GTN Damage Model Considering Anisotropy and Shear Behavior and Application in Forming Limit Prediction

doi:10.3901/JME.2025.06.141

Abstract

Abstract: The traditional forming limit theory model is not applicable to aluminum alloy sheets with low elongation. In order to accurately predict the forming limit of aluminum alloy sheets, a modified GTN model is established based on the Gurson-Tvergaard-Needlemen (GTN) microscopic damage model, taking into account the effects of sheet anisotropy and pore shear mechanism on damage evolution. A method for predicting the forming limit curve of aluminum alloy sheets from the perspective of microscopic damage is proposed. Taking 6061-T6 aluminum alloy sheet as the research object, the damage parameters of the GTN model are determined using a finite element reverse calibration method combining central composite design, response surface model, and multi-objective genetic algorithm. And write a VUMAT user-defined material subroutine to modify the GTN model, use finite element analysis software ABAQUS to numerically simulate NAKAZIMA punch bulging experiments, and obtain the aluminum alloy forming limit curve. The results indicate that the modified GTN model considering anisotropy and shear behavior has better accuracy and applicability for predicting the forming limit of aluminum alloys, and improves the problem of inaccurate prediction of the original GTN model at the inflection point of the forming limit curve.

Key words: GTN damage model, anisotropy, aluminum alloy, forming limit curve, response surface method

CLC Number:

TG146

CHEN Xin, GONG Yingying, YANG Lifei. GTN Damage Model Considering Anisotropy and Shear Behavior and Application in Forming Limit Prediction[J]. Journal of Mechanical Engineering, 2025, 61(6): 141-150.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.2025.06.141

http://www.cjmenet.com.cn/EN/Y2025/V61/I6/141

References

[1] 韩非，连昌伟，胡卫龙. 材料特性数据对成形仿真精度的影响(下)——实验方法的完善[J]. 塑性工程学报，2020，27(12)：9-17. HAN Fei，LIAN Changwei，HU Weilong. The influence of material property data on the precision of forming simulation (Ⅱ) - Improvement of experimental methods [J]. Journal of Plastic Engineering，2020，27(12)：9-17.
[2] SWIFT H. Plastic instability under plane stress[J]. Journal of the Mechanics and Physics of Solids，1952，1(1)：1-18.
[3] HILL R. On discontinuous plastic states with special reference to localized necking in thin sheets[J]. Journal of the Mechanics and Physics of Solids，1952，1(1)：19-30.
[4] MARCINIAK Z，KUCYNSKI K. Limit strains in the processes of stretch forming sheet metal[J]. International Journal of Mechanical Sciences，1967，9(9)：609-620.
[5] 张学广，刘纯国，郑愿，等. 基于延性损伤和剪切损伤的铝合金成形极限预测[J]. 吉林大学学报(工学版)，2016，46(5)：1558-1566. ZHANG Xueguang，LIU Chunguo，ZHENG Yuan，et al. Prediction of forming limit of aluminum alloys based on ductile and shear damage[J]. Journal of Jilin University (Engineering Edition)，2016，46(5)：1558-1566.
[6] 贾哲，穆磊，臧勇. 金属塑性成形中的韧性断裂微观机理及预测模型的研究进展[J]. 工程科学学报，2018，40(12)：1454-1467. JIA Zhe，MU Lei，ZANG Yong. Research progress on the micro mechanism and prediction model of ductile fracture in metal plastic forming[J]. Journal of Engineering Science，2018，40(12)：1454-1467.
[7] 荣海，盈亮，胡平，等. 基于连续介质损伤力学的7075铝合金高温成形极限理论预测与数值仿真[J]. 机械工程学报，2020，56(24)：51-60. RONG Hai，YING Liang，HU Ping，et al. Theoretical prediction and numerical simulation of 7075 aluminum alloy forming limit at high temperature based on continuum damage mechanics[J]. Journal of Mechanical Engineering，2020，56(24)：51-60.
[8] 徐戊矫，谢丹，李芳，等. 基于细观损伤力学的铅套成形破裂预测[J]. 中国有色金属学报，2020，30(8)：1866-1875. XU Wujiao，XIE Dan，LI Fang，et al. Prediction of lead sleeve forming fracture based on microscopic damage mechanics[J]. Chinese Journal of Nonferrous Metals，2020，30(8)：1866-1875.
[9] 顾彬，何霁，李淑慧，等. 金属板料各向异性断裂模型及断裂实验研究进展[J]. 塑性工程学报，2019，26(1)：1-14. GU Bin，HE Ji，LI Shuhui，et al. Research progress on anisotropic fracture models and fracture experiments of metal sheets[J]. Journal of Plastic Engineering，2019，26(1)：1-14.
[10] 刘文权，盈亮，王丹彤，等. 热冲压成形过程细观损伤演化机理研究[J]. 机械工程学报，2016，52(14)：31-39. LIU Wenquan，YING Liang，WANG Dantong，et al. Study on the evolution mechanism of micro damage during hot stamping process[J]. Journal of Mechanical Engineering，2016，52(14)：31-39.
[11] YING Liang，LIU Wenquan，WANG Dantong，et al. Parameter calibration of GTN damage model and formability analysis of 22MnB5 in hot forming process[J]. Journal of Materials Engineering and Performance，2017，26(11)：5155-5165.
[12] LIANG Ying，GAO Tianhai，RONG Hai，et al. On the thermal forming limit diagram (TFLD) with GTN mesoscopic damage model for AA7075 aluminum alloy：Numerical and experimental investigation[J]. Journal of Alloys and Compounds，2019，802：675-693.
[13] CUI Xiaolei，ZHANG Wenhua，ZHANG Zhichao，et al. Prediction of forming limit of dual-phase 500 steel sheets using the GTN ductile damage model in an innovative hydraulic bulging test[J]. JOM，2018，70(8)：1542-1547.
[14] YILDIZ R，YILMAZ S. Influence of heat treatments on the formability of the 6061 Al alloy sheets：Experiments and GTN damage model[J]. The International Journal of Advanced Manufacturing Technology，2021，113(7-8)：2277-2299.
[15] BARNWAL V，TEWARI A，NARASIMHAN K，et al. Effect of plastic anisotropy on forming behavior of AA-6061 aluminum alloy sheet[J]. The Journal of Strain Analysis for Engineering Design，2016，51(7)：507-517.
[16] 陈志英，董湘怀. 各向异性GTN损伤模型及其在板料成形中的应用[J]. 上海交通大学学报，2008(9)：1414-1419. CHEN Zhiying，DONG Xianghuai. Anisotropic GTN damage model and its application in sheet metal forming [J]. Journal of Shanghai Jiao Tong University，2008(9)：1414-1419.
[17] KAMI A，DARIANI B，VANINI A，et al. Numerical determination of the forming limit curves of anisotropic sheet metals using GTN damage model[J]. Journal of Materials Processing Technology，2015，216：472-483.
[18] GURSON A. Continuum theory of ductile rupture by void nucleation and growth：Part I-Yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology，1977，99(1)：2-15.
[19] TVERGAARD V，NEEDLEMAN A. Analysis of the cup-cone fracture in a round test bar[J]. Acta Metallurgica，1984，32(1)：157-169.
[20] TVERGAARD V. On localization in ductile materials containing spherical voids[J]. International Journal of Fracture，1982，18：237-252.
[21] NEEDLEMAN A，TVERGAARD V. An analysis of ductile rupture in notched bars[J]. Journal of the Mechanics and Physics of Solids，1984，32(6)：461-490.
[22] NAHSHON K，HUTCHISON J．Modification of the Gurson model for shear failure[J]．European Journal of Mechanics，2008，27(1)：1-17．
[23] 江帅，胡玉梅，肖晋，等. 6016铝合金冲压损伤演化和韧性断裂的细观力学表征[J]. 塑性工程学报，2019，26(5)：133-140. JIANG Shuai，HU Yumei，XIAO Jin，et al. Meso- mechanical characterization of damage evolution and ductile fracture of 6016 aluminum alloy during stamping[J]. Journal of Plastic Engineering，2019，26(5)：133-140.
[24] HILL R. Theory of the yielding and plastic flow of anisotropic metals[J]．Proceedings of the Royal Society A，1948，193(1033)：281-297．
[25] 马向东，官英平. 基于GTN细观损伤模型的激光拼焊板成形极限预测[J]. 中国机械工程，2015，26(22)：3057-3063. MA Xiangdong，GUAN Yingping. Prediction of the forming limit of laser welded blanks based on GTN microscopic damage model[J]. China Mechanical Engineering，2015，26(22)：3057-3063.