mechanism of transverse-ply failure in cross-ply laminates of glass fibre/thermoset composites. J Mater Sci 16(3):649–659CrossRefGoogle Scholar
  2. Birman V, Byrd L (2001) Matrix cracking in transverse layers of cross-ply beams subjected to bending and its effect on vibration frequencies. Compos Part B Eng 32(1):47–55CrossRefGoogle Scholar
  3. Blázquez A, Mantič V, París F (2006) Application of BEM to generalized plane problems for anisotropic elastic materials in presence of contact. Eng Anal Bound Elem 30(6):489–502CrossRefGoogle Scholar
  4. Camanho PP, Dávila CG, Pinho ST, Iannucci L, Robinson P (2006) Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear. Compos Part A Appl Sci Manufact 37(2):165–176CrossRefGoogle Scholar
  5. Cornetti P, Pugno N, Carpinteri A, Taylor D (2006) Finite fracture mechanics: a coupled stress and energy failure criterion. Eng Fract Mech 73(14):2021–2033CrossRefGoogle Scholar
  6. Correa E, Mantič V, París F (2011) Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: a numerical and experimental analysis. Compos Sci Technol 71(5):622–629CrossRefGoogle Scholar
  7. Dvorak GJ (2013) Micromechanics of composite materials. Springer, BerlinCrossRefGoogle Scholar
  8. Dvorak GJ, Laws N (1986) Analysis of first ply failure in composite laminates. Eng Fract Mech 25(5–6):763–770CrossRefGoogle Scholar
  9. Dvorak GJ, Laws N (1987) Analysis of progressive matrix cracking in composite laminates—II. First ply failure. J Compos Mater 21(4):309–329CrossRefGoogle Scholar
  10. Fiedler B, Hojo M, Ochiai S, Schulte K, Ochi M (2001) Finite-element modeling of initial matrix failure in CFRP under static transverse tensile load. Compos Sci Technol 61(1):95–105CrossRefGoogle Scholar
  11. Fukunaga H, Chou T-W, Peters P, Schulte K (1984) Probabilistic failure strength analyses of graphite/epoxy cross-ply laminates. J Compos Mater 18(4):339–356CrossRefGoogle Scholar
  12. García IG, Carter BJ, Ingraffea AR, Mantič V (2016) A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics. Compos Part B Eng 95:475–487CrossRefGoogle Scholar
  13. García I.G, Justo J, Simon A, Mantič V (2018) Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models (in preparation) Google Scholar
  14. García IG, Mantič V, Blázquez A, París F (2014) Transverse crack onset and growth in cross-ply [0/90]s laminates under tension. Application of a coupled stress and energy criterion. Int J Solids Struct 51:3844–3856CrossRefGoogle Scholar
  15. Garrett KW, Bailey JE (1977) Multiple transverse fracture in \(90^{\circ }\) cross-ply laminates of a glass fibre-reinforced polyester. J Mater Sci 12(1):157–168CrossRefGoogle Scholar
  16. Han YM, Hahn HT (1989) Ply cracking and property degradations of symmetric balanced laminates under general in-plane loading. Compos Sci Technol 35(4):377–397CrossRefGoogle Scholar
  17. Han YM, Hahn HT, Croman RB (1988) A simplified analysis of transverse ply cracking in cross-ply laminates. Compos Sci Technol 31(3):165–177CrossRefGoogle Scholar
  18. Hashin Z (1996) Finite thermoelastic fracture criterion with application to laminate cracking analysis. J Mech Phys Solids 44(7):1129–1145CrossRefGoogle Scholar
  19. Hosoi A, Kawada H (2008) Stress analysis of laminates of carbon fiber reinforced plastics, containing transverse cracks, considering free-edge effect and residual thermal stress. Mater Sci Eng A 498(1–2):69–75CrossRefGoogle Scholar
  20. Jun T-S, Korsunsky AM (2010) Evaluation of residual stresses and strains using the eigenstrain reconstruction method. Int J Solids Struct 47(13):1678–1686CrossRefGoogle Scholar
  21. Kaddour AS, Hinton MJ (2013) Maturity of 3D failure criteria for fibre-reinforced composites: comparison between theories and experiments: part B of WWFE-II. J Compos Mater 47(6–7):925–966CrossRefGoogle Scholar
  22. Kotoul M, Ševeček O, Profant T (2009) Analysis of multiple cracks in thin coating on orthotropic substrate under mechanical and residual stresses. Eng Fracture Mech 77:229–248CrossRefGoogle Scholar
  23. Kravchenko OG, Kravchenko SG, Pipes RB (2016) Chemical and thermal shrinkage in thermosetting prepreg. Compos Part A Appl Sci Manuf 80:72–81CrossRefGoogle Scholar
  24. Lee JH, Hong CS (1993) Refined two-dimensional analysis of cross-ply laminates with transverse cracks based on the assumed crack opening deformation. Compos Sci Technol 46(2):157–166CrossRefGoogle Scholar
  25. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech Solids 21(1):61–72CrossRefGoogle Scholar
  26. Leguillon D, Martin E, Ševeček O, Bermejo R (2015) Application of the coupled stress-energy criterion to predict the fracture behaviour of layered ceramics designed with internal compressive stresses. Eur J Mech A/Solids 54:94–104CrossRefGoogle Scholar
  27. Li DS, Wisnom MR (1997) Evaluating Weibull parameters for transverse cracking in cross-ply laminates. J Compos Mater 31(9):935–951CrossRefGoogle Scholar
  28. Mantič V (2009) Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion. Int J Solids Struct 46(6):1287–1304CrossRefGoogle Scholar
  29. McCartney LN (1992) Theory of stress transfer in a 0–90–0 cross-ply laminate containing a parallel array of transverse cracks. J Mech Phys Solids 40(1):27–68CrossRefGoogle Scholar
  30. McCartney LN (2000) Model to predict effects of triaxial loading on ply cracking in general symmetric laminates. Compos Sci Technol 60(12–13):2255–2279CrossRefGoogle Scholar
  31. Nairn JA (1997) Fracture mechanics of composites with residual thermal stresses. J Appl Mech 64:804–815CrossRefGoogle Scholar
  32. Nairn JA (2000) Matrix microcracking in composites. In: Kelly A, Zweben C (eds) Comprehensive composite materials, vol 2. Pergamon, Oxford, pp 403–432CrossRefGoogle Scholar
  33. Parvizi A, Garrett K, Bailey J (1978) Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates. J Mater Sci 13(1):195–201CrossRefGoogle Scholar
  34. Takeda N, Ogihara S (1994) In situ observation and probabilistic prediction of microscopic failure processes in CFRP cross-ply laminates. Compos Sci Technol 52(2):183–195CrossRefGoogle Scholar
  35. van der Meer FP, Dávila CG (2013) Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply. Int J Solids Struct 50(20):3308–3318CrossRefGoogle Scholar
  36. Ševeček O, Bermejo R, Kotoul M (2013) Prediction of the crack bifurcation in layered ceramics with high residual stresses. Eng Fract Mech 108:120–138CrossRefGoogle Scholar
  37. Ševeček O, Kotoul M, Leguillon D, Martin E, Bermejo R (2016) Modelling of edge crack formation and propagation in ceramic laminates using the stress-energy coupled criterion. Eng Fract Mech 167:45–55CrossRefGoogle Scholar
  38. Wisnom MR (2000) Size effects in composites. In: Kelly A, Zweben C (eds) Comprehensive composite materials, vol 2. Pergamon, Oxford, pp 23–47CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Grupo de Elasticidad y Resistencia de Materiales, Escuela Técnica Superior de IngenieríaUniversidad de SevillaSevillaSpain

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