On the contact zone of a subinterfacial Zener-Stroh crack

Summary A Zener-Stroh crack is initiated by dislocations pile-up. Due to this displacement loading mechanism, only one of the two crack tips is sharp, and crack propagation is possible along the sharp tip only. When such a crack is initiated near an interface, the crack faces behind the sharp crack tip may contact each other due to material mismatch and loading combination. In the present study, a subinterface Zener-Stroh crack is analyzed with contact zone consideration near the tip. The problem is formulated as a set of nonlinear Cauchy-type singular integral equations which are solved numerically using Erdogan and Gupta's method. The physically pathological features of interpenetration of the crack surfaces and oscillation of the near tip fields are eliminated in the solutions due to the presence of a contact zone near the crack tip. It is found that the normal traction is bounded at the crack tip where a contact zone exists; while the shear traction has square-root singularities at both the crack tips. This result, is totally different to the case of an interface crack where Mode I and Mode II stress intensity factors, are inter-related at the sharp crack tip.     

Numerical simulation of crack deflection and penetration at an interface in a bi-material under dynamic loading by time-domain boundary element method

The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular traction BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material.     

Fracture of coated plates and shells under thermal shock

The main interest in this study is in the subcritical crack propagation and fracture of coated materials, specifically of cylindrical shells under repeated thermal shock. First it is shown that the circumferential crack problem in a cylindrical shell may be approximated by a plate on an elastic foundation under plane strain conditions. The thermal shock problem for a layered plate supported by an elastic foundation containing a crack in each layer of arbitrary sizes and locations is then considered. An additional factor studied is the influence of the cooling rate of the plate surface on the stress intensity factors at the crack tips. The problem is formulated in terms of a pair of singular integral equations which are solved for a number of typical crack geometries such as an edge crack, a crack terminating at the interface, an undercoat crack, and a crack crossing the interface. The main results of this paper are the stress intensity factors.     

Internal failures in model elastomeric composites

Finite element methods have been used to calculate the rate of release of strain energy caused by growth of an internal crack in some model elastic composites under tension. A layer of a linearly elastic material was considered, bonded between two flat or two spherical rigid surfaces. The reduction in strain energy caused by a small circular crack at the interface was found to be only about one-half of that due to a similar crack in the centre of the layer, in accord with the conjecture of Andrews and King. Cracks in the centre of a thin layer bonded between flat surfaces caused about the same release of energy as a crack in the centre of a thick specimen under the same tensile stress. On the other hand, a crack in a thin layer bonded between two spherical surfaces caused a much larger rate of energy release, depending on the radius of the layer relative to its minimum thickness. Growth of an initial crack would thus occur at a small applied stress. For thin layers between both flat and spherical surfaces, the rate of release of energy decreased as the crack grew, indicating that the crack would stabilize at a finite size. These conclusions are in accord with some observations of cracks in thin elastic layers.     

Analysis of a crack at a weak interface

The problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface is considered. The central part of the joint is detached, while in the remaining part there is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap. The adherents are homogeneous and isotropic, while the interface is allowed to be orthotropic with principal directions normal and tangential to the interface, respectively. The body is subjected to constant normal and tangential loads applied at infinity and at the crack faces. Using classical solutions for elastic half-planes as Green functions, the integral equation governing the problem is obtained and solved numerically. Attention is paid to the analysis of the solution around the crack tip, and an asymptotic estimate showing that the derivative of the solution is logarithmically unbounded is obtained analytically. Accordingly, it is shown that there may exist, at most, logarithmic stress singularities. It is further shown how, contrary to the case of perfect bonding, stress singularities are not related to the normal propagation of the crack, but possibly to the crack deviation. The crack propagation is analyzed by the energy Griffith criterion, and it is shown that some drawbacks of linear elastic fracture mechanics disappear in the case of weak interface.     

A Boussinesq wedge analysis of the tensile stress region in a rail head beneath compressive and traction point loads

Investigations into the causes of damage to rail heads and on rolling contact fatigue, date back a considerable time and are described in a large number of expertise literature on the many different aspects of this complex problem. The present paper is prompted by the naïve observation that fatigue crack propagation is more likely to occur in a tensile stress environment than in a highly compressive one and it therefore seeks to locate a region of radial or longitudinal tensile stresses on a rail head during the rectilinear motion of the train, providing favourable conditions for mode I or mixed‐mode crack propagation.     

Penny-shaped crack in an elastic layer bonded to dissimilar half spaces

Two axially symmetric mixed boundary value problems in an elastic dissimilar layered medium are considered. It is assumed that an elastic layer is bonded to two semi-infinite half spaces along its plane surfaces, and contains a penny-shaped crack parallel to the interfaces. In the first problem the two half spaces are assumed to have the same elastic properties and the crack is located in the mid-plane of the layer. In the second problem we consider the case of three different materials and arbitrary crack location in the layer. The numerical examples are given for a constant pressure on the crack surface. The stress intensity factors are evaluated and are plotted as functions of the layer thickness-to-crack radius ratio or the relative distance of the crack from an interface.     

Similarities of stress concentrations in contact at round punches and fatigue at notches: implications to fretting fatigue crack initiation

A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P , the ensuing contact is of width 2 b which includes an initial flat part of width 2 a . The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q , is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q /(√( b − a )√ π b ). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a 'notch analogue' by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.     

Estimation of fatigue crack propagation life of steel plates and of structural member model of ship hull

The authors carried out experimental and analytical investigation for the purpose of finding out a method of estimating the fatigue crack propagation life of large flat steel plate and of ship hull structure model quantitatively.We theoretically derived a formula indicating that fatigue crack propagation rate is in proportion to the $\text{m-}\text{th}$ power of the plastic displacement of the tip of a crack based on a B.C.S. dislocation model. The crack propagation rate is proportional to $\text{2m-}\text{th}$ power of stress intensity factor in the case stress is small.We proved experimentally that this relation holds generally, from fatigue crack propagation tests for flat plates with a center notch (mild steel, high tensile strength steel), large flat plate with an edge notch and ship hull corner model (mild steel), and from the $\text{K-}\text{value}$ calculation by the finite element method for these specimens. The fatigue crack propagation life is obtained by integrating the reciprocal number of crack propagation rate from the initial crack length to the final crack length. The life calculated agreed well with the one observed. But for the two stress level test, the life calculated was smaller than the experimental value due to slackened progress of crack. We also stated the general characteristics of the rate curve.     

Propagation of a crack due to shear waves in a medium of monoclinic type

Summary In this paper the propagation of a crack due to shear waves in a medium having monoclinic symmetry is investigated. The stress intensity factor at the crack tip for concentrated force of a constant intensity and for constant loading is separately calculated. The Wiener-Hopf technique has been used to solve the problem. It has been shown that the stress intensity factor decreases as the length of the crack increases. The effect of anisotropy being distinctly marked.With 5 Figures     

A moving Griffith crack at the interface of two dissimilar elastic layers

The anti-plane shear problem of a Griffith crack traveling with a constant velocity at the interface of two dissimilar isotropic elastic layers is considered. Integral transform method is used to reduce the problem to the solution of a singular integral equation which is further reduced, by using Chebyshev polynomials, to a system of algebraic equations. The results for the particular cases of a moving Griffith crack at the interface of a layer and a half-space and two half-spaces are derived. Numerical results for the stress intensity factor are displayed graphically.     

On fracture mechanics in lifting an ice sheet

The penetration of a wedge-like tool into an ice sheet at the interface with its substrate may develop a semi-elliptic interfacial crack. The Griffith energy-balance concept is employed to determine the critical conditions for interfacial crack propagation. The results show that an interfacial crack of any semi-elliptic shape tends to propagate in a stable manner and change the shape to a critical shape at which the propagation becomes unstable. The interfacial crack propagation may be interrupted by transverse fractures in the ice sheet.

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Résumé En faisant pénétrer un outil en forme de coin à l'interface entre un film de glace et le substrat sur lequel il est déposé sur une épaisseur uniforme, il peut se développer dans cet interface une fissure semi-elliptique.On fait appel au concept d'équilibre énergétique de Griffith afin de déterminer les conditions critiques pour que se propage la fissure.Les résultats démontrent que, quelle que soit sa forme, une fissure interfaciale semi-elliptique tend à se propager de manière stable, et à atteindre une forme critique pour laquelle la propagation devient instable.Des ruptures transversales dans le film de glace peuvent avoir pour effet d'interrompre la propagation de la fissure.

     

The mechanics of splitting a strip through penetration with a sharp wedge

This paper deals with the mechanics involved in splitting a strip through penetration with a sharp wedge along the center line. First, a quasi-static problem is considered. The crack propagation can be associated with the loss in stability when the applied load reaches the critical value for bifurcation. Next, the static problem is extended to a dynamic case by including the inertia force of the wedge in the analysis. An initial value problem is formulated for the motion of the wedge. For any given weight of the wedge, the critical velocity of the wedge for indefinite crack propagation can be determined by means of the theory of dynamic stability. Finally, the case of splitting a strip under repeated applications of impulsive load is considered. The critical number of applications of impulsive load for indefinite crack propagation is determined numerically.     

爆炸载荷下空孔缺陷与爆生裂纹扩展行为研究

空孔在岩石巷道直眼掏槽爆破中具有重要作用,为研究空孔及其缺陷在爆炸荷载作用下的扩展行为和作用机理,以PMMA代替岩石材料,利用预制裂纹代替空孔缺陷,借助动态焦散线系统和理论分析为手段,研究不同间距下空孔、空孔处预制裂纹、爆生裂纹动态扩展规律及机理,分析不同"径距比"与掏槽效果的关系。研究结果表明:在装药量一定的情况下,随着炮孔与空孔距离的变化,爆生裂纹扩展距离呈现递增而预制裂纹扩展距离呈现递减的趋势,但都存在极值;当炮孔与空孔距离较小时,爆生裂纹和预制裂纹扩展及相互作用最复杂,爆生裂纹扩展经历由压缩应力波为主,表现为直线的前期扩展;由空孔处发射应力波和压缩应力波共同作用下,爆生裂纹偏离炮孔与空孔连心线的中期扩展,以及由空孔应力集中区作用使爆生裂纹向空孔方向偏移的后期阶段;预制裂纹扩展经历由空孔处应力集中作用下,表现为直线的前期扩展,以及由爆生裂纹处反射拉伸波作用使其向爆生裂纹发展的后期阶段;当炮孔与空孔距离较大时,反射应力波及应力集中效应对爆生裂纹和预制裂纹扩展在减弱,爆生裂纹与预制裂纹扩展行为仅有前期直线扩展阶段。"径距比"的大小对爆破效果影响较大,直眼掏槽爆破应以最优"径距比"作为掏槽爆破参数设计的依据。     

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface—I. Analysis

In this paper the basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled system of four integral equations. For each relevant crack configuration of practical interest the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of delamination crack intersecting a crack which is perpendicular to the interface and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered as examples. The formulation of the problem is given in Part I of the paper. Part II deals with the solution of the integral equations and presentation of the results.     

Freeze-thaw degradation of FRP-concrete interface: Impact on cohesive fracture response

Results from an experimental investigation into the influence of freeze-thaw action on the FRP-concrete interface fracture properties are presented. The FRP-concrete bond behavior is investigated using a direct shear test. The cohesive stress transfer between FRP and concrete during debonding is determined from spatially continuous measurements of surface strains obtained at different stages of the debonding load response. The non-linear material law for the interface shear fracture, which provides a relation between the interface shear stress as a function of relative slip between the FRP and concrete, is established for specimens subjected to different levels of damage associated with freezing and thawing action. The influence of freeze-thaw action on the cohesive stress transfer during crack propagation, and on the cohesive interface fracture parameters is evaluated using a statistical hypothesis testing method. A larger percentage decrease in the interface fracture energy due to freeze-thaw cycles compared to the corresponding decrease in the ultimate nominal stress at debonding was noted. A decrease in the length of the cohesive stress transfer zone and the maximum interface cohesive stress were also observed with freeze-thaw cycling.     

On interface crack propagation with variable velocity for longitudinal shear problems

The antiplane strain problem of straight interface crack propagation between two elastic half-spaces under arbitrary variable loading is considered. The crack edge is specified as an arbitrary smooth function of time. It is assumed that the crack speed is less than the smaller of the shear wave velocities of two media. An integral transform method and factorization technique are used to solve the problem. The solutions are worked out for semi-infinite crack and finite crack problems. The dynamic stress intensity factors at the crack tip of the moving interface crack are given and it is found that the stress intensity factor of the interface crack is slightly higher than that in the homogeneous medium with slower shear wave velocity.     

Transverse fracture in multilayers from tension and line-wedge indentation

Crack propagation across laminated brittle solids from uniaxial tension or line-wedge loading is studied in real time using a model glass/epoxy architecture. The fracture progresses from one layer to the next via reinitiation from pre-existing flaws on the glass surfaces ahead of the primary crack in a process accompanied by some penetration through the interlayer but generally little or no delamination or deflection along the glass/epoxy interface. Depending on the system parameters, the material behind the crack front may be fully or intermittently severed. A 2D brittle fracture analysis is developed with the aid of the FEM technique taking into consideration stress gradients over flaws and flexure from contact loading. The analysis identified the flaw size and misfit in modulus, toughness and thickness between the layer and interlayer as the prime system variables. The results generally collaborate well with the experiments. Thick and compliant interlayers are generally advantageous except for contact loading, where they may promote crack reinitiation from the back surface of a layer. The explicit relations for crack penetration and reinitiation presented in this work facilitate convenient means for optimal design. Herzl Chai—on leave, School of Mechanical Engineering, Tel Aviv University, Israel.     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.