Effective Crack Resistance of a Simplified Ductile Heterogeneous Material With Circular Inclusions

ABSTRACT This contribution investigates the effective crack resistance obtained from a numerical crack‐growth experiment for a simplified two‐dimensional ductile heterogeneous material. The resolved microstructure contains circular inclusions. Their stiffness and fracture resistance are varied independently together with the ligament width between neighboring inclusions. Crack evolution is simulated with a phase field model for ductile fracture based on von Mises plasticity. The maximum boundary J‐integral during enforced macroscopic crack advance is used as the operational measure of effective crack resistance. The results show that inclusion fracture resistance and stiffness are strongly coupled. Weak, compliant inclusions yield the lowest effective crack resistance, whereas stiff, tough inclusions yield the highest values in the investigated parameter range. Increasing inclusion stiffness generally raises the resistance for weak and tough inclusions, while the ligament‐width dependence is most pronounced for weak inclusions. These findings demonstrate that the effective response is governed by the combined inclusion properties and their spacing rather than by the local fracture resistance alone.