A theoretical model is proposed to evaluate effective stiffness in general symmetric composite laminates due to transverse cracking. In the model, the crack shape is assumed to be a function of crack density. The original contribution of this article is that crack geometries are not constrained to the forms of assumed shape functions. Instead, the natural forms of the crack shape functions are shown to have forms containing hyperbolic sine and hyperbolic cosines based on elastic analysis. Displacement fields and stress components satisfy the boundary and continuity conditions. The change in stiffness reduction is examined theoretically. Predicted results are compared with experimental data for [τm/90n]s glass/epoxy laminates and [τm/90n]s AS4/epoxy laminates.
Berthelot, J. M. (1997). Analysis of the Transverse Cracking of Cross-Ply Laminates: A Generalized Approach , Journal of Composite Materials, 31(18): 1780-1805 .
2.
Abdelrahman, W. G. and Nayfeh, A. H. (1999). Stress Transfer and Stiffness Reduction in Orthogonally Cracked Laminates , Mechanics of Materials, 31(5): 303-316 .
3.
McCartney, L. N. (1992). Theory of Stress Transfer in a 0-90-0 Cross-ply Laminates Containing a Parallel Array of Transverse Cracks , Journal of the Mechanics and Physics of Solids, 40(1): 27-68 .
4.
McCartney, L. N. (2000). Model to Predict Effects of Triaxial Loading on Ply Cracking in General Symmetric Laminates , Composite Science and Technology, 60(12-13): 2255-2279 .
5.
Pagano, N. J. and Soni, S. R. (1983). Global-local Variational Model , International Journal of Solids and Structures, 19(3): 207-228 .
6.
Whitney, J. M. (2001). Effective Thermo-elastic Constants of Angle-ply Laminates Containing 90 Degree Ply Cracks , Journal of Composite Materials, 35(15): 1373-1391 .
7.
Whitney, J. M. (2003). Effective Thermo-elastic Constants for Monoclinic Laminates Containing Transverse Ply Cracks , Journal of Reinforced Plastics & Composites, 22(3): 203-227 .
8.
Praveen, G. N. and Reddy, J. N. (1998). Transverse Matrix Cracks in Cross-ply Laminates: Stress Transfer, Stiffness Reduction and Crack Opening Profiles , Acta Mechanica, 130(3-4): 227-248 .
9.
Yuan, F. G. and Selek, M. C. (1993). Transverse Cracking and Stiffness Reduction in Composite Laminates , Journal of Reinforced Plastics & Composites, 12(9): 987-1015 .
10.
Leblond, P. , Elmahi, A. and Berthelot, J. M. (1996). 2D and 3D Numerical Models of Transverse Cracking in Cross-ply Laminates , Composite Science and Technology, 56(7): 793-796 .
11.
Noh, J. and Whitcomb, J. (2001). Effect of Various Parameters on the Effective Properties of a Cracked Ply , Journal of Composite Materials, 35(8): 689-712 .
12.
Hashin, Z. (1985). Analysis of Cracked Laminates: A Variational Approach , Mechanics of Materials, 4(2): 121-136 .
13.
Hashin, Z. (1987). Analysis of Orthogonally Cracked Laminates under Tension , Journal of Applied Mechanics, 54(4): 872-879 .
14.
Varna, J. and Berglund, L. (1991). Multiple Transverse Cracking and Stiffness Reduction in Cross Ply Laminates , Journal of Composites Technology and Research, 13(2): 99-106 .
15.
Nairn, J. A. (1989). The Strain Energy Release Rate of Composite Microcracking: A Variational Approach , Journal of Composite Materials, 23(11): 1106-1129 .
16.
Nairn, J. A. and Hu, S. (1992). The Initiation and Growth of Delaminations Induced by Matrix Microcracks in Laminated Composites , International Journal of Fracture, 57(1): 1-24 .
17.
Nairn, J. A. (1995). Some New Variational Mechanics Results on Composite Micro-cracking , In: Proceedings of ICCM-10, I: 423-430 .
18.
Anderssen, R. , Gradin, P. A. and Gustafson, C. G. (1998). Prediction of the Stiffness Degradation in Cross-ply Laminates due to Transverse Matrix-cracking: An Energy Method Approach , Advanced Composite Materials, 7(4): 325-346 .
19.
Tong, J. , Guild, F. J. , Ogin, S. L. and Smith, P. A. (1997). On Matrix Crack Growth in Quasi-isotropic Laminates—II. Finite Element Analysis , Composites Science and Technology, 57(11): 1537-1545 .
20.
Zhang, J. , Fan, J. and Soutis, C. (1992). Analysis of Multiple Matrix Cracking in [τm/90n]s Composite Laminates Part 1: In-plane Stiffness Properties , Composites, 23(5): 291-298 .
21.
Zhang, J. , Fan, J. and Soutis, C. (1992). Analysis of Multiple Matrix Cracking in [τm/90n]s Composite Laminates Part 2: Development of Transverse Ply Cracks , Composites, 23(5): 299-304 .
22.
Kashtalyan, M. and Soutis, C. (2000). Modelling Stiffness Degradation due to Matrix Cracking in Angle-ply Composite Laminates , Plastics Rubber and Composites, 29(9): 482-488 .
23.
Joffe, R. and Varna, J. (1999). Analytical Modeling of Stiffness Reduction in Symmetric and Balanced Laminates due to Cracks in 90 Layers , Composite Science and Technology, 59(11): 1641-1652 .
24.
Joffe, R. , Krasnikovs, A. and Varna, J. (2001). COD-based Simulation of Transverse Cracking and Stiffness Reduction in [S/90n]s Laminates , Composite Science and Technology, 61(5): 637-656 .
25.
Groves, S. E. , Harris, C. E. , Highsmith, A. L. , Allen, D. H. and Norvell, R. G. (1987). An Experimental and Analytical Treatment of Matrix Cracking in Cross-ply Laminates , Experimental Mechanics, 27(1): 73-79 .
