دانلود رایگان مقاله یک ارزیابی از فرمول بندی زمینه فازی برای رشد شکاف

Abstract

The phase field description for crack growth and fracture is an attractive alternative to numerical methods based on discrete representations of cracks, since the phase field methodology avoids the numerically challenging monitoring of the discontinuities introduced by the crack. In particular, for the simulation of complex crack growth topologies and application to coupled systems, e.g. with thermal or electrical fields, the phase field method has shown promise. However, an accurate prediction of the crack growth initiation is mandatory for a reliable simulation of crack trajectories both in terms of load history and the path followed through the material. In this work, we therefore investigate predictions of crack growth derived from the phase field method and compare them with established relations from fracture mechanics. To implement the phase field method for crack growth, a parallelized finite element method computer code using adaptive mesh refinement is developed and implemented. Results from it are presented. For these results, pre-existing cracks are introduced into the finite element model in two ways, including their representation as discrete discontinuities and as heterogeneities in the phase field order parameter.

6. Conclusion

In this work, a study on the accuracy of predictions from a fracture phase field formulation on crack growth initiation is undertaken and compared with relations from fracture mechanics. We investigate the influence of the numerical length scale parameter l, determining the width of smoothing of the represented crack, and two methods of introducing an initial crack. Two setups are examined, a pure bending specimen and a single edge notch specimen.Due to requirement of a fine mesh for small values of l, the model is implemented in a parallelized finite element computer code supporting both mesh and time adaption. We find that results of the phase field simulations are in very good agreement if l is small and the initial crack is induced as a heterogeneity in the phase field through an initially non-zero history field (phase field induced initial crack). Predictions become less satisfying for large values of l. In situations, where the initial crack is prescribed through free surfaces of the mesh (mesh induced initial crack), predictions from the phase field simulations deviate significantly from analytic relations found in the literature. This is neither a consequence of an overly coarse mesh, nor of the staggered implementation scheme, and can also not be resolved using a smaller value of l.