Modelling the nucleation and propagation of cracks at twin boundaries

Fracture arising from cracks nucleating and propagating along twin boundaries is commonly observed in metals that exhibit twinning as a plastic deformation mechanism. This phenomenon affects the failure of macroscopic mechanical components, but it is not fully understood. We present simulations in which a continuum model for discrete twins and a cohesive zone model are coupled to aid the understanding of fracture at twin boundaries. The interaction between different twin systems is modelled using a local term that depends on the continuum twin variables. Simulations reveal that the resolved shear stress necessary for an incident twin to propagate through a barrier twin can be up to eight times the resolved shear stress for twin nucleation. Interface elements are used at the interfaces between all bulk elements to simulate arbitrary intragranular cracks. An algorithm to detect twin interfaces is developed and their strength has been calibrated to give good agreement with the experimentally observed fracture path. The elasto-plastic deformation induced by discrete twins is modelled using the crystal plasticity finite element method and the stress induced by twin tips is captured. The tensile stress caused by the tip of an incident twin on a barrier twin is sufficient to nucleate a crack. A typical staircase fracture path, with cracks propagating along the twin interfaces, is reproduced only if the strength of the twin interfaces is decreased to about one-third of the strength of the bulk material. This model can be used to help understand fracture caused by the activation of multiple twin systems in different materials.

CO2 fracturing using the phase field approach for the brittle fracture

<p>To simulate CO<sub>2</sub> fracturing under an isothermal condition, we propose a phase field model. We take advantage of the ability of the phase field approach to predict fracture initiation and branching, as well as to avoid tracking the fracture path. We model the CO<sub>2</sub> as a compressible fluid by modifying Darcy's law. In particular, we assume that the permeability is correlated to the value of the phase field by the exponential function. The dependence of the CO<sub>2</sub> density as a function of the pressure is captured by the Span-Wagner state equation. The computed pressure breakdown values show good agreement with analytical solutions and experimental results.</p>

Numerical Simulation of Fracture Behavior of Brittle Solids under I/III Loading

This study used numerical analysis to carry out a large number of numerical model calculations based on a new semicircular bend (SCB) model. Instead of existing numerical computation methods (J-integral), the M-integral method was used to calculate the mixed mode fracture parameters (KI, KII, and KIII), investigate the influence of the geometry and material parameters on the fracture behavior under mixed mode I/III loading, and predict the fracture path. The results revealed that the limitations in the scope of the mixity parameter Me in the previous studies can be overcome to a certain extent. The range of Me was established under different Poisson ratios and can be used as a reference for actual material testing. The simulation path is in good agreement with the experimentally obtained fracture path, and the proposed method can be used to simulate the fracture path under mixed mode I/III loading.