A theory of caustics for mixed-mode fast running cracks

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. Completely analytical expressions were derived for the caustic curves as well as for the initial curves for fast running cracks under inplane mixed-mode conditions. The effects of crack velocity and mixed-mode condition on the caustic pattern and the initial curve were investigated. New procedures were also proposed for the evaluation of the dynamic stress intensity factors K_I and K_II using the overall dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.     

Response of cracks to impact by caustics

A study of the behaviour of notched plexiglas specimens under stress pulses created from an air-gun was undertaken. It was concluded that the initial notch is propagated by steps under the action only of tensile stress pulses, while the compressive stress pulses do not have any influence on crack propagation. It was also found that the maximum crack propagation velocity depends on the magnitude of the applied stress pulse, as well as on the initial notch length. Furthermore, the dependence of the crack-tip stress intensity factor on the crack propagation velocity was established and the critical strain energy release rate was determined. Finally, a comparison of the results of the present paper with the corresponding theoretical or experimental data of previous investigations was made.     

Elastodynamic response of a finite strip with two coplanar cracks under impact load

The elastodynamic response of two coplanar Griffith cracks in a finite elastic strip under in-plane compression and anti-plane shear impact is considered in this paper. Laplace and Fourier transforms are used to reduce two mixed boundary value problems to Cauchy-type singular integral equations in Laplace transform plane, which are solved numerically. The elastodynamic stress-intensity factors are obtained as functions of time and geometry parameters.     

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.     

Optically exact equations of caustics for slant cracks biaxially loaded

The equations of caustics have been derived based on the exact theory of geometrical optics, and they have been adapted to the problem of a slanting internal crack in a disk under biaxial loading. A comparison of the exact caustics with those derived from the far-field theory used in the past in the applications showed negligible difference between the two theories. Thus, it is shown that the approximate theory of caustics used before for determining singular fields in mechanics is sufficiently accurate for engineering applications.     

Growth of surface cracks under constant and variable amplitude loading

Fatigue crack growth experiments were performed on surface cracked tensile specimens of Inconel 718 at 400 °C. The loading was carried out at constant as well as at variable amplitude. The experimental results for the mean growth rate were compared with predictions based on data obtained from testing of compact tension specimens. Both nominal data as well as data corrected from measured crack closure were used in the predictions. The corrected data provided much better predictions than the nominal ones indicating that the level of crack closure during the testing of the surface cracked specimens was much lower than in compact tension specimens.     

Fatigue propagation threshold of short cracks under constant amplitude loading

In this study a threshold for fatigue crack propagation as a function of crack length is defined from a depth given by the position d of the strongest microstructural barrier to crack propagation, which defines the plain fatigue limit. The material threshold is estimated from the plain fatigue limit Δσ_eR, the position d of the strongest microstructural barrier and the threshold for long cracks, ΔK_thR. The threshold for eight different materials for which experimental results can be obtained from the literature was estimated. Good agreement was observed in all cases. Some quantitative analyses of the fatigue propagation behavior of short cracks are carried out and discussed.     

Problem of two coplanar Griffith cracks running steadily under three-dimensional loading

In this paper, the three-dimensional problem of two coplanar Griffith cracks propagating uniformly in an elastic medium has been considered. Equal and opposite tractions which are triaxial in nature are applied to the crack surfaces. The two-dimensional Fourier transforms have been used to reduce the mixed boundary value problem to the solution of triple integral equations. In order to solve the problem, the transformed surface displacement has been expanded in a series of Chebyshev polynomials which is automatically zero outside the cracks and also satisfies the edge conditions. Finally Schmidt method has been used to determine the unknown constants occurring in the series. Numerical calculations are carried out to obtain the crack opening displacement and also the stress intensity factors for different values of the parameters.     

Dugdale crack closure analysis of fatigue cracks under constant amplitude loading

Fatigue fracture mechanics which means structural analysis including crack propagation and crack closure in conjunction with a local failure criterion provides detailed insight into mechanisms of cyclic loaded crack sheets. Using the Dugdale method and rigid-perfectly plastic strip material law the infinite sheet with colinear cracks was parametrically investigated in respect of: SSY limits, crack closure occurrence, formation of contact stresses and displacements, influences of material parameters, $\text{R-}\text{ratio}$ and maximum load on effective stress ratio. Rationales for the load ratio, mean load and maximum load dependence and the form of $\text{da/dN-}\text{curves}$ are given based on crack closure analysis.     

Short surface fatigue cracks growth under constant and variable amplitude loading

This paper deals with the fatigue strength of S355NL steel, of a common use within the shipbuilding industry, under uniaxial constant and variable loading. Indeed, ship structures are subjected to variable loading due to various sea states, wind and waves. As a consequence, a better knowledge of fatigue behavior under real loading conditions is needed. This study aims at analyzing the influence of loading conditions (load ratio and variable amplitude loading) on the short crack behavior and last, with a proposed model to assess the fatigue crack life. The tools used to prepare inspections in critical areas only take into account the long crack behavior. The results from the proposed model were compared to the assessments these tools are providing with.     

Dynamic studies of running half-plane and cruciform cracks

The dynamic problems of a crack running perpendicularly into a half-plane surface and a cruciform crack running in an unbounded solid under the action of moving point forces are analyzed. The cracks are treated as dislocations distributed w.r.t. Speed, so that the problems reduce to singular integral equations with Dirac functions as non-homogeneous terms. By extracting physically significant limit cases with analytical solutions, the terms are removed, and the resulting equations solved numerically by a standard technique. Dynamic stress intensity factor and crack opening data are presented. For the cruciform crack, this data is compared with that for the plane crack limit case.     

Crack expanding with constant velocity in an anisotropic solid under anti-plane strain

An analytic solution is given for a crack expanding with constant velocity from zero length in an anisotropic material under anti-plane strain. Not all anisotropic materials can support anti-plane strain, and the study is therefore by necessity limited to a certain class of materials, including monoclinic materials. A double Laplace transform is used and the inversion technique is based on the self-similarity of the problem. The result shows that the crack shape is elliptic, as in the corresponding isotropic case. The displacement on the crack plane outside the crack is found to be zero. Expressions are given for the stresses, the stress intensity factor and the energy flux into the crack edge. In contrast to the isotropic case a transverse normal stress may appear, singular at the crack edge. This revised version was published online in July 2006 with corrections to the Cover Date.     

The stress intensity factors of internal radial cracks in rotating disks by the method of caustics

A technique based on the method of caustics is used to evaluate the stress intensity factors of internal radial cracks in rotating disks. The measurement strategy, experimental procedures and results are presented. The accuracy of the technique is demonstrated by comparing experimental results to theory.     

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.     

Local variations of the dynamic elastic modulus around running cracks

The variation of the dynamic elastic modulus in the immediate vicinity of the tip of the running crack was studied through an iterative procedure, based on the theoretical expressions for the stress-field components and the experimental relation between strain rate and elastic modulus. It was found that the elastic modulus varied strongly around the tip of the crack, both in radial and polar sense. Also it was observed that the polar distribution of the elastic modulus presented clear off-axis extrema in directions that were in good agreement with experimentally measured branching angles, thus indicating a possible relation between these two phenomena.     

Propagation of a slant crack under impact studied by caustics

In the present paper the propagation of a slant crack under an impact load was studied by the method of caustics. An air gun was employed for the production of the load pulse. It was concluded that the steady crack velocity increases linearly with the angle of crack inclination, reaching a maximum value when the initial crack is normal to the load direction. The crack starts to propagate in the presence of both K_I- and K_II-stress intensity factors. The K_II-factor has a maximum value of one-tenth of the K_I-factor and an oscillatory character. This becomes zero in the first third of the crack-path, as the crack tends, gradually, to follow its final direction, normal to the direction of the applied pulse. An apparently distinctive effect relating the crack velocities and stress intensity factors may be concluded from the experimental results. For the same values of K_I and K_II, the crack propagates in some cases with different velocities, depending, apparently, on the initial crack inclination. It is believed that it is related to the validity of energy fracture-criteria and requires further study.     

球笼式等速万向联轴器强度设计缺陷的回归辨识

复杂机械产品零部件的强度受多因素影响,且这些影响因素与零部件强度之间的关系非常复杂,常常难以建立其解析的数学模型,这给复杂机械产品零部件强度设计缺陷的辨识带来了困难．以球笼式等速万向联轴器为研究对象,将其内外沟道的接触应力作为强度判断的依据,将历史设计方案中影响零部件接触应力的设计参数作为因变量,建立接触应力与各相关影响因素的回归方程,通过拟合后的回归方程分析各因素对内外沟道强度的影响程度,计算出各影响因素的最大拟合误差值．将新设计方案中影响零部件接触应力的设计参数代入回归方程,求得参数设计值与回归方程的输出值之间的差值,将此差值与回归方程最大拟合误差值进行对比分析,辨识出球笼式等速万向联轴器设计中存在的强度设计缺陷,有效提高了设计质量和效率．     

基础简谐激励下匀速旋转运动电流变夹层梁的振动稳定性

摘 要：建立了基础激励和定轴转动联合作用时电流变夹层梁的运动微分方程,着重研究了基础简谐激励和匀速旋转运动作用时电流变夹层梁的振动稳定性。采用多尺度法获得了梁的一次近似解析解和参激振动失稳的条件。通过对电流变夹层梁在不同激励参数、控制电场和旋转角速度时的振动响应时间历程曲线和对应相图的数值分析,探讨了电场作用下电流变夹层梁的参激振动稳定性。仿真结果表明,在一定的条件下,可以通过控制作用于电流变夹层梁的电场强度来改变系统出现运动不稳定的临界激励幅值,提高结构的动力稳定性。     

Solution of a rectangular sheet containing a central crack propagating at constant velocity under antiplane shear

Making use of the Fourier transform and Fourier series, the dynamic stress intensity factor of a rectangular sheet with a central crack moving at a constant velocity under antiplane shear is obtained. It is also proved that the solutions of a strip with a central crack propagating at constant velocity for Mode III are the special cases of the solution in the present paper.