高速压制成形中金属粉末本构方程的研究
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摘要
高速压制成形(HVC)技术以高效率、高性能、低成本等优点成为近年来压制成形研究的热点。为了研究金属粉末的变形特征,得到一个封闭数学方程组,本构方程是必不可少的。本文在综述高速压制成形研究现状、特点的基础上,详细介绍了经典的压制方程、损伤力学等相关理论。
首先根据高速压制的压制机理,将压制过程分成硬化和软化两个阶段。由于金属粉末在硬化阶段压制力和密度呈线性关系,所以用heckel模型进行模拟,利用黄培云应变双对数计算公式,推导出硬化阶段的本构方程。第二阶段考虑到高温引起软化效应,同时应力-应变表现为非线性,对ZWT模型进行修正,去掉低应变率项,加入粘塑性项,得到此软化阶段的本构方程。数值模拟表明对硬化和软化两阶段分别建立本构方程是合理的,与试验的结果基本一致。
其次,利用损伤力学原理分析高速压制过程的损伤现象,将金属粉末看成柔度矩阵与弹性模量有关的E材料和柔度矩阵与剪切模量有关的G材料的复合体,在热力学第二定律的基础上,得到了金属粉末各向异性弹性损伤本构方程、相应的有效柔度矩阵以及损伤能量释放率。
最后,考虑金属粉末损伤过程的体积变形特征和软化效应,构造合适的塑性耗散势函数,构造高速压制成型金属粉末的弹塑性各向异性损伤本构方程。
High velocity compaction (HVC) technology became a hot research topic because of its efficient, high-performance and low-cost. In order to get closed mathematical equations in studying the deformation characteristics of the metal powder, constitutive equation was essential. Based on HVC theories, the classical suppress equation and damage mechanics were introduced.
At first, according to the relevant principles of HVC, the compaction process was divided into two stages: softening and hardening. The Heckel model was used for stimulation in the first stage because of its pressure and density e was a nearly linear relation. And the constitutive equation was deduced by using Huang's double logarithmic strain formula. The ZWT model was adopted in the second stage so as to reveal the nonlinearity. The item of low strain rate was eliminated, but the viscoplastic item was added. Thus the constitutive equation was established for the hot softening viscoelastic-plastic of HVC. It was proved reasonable to deduce the constitutive equation apart by the numerical simulation.
Secondly, the principles of damage mechanics were applied to analyze the damage phenomena in HVC process. According to the complex characteristics of the deformation of the metal powder, the metal powder is considered as a compound of two categories of materials. The flexibility matrix of one category of material (E material) is only relevant to the modulus of elasticity of the metal powder, while the flexibility matrix of the other category of material (G material) is only relevant to the shear modulus of the metal powder. In light of the second law of thermodynamics, the constitutive relation, the corresponding effective flexibility matrix and the damage energy release rate of the damage model of anisotropic elasticity of the metal powder were established.
Ultimately, according to the characteristics of the volume deformation of the powder, an appropriate dissipation potential function was selected to construct a constitutive equation of the Elastoplastic anisotropic damage of HYC powder.
首先根据高速压制的压制机理,将压制过程分成硬化和软化两个阶段。由于金属粉末在硬化阶段压制力和密度呈线性关系,所以用heckel模型进行模拟,利用黄培云应变双对数计算公式,推导出硬化阶段的本构方程。第二阶段考虑到高温引起软化效应,同时应力-应变表现为非线性,对ZWT模型进行修正,去掉低应变率项,加入粘塑性项,得到此软化阶段的本构方程。数值模拟表明对硬化和软化两阶段分别建立本构方程是合理的,与试验的结果基本一致。
其次,利用损伤力学原理分析高速压制过程的损伤现象,将金属粉末看成柔度矩阵与弹性模量有关的E材料和柔度矩阵与剪切模量有关的G材料的复合体,在热力学第二定律的基础上,得到了金属粉末各向异性弹性损伤本构方程、相应的有效柔度矩阵以及损伤能量释放率。
最后,考虑金属粉末损伤过程的体积变形特征和软化效应,构造合适的塑性耗散势函数,构造高速压制成型金属粉末的弹塑性各向异性损伤本构方程。
High velocity compaction (HVC) technology became a hot research topic because of its efficient, high-performance and low-cost. In order to get closed mathematical equations in studying the deformation characteristics of the metal powder, constitutive equation was essential. Based on HVC theories, the classical suppress equation and damage mechanics were introduced.
At first, according to the relevant principles of HVC, the compaction process was divided into two stages: softening and hardening. The Heckel model was used for stimulation in the first stage because of its pressure and density e was a nearly linear relation. And the constitutive equation was deduced by using Huang's double logarithmic strain formula. The ZWT model was adopted in the second stage so as to reveal the nonlinearity. The item of low strain rate was eliminated, but the viscoplastic item was added. Thus the constitutive equation was established for the hot softening viscoelastic-plastic of HVC. It was proved reasonable to deduce the constitutive equation apart by the numerical simulation.
Secondly, the principles of damage mechanics were applied to analyze the damage phenomena in HVC process. According to the complex characteristics of the deformation of the metal powder, the metal powder is considered as a compound of two categories of materials. The flexibility matrix of one category of material (E material) is only relevant to the modulus of elasticity of the metal powder, while the flexibility matrix of the other category of material (G material) is only relevant to the shear modulus of the metal powder. In light of the second law of thermodynamics, the constitutive relation, the corresponding effective flexibility matrix and the damage energy release rate of the damage model of anisotropic elasticity of the metal powder were established.
Ultimately, according to the characteristics of the volume deformation of the powder, an appropriate dissipation potential function was selected to construct a constitutive equation of the Elastoplastic anisotropic damage of HYC powder.
引文
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[2]Skoglund P.High density P/M component by high velocity compaction [J].PM,2001,44(3):15-17
[3]Caroline E.Hoganaos promotes potential of high velocity compaction[J].Metal Powder Report,2001,56(9):6-9
[4]沈元勋,肖志瑜,温利平.粉末冶金高速压制技术的原理、特点及其研究进展[J].粉末冶金工业,2006,16(3):19-23
[5]Richard F.HVC Punches PM to New Mass Production Limits[J].Metal Powder Report,2002,57(9):26-30
[6]果世驹,迟悦,孟飞等.粉末冶金高速压制成形的压制方程[J].粉末冶金材料科学与工程,2006,11(1):24-26
[7]迟悦,果世驹,孟飞等.粉末冶金高速压制成形技术[J].粉末冶金工业,2005,15(6):41-45
[8]#12
[9]Zhoum,Osakisaj,Ravi chandrang.Dynamically propagatings hear bands impact-loaded re-notchedl.Experimental investigations of temperature signatures and propagation speed[J].MecPhys Solid,1996,44(6):981-1006
[10]G.Sethi,E.Hauck and R.M.German.High velocity compation compared with conventional compaction[J].Powder Technology,2004,154(1):45-49
[11]迟悦.粉末冶金高速压制成形技术的研究[D].北京:北京科技大学粉末冶金研究所,2005
[12]周晟宇,尹海清,曲选辉.粉末冶金高速压制技术的研究进展[J].材料导报,2007,21(7):79-81.
[13]San Yukio,Miyagi Kiyohiro.Dinamic compation and the effect of contained within powder pores[J].Powder Met,1984,20(2):115-118
[14]肖志瑜,沈元勋,吴苑标.粉末冶金高速压制技术及其应用[J].粉末冶金材料科学与工程,.2007,49(2):163-166
[15]黄培云.粉末冶金原理[M].北京:冶金工业出版社,1982
[16]杨琳[摘译].高速压制技术在粉末冶金工业中的应用[J].粉末冶金材料科学与工程.2007,12(3)
[17]Torsten Ericsson,Petri Luukkonen.Residual stresses in green bodies of steel powder after conventional and high speed compaction[J].Journal of energy resources technology,1992,114(5):117-138
[18]Schaefer Dale W,Chen Chunyuan,Yang Arthur Jing-Min.Methods for synthesizing precipitated silica and use thereof US Pat[J],2005,10(13):7-10
[19]Bruska Azhdara,Bengt Stenberga,and Leif Karib.Determination of springback gradient in the die on compacted polymer powders during high-velocity compaction[J].Polymer Testing.2006,25(1) 114-123
[20]周晟宇,铁粉高速压制成形的研究[D].北京科技大学,2008.
[21]王盘鑫.粉末冶金学[M].北京:冶金工业出版社,2003
[22]刘军,佘正国.粉末冶金与陶瓷成型技术[M].北京:化学工业出版社,2005
[23]石富.稀土永磁材料制备技术[M].北京;冶金工业出版社,2007
[24]刘开琪.金属陶瓷的制备与应用[M].北京:冶金工业出版社,2008
[25]孙杏囡,谈萍,崔永福.影响铜-石墨材料密度的工艺因素[J].材料工程,1997,9(2):33-37
[26]王延庆,王广春,孙金平.金属型腔模具粉浆浇注成型工艺的实验研究[J].模具设计,2004,6(4):3-6
[27]王建忠;曲选辉;尹海清;周晟宇;易明军.电解铜粉高速压制成形[J].有色金属学报,2008,8(1):9-13
[28]刘全坤.粉末成形基本原理[M].北京:机械工业出版社,2005
[29]Ge Rongde;A new powder compaction equation[M];Int J Powder Metall;1991,45(8):106-112
[30]黄培云,金展鹏,陈振华.粉末冶金基础理论与新技术[M].长沙:中南工业大学出版社,1995
[31]R.W.Heckel.Trans.Met.Soc.AIME,1961,221,671
[32]R.W.Heckel.in Proc.17~(th) Annual Technical Meeting of the Metal Powder Industries Federation,New York,1961,66
[33]王军.损伤力学的理论与应用[M].北京:科学出版社,1997
[34]李灏.损伤力学基础[M].济南:山东科学技术出版社,1992
[35]C.Truesdell.A first course in rational continuum mechanics[J].Academic Press,1977,49(1):74-79
[36]Rabotnov Yu N.On the Equation of State for Creep[J].Prog.inAppl,Mech, 1963,24(3):307-315
[37]傅秦生.能量系统的热力学分析方法[M].西安:西安交通大学出版社,2006
[38]沃德IM.高聚物的力学性能[M].北京:科学出版社,1966:16
[39]姜乃斌.弹粘塑性饱和多孔介质动力响应的有限元分析[D].重庆大学,2005
[40]王礼立.应力波基础[M].北京:国防工业出版社,2005
[41]Yang J Gao,W X,Jin Q K;Experimental study on damage properties of rocks under dynamic loading[M];Journal of Beijing Institute of Technology;2000
[42]朱兆祥,徐大本,王礼立.环氧树脂在高应变率下的热粘弹性本构方程和时温等效性[J].宁波大学学报.1988,1(1):58-68.
[43]陈江瑛,王礼立.水泥砂浆的率型本构方程[J].宁波大学学报,2000,13(2):1-5
[44]刘建秀,李蔚,宋宇伟等.铜基粉末冶金多孔材料在高应变率下的力学性能及本构关系[J].机械强度,2003,25(5):499-503
[45]Hayhurst D R,Leckie A M.The Effect of Creep Constitutive and Damage Relationships upon the Rupture Time of a Solid Circular Torsion Bar.J.of Mech[J].Solids,1973,21(3):431-446
[46]何思明.双标妞描述的土的损伤模型及其应用[J].岩七力学,2002,3(3):51-56
[47]梁小燕,兑关锁,黄海明.高孔隙率多孔介质材料有效复合模量的预估[J].科学技术与工程,2005,10(5):32-38
[48]Chow C.L and Wang J.An-isotropic theory of elasticity of continuum damage mechanics[J].International Journal of Fracmrc.1987,33(5),3-16.
[49]严杰,张瑞珠,王立平.MTS SINTECH 65/G材料试验系统“先进方法生成器”的应用.材料与结构之力学测试国际学术会议.香港,1998
[50]马鑫,Yoshida,F.相对损伤应力-Lemaitre等效损伤应力概念的修正及其在温度循环载荷下的应用[J].自然科学进展2001,11(1):86-89
[51]Lemaitre J.A course on damage mechanics[M];New York:1992
[52]Wang Lingyun.,Liu Xuefeng,Tang Aitao,Huang Guangjie.Damage evolution of metallic materials during high temperature plastic deformation[J].Trans.Nonferrous Met.Soc.China,2002,3(12):379-382
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