Phase-field modelling of interface failure in brittle materials

Abstract

A phase-field approach is proposed for interface failure between two possibly dissimilar materials. The discrete adhesive interface is regularised over a finite width. Due to the use of a regularised crack model for the bulk material, an interaction between the length scales of the crack and the interface can occur. An analytic one-dimensional analysis has been carried out to quantify this effect and a correction is proposed, which compensates influences due to the regularisation in the bulk material. For multi-dimensional analyses this approach cannot be used straightforwardly, as is shown, and a study has been undertaken to numerically quantify the compensation factor due to the interaction. The aim is to obtain reliable and universally applicable results for crack propagation along interfaces between dissimilar materials, such that they are independent from the regularisation width of the interface. The method has been tested and validated on three benchmark problems. The compensation is particularly relevant for phase-field analyses in heterogeneous materials, where cohesive failure in the constituent materials as well as adhesive failure at interfaces play a role.

A diffuse modeling approach for embedded interfaces in linear elasticity

“…25 In the vicinity of material interfaces, an adaptive grid refinement is realized by adding several levels of hierarchical refinement. The proposed method leads to good convergence rates, but did not prevent the stress and strain oscillations that can be an error source for example in the simulation of interface failure …”

“…The proposed method leads to good convergence rates, but did not prevent the stress and strain oscillations that can be an error source for example in the simulation of interface failure. [26] Other techniques include composite finite elements [27] and advanced numerical homogenization approaches [28][29][30][31] based on cell problems as in the FE 2 method. [32] In this contribution we present a modeling approach to embed material interfaces in nonconforming background meshes with a focus on linear elasticity.…”

Adaptive isogeometric discretizations for diffuse modeling of discontinuities

“…The influence of the interaction between i and s on the actual fracture toughness of bulk and interface is compensated following the the findings in [8]. Both, the bulk and the interface fracture toughness are taken into account by multiplying the fracture toughness G s with a scalar function α(x sd , i ), where x sd is a level set function.…”

“…To account for interface failure between two materials we combine the phase field model with a local reduction of the critical fracture energy in the area of the regularized material interface as proposed in [8]. To account for interface failure between two materials we combine the phase field model with a local reduction of the critical fracture energy in the area of the regularized material interface as proposed in [8].…”

“…The phase-field approach allows for the proper modeling of crack initiation and propagation by solving an additional scalar field problem for the evolution of the crack phase which is coupled to the mechanical boundary value problem. To account for interface failure between two materials we combine the phase field model with a local reduction of the critical fracture energy in the area of the regularized material interface as proposed in [8]. The Helmholtz free energy for a brittle, linear elastic material reads…”