Impact response of a finite crack in a finite strip under anti-plane shear

The response of a through-the thickness crack with finite dimensions to impact in a finite elastic strip is investigated in this study. The elastic strip is assumed to be subjected to anti-plane shear deformation. Laplace and Fourier transform were used to formulate the mixed boundary value problem. The dynamic stress intensity factor and crack opening displacement are obtained as a function of time and the strip width to crack length ratio, h/a. The results indicate that the intensity of the crack-tip stress field reaches a peak very quickly and then decreases in magnitude oscillating about the static value. In general, the dynamic stress intensity factor is higher for small $\text{h/a}$. Similar behavior has also been found for the crack surface displacement.     

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

Summary The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.     

A Griffith crack shielded by a dislocation pile-up

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.     

Elastodynamic response of a penny-shaped crack in a cylinder of finite radius

The elastodynamic response of a penny-shaped crack in a cylinder of finite radius is investigated in this study. A step stress is applied to the crack surface resulting in transient behavior. The stress field near the crack front and the dynamic stress intensity factor are determined. Numerical resifits on the dynamic stress intensity factor are obtained to show the influence of inertia, geometry and their interactions on the load transfer to the crack.     

Elastodynamic stress-intensity factors for a semi-infinite crack under 3-D combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.     

Hybrid stress finite element analysis of bending of a plate with a through flaw

A hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through-the-thickness crack is presented. Reissner's sixth-order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated. The effects of the explicit enforcement of traction-free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction-free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensity factor.     

STRESS-RATIO EFFECT OF FATIGUE CRACK PROPAGATION IN A BIAXIAL STRESS FIELD

Fatigue crack propagation tests were conducted under conditions of equibiaxial, uniaxial and shear loading by using a cruciform specimen in a servo hydraulic testing machine. The effect of non-singular stress cycling on the fatigue crack propagation rate was examined based on the observation of crack opening behavior. The crack propagation rate was significantly influenced by the non-singular stress parallel to the crack when it was correlated to the stress intensity range. The crack closure behavior was greatly affected by the non-singular stress. The crack propagation rate was uniquely correlated to the effective range of the stress intensity factor except for the case of completely reversed shear loading where significant plasticity was detected. The crack opening displacement range was concluded to be a parameter controlling the crack propagation rate for all the stress conditions examined in the present experiments. Some discussion is made on the effect of material anisotropy on fatigue crack propagation in a biaxial stress field.     

Analytical calculation of the stress intensity factor in a surface cracked plate submitted to thermal fatigue loading

A stainless steel specimen with a pre-existing surface notch is exposed to a convective medium of cyclic temperature. The history of stress intensity factor of the cracked body for different crack lengths is obtained by a closed-form integration of the stress field, using Duhamel’s theory with principle of superposition and appropriate weight functions. The obtained results are compared with numerical simulations performed with ABAQUS and they appear to be in very good agreement. The stress intensity factor history shows that fatigue behavior does not depend only on temperature amplitude ΔT=T_max-T_min, quenching rate, and duration of thermal shock but also on heating rate and duration.     

Yoffe-type moving edge crack in a piezoelectric block

Summary We consider an anti-plane edge moving crack problem with the constant velocity in a piezoelectric ceramic block. The far-field anti-plane shear mechanical and in-plane electrical loads are applied to the piezoelectric block. It is expressed to a Fredholm integral equation of the second kind. Expressions for the dynamic field intensity factors and the dynamic energy release rate are obtained. The dynamic stress intensity factor and the dynamic energy release rate depend on the crack propagation speed. Numerical results for several piezoelectric materials are also presented.     

爆炸载荷下边界锐V型切口尖端裂纹扩展行为

为了研究爆炸应力波作用下板条边界锐V型切口端部的动态扩展行为,采用动态焦散线实验方法,进行了爆炸载荷下板条边界锐V型切口端部裂纹扩展规律的实验研究。研究结果表明,爆炸应力波作用下,板条试件边界锐V型切口端部的扩展过程中,裂纹扩展速度、加速度和切口端部动态应力强度因子随时间是波动变化的。扩展速度最大值达到210m/s,裂纹扩展加速度最大值为9.47Mm/s2,切口端部动态应力强度因子KdⅠ最大值为0.6MN/m3/2。     

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

The elastodynamic response of an infinite non-homogeneous orthotropic material with an interfacial finite crack under distributed normal and shear impact loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some materials are obtained. Interfacial cracks between two different materials and between two pieces of the same material but different fiber orientation are considered. Bimaterial formulation of a crack problem is shown to converge to the mono-material formulation, derived independently, in the limiting case when both materials are the same.     

爆炸载荷下边界锐V型切口尖端裂纹扩展行为

为了研究爆炸应力波作用下板条边界锐V型切口端部的动态扩展行为,采用动态焦散线实验方法,进行了爆炸载荷下板条边界锐V型切口端部裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界锐V型切口端部的扩展过程中,裂纹扩展速度、加速度和切口端部动态应力强度因子随时间是波动变化的.扩展速度最大值达到210m/s,裂...     

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.     

Stress concentration around a strongly oblate cavity in a cubic crystal and its associated crack problems

The stress distribution around a strongly oblate spheroidal cavity in a cubic crystal is determined by the equivalent inclusion method. The stress concentration factor is shown to be a product of two factors: one factor is purely geometric; the other factor depends on the material properties. By allowing the aspect ratio of the cavity to approach zero, the stress intensity factor of the associated penny-shaped crack is deduced. The energy release rates of cracks on {1 0 0} planes are computed for different growth directions. Theses results are found to be correlated well with Zener’s anisotropy factor.     

On the dynamic behavior of a piezoelectric-elastic laminate with a crack in the piezoelectric material under electro-mechanical loads

The dynamic behavior of a piezoelectric-elastic laminate with a crack in the piezoelectric material under in-plane steady-state electro-mechanical loads is considered. Based on the use of integral transform techniques, the problem is reduced to a set of singular integral equations, which are solved using Chebyshev polynomial expansions. Numerical results are provided to show the variation of both the dynamic stress intensity factors and electric displacement intensity factor with frequencies of the applied electro-mechanical loads. A phenomenon similar to “resonance” is observed when the applied loads act in some specific ranges of frequencies, and both the dynamic stress intensity factors and electric displacement intensity factor may increase significantly, which will lead to the failure of piezoelectric material. The effects of applied electric fields, crack geometry and elastic layer thickness on the phenomenon are also discussed.     

Scattering of SH wave by a crack terminating at the interface of a bimaterial

A general method for solving the scattering of plane SH wave by a crack terminating at the interface of a bimaterial is presented. The crack can terminate at the interface in an arbitrary angle. In order to solve the proposed problem, the Greens function for a point harmonic force applied at an arbitrary point of the bimaterial is established by the Fourier transformation method. Using the obtained Greens function and the Betti-Rayleigh reciprocal theorem, the total scattered field of the crack is constructed. The total scattered field of the crack is divided into a regular part and a singular part. The hypersingular integral equation of the crack is obtained in terms of the regular and singular scattered field as well as the free wave field. The stress singularity order and singular stress at the terminating point are analyzed by the hypersingular integral equation and the singular scattered field of the crack. The dynamic stress intensity factor (DSIF) at the terminating point is defined in terms of the singular stresses at the terminating point. Numerical solution of the hypersingular integral equation gives the DSIFs at the crack tips. Comparison of our results with known results confirms the proposed method. Some numerical results and corresponding analysis are given in the paper.Constructive advice from the anonymous reviewers is acknowledged.     

An analytical and numerical study of a dynamically accelerating semi-infinite crack in a linear viscoelastic material

In a previous paper, a general method was presented for constructing the solution to the problem of a semi-infinite, mode III crack propagating dynamically through an infinite, general linear viscoelastic body. The only restrictions placed upon the crack tip speed were that it have constant sign and in magnitude not exceed the glassy shear wave speed. In the present contribution, those previous analytical results are applied to a study of dynamic unsteady crack growth in a linear viscoelastic body. In particular, a numerical algorithm for computing the stress intensity factor is given along with example simulations of running cracks using the Achenbach-Chao viscoelastic model and a stress intensity factor (SIF) fracture criterion. We also compare the transient SIF with the dynamic steady state SIF, and examine the transition to constant crack speed for a dynamically accelerating crack in a viscoelastic material.     

Initiation and propagation of a penny-shaped crack in a finitely deformed incompressible elastic medium

The effects that the initial lateral stress has on the initiation and the propagation of a penny-shaped crack are investigated on the basis of the theory of small deformations superposed on finite deformation for an incompressible elastic material. Using the methods of the Laplace and Hankel transforms, the crack shape function and the stress distribution with singularities in the crack plane are obtained in closed forms for the crack propagating at a constant speed in the Mooney material. The dynamic stress-intensity factor is obtained as a function of the initial lateral stretch and the ratio of the crack speed to the shear wave speed. For the same crack speed, the value of the dynamic stress-intensity factor increases with increasing lateral stretch, but decreases if the lateral compression increases.The dynamic solutions reduce to the associated static solutions at zero crack speed. For the stationary crack, the stress-intensity factor is shown to be independent of the initial stress. However, the initial lateral stretch increases, but the lateral compression decreases the value of the critical stress required for the initiation of crack growth on the basis of the Griffith theory. The central crack opening displacement is shown to decrease if the lateral stretch increases or the lateral compression decreases.     

Dynamic crack growth along an elastoplastic bimaterial interface

Summary The near-tip stress and deformation rate fields of a crack dynamically propagating along an interface between dissimilar elastic-plastic bimaterials are presented in this paper. The elastic-plastic materials are characterised by theJ ₂-flow theory with linear plastic hardening. The solutions are assumed to be of variable-separable form with a power-law singularity in the radial direction. Two distinct solutions corresponding to the tensile and shear solutions exist with slightly different singularity strengths and very different mixities at the crack tip. The phenomenon of discrete and determinate mixities at the interfacial crack tip is confirmed in dynamic crack growth. This is not an artifact of the variable-separable solution assumption, arising from the linear-hardening material model. The dynamic crack analysis shows that the mixity of the near-tip field is mainly determined by the given material parameters and affected slightly by the crack propagation velocity. A significant variation of the mixity is observed near to the coalescing point of the tensile and shear solutions. The strength of the singularity is almost determined by the smaller strain-hardening alone, and dynamic inertia decreases the stress intensity. The asymptotic solutions reveal that the crack propagation velocity changes only the stress field of the tensile mode significantly. With increasing the crack propagation velocity, the stress singularity of the tensile solutions decreases obviously and the stress triaxiality at the tip (=0) falls considerably at the unity effective stress. These observations imply that the fracture toughness of the interface crack under tensile mode may be significantly higher than that under quasi-static conditions.     

Weight Function for a Crack in a Two-dimensional Orthotropic Medium Under Impact Shear Loading

The paper examines the elastodynamic response of an infinite two-dimensional orthotr- opic medium containing a central crack under impact shear loading. Laplace and Fourier integral transforms are employed to reduce the problem to a pair of dual integral equations in the Laplace transformed plane. These equations are reduced to integral differential equations, which have been solved in the low frequency domain by iterations. To determine time dependence, these equations are inverted to yield the dynamic stress intensity factor (SIF) for shear point force loading that corresponds to the weight function for the crack under shear loading. It is used to derive SIF for polynomial loading.