Damage Mechanics for Hybrid Laminates
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AbstractDamage in composite materials accumulates in a diffuse manner. Accounting for this damage in a progressive failure analysis requires an accurate measure of the degraded stiffness coefficients. This paper describes micromechanics models for predicting the effect of distributed cracks on the engineering properties (extensional and shear moduli, Poissons ratios, and thermal expansion coefficients). The configuration is shown schematically in Figure 1. The unit cell consists of three laminae: a cracked central lamina and two adjacent laminae. The adjacent laminae may or may not be damaged.The effective properties of a cracked lamina are affected by the presence of the adjacent laminae. However, in an earlier paper by the authors (Reference. 1), it was shown that the effective properties of a cracked lamina normalized by their original values were quite insensitive to the adjacent lamina orientation and even the material system of the laminae group. This is illustrated in Figure 2. The results in Reference 1 were for a single cracked lamina, the adjacent lamina had the same orientation, and all three laminae had the same undamaged unidirectional properties. Also, in calculating the effective engineering moduli, shear-extension coupling terms were ignored. The current effort builds on the results in Reference 1. This paper considers hybrid laminates, adjacent plies with different orientations, damage in single and multiple laminae, a wider range of material systems, and thermal expansion coefficients. Quantitative measures are presented for the errors introduced when shear-extension coupling terms are ignored. Reference 1 used fully three-dimensional finite element models. This paper discusses the use of much more efficient quasi-3D models.
