Effect of the shape of the softening damage law on the predicted fracturing behavior of composites

The fracturing behavior of fiber-reinforced composites is often modeled using continuum damage mechanics-based approaches which commonly assume linear softening, i.e. a linearly decreasing stress with increasing damage. The objective of this paper is to analyze the effect of the assumed shape of the softening damage law at material point, on the predicted fracturing behavior of the structure. The material considered is an epoxy/carbon-fiber twill woven composite. Numerical evaluations are conducted by predicting important phenomena associated with fracturing viz. the strength size effect and progressive accumulation of damage in a structure. Damage models with a wide range of shapes of softening laws are implemented as user-defined subroutines (VUMAT) in the commercial finite element analysis software ABAQUS. These shapes include linear, bilinear, trilinear, exponential, power law and sigmoidal. All the modeling is conducted via the crack band model (CBM), to ensure the mesh objectivity of results. It is found that despite the same strength and fracture energy used as input at the material point level, the structure level predictions can differ considerably. It is found that not all softening law shapes accurately capture the strength size effect and the post-peak softening behavior. The bilinear softening law shows the best combination of simplicity and accuracy, especially if formulated via the R-curve approach. Even for the bilinear shape, the precise position of the “knee point” is shown to be important. It is thus demonstrated that in addition to material strength and fracture energy, it is important to correctly formulate the shape of the softening law for accurate predictions of structural failure.