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非均匀材料断裂力学(英文版) 版权信息
- ISBN：9787030700711
- 条形码：9787030700711 ; 978-7-03-070071-1
- 装帧：一般胶版纸
- 册数：暂无
- 重量：暂无
- 所属分类：>
非均匀材料断裂力学(英文版) 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。
非均匀材料断裂力学(英文版) 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。
非均匀材料断裂力学(英文版) 目录
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
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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非均匀材料断裂力学(英文版) 节选
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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