非线性塑性材料内部空洞闭合模型的研究

张效迅; 崔振山

doi:10.3879/j.issn.1000-0887.2009.05.009

非线性塑性材料内部空洞闭合模型的研究

doi: 10.3879/j.issn.1000-0887.2009.05.009

上海交通大学国家模具CAD工程研究中心,上海 200030

基金项目: 国家重点基础研究发展计划资助项目(973计划,2006CB705401)

详细信息

作者简介:
张效迅(1975- ),男,江西万载人,博士生(E-mail:xx.zhang.cn@gmail.com);崔振山.教授,博士生导师(联系人.E-mail:cuizs@sjtu.edu.cn).

中图分类号: O344;TG316
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- 被引次数: 0
出版历程
- 收稿日期: 2008-05-20
- 修回日期: 2009-03-10
- 刊出日期: 2009-05-15

Theoretical Study of Void Closure in Nonlinear Plastic Materials

National Die and Mold CAD Engineering Research Center, Shanghai Jiao Tong University, Shanghai 200030, P. R. China

摘要

摘要: 基于典型体元(RVE)模型和Rayleigh-Ritz法，对材料内部空洞从球形闭合成裂纹的过程进行了定量研究．基体材料的本构关系采用幂次粘性方程．通过研究材料变形过程中内部球形空洞和圆形裂纹的演化规律，得到了各自的体积应变率的表达式．采用插值近似，建立了空洞闭合的解析模型，发现空洞变形的主要机理来自于空洞周围基体材料的塑性流动．空洞闭合模型反映了材料属性、远场应力三轴度、远场等效应变对空洞闭合的定量规律．空洞闭合模型的预测结果与文献中的数值结果和有限元计算结果相吻合．空洞闭合模型与CAE（computer aided engineering）技术相结合可对材料加工工艺进行优化设计，为消除材料内部空洞提供了一条有应用前景的新途径．
- 空洞闭合 /
- RVE（典型体元） /
- 细观力学 /
- 应力三轴度 /
- CAE
Abstract: Void closing from a spherical shape to a crack is investigated quantitatively in the present study. The constitutive relation of the void-free matrix was assumed to obey the Norton power law. A representative volume element (RVE) which includes matrix and void was employed and a Rayleigh-Ritz procedure was developed to study the deformation-rates of a spherical void and a pennyshaped crack. Based on an approximate interpolation scheme, an analytical model for void closure in nonlinear plastic materials was established. It is found that the local plastic flows of the matrix material are the main mechanism of void deformation. It is also shown that the relative void volume during the deformation depends on the Norton exponent, on the far-field stress triaxiality, as well as on the far-field effective strain. The predictions of void closure using the present model are compared with the corresponding results in the literature, arriving at good agreement. The model for void closure provides a novel way for process design and optimization in terms of elimination of voids in billets because the model for void closure can be easily applied in the CAE(computer aided engineering) analysis.
- void closure /
- representative volme element (RVE) /
- mesomechanics /
- stress triaxiality /
- CAE

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参考文献(41)

[1]	Dudra S P,Im Y T.Analysis of void closure in open-die forging[J].Internat J Mach Tools Manufact,1990,30(1):65-75. doi: 10.1016/0890-6955(90)90042-H
[2]	Waller A.Closing of a central longitudinal pore in hot rolling[J].J Mech Work Technol,1985,12(2):233-242. doi: 10.1016/0378-3804(85)90138-X
[3]	Keife H,St[KG-*5]. ahlberg U.Influence of pressure on the closure of voids during plastic deformation[J].J Mech Work Technol,1980,4（2）:133-143. doi: 10.1016/0378-3804(80)90031-5
[4]	St[KG-*5]. ahlberg U,Keife H,Lundberg M,et al.A study of void closure during plastic deformation[J].J Mech Work Technol,1980,4（1）:51-63. doi: 10.1016/0378-3804(80)90005-4
[5]	St[KG-*5]. ahlberg U.Influence of spread and stress on the closure of a central longitudinal hole in the hot rolling of steel[J].J Mech Work Technol,1986,13(1):65-81. doi: 10.1016/0378-3804(86)90043-4
[6]	Tanaka M,Ono S,Tsuneno M.Factors contributing to crushing of voids during forging[J]. J Jpn Soci Technol Plast,1986,27（306）:825-859.
[7]	Tanaka M,Ono S,Tsuneno M.A numerical analysis on void crushing during side compression of round bar by flat dies[J]. J Jpn Soci Technol Plast,1987,28（314）:238-244.
[8]	Tanaka M,Ono S,Tsuneno M,et al.An analysis of void crushing during flat die free forging[A].In:Lange K，Ed.Proceedings of the 2nd International Conference on Technology of Plasticity (ICTP)[C].Vol 2. Stuttgart,Germany:Springe-Verlag,1987,1035-1042.
[9]	Park C Y,Yang D Y.Modelling of void crushing for large-ingot hot forging[J].J Mater Process Technol,1997,67(1/3):195-200. doi: 10.1016/S0924-0136(96)02843-9
[10]	Pietrzyk M,Kawalla R,Pircher H.Simulation of the behavior of voids in steel plates during hot rolling[J]. Steel Res,1995,66(12):526-529.
[11]	崔振山,任广升,徐秉业,等.圆柱体内部空洞的热锻闭合条件[J].清华大学学报,2003,43(2):227-229,233.
[12]	Wang A,Thomson P F,Hodgson P D.A study of pore closure and welding in hot rolling process[J].J Mater Process Technol, 1996,60(1/4):95-102. doi: 10.1016/0924-0136(96)02313-8
[13]	Chaaban M A,Alexander J M.A study of the closure of cavities in swing forging[A].In:Tobias S A,Ed.Proceedings of the 17th International Machine and Tool Design Research Conference[C].Birmingham,UK:Macmillan,1976,633-645.
[14]	Nakasaki M,Takasu I,Utsunomiya H.Application of hydrostatic integration parameter for free-forging and rolling[J].J Mater Process Technol,2006,177(1/3):521-524. doi: 10.1016/j.jmatprotec.2006.04.102
[15]	McClintock F A.A criterion for ductile fracture by growth of holes[J].J Appl Mech,1968,35(2):363-371. doi: 10.1115/1.3601204
[16]	Rice J R,Tracey D M.On the ductile enlargement of voids in triaxial stress fields[J].J Mech Phys Solids,1969,17(3):201-217. doi: 10.1016/0022-5096(69)90033-7
[17]	Gurson A L.Continuum theory of ductile rupture by void nucleation and growth—part Ⅰ:yield criteria and flow rules for porous ductile media[J].J Eng Mater Technol,1977,99(1):2-15. doi: 10.1115/1.3443401
[18]	Svik O P,Thaulow C.Growth of spheroidal voids in elastic-plastic solids[J].Fatigue Fract Engng Mater Struct,1997,20(12):1731-1744. doi: 10.1111/j.1460-2695.1997.tb01525.x
[19]	Budiansky B,Hutchinson J W,Slutsky S.Void growth and collapse in viscous solids[A].In:Hopkins H G,Sewell M J,Eds.Mechanics of Solids[C].Oxford:Pergamon Press,1982,13-45.
[20]	Duva J M.A constitutive description of nonlinear materials containing voids[J].Mechanics Materials,1986,5(2):137-144. doi: 10.1016/0167-6636(86)90029-3
[21]	Cocks A.Inelastic deformation of porous materials[J].J Mech Phys Solids,1989,37(6):693-715. doi: 10.1016/0022-5096(89)90014-8
[22]	王自强,秦嘉亮.含空洞非线性材料的本构势和空洞扩展率[J].固体力学学报,1989,10（2）:127-142.
[23]	Leblond J B,Perrin G,Suquet P.Exact results and approximate models for porous viscoplastic solids[J].International Journal of Plasticity,1994,10(3):213-235. doi: 10.1016/0749-6419(94)90001-9
[24]	Liu Y,Huang Z P.Macroscopic strain potentials in nonlinear porous materials[J].Acta Mech Sinica,2003,19(1):52-58. doi: 10.1007/BF02487453
[25]	Huang Z P,Wang J.Nonlinear mechanics of solids containing isolated voids[J].ASME Appl Mech Rev,2006,59(4):210-229. doi: 10.1115/1.2192812
[26]	Hsu C Y,Lee B J,Mear M E.Constitutive models for power-law viscous solids containing spherical voids[J].Internat J Plasticity,2009, 25(1):134-160. doi: 10.1016/j.ijplas.2007.11.003
[27]	Flandi L,Leblond J B.A new model for porous nonlinear viscous solids incorporating void shape effects—I:theory[J].Eur J Mech A/Solids,2005,24(4):537-551. doi: 10.1016/j.euromechsol.2005.03.003
[28]	Gologanu M,Leblond J B,Devaux J.Approximate models for ductile metals containing nonspherical voids—case of axisymmetric prolate ellipsoidal cavities[J].J Mech Phys Solids,1993,41(11):1723-1754. doi: 10.1016/0022-5096(93)90029-F
[29]	Gologanu M,Leblond J B,Devaux J.Approximate models for ductile metals containing nonspherical voids—case of axisymmetric oblate ellipsoidal cavities[J].J Eng Mater Technol,1994,116(3):290-297. doi: 10.1115/1.2904290
[30]	LI Zhen-huan,HUANG Min-sheng.Combined effects of void shape and void size—oblate spheroidal microvoid embedded in infinite non-linear solid[J].Internat J Plasticity,2005,21(3):625-650. doi: 10.1016/j.ijplas.2004.05.006
[31]	Pardoen T,Hutchinson J W.An extended model for void growth and coalescence[J].J Mech Phys Solids,2000,48(12):2467-2512. doi: 10.1016/S0022-5096(00)00019-3
[32]	Lee B J,Mear M E.Axisymmetric deformations of power-law solids containing a dilute concentration of aligned spheroidal voids[J].J Mech Phys Solids,1992,40(8):1805-1836. doi: 10.1016/0022-5096(92)90052-4
[33]	Lee B J,Mear M E.Studies of the growth and collapse of voids in viscous solids[J].J Eng Mater Technol,1994,116(3):348-358. doi: 10.1115/1.2904298
[34]	Yee K C,Mear M E.Effect of void shape on the macroscopic response of non-linear porous solids[J].Internat J Plasticity,1996,12(1):45-68. doi: 10.1016/S0749-6419(95)00044-5
[35]	Norton F H.Creep of Steel at High Temperature[M].New York:McGraw-Hill,1929.
[36]	Duva J M,Hutchinson J W.Constitutive potentials for dilutely voided nonlinear materials[J].Mechanics Materials, 1984,3(1):41-54. doi: 10.1016/0167-6636(84)90013-9
[37]	Wilkinson D S,Ashby M F.Pressure sintering by power law creep[J].Acta Metall,1975,23(11):1277-1285. doi: 10.1016/0001-6160(75)90136-4
[38]	Tvergaard V.On the creep constrained diffusive cavitation of grain boundary facets[J]. J Mech Phys Solids,1984,32(5):373-393. doi: 10.1016/0022-5096(84)90021-8
[39]	He M Y,Hutchinson J W.The penny-shaped crack and the plane strain crack in an infinite body of power-law material[J]. J Appl Mech, 1981,48(4):830-840. doi: 10.1115/1.3157742
[40]	Hutchinson J W.Constitutive behavior and crack tip fields for materials undergoing creep-constrained grain boundary cavitation[J].Acta Metal,1983, 31(7):1079-1088. doi: 10.1016/0001-6160(83)90204-3
[41]	Banks-sills L,Budiansky B.On void collapse in viscous solids[J].Mechanics of Materials,1982,1(3):209-218. doi: 10.1016/0167-6636(82)90014-X