Loughborough University
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M-integral analysis for cracks in a viscoplastic material with extended finite element method

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journal contribution
posted on 2018-06-12, 09:56 authored by Junling Hou, Hong Zuo, Qun Li, Rong Jiang, Liguo Zhao
The M-integral can be used to quantify complex damage in materials subjected to mechanical deformation. However, the effect of viscoplasticity on the damage level associated with the M-integral has not been studied yet. In this paper, the variation of the M-integral associated with viscoplastic deformation was investigated numerically using a user-defined material subroutine. Effects of creep deformation and loading rate on the M-integral were also evaluated. In particular, the association of crack growth with the evolution of the M-integral was captured by the extended finite element method for different crack configurations. It was found that viscoplastic deformation has a great effect on the damage evolution of viscoplastic materials characterized by the M-integral. Crack growth leads to an increase of the M-integral, indicating progressive damage of the materials. Concerning the secondary cracks formed around a major crack, the results show that the M-integral is highly dependent on the numbers and locations of those secondary cracks. Shielding effect is mostly evident for microcracks with centres located just behind or vertically in line with the major crack tip. With the increasing number of microcracks, the shielding effect tends to decrease as reflected by the increasing M-integral values


This work was supported by the National Natural Science Foundation of China (Nos. 11572235, 11772245, 11472205), Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2014K10-16), and the Fundamental Research Funds for the central Universities in China.



  • Mechanical, Electrical and Manufacturing Engineering

Published in

Engineering Fracture Mechanics


HOU, J. ... et al., 2018. M-integral analysis for cracks in a viscoplastic material with extended finite element method. Engineering Fracture Mechanics, 200, pp. 294-311.




  • AM (Accepted Manuscript)

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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This paper was accepted for publication in the journal Engineering Fracture Mechanics and the definitive published version is available at https://doi.org/10.1016/j.engfracmech.2018.05.042




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