On dissolution driven crack growth

The formation and growth of a crack in a body subjected to stress driven material dissolution is studied. The rate of material dissolution is proportional to strain energy and curvature of the body surface. The formation of a crack from a plane surface is preceded by an evolving surface roughness. The continued dissolution enhances roughness amplitude resulting in pit formation. As the pit grows deeper into the material, it assumes the shape of a crack. The sharpness of the crack reaches its maximum during this transition from a pit to a crack. As the crack grows, a self-similar state is gradually assumed. During this phase characteristic lengths of the crack shape scale with the crack length. In line with this the crack progressively becomes blunt. The widest part of the crack when unloaded is in the vicinity of the crack tip. A consequence of the model is that no criterion is needed for crack growth. Neither is a criterion needed for determination of the crack path. It also follows that the crack growth rate is almost independent of the remote load. Further, spontaneous crack branching is anticipated. A motivation for this is given.     

Fatigue life prediction of in-plane gusset welded joints using strain energy density factor approach

Fatigue crack growth behavior of in-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis was carried out to show the effects of the initial crack shape, the initial crack length, and the stress ratio on the crack types of in-plane gusset welded joints. The assumed crack types were edge crack, semi-elliptical crack, and corner crack. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes for the given crack types. The results of analysis for the assumed crack types agreed well with the experimental data. The fatigue life did not change as initial crack shape varied for a given initial crack length.     

A Piezoelectric Technique for Evaluation of Crack Closure

The ability of the piezoelectric materials to work as sensors and actuators was employed in a technique for monitoring the degree of crack closure and to detect the crack opening load. The technique is demonstrated through experiments with a cracked beam. It consists in exciting the specimen with a piezoelectric actuator and recording the electromechanical response of piezoelectric sensors placed near the crack mouth, while applying a bending moment to open the crack. The sensors in the neighborhood of the crack present a reduction in the amplitude response signal due to the progressive decrease of the dynamic strains near the crack, as the bending load causes the crack to open, reducing the contact between the surfaces of the fatigue crack and the load transmission through the contact area. The results show that the method has a high sensitivity to the state of crack closure, allowing for the direct determination of the crack opening load.     

A cyclic steady-state method for fatigue crack propagation: Evaluation of plasticity-induced crack closure in 3D

The numerical study of plasticity-induced crack closure using the node-release technique presents many difficulties widely studied in literature. For instance various rules, proposed for overcoming mesh sensitivity, are challenged by more recent studies. This paper intends to propose and evaluate a numerical method for the investigation of crack propagation under fatigue loading, and particularly for the assessment of plasticity-induced crack closure in three-dimension. The method is an extension of the “steady-state method” to cyclic loadings. The steady-state method allows a direct computation (on a fixed mesh, without releasing nodes) of stress and strain fields around the crack tip and in the wake for a steady crack growth. The method is extended to simulate crack propagation under fatigue loading. Therefore it constitutes a valuable numerical tool for gaining insight into the physics of crack propagation, as it provides accurate mechanical fields around the crack tip and their relation with crack growth rate, various loading modes and parameters. The proposed method is also compared with the classical node-release technique. A very good agreement between the two methods is found. However the steady-state method needs much less mesh refinement and computational time. Following an analysis of some features of the fatigue crack, a discussion on a crack closure criterion is opened, and a reliable criterion for the determination of local crack closure is proposed.     

Boundary element weight function analysis of a strip yield crack in a rotating disk

The boundary element method combined with subtration of Bueckner singular fields are used to obtain weight functions for an internal edge crack in a rotating annular disk. A previously developed, general representation of the weight function is used which leads to integrals that can be evaluated analytically to obtain the stress intensity factor and surface displacements of the crack. The determination of crack tip opening displacements for the strip yield crack is reduced to a non-singular integral which can be evaluated in closed form. The strip yield zone length and crack tip opening displacement are determined for an internal radial crack in a rotating annular disk for a range of crack lengths and rotational speeds.     

Crack solutions and weight functions for plane problems in three-dimensional quasicrystals

The plane problems of an elliptic hole and a crack in three-dimensional quasicrystals subject to far-field loadings are studied. The generalized Stroh formalism is adopted here, and the explicit solutions for the coupled fields are obtained in the closed form. When the elliptic hole reduces to a crack, the analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The crack theory of quasicrystals, including the determination of the field intensity factors, crack opening displacements, crack tip energy release rates and so on, is a prerequisite. Applying Betti’s theorem of reciprocity, the weight functions for a quasicrystal body with a crack are derived. The weight functions provide a means of calculating the intensity factors for the crack when both phonon and phason point forces are imposed at arbitrary locations.     

The Stress State of a Transversally Isotropic Piezoceramic Body with a Parabolic Crack in a Uniform Heat Flow

The explicit solution is constructed for a static thermoelastic problem for an infinite transversally isotropic piezoceramic body containing a heat-insulated parabolic crack in the isotropy plane. The crack surface is assumed free of forces. The body is under a uniform heat flow, which is perpendicular to the crack surface and is far from the crack itself. The problem is solved for two cases of electric conditions on the crack surface. In the first case, an electric potential is absent on the crack surface and, in the second case, the normal component of the electric-displacement vector is equal to zero. The intensity factors, which depend on the heat flow, crack geometry, and the thermoelectroelastic properties of the piezoceramic body, are determined for the force field and electric displacement near the crack tip     

Limited permeable crack moving along the interface of a piezoelectric bi-material

A plane problem for a crack moving with a subsonic speed along the interface of two piezoelectric semi-infinite spaces is considered. The crack is assumed to be free from mechanical loading. The limited permeable electric condition with an account of electric traction is adopted at its faces. A uniformly distributed mixed mode mechanical loading and an electric flux are prescribed at infinity. The problem is reduced to the Riemann–Hilbert problem by means of introducing a moving coordinate system and assuming that the electric flux is uniformly distributed along the crack region. An exact solution of this problem is proposed. It permits to find in closed form all necessary electromechanical characteristics at the interface and to formulate the equation for the determination of the electric flux. Analysis of this equation confirms the correctness of the assumption concerning the uniform distribution of the electric flux in the crack region. The values of the electric flux are determined by solving the obtained equation. Thereafter, the stress and electric intensity factors as well as their asymptotic fields at the crack tip are also found. The particular case of a crack moving in a homogeneous piezoelectric material is considered. The values of the electric flux and the fracture parameters are found exactly in a simple form for this case. Also, a numerical analysis is performed for a crack propagating with a subsonic speed between PZT4 and PZT5 materials and for a crack moving in PZT4 material. The electric flux in the crack region, stress and electric intensity factors, crack opening and the energy release rate (ERR) are found as functions of the crack speed, loading and electric permeability of the crack medium. The influence of the electric traction on the crack faces upon the mentioned parameters is demonstrated.     

Mode I crack growth rate for yield strip model of a narrow piezoelectric ceramic body

A crack growth rate equation is found for a finite crack in a narrow transversely isotropic piezoelectric ceramic body under tensile loading. Use is made of the yield strip model. The crack is situated in the mid-plane and is parallel to the edges of the body. Integral transforms are applied to reduce the problem to a Fredholm integral equation of the second kind. The accumulated plastic displacement criterion is applied to crack growth at low stress levels. This results in a small crack growth rate equation with fourth-power stress intensity factor dependence. Numerical examples are given for piezoelectric ceramics and the crack growth rates are plotted as a function of body height to crack length ratio for various values of the electrical loads.     

Analytic solutions to crack tip plastic zone under various loading conditions

Based on stress field equations and Hill yield criterion, the crack tip plastic zone is determined for orthotropic materials and isotropic materials under small-scale yielding condition. An analytical solution to calculating the crack tip plastic zone in plane stress states is presented. The shape and size of the plastic zone are analyzed under different loading conditions. The obtained results show that the crack tip plastic zones present “butterfly-like” shapes, and the elastic–plastic boundary is smooth. The size of the plastic zone for orthotropic composites is less at the crack tip for various loading conditions, compared with the case of isotropic materials. Crack inclination angle and loading conditions affect greatly the size and shape of crack tip plastic zone. The mode I crack has a crucial effect on the plastic zone for mixed mode case in plane stress state. The plastic zone for pure mode I crack and pure mode II crack have a symmetrical distribution to the initial crack plane.     

Stress intensity factors for curved and kinked cracks in plane extension

A singular integral equation containing the crack opening displacement (COD) is developed for solving plane elasticity problems. The crack may contain any number of kinks at different intervals and orientations, such as a saw-tooth shape. Cracks in the form of a sine wave can also be treated. The crack tip stress intensity factors are evaluated for a variety of crack shapes and the results are displayed graphically. The distance between the crack tips is found to be a dominant factor on the crack tip stress intensity while the angle between the tangent to the crack tip and load direction determines the proportion of Mode I and II stress intensity factors.     

Mixed mode fatigue crack growth in test coupons made from 2024-T3 aluminum

In this paper, two different fracture criteria are applied to determine the crack trajectory or angle of crack propagation in test specimens containing inclined cracks emanating from open holes. Also, different crack growth rate models are assumed for each criterion. The maximum principal stress criterion is used with a crack growth-rate equation based on an effective stress intensity factor. The strain energy density criterion is used with a crack growth-rate equation corresponding to an effective strain energy density factor. The crack growth-rate models for each criterion were constructed using unpublished fatigue crack growth data for 2024-T3 aluminum.     

Growth of an arc-crack in bonded dissimilar materials

The problem of growth of a crack lying along the interface of a circular inclusion embedded in an infinite plate is studied within the framework of linear elasticity. The plate is subjected to a uniform uniaxial stress at infinity at any angle of inclination relatively to the crack. The critical load for unstable crack growth, the angle of initial crack extension and the subsequent crack path are investigated using the strain energy density fracture criterion. The combined effect of crack length and orientation on the fracture stress is considered for the case of an aluminum-epoxy composite.     

Empirical modelling of subcritical crack growth size and profile under continued loading

During continued loading the slow crack growth regions at the crack tip assume different shapes and sizes. Two different crack front profiles may be identified in practice depending on the extent of crack growth. They may be approximated as parabolic and semi-circular in shape. Crack fronts tend to be semi-circular for relatively large extent of crack growth and parabolic during the early stages of crack growth. Modelling of crack growth size and profile for each crack growth increment is carried out by two approaches; namely, offset measurement and area consideration. The variation of average crack growth size as well as the convergence of as a function of measurement number is studied. The difference in the values obtained by the offset method and area method is also investigated in addition to the influence of specimen thickness and maximum crack growth on ø. Experimental verification of crack growth front profiles and the change in the value with ø is carried out. It suffices to consider eight to ten measurements for modelling crack growth size and profile in commonly used specimen thickness.     

DETERMINATION OF CRACK SURFACE DISPLACEMENTS FOR A RADIAL CRACK EMANATING FROM A SEMI-CIRCULAR NOTCH USING WEIGHT FUNCTION METHOD

A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate.Results are presented for two load conditions: remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the WuCarlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

Bifurcation of collinear crack system under dynamic compression

The evolution pattern of collinear crack array plays a very important role in the final failure pattern of rock and predicting earthquake. Crack interactions lead to the nonhomogeneous pseudo-traction, then result in bifurcation of crack growth pattern. Bifurcation condition of crack growth pattern can be expressed by the crack growth length/spacing ratio. For collinear cracks loaded by dynamic compressive loads, uniform crack growth pattern yields to non-uniform crack growth pattern when the crack growth length/spacing ratio is larger than a critical value. In this paper, crack interactions are studied using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. The analytical solution of the critical value for two collinear cracks and infinite collinear cracks is given out. The critical value is sensitive to pre-existing crack length, the friction coefficient, the orientation of pre-existing crack, crack growth velocity.     

Stress intensity factor for an edge crack in two bonded dissimilar materials under convective cooling

The transient thermal stress crack problem for two bonded dissimilar materials subjected to a convective cooling on the surface containing an edge crack perpendicular to the interface is considered. The problem is solved using the principle of superposition and the uncoupled quasi-static thermoelasticity. The crack problem is formulated by applying the transient thermal stresses obtained from the uncracked medium with opposite sign on the crack surfaces to be the only external loads. Fourier integral transform is used to solve the perturbation problem resulting in a singular integral equation of Cauchy type in which the derivative of the crack surface displacement is the unknown function. The numerical results of the stress intensity factors are calculated for both the edge crack and the crack terminating at the interface using two different composite materials and illustrated as a function of time, crack length, coefficient of heat transfer, and the thickness ratio.     

Analysis of crack moving and curving in anisotropic solids

The general equations for a dynamically curved crack in an anisotropic solid are derived, and the asymptotic fields of a moving crack under arbitrary distributed loading on the crack surface are calculated from them. For a moving crack under mixed-mode loading conditions a general Muskhelishvili type approach is proposed to calculate intensity factors due to crack surface loading in anisotropic materials. The kinking and curving caused by dynamic loading in anisotropic materials are calculated using the maximum normal stress ratio criterion. The results show that cracks in anisotropic solids may deviate from the straight path and approach a direction parallel to the stiff axis even under symmetric loading and that a crack will tend to deviate more from the crack path to the direction of the stiff axis as the crack speed becomes higher.     

裂纹扩展独立于网格的一种有限元单元子划分方法

提出了一种有限元模拟裂纹扩展的单元子划分结合子结构的方法。本方法中,裂纹可以进入或穿过一个单元,或沿单元的边界扩展,因此裂纹可以沿任意路径扩展而不受初始网格的限制。对上述几类包含裂纹的单元按照裂纹的路径进行子划分,覆盖一条裂纹的所有子划分单元就组成了一个子结构,子结构规模随裂纹的扩展而增大。子结构中因单元子划分而新增的结点自由度,通过自由度的凝聚用初始网格结点的自由度表示,因此结构整体分析的总自由度不变。以上述方法为基础建立了裂纹萌生和扩展的准则。用本文的方法分析了单（双）材料无限大平面中心（界面）裂纹的裂尖场,验证了本文方法的精度,并模拟了颗粒复合材料中微裂纹在颗粒、基体和界面中逐步扩展的过程,考核了本文方法对复杂裂纹扩展问题模拟的适用性。     

裂尖曲率对裂纹前缘塑性区的影响

考虑尖端为圆弧形的钝头裂纹模型，在外围取线弹性无裂纹体的解，应用线场分析方法。形成一套估计钝头裂纹前缘塑性区尺寸的方法。对含径向裂纹和圆弧形裂尖的圆盘受均匀张力作用情况，给出了塑性区的裂纹前缘尺寸与裂纹尖端曲率的关系。得到的结论是，塑性区的裂纹前缘尺寸与裂纹尖端曲率有关；对于给定的塑性区的裂纹前缘尺寸，载荷反比于外缘尺寸的平方。前一结论说明了塑性区的裂前尺寸作为裂纹失稳扩展判断的局限性；后一结论说明了裂纹体强度失效的尺寸效应规律：抗断强度与总体线尺寸的平方成反比。