Phase field methods allow for convenient and efficient moving interface simulations. In this paper phase field approaches of different order are presented, and applied to simulate damage in solids of temperature dependent and non‐linear elastic materials. The numerical framework provides a NURBS based finite element method which minimizes the numerical and computational effort without impairing the smoothness required by the problem. In order to demonstrate the possibilities of such general phase field approaches a series of different models from material science and fracture mechanics is investigated. Specifically, a priori unknown crack propagation in different fracture modes is studied, simulations of thermomigration in a technical alloy and of void growth are presented and an inverse analysis of a dynamic fracture experiment is performed. The examples show the versatility of the presented low‐order and high‐order phase field approaches. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

In a phase-field approach to fracture crack propagation is modeled by means of an additional continuous field. In this paper, two problems of linear elastic fracture mechanics are studied experimentally and numerically in order to evaluate the practicability of the phase-field approach and to validate the measured parameters. At first, a three-point bending experiment of silicon dies is simulated assuming static plate bending. Then, wave propagation and spallation in a Hopkinson bar test are analyzed in a dynamic regime. The simulations show that phase-field fracture reproduces the experimental results with high accuracy. The results are comparable to other fracture simulations, e.g., the cohesive element technique. In total, the phase-field approach to fracture is capable of tracking crack evolution in a very convenient and quantitatively correct way.

Metastable austenitic stainless steels can undergo a deformation-induced phase transformation from austenite (fcc) into e-martensite (hcp) and the harder a 0 -martensite (bcc). This class of materials is widely used in sheet metal forming processes because of a beneficial combination of strength, ductility, and corrosion resistance. In such manufacturing processes phase transformation can be exploited in order to optimize the monotonic and cyclic strength of the components locally. In this paper it is shown that the amount of transformation can be controlled by a variation of process parameters such as deformation rate, temperature, and amount of deformation. An increase in initial temperature and strain rate reduces the rate of martensite formation. The effect of martensite volume fraction on the fatigue behavior is systematically investigated and the damage mechanisms in the VHCF regime are analyzed. For a very high number of cycles (beyond 10 7 ) a high martensite volume fraction (of more than 50%) leads to internal crack initiation from oxidic inclusions. Form and dimension of the inclusion are found to determine the number of cycles up to failure. An optimum volume fraction of the martensite phase is proposed for both the HCF as well as for the VHCF regime.