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Experimental and Numerical Study on Ductile Fracture Prediction of Aluminum Alloy 6016-T6 Sheets Using a Phenomenological Model

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Abstract

A phenomenological ductile fracture model is proposed by a careful consideration of void nucleation, growth and coalescence during plastic deformation. Within the model framework, void nucleation is controlled by an equivalent plastic strain function. Void growth takes place through two ways, namely void dilation and void elongation, which are characterized by the normalized hydrostatic stress and normalized maximum shear stress, respectively. Void coalescence is characterized by the maximum shear stress. Aluminum alloy (AA) 6016-T6 sheets are selected to conduct ductile fracture (DF) experiments on specimens with different geometries, which can cover a wide range of stress states from simple shear to balanced biaxial tension. Subsequently, the new DF model is calibrated by using a robust hybrid numerical-experimental approach with a three-dimensional (3D) fracture surface constructed for AA 6016-T6. Ductile fracture data of other two aluminum alloys (AA 2024-T351 and AA 5083-O) are also used to evaluate DF model performance by establishing their 3D fracture surfaces. Finally, a cup drawing test is conducted and simulated as a case study showing how an applicable way of using the new model. Furthermore, the predictive accuracy of the proposed DF model for fracture initiation is compared with other three uncoupled models (modified Mohr–Coulomb criterion (MMC), Lou-Yoon-Huh model and Mu-Zang model) by ABAQUS/Explicit with a user subroutine (VUMAT), which shows a good performance of the proposed DF model.

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Acknowledgments

The authors are grateful for the financial support from the National Natural Science Foundation of China (Nos. 51805024, 51805023), and Scientific and Technological Innovation Foundation of Foshan, University of Science and Technology Beijing (USTB), China (Nos. BK20BE007, BK21BE015).

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Authors and Affiliations

  1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Zhe Jia, Ben Guan, Ling-Yun Qian & Yong Zang

  2. Beijing Key Laboratory of Lightweight Metal Forming, Beijing, 100083, China

    Zhe Jia, Ben Guan, Ling-Yun Qian & Yong Zang

  3. Shunde Graduate School, University of Science and Technology Beijing, Guangdong, 583000, China

    Zhe Jia, Ben Guan, Ling-Yun Qian & Yong Zang

  4. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM, 88003, USA

    Lei Mu

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Appendix

Appendix

Modified Mohr–Coulomb (MMC) mode could be expressed as follows (Ref 20):

$$\overline{\varepsilon }_{f - MMC} = \left\{ {\frac{A}{{C_{7} }}\left[ {C_{8} + \left( {2 + \sqrt 3 } \right)\left( {1 - C_{8} } \right)\left( {\sqrt {L^{2} + 3} - \sqrt 3 } \right)} \right]\left[ {\sqrt {\frac{{1 + C_{6}^{2} }}{{L^{2} + 3}}} + C_{6} \left( {\eta - \frac{L}{{3\sqrt {L^{2} + 3} }}} \right)} \right]} \right\}^{{ - \frac{1}{n}}}$$
(18)

where A, n and C6~C8 are the material constants.

Lou-Yoon-Huh model could be expressed as follows under proportional loading (49):

$$\overline{\varepsilon }_{f - Lou} = C_{11} \left( {\frac{{\sqrt {L^{2} + 3} }}{2}} \right)^{{C_{9} }} \left[ {\frac{{3\left( {1 + C_{12} } \right)\sqrt {L^{2} + 3} }}{{3\left( {\eta + C_{12} } \right)\sqrt {L^{2} + 3} - L + 3}}} \right]^{{C_{10} }}$$
(19)

where C9~C12 are the material constants.

Mu-Zang model could be expressed as follows under proportional loading (Ref 24):

$$\overline{\varepsilon }_{f - Mu} = C_{15} \left\langle {\frac{{3\sqrt {L^{2} + 3} }}{{C_{13} \left( {3\eta \sqrt {L^{2} + 3} - L} \right) + 3}}} \right\rangle^{{C_{14} }}$$
(20)

where C13~C15 are the material constants.

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Jia, Z., Mu, L., Guan, B. et al. Experimental and Numerical Study on Ductile Fracture Prediction of Aluminum Alloy 6016-T6 Sheets Using a Phenomenological Model. J. of Materi Eng and Perform 31, 867–881 (2022). https://doi.org/10.1007/s11665-021-06248-4

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