Fracture instability of reinforced panel with cracks emanating from hole

Initiation of failure by yielding and/or fracture depends on the magnitude of the distortion and dilatation of material elements. According to the strain energy density theory (SED), failure is assumed to initiate at the site of the local maximum of maxima [(dW/dV)^max_max]_L by yielding and the maximum of minima [(dW/dV)^max_min]_L by fracture. The fracture is assumed to start from point L where [(dW/dV)^max_min]_L appears and tends toward G where the global maximum of dW/dV minima appears, denoted by [(dW/dV)^max_min]_G. The distance l between L and G along the anticipated crack trajectory is an indication of failure instability of the system by fracture. If l is sufficiently large and [(dW/dV)^max_min]_L exceeds the threshold, fracture initiation could lead to global failure. The local and global failure instability of a composite structural component is studied by application of the strain energy density theory. The depicted configuration is that of a panel with a circular hole reinforced by two side strips made of different material. The case of two symmetric cracks emanating from the hole and normal to the applied uniaxial tensile stress is also analyzed. Results are displayed graphically to illustrate the geometry and dissimilar material properties influence the fracture instability behavior of the two examples.     

A multiresolution continuum simulation of the ductile fracture process

With the advancement in computational science that is stepping into the Exascale era and experimental techniques that enable rapid reconstruction of the 3D microstructure, quantitative microstructure simulations at an unprecedented fidelity level are giving rise to new possibilities for linking microstructure to property. This paper presents recent advances in 3D computational modeling of ductile fracture in high toughness steels. Ductile fracture involves several concurrent and mutually interactive mechanisms at multiple length scales of microstructure. With serial sectioning tomographic techniques, a digital dataset of microstructure features associated with the fracture process has been experimentally reconstructed. In this study, primary particles are accurately and explicitly modeled while the secondary particles are modeled by a two scale multiresolution continuum model. The present numerical simulation captures detailed characteristics of the fracture process, such as zigzag crack morphology, critical void growth ratios, local stress triaxiality variation, and intervoid ligament structure. For the first time, fracture toughness is linked to multiscale microstructures in a realistic large 3D model.     

Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

This paper presents a modified regularized formulation of the Ambrosio-Tortorelli type to introduce the crack non-interpenetration condition in the variational approach to fracture mechanics proposed by Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (8), 1319-1342]. We focus on the linear elastic case where the contact condition appears as a local unilateral constraint on the displacement jump at the crack surfaces. The regularized model is obtained by splitting the strain energy in a spherical and a deviatoric parts and accounting for the sign of the local volume change. The numerical implementation is based on a standard finite element discretization and on the adaptation of an alternate minimization algorithm used in previous works. The new regularization avoids crack interpenetration and predicts asymmetric results in traction and in compression. Even though we do not exhibit any gamma-convergence proof toward the desired limit behavior, we illustrate through several numerical case studies the pertinence of the new model in comparison to other approaches.