A size-dependent ductile fracture model: Constitutive equations, Numerical implementation and Validation

TL;DR

This paper introduces a size-dependent ductile fracture model that incorporates void size effects into constitutive equations, validated through finite element simulations, addressing a gap in existing size-independent models for porous materials.

Contribution

A novel size-dependent homogenized model for porous ductile materials is proposed, including detailed numerical implementation and validation against finite element simulations.

Findings

Model captures size effects at micro- and nano-scale.

Validation shows good agreement with finite element simulations.

Highlights importance of void size in ductile fracture behavior.

Abstract

Size effects have been predicted at the micro- or nano-scale for porous ductile materials from Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Mechanics numerical simulations, as a consequence of Geometrically Necessary Dislocations or due to the presence of a void matrix interface. As voids size decreases, higher stresses are needed to deform the material, for a given porosity. However, the majority of the homogenized models for porous materials used in ductile fracture modeling are size-independent, even though micrometric or nanometric voids are commonly observed in structural materials. Based on yield criteria proposed in the literature for nanoporous materials, a size-dependent homogenized model for porous materials is proposed for axisymmetric loading conditions, including void growth and coalescence as well as void shape effects. Numerical implementation of the constitutive equations is detailed. The homogenized model is validated through comparisons to porous unit cells finite element simulations that consider interfacial stresses, consistently with the model used for the derivation of the yield criteria, aiming at modeling an additional hardening at the void matrix interface. Potential improvements of the model are finally discussed with respect to the theoretical derivation of refined yield criteria and evolution laws.