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Prediction of ductile fracture for DP590 high-strength steel with a new semi-coupled ductile fracture criterion

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Abstract

This paper is concerned with prediction of the damage evolution and fracture of DP590 by exploring a new semi-coupled ductile fracture criterion. The new semi-coupled ductile fracture criterion uses the DF2010 ductile fracture criterion as the initial damage model with modifying the original fracture strain \({\overline{\varepsilon }}_{f}^{p}\) to the initial damage strain \({\overline{\varepsilon }}_{i}^{p}\) in the model. In order to further describe the softening phenomenon after damage, this model introduces a damage variable D to measure the cumulative damage and couples the damage variable D to the plastic model to construct a damage evolution model. In order to verify the semi-coupled ductile fracture criterion, the fracture experiment of DP590 was carried out. The resistance method was used to measure the initial damage and fracture of the sample, and the DIC technique was used to measure the strain distribution on the surface of the sample. The initial damage model and damage evolution parameters were calibrated using the experiment–simulation hybrid method and the reverse analysis method, respectively. The VUMAT user subroutine of the calibrated semi-coupled model is implemented into ABAQUS and used to simulate the stretching of each sample. The results show that the semi-coupled ductile fracture criterion can accurately predict the fracture behavior of DP590 materials under different stress states and describe the damage-induced softening phenomenon during the forming process of DP590.

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Abbreviations

\({c}_{1}, {c}_{2}, {c}_{3}\) :

Material-related parameters

A, m:

Fitting coefficient of the hardening model

n:

Hardening index

K:

Hardening coefficient

\(w\) :

Weight coefficient in the linear combination hardening model.

\({q}_{1},{q}_{2}\) :

Calibration parameters of GTN model

\(v_{i}\) :

Initial damage displacement

\(\mathrm{L}\) :

Lode parameter

\(\eta\) :

Stress triaxiality.

D:

Damage variable

\({D}_{0}\) :

Internal variable (The damage process remains inactivated)

\(\dot{D}\) :

Damage evolution rate

\({G}_{f}\) :

Energy required to open a crack per unit area

\({L}_{e}\) :

Characteristic length related to the integral point

Dcr:

Critical value of damage accumulation

\({{\varvec{C}}}^{{\prime}}, {{\varvec{C}}}^{{\prime}}{\prime}\) :

Matrix of anisotropic coefficients

T :

Transformation matrix

\(\bar{\sigma }_{{eq}}\) :

Yield stress

\(\bar{\sigma }\left( {\bar{\varepsilon }} \right),\bar{\sigma }\) :

Flow stress

\({\sigma }_{0}\) :

Initial yield strength

\({\sigma }_{y0}\) :

Yield stress value at the beginning of the damage

\({\varvec{\sigma}}\) :

Cauchy stress tensor

\({\varepsilon }_{0}\) :

Pre-strain

Δε:

Equivalent plastic strain increment

\({\dot{\varepsilon }}^{p}\) :

Equivalent plastic strain rate

\({\overline{\varepsilon }}^{p}\) :

Equivalent plastic strain

\({\overline{\varepsilon }}_{i}^{p}\) :

Initial damage strain

\({\overline{\varepsilon }}_{f}^{p}\) :

Original fracture strain

\({\sigma }_{0 }, {\sigma }_{45}, {\sigma }_{90}, {r}_{0}, {r}_{45}, {r}_{90}, {\sigma }_{b}, {r}_{b}\) :

Calibration parameters of yield function

DIC:

Digital image correlation

MMC:

Modified Mohr–Coulomb damage criterion

GTN:

Gurson–Tvergaard–Needleman model

CDM:

Continuum damage mechanics

DF2012:

Lou’s fracture criterion

\({\overline{S} }^{\mathbf{^{\prime}}},\boldsymbol{ }{\overline{S} }^{\mathbf{^{\prime}}\mathbf{^{\prime}}},\boldsymbol{ }{\mathrm{L}}^{^{\prime}}, {\mathrm{L}}^{{^{\prime}}{^{\prime}}}, {\mathrm{L}}_{2}^{\mathbf{^{\prime}}\mathbf{^{\prime}}}\) :

Stress tensors

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Acknowledgements

This project was supported by the Guangdong National Natural Science Foundation [Grant No. 2021A1515010598].

Funding

This study was funded by Natural Science Foundation of Guangdong Province, 2021A1515010598, Saijun Zhang.

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive Engineering, South China University of Technology, Wushan RD, Tianhe District, Guangzhou, 510640, China

    Saijun Zhang, Weiyang Ding, Kanzhen Li & Shiguang Song

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  1. Saijun Zhang
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  2. Weiyang Ding
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Correspondence to Saijun Zhang.

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Zhang, S., Ding, W., Li, K. et al. Prediction of ductile fracture for DP590 high-strength steel with a new semi-coupled ductile fracture criterion. J Braz. Soc. Mech. Sci. Eng. 44, 17 (2022). https://doi.org/10.1007/s40430-021-03275-z

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