skip to main content


Title: Influence of Grain Size Distribution on Ductile Intergranular Crack Growth Resistance
Abstract The influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full-field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain slice with planar grains subjected to mode I small-scale yielding conditions. The finite element formulation accounts for finite deformations, and the constitutive relation models the loss of stress carrying capacity due to progressive void nucleation, growth, and coalescence. The discrete unit events are characterized by a set of finite element calculations for crack growth at a single-grain boundary junction. A directed graph of the connectivity of grain boundary junctions and the distances between them is used to create a directed graph in J-resistance space. For a specified grain boundary distribution, this enables crack growth resistance curves to be calculated for all possible crack paths. Crack growth resistance curves are calculated based on various path choice criteria and compared with the results of full-field finite element calculations of the initial boundary value problem. The effect of unimodal and bimodal grain size distributions on intergranular crack growth is considered. It is found that a significant increase in crack growth resistance is obtained if the difference in grain sizes in the bimodal grain size distribution is sufficiently large.  more » « less
Award ID(s):
1663130
NSF-PAR ID:
10151046
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of Applied Mechanics
Volume:
87
Issue:
3
ISSN:
0021-8936
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Fatigue short‐cracks in Mg alloys display complex growth behavior due to high plastic anisotropy and crack path dependence on local microstructural features. In this study, the three‐dimensional crystallography of short‐crack paths in Mg alloy WE43 was characterized by mapping near‐field high‐energy X‐ray diffraction microscopy (HEDM) reconstructed grain maps to high‐resolution X‐ray CT reconstructions of the fracture surfaces in the crack initiation and short‐crack growth regions of six ultrasonic fatigue specimens. Crack–grain–boundary intersections were analyzed at 81 locations across the six crack paths. The basal intragranular, non‐basal intragranular, or intergranular character of short‐crack growth following each boundary intersection was correlated to crystallographic and geometric parameters of the trailing and leading grains, three‐dimensional grain boundary plane, and advancing crack front. The results indicate that crack paths are dependent on the combined crystallographic and geometric character of the local microstructure, and crack path prediction can be improved by use of dimensionality reduction on subsets of high‐linear‐correlation microstructural parameters.

     
    more » « less
  2. Summary

    The discrete crack mechanics (DCM) method is a dislocation‐based crack modeling technique where cracks are constructed using Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite‐medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi‐static growth problems. Convergence and accuracy of the DCM method are verified with two‐ and three‐dimensional problems with well‐known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated.

     
    more » « less
  3. We demonstrate the possibility of spatially controlling the degree of grain boundary serration in functionally graded stainless steels, by alloying powder mixtures on-the-fly during directed energy deposition additive manufacturing. Grain boundary serration is an attractive feature in polycrystalline microstructures, as it confers superior resistance to crack propagation and hot corrosion. Quantitative measurements at the microstructure scale coupled with thermodynamic calculations allow us to propose a mechanism to explain the origin of grain boundary serration. The formation of transient δ ferrite during solidification and its subsequent dissolution during cooling, governed by the Cr/Ni ratio, leads to the formation of remnant ferrite particles that hinder the growth of austenite grains in the solid state via a Smith-Zener pinning phenomenon. This finding opens new perspectives for grain boundary engineering, in-situ during additive manufacturing. 
    more » « less
  4. The inclusion-based boundary element method (iBEM) is developed to calculate the elastic fields of a bi-layered composite with inhomogeneities in one layer. The bi-material Green’s function has been applied to obtain the elastic field caused by the domain integral of the source fields on inclusions and the boundary integral of the applied loads on the surface. Using Eshelby’s equivalent inclusion method (EIM), the material mismatch between the particle and matrix phases is simulated with a continuously distributed source field, namely eigenstrain, on inhomogeneities so that the iBEM can calculate the local field. The stress singularity along the interface leads to the delamination of the bimaterials under a certain load. The crack’s energy release rate (  J) is obtained through the J-integral, which predicts the stability of the delamination. When the stiffness of one layer increases, the J-integral increases with a higher gradient, leading to lower stability. Particularly, the effect of the boundary and inhomogeneity on the J-integral is illustrated by changing the crack length and inhomogeneity configuration, which shows the crack is stable at the beginning stage and becomes unstable when the crack tip approaches the boundary; a stiffer inhomogeneity in the neighborhood of a crack tip decreases J and improves the fracture resistance. For the stable cracking phase, the J-integral increases with the volume fraction of inhomogeneity are evaluated. The model is applied to a dual-glass solar module with air bubbles in the encapsulant layer. The stress distribution is evaluated with the iBEM, and the J-integral is evaluated to predict the delamination process with the energy release rate, which shows that the bubbles significantly increase the J-integral. The effect of the bubble size, location, and number on the J-integral is also investigated. The present method provides a powerful tool for the design and analysis of layered materials and structures.

     
    more » « less
  5. Abstract

    Microstructurally small fatigue‐crack growth in polycrystalline materials is highly three‐dimensional due to sensitivity to local microstructural features (e.g., grains). One requirement for modeling microstructurally sensitive crack propagation is establishing the criteria that govern crack evolution, including crack deflection. Here, a high‐fidelity finite‐element modeling framework is used to assess the performance and validity of various crack‐growth criteria, including slip‐based metrics (e.g., fatigue‐indicator parameters), as potential criteria for predicting three‐dimensional crack paths in polycrystalline materials. The modeling framework represents cracks as geometrically explicit discontinuities and involves voxel‐based remeshing, mesh‐gradation control, and a crystal‐plasticity constitutive model. The predictions are compared to experimental measurements of WE43 magnesium samples subject to fatigue loading, for which three‐dimensional grain structures and fatigue‐crack surfaces were measured post‐mortem using near‐field high‐energy x‐ray diffraction microscopy and x‐ray computed tomography. Findings from this work are expected to improve the predictive capabilities of simulations involving microstructurally small fatigue‐crack growth in polycrystalline materials.

     
    more » « less