材料构型力学及其在复杂缺陷系统中的应用

李群

doi:10.6052/0459-1879-14-240

材料构型力学及其在复杂缺陷系统中的应用

doi: 10.6052/0459-1879-14-240

李群^,

西安交通大学航天航空学院, 机械结构强度与振动国家重点实验室, 西安710049

基金项目: 国家自然科学基金项目(11472205, 11202156, 11321062, 11172228) 和德国洪堡基金项目资助.

详细信息

通讯作者:
李群,副教授,主要研究方向:材料构型力学,断裂与损伤力学.E-mail:qunli@mail.xjtu.edu.cn

中图分类号: O346.1
计量
- 文章访问数: 1649
- HTML全文浏览量: 53
- PDF下载量: 2265
- 被引次数: 0
出版历程
- 收稿日期: 2014-08-18
- 修回日期: 2014-09-29
- 刊出日期: 2015-03-18

MATERIAL CONFIGURATIONAL MECHANICS WITHAPPLICATION TO COMPLEX DEFECTS

Li Qun^,

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China

Funds: The project was supported by the National Natural Science Foundation of China (11202156, 11321062, 11172228, 10932007) and Alexander von Humboldt Foundation in Germany.

摘要

摘要: 基于材料构型力学描述复杂缺陷力学系统中的破坏行为, 可以为预测材料临界失效载荷和评估结构完整性提供新的思路. 首先, 通过对拉格朗日能量密度函数的梯度、散度、旋度操作分别获取3 类材料构型应力张量的定义式、平衡方程、物理意义以及其对应的守恒积分表达式. 其次, 基于材料构型力学概念建立描述材料屈服的屈服准则、预测裂纹起裂的断裂准则、以及评估复杂缺陷系统最终失效的破坏准则. 然后, 利用数字散斑图像相关技术, 开发材料构型力学相关参量的无损测量方法. 最后, 将材料构型力学概念应用于纳米损伤力学和铁电多晶材料的断裂力学中, 为此类新型材料的损伤水平评估提供理论支撑.
- 材料构型力学 /
- 复杂缺陷 /
- 断裂 /
- 铁电 /
- 纳米
Abstract: Material configurational mechanics with application to describe the failure behavior of complex defects does provide an innovative way to predict the failure criteria load and assess the integrity of structures. First, the definitions of material configurational stress as well as the equilibrium equation, physical meaning, and the corresponding invariant integrals are obtained by the gradient, divergence, and curl operation of the Lagrangian function, respectively. Second, the material yielding, fracture, and final failure criteria are newly proposed within the frame of material configurational mechanics. Next, the proposed experimental technique provides an effective and convenient tool to evaluate the material configurational quantities by Digital Image Correlation. Finally, the concept of material configurational mechanics is used to evaluate the damage level of functional materials or structures, such as nano material and ferroelectrics.
- material configurational mechanics /
- complex defects /
- fracture /
- ferroelectrics /
- nano material

HTML全文

参考文献(81)

Griffith A A. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London, Series A, 1921, 221: 163-197

Irwin G R. Analysis of stresses and strains near the end of a crack traversing a plate. ASME Journal of Applied Mechanics, 1957, 24: 361-364

Sih G C. Method of analysis and solutions of crack problems. Noordhoff 1973

Orowan E. Energy criteria of fracture. Welding Journal, 1955, 34: 1575-1605

Irwin G R. Plastic zone near a crack tip and fracture toughness. In: Proc. 7th Sagamore Conference 1960, IV-63

Dugdale D S. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8: 100-108

Wells A A. Unstable crack propagation in metals cleavage and fast fracture. Proceedings of the Crack Propagation Symposium, 1961, 1: 210-230

Rice J R. A path independent integral and the approximate analysis of strain concentration by notch and cracks. ASME Journal of Applied Mechanics, 1968, 35: 379-386

Cherepanov G P. The propagation of cracks in a continuous medium. Journal of Applied Mathematics and Mechanics, 1967, 31: 503-512

Begley J A, Landes J D. The J-integral as a fracture criterion. Fracture Toughness. In: Proceedings of the 1971 National Symposium on Fracture Mechanics Part II, ASTM STP 514, American Society for Testing and Materials, 1972, 514: 1-26

Kachanov L M. Time of rupture process under creep conditions. Izvestia Akademii Nauk, USSR 1958, 8: 26-31

Kachanov L M. Introduction to Continuum Damage Mechanics. Martinus Nijhoff Publishers, 1986

Bazant Z. Why continuum damage is nonlocal: Micromechanics arguments. Journal of Engineering Mechanics, 1991, 117: 1070-1087

Maugin G A. Material Inhomogeneities in Elasticity. London: Chapman Hall 1993.

Kienzler R, Herrmann, G. Mechanics of Material Space: With Applications to Defect and Fracture Mechanics. Berlin: Springer, 2000

Gurtin M E. Configurational Forces as Basic Concepts of Continuum Physics. Berlin: Springer, 2000

Chen Y H. Advances in Conservation Laws and Energy Release Rates. The Netherlands: Kluwer Academic Publishers, 2002

Eshelby J D. The Force on an Elastic Singularity. Philosophical Transactions of the Royal Society of London, Series A, 1951, 244: 87-112

Eshelby J D. The continuum theory of lattice defects. Solid State Physics, 1956, 3: 79-144

Eshelby J D. Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics. New York: McGraw-Hill, 1970

Eshelby J D. The elastic energy-momentum tensor. Journal of Elasticity, 1975, 5: 321-335

Knowles J K, Sternberg E. On a class of conservation laws in linearized and finite elastostatics. Archive for Rational Mechanics and Analysis, 1972, 44: 187-211

Noether E. Invariante variationsprobleme. Nuchrichten van der Gesellschaft der Wissenschuften zu Göttingen Mathematisch-physikalische Klasse, 1918, 2: 235 Nuchrichten van der Gesellschaft der Wissenschuften zu G">

Budiansky B, Rice J R. Conservation laws and energy release rates. ASME Journal of Applied Mechanics, 1973, 40: 201-203

Kanninen M F, Poplar C F. Advanced Fracture Mechanics. New York: Oxford University Press, 1985

Herrmann A G, Herrmann G. On energy-release rates for a plane crack. Journal of Applied Mechanics, 1981, 48: 525-530

Chen Y Z. A survey of new integral equations in plane elasticity crack problem. Engineering Fracture Mechanics, 1995, 51: 97-134

Gurtin M E, Podio-Guidugli P. Configurational forces and the basic laws for crack propagation. Journal of the Mechanics and Physics of Solids, 1996, 44: 905-927

Gurtin M E, Shvartsman M M. Configurational forces and the dynamics of planar cracks in three-dimensional bodies. Journal of Elasticity, 1997, 48: 167-191

Steinmann P. Application of material forces to hyper-elastostatic fracture mechanics. I. Continuum mechanical setting. International Journal of Solids and Structures, 2000, 37: 7371-7391

Steinmann P, Ackermann D, Barth F J. Application of material forces to hyper- elastostatic fracture mechanics. II. Computational setting. International Journal of Solids and Structures, 2001, 38: 5509-5526

Kienzler R, Herrmann G. On the properties of the Eshelby tensor. Acta Mechanica, 1997, 125: 73-91

Kienzler R, Herrmann G. Fracture criteria based on local properties of the Eshelby tensor. Mechanics Research Communications, 2002, 29: 521-527

Larsson R, Fagerström M. A framework for fracture modeling based on the material forces concept with XFEM kinematics. International Journal for Numerical Methods in Engineering, 2005, 62: 1763-1788

Mueller R, Maugin G A. On material forces and finite element discretizations. Computational Mechanics 2002, 29: 52-60

Mueller R, Kolling S, Gross D. On configurational forces in the context of the finite element method. International Journal for Numerical Methods in Engineering, 2002, 53: 1557-1574

Liebe T, Denzer R, Steinmann P. Application of the material force method to isotropic continuum damage. Computational Mechanics, 2003, 30: 171-184

Chen Y Z. Analysis of L-integral and theory of the derivative stress field in plane elasticity. International Journal of Solids and Structures, 2003, 40: 3589-3602

Chen Y Z, Hasebe N, Lee K Y. Multiple Crack Problems in Elasticity. Southampton: WIT Press, 2003

Simha N K, Fischer F D, Kolednik O, et al. Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials. Journal of the Mechanics and Physics of Solids, 2003, 51: 209-240

Chen Y Z, Lee K Y. Analysis of the M-integral in plane elasticity. ASME Journal of Applied Mechanics, 2004, 71: 572-574

Mueller R, Gross D, Maugin G A. Use of material forces in adaptive finite element methods. Computational Mechanics, 2004, 33: 421-434

Nguyen T D, Govindjee S, Klein P A, et al. A material force method for inelastic fracture mechanics. Journal of the Mechanics and Physics of Solids, 2005, 53: 91-121

Fagerström M, Larsson R. Approaches to dynamic fracture modeling at finite deformations. Journal of the Mechanics and Physics of Solids, 2008, 56: 613-639

Agiasofitou E K, Kalpakides V K. The concept of balance law for a cracked elastic body and the configurational force and moment at the crack tip. International Journal of Engineering Science, 2006, 44: 127-139

Lubarda V, Markenscoff X. Complementary energy release rates and dual conservation integrals in micropolar elasticity. Journal of the Mechanics and Physics of Solids, 2007, 55: 2055-2072

Li Q, Chen Y H. Inherent relations between the Bueckner integral and the Jk-integral or the M-integral in multi-defects damaged piezoelectric materials. Acta Mechanica, 2009, 204: 125-136

Xu B X, Schrade D, Mueller R, et al. Micromechanical analysis of ferroelectric structures by a phase field method. Computation Materials Science, 2009, 45: 832-836

Yu N Y, Li Q. Failure theory via the concept of material configurational forces associated with the M-integral. International Journal of Solids and Structures, 2013, 50: 4320-4332

贺启林. 基于J积分和构型力理论的材料断裂行为研究. 哈尔滨: 哈尔滨工业大学, 2010 (He Qilin. Study of Material Fracture Behavior Based on J-integral and Configurational Force Theory. Harbin: Harbin Institute of Technology, 2010 (in Chinese))

周荣欣. 裂纹与夹杂之间的构型力及II型裂纹裂尖塑性区的屏蔽效应. 上海: 上海交通大学, 2012 (Zhou Rongxin. The Configuration Force Between Crack and Inclusion & the Shielding Effects of Plastic Zone at Mode II Crack Tip. Shanghai: Shanghai Jiao Tong University, 2012 (in Chinese))

Li Q, Chen Y H. Surface effect and size dependent on the energy release due to a nanosized hole expansion in plane elastic materials. ASME Journal of Applied Mechanics, 2008, 75: 061008

Hui T, Chen Y H. The M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. ASME Journal of Applied Mechanics, 2010, 77: 021019

Hui T, Chen Y H. Two state M-integral analyses for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. ASME Journal of Applied Mechanics, 2010, 77: 024505

Li Q, Kuna M. Evaluation of electromechanical fracture behavior by configurational forces in cracked ferroelectric polycrystals. Computational Materials Science, 2012, 57: 94-101

Li Q, Kuna M. Inhomogeneity and material configurational forces in three dimensional ferroelectric polycrystals. European Journal of Mechanics A/Solids, 2012, 31: 77-89

Li Z, Yang L. The application of the Eshelby equivalent inclusion method for unifying modulus and transformation toughening. International Journal of Solids and Structure, 2002, 39: 5225-5240

Li Z, Chen Q. Crack-inclusion for mode-I crack analyzed by Eshelby equivalent inclusion method. International Journal of Fracture 2002, 118: 29-40

Yang L, Chen Q, Li Z. Crack-inclusion interaction for mode-II crack analyzed by Eshelby equivalent inclusion method. Engineering Fracture Mechanics, 2004, 71: 1421-1433

Zhou R, Li Z, Sun J. Crack deflection and interface debonding in composite materials elucidated by the configuration force theory. Composites Part B: Engineering, 2011, 42: 1999-2003

Chen Y H. M-integral analysis for two-dimensional solids with strongly interacting microcracks. Part 1: In an infinite brittle solid. International Journal of Solids and Structures, 2001, 38: 3193-3212

Chen Y H. M-integral analysis for two-dimensional solids with strongly interacting microcracks. Part 2: In the brittle phase of an infinite metal/ceramic bimaterial. International Journal of Solids and Structures, 2001, 38: 3213-3232

Ma L F, Chen Y H, Liu C S. On the relation between the M-integral and the change of the total potential energy in damaged brittle solids. Acta Mechanica, 2001, 150: 79-85

Chang J H, Chien A J. Evaluation of M-integral for anisotropic elastic media with multiple defects. International Journal of Fracture, 2002, 114: 267-289

Chang J H, Peng D J. Use of M integral for rubbery material problems containing multiple defects. Journal of Engineering Mechanics, 2004, 130: 589-598

Chang J H, Wu W H. Using M-integral for multi-cracked problems subjected to nonconservative and nonuniform crack surface tractions. International Journal of Solid and Structure, 2011, 48: 2605-2613

Wang F W, Chen Y H. Fatigue damage driving force based on the M-integral concept. Procedia Engineering, 2010, 2: 231-239

Eischen J, Herrmann G. Energy release rates and related balance laws in linear elastic defect mechanics. Journal of Applied Mechanics, 1987, 54: 388-392

Li Q, Hu Y F, Chen Y H. On the physical interpretation of the M-integral in nonlinear elastic defect mechanics. International Journal of Damage Mechanics 2012, 22: 602-613

Guo Y L, Li Q. On some fundamental properties of the L-integral in plane elasticity, Acta Mechanica, 2014, DOI 10.1007/s00707-014-1152-y

Lü J N, Li Q. The newly proposed yielding and fracture criteria by the material configurational stress tensor. Submitted, 2014

于宁宇, 李群. M 积分与夹杂/缺陷弹性模量的显式关系. 力学学报 2014, 46: 87-93 (Yu Ningyu, Li Qun. The explicit relation between the M-integral and the elastic moduli of inclusion/damages. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46: 87-93 (in Chinese))

King R, Herrmann G. Nondestructive evaluation of the J and M integrals. ASME Journal of Applied Mechanics, 1981, 48: 83-87

Yu N Y, Li Q, Chen Y H. Measurement of the M-integral for a hole in an aluminum plate or strip. Experimental Mechanics, 2012, 52: 855-863

Yu N Y, Li Q, Chen Y H. Experimental evaluation of the M-integral in an elastic-plastic material containing multiple defects. ASME Journal of Applied Mechanics, 2013, 80: 011021

于宁宇, 李群. 基于数字散斑相关实验测量的材料构型力的计算方法. 实验力学 2014, DOI:10.7520/1001-4888-13-132 (Yu Ningyu, Li Qun. On the algorithm of material configurational force based on digital image correlation measurement. Journal of Experimental Mechanics, 2014, DOI:10.7520/1001-4888-13-132 (in Chinese))

Hu Y F, Li Q, Shi J P, et al. Surface/interface effect and size/configuration dependence on the energy release in nanoporous membrane. Journal of Applied Physics, 2012, 112: 034302

Pan S X, Hu Y F, Li Q. Numerical simulation of mechanical properties in nanoporous membrane. Computational Materials Science, 2013, 79: 611-618

Gurtin M E, Murdoch A I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 1975, 57: 291-323

Mogilevskaya S G, Crouch S L, Stolarski H K. Multiple interacting circular nano-inhomogeneities with surface/interface effects. Journal of the Mechanics and Physics of Solids, 2008, 56: 2298-2327

Huber J E, Fleck N A, Landis C M, et al. A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids, 1999, 47: 1663-1697

施引文献

资源附件(0)

访问统计