金属粉末的粘弹塑性本构方程的研究
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摘要
高速压制技术是2001年提出的一项新的粉末冶金压制技术,由于高速压制速度快、时间短,粉末的变形特性非常复杂。数值模拟是研究高速压制过程的重要途径,而构造本构关系又是数值模拟必要的部分。本文结合流变学理论,利用流变本构模型的构造方法,构造了一种粉末的本构模型,并在此基础上对金属粉末的变形特性进行了讨论。
文中首先介绍了两种有关金属粉末压制的粘弹性本构模型,并在改进模型的基础上,通过引入弹簧元件的热膨胀系数,来反映温度对压制过程的影响,推导出相应的热粘弹性本构方程。对所建立方程的分析显示,在高速压制中由于温度的变化,使得金属粉末出现软化现象,即粉末更容易被压实,从而使压坯零件有较高的密度。
其次,高速压制中粉末会发生塑性变形,为了描述这种现象,在改进的粘弹性本构模型的基础上引入理想塑性体,构造了金属粉末的粘弹塑性本构模型,推导出相应的本构方程,并引入弹簧的热膨胀系数来描述温度的影响,得到粉末的热粘弹塑性本构方程。通过对比分析,体现了塑性变形的存在和温度的提高使得粉末应力变化速率减小,从而提高压坯密度。
最后分析了高速压制成形中的卸载过程,得到了卸载方程。通过对卸载方程的分析显示,压制中粉末温度升高使得压坯的变形恢复更小,体现了高速压制弹性后效低、脱模压力小的特点。
High velocity compaction technology which was put forward in 2001 is a new powder metallurgy compaction technology. Because of high speed and short time, deformation characteristics of metal powder are very complex. Numerical simulation is of great importance in the research of deformation characteristics of metal powder. And the constitutive equation is necessary to the numerical simulation. In this article, combining with rheological theory, constitutive model of metal power is constructed. Based on the model, the deformation characteristics of metal powder are discussed.
At first, two kinds of viscoelastic constitutive model of powder compaction are introduced. In order to reflect the influence of temperature in the compaction, the spring element's coefficient of thermal expansion is introduced, and the corresponding thermo viscoelastic constitutive equation is derived based on the improved constitutive model. Because of the increasing of temperature during high velocity compaction, the metal powder is softened and easy to compact. As a result, the density of compacting components is increased.
Second, to explain plastic deformation during high velocity compaction, viscoelastic plastic constitutive model is constructed by introducing the ideal plasticity element and the spring element's coefficient of thermal expansion. The corresponding constitutive equations are derived. By comparative analysis, the influence of plasticity and temperature on the compaction of metal powder can be observed.
At the end, the unloading equation is derived by analyzing unloading process in compaction. The equation shows that the increasing of temperature makes the elastic aftereffect lower. The characteristics of high velocity compaction can be observed that elastic aftereffect is low and ejection pressure is small.
文中首先介绍了两种有关金属粉末压制的粘弹性本构模型,并在改进模型的基础上,通过引入弹簧元件的热膨胀系数,来反映温度对压制过程的影响,推导出相应的热粘弹性本构方程。对所建立方程的分析显示,在高速压制中由于温度的变化,使得金属粉末出现软化现象,即粉末更容易被压实,从而使压坯零件有较高的密度。
其次,高速压制中粉末会发生塑性变形,为了描述这种现象,在改进的粘弹性本构模型的基础上引入理想塑性体,构造了金属粉末的粘弹塑性本构模型,推导出相应的本构方程,并引入弹簧的热膨胀系数来描述温度的影响,得到粉末的热粘弹塑性本构方程。通过对比分析,体现了塑性变形的存在和温度的提高使得粉末应力变化速率减小,从而提高压坯密度。
最后分析了高速压制成形中的卸载过程,得到了卸载方程。通过对卸载方程的分析显示,压制中粉末温度升高使得压坯的变形恢复更小,体现了高速压制弹性后效低、脱模压力小的特点。
High velocity compaction technology which was put forward in 2001 is a new powder metallurgy compaction technology. Because of high speed and short time, deformation characteristics of metal powder are very complex. Numerical simulation is of great importance in the research of deformation characteristics of metal powder. And the constitutive equation is necessary to the numerical simulation. In this article, combining with rheological theory, constitutive model of metal power is constructed. Based on the model, the deformation characteristics of metal powder are discussed.
At first, two kinds of viscoelastic constitutive model of powder compaction are introduced. In order to reflect the influence of temperature in the compaction, the spring element's coefficient of thermal expansion is introduced, and the corresponding thermo viscoelastic constitutive equation is derived based on the improved constitutive model. Because of the increasing of temperature during high velocity compaction, the metal powder is softened and easy to compact. As a result, the density of compacting components is increased.
Second, to explain plastic deformation during high velocity compaction, viscoelastic plastic constitutive model is constructed by introducing the ideal plasticity element and the spring element's coefficient of thermal expansion. The corresponding constitutive equations are derived. By comparative analysis, the influence of plasticity and temperature on the compaction of metal powder can be observed.
At the end, the unloading equation is derived by analyzing unloading process in compaction. The equation shows that the increasing of temperature makes the elastic aftereffect lower. The characteristics of high velocity compaction can be observed that elastic aftereffect is low and ejection pressure is small.
引文
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[3]Skoglund P,Mikael K,Ingrid H.High density PM parts by high velocity compaction[J].PowderMetallurgy,2001,44(3):199-210
[4]Andersson O.High velocity compaction of soft magnetic composites[J].Advances in Powder Metallurgy & Pariculate Materials,2002,14:1-13
[5]Wang Jianzhong,Qu Xuanhui,Yin Haiqing.High velocity compaction of ferrous powder[J].Powder Technology,2009,192(1):131-136
[6]王建忠,曲选辉,尹海清等.电解铜粉高速压制成形[J].中国有色金属学报,2008,18(8)：1498-1503
[7]曲选辉,尹海清.粉末高速压制技术的发展现状[J].中国材料进展,2010,29(2):46-47
[8]邓三才,肖志瑜,陈进,许阳,关航键.粉末冶金高速压制技术的研究现状及展望[J].粉末冶金材料科学与工程,2009,14(4)：214-215
[9]闫志巧,蔡一湘,陈峰.粉末冶金高速压制技术及其应用[J].粉末冶金技术,2009,27(6)：456-459
[10]Jonsen P,Haggblad H A,Troive L.Green body behaviour of high velocity pressed metal powder[J].Materials Science Forum,2007,534-536:289-292
[11]Ericsson P,Luukkonen.Residual stresses in green bodies of steel powder after conventional and high speed compaction[J]. Materials Science Forum,2002,404-407:77-82
[12]Wang J Z,Qu X H,Yin H Q.Effect of particle size distribution on green properties during high velocity compaction[J].Frontier of Materials Science in China,2008,2-4:392-396
[13]Trovie L,Skoglund P.EuroPM2005 Congress & Exhibition,2-5 Oct,2005,Prague, Czech Republic
[14]迟悦,果世驹,孟飞.粉末冶金高速压制成形技术[J].粉末冶金工业,2005,15(6)：41-45
[15]Skoglund P.Hogonas promote potential of high veocity compaction[J].Metal Powder Report,2001,6
[16]沈世勋,肖志瑜,温利平等.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
[17]黄培云.粉末冶金原理[M].北京：冶金工业出版社,2008,166-217
[18]王建忠.铁粉和铜粉高速压制成形及致密化规律研究：[博士学位论文].北京：北京科技大学,2009
[19]易明军.铜粉高速压制成形的工艺及机理研究：[硕士学位论文].北京：北京科技大学,2009
[20]史晓明,韩再春.还原铁粉的粒度组成对其压缩性能的影响[J].粉末冶金技术,1983,3：31-34
[21]Seihi QHauck E,German R M.High velocity compaction compared with conventi-onal compaction[J].Materials Science and Technology,2006,22(8):955-959
[22]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)：24-27
[23]Zhou M,Rosakis A J,Ravichandran G..Dynamically propagating shear bands in impact-loaded pre-notched plates-1.Experimental investigations of temperature signatures and propagation speed[J].Mech Phys Solid,1996,44(6):981-1003
[24]卓家寿,黄丹.工程材料的本构演绎[M].北京：科学出版社,2009,1-3
[25]杨桂通.土动力学[M].北京：中国建材工业出版社,2000.39-43
[26]Zhu Yuanlin,et al..Constitutive relations offrozen soil in uni-axial compression [C].Proceedings of the 6th international symposion on ground freezing,1991
[27]朱元林,张家懿,彭万巍等.冻土的单轴压缩本构关系[J].冰川冻土,1992,14(3)：210-216
[28]蔡中民,朱元林,张长庆.冻土的粘弹塑性本构模型以及材料参数的确定[J].冰川冻土,1992,12(1)：30-40
[29]He Ping,et al..Constitutive models of frozen soil[J].Canadian geotechnical Journ-al,2000,37(4):811-816
[30]何平,程国栋,朱元林等.饱和正冻土中水、热、力场耦合模型[J].冰川冻土,2000,22(2)：135-138
[31]孙钧.岩土材料流变及其工程应用[M].北京：中国建筑工业出版社,1999
[32]余启华.岩石的流变破坏过程及有限元分析[J].水利学报,1985,55-61
[33]陶振宇.岩石流变试验与现场观测的比较分析[J].水利学报,1985,10：49-54
[34]曹树刚等.岩石蠕变本构关系及改进的西原正夫模型[J].岩石力学与工程学报,2002,21(5)：632-634
[35]李良权,徐卫亚,王伟.基于西原模型的非线性粘弹塑性流变模型[J].力学学 报,2009,41(5)：672-680
[36]Dougill J.W.,Lau J.C.and Burt N.J..Toward a theoretical model for progressive failure and softening in rock,concrete and similar materials[J].Mech in-Engng. ASCE—END,1076,335-355
[37]秦跃平,王林,孙文标,王磊.岩石损伤流变理论模型研究[J].岩石力学与工程学报,2002,21(增2)：2291-2295
[38]秦跃平.岩石损伤力学模型及其本构方程探讨[J].岩石力学与工程学报,2001,20(4)：560-562
[39]谢兴华,速宝玉,詹美礼.基于应变的岩石类脆性材料损伤研究[J].岩石力学与工程学报,2004,23(12)：1966-1970
[40]熊玉春,房营光.饱和软粘土地基的损伤模型与震陷计算[J].振动工程学报,2006,19(3)：359-363
[41]Lemaitre J..A continous damage mechanics model for ductile-fracture[J].Eng. Material Tech,1985,Vol 83
[42]Conil,Irini Djeran-Maigre,Richard Cabrillac,Kun Suc.Thermodynamics modellin-g of plasticity and damage of argillite[J].C.R.Mecanique,2004,332:851-848
[43]J.F.Shao,Y.Jia,D.Kondo,A.S. Chiarelli.A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions [J].Mechanics of Materials,2006,38:218-232
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