J. Mater. Sci. Technol. ›› 2023, Vol. 133: 209-229.DOI: 10.1016/j.jmst.2022.05.040
• Research article • Previous Articles Next Articles
Kai Dua,b, Shaohui Huangb, Yong Houc, Haibo Wangd, Yinxiao Wanga,*(), Wentao Zhenga,*(
), Xiaoguang Yuana,*(
)
Received:
2022-02-01
Revised:
2022-04-19
Accepted:
2022-05-13
Published:
2022-06-21
Online:
2022-06-21
Contact:
Yinxiao Wang,Wentao Zheng,Xiaoguang Yuan
About author:
yuanxg@sut.edu.cn (X. Yuan).Kai Du, Shaohui Huang, Yong Hou, Haibo Wang, Yinxiao Wang, Wentao Zheng, Xiaoguang Yuan. Characterization of the asymmetric evolving yield and flow of 6016-T4 aluminum alloy and DP490 steel[J]. J. Mater. Sci. Technol., 2023, 133: 209-229.
Fig. 2. Schematic diagram of the corresponding locations of the yield stresses measured by the uniaxial tensile and compressive tests, simple shear tests, and biaxial tensile tests using cruciform specimens on the (a) NP-PWC and (b) DP-PWC.
Sheet | Deformation | aσ (MPa) | bσ (MPa) | cσ (MPa) | dσ | eσ |
---|---|---|---|---|---|---|
6016-T4 | σC0 | 294.83 | 0.00 | 165.42 | 11.0610 | 0.9684 |
σC45 | 333.29 | 0.11 | 192.29 | 9.5422 | 0.9862 | |
σC90 | 307.84 | 0.11 | 187.62 | 8.9018 | 0.9401 | |
σS0 | 177.49 | 0.00 | 96.84 | 6.2698 | 0.8880 | |
σS45 | 180.88 | 0.00 | 111.30 | 3.9371 | 0.7572 | |
σS90 | 173.59 | 0.00 | 87.52 | 7.8244 | 0.9846 | |
DP490 | σC0 | 849.09 | 94.89 | 484.24 | 3.2403 | 0.6026 |
σC45 | 879.60 | 103.62 | 489.92 | 3.5757 | 0.6710 | |
σC90 | 846.91 | 29.22 | 449.79 | 4.1095 | 0.6647 | |
σS0 | 512.00 | 7.04 | 302.61 | 1.9535 | 0.5513 | |
σS45 | 476.33 | 4.54 | 276.08 | 2.4179 | 0.5381 | |
σS90 | 498.69 | 6.91 | 301.66 | 2.0769 | 0.5237 |
Table 1. Stress-related fitting parameters calculated for 6016-T4 aluminum alloy and DP490 steel under uniaxial compressive and pure shear stress states.
Sheet | Deformation | aσ (MPa) | bσ (MPa) | cσ (MPa) | dσ | eσ |
---|---|---|---|---|---|---|
6016-T4 | σC0 | 294.83 | 0.00 | 165.42 | 11.0610 | 0.9684 |
σC45 | 333.29 | 0.11 | 192.29 | 9.5422 | 0.9862 | |
σC90 | 307.84 | 0.11 | 187.62 | 8.9018 | 0.9401 | |
σS0 | 177.49 | 0.00 | 96.84 | 6.2698 | 0.8880 | |
σS45 | 180.88 | 0.00 | 111.30 | 3.9371 | 0.7572 | |
σS90 | 173.59 | 0.00 | 87.52 | 7.8244 | 0.9846 | |
DP490 | σC0 | 849.09 | 94.89 | 484.24 | 3.2403 | 0.6026 |
σC45 | 879.60 | 103.62 | 489.92 | 3.5757 | 0.6710 | |
σC90 | 846.91 | 29.22 | 449.79 | 4.1095 | 0.6647 | |
σS0 | 512.00 | 7.04 | 302.61 | 1.9535 | 0.5513 | |
σS45 | 476.33 | 4.54 | 276.08 | 2.4179 | 0.5381 | |
σS90 | 498.69 | 6.91 | 301.66 | 2.0769 | 0.5237 |
Sheet | Deformation | ar | br | cr | dr |
---|---|---|---|---|---|
6016-T4 | rC0 | 0.7483 | 0.5398 | 2.5568 | 0.3609 |
rC45 | 0.3783 | 0.2421 | 65.7815 | 1.2317 | |
rC90 | 0.8988 | 0.7482 | 0.5677 | 0.1852 | |
DP490 | rC0 | 0.7549 | 0.0000 | 0.0000 | 0.0000 |
rC45 | 0.6403 | 0.0000 | 0.0000 | 0.0000 | |
rC90 | 0.7724 | 0.0000 | 0.0000 | 0.0000 |
Table 2. r-value-related fitting parameters calculated for 6016-T4 aluminum alloy and DP490 steel under uniaxial compressive stress states.
Sheet | Deformation | ar | br | cr | dr |
---|---|---|---|---|---|
6016-T4 | rC0 | 0.7483 | 0.5398 | 2.5568 | 0.3609 |
rC45 | 0.3783 | 0.2421 | 65.7815 | 1.2317 | |
rC90 | 0.8988 | 0.7482 | 0.5677 | 0.1852 | |
DP490 | rC0 | 0.7549 | 0.0000 | 0.0000 | 0.0000 |
rC45 | 0.6403 | 0.0000 | 0.0000 | 0.0000 | |
rC90 | 0.7724 | 0.0000 | 0.0000 | 0.0000 |
Flow rule | Yield criterion | Mechanical properties |
---|---|---|
AFR | CPB06ex2 | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{C} 0}, \sigma_{\mathrm{C} 45}, \sigma_{\mathrm{C} 90}, \sigma_{\mathrm{b}}, \sigma_{\mathrm{Cb}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 90}, r_{\mathrm{C} 0}, r_{\mathrm{C} 45}, r_{\mathrm{C} 90}, r_{\mathrm{b}} \end{array}$ |
LHY2013 | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{C} 0}, \sigma_{\mathrm{C} 90}, \sigma_{\mathrm{b}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 90}, r_{\mathrm{b}} \end{array}$ | |
Hu et al. 2017 | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{C} 0}, \sigma_{\mathrm{C} 45}, \sigma_{\mathrm{C} 90}, \sigma_{\mathrm{b}}, \sigma_{\mathrm{Cb}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 90}, r_{\mathrm{C} 0}, r_{\mathrm{C} 45}, r_{\mathrm{C} 90}, r_{\mathrm{b}} \end{array}$ | |
non-AFR | PSY2019 YSF | |
S-Y2009 PPF | ||
Hou et al. 2020 YSF | \sigma_{\mathrm{T0}},\sigma_{\mathrm{T45}},\sigma_{\mathrm{T90}},\sigma_{\mathrm{C0}},\sigma_{\mathrm{C45}},\sigma_{\mathrm{C90}},\\ \sigma_{\mathrm{PS}}^0,\sigma_{\mathrm{PS}}^{45},\sigma_{\mathrm{PS}}^{90},\sigma_{\mathrm{b}} \end{array}$ | |
Hou et al. 2020 PPF | ||
Analytical Yoon2014 (2021) YSF | ||
Analytical Poly4 (2021) PPF | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 60}^{*}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{b}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 60}^{*}, r_{\mathrm{T} 90}, r_{\mathrm{C} 0}, r_{\mathrm{C} 45}, r_{\mathrm{C} 90} \end{array}$ |
Table 3. Experimental data required to calibrate the material parameters of several asymmetric yield criteria under the AFR and non-AFR.
Flow rule | Yield criterion | Mechanical properties |
---|---|---|
AFR | CPB06ex2 | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{C} 0}, \sigma_{\mathrm{C} 45}, \sigma_{\mathrm{C} 90}, \sigma_{\mathrm{b}}, \sigma_{\mathrm{Cb}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 90}, r_{\mathrm{C} 0}, r_{\mathrm{C} 45}, r_{\mathrm{C} 90}, r_{\mathrm{b}} \end{array}$ |
LHY2013 | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{C} 0}, \sigma_{\mathrm{C} 90}, \sigma_{\mathrm{b}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 90}, r_{\mathrm{b}} \end{array}$ | |
Hu et al. 2017 | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{C} 0}, \sigma_{\mathrm{C} 45}, \sigma_{\mathrm{C} 90}, \sigma_{\mathrm{b}}, \sigma_{\mathrm{Cb}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 90}, r_{\mathrm{C} 0}, r_{\mathrm{C} 45}, r_{\mathrm{C} 90}, r_{\mathrm{b}} \end{array}$ | |
non-AFR | PSY2019 YSF | |
S-Y2009 PPF | ||
Hou et al. 2020 YSF | \sigma_{\mathrm{T0}},\sigma_{\mathrm{T45}},\sigma_{\mathrm{T90}},\sigma_{\mathrm{C0}},\sigma_{\mathrm{C45}},\sigma_{\mathrm{C90}},\\ \sigma_{\mathrm{PS}}^0,\sigma_{\mathrm{PS}}^{45},\sigma_{\mathrm{PS}}^{90},\sigma_{\mathrm{b}} \end{array}$ | |
Hou et al. 2020 PPF | ||
Analytical Yoon2014 (2021) YSF | ||
Analytical Poly4 (2021) PPF | \sigma_{\mathrm{T} 0}, \sigma_{\mathrm{T} 45}, \sigma_{\mathrm{T} 60}^{*}, \sigma_{\mathrm{T} 90}, \sigma_{\mathrm{b}} \\ r_{\mathrm{T} 0}, r_{\mathrm{T} 45}, r_{\mathrm{T} 60}^{*}, r_{\mathrm{T} 90}, r_{\mathrm{C} 0}, r_{\mathrm{C} 45}, r_{\mathrm{C} 90} \end{array}$ |
Yield criterion / Materlas | Material parameters |
---|---|
CPB06ex2 | {c}k,C_{11},C_{22},C_{33},C_{12},C_{13},C_{23},C_{66}, \\ k',C_{11}',C_{22}^{\prime},C_{33}^{\prime},C_{12}^{\prime},C_{13}^{\prime},C_{23}^{\prime},C_{66}^{\prime},a \end{array}$ |
6016-T4 | −0.0171, 0.1340, 0.8036, −0.3907, −0.9573, 1.0373, −0.3895, −1.2703, −0.0547, 0.1340, 0.9352, 0.3857, 0.1928, −1.3004, −0.1270, 1.2534, 12.0 |
DP490 | −0.6520, 0.3912, 0.4692, −0.8347, −0.5324, −0.3872, 0.0562, −0.9880, −0.0335, 0.3912, −0.1007, 0.5818, −0.7976, 0.7167, 0.9466, 0.9882, 5.0 |
LHY2013 | |
6016-T4 | 0.9291, 1.1122, 1.1661, 1.1082, 1.0254, 0.9716, 0.9381, 1.2166, −0.0192, −0.0018, 8.0 |
DP490 | 0.9545, 0.9705, 0.9060, 0.9618, 1.0041, 0.9352, 0.9928, 1.0516, 0.0037, 0.0195, 6.0 |
Hu et al. 2017 | c_{12}^{(1)}, c_{13}^{(1)}, c_{23}^{(1)}, c_{66}^{(1)}, a^{(1)}, b^{(1)}, c^{(1)}, \mu_{x}^{(1)} \\ c_{12}^{(2)}, c_{13}^{(2)}, c_{23}^{(2)}, c_{66}^{(2)}, a^{(2)}, b^{(2)}, c^{(2)}, \mu_{y}^{(2)} \end{array}$ |
6016-T4 | −0.7679, 0.6471, −0.0327, 1.1998, −0.1857, −0.2162, 0.6744, −0.0293, −0.7679, 1.3781, 1.2934, −0.2621, 0.0563, 0.2882, −0.6745, 0.0339 |
DP490 | −0.8021, 1.2029, 1.1482, 0.8658, 0.0721, 0.1251, −0.6656, 0.0093, −0.8021, 0.2941, 0.6901, 0.8367, −0.1283, −0.1113, 0.6617, 0.0074 |
Hou et al. 2020 YSF | |
6016-T4 | 0.0002, −0.0061, 0.2584, 0.9996, 1.5107, 1.0940, 3.1876, 1.0000, 2.7 |
DP490 | 0.0110, 0.0553, 0.0416, 0.9781, 0.8503, 1.0307, 3.0535, 1.1811, 2.7 |
Analytical Yoon2014 | |
6016-T4 | −0.0119, −0.0169, −27.0097, 1.1476, 1.0670, 1.0468, 0.0081 |
DP490 | −0.0033, 0.0195, 19.2182, 0.9540, 0.9678, 0.9944, 0.0059 |
S-Y2009 PPF | |
6016-T4 | 1.1212, 0.4523, 0.9837 |
DP490 | 0.8489, 0.4077, 1.4882 |
Hou et al. 2020 PPF | |
6016-T4 | −0.0591, −0.0350, −0.1814, 1.0000, 0.5829, 1.0985, 1.0889, 0.4766, 8.0 |
DP490 | −0.0335, 0.0256, 0.1486, 0.6560, 0.5623, 0.9760, 0.9334, 0.4846, 6.0 |
Analytical Poly4 (2021) PPF | |
6016-T4 | 1.2883, −2.0406, 3.0085, −1.9474, 1.4629, 11.0501, −0.8903, 11.6643, 10.0631, −0.0654, −0.0304, 0.0, −0.1881 |
DP490 | 1.1395, −1.9112, 2.4773, −1.6035, 0.8741, 5.4162, −4.4415, 4.2426, 6.6253, −0.0332, 0.0255, 0.0, 0.1387 |
Table 4. Material parameters of several asymmetric AFR and non-AFR models for 6016-T4 aluminum alloy and DP490 steel with EPS at 0.056 and 0.030, respectively.
Yield criterion / Materlas | Material parameters |
---|---|
CPB06ex2 | {c}k,C_{11},C_{22},C_{33},C_{12},C_{13},C_{23},C_{66}, \\ k',C_{11}',C_{22}^{\prime},C_{33}^{\prime},C_{12}^{\prime},C_{13}^{\prime},C_{23}^{\prime},C_{66}^{\prime},a \end{array}$ |
6016-T4 | −0.0171, 0.1340, 0.8036, −0.3907, −0.9573, 1.0373, −0.3895, −1.2703, −0.0547, 0.1340, 0.9352, 0.3857, 0.1928, −1.3004, −0.1270, 1.2534, 12.0 |
DP490 | −0.6520, 0.3912, 0.4692, −0.8347, −0.5324, −0.3872, 0.0562, −0.9880, −0.0335, 0.3912, −0.1007, 0.5818, −0.7976, 0.7167, 0.9466, 0.9882, 5.0 |
LHY2013 | |
6016-T4 | 0.9291, 1.1122, 1.1661, 1.1082, 1.0254, 0.9716, 0.9381, 1.2166, −0.0192, −0.0018, 8.0 |
DP490 | 0.9545, 0.9705, 0.9060, 0.9618, 1.0041, 0.9352, 0.9928, 1.0516, 0.0037, 0.0195, 6.0 |
Hu et al. 2017 | c_{12}^{(1)}, c_{13}^{(1)}, c_{23}^{(1)}, c_{66}^{(1)}, a^{(1)}, b^{(1)}, c^{(1)}, \mu_{x}^{(1)} \\ c_{12}^{(2)}, c_{13}^{(2)}, c_{23}^{(2)}, c_{66}^{(2)}, a^{(2)}, b^{(2)}, c^{(2)}, \mu_{y}^{(2)} \end{array}$ |
6016-T4 | −0.7679, 0.6471, −0.0327, 1.1998, −0.1857, −0.2162, 0.6744, −0.0293, −0.7679, 1.3781, 1.2934, −0.2621, 0.0563, 0.2882, −0.6745, 0.0339 |
DP490 | −0.8021, 1.2029, 1.1482, 0.8658, 0.0721, 0.1251, −0.6656, 0.0093, −0.8021, 0.2941, 0.6901, 0.8367, −0.1283, −0.1113, 0.6617, 0.0074 |
Hou et al. 2020 YSF | |
6016-T4 | 0.0002, −0.0061, 0.2584, 0.9996, 1.5107, 1.0940, 3.1876, 1.0000, 2.7 |
DP490 | 0.0110, 0.0553, 0.0416, 0.9781, 0.8503, 1.0307, 3.0535, 1.1811, 2.7 |
Analytical Yoon2014 | |
6016-T4 | −0.0119, −0.0169, −27.0097, 1.1476, 1.0670, 1.0468, 0.0081 |
DP490 | −0.0033, 0.0195, 19.2182, 0.9540, 0.9678, 0.9944, 0.0059 |
S-Y2009 PPF | |
6016-T4 | 1.1212, 0.4523, 0.9837 |
DP490 | 0.8489, 0.4077, 1.4882 |
Hou et al. 2020 PPF | |
6016-T4 | −0.0591, −0.0350, −0.1814, 1.0000, 0.5829, 1.0985, 1.0889, 0.4766, 8.0 |
DP490 | −0.0335, 0.0256, 0.1486, 0.6560, 0.5623, 0.9760, 0.9334, 0.4846, 6.0 |
Analytical Poly4 (2021) PPF | |
6016-T4 | 1.2883, −2.0406, 3.0085, −1.9474, 1.4629, 11.0501, −0.8903, 11.6643, 10.0631, −0.0654, −0.0304, 0.0, −0.1881 |
DP490 | 1.1395, −1.9112, 2.4773, −1.6035, 0.8741, 5.4162, −4.4415, 4.2426, 6.6253, −0.0332, 0.0255, 0.0, 0.1387 |
Fig. 6. Comparison of the NP-PWCs calculated by several AFR and non-AFR models for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental NP-PWCs.
Fig. 7. Comparison of the DP-PWCs calculated by several AFR and non-AFR models for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental DP-PWCs.
Fig. 8. Prediction errors of the NP-PWCs ($\Delta_{\mathrm{PWC}}^{\mathrm{NP}}$), DP-PWCs ($\Delta_{\mathrm{PWC}}^{\mathrm{DP}}$), and overall plastic work contours ($\Delta_{\mathrm{PWC}}^{\mathrm{ALL}}$) for (a) 6016-T4 aluminum alloy and (b) DP490 steel calculated by several AFR and non-AFR models.
Fig. 9. Comparison of the σTα calculated by several AFR and non-AFR models for (a) 6016-T4 aluminum alloy and (b) DP490 steel with the experimental results.
Fig. 10. Comparison of the σCα calculated by several AFR and non-AFR models for (a) 6016-T4 aluminum alloy and (b) DP490 steel with the experimental results.
Yield criterion | ΔU | |
---|---|---|
6016-T4 | DP490 | |
Empty Cell | 0.0760 | 0.0068 |
LHY2013 | 0.0057 | 0.0038 |
Hu et al. 2017 | 0.0154 | 0.0031 |
PSY2019 | 0.0045 | 0.0036 |
Hou et al. 2020 | 0.0054 | 0.0033 |
Analytical Yoon2014 (2021) | 0.0070 | 0.0057 |
Table 5. Prediction errors ΔU of the σTα for 6016-T4 aluminum alloy and DP490 steel calculated by several AFR and non-AFR models.
Yield criterion | ΔU | |
---|---|---|
6016-T4 | DP490 | |
Empty Cell | 0.0760 | 0.0068 |
LHY2013 | 0.0057 | 0.0038 |
Hu et al. 2017 | 0.0154 | 0.0031 |
PSY2019 | 0.0045 | 0.0036 |
Hou et al. 2020 | 0.0054 | 0.0033 |
Analytical Yoon2014 (2021) | 0.0070 | 0.0057 |
Fig. 11. Comparison of the NP-DPSRs calculated by several AFR and non-AFR models for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental results.
Fig. 12. Comparison of the DP-DPSRs calculated by several AFR and non-AFR models for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental results.
Fig. 13. Prediction errors in the NP-DPSRs ($\Delta_{\mathrm{DPSR}}^{\mathrm{NP}}$), DP-DPSRs ($\Delta_{\mathrm{DPSR}}^{\mathrm{DP}}$), and overall DPSRs ($\Delta_{\mathrm{DPSR}}^{\mathrm{ALL}}$) for (a) 6016-T4 aluminum alloy and (b) DP490 steel calculated by several AFR and non-AFR models.
Fig. 14. Comparison of the rTα-values calculated by several AFR and non-AFR models for (a) 6016-T4 aluminum alloy and (b) DP490 steel with the experimental data.
Fig. 15. Comparison of the rCα-values calculated by several AFR and non-AFR models for (a) 6016-T4 aluminum alloy and (b) DP490 steel with the experimental data.
Yield criterion | Δr | |
---|---|---|
6016-T4 | DP490 | |
Empty Cell CPB06ex2 | 0.2171 | 0.0449 |
LHY2013 | 0.0741 | 0.0347 |
Hu et al. 2017 | 0.1425 | 0.0681 |
S-Y2009 | 0.0541 | 0.0341 |
Hou et al. 2020 | 0.0473 | 0.0276 |
Analytical Poly4 (2021) | 0.0501 | 0.0305 |
Table 6. Prediction errors Δr of the rTα-values for 6016-T4 aluminum alloy and DP490 steel calculated by several AFR and non-AFR models.
Yield criterion | Δr | |
---|---|---|
6016-T4 | DP490 | |
Empty Cell CPB06ex2 | 0.2171 | 0.0449 |
LHY2013 | 0.0741 | 0.0347 |
Hu et al. 2017 | 0.1425 | 0.0681 |
S-Y2009 | 0.0541 | 0.0341 |
Hou et al. 2020 | 0.0473 | 0.0276 |
Analytical Poly4 (2021) | 0.0501 | 0.0305 |
Fig. 16. Comparison of the NP-PWCs and DP-PWCs calculated by the PSY2019 YSF with the IH and AH models for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental results.
Fig. 17. Comparison of the σTα and σCα calculated by the PSY2019 YSF with the IH and AH models for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental data.
Fig. 18. Plastic potential surfaces calculated by Hou et al. 2020 PPF with constant and variable parameters for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel.
Fig. 19. Comparison of the rα-values calculated by the Hou et al. 2020 PPF with constant and variable parameters for (a, b) 6016-T4 aluminum alloy and (c, d) DP490 steel with the experimental data.
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