Fracture analysis and improved design for a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties

The mechanical model was established for the anti-plane interfacial fracture problem of a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties. The system of Cauchy singular integral equations for the interfacial crack was derived by Fourier integral transform. The numerical solutions of the Cauchy singular integral equations were obtained by the Lobatto-Chebyshev collocation method put up by Erdogan and Gupta. The mechanical strain energy release rate and the total energy release rate were chosen as fracture parameters to discuss the effect of the non-homogeneity parameter on the extension force of the crack. A conclusion was drawn that, to reduce the weak-discontinuity of the interface in the magnetoelectroelastic structure would be beneficial to decrease the extension force of the interfacial crack. Based on this conclusion, a new improved design was suggested for the symmetrically bonded linearly non-homogeneous magnetoelectroelastic composite. The enhancement of the capability of the improved structure to resist interfacial fracture was validated by comparison between the improved and unimproved structures for their fracture responses.     

An anti-plane crack perpendicular to the weak/micro-discontinuous interface in a bi-FGM structure with exponential and linear non-homogeneities

Treated was an anti-plane crack perpendicular to the interface of an exponential-type FGM strip bonded to another linear-type FGM substrate with infinite thickness. Through Fourier integral transform, the problem was reduced as a Cauchy singular integral equation, which was further solved numerically by the Lobatto–Chebyshev collocation method. Based on the numerical solution, the effects of the geometrical and physical parameters on the stress intensity factor (SIF) were analyzed and the following conclusions were obtained: (a) A notable discrepancy between the interface-perpendicular crack and the interfacial one is that, to reduce the weak-discontinuity of interface or to make the interface micro-discontinuous will not necessarily decrease the SIF of the former, but will surely decrease that of the latter. (b) When a crack tip is situated very near to the interface (or free surface), its SIF will be high and totally dominated by the interface (or free surface). (c) To increase the stiffness of the FGM on one side of the interface is beneficial to preventing the crack on the other side from growing toward the interface. Besides, some practical suggestions were further given for material design in the field of composites.     

One-Dimensional Transient Dynamic Response in Functionally Graded Layered Media

In this study, one-dimensional transient wave propagation in multilayered functionally graded media is investigated. The multilayered medium consists of N different layers of functionally graded materials (FGMs), i.e., it is assumed that the stiffness and the density of each layer are varying continuously in the direction perpendicular to the layering, but isotropic and homogeneous in the other two directions. The top surface of the layered medium is subjected to a uniform dynamic in-plane time-dependent normal stress; whereas, the lower surface of the layered medium is assumed free of surface tractions or fixed. Moreover, the multilayered medium is assumed to be initially at rest and its layers are assumed to be perfectly bonded to each other. The method of characteristics is employed to obtain the solutions of this initial-boundary-value problem. The numerical results are obtained and displayed in curves showing the variation of the normal stress component with time. These curves reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers. The curves also display the effects of non-homogeneity in the wave profiles. The curves further show that the numerical technique applied in this study is capable of predicting the sharp variations in the field variables in the neighborhood of the wave fronts. By suitably adjusting the material constants, solutions for the case of isotropic, homogeneous and linearly elastic multilayered media and for some special cases including two different functionally graded layers are also obtained. Furthermore, solutions for some special cases are compared with the existing solutions in the literature; very good agreement is found.     

A model for interface cracks in layered orthotropic solids: Convergence of modal decomposition using the interaction integral method

The mode‐partitioning problem for bimaterial interfaces is still not resolved by the classical fracture mechanics approach in a satisfactory manner. Stress oscillations and overlapping crack faces are a direct consequence of the rigorous solution of the elastic boundary value problem, if the constitutive law changes discontinuously across the interface. Conversely, continuously varying material properties, also referred to as functionally graded materials (FGM), avoid these physically not admissible drawbacks. In this case the crack tip fields are of the same nature as those known from homogeneous materials. Therefore, the well‐established stress intensity factor concept can be used without any changes. Following this motivation an FGM‐interface model for delaminated composite beam structures was developed and its characteristics with respect to the modal decomposition of the crack tip fields were investigated. The considered beam structures consisted of two orthotropic layers, each of a different material. The spatial variation of the material properties in the interface region was modeled by a tanh ‐function introducing one transition parameter that controlled the FGM‐gradient. Four load cases were analyzed for each structural configuration: either a unit normal force or a unit bending moment was imposed on each end of the split beam. Thus, any load case can be simply reconstructed from the presented results by means of superposition. The stress intensity factors for modes I and II were then evaluated using an interaction integral method along with the finite element method. The corresponding results are given depending on the mesh density of the interface region, the integration domain and the transition parameter. In this manner, the influence of the transition parameter on the mode ratio and on the convergence behavior of the modal decomposition scheme with respect to its integration domain was identified. Finally, the ability of the FGM‐interface model to represent bimaterial interfaces while still maintaining the advantages of crack analysis in homogeneous materials was highlighted. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of higher-order interface stresses on the elastic states of two-dimensional composites

We propose a simple model to simulate higher-order interface stresses along the interface between two neighboring media in two dimensions. The interface behavior is modeled from a thin interphase of constant thickness by taking a proper limit process. In the formulation the deformation of the thin interphase is approximated by the Kirchhoff-Love assumption of thin shell. To incorporate the higher-order interface stresses, we consider the bending effects resulting from the non-uniform surface stress across the layer thickness. The stress equilibrium conditions is fulfilled by consideration of balance for forces as well as stress couples. Depending on the difference in stiffness and length scales of the interphase, we show that the interfaces can be classified into four different types. This findings, upon suitable definitions of material parameters, agree with a rigorous asymptotic analysis proposed by Benveniste and Miloh [Benveniste, Y., Miloh, T., 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33 309-323]. To illustrate the higher-order effects, we derive analytically the stress concentration factor of an infinite plate containing a circular cavity with interface stresses of different orders subjected to a remote transverse shear loading. The closed-form expressions show how the orders of interface stresses influence the concentration factor in a successive manner. In addition, we examine the effective shear modulus of composites with circular inclusions with higher-order interface effects. The effective transverse shear modulus is derived based on the generalized self-consistent method.     

Micromechanical modeling of interface damage of metal matrix composites subjected to transverse loading

A three-dimensional finite element micromechanical model was developed to study effects of thermal residual stress, fiber coating and interface bonding on the transverse behavior of a unidirectional SiC/Ti–6Al–4V metal matrix composite (MMC). The presented model includes three phases, i.e. the fiber, coating and matrix, and two distinct interfaces, one between the fiber and coating and the other between coating and matrix. The model can be employed to investigate effects of various bonding levels of the interfaces on the initiation of damage during transverse loading of the composite system. Two different failure criteria, which are combinations of normal and shear stresses across the interfaces, were used to predict the failure of the fiber/coating (f/c) and coating/matrix (c/m) interfaces. Any interface fails as soon as the stress level reaches the interfacial strength. It was shown that in comparison with other interface models the predicted stress–strain curve for damaged interface demonstrates good agreement with experimental results.     

Mesoscale models of interface mechanics in crystalline solids: a review

Theoretical and computational methods for representing mechanical behaviors of crystalline materials in the vicinity of planar interfaces are examined and compared. Emphasis is on continuum-type resolutions of microstructures at the nanometer and micrometer levels, i.e., mesoscale models. Grain boundary interfaces are considered first, with classes of models encompassing sharp interface, continuum defect (i.e., dislocation and disclination), and diffuse interface types. Twin boundaries are reviewed next, considering sharp interface and diffuse interface (e.g., phase field) models as well as pseudo-slip crystal plasticity approaches to deformation twinning. Several classes of models for evolving failure interfaces, i.e., fracture surfaces, in single crystals and polycrystals are then critically summarized, including cohesive zone approaches, continuum damage theories, and diffuse interface models. Important characteristics of compared classes of models for a given physical behavior include complexity, generality/flexibility, and predictive capability versus number of free or calibrated parameters.     

A fracture mechanics problem of a functionally graded layered structure with an arbitrarily oriented crack crossing the interface

In this paper, the fracture mechanics problem for an arbitrarily oriented crack crossing the interface in a functionally graded layered structure is investigated. The elastic modulus is assumed to be continuous at the interface, but its derivative may be discontinuous. Applying the superposition principle and Fourier integral transform, the stress fields and displacement fields are derived. A group of auxiliary functions defined in both layers are introduced and then the mixed-mode crack problem is turned into solving a group of singular integral equations. The mixed-mode stress intensity factors (SIFs) are obtained by solving the singular integral equations. The influences of the material nonhomogeneity parameter, normalized crack length and crack angle on the SIFs are investigated. It is found that the mixed-mode SIFs can be affected greatly by the crack angle. Moreover, the mixed-mode SIFs usually attain their extremum when the crack tips get to the interface during one crack moves from one layer into another layer. The present work may form the basic work for establishing a multi-layered fracture mechanics model of FGMs with an arbitrarily oriented crack and general mechanical properties.     

含不完美界面的磁电复合材料倾斜裂纹问题

研究了含非完美界面的双层压电/压磁复合材料中压电相存在一个倾斜于界面的Ⅲ型裂纹问题。采用弹簧型耦合界面模型模拟非完美界面,运用Fourier积分变换法将裂纹面条件转化为奇异积分方程,并使用Lobatto-Chebyshev方法数值求解了裂纹尖端应力强度因子（SIF）。详细地研究了裂纹尖端SIF与界面参数、压电/压磁材料参数和材料的层厚、裂纹的倾斜角、裂纹与界面的距离等几何参数的关系。结果表明：力学不完美性可以独立地增大SIF,而磁学、电学不完美性只有与力学不完美性耦合时才会减小SIF;力学-电学、力学-磁学不完美性的耦合会减小SIF,而磁学-电学不完美性的耦合不会影响SIF;磁场作用下,增大压磁层弹性模量会减小SIF,而增大压电层压电系数,减小压电层弹性模量和介电常数,均会减小SIF;界面不完美性会影响SIF随裂纹倾斜角度或裂纹与界面之间距离的变化规律;在一定范围内增加压电层或压磁层厚度可以减小SIF。     

Interaction integrals for thermal fracture of functionally graded materials

This paper addresses finite element evaluation of the non-singular T-stress and mixed-mode stress intensity factors in functionally graded materials (FGMs) under steady-state thermal loads by means of interaction integral. Interaction integral provides an accurate and efficient numerical framework in evaluating these fracture parameters in FGMs under thermal as well as mechanical loads. We use a non-equilibrium formulation and the corresponding auxiliary (secondary) fields tailored for FGMs. Graded finite elements have been developed to account for the spatial gradation of thermomechanical properties. This paper presents various numerical examples in which the accuracy of the present method is verified.     

3D crack analysis in functionally graded materials

Elastostatic crack analysis in three-dimensional, continuously non-homogeneous, isotropic and linear elastic functionally graded materials and structures is presented in this paper. A boundary-domain-integral equation formulation is applied for this purpose, which uses the elastostatic fundamental solutions for homogeneous, isotropic and linear elastic materials and involves a domain-integral due to the material’s non-homogeneity. To avoid displacement gradients in the domain-integral, normalized displacements are introduced. The domain-integral is transformed into boundary-integrals over the global boundary of the cracked solids by using the radial integration method. A meshless scheme is developed, which requires only the conventional boundary discretization and additional interior nodes instead of interior cells or meshes. Numerical examples for three-dimensional crack problems in continuously non-homogeneous, isotropic and linear elastic FGMs are presented and discussed, to show the effects of the material gradation on the crack-opening-displacements and the stress intensity factors.     

界面对颗粒增强金属基复合材料强化性能的影响

为提高颗粒增强金属基复合材料的力学性能,采用基于微观组织的胞元模型建模方法,并利用有限元软件ABAQUS着重分析了界面层厚度以及界面层强度对复合材料性能的影响,通过对复合材料中各组成部分的应力、应变云图的获取,形象地说明了各部分的变形规律.研究结果表明,在弱界面层下,随着界面层厚度的增加,复合材料的强化效果并不显著,而在强界面层下,随着界面层厚度的增加,强化效果非常明显;就界面层强度来说,界面越强,所表现出的强化效果就越明显,但当界面层强度比基体大得多时,随着界面层强度的增加,虽然复合材料的强化呈递增趋势,但是递增的幅度已逐渐降低.     

高温下短纤维增强金属基复合材料界面的微观结构和热残余应力状态研究

利用透射电镜观察了δ-Al₂O₃短纤维增强Al-5.5Mg合金复合材料界面在不同环境温度下的微观结构特征。 同时, 基于该类复合材料的单纤维模型, 利用弹塑性有限元分析方法, 研究了在不同温度下界面热残余应力的大小和分布情况, 并讨论了热残余应力对界面行为的影响。 最后, 讨论了界面的微观结构和热残余应力特征对复合材料整体性能的影响。 研究表明, 不同环境温度下, 界面具有不同的微观结构和热残余应力特征, 这些特征的变化将引起复合材料整体性能的明显变化。     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

Dynamic strength around two interacting piezoelectric nano-fibers with surfaces/interfaces in solid under electro-elastic waves

Considerable efforts have been devoted to the characterization of the strength at the surfaces/interfaces of piezoelectric nanocomposites. In this paper, the multiple scattering of electro-elastic waves from two piezoelectric nano-fibers in piezoelectric matrix is considered and the dynamic stress at the interface is obtained. A decoupling function is introduced to solve the governing equation in piezoelectric materials. The displacement and electric potential are described by a wave function expansion method. The addition theorem for cylindrical wave function is used to obtain the total coupling wave field. The conventional surface/interface model of Gurtin and Murdoch is extended to the case of coupling stress and electric displacement. The dynamic stress concentration factor around two nano-fibers is obtained. Through numerical analysis, it is found that the interaction between the two nano-fibers has a significant effect on the coupling of stress and electric displacement at the interface, especially in the region of high frequency. The interacting effect of the two piezoelectric interfaces is also related to the properties of the nano-fibers and interface. To show the validity of the dynamic model, comparison with existing results is also given.     

Fracture mechanics parameters for cracks on a slightly undulating interface

Typical bimaterial interfaces are non-planar due to surface facets or roughness. Crack-tip stress fields of an interface crack must be influenced by non-planarity of the interface. Consequently, interface toughness is affected. In this paper, the crack-tip fields of a finite crack on an elastic/rigid interface with periodic undulation are studied. Particular emphasis is given to the fracture mechanics parameters, such as the stress intensity factors, crack-tip energy release rate, and crack-tip mode mixity. When the amplitude of interface undulation is very small relative to the crack length (which is the case for rough interfaces), asymptotic analysis is used to convert the non-planarity effects into distributed dislocations located on the planar interface. Then, the resulting stress fields near the crack tip are obtained by using the Fourier integral transform method. It is found that the stress fields at the crack tip are strongly influenced by non-planarity of the interface. Generally speaking, non-planarity of the interface tends to shield the crack tip by reducing the crack-tip stress concentration.     

对称型陶瓷层状复合材料中的残余应力分析

针对由层间约束引起的层内残余应力，提出了用于描述层合材料应力应变状态的非均匀应变模型。利用非均匀应变模型推导出对称型层合材料由层间约束引起的层内残余应力的解析表达式，得到层内应力和界面应力沿长度方向分布的变化规律，指出轴向残余应力是层间界面剪应力造成的，是位置的函数；论证了由于表层材料受力的非对称性，界面必定存在正应力，且界面正应力须自平衡，界面正应力亦为长度方向上位置的函数，针对Si3N4-Si3N4/TiN-Si3N4三层及多层（2N＋1）对称型陶瓷基层状复合材料，研究了残余应力对强界面结合的层合材料宏观力学性能和裂纹扩展行为的影响和作用。结果表明，材料的宏观性能随着残余应力的变化而变化，其变化规律与理论计算的结果吻合。     

Transient thermo-mechanical analysis of dynamic curving cracks in functionally graded materials

Mixed-mode dynamic crack growth behavior along an arbitrarily smoothly varying path in functionally graded materials (FGMs) under transient thermo-mechanical loading is studied. An asymptotic analysis in conjunction with displacement potentials is used to develop transient thermo-mechanical stress fields around the propagating crack-tip. Asymptotic temperature field equations are derived for exponentially varying thermal properties, and later, these equations are used to derive transient thermo-mechanical stress fields for a curving crack in FGMs. The effect of the transient parameters (loading rate, crack-tip acceleration, and temperature change) and temperature gradient on the maximum principal stress and circumferential stress associated with the propagating crack-tip is discussed. Finally, using the minimum strain energy density criterion, the effect of temperature gradient, crack-tip speeds, and T-stress on crack growth directions is determined and discussed.     

K‐dominance of static crack tip in functionally gradient materials

K‐dominance of static crack tip in functionally gradient materials (FGMs) with a crack oriented along the direction of the elastic gradient is studied through coherent gradient sensing (CGS), digital speckle correlation method (DSCM) and finite element method (FEM). In the direction of crack propagation, the shear modulus has a linear variation with constant mass density and Poisson's ratio. First, the CGS and DSCM governing equations related to the measurements and the elastic solutions at mode I crack in FGMs are obtained in terms of the stress intensity factor, material constants and graded index. Secondly, two kinds of FGMs specimens and one homogenous specimen are prepared to observe the influences of the property variation on the K‐dominance. Then, CGS and DSCM experiments using three‐point‐bending of FGMs and homogenous beams are performed. Thirdly, based on the results of the experiments, the stress intensity factors of three kinds of specimens are calculated by CGS and DSCM. Meanwhile, the stress intensity factors are obtained by FEM. Finally, comparing the results from CGS, DSCM and FEM, the K‐dominance of mode‐I static crack tip in FGMs is discussed in detail.     

Stress field of a disclination dipole in hcp bicrystal with imperfect interface

In this paper, exact stress field solutions are derived for an interfacial disclination dipole in an hcp bicrystal with an imperfect interface described by the traction discontinuity, displacement discontinuity and slipping models. The solutions show that the stress variation is not necessarily monotonic with worsening imperfection and can exceed 100% of the stresses in bicrystals with perfect interfaces. A strong bias exists between the influence of the normal and shear traction jump parameters, and between the influence of the normal and tangential displacement jump parameters, on the interfacial stresses. The traction and displacement discontinuity models also predict very different dependence of the interfacial stresses on the jump parameters. These results suggest that imperfect interfaces may significantly raise the internal stresses and thus drastically alter the damage mechanisms (nucleation and propagation of dislocations/cracks, fatigue, etc.) as well as the mechanical properties (effective properties, failure modes, strength, etc.) of polycrystalline materials.