# Analysis of fracture limit curves and void coalescence in high strength interstitial free steel sheets formed under different stress conditions

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## Abstract

Void formation, which is a statistical event, depends on inhomogeneities present in the microstructure. The analysis on void nucleation, their growth and coalescence during the fracture of high strength interstitial free steel sheets of different thicknesses is presented in this article. The analysis shows that the criterion of void coalescence depends on the d-factor, which is the ratio of relative spacing of the ligaments (δd) present between the two consecutive voids to the radius of the voids. The computation of hydrostatic stress (σ_{m}), the dominant factor in depicting the evolution of void nucleation, growth and coalescence and the dimensional analysis of three different types of voids namely oblate, prolate and spherical type, have been carried out. The ratio of the length to the width (L/W) of the oblate or prolate voids at fracture is correlated with the mechanical properties, microstructure, strains at fracture, Mohr’s circle shear strains and Triaxiality factors. The Lode angle (θ) is determined and correlated with the stress triaxiality factor (T), ratio of mean stress (σ_{m}) to effective stress (σ_{e}). In addition, the Void area fraction (*V*_{a}), which is the ratio of void area to the representative area, is determined and correlated with the strain triaxiality factor (T_{o}).

## Keywords

Steel Sheet Hydrostatic Stress Minor Strain Lode Angle Triaxial Stress State## Nomenclature

- ɛ
_{1} Major strain

- ɛ
_{2} Minor strain

- ɛ
_{3} Thickness strain

- ɛ
_{e} Effective strain of macroscopic equivalent strain

- ɛ
_{m} Hydrostatic or mean strain

- γ
_{12}, γ_{23}, γ_{13} Mohr’s circle shear strains (the subscripts 1, 2 & 3 represent major, minor and thickness strains)

- δd
Ligament thickness

- d-factor/ ratio
Ratio of δd to radius of void

- θ
Lode factor or lode angle

- T
Stress triaxiality factor or ratio

- T
_{0} Stress triaxiality factor or ratio

- σ
_{e} Effective stress

- σ
_{m} Mean or hydrostatic stress

*V*_{a}Void area fraction

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