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A semi-analytical method to evaluate the J-R curve for the surface-cracked round bar under three-point bending
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  • Guangwei He,
  • Lixun CAI,
  • Chen Bao,
  • Xudong Qian
Guangwei He
Southwest Jiaotong University School of Mechanics and Engineering

Corresponding Author:[email protected]

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Lixun CAI
Southwest Jiaotong University School of Mechanics and Engineering
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Chen Bao
Southwest Jiaotong University School of Mechanics and Engineering
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Xudong Qian
National University of Singapore Department of Civil and Environmental Engineering
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Abstract

The current paper presents a semi-analytical method for obtaining J-R curves of round bars with elliptical cracks. This method derives the semi-analytical expressions between load and displacement, J-integral and displacement for surface-cracked round bars, based on the energy density equivalence principle, taking into account the effect of material and crack size. The validity of semi-analytical expressions examined by three-dimensional finite element analysis shows that load~displacement curves and J-integral~load curves predicted by the expressions match well with the simulation results. Through fracture toughness testing conducted on the carbon steel 45, the load~displacement data are used to calculate the average J-R curves for the surface-cracked round bar by the semi-analytical expressions. With the distributions of J-integral along the crack front obtained from three-dimensional finite element analyses, this study also determines the J-R curves at different crack-front points.