Thermal stress intensity factors of interface cracks in bimaterials

In this communication numerical results for thermal stress intensity factors (TSIFs) of interface cracks are presented for arbitrary material combinations which are characterized by Dundurs' parameters and . It is shown that TSIFs are linear in crack length ratio a/w and quadratic in and depend also on . The local phase angle at the interface crack tip is a linear function of . The striking feature of residual thermal stresses is their strong mode II character at the tip of an interface crack. In the framework of linear elasticity these TSIFs can be linearly superimposed on the stress intensity factors (SIFs) from applied loads for interface cracks in composites.     

SiC纤维补强微晶玻璃基复合材料的界面结合

本文通过ＳｉＣ纤维对ＬＣＡＳ（Ｌｉ２Ｏ－ＣａＯ－Ａｌ２Ｏ３－ＳｉＯ２）和ＭＡＳ（ＭｇＯ－Ａｌ２Ｏ３－ＳｉＯ２）微晶玻璃的补强，观察和分析了在不同复合系统中纤维与基体的界面结合。在ＳｉＣ纤维／ＬＣＡＳ微晶玻璃复合系统中，发现纤维与基体之间有一中间界面层，它主要是在复合材料的烧结过程中通过扩散形成，并且于１２００℃时在界面上形成富Ｃ层。ＳｉＣ纤维／ＭＡＳ微晶玻璃基复合材料由于在烧结过程中有化学反应发生     

A Thermally Shocked Unit Cell of a Fibre-reinforced Composite Material including interface cracks

The influence of a crack at the interface between the fibre and the matrix of a thermally shocked composite material has been considered theoretically. The time-dependending crack extension force has been calculated. A glass-aluminium composite is compared with a SiC? Al-composite.     

Plastic yielding through a two-material interface from cracks under antiplane deformation

The antiplane deformation problem of two bonded ductile half planes containing a crack with associated plastic zones at its tips and lying normal to the interface is considered. The analysis utilizes the approximate Gauss-Chebyshev integration of bounded distribution functions to obtain the magnitude of plastic strain or slip at the crack tips and the growth of plastic zones. The boundedness condition together with single valuedness of displacements in the far field is shown to provide the necessary additional conditions to locate the ends of the crack. For the case of a crack located entirely in one material, numerical examples are provided showing how the plastic zone spreads out from the crack tip with increased loading, eventually penetrating the interface and moving into the adjacent material.

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Résumé On considère dans le mémoire le problème de la déformation antiplanaire de 2 demi-plans ductiles, solidaires l'un de l'autre, comportant une fissure avec des zônes de déformations plastiques à ses extrémités et situées dans un plan normal à l'interface. Pour obtenir l'intensité de la déformation plastique ou du glissement aux extrémités de la fissure ainsi que l'accroissement des zônes plastiques, l'analyse recourt à l'intégration approximative de Gauss-Chebyshev faisant appel à des fonctions de distribution fermée. On montre que la condition de nonliaison associée à l'absence d'une simple valeur de déplacement dans le champ éloigné fournissent les conditions supplémentaires nécessaires à la localisation des extrémités de la fin de la fissure. Dans le cas d'une fissure située entièrement dans un des deux matériaux, des exemples numériques montrent comment la zône plastique s'étend à partir de l'extrémité de la fissure lorsqu'augmente la contrainte, et pénètre ensuite l'interface pour se prolonger dans le matériau adjacent.

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This work was supported by the United States Energy Research and Development Administration.     

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

径向载荷作用下复合材料圆柱壳的非线性动力屈曲

采用半解析法求解径向阶跃载荷作用下复合材料圆柱壳的非线性动力屈曲。基于一阶剪切变形理论，由Hamilton原理推导出包含横向剪切变形以及几何初缺陷的圆柱壳的非线性动力方程，位移及载荷沿周向采用级数展开，由Galerkin方法得到微分方程组，通过有限差分法求解；根据响应情况，由B—R准则判定屈曲，确定屈曲临界载荷。     

Dynamic response of bimaterial and graded interface cracks under impact loading

The interfacial fracture in bimaterial and functionally graded material (FGM) under impact loading conditions is investigated using experimental and numerical techniques that are valid for both type of interfaces. Experiments are conducted on epoxy based specimens in three point bend configuration and the complex SIF is measured using an electrical strain gage mounted close to the crack-tip. A complementary two-dimensional finite element simulation is performed using tup force and support reactions as input tractions, and the SIF-time history is determined using a displacement extrapolation technique. The experimentally determined SIF-histories match closely with numerical simulation up to the time of fracture initiation. The test results show that the mode-mixity remains nearly constant through out the test in both the materials, and the mixity values correspond to their respective static counterparts. The general dynamic response of the bimaterial and FGM specimens in terms of impact load, support reaction and the magnitude of complex SIF are comparable, and the mode-mixity is the parameter that distinguishes the graded interface from the bimaterial case.     

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

Transient elastodynamic crack analysis in two-dimensional (2D), layered, anisotropic and linear elastic solids is presented in this paper. A time-domain boundary element method (BEM) in conjunction with a multi-domain technique is developed for this purpose. Time-domain elastodynamic fundamental solutions for homogenous, anisotropic and linear elastic solids are applied in the present time-domain BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method, while a collocation method is adopted for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the unknown boundary data and the crack-opening-displacements (CODs). To show the effects of the crack configuration, the material anisotropy, the layer combination and the dynamic loading on the dynamic stress intensity factors and the scattered elastic wave fields, several numerical examples are presented and discussed.     

Diffraction of SH-waves on interface cracks under the action of concentrated forces

In the mathematically rigorous statement, we solve the problem of diffraction of elastic SH-waves on a finite (semiinfinite) crack located on the plane boundary of two perfectly joined materials. As a sounding field, we consider the field of a point source. The problem is reduced to the Wiener – Hopf functional equation, which is solved by the method of factorization. An approximate solution of this equation is obtained. We numerically study the distribution of the field in the radiation zone and the distinctive features of its formation depending on the location of the source of radiation. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 67–77, November–December, 2008.     

低能载条件下C/C复合材料滑动摩擦磨损性能

采用MM-200型环-块摩擦磨损试验机测试了针刺碳毡增强C/C复合材料试样在不同载荷和转速条件下的摩擦磨损性能,借助数码显微镜和扫描电镜观察分析了摩擦表面形貌。结果表明:当转速较低时,摩擦系数比较稳定,磨损率随载荷提高而增大;当转速较高时,低载荷试样摩擦系数不大,磨损率有所增加,而高载荷试样的摩擦系数在5分钟左右时出现峰值然后回落并保持稳定,磨损率急剧增加,说明磨损机制发生变化;摩擦面平行于X-Y向的C/C复合材料磨损率较小,具有较好的摩擦磨损性能。     

Boundary integral equations in elastodynamics of interface cracks

The paper concerns the validation of a method for solving elastodynamics problems for cracked solids. The proposed method is based on the application of boundary integral equations. The problem of an interface penny-shaped crack between two dissimilar elastic half-spaces under harmonic loading is considered as an example.     

Three-dimensional analysis of interface cracks in rubber materials

Three-dimensional and plane stress finite element analyses were carried out to investigate the stress fields and fracture parameters of interface cracks in rubber materials. The tearing energy computations for any arbitrarily shaped 3D crack front in dissimilar materials were obtained using the virtual crack extension method. The finite element results obtained are validated against existing alternate solutions and experimental data for cracks in homogeneous as well as bimaterial cases. The effects of different rubber material models, tearing energy distributions, crack extension angles, and three-dimensional regions at the crack tip for interface cracks are presented and discussed. It is shown that nonlinear materials have larger three-dimensional effects near the interface crack front, and that this effect increases as the material mismatch increases.     

Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure

In this paper, the interface cracking between a functionally graded material (FGM) and an elastic substrate is analyzed under antiplane shear loads. Two crack configurations are considered, namely a FGM bonded to an elastic substrate containing a single crack and a periodic array of interface cracks, respectively. Standard integral-transform techniques are employed to reduce the single crack problem to the solution of an integral equation with a Cauchy-type singular kernel. However, for the periodic cracks problem, application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem for a typical strip to triple series equations, then to a singular integral equation with a Hilbert-type singular kernel. The resulting singular integral equation is solved numerically. The results for the cases of single crack and periodic cracks are presented and compared. Effects of crack spacing, material properties and FGM nonhomogeneity on stress intensity factors are investigated in detail.     

Elastic-plastic and asymptotic fields of interface cracks

In previous analyses [1, 2, 13], and full-field computational investigations, we found that the near tip plastic fields of cracks on a bimaterial interface do not have a separable form of the HRR type. Nevertheless they appear to be nearly separable in an annular region well within the plastic zone. Asymptotically, as the crack tip is approached, the material system responds like that of a plastically deforming solid bonded to a rigid substrate; in particular, the stress and strain fields in the more compliant (lower hardening) material behave like those of a material with identical plastic properties bonded to a rigid substrate. Furthermore, the asymptotic fields of the interface crack bear strong similarities to mixed mode HRR fields for the homogeneous medium characterized by the plastic properties appropriate to the more (plastically) compliant material. In this investigation, we elucidate the behaviour of the material system over two length scales which are physically relevant, namely, distances comparable to the dominant plastic zone and the crack tip opening displacement. The latter is approximately given by the plastic zone size times and the relevant yield strain. Over length scales comparable to the dominant plastic zone, the stress fields are governed by the characteristics of the weaker (lower yield strength) material. On the other hand, the near tip plastic fields are governed by the strain hardening characteristics of the more plastically compliant (lower hardening) material.

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Résumé Dans des études précédentes, et lors de travaux de calculs, on a trouvé que les champs plastiques au voisinage de l'extrémité de fissures dans un matériau bimétallique n'ont pas une forme séparable de type HRR. Néanmoins, ils présentent une caractéristique quasi-séparables dans une zone annulaire incluse dans la zone plastique. Lorsqu'on approche de la pointe de fissure, le matériau réagit de manière asymptotique, à la manière d'un solide qui se déforme plastiquement tout en étant collé à une substrat rigide. En particulier, les champs de contraintes et de dilatations dans le matériau qui présente la compliance la plus élevée (durcissement le plus bas) se comportent comme ceux d'un matériau qui aurait de propriétés plastiques identiques et qui serait collé à un substrat rigide.De plus, les champs asymptotiques d'une fissure d'interface présentent des similitudes intéressantes avec les champs HRR de mode mixte relatifs à un milieu homogène caractérise par les propriétés plastiques adaptées au matériau le plus compliant (ou plastique).Dans cette étude, on éclaircit le comportement du système de matériaux sur deux échelles de longueurs qui ont un sens physique, à savoir des distances comparables à la taille de la zone plastique dominante d'une part, et du COD d'autre part. Ce dernier est fourni de manière approchée par la taille de la zone plastique divisée par le module d'élasticité. Sur la première échelle de longueurs, les champs de contraintes sont déterminé par les caractéristiques du matériau le plus faible (celui qui a la plus basse limite élastique). Sur la deuxiéme échelle, les champs plastiques près de l'extrémité de la fissure sont déterminés par les caractéristiques d'écrouissage du matériau qui a la compliance plastique la plus élevée, ou le durcissement le plus faible.

     

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.     

Elastic cracks and screw dislocation pile-ups crossing a bimaterial interface

The concept of continuously distributed dislocations is employed to study the behavior of anti-plane shear cracks crossing a bimaterial interface. The governing equations of the dislocation distribution function are dual singular integral equations. It is noticed that close to the tip, the crack opening displacement behaves as if the crack were imbedded in a homogeneous medium. C onsequendy, the stress in the immediate vicinity of the crack tip varies with the inverse square root of the distance from the tip. Moreover, the stress intensity near the crack tip in the comparatively harder phase is higher than that in the softer phase. The present method of analysis can be applied to the study of screw dislocation pile-ups crossing a phase boundary.     

Cylindrical interface cracks in 1-3 piezocomposites

1-3 Piezocomposites are made by embedding piezoelectric fibers/rods in polymer matrix materials. Fiber–matrix interface fracture can affect the performance of piezocomposites. In this paper, axisymmetric interfacial cracks in piezocomposites are studied by considering an idealized model of a single piezoelectric fiber in a matrix material. The displacement discontinuity method is used to formulate the Mode I and II crack problems. The fundamental solutions required for DDM are derived explicitly by using the electroelastic field equations and Fourier integral transforms. The dependence of Mode I and II stress intensity factors of single and multiple interface cracks on fiber and matrix material properties, crack length and distance between cracks are investigated.