Effect of thermomechanical loading on fracture properties of brittle materials: A fully-coupled transient thermoelastic analysis using a lattice approach

The influence of simultaneous thermomechanical loadings on the fracture behavior of linear thermoelastic brittle materials with a propagating crack and transient temperature diffusion is investigated. A planar two-way coupled thermoelastic lattice with a brittle erosion algorithm, implemented in MATLAB, is used in the context of LEFM to study two well-known classic fracture problems in Mode I, i.e., center and double-edge crack configurations, under thermal, mechanical, and thermomechanical loadings for a brittle crystalline Silicon, as an example material. The approach can also be applied to other brittle materials like brick or concrete. Validated by the well-developed analytical solutions for these configurations under separate thermal and mechanical loads, the numerical lattice analyzes the crack tip's energy release rates and stress intensity factors based on the change of the global stiffness matrix of mesh before and after crack growth with no need for strain/stress calculations. Under the thermomechanical loading scenario, the response of the configurations in terms of the load-displacement and fracture toughness-crack length curves are then analyzed with respect to different loading rates and temperature gradients at crack surface and ambient environment. Having more pronounced effects on the toughness curves than the loading rate does, higher temperature difference results in lower values for the toughness curves. These curves also exhibit a rising jump for very short crack lengths and then approach to constant uniform values as a typical behavior for brittle materials. Considering the average trend of the toughness curves, it is observed that the thermomechanical fracture growth is highly unstable for very short cracks and it approaches a more stable condition as the crack length grows. Having a simple constitutive formulation and failure criterion, the proposed lattice approach is a convenient tool to obtain fracture properties of brittle materials under thermomechanical loading.