Shear band propagation from a crack tip subjected to Mode II shear wave loading

Results are reported for pressure–shear plate impact experiments in which pre-cracked 4340 steel plates are subjected to Mode II loading. Experiments show the propagation of a shear band ahead of the initial crack. Finite element simulations are used to interpret the results. Normal and transverse velocity–time profiles measured at the rear surface of the target can be simulated reasonably well using even an elastic model for the material response. A propagating shear band is obtained when the material is modeled as having reduced shearing resistance described by a thermo-viscoplastic power law, and complete loss of shearing resistance when the shear strain reaches a critical value. However, the predicted speed of propagation of the tip of the shear band is substantially less than required to explain the lengths of the bands observed in the experiments. Adjustments of parameters of the power-law model have little effect on the overall length of the band. Possible reasons for differences between predicted and measured shear band speeds are examined. Further reduction in the shearing resistance in the shear band appears to be essential for the simulated bands to be as long as those observed in the experiments.     

A three-dimensional rectangular crack subjected to shear loading

In this paper a solution is derived to treat the three-dimensional elastostatic problem of a narrow rectangular crack embedded in an infinite elastic medium and subjected to equal and opposite shear stress distribution across its faces. Employing two-dimensional integral transforms and assuming a plane-strain solution across the width of the crack, the stress field ahead of the crack length is reduced to the solution of an integral equation of Fredholm type. A numerical solution of the integral equation and the corresponding mode II stress-intensity factor is obtained for several crack dimensions and Poisson's ratios of the material.     

Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

Energy dissipation due to frictional shake-down on a closed crack subjected to shear

The behaviour of a horizontal crack, subjected to cyclic shear and normal compressive stresses, is investigated with the aim of studying the shake-down and alternating plasticity phenomena. The analysis is carried out by means of the displacement discontinuity numerical method, conveniently modified so as to simulate the development of frictional stresses on the crack surfaces. The assumptions that the crack does not propagate and that the material behaves elastically are made. The critical values of the physical and geometrical parameters which determine the occurrence of frictional shake-down or alternating plasticity are identified. An evaluation of the amount of energy dissipated because of alternating plasticity is also provided.

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Sommario Nel presente articolo viene esaminato il comportamento di una fessura orizzontale soggetta a taglio ciclico e a sforzo normale di compressione. L'analisi è condotta mediante il metodo della Discontinuità di Spostamento, opportunamente modificato in modo da simulare lo sviluppo di sforzi di attrito sulle superfici della fessura. Vengono ricavati i valori critici dei parametri fisici e geometrici che determinano la comparsa del fenomeno dello shake-down. Viene infine valutata la quantità di energia dissipata in ogni ciclo di applicazione del taglio.

     

Transient contact shear stress in a layered elastic quarter space subjected to anti-plane shear loads

In this paper the transient behaviour of a contact shear stress in a layered elastic quarter space subjected to anti-plane shear loads is investigated. The loads are suddenly applied to upper and side edges of the layer. The effects of the reflected waves, the loaded position and the material properties to the contact shear stress are shown graphically.     

Elastic-viscoplastic fields near the tip of a propagating crack under anti-plane shear

The elastic-viscoplastic model proposed by Bingham was used to analyse the stress and strain surrounding the tip of a propagating crack under antiplane shear. The proper displacement pattern was given ; the asymptotic equations were derived and solved numerically. The analysis and calculation show that for smaller viscosity the crack-tip possesses logarthmic singularity, and for larger viscosity it possesses power-law singularity.In critical case, the two kinds of singularity are consistent with each other. The result revealed the important role of viscosity for crack-tip field.     

圆柱形爆炸容器绝热剪切瞬态失效过程

开展了圆柱形爆炸容器逐级加载和破坏实验,根据容器最终的断裂面和微观形貌观测,提出了爆炸容器绝热剪切失效模式。建立了应变率-应变空间内的绝热剪切损伤演化模型,将绝热剪切不同演化阶段的临界状态与宏观的力学条件联系起来,并将这些力学临界条件作为动态失效准则引入到宏观计算程序中,模拟爆炸容器发生绝热剪切的的瞬态过程,模拟结果成功预测了爆炸容器最终的断裂形貌。数值模拟结果还表明,爆炸载荷和率相关失效准则是控制绝热剪切失效模式的2个主要因素,细观初始缺陷往往导致绝热剪切的激发,但对容器最终的失效模式的影响是次要的。当容器在爆炸载荷作用下发生绝热剪切破坏模式时,裂纹(剪切带)扩展速度较快,此时若仍采用整体塑性应变失效准则考察容器的动力响应并作为失效判据,将不能预见材料局部的弱化和破坏。     

Transient response of a layered elastic half space subjected to a reciprocating anti-plane shear load

The well-known Cagniard's technique seems very useful for analyzing the transient problem of an elastic body subjected to a moving load with uniform velocity, but, in the cases of non-uniform velocity it would be difficult to apply the technique directly to analyze the problem. For such cases, instead of the technique, the convolution theorem of the Laplace transform or the dynamic Betti-Rayleigh reciprocal theorem has been applied usefully by many authors.In this paper, an inversion scheme which enables us to apply the Cagniard's technique directly to those difficult problems is presented by solving the problem of a reciprocating anti-plane shear load applied to a layered elastic half space. In this treatment it will be found clearly that our technique is simpler and more systematic than any other techniques for solving the problem. Numerical results are shown in the form of curves and the wave-front singularities are also investigated.     

Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading

We have developed a three-dimensional cohesive element and a class of irreversible cohesive laws which enable the accurate and efficient tracking of three-dimensional fatigue crack fronts and the calculation of the attendant fatigue life curves. The cohesive element governs the separation of the crack flanks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional finite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of the axial fatigue tests of aluminum shafts of Thompson and Sheppard, 1992a, Thompson and Sheppard, 1992b, Thompson and Sheppard, 1992c . The ability of the method to reproduce the experimentally observed progression of beachmarks and fatigue life curves is particularly noteworthy.     

Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading

The behaviour of a bi-piezoelectric ceramic layer with a centre interfacial crack subjected to anti-plane shear and in-plane electric loading has been studied. The dislocation density functions and the Fourier integral transform method have been employed to eliminate the problem of singular integral equations. The normalized energy release rate, stress and electrical displacement intensity factors, G/G₀,K_III/K_III0 and K_D/K_D0, respectively, were determined for different geometric and property parameters by use of two different crack surface electric boundary conditions, i.e. impermeable and permeable. It has been shown that the effects of the thickness and material constants of the piezoelectric layer on all the three parameters, i.e. G/G₀,K_III/K_III0 and K_D/K_D0 were significant.     

Dynamic crack propagation in a magneto-electro-elastic solid subjected to mixed loads: Transient Mode-III problem

The transient response of a Mode-III crack propagating in a magneto-electro-elastic solid subjected to mixed loads is investigated through solving the corresponding boundary-initial-value problem in both the cracked solid region and the interior fluid region with treatment of electro-magnetically permeable and impermeable crack face conditions in a unified way. The closed-form results for the dynamic field intensity factors are used to evaluate the dynamic energy release rate through the crack-tip dynamic contour integral. The permeability of the interior fluid region relative to the cracked solid region significantly affects the magneto-electro-mechanical coupling coefficient in the Bleustein–Gulyaev wave function and, consequently, the horizontal shear surface wave speed, the dynamic field intensity factors and the dynamic energy release rate. It is revealed from dynamic fracture mechanics analysis that the dynamic energy release rate thus obtained has an odd dependence on the dynamic electric displacement intensity factor and the dynamic magnetic induction intensity factor. It is also found that the horizontal shear surface wave speed provides the limiting velocity for the propagation of a Mode-III crack in a magneto-electro-elastic solid when there is only applied traction loading.     

Dynamic stability of a propagating crack

In this work we investigate the stability of a straight two-dimensional dynamically propagating crack to small perturbation of its path. Willis and Movchan (J. Mech. Phys. Solids 43 (1995) 319; J. Mech. Phys. Solids 45 (1997) 591) constructed formulae for the perturbations of the stress intensity factors induced by a small three-dimensional dynamic perturbation of a nominally plane crack. Their solution is exploited here to derive equations for the in-plane and out-of-plane perturbations of the crack path making use of the Griffith fracture criterion and the principle of “local symmetry” (i.e the crack propagates so that local K_II=0). We consider a crack propagating in a body loaded by a pair of point body forces and subjected to a remote uniaxial stress, aligned with the direction of the unperturbed crack. We assume that the loading follows the crack as the crack advances and is such that the unperturbed crack is subjected to Mode I loading. We perform an analysis of the stability of the dynamic crack in a similar way as in earlier work (Obrezanova et al., J. Mech. Phys. Solids 50 (2002) 57) on the quasistatically advancing crack. We present numerical results illustrating the influence of the crack velocity on the crack stability. Numerical computations of the possible crack paths have been performed which show that at velocities of crack propagation exceeding about one-third of the speed of Rayleigh waves the crack may admit one or more oscillatory modes of instability.     

Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods

This study applies two analytical approaches, Laplace transform and normal mode methods, to investigate the dynamic transient response of a cantilever Timoshenko beam subjected to impact forces. Explicit solutions for the normal mode method and the Laplace transform method are presented. The Durbin method is used to perform the Laplace inverse transformation, and numerical results based on these two approaches are compared. The comparison indicates that the normal mode method is more efficient than the Laplace transform method in the transient response analysis of a cantilever Timoshenko beam, whereas the Laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi-span Timoshenko beam. Furthermore, a three-dimensional finite element cantilever beam model is implemented. The results are compared with the transient responses for displacement, normal stress, shear stress, and the resonant frequencies of a Timoshenko beam and Bernoulli–Euler beam theories. The transient displacement response for a cantilever beam can be appropriately evaluated using the Timoshenko beam theory if the slender ratio is greater than 10 or using the Bernoulli–Euler beam theory if the slender ratio is greater than 100. Moreover, the resonant frequency of a cantilever beam can be accurately determined by the Timoshenko beam theory if the slender ratio is greater than 100 or by the Bernoulli–Euler beam theory if the slender ratio is greater than 400.     

Study of a propagating finite crack in functionally graded piezoelectric materials considering dielectric medium effect

This paper provides a study of the problem of a propagating finite crack under in-plane loading in functionally graded piezoelectric materials (FGPMs). The analytical formulations are developed by Fourier transforms and the resulting singular integral equations are solved by using Chebyshev polynomials. By using a dielectric crack model with deformation-dependent electric boundary condition, numerical simulations are made to show the effects of the dielectric medium, the gradient of material properties and the speed of crack propagation on the fracture parameters, such as the stress, electric displacement and crack opening displacement intensity factors. A critical state for the electromechanical loading applied to the FGPMs is observed, which determines whether the traditionally impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric model. The validity of this dielectric crack model is also examined by comparing the results of different existing crack models.     

Anti-plane shear crack growth rate of piezoelectric ceramic body with finite width

The theory of linear piezoelectricity is applied to develop an anti-plane crack growth rate equation of a finite crack in a piezoelectric ceramic body with finite width. Plastic zone is assumed to be confined to a sheet ahead of both crack edges similar to the strip model for in-plane loading. The procedure consists of reducing a system of dual integral equations to a Fredholm integral equation of the second kind. The accumulated plastic displacement criterion is used for developing a solution for the crack growth rate. Numerical values of crack growth rate are obtained and the results are displayed graphically to exhibit the electroelastic interactions.     

Stress intensity factors of an oblique edge crack subjected to normal and shear tractions

Stress intensity factors (SIFs) were obtained for an oblique crack under normal and shear traction and remote extension loads. The oblique crack was modeled as the pseudodislocation. The stress field due to tractions was solved by the Flamant solution. The SIR of Mode I and Mode II (K_Iand K_II) were then obtained. Finite element analysis was performed with ABAQUS and compared with the analytical solutions. The analytical solutions were in good agreement with the results of FEM. From investigating SIFs and their ranges, the following results were obtained. The growth rate of an oblique edge crack decreased due to the reduction in the SIF ranges. The crack driving force depended on the obliquity, the normal traction and the ratio of crack to traction length. The peak value of shear traction was found as a key parameter to accelerate the crack growth.     

Diffraction of a shear plane wave in a compound elastic space with a half-infinite crack parallel to the inhomogeneity line

Problems of stress wave propagation and diffraction in elastic inhomogeneous media are undoubtedly of interest to scientists from the viewpoint of investigation of fundamental laws of dynamic processes and of the use of the results in technical and technological applications. The paper deals with the dynamic contact problem of shear plane wave diffraction at the edge of a semi-infinite crack in a compound space consisting of two elastic half-spaces. The questions related to the onset of surface waves and the wave field behavior in far-field regions are also considered.     

Time-domain finite difference calculations for interaction of an ultrasonic wave with a surface-breaking crack

Four two-dimensional configurations are considered in this paper. The first two concern a homogeneous slab (0⩽y⩽H, −∞<x<∞), with a surface-breaking crack (x=0, 0⩽y⩽a), and without such a crack. The other two configurations concern semi-infinite slabs of different mechanical properties which are in welded contact over x=0, 0⩽y⩽H. One of these has a surface-breaking crack in the interface (x=0, 0⩽y⩽a), and the other has perfect contact over the whole interface. Results are presented for diffraction and corner reflection of an ultrasonic displacement pulse. Time-domain calculations have been carried out bu the use of the finite difference method. The results are presented as full-field snapshots of the displacement fields at specified times, and as time histories of the particle velocity at the midpoint of the transducer-specimen interface at x=−H, y=H.     

Contact problem for a plane crack under a normally incident antiplane shear wave

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied Published in Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 138–142, May 2007.