On the accuracy of isotropic damage descriptions for complex load paths—Limits quantified by numerical optimization

The stress triaxiality and the Lode angle parameter are two well established stress invariants for the characterization of damage evolution. At the same time, their limitations are known in principle as they are not sufficient, but remain to be quantified for a full damage description. This work contributes precisely by quantifying these restrictions through numerical optimization in terms of load paths and characteristic damage values. This is a key requirement for an accurate distinction between damage-mitigating and damage-prone scenarios. Such isotropic damage approximations – among others – are utilized in this work for damage predictions in a continuum damage mechanics framework. For that purpose, two well-established damage models are considered and analyzed for different complex load paths. Two models are used in order to avoid model-specific restrictions. For the different load paths, different isotropic damage indicators such as the stress triaxiality and the Lode angle parameter are controlled. The analyses show that well-established concepts such as fracture surfaces depending on the triple stress triaxiality, Lode angle parameter and equivalent plastic strain have to be taken with care, if complex paths are to be investigated. These include, e.g., load paths observed during metal forming applications with varying load directions or multiple stages. • Derivation of a computational framework to quantify limits of isotropic damage descriptions based on load path optimization. • Model independent statements due to the consideration of two different damage models with an identical calibration based on case-hardened steel. • Computational optimization based identification of load paths dependencies of up to 13% in damage—despite identical final values of stress triaxiality, Lode angle parameter and equivalent plastic strain. • Computational optimization based identification of load paths dependencies of up to 10% in damage—despite identical histories and final values of stress triaxiality, Lode angle parameter and equivalent plastic strain.