Crack propagating in a functionally graded strip under the plane loading

In the present paper, a finite crack with constant length (Yoffe type crack) propagating in the functionally graded strip under the plane loading is investigated by means of the Schmidt method. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of the material properties, the thickness of the functionally graded strip, and speed of the crack propagating upon the dynamic fracture behavior.     

Crack propagation experiments on strip specimens

A method for measuring dynamic fracture properties is briefly described. The method employs the strip specimen and this configuration is discussed from a practical point of view. Results from experiments performed to determine the velocity variation of the fracture energy are presented. Some observations are made regarding the physical nature of the fracture process.     

Crack propagation in a material with random toughness

An efficient Monte Carlo procedure is presented for characterizing the propagation of a crack in a material whose fracture toughness is a random field. The simulations rely on accurate approximate solutions of the integral equations that govern the dislocation densities, stress intensity factors, and energy release rates of curvilinear cracks. For a plate containing an edge crack that propagates towards a subsurface crack representing a traction-free boundary, results for the distributions of crack trajectories, critical applied far-field stresses, and nominal fracture toughness are presented for various parameters that quantify the randomness of the material's critical energy release rate. A demonstrative probabilistic model for crack trajectories is built and size effects are discussed.     

Crack extension under compressive loading

Non-planar extension (kinking) of a crack subjected to remote biaxial compression is studied to gain insight into compressive failure of brittle solids. Approximate expressions are developed for the stress intensity factors at the tips of the resulting wing cracks. Assuming the wing crack propagates at a constant value of $\text{K}{}_{\mathrm{Ic}}$, one can calculate wing crack extension vs load. The significance of the dependence on various parameters is discussed.     

Edge delamination in a laminated composite strip under generalized plane deformations

Edge delamination cracks in an elastic laminated composite strip are considered within the range of generalized plane deformations. By way of a simple regular finite element method, the method of mutual integral, wherein generalized plane strain solutions are employed as auxiliary fields, is applied to edge delamination cracks to obtain the complex stress intensities. The proposed numerical scheme is found to be very efficient and accurate. Moreover, the crack growth stability is examined for various loadings, including compression, bending and torsion, in terms of the energy release rate and mode mixity.     

Crack propagation in polystyrene under fixed elongation

Microscopic observations of precracked polystyrene samples under fixed elongation conditions reveal that discontinuous crack propagation occurs under stress relaxation asymptotically approaching a stable configuration. A zone of intensive crazes in the vicinity of the crack tip evolves concurrently with crack growth. The evolution of the crazed zone occurs as translation and isotropic expansion. The phenomenon has been successfully explained using a crack layer model. Crack propagation is found to be controlled by the difference between the energy dissipated on damage (crazing) growth and the relevant energy release rate.     

Crack propagation in ceramics under cyclic loads

Stable crack growth is observed in notched plates of polycrystalline alumina subject to fully compressive far-field cyclic loads at room temperature in a moist air environment andin vacuo. The fatigue cracks propagate at a progressively decreasing velocity along the plane of the notch and in a direction macroscopically normal to the compression axis. The principal failure events leading to this effect are analysed in terms of notch-tip damage under the far-field compressive stress, microcracking, frictional sliding and opening of microcracks, and crack closure. An important contribution to such Mode I crack growth arises from the residualtensile stresses induced locally at the notch-tip when the deformation within the notch-tip process zone leaves permanent strains upon unloading from the maximum nominal compressive stress. It is shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials. The mechanisms of fatigue in ceramics are compared and contrasted with the more familiar examples of crack propagation under far-field cyclic compression in metallic systems and the implications for fracture in ceramic-metal composites and transformation toughened ceramic composites are highlighted. Strategies for some important applications of this phenomenon are recommended for the study of fracture mechanisms and for the measurement of fracture toughness in brittle solids.     

Crack propagation under constant amplitude loading

A crack propagation law is derived on the concept that net energy released in one cycle in the vicinity of crack tip is absorbed in cyclic plastic zone incorporating the concept of crack closure. Further, the derived law is modified by introducing some more material properties, as an attempt towards generalization. The finally developed law is dimensionally correct. The crack growth rates predicted by the developed crack growth rate law are compared with the experimental data of 16 materials and a good correlation is achieved.     

Crack propagation behavior under creep conditions

The creep crack propagation behavior of a Cr–Mo–V rotor steel has been investigated at 538°C using time-dependent fracture mechanics concepts. The creep crack propagation lives and the creep deflection rates of double-edge-notched (DEN) specimens were estimated using previous data from compact-type specimens. The predicted crack growth lives and deflection rates compared favorably with the experimental data. When plotted as a function of the C _t parameter, the experimentally determined creep crack propagation rates of DEN specimens were found to be in agreement with those of compact and center-crack-tension specimens. These results provide further experimental verification for the validity of the C _t parameter for characterizing creep crack growth behavior. Some discrepancies between the predicted and the observed behavior are attributed to primary creep deformation behavior which was not considered in estimating the value of C _t .     

Crack propagation under combined stresses in three-dimensional medium

By using the expressions of Hartranft and Sih for the stress field at the tip front of an arbitrary crack, the problem of crack propagation under combined stresses in a three-dimensional medium has been discussed on the basis of (σθ)_mas theory and its modification, (σw)_max theory. General results have been obtained, calculations carried out for some special cases, and a comparison made with experimental data available in literature.     

Electromagnetic wave propagation in a plane dielectric layer under critical conditions

An exact solution to the problem of a plane wave propagation in a plane-stratified dielectric layer of arbitrary thickness is studied. An approach based on self-consistent finite differences is suggested, replacing the layer by a stack of homogeneous sublayers of variable thickness matched to the local behavior of the permittivity profile. For the region around zero permittivity, it is predicted that small perturbations of the physical parameters of the problem cause qualitative and quantitative changes in the solution. The conditions for the excitation of a surface wave are formulated. Computed data for the wave are presented.     

Direction of crack extension under general plane loading

An explicit expression of the amount of elastic energy release for crack extension under general two dimensional loading is presented through linear elasticity theory. It is shown that the direction of crack extension under general plane loading can be obtained directly by the minimization of the potential energy with respect to the crack direction. The minimization process indicates that the crack extension direction provided by maximum stress criterion is the same as the derived from minimum potential energy.     

Crack propagation in a Tantalum nano-slab

Using molecular dynamics with an accurate many-body potential for metallic Tantalum, we studied crack propagation in a pre-notched nano-slab under uniaxial strain in a [100] direction. We study dislocation emission from the crack tip for various strain rate and temperatures, focusing on the influence of the local temperature at the crack tip on the propagation of the crack. We find a close connection between the local temperature at the crack tip and dislocation emission. This revised version was published online in June 2006 with corrections to the Cover Date.     

Initial response of a micro-polar hypoplastic material under plane shearing

The behavior of an infinite strip of a micro-polar hypoplastic material located between two parallel plates under plane shearing is investigated. The evolution equation of the stress tensor and the couple-stress tensor is described using tensor-valued functions, which are nonlinear and positively homogeneous of first order in the rate of deformation and the rate of curvature. For the initial response of the sheared layer an analytical solution is derived and discussed for different micro-polar boundary conditions at the bottom and top surfaces of the layer. It is shown that polar quantities appear within the shear layer from the beginning of shearing with the exception of zero couple stresses prescribed at the boundaries.     

Crack propagation in a commercial steel

In this work, the fatigue crack propagation behaviour of commercial steel sheet specimens containing a circular hole, under uniaxial loading conditions at room temperature was investigated.The experimental data have been analysed in terms of variability of material constants. The results were presented in the form of power relationship between the crack growth rate and the stress intensity factor range.

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Résumé Dans ce travail, on a étudié le comportement à la propagation des fissures de fatique d'éprouvettes de tôle mince en acier de construction, présentant un trou circulaire et sujettes à une mise en charge uniaxiale à température ambiante.On a analysé les données expérimentales en termes de variabilité des constantes du matériau. Les résultats sont présentés sous forme d'une relation parabolique entre la vitesse de croissance de la fissure et la variation du facteur d'intensité de contrainte.