Parametric study of oblique edge cracks under cyclic contact loading

The problem of a two-dimensional elastic body, carrying an inclined edge crack and loaded by a cylinder rolling on the surface, is solved by the weight function method. The load induced by the cylinder on the cracked body was represented by the Hertzian pressure distribution, and the nominal stress distribution in the uncracked body was numerically evaluated by the superposition principle. The crack opening displacement components were obtained by an analytical Green's function. The partial crack closure was considered and the influence of the mutual forces between the crack faces included in the analysis, by which the effective stress intensity factors K _I and K _II could be evaluated. By considering different friction conditions between the crack surfaces and several crack inclinations, the evolutions of the effective K _I and K _II during typical loading cycles were analysed.     

Multiple 3D inhomogeneous inclusions in a half space under contact loading

A semi-analytic solution is given for multiple three-dimensional inhomogeneous inclusions of arbitrary shape in an isotropic half space under contact loading. The solution takes into account interactions between all the inhomogeneous inclusions as well as the interaction between the inhomogeneous inclusions and the loading indenter. In formulating the governing equations for the inhomogeneous inclusion problem, the inhomogeneous inclusions are treated as homogenous inclusions with initial eigenstrains plus unknown equivalent eigenstrains, according to Eshelby’s equivalent inclusion method. Such a treatment converts the original contact problem concerning an inhomogeneous half space into a homogeneous half-space contact problem, for which governing equations with unknown contact load distribution can be conveniently formulated. All the governing equations are solved iteratively using the Conjugate Gradient Method. The iterative process is performed until the convergence of the half-space surface displacements, which are the sum of the displacements due to the contact load and the inhomogeneous inclusions, is achieved. Finally, the obtained solution is applied to two example cases: a single inhomogeneity in a half space subjected to indentation and a stringer of inhomogeneities in an indented half-space. The validation of the solution is done by modeling a layer of film as an inhomogeneity and comparing the present solution with the analytic solution for elastic indentation of thin films. This general solution is expected to have wide applications in addressing engineering problems concerning inelastic deformation and material dissimilarity as well as contact loading.     

Tunneling radial cracks in layered structures from contact loading

Glass/epoxy laminates glued onto a compliant substrate are indented with a hard ball. The damage is characterized by a set of transverse cracks which pop out from the subsurface of the glass layers due to flexure and propagate stably in the radial direction with load in a bell-shape front under a diminishing stress field. Compliant interlayers, even extremely thin ones, are effective in inhibiting crossover fracture. This leads to crack tunneling and crack multiplication in the hard layers, which enhances energy dissipation and reduces the spread of damage relative to the basic bilayer configuration. The experiments show that the fracture in a given layer is well approximated by a power-law relation of the form c^3/2K_C/P = δ, where P, c, and K_C are the indentation load, crack length and fracture toughness, in that order, and δ an implicit function of the layer position and material and geometric variables, derived with the aid of available tunnel crack solutions.The model specimen studied provides a useful insight into the fracture behavior of natural, biological and synthetic layered structures from concentrated loading. The analysis shows that the crack arrest capability of a thin interlayer increases in proportion to the modulus misfit ratio between the layer and interlayer, and that the spread of radial cracks in a laminate of given thickness reduces in proportion to n^1/3, where n is the number layers in the laminate.     

Elastodynamic analysis of nonplanar cracks in a half-space

Summary The interaction of time harmonic antiplane shear waves with nonplanar cracks embedded in an elastic half-space is studied. Based on the qualitatively similar features of crack and dislocation, with the aid of image method, the problem can be formulated in terms of a system of singular integral equations for the density functions and phase lags of vibrating screw dislocations. The integral equations, with the dominant singular part of Hadamard's type, can be solved by Galerkin's numerical scheme. Resonance vibrations of the layer between the cracks and the free surface are observed, which substantially give rise to high elevation of local stresses. The calculations show that near-field stresses due to scattering by a single crack and two cracks are quite different. The interaction between two cracks is discussed in detail. Furthermore, by assuming one of the crack tips to be nearly in contact with the free surface, the problem can be regarded as the diffraction of elastic waves by edge cracks. Numerical results are presented for the elastodynamic stress intensity factors as a function of the wave number, the incident angle, and the relative position of the cracks and the free surface.     

Interaction of coplanar surface cracks in a half-space

Boundary integral equations are applied to the interaction of closely spaced surface-coplanar cracks with various geometrical dimensions in a half-space that is tensioned by forces perpendicular to the crack surfaces. The numerical results show that the crack depths and the distances between them greatly influence the stress intensity coefficients at the edges of the cracks, and the interaction between the cracks can be neglected only for shallow ones.Translated from Problemy Prochnosti, No. 10, pp. 12–16, October, 1994.     

Approximation of curved cracks under mixed-mode loading

The calculation of stress intensity factors or mechanical energy release rate for non-straight cracks can be complicated. Approximation to equivalent crack shapes can simplify calculations considerably, but this requires an understanding of the influence of key shape parameters on crack-tip stresses. A simple analytical model has been developed, based on the concept of a relaxed volume, to predict mechanical energy release rate and deflection angle for a range of crack shapes under mixed-mode loading. Results from this model compared well with those obtained from finite element (FE) simulations, and with predictions from previous analytical models. It was found that the crack length and orientation of the crack-tip with respect to loading direction are the key influences on fracture parameters, whilst curvature near the crack-tip can also affect results.     

Failure probability under axisymmetric loading in a body having internal diskoid cracks

Conclusion Formulas have been derived for the failure probability of a body containing internal (structural) disk-type cracks of random size and orientation on axisymmetric loading. The calculations are based on the assumption that the cracks do not interest, where Sack's criterion is used with radius and orientation-angle distributions. Trends in the failure probability are related to the load, state of strain, material strength and structural characteristics, and body size (number of cracks in the body).Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 6, pp. 50–57, November–December, 1989.     

Fatigue of alumina under contact loading

Bars cyclically loaded by opposite concentrated forces via rollers are appropriate test specimens for the determination of fatigue under contact loading. As practical applications of the proposed test, the contact strengths and numbers of cycles to failure under contact loading were determined for three Al₂O₃. In additional tests the residual strength after a pre-loading under contact loading conditions was determined in four-point bending tests.     

Interface cracks with initial opening under harmonic loading

The study is devoted to the application of boundary integral equations to problems for interface cracks with initial opening under harmonic loading. As a numerical example the initially opened linear interface crack under the normally incident tension–compression wave is considered. The problem is solved taking the contact interaction of the crack’s faces into account. The convergence of the iterative algorithm is analysed and the stress intensity factors (opening and transverse shear modes) are given for the wide range of the wave number.     

Interaction between coplanar cracks under dynamic shock loading

Summary A study is made on the interaction between coplanar cracks in an unbounded body when dynamic loads act on thier surfaces that are described as Heaviside or Dirac delta functions. Graphs are given relating the stress intensity coefficients when there are two disk cracks in the body whose surfaces are loaded by shock external forces.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 50–55, May–June, 1991.     

Atomic simulation of cracks under mixed mode loading

A discrete atomic model of a crack tip in iron under mixed mode loads is examined. The results indicate that the behavior of the crack at the atomic scale as a function of the ratio of mode I to mode II component of load is quite complex. In general, crack tip plasticity appears to increase as the mode II component of load increases.

---

Résumé On examine un modèle atomique discret de l'extrémité d'une fissure dans du fer soumis à des charges de mode mixte. Les résultats indiquent que le comportement de la fissure à l'échelle atomique en fonction du rapport des composantes de charge du mode I sur celles du mode II est totalement complexe. En général, la plasticité à l'extrémité d'une fissure parait s'accroitre lorsque la composante de mode II de la contrainte s'accroit.

     

A contact problem for a nonhomogeneous half-space

A solution of a contact problem for a non-homogeneous half-space is given. The analysis is based on the assumption that the shearing displacement is prescribed within the band $\text{y = 0, ¦x¦<1, ¦z¦< ∞}$ and shearing stress is zero in the outside area $\text{|x|> 1, y = 0, ¦z¦<∞}$. The shear modulus of the non-homogeneous half-space is assumed in the following form μ = μ₀(1 + α₁x)² (1 + β₁y)², where α₁, β₁ and μ₀ are constants. Here x, y and z are referred to a rectangular coordinates system.     

Core compression in sandwich beams under contact loading

Failure of the core in sandwich structures under concentrated loading is of potential concern, and it is difficult to compute the core compressive stress by simple means. Contact loading adds additional complexity, as surface displacements are imposed and the contact zone size and pressure distribution is initially unknown. However contact loading is important as it is widely used in three or four point bend tests to determine failure properties, and is also typically involved in impact loading. The calculation of core compressive stress was addressed in the present work by utilizing an elasticity solution due to Pagano and Srinivas and Rao for transverse loading of layered orthotropic materials. Contact pressure distributions were obtained by systematically varying pressures and comparing the computed surface displacements with the indentor profile. The results show that the pressure distribution for an orthotropic half-space is applicable to sandwich beams over a wide range of variables. A beam-on-elastic-foundation model was found to be useful in correlating the analysis results for core compressive stress.     

Analysis of interfacial cracks in a TBC/superalloy system under thermal loading

Thermal barrier coatings (TBCs) provide thermal insulation to high temperature superalloys. Residual stresses develop in TBCs during cool down from processing temperatures and subsequent thermal cyclic loading due to the thermal expansion mismatch between the different layers (substrate, bond coat, and TBC). These residual stresses can initiate microcracks at the bond coat/TBC interface and can lead to debonding at the bond coat/TBC interface. The highest residual stresses occur at the interfaces. The effect of voids or crack like flaws at the interface can be responsible for initiating debonding and accelerate the oxidation process. The effect of interfacial microcracks has been investigated using the fracture mechanics approach. In particular, J-integral and the energy release rate G, for both mode I and mode II using the virtual crack extension method were evaluated. Two types of specimens were studied. The specimens were cooled down from processing temperature of 1000°C to 0°C. The variation of the properties as a function of temperature were used for the analysis. It was found that the use of temperature dependent properties in contrast to constant properties provide significantly different values of J-integral and G. For the stepped-disc specimen with an edge crack, crack growth is only due to mode II, while for the cylinder specimen with an internal crack, crack growth is due to mixed-mode loading. An important implication of this result is that edge delaminations in a disk specimen may only grow due to mode II conditions under pure thermal loading. Shear fracture characteristics of interfacial crack thus become important in the failure of the TBC.     

Providing adhesion strength for a substrate-coating system under contact loading

The authors of the article discuss some feasible means of determining geometrical parameters of a discrete-type coating with a view to ensure adhesion strength of the substrate-coating composite. The stress-strain calculations are performed for an element of a carbide tool with a vacuum-plasma-deposited coating, under contact loading, allowing for friction forces.     

爆炸荷载作用下煤体裂纹扩展机理模型实验研究

为研究煤体在柱状装药爆炸荷载作用下裂纹扩展机理,以Froude比例法为指导,建立煤层预裂爆破的模型实验。得到爆炸波在模型介质中传播的压力波形及模型表面加速度、应变、位移波形。描述模型在爆炸荷载作用下的宏观破坏现象。研究结果表明:模型实验与现场试验结果基本一致;裂纹主要是由压缩波与卸载波共同作用形成的;裂纹扩展方向与炮孔轴线方向垂直。