非均匀材料断裂力学(英文版)

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作者：果立成，于红军，吴林志

出版社：科学出版社

本类榜单：自然科学

分类：自然科学 > 物理学

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ISBN：9787030700711
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：B5
页数：356
出版时间：2022-10-01
条形码：9787030700711 ; 978-7-03-070071-1

本书特色

该书完善了模型建立的思想体系，阐明了区域无关积分模型对材料界面具有区域无关性的根源。

内容简介

本书剖析非均匀材料断裂特性、理论模型及仿真方法，从基础理论到仿真方法多个层面提出了饶有特色的研究和工作思路。**章分析非均匀材料裂纹很好场特点，阐明材料非均匀性对材料裂纹很好场的影响机制；第二至四章提出一般属性梯度功能材料（非均匀材料）的断裂难题，拓展并完善非均质材料断裂力学的理论体系；第五至七章提出区域无关积分（DII积分）方法，去除传统断裂力学模型对材料属性连续性要求，提出设计区域无关积分的理论框架，解决长期以来阻碍含复杂界面非均匀材料断裂力学研究发展的根本问题，拓展断裂力学方法研究范围。该书完善了模型建立的思想体系，阐明了区域无关积分模型对材料界面具有区域无关性的根源。

目录
Contents
Preface
Chapter 1　Fundamental theory of fracture mechanics of nonhomogeneous
materials　1
1.1　Internal crack　2
1.1.1　Basic equations for nonhomogeneous materials　2
1.1.2　Crack-tip fields for homogeneous materials　3
1.1.3　Crack-tip fields for nonhomogeneous materials　6
1.1.4　Crack-tip fields for nonhomogeneous orthotropic materials　12
1.2　Interface crack　14
1.2.1　Crack-tip fields of an interface crack　14
1.2.2　Crack-tip fields of an interface crack between two nonhomogeneous media　19
1.3　Three-dimensional curved crack　23
1.3.1　Internal crack　23
1.3.2　Interface crack　25
References　26
Chapter 2　Exponential models for crack problems in nonhomogeneous materials　28
2.1　Crack model for nonhomogeneous materials with an arbitrarily oriented crack　29
2.1.1　Basic equations and boundary conditions　29
2.1.2　Full field solution for a crack in the nonhomogeneous medium　31
2.1.3　Stress intensity factors (SIFs) and strain energy release rate (SERR)　36
2.2　Crack problems in nonhomogeneous coating-substrate or double-layered structures　38
2.2.1　Interface crack in nonhomogeneous coating-substrate structures　38
2.2.2　Cross -interface crack parallel to the gradient of material properties　45
2.2.3　Arbitrarily oriented crack in a double-layered structure　54
2.3　Crack problems in orthotropic nonhomogeneous materials　69
2.3.1　Basic equations and boundary conditions　69
2.3.2　Solutions to stress and displacement fields　71
2.3.3　Crack-tip SIFs　77
2.4　Transient crack problem of a coating-substrate structure　78
2.4.1　Basic equations and boundary conditions　78
2.4.2　Solutions to stress and displacement fields　79
2.4.3　Crack-tip SIFs　84
2.5　Representative examples　85
2.5.1　Example 1: Arbitrarily oriented crack in an infinite nonhomogeneous medium　85
2.5.2　Example 2: Interface crack between the coating and the substrate　88
2.5.3　Example 3: Crossing-interface crack perpendicular to the interface in a double-layered structure　89
2.5.4　Example 4: Inclined crack crossing the interface　94
2.5.5　Example 5: Vertical crack in a nonhomogeneous coating-substrate structure subjected to impact loading　96
Appendix 2A　98
References　99
Chapter 3　General model for nonhomogeneous materials with general elastic properties　101
3.1　Piecewise-exponential model for the mode I crack problem　102
3.1.1　Piecewise-exponential model (PE model)　102
3.1.2　Solutions to stress and displacement fields　105
3.1.3　Crack-tip SIFs　111
3.2　PE model for mixed-mode crack problem　112
3.2.1　Basic equations and boundary conditions　112
3.2.2　Solutions to stress and displacement fields　114
3.2.3　Crack-tip SIFs　119
3.3　PE model for dynamic crack problem　119
3.3.1　Basic equations and boundary conditions　119
3.3.2　Solutions to stress and displacement fields　123
3.3.3　Crack-tip SIFs　126
3.4　Representative examples　127
3.4.1　Example 1: Mode I crack problem for nonhomogeneous materials with general elastic properties　127
3.4.2　Example 2: Mixed-mode crack problem for nonhomogeneous materials with general elastic properties and an arbitrarily oriented crack　134
3.4.3　Example 3: Dynamic Mode I crack problem for nonhomogeneous materials with general elastic properties　139
Appendix 3A　145
References　151
Chapter 4　Fracture mechanics of nonhomogeneous materials based on piecewise-exponential model　153
4.1　Thermomechanical crack models of nonhomogeneous materials　154
4.1.1　Crack model for nonhomogeneous materials under steady thermal loads　154
4.1.2　Crack model for nonhomogeneous materials under thermal shock load　157
4.2　Viscoelastic crack model of nonhomogeneous materials　170
4.2.1　The correspondence principle for viscoelastic FGMs　170
4.2.2　Viscoelastic models for nonhomogeneous materials　173
4.2.3　PE model for the viscoelastic nonhomogeneous materials　174
4.3　Crack model for nonhomogeneous materials with stochastic properties　177
4.3.1　Stochastic micromechanics-based model for effective properties　177
4.3.2　Probabilistic characteristics of effective properties at transition region　182
4.3.3　Crack in nonhomogeneous materials with stochastic mechanical properties　183
4.4　Examples　188
4.4.1　Example 1: Steady thermomechanical crack problem　188
4.4.2　Example 2: Viscoelastic crack problem　195
4.4.3　Example 3: Crack problem in FGMs with stochastic mechanical properties　198
References　202
Chapter 5　Fracture of nonhomogeneous materials with complex interfaces　205
5.1　Interaction integral (I-integral)　207
5.1.1　J-integral　207
5.1.2　I-integral　208
5.1.3　Auxiliary field　208
5.1.4　Extraction of the SIFs　210
5.2　Domain-independent I-integral (DII-integral)　211
5.2.1　Domain form of the I-integral　211
5.2.2　DII-integral　214
5.3　DII-integral for orthotropic materials　220
5.4　Consideration of dynamic process　223
5.5　Calculation of the T-st

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Chapter 1 Fundamental theory of fracture mechanics of nonhomogeneous materials Nonhomogeneous materials either exist naturally or are used intentionally to attain a required structural performance， such as bones， bamboo， shells，masonry composed of crushed stone， particulate composite materials， fiber-reinforced composite materials， etc. Nonhomogeneous materials are usually formed of two or more constituent phases with a variable composition， and they are prone to crack propagation during use which is due to the defects (holes， microcracks， debonding) introduced during manufacturing process. In recent decades，studies on fracture mechanics of nonhomoeneous materials have been carried out to ensure their reliable applications. To facilitate theoretical analysis，the interfaces between components are ignored， and the nonhomogeneous material is equivalent to a material with continuous macroscopic properties. This approach has been widely used in the fracture mechanics analysis of nonhomogeneous in the past few decades. Recently， due to the rapid development of computer technology，the real properties of components and interface conditions between components have been considered. This chapter will show the images of the near-tip field of a crack in nonhomogeneous material. Please note that throughout this book， an interface crack refers to the crack located along the interface between two neighboring materials while an internal crack refers to the crack with two surfaces located in the same materials. In addition，an embedded crack means that the crack is completely in a body， while an edge crack means that the crack intersects with the edge of the body. As a result，an embedded crack has two tips， while an edge crack has only one tip in the two-dimensional case. 1.1 Internal crack 1.1.1 Basic equations for nonhomogeneous materials A distinctive feature of nonhomogeneous materials is that the material parameters vary with coordinates. Taking an isotropic nonhomogeneous material as an example， the Young’s modulus E and Poisson’s ratio v need to be expressed respectively as E = E(x)， v = v(x) (1.1) where jc denotes the coordinate vector， which is given by. The readers should remember the Eq. (1.1) firmly for nonhomogeneous materials. That is， even if only a single symbol E appears in some expression， it is usually not a constant but a function E(x) for nonhomogeneous materials. This is very important in the following study on nonhomogeneous materials. Then， the constitutive equation for the isotropic nonhomogeneous material is given in polar coordinate system by (1-2) where eap and aap represent the components of strain and stress， respectively，is the shear modulus， and fc(x) is the Kolosov constant defined by following formula: The symbol 8ap is the Kronecker delta function and given by In addition， the elastic fields need to satisfy the strain-displacement relations: (1.3) and the equilibrium equations: (1.4) This chapter will discuss the crack-tip fields in this frame. 1.1.2 Crack-tip fields for homogeneous materials For an internal crack in a homogeneous elastic solid， the stress has a singularity of r~in， as shown in Fig. 1.1， where r represents the distance from the current point to the crack tip. As r tends to be zero， the stress tends to be infinite. Williams (1957) first provided the crack-tip fields by using the eigenfunction expansion technique. The near-tip displacements and stresses of a two-dimensional internal crack are given by (1.5) (1.6) The parameter V2ttt and llnr are mode-I and mode- II stress intensity factors (SIFs)，showing tensile and shear effects near the crack tip. Generally， the stress intensity factor depends on the material properties， geometry and loading conditions. T represents the constant term of the stress crn ， known as the T-stress. The angular functions of the stress and displacement are given by (Gdoutos，2005) (1.7) (1.8) In order to give readers an intuitive impression of stress distributions with respect to the angle 0， Fig. 1.2 provides the stress angular functions in Eq. (1.7). Here， the angular function can be regarded as the stresses on the circle of ，II denote opening and sliding crack modes， respectively. 1.1.3 Crack-tip fields for nonhomogeneous materials Eischen (1987) extended the eigenfunction expansion technique to derive the crack-tip fields of nonhomogeneous materials with continuously differentiable properties. For a traction-free crack， the stress equilibrium equations are satisfied identically by an Airy stress function as (1.9) (1.10) one obtains the following equation governing the stress function for generalized plane stress condition (Eischen， 1987):

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