爆炸力学中球形孔洞膨胀问题的损伤力学分析
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摘要
随着科学技术的发展,在军事工程、建筑工程和航天航空材料工程提出许多有待于解决的复杂问题,需要从微观、细观以及宏观等不同层次上深入认识材料和结构的力学行为。在爆炸力学中,通常采用球形孔洞膨胀理论模型研究爆炸力学中一些问题。这是由于该模型具有对称性、简便明确,易于给出爆炸过程中物理量的分布,从而揭示材料的变形本质。
采用球形孔洞膨胀模型研究爆炸力学问题,大多采用弹塑性模型,由于岩石中存在着随机分布的微裂纹,用损伤力学的方法研究材料在爆炸过程中的变形机理是十分重要的。认为材料的损伤区中仅存在径向应力σr,而球向应力σθ=0,只是损伤的极端情况。考虑到塑性区和弹性区对损伤变形的限制,从连续介质损伤力学的角度,深入研究爆炸过程中损伤区的变形状态,更具有理论意义和工程应用前景。
在本文中,首先从连续介质损伤力学的热力学内变量理论出发,通过引入一个带损伤内变量的自由能函数,构造了损伤材料的本构方程。其次,在球对称条件下,推导出求解损伤区场量的控制方程和边界条件,再次通过数值计算得出球形孔洞膨胀的应力和位移分布,为进一步研究塑性—损伤—弹性爆炸模型提供参考依据。最后讨论了球形孔洞膨胀问题研究的发展趋势。
本文从损伤力学角度,对球形孔洞膨胀问题进行较深层次的研究工作,这会使人们更深刻地认识材料(结构)的变形本质,为理论研究和工程应用奠定基础。
With the development of science and technology, many complicated problems are presented in areas of military engineering, architectural engineering and material engineering of aerospace, it need to understand the mechanical behavior of material and structure deeply from different levels such as microscopic view and macroscopic view, In explosion mechanics, it usually adopts the spherical cavity expansion model to research some issues because of the symmetry of the model, it is very simple and specific, which can given the distribution of physical quantity conveniently, thus it reveal the essence of material deformation.
Using the spherical cavity expansion model to research explosion problem, the elastic-plastic model is adopted mostly. It is important that using the damage mechanics method to research the deformation mechanism of material during the explosion process, because there are many microcracks distributing randomly in rocks. It is a extreme case that considered only radial stress is transferred and circumferential stress is zero. Considering the restriction of elastic region and plastic region, researching the deformation state of damage region deeply in explosion process, it have more theoretical significance and more application prospect on engineering.
In this paper, first, starting form the thermodynamics internal variable theory of the continuous medium damage mechanics, construct the damage constitutive equations by introduced free energy function with damage internal variable. Secondly, this paper deduced governing equations and boundary conditions that based on the assumption of spherical symmetry for solving the field quantities of damage region, and get the distribution of displacement and the distribution of stress to provide the reference for researching the elastic-cracked-plastic model furtherly. At last, this paper discuss the research prospect of spherical cavity expansion problem.
This paper research the spherical cavity expansion problem on deeper level, it makes people recognizes the deformation essence of material(or structure), and lay a foundation for theoretical research or engineering application.
采用球形孔洞膨胀模型研究爆炸力学问题,大多采用弹塑性模型,由于岩石中存在着随机分布的微裂纹,用损伤力学的方法研究材料在爆炸过程中的变形机理是十分重要的。认为材料的损伤区中仅存在径向应力σr,而球向应力σθ=0,只是损伤的极端情况。考虑到塑性区和弹性区对损伤变形的限制,从连续介质损伤力学的角度,深入研究爆炸过程中损伤区的变形状态,更具有理论意义和工程应用前景。
在本文中,首先从连续介质损伤力学的热力学内变量理论出发,通过引入一个带损伤内变量的自由能函数,构造了损伤材料的本构方程。其次,在球对称条件下,推导出求解损伤区场量的控制方程和边界条件,再次通过数值计算得出球形孔洞膨胀的应力和位移分布,为进一步研究塑性—损伤—弹性爆炸模型提供参考依据。最后讨论了球形孔洞膨胀问题研究的发展趋势。
本文从损伤力学角度,对球形孔洞膨胀问题进行较深层次的研究工作,这会使人们更深刻地认识材料(结构)的变形本质,为理论研究和工程应用奠定基础。
With the development of science and technology, many complicated problems are presented in areas of military engineering, architectural engineering and material engineering of aerospace, it need to understand the mechanical behavior of material and structure deeply from different levels such as microscopic view and macroscopic view, In explosion mechanics, it usually adopts the spherical cavity expansion model to research some issues because of the symmetry of the model, it is very simple and specific, which can given the distribution of physical quantity conveniently, thus it reveal the essence of material deformation.
Using the spherical cavity expansion model to research explosion problem, the elastic-plastic model is adopted mostly. It is important that using the damage mechanics method to research the deformation mechanism of material during the explosion process, because there are many microcracks distributing randomly in rocks. It is a extreme case that considered only radial stress is transferred and circumferential stress is zero. Considering the restriction of elastic region and plastic region, researching the deformation state of damage region deeply in explosion process, it have more theoretical significance and more application prospect on engineering.
In this paper, first, starting form the thermodynamics internal variable theory of the continuous medium damage mechanics, construct the damage constitutive equations by introduced free energy function with damage internal variable. Secondly, this paper deduced governing equations and boundary conditions that based on the assumption of spherical symmetry for solving the field quantities of damage region, and get the distribution of displacement and the distribution of stress to provide the reference for researching the elastic-cracked-plastic model furtherly. At last, this paper discuss the research prospect of spherical cavity expansion problem.
This paper research the spherical cavity expansion problem on deeper level, it makes people recognizes the deformation essence of material(or structure), and lay a foundation for theoretical research or engineering application.
引文
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[2]杨桂通.土动力学.北京：中国建材工业出版社,2000：92-134页
[3]Bishop R.F,Hill R,Mott N.F.The theory of indentation and hardness.Test.Proc. Phys.Soc.1945,57(3):147-159P
[4]Satapathy S.Dynamic spherical cavity expansion in brittle ceramics International Journal of Solids and Structures.38(2001):5833-5845P
[5]Satapathy S,Blss S.J.Cavity expansion resistance of in brittle materials obeying a two curve pressure-shear behavior.J.Appl.Phys.2000,88(7):4004-4012P
[6]陈颙,黄庭芳.岩石物理学.北京：北京大学出版社,2001
[7]Carroll M.M.Radial expansion of hollow spheres of elastic-plastic hardening material.Appl.Mech.Rew.1985,38(10):1256-1260P
[8]Collins I.F.Elastic/Plastic models for Soils and Sands.IntJ.of Mechanical Sciences.2005,Vol.47:493-508P
[9]Collins I.F,Hilder T.A Theoretical framework for construction elastic/plastic constitutive models for fraxial tests.Int.J.of Numerical and Analytical Methods in Geomechanics.2002,Vol.26:1313-1347P
[10]Lubarda V.A.Elasto-plasticity theory.CRC Press LLC,2002
[11]王仁,黄可智,朱兆祥.塑性力学进展.北京：中国铁道出版社,1988
[12]陈惠发.土木工程材料的本构关系(塑性与建模).武汉：华中科技大学出版社,2001
[13]陈惠发,萨里普遍A F.混凝土和土的本构关系.北京：中国建筑工业出版社,2004
[14]张学言.岩土塑性力学基础.天津：天津大学出版社,2004
[15]余寿文,冯西桥.损伤力学.北京：清华大学出版社,1997
[16]卡恰诺夫L.M.连续介质损伤力学.哈尔滨：哈尔滨工业大学出社,1989
[17]Duva J.M,Hutchinson J.W.Constitutive potentials for dilutely voided nonlinear materials.Mech Mater.1984(3):41-54P
[18]Mura T.Miero mechanics of Defects in Solids.Martinus Nijhoff Publishers,1987
[19]Leblond J.B,Perrin G.Theoretical models for void coalescence in porous ductile solids.Int.J.Solids Struct.2001,Vol.(32):5581-5604P
[20]俞茂宏.强度理论百年总结.力学进展.2004,34(4)：529-56()页
[21]Sturmer G.S, Schulz A,Wittig S. Life time prediction for ceramic gas turbine components.1991,ASME-Paper.No 91,GT-96P
[22]Wilson C.D.A critical reexamination of classical metal plasticity.J.Applied Mechanics.2002,69:63-68P
[23]Drucker D.C,Prager W.J.Soil mechanics and plastic analysis or limit design. Quat.of Appl.Math.1952,Vol.10:157-165P
[24]Morris A.P,Ferrill D.A.The importance of the effective intermediate principal stree(σ2)to fault slip patterns. Journal of Structure Geologe.2008,30(1):1-10P
[25]Tschoegl N.W.Failure Surfaces in Principal Stress Space.J.of Polymer Sci.Sym.1971,Vol.32:239-267P
[26]唐立强,田德谟.一个压力敏感材料的本构方程.哈尔滨船舶工程学院学报.1994,15(1)：6-12页
[27]Chandler H.W.Homogeneous and localized deformation in granular materials:A mechanistic model.Int.J.Eng.Sci.1990,28(8):719-134 P
[28]Deshpande V.S,Fleck N.A.Isotropic constitutive models for metallic foams,Journal of the Mechanics and Physics of Solids,2000,48:1253-1283P
[29]Gioux G, McCormack T.M,Gibson L.J.Failure of aluminum foams under multiaxial loads.International Journal of Mechanical Sciences,2000, 42:1097-1117P
[30]黄克智,萧纪美.材料的损伤断裂机理和宏微观力学理论.北京：清华大 学出版社,1999：62-85页
[31]卡恰诺夫LM.连续介质损伤力学.哈尔滨：哈尔滨工业大学出社,1989.
[32]Rabotnov Y.N.Creep problems in structural members.North-Holland. Amsterdam.1969
[33]Lemaitre J.Chaboche J.L.Aspect phenomenologique de la rupture par endommagemeat.J.Meca.Appl.1978,2(3):317-365P
[34]Cheboche J.L.and Rousselier G.On the plasticand viscoplastiec constitutive equation-PartⅠ:Rules developed with internal variable concept; Partll: Application of internal variable concepts to the 316 stainless steel.Journal of Pressure Vessel Technology.1983,(105):153-158P,159-164P
[35]Krajcinovic D. Continuum damage mechanics.J. Appl. Mech. Reviews. 1884,37(1):1-6P
[36]Lemaitre J,Chaboche J L. Mechanics of solid materials. Cambridge: Cambridge University Press,1988
[37]Krajcinovic D,Fonseka G. U.The continuous damage theory of brittle materials.Part1:general theory.J.Appl.Mech.1981,48:809-815P
[38]Whitmen L.Int.J.Numerical Analy.Methods Geomech.1985,9-71P
[39]Budiansky B,Hutchinson J.W, Slutsky S.Void growth and collapse in viscous solids.Mechanics of solids.The Rodney Hill 60th Anniversary Volume, eds. Hopkins.H.G,Selvell M.J.I982
[40]Murakami S, Ohno N. A continuum theory of creep and creep damage.In:Ponter A R S,Hayhurst D.R.ed,Proceedings of 3rd IUTAM symposium on creep in structures.Berlin Springe-Verlag,1980:422-443P
[41]Sidoroff F.Description of anisotropic damage application to elasticity in Proc.Of IUTAM colloquium.Physical Nonlinearities in Strnctural Analysis. 1981:237-244P
[42]王自强,段祝平.塑性细观力学.北京：科学出版社,1995
[43]Eshelby.J.D.The determination of the elastic field of an ellipsoidal inclusion and related problems.Proc. Roy. Soc. London: A241,1957:376-396P
[44]Eshelby. J.D, Elastic inclusion and inhomogeneities In"Progress on Solid Mechanics, Ⅱ".North-Holland: Publ,1961
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