基于线性强化模型的双层厚壁圆筒极限内压统一解
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摘要
基于双剪统一强度理论与双线性强化模型,考虑材料拉压强度的不同及中间主应力效应的影响,推导了均匀内压作用下双层厚壁圆筒的弹、塑性极限内压解,分析了强化模量系数、拉压强度比、统一强度理论参数、内外半径比及分层半径对弹、塑性极限内压统一解的影响。结果表明:随着外径与内径之比的增大,弹、塑性极限内压增加,随着统一强度理论参数的增大,其值增加,随着拉压强度比的增大,其值减小;弹性极限内压与强化模量系数的取值无关,塑性极限内压随着强化模量系数的增大而增加;内外筒的分层半径对弹性极限内压有显著影响,而对塑性极限内压的影响较小。工程应用中,应选择较为合理的壁厚,使其在安全的基础上承受更大的内力;应充分考虑材料中间主应力及拉压强度比的影响,更准确的计算其受力情况,充分发挥材料的潜能。
Considering the different tensile-compressive strength of materials and the effect of intermediate principal stress, the unified solutions of the elastic limit internal pressure and the plastic limit internal pressure of a double-layered thick-walled cylinder under internal pressure are deduced, based on twin shear unified strength theory and a bilinear hardening model. The influence of parameters on the unified solution of elastic and plastic limit internal pressure is analyzed. It is shown that: each unified solution increases with increase of the radius ratio and unified strength theory parameter, but decreases with increase of the tension-compression ratio. The elastic limit internal pressure is irrelevant to the strain-hardening modulus coefficient, but the plastic limit internal pressure increases with the increase of the strain-hardening modulus coefficient. The delamination radius has a significant influence on the elastic limit internal pressure, but has a slight influence on the plastic limit internal pressure. For the engineering applications, reasonable wall thickness should be chosen so as to bear a greater internal force on the basis of safety. The consideration of the intermediate principal stress effect and tension-compression ratio can make materials develop their full potential ability.
Considering the different tensile-compressive strength of materials and the effect of intermediate principal stress, the unified solutions of the elastic limit internal pressure and the plastic limit internal pressure of a double-layered thick-walled cylinder under internal pressure are deduced, based on twin shear unified strength theory and a bilinear hardening model. The influence of parameters on the unified solution of elastic and plastic limit internal pressure is analyzed. It is shown that: each unified solution increases with increase of the radius ratio and unified strength theory parameter, but decreases with increase of the tension-compression ratio. The elastic limit internal pressure is irrelevant to the strain-hardening modulus coefficient, but the plastic limit internal pressure increases with the increase of the strain-hardening modulus coefficient. The delamination radius has a significant influence on the elastic limit internal pressure, but has a slight influence on the plastic limit internal pressure. For the engineering applications, reasonable wall thickness should be chosen so as to bear a greater internal force on the basis of safety. The consideration of the intermediate principal stress effect and tension-compression ratio can make materials develop their full potential ability.
引文
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[2]Yang Q H,Chen X,Meng B,et al.Optimum design of combined cold extrusion die for bevel gear[J].International Journal of Engineering and Technology,2012,4(4):348―351.
[3]杨丰钰,胡成亮,赵震,等.自增强理论在线性强化材料组合凹模设计中的应用[J].锻压技术,2016,41(6):78―82.Yang Fengyu,Hu Chengliang,Zhao Zhen,et al.Application of autofrettage theory in the design of linear strengthening material combined die[J].Forging Stamping Technology,2016,41(6):78―82.(in Chinese)
[4]张宁.功能梯度混凝土立井井壁承载性能研究[D].北京:华北电力大学,2012:1―8.Zhang Ning.study on bearing behavior of functionally graded concrete shaft lining[D].Beijing:North China Electric Power University,2012:1―8.(in Chinese)
[5]曹雪叶,赵均海,张常光.基于三剪统一强度准则的厚壁圆筒自增强分析[J].中国机械工程,2017,28(1):75―81.Cao Xueye,Zhao Junhai,Zhang Changguang.Autofrettage analysis of thick-walled cylinder based on triple-shear unified strength criterion[J].China Mechanical Engineering,2017,28(1):75―81.(in Chinese)
[6]徐秉业,刘信声.应用弹塑性力学[M].北京:清华大学出版社,1995:183―229.Xu Bingye,Liu Xinsheng.Application of elastic-plastic mechanics[M].Beijing:Tsinghua University Press,1995:183―229.(in Chinese)
[7]袁格侠,刘宏昭,赵迎祥,等.双层缩套厚壁筒自增强残余应力分析[J].中国机械工程,2012,23(11):1364―1368.Yuan Gexia,Liu Hongzhao,Zhao Yingxiang,et al.Analysis of autofrettaged residual stress of shrink-fit two-layer thick-wall cylinders[J].China Mechanical Engineering,2012,23(11):1364―1368.(in Chinese)
[8]赵均海,朱倩,张常光,等.基于统一强度理论的组合厚壁圆筒弹塑性统一解[J].固体力学学报,2014,35(1):63―70.Zhao Junhai,Zhu Qian,Zhang Changguang,et al.Elastic-plastic unified solutions for combined thick wall cylinder based on unified strength theory[J].Chinese Journal of Solid Mechanics,2014,35(1):63―70.(in Chinese)
[9]Zhu Qian,Zhao Junhai,Zhang Changguang,et al.Elastic-brittle-plastic analysis of double-layered combined thick-walled cylinder under internal pressure[J].Journal of Pressure Vessel Technology,2016,138(1):011201.
[10]Yu Maohong.Unified strength theory and its applications[M].Berlin:Springer Press,2004:129―156.
[11]马景槐.线性强化材料厚壁圆筒统一自增强分析[J].石油化工设备,2003,32(3):26―30.Ma Jinghuai.Autofrettage analysis of thick wall cylinder of linear strength material based on the unified strength theory[J].Petro-Chemical Equipment,2003,32(3):26―30.(in Chinese)