13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- An Advanced Damage Percolation Model of Ductile Fracture Cliff Butcher1,*, Zengtao Chen2, Michael Worswick1 1 Department of Mechanical and Mechatronics Engineering, University of Waterloo, Canada 2 Department of Mechanical Engineering, University of New Brunswick, Canada * Corresponding author: cbutcher@uwaterloo.ca Abstract A multi-scale damage percolation model has been developed to predict fracture in advanced materials with heterogeneous particle distributions. The percolation model was implemented into a commercial finite-element code using so-called “percolation elements” to capture the complex stress- and strain-gradients that develop within the microstructure during deformation. In this approach, fracture is predicted as a direct consequence of the stress state, material properties and local conditions within the microstructure. Void nucleation, growth and coalescence models are applied for ellipsoidal voids subjected to general loading conditions. A novel void nucleation rule is employed for particle cracking based upon the particle morphology and stress state. A particle field generator has been implemented into the percolation software to generate representative particle fields based upon the field statistics obtained using x-ray micro-tomography. The percolation model was validated numerically and experimentally for an automotive-grade aluminum alloy in a notched tensile test used for material characterization. Keywords: Void, Particle, Nucleation, Coalescence, Multi-scale 1. Introduction The traditional approach to modeling ductile fracture involves homogenizing the microstructure of a material into a simple, equivalent geometry from which the relevant constitutive laws can be derived [1]. While attractive from a modeling perspective, critical details of the microstructure are lost in this homogenization process such as the particle size, shape, orientation, distribution and degree of clustering. Since void initiation and evolution is a highly localized phenomenon originating within heterogeneous particle clusters, these models fail to reliably predict fracture without requiring many calibration parameters. These limitations can be overcome using a damage percolation model that relies upon measured particle distributions obtained using digital imaging or x-ray micro-tomography. Micromechanical models can then be applied to each void and particle within the material to forge a direct link between local changes in the microstructure and the overall material behaviour. An advanced damage percolation model has been developed by Butcher [2] that was directly integrated into a commercial finite-element code as illustrated in Figure 1. The performance of this percolation model is evaluated by applying it to a notched tensile test specimen of AA5182 sheet. The predicted fracture strains, porosity and nucleation trends are compared and validated with the experiment data and the porosity data available in the literature. 1.1 Basics of the percolation model The basics of the damage percolation model were established by Worswick et al. [3-4] and Chen [5] where particle fields are obtained via digital imaging techniques or micro-tomography. The particle field is then tessellated to extract the size, shape, location, and nearest neighbours of each particle and void within the field. This information is then used to re-create the particle field so that micromechanical models can be applied to each particle and void and thus predict fracture within heterogeneous particle distributions. The particles, voids and cracks are all assumed to be ellipsoidal where cracks are first formed by the coalescence of voids. The cracks are formed via a bounding box method and are subject to the same evolution laws as the voids. In the coupled
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