Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites

Abstract

An element-failure algorithm is proposed and incorporated into a finite element code for simulating dynamic crack propagation and impact damage in laminated composite materials. In this algorithm, when a crack is propagating within a finite element, the element is deemed to have partially failed, but not removed from the computations. Consequently, only a fraction of the stresses that were computed before the crack tip entered the element contribute to the nodal forces of the element. When the crack has propagated through the element, the element is completely failed and therefore can only resist volumetric compression. This treatment of crack propagation in isotropic solids allows fracture paths within individual elements and is able to accommodate crack growth in any arbitrary direction without the need for remeshing. However, this concept is especially powerful when extended to the modeling of damage and delamination in fibre-reinforced composite laminates. This is because the nature of damage in composite laminates is generally diffused, characterized by multiple matrix cracks, fibre pullout, fibre breakage and delaminations. It is usually not possible to define or identify crack tips in the tradition of fracture mechanics. Since parts of a damaged composite structure are often able to partially transmit load despite the presence of some damage, it is advantageous to model the damaged portions with partially failed elements. The damage may be efficiently modeled and tracked using element-failure concepts, with the application of appropriate failure criteria and damage evolution laws. The idea is to embody the effects of damage into the effective nodal forces of the finite element. In this paper, we report the novel use of element-failure concepts in the analysis of low-velocity impact damage of composite laminates. The initiation and propagation of delaminations arising from the impact are predicted and the results show qualitative agreement with experimental observation of the formation of multiple delaminations in impact-damaged specimens. While such delaminations do not permit transmission of tensile stress waves across the cracked surfaces, transmission of compressive stress waves are allowed in the simulation. It is further shown that, when elements are allowed to fail, the dynamic stress wave distributions are altered significantly. In the element-failure algorithm, the issue of interpenetration of delamination surfaces in the model does not arise. This is a significant advantage over the conventional method of explicitly modeling the delamination surfaces and crack front, where generally, much computational time must be spent in employing contact algorithms to ensure physically admissible solutions. Finally, we also demonstrate the simulation of crack propagation of pre-notched specimens of an isotropic material under initial conditions of mode II loading using the element-failure algorithm. The numerical results showed that the cracks propagated at an angle of about 70° with respect to the notches, in agreement with the experimental results of Kalthoff.