How to compute plastic zones of heterogeneous materials: A simple approach using classical continuum and fracture mechanics

This is a short technical paper on how to use classical continuum and fracture mechanics to calculate the plastic zones caused by cracks on heterogeneous or composite materials. As an example, a sample consisting of an α-phase and β-phase is used. A crack is introduced to the sample, and stress is then applied. The plastic zone in front of the crack resulting from the applied stress is then calculated using commercial software. The concept uses two-level modeling: a global model using homogenized stiffness from a unit cell of heterogeneous material and a local model for the α-phase and β-phase. While this paper is written for general purposes, a concrete example using ferrite and martensite is also presented along with the experimental data. General agreement between the model and the experiment is observed. This method eliminates the need for a cumbersome analytical approach.