Analysis of cracks in nonlinear fiber composite materials
The effect of effective material nonlinear properties of fiber composites on crack behavior is studied. Three-dimensional nonlinear constitutive equations are established, based on both complementary energy density and deformation plasticity approaches. A system of highly nonlinear, coupled governing partial differential equations are derived for a generalized plane deformation problem of the composites. Orders of stress singularity near cracks in both 0$\sp\circ$- and 90$\sp\circ$-fiber composites are obtained. A dimensional analysis based on conservation integrals in nonlinear mechanics is used first to achieve this goal. Also, the stress singularities and asymptotic stress fields of the fiber composites are obtained by directly solving the governing partial differential equations. Detailed solutions for complete stress fields and associated near-field stress amplitudes in the cracked nonlinear fiber composites under pure single loading modes and mixed-mode loading are determined by employing an advanced finite-element method with surrounding nonlinear elements and crack-tip singular element formulations. The results reveal that in a 0$\sp\circ$-fiber composite, stresses in the transversely isotropic plane have a classical r$\sp{-{1\over 2}}$ singularity as in the linear case; however, the stresses in the orthogonal planes possess an r$\sp{-{1\over 4}}$ singularity. The mode-I and II deformations and stresses in the 0$\sp\circ$-fiber composite are uncoupled from those under a mode-III loading. In a 90$\sp\circ$ nonlinear fiber composite, all the stresses have an unusual r$\sp{-{1\over 4}}$ singularity and the three modes are strongly coupled. The stress field near the crack tip in the nonlinear 90$\sp\circ$-fiber composite is significantly different from that of a linear case.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign