Fracture mechanics analysis of spherical shell with surface crack

The nonclassical spherical shell theory and nonlinear line-spring model is applied to study the elastic-plastic fracture of a spherical shell with a surface crack. Experimental verification is also carried out.     

Rail-end bolt hole fatigue crack in three dimensions

This work is concerned with subcritical crack growth in rail-end bolt hole caused by fatigue. Included in the analysis are the mechanical wheel loads and thermal fluctuations experienced by the rail. The interaction of cyclic loading with the rail geometry is considered to be essential. Finite element stress analysis is coupled with the strain energy density criterion for determining the subcritical crack growth steps. The crack can grow and follow any arbitrary surface in the three-dimensional space depending on the symmetry or antisymmetry conditions of the load and geometry. Results on crack shapes and growth rates compare favorably with those observed experimentally.     

Fracture mechanics for a mode III crack in a magnetoelectroelastic solid

In this paper, we developed a Stroh-type formalism for anti-plane deformation and then investigated the fracture mechanics for an elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-plane electromagnetic and/or anti-plane mechanical loading, which allowed us to take the electromagnetic field inside the cavity into account. Reducing the cavity into a crack, we had explicit solutions in closed forms for a mode III crack, which included the extreme cases for an impermeable crack and a permeable crack. The results were illustrated with plots, showing that in the absence of mechanical loads, an applied electric or magnetic field, positive or negative, always tended to close the crack. On the other hand, in the presence of a mechanical load, a negative electric or magnetic field retarded crack growth, while a positive field could either enhance or retard crack propagation, depending on the strengths of the applied electric/magnetic fields and the level of the mechanical load as well. In other words, the effect of electric/magnetic fields on the fracture behavior is mechanical load-dependent.     

基于表面弹性理论的开裂椭圆孔断裂力学研究

研究纳米尺度时开裂椭圆孔的III型断裂性能。基于表面弹性理论和保角映射技术,利用复势函数理论获得了缺陷(裂纹和椭圆孔)周围应力场和裂纹尖端应力强度因子的闭合解答。所得结果具有一般性,许多已有和新的解答可由本文退化的特殊情形得到。利用解析结果讨论了缺陷的绝对尺寸、椭圆孔的形状比以及裂纹的相对尺寸对应力强度因子的影响。结果表明：考虑表面效应且缺陷尺寸在纳米尺度时,应力强度因子具有显著的尺寸依赖效应;应力强度因子随椭圆孔形状比的变化规律受缺陷表面常数的影响;缺陷表面效应的影响取决于椭圆孔的形状比,非常大的形状比屏蔽了表面效应的影响;裂纹相对尺寸非常小时表面效应影响较弱,裂纹相对尺寸较大时表面效应较为明显。     

Nonlinear crack mechanics

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 11, pp. 3–9, November, 1994.     

Fracture mechanics analysis of thin coatings under plane-strain indentation

A combined experimental/analytical work is carried out to elucidate the fracture resistance of a thin, hard coating bonded to a semi-infinite substrate due to indentation by a cylindrical surface. The bending of the coating under the softer substrate induces concentrated tensile stress regions at the lower and upper surfaces of the coating, from which cracks may ensue. The evolution of such damage in a model transparent system (glass/polycarbonate) is viewed in situ from below and from the side of the specimen. The critical load needed to initiate a crack on the lower coating surface generally increase proportionally to the coatings thickness, d. An interesting departure from this trend occurs for thin coatings, where the fracture load, although marred by a large scatter, increases somewhat with decreasing d. The fracture data for the upper coating surface are limited to relatively thick coatings due to the recurrence of premature failure from the coating edges. The behavior in this range is similar to that for the lower surface crack, albeit with an order of magnitude greater fracture resistance.A fracture mechanics analysis in conjunction with FEM is performed to elucidate the stress intensity factors responsible for crack propagation. A crack normal to the coating surface is assumed to emanate either from the lower or upper surface of the coating. A major feature of the solution is the occurrence of a bending-induced compression stress field over a region ahead of the crack tip. This effect, which become more dominant as the ratio between the contact length and the coating thickness is increased, tends to delay the onset of crack propagation, especially for the lower surface crack. Consequently, in applications associated with large indenters, thin and/or tough coatings and stiff substrates, cracking from the upper coating surface may precede that from the lower surface. An interesting feature of this crack shielding mechanism is that when the coating surface contains a distribution of flaws rather than a single crack, small flaws in this population may be more detrimental than large ones. Incorporation of these aspects into the analysis leads to a good correlation with the test results. In the special case of line loading, which constitutes a lower bound for the critical loads, a closed-form, approximate solution for the stress intensity factors or the critical loads are obtained.Plane-strain indentation, although less common than spherical indentation, allows for characterizing the fracture resistance of opaque films through observation from the specimen edge. This approach is not easily implemented to thin films (i.e., less than about a hundred microns), however.     

Fracture mechanics analysis of curved stiffened panels using BEM

A dual boundary element method is developed for a analysis of reinforced cracked shallow shells. Boundary integral equations are derived from the Betti’s reciprocal theorem for a cracked shallow shell with transverse frames and longitudinal stiffeners. The effect of frames and stiffeners are treated as a distribution of line body forces. The radial basis function is used to transform domain integrals to boundary integrals. Stress intensity factors are evaluated from crack opening displacements. The effect of curvature on the stress intensity factors is illustrated by numerical examples. Three examples are presented to demonstrate the accuracy of this method compared with solutions obtained using the finite element method.     

含斜裂纹剪切型橡胶减振垫的断裂分析

通过非线性有限元方法分别对含角斜裂纹和含边缘斜裂纹的剪切型橡胶减振垫分别进行了数值计算,橡胶材料采用Mooney本构模型。对受剪切载荷作用的减振垫,分别给出了减振垫的切向刚度和撕裂能随裂纹倾角、裂纹深度、载荷大小的变化规律。研究表明,随着裂纹长度的增加,撕裂逐渐增加,两者基本显非线性关系。     

Fracture mechanics analysis of a composite piezoelectric strip with an internal semi-infinite electrode

IA piezoelectric strip with semi-infinite electrode is investigated. Two combinations of mechanical–electrical loadings are considered. They consist of the anti-plane deformation with in-plane electrical field and the in-plane electroelastic field. Based on the Fourier transform and the Wiener–Hopf technique, the electroelastic local stress fields are found to exhibit the square root singularity near the electrode tip. The energy density factor criterion is applied to examine the fracture behavior near the electrode tip.     

Fracture mechanics of a tension-shear macrocrack in rocks

Fracture in rocks is influenced by anisotropy and existence of faults. Fracture initiation and propagation is often under the combined presence of sliding and opening of preexisting cracks. Linear-elastic fracture-mechanics (LEFM) has been used as a model for describing the propagation of a main crack in materials such as rocks, concrete, ceramics, etc. However, the presence of the fracture process zone which includes interlocking of grains and ligament connections results in deviations from perfectly brittle behavior. These effects are more pronounced in mixed-mode fracture, which involves crack initiation under the combined presence of tension-shear or compression-shear stresses.Specimens of Indiana limestone with a preexisting inclined notch were studied to observe the fracture process under a mixed-mode state of stress. Experimental monitoring involved using the electronic speckle-pattern interferometry (ESPI) technique to monitor strains and crack-propagation paths with high sensitivity. A scanning electron microscope (SEM) was used to examine the specimen for the presence of microcracks. Experimental results were subsequently evaluated using a mixed-mode fracture theory and finite-element computations.It was possible to visually observe the pre-peak and post-peak development of the fracture process zone. Developments in the crack-tip strain concentration were observed at and beyong the peak load. While the experiments conducted involved tension-shear cracks, the possibility of extending the concepts to compression-shear cracks was also explored. The possibilities and limitations of using the fracture-mechanics approach to understanding fracture in rocks were subsequently discussed.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

Fracture mechanics in fatigue

The linear-elastic fracture-mechanics approach to the design against high-cycle-fatigue failure is described. The basic concepts underlying the technology are presented and the techniques used to establish realistic design criteria are demonstrated. An example problem is also included and the associated considerations and computations described in detoil.     

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

The problem of a mode-II crack close to and perpendicular to an imperfect interface of two bonded dissimilar materials is investigated.The imperfect interface is modelled by a linear spring with the vanishing thickness.The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel.The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation.Several special cases of the mode-II crack problem with an imperfect interface are studied in detail.The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically.The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.     

Fracture mechanics analysis of delamination in a thermoelectric pn-junction sandwiched by an insulating layer

A fracture mechanics analysis is conducted for a delamination problem of a multilayered thermoelectric material (TEM) that consists of an n-type layer and a p-type layer sandwiched by an insulating layer. A time-varying energy release rate is presented when the n-type layer delaminates from the insulating layer. Effects of the temperature difference across the system and the applied electric current on the energy release rate are identified. The influence of the thickness ratio of the insulating layer to the thermoelectric (TE) layer is also examined. Based on the energy release rate criterion, the critical temperature difference for delamination propagation is obtained. Some useful conclusions are given.     

Fracture analysis of mode III crack problems for the piezoelectric bimorph

In this paper, a symplectic method based on the Hamiltonian system is proposed to analyze the interfacial fracture in the piezoelectric bimorph under anti-plane deformation. A set of Hamiltonian governing equations is derived from the Hamiltonian function by introducing dual variables of generalized displacements and stresses which can be expanded in series in terms of the symplectic eigensolutions. With the aid of the adjoint symplectic orthogonality, coefficients of the series are determined by the boundary conditions along the crack faces and along the external geometry. The stress\electric displacement intensity factors and energy release rates (G) directly relate to the first few terms of the nonzero eigenvalue solutions. The two ideal crack boundary conditions, namely the electrically impermeable and permeable crack assumptions, are considered. Numerical examples including the complex mixed boundary conditions are considered to show fracture behaviors of the interface crack and discuss the influencing factors.     

Fracture analysis on the arc-shaped interfacial crack between a homogeneous cylinder and its coating

The mechanical model is established for a mode I arc-shaped crack along the interface between a functionally graded layer and a homogeneous cylinder. The displacement and stress fields are expressed in the form of infinite series by the method of variable separation. By introducing two dislocation density functions, the mixed boundary conditions of the crack are recast into a system of Cauchy singular integral equations, which are then solved numerically. Parametric studies on the stress intensity factors (SIFs) yield two aspects of guidelines for engineering designs. (a) The SIFs depend on the ratio between the outer and inner radii rather than their respective values, and 1.5 seems to be an optimal value for this ratio. (b) The outer graded layer should be stiffer than the inner homogeneous cylinder and large non-homogeneity parameter is beneficial to SIF reduction.     

Fracture mechanics and crack contact analyses of the active repair of multi-layered piezoelectric patches bonded on cracked structures

In this paper, two-dimensional plane strain finite element analyses of the active repair for cracked structures by using multi-layered piezoelectric patches have been studied. The reductions of stress intensity factors and strain energy density factor at the crack tips are obtained. Also, the repair voltages for various conditions are obtained for estimating the repair performances. Lower repair voltage is a better choice because it is low-energy-consuming and safer for the operation. From the results of numerical fracture mechanics, it shows the crack contact conditions must be considered in the analysis. However, the friction on the crack has few effects on the repair performances for this mode-I dominated case. The better design choices for the piezoelectric patch are as follows: increasing the layer number, increasing the patch length, and reducing the patch thickness. In additions, it is not a good idea to use higher input voltage that is larger than the repair voltage because it will enlarge the crack open near the crack tip. Too long patch length has no advantage for the active repair.