Fracture of viscoplastic materials is a complex process due to its time-dependent and plastic responses. Numerical simulation for fracture plays a significant role in crack prediction and failure analysis. In recent years, the phase field model is becoming a competitive approach to predict crack growth and has been extended to inelastic materials such as elasto-plastic, viscoelastic and viscoplastic materials, etc. However, the contribution of inelastic energy to crack growth is seldom studied. For this reason, we implement the phase field model coupled with a viscoplastic constitutive in finite element framework, in which the elastic energy and inelastic energy are used as crack driving energy. The implicit algorithm for a viscoplastic constitutive is presented, this procedure is suitable for other viscoplastic constitutive relations. The strain rate effect, creep effect, stress relaxation effect and cyclic loading responses are tested using a single element model with different inelastic energy contributions; A titanium alloy plate specimen and a stainless-steel plate specimen under tension are studied compared with the experimental observations in existing literature. The results show that the above typical damage phenomenon and fracture process can be well reproduced; The inelastic energy significantly affects the force-displacement responses but has slight effect on the crack paths.

High-strength low-alloy steels (HSLAs) are widely used in the structural body components of many domestic motor vehicles owing to their better mechanical properties and greater resistance. The real production process of HSLA steelmaking can be regarded as a model that builds on the relationship between process parameters and product quality attributes. A surrogate modeling method is used, and the resulting production process model can be applied to predict the optimal manufacturing process parameters. We used different methods in this paper to build such a surrogate model, including linear regression, random forests, support vector regression, multilayer perception, and a simplified VGG model. We then applied three bio-inspired search algorithms, namely particle swarm optimization, the artificial bee colony algorithm, and the firefly algorithm, to search for the optimal controllable manufacturing process parameters. Through experiments on 9,000 test samples used for building the surrogate model, and 299 test samples for making the optimal process parameter selection, we found that the combination of a simplified VGG model and the firefly algorithm was the most successful at reaching a success rate of 100%—in other words, when the product quality attributes of all test samples satisfy the mechanical requirements of the end products.