滑移线教学中粗糙平冲头压入半无限体的非Prandtl解探讨  

RESEARCH ON NON-PRANDTL SOLUTION OF COARSE PLANE PUNCH PIN PRESSED IN THE SEMI-UNFINITE BODY IN SLIP LINE TEACHING

作　　者：梅瑞斌[1] 包立[2] 刘相华[1] MEI Ruibin;BAO Li;LIU Xianghua(School of Materials Science and Engineering,Northeastern University,Shenyang 110819,China;Northeastern University at Qinhuangdao,Qinhuangdao 066004,Hebei,China)

机构地区：[1]东北大学材料与科学工程学院,沈阳110819 [2]东北大学秦皇岛分校,河北秦皇岛066004

出　　处：《力学与实践》2022年第5期1202-1205,共4页Mechanics in Engineering

基　　金：河北省教育厅精品课程建设项目(2020JPKC061);东北大学课程思政示范课程(2021KCSZ018);东北大学秦皇岛分校教改重点项目(2021JG-A03)资助。

摘　　要：针对经典教材滑移线理论教学中光滑平冲头和粗糙平冲头压入半无限体计算结果相同问题,构建了粗糙平冲头压入半无限体的非Prandtl滑移线场。与Prandtl场解相比,摩擦的存在使单位接触压力和应力状态影响系数增加了11%,与光滑平冲头压入半无限体计算结果相比,x方向的应力增加约82%,计算结果更能准确反映摩擦使变形力增加的塑性理论,有助于学生理解滑移线法以及滑移线理论的研究和应用。It is difficult for students to understand that the calculation results of smooth punch and coarse punch pin pressed into semi-unfinite body are the same in slip line teaching.A non-Prandtl slip line field of coarse punch pin pressed into semi-unfinite body is proposed and constructed.Compared with solution of Prandtl field,the unit pressure and coefficient of stress state are increased by 11%because of friction.Furthermore,the normal stress in x direction is increased by about 82%compared with the calculation results of smooth punch pin pressed in semi-unfinite body.The calculation results reflect accurately the influence of friction on increasing plastic deformation force,and it is helpful for students to study and apply the slip line theory.

关 键 词：滑移线 半无限体 摩擦 Prandtl 场 压力 

分 类 号：O34[理学—固体力学]