工程科学学报，第40卷，第4期：485-491,2018年4月 Chinese Journal of Engineering,Vol.40,No.4:485-491,April 2018 DOI:10.13374/j.issn2095-9389.2018.04.012:http://journals.ustb.edu.cn 基于M-K理论的6016铝合金成形极限曲线预测 杨晓明，王宝雨，校文超，马卫平，康艺 北京科技大学机械工程学院，北京100083 ☒通信作者，E-mail:bywang@ustb.cdu.cn 摘要近年来，为实现汽车车身轻量化，大量的铝合金材料被用于汽车车身制造，由于6016铝合金具有良好的烘烤性能，被 大量使用.但是传统的冷成形技术并不能成形复杂零件，因此热冲压一冷模具淬火成形技术被用到铝合金的成形过程中，板材 成形领域中一个重要的性能指标是成形极限.本论文使用理论预测和试验两种方法对6016铝合金成形极限曲线进行了研 究.首先，建立了考虑应变强化和应变速率强化的Fields--Bachofen本构方程，并将此本构方程引入到成形极限理论推导过程 中：然后，基于M-K凹槽理论，对6016铝合金成形极限曲线进行了理论预测，并且采用Nakazima试验方法对预测结果进行了 验证.结果显示，随着初始厚度不均度的增加，预测曲线向纵坐标的正方向移动：通过实验值和预测值的对比发现M-K凹槽 理论对成形极限曲线的预测是可行的、准确的. 关键词铝合金：M一K理论：成形极限曲线：理论预测：本构方程 分类号TG146.2+1 Prediction of forming limit curve of 6016 aluminum alloy based on M-K theory YANG Xiao-ming,WANG Bao-yu,XIAO Wen-chao,MA Wei-ping,KANG Yi School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:bywang@ustb.edu.cn ABSTRACT In recent years,due to the increasing demand for lightweight products in automotive industries to save energy and de- crease CO gas emissions,many aluminum alloy materials are being used in cars.Due to its good baking performance,6016 aluminum alloy is popular.However,traditional forming technology cannot produce complex parts.Furthermore,recent studies have focused on the hot stamping of aluminum alloy sheets and,in particular,of 6016 aluminum alloy sheets.It is well-known that sheet-metal form- ability is enhanced when the blanks are formed in hot temperatures.When this is done,the forming limit curve will rise.The forming limit of the material during the hot forming process is an important index and studying the forming limit of aluminum alloys at high tem- perature is of direct significance to production practices.In this paper,the forming limit curve of 6016 aluminum alloy was studied by theoretical prediction and experimentation.First,to evaluate the flow stress of a 6016 aluminum alloy sheet,the uniaxial hot tensile tests were conducted over a strain rate range of 0.01-1s and a temperature range of 400-500 C.Then,the Fields-Bachofen consti- tutive equation was established with considering strain hardening and strain rate enhancement,which matched well with the experimen- tal measurements.Then this constitutive equation was introduced into the forming limit theory.Finally,based on the M-K groove theo- ry,the forming limit curve of 6016 aluminum alloy was theoretically predicted,and the prediction results were validated by using the Nakazima test method.The comparison of the experimental and predicted values shows that the M-K groove theory is reasonable and accurate in predicting the forming limit curve.The effect of the initial inhomogeneity factor was analyzed on the forming limit curve. The results show that the prediction curve moves in the positive direction of the vertical coordinate,with an increase in the initial inho- mogeneity factor.Also,the effect of the initial inhomogeneity factor on different strain paths differs,and the impact on the tension-ten- 收稿日期：201707-30 基金项目：国家自然科学基金资助项目(U1564202,51705018)工程科学学报，第 40 卷，第 4 期: 485--491，2018 年 4 月 Chinese Journal of Engineering，Vol． 40，No． 4: 485--491，April 2018 DOI: 10． 13374 /j． issn2095--9389． 2018． 04． 012; http: / /journals． ustb． edu． cn 基于 M--K 理论的 6016 铝合金成形极限曲线预测 杨晓明，王宝雨，校文超，马卫平，康 艺 北京科技大学机械工程学院，北京 100083 通信作者，E-mail: bywang@ ustb． edu． cn 摘 要 近年来，为实现汽车车身轻量化，大量的铝合金材料被用于汽车车身制造，由于 6016 铝合金具有良好的烘烤性能，被 大量使用． 但是传统的冷成形技术并不能成形复杂零件，因此热冲压--冷模具淬火成形技术被用到铝合金的成形过程中，板材 成形领域中一个重要的性能指标是成形极限． 本论文使用理论预测和试验两种方法对 6016 铝合金成形极限曲线进行了研 究． 首先，建立了考虑应变强化和应变速率强化的 Fields--Bachofen 本构方程，并将此本构方程引入到成形极限理论推导过程 中; 然后，基于 M--K 凹槽理论，对 6016 铝合金成形极限曲线进行了理论预测，并且采用 Nakazima 试验方法对预测结果进行了 验证． 结果显示，随着初始厚度不均度的增加，预测曲线向纵坐标的正方向移动; 通过实验值和预测值的对比发现 M--K 凹槽 理论对成形极限曲线的预测是可行的、准确的． 关键词 铝合金; M--K 理论; 成形极限曲线; 理论预测; 本构方程 分类号 TG146. 2 + 1 收稿日期: 2017--07--30 基金项目: 国家自然科学基金资助项目( U1564202，51705018) Prediction of forming limit curve of 6016 aluminum alloy based on M--K theory YANG Xiao-ming，WANG Bao-yu ，XIAO Wen-chao，MA Wei-ping，KANG Yi School of Mechanical Engineering，University of Science and Technology Beijing，Beijing 100083，China Corresponding author，E-mail: bywang@ ustb． edu． cn ABSTＲACT In recent years，due to the increasing demand for lightweight products in automotive industries to save energy and de￾crease CO2 gas emissions，many aluminum alloy materials are being used in cars． Due to its good baking performance，6016 aluminum alloy is popular． However，traditional forming technology cannot produce complex parts． Furthermore，recent studies have focused on the hot stamping of aluminum alloy sheets and，in particular，of 6016 aluminum alloy sheets． It is well-known that sheet-metal form￾ability is enhanced when the blanks are formed in hot temperatures． When this is done，the forming limit curve will rise． The forming limit of the material during the hot forming process is an important index and studying the forming limit of aluminum alloys at high tem￾perature is of direct significance to production practices． In this paper，the forming limit curve of 6016 aluminum alloy was studied by theoretical prediction and experimentation． First，to evaluate the flow stress of a 6016 aluminum alloy sheet，the uniaxial hot tensile tests were conducted over a strain rate range of 0. 01--1 s － 1 and a temperature range of 400--500 ℃ ． Then，the Fields--Bachofen consti￾tutive equation was established with considering strain hardening and strain rate enhancement，which matched well with the experimen￾tal measurements． Then this constitutive equation was introduced into the forming limit theory． Finally，based on the M--K groove theo￾ry，the forming limit curve of 6016 aluminum alloy was theoretically predicted，and the prediction results were validated by using the Nakazima test method． The comparison of the experimental and predicted values shows that the M--K groove theory is reasonable and accurate in predicting the forming limit curve． The effect of the initial inhomogeneity factor was analyzed on the forming limit curve． The results show that the prediction curve moves in the positive direction of the vertical coordinate，with an increase in the initial inho￾mogeneity factor． Also，the effect of the initial inhomogeneity factor on different strain paths differs，and the impact on the tension--ten-