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Failure criterion taking into account porosity and microstructural anisotropy

L. M. Nogueira 1 , 2 , ∗ , L. Borges 1 , D. A. Castello 1

1 Department of Mechanical Engineering (PEM/COPPE), Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-972, Brazil 2 Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ), Nova Iguaçu 26041-271, Brazil

∗ livia.nogueira@cefet-rj.br

Keywords: failure criterion, microstructure, anisotropy

The present work considers a fabric and density-based criterion for predicting the safe limits for porous and anisotropic materials under a general stress state. There are several classic and well established criteria given in the literature for homogeneous and isotropic materials [1,2]. However, when the material is porous (heterogeneous) and mechanical properties are orientation-dependent (anisotropic), the failure mechanism establishment and the influence of these parameters in pre dicting failure are still challenging [3]. Natural materials like wood, rock, and biological tissues like bones, as well as synthetic fiber-reinforced composites, exhibit these microstructure features at a significant level. The failure criterion presented in this work is based on morphological mea surements and characterization. The volume fraction is considered the primary parameter and microstructure orientation is addressed by the fabric tensor approach. Fabric tensors are under stood as symmetric second-rank tensors that characterize a material’s structural sensitivity. The concept lies in modeling the material microstructure through tensors of higher rank which char acterize both anisotropy and orientation [5]. Among the available methods, the Mean Intercept Length (MIL) boundary-based approach is considered to estimate the fabric tensors. This method proposes to construct the fabric tensor for biphasic materials from planar image sections obtained in micro-CT scans. The approach is based on defining the mean distance between a change from one phase to the other along a specific orientation. In partially oriented microstructures, Under wood (1973) [6] and Whitehouse (1975) [7] observed that when MIL data was disposed on a polar plot and fitted in an ellipse, the corresponding ellipse parameters could be correlated to the material orientation. As imaging techniques become increasingly powerful, this work expects to contribute as a tool to provide more accurate yield criteria by including the effects of porosity and microstructural anisotropy. [2] Hill, R. (1998). The mathematical theory of plasticity (Vol. 11). Oxford university press. [3] Keralavarma, S. M., & Chockalingam, S. (2016). A criterion for void coalescence in anisotropic ductile materials. International Journal of Plasticity, 82, 159-176. [4] Oda, M. (1982). Fabric tensor for discontinuous geological materials. Soils and foundations, 22(4), 96-108. [5] Whitehouse, W. J. (1974). The quantitative morphology of anisotropic trabecular bone. Jour nal of microscopy, 101(2), 153-168. References [1] Chakrabarty, J. (2012). Theory of plasticity. Elsevier.

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