Intergranular fracture prediction and microstructure design

Abstract

A model based on discrete unit events coupled with a graph search algorithm is developed to predict intergranular fracture. The model is based on two hypotheses: (i) the key unit event associated with intergranular crack propagation is the interaction of a grain boundary crack with a grain boundary segment located at an angle with the initial crack plane; and (ii) for a given crack path, the overall crack growth resistance can be calculated using the crack growth resistance of a collection of unit events. Next, using a directed graph containing the connectivity of grain boundary junctions and the distances between them, and crack deflection versus crack growth resistance data, a directed graph in the J-resistance space is created. This graph contains information on the crack growth resistance for all possible crack paths in a given grain microstructure. Various crack growth resistance curves are then calculated including those corresponding to: (i) a local resistance minimum; (ii) a global minimum; and (iii) for verification, a path specified by microstructure-based finite element calculations. The results show that the proposed method based on discrete unit events and graph search can predict the crack path and the crack growth resistance for cracks that propagate from one grain boundary junction to another. The proposed computationally inexpensive model can be used to design material mi

Influence of Grain Size Distribution on Ductile Intergranular Crack Growth Resistance

“…The material model and the numerical implementation are the same as in [2,4]. Here, for completeness, we briefly describe the formulation.…”

“…Here, for completeness, we briefly describe the formulation. Further details and more complete references are given in [2,4].…”

“…Several physical processes can be viewed as a problem of path selection, for example, flow of a river stream [1] or crack growth in a complex heterogeneous material microstructure [2][3][4]. Although the problems of path selection for flow of a river stream and of crack growth in a heterogeneous material involve very different length-scales, their solutions share common features.…”

“…Although the problems of path selection for flow of a river stream and of crack growth in a heterogeneous material involve very different length-scales, their solutions share common features. For example, path selection criteria based on fracture mechanics can be used to predict growth of streams in a diffusion field [1], while a directed graph constructed using microstructure specific discrete unit events can be used to predict crack growth in heterogeneous materials [4]. Intuitively, one expects that the path of a physical process involving path selection can be controlled by engineering the discrete unit events.…”

“…Ductile intergranular crack growth is analyzed using both microstructure-based finite element crack growth calculations based on a constitutive framework for a progressively cavitating ductile solid with an isotropic and isotropically hardening matrix material as in [2], and a simple model based on discrete unit events and graph search developed in [4]. In [4], the key unit event associated with intergranular crack propagation was found to be the interaction of a grain boundary crack with a grain boundary segment located at an angle with the initial crack plane. Finite element calculations are also carried out for various orientations of a single grain boundary segment with the initial crack plane to characterize the unit events.…”