Effect of the shape of the softening damage law on the predicted tensile fracturing and energy dissipation in textile composites

The fracturing behavior of fiber-reinforced composites is often modeled using continuum damage mechanics-based approaches which commonly assume a linear softening damage law, i.e. a linearly decreasing stress with increasing strain. The objective of this paper is to assess the suitability of this assumption for composites and to systematically 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 the strength size effect and progressive accumulation of damage in a structure and comparing with experimental measurements. Damage models with a wide range of shapes of softening laws are considered. These include linear, bilinear, trilinear, exponential, power law and sigmoidal. The effect of introducing a sudden drop in the damage law is also evaluated. All modeling is conducted via the crack band model (CBM), to ensure the mesh objectivity of results. It is found that despite using the right strength and fracture energy as input at the material point level, not all softening law shapes can accurately predict the strength size effect and post-peak softening. Especially the sudden drop feature leads to severe underprediction of strength. Bilinear softening shows the best combination of simplicity and accuracy, especially if formulated via the R-curve approach. Further insights are obtained by assessing the predicted fracture process zone size and fracture energy via the size effect method. Finally structure level predictions are made by considering plug initiated axial crushing of a cylindrical crushcan. The close ties between the shape of the material softening law and predicted process zone, and structural fracturing are revealed, and shown to be an important consideration in formulating damage models.