含圆孔缺陷三点弯曲梁的裂纹扩展特性实验研究

采用动态焦散线实验系统,对含圆孔缺陷的PMMA材料进行冲击断裂力学实验,研究三点弯曲梁中不同直径和位置的圆孔缺陷对扩展裂纹的影响。实验结果表明:扩展裂纹与圆孔缺陷相互作用前,呈现Ⅰ型拉伸断裂,扩展路径平直;与圆孔缺陷相互作用后,贯通萌生的次裂纹沿直线继续扩展,未贯通的裂纹偏移扩展。扩展裂纹与路径上圆孔缺陷贯通过程中,裂纹扩展速度和动态应力强度因子快速降为零,裂纹的扩展受到抑制,且圆孔直径越大、距离越近,抑制作用越显著;贯通萌生次生裂纹的起裂速度和起裂韧度,随着圆孔缺陷直径的增大而变大。扩展裂纹与偏置圆孔缺陷相互作用过程中,当圆孔缺陷直径越大、偏置距离越小,裂纹起偏距离越短,最大偏移量越大,并且扩展裂纹动态应力强度因子和扩展速度局部小幅增大。研究结果为分析动态裂纹扩展特征和材料破坏模式提供借鉴。     

Some problems involving distributions of screw dislocations in a finite slab

This paper considers two problems involving distributions of screw dislocations in a finite slab. The first problem is concerned with the spread of plasticity from a crack ¦x₁¦c, x₂ = 0 in the finite slab ¦x₂¦ h/2 subject to an externally applied shear stress p₂₃ = σ, and is treated in terms of the theory of continuous distributions of dislocations. The extent to which the dislocations describing the plastic relaxation spread from a crack tip is determined, together with the relative displacement of the crack surfaces at its tips. Thus the criterion for crack extension is calculated, particular attention being given to the case when fracture occurs at low applied stresses. The second problem studied is the special case of the first problem that arises when no plastic relaxation is allowed; the criterion for crack extension is then determined from energetic considerations; the similarity between the two sets of results for low stress fractures is emphasized.     

A fracture criterion for three-dimensional crack problems

A criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems. Fracture is assumed to initiate from the nearest neighbor element located by a set of spherical coordinates (r, θ, φ) attached to the crack border. The new fracture surface is described by a locus of these elements whose locations correspond to the strain energy function, dW/dV, being a minimum. The function dW/dV is found to be singular of the type 1/r and is of quadratic form in the three stress intensity factors k₁, k₂ and k₃ expressed through the strain energy density factor S. It is postulated that unstable crack propagation initiates from a region where S reaches a critical value S_cr = r₀(dW/dV)_cr. The locations of failure lying on the fracture surface is determined by holding (dW/dV)_cr = S_min/r₀ constant. The quantity S_min stands for the value of S minimized with respect to θ and φ and r₀ is a radial distance measured from the crack border.

An example of failure prediction for an embedded elliptical crack subjected to both normal and shear loads is presented. According to the S-criterion, fracture initiation takes place at the ends of the minor axis. An unexpected result is that for a narrow elliptical crack and Poisson's ratio of 1/3 the lowest failure load occurs when the uniaxial tensile load makes an angle of approximately 60° with the crack surface and is in the plane of the major axis. This is in contrast to the expectation that the lowest critical load occurs when the uniaxial tension is perpendicular to the crack surface. In the limit as the elliptical crack becomes increasingly narrower, the result reduces to the two dimensional line crack case of Mode I and III loading. The S-criterion is also applied to the failure prediction of three dimensional cracks under compressive loads.     

The elastically equivalent softening zone size for an elastic-softening material: II. A simple piece-wise softening law

The paper determines the elastically equivalent softening zone size R_E for an elastic-softening material when there is a semi-infinite crack in a remotely loaded infinite solid; the parameter R_E plays a central role in size effect expressions that are used to correlate the maximum loads that can be sustained by solids having different dimensions. The stress (p) versus displacement (v) softening law considered is that for which P = p_c for oc and P = ; qp_c = p_* for λδ_c< v <δ_c. Particular attention is focussed on the case where the parameters λ and q are both small. Such a softening law simulates the softening behaviour of plain concrete, where there is an initially rapid softening to a low stress value at a small displacement, followed by a long tail that is associated with a low stress. The paper shows that the behaviour of a material with such a softening law can be conveniently analysed by assuming that there is a non-zero stress intensity (K_IC) at the crack tip followed by a constant stress p_* within the softening zone; , where E_o is the reduced modulus and G_{I = λpcδc} is the contribution to the specific fracture energy arising from the initially rapid softening region. Analysis of a specific model demonstrates the viability of this approach by showing that there is consistency with the proposed size effect expressions based on R_E.     

Fatigue crack closure study based on whole-field displacements

This study is concerned with crack tip strain field fluctuations at loads below the point of crack closure in fatigue cycling. Moiré interferometry was used to investigate crack tip fields in compact tension specimens, cracked under constant stress intensity range and fixed R-ratio conditions. An elastic-plastic finite element model of simulated closure was developed to provide a theoretical cross-reference for the moiré studies. The ‘stretched zone’, which is believed to be the most significant source of closure effects, was simulated by inserting a constant thickness strip of elements into the crack before unloading from the maximum load point. Analysis of the crack tip fields in the experimental and theoretical cases was made in terms of crack face opening profiles, compliance changes and elastic stress intensity parameters. The latter were inferred through stress and displacement measurements made along circular and radial paths relative to the crack tip. Closure on the stretched zone was found to generate non-proportional loading in the crack tip field, so that the resulting stress changes were not well characterized by the asymptotic elastic equations. It is concluded firstly, that significant strain fluctuations occur below the point of closure load and that these should not be ignored in crack propagation studies. Secondly, the effective stress intensity range in fatigue cycling is not simply related to the open-crack stress intensity range and the need therefore remains for R-ratio and geometry effects to be treated as variables in crack propagation data collection programmes.     

Recent considerations in experimental compliance calibration of the WOL specimen

This report summarizes work directed at the verification of currently used compliance relationships for the wedge-open-loading (WOL) specimen geometry frequently used in fatigue crack propagation testing. An overview is given of compliance curve fitting procedures. A new procedure is proposed which appears to offer significant advantages. Extensive testing and analytical details are included so that compliance procedures for crack growth monitoring can be improved. Compliance calibration results are presented for Ti-6Al-4V(RA) and Ti-6Al-4V(β) alloys.

Analytical procedures for obtaining the stress intensity calibration function (C₃) from experimental compliance results were compared and the proposed three parameter fit was found to be superior. The advantages of this proposed data analysis procedure are: small numbers of constants; relationship between normalized compliance (compliance × modulus × thickness) and normalized crack length (crack length/specimen width) is differentiable and invertible; consistency with physical reasoning; and discussion of possible differences in compliance due to material differences can be restricted to a single parameter.

For Ti-6Al-4V(β), the experimentally based C₃ values were found to be similar to analytically derived values, while for Ti-6Al-4V(RA) they differed significantly. Possibly this difference in RA results was due to the highly textured material used for the experimental investigation.     

The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-local theory

In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material plane under anti-plane shear waves is investigated by using the non-local theory for impermeable crack face conditions. For overcoming the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical elasticity solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the circular frequency of incident wave and the lattice parameter. For comparison results between the non-local theory and the local theory for this problem, the same problem in the piezoelectric materials is also solved by using local theory.     

Energy release rate and bifurcation angles of piezoelectric materials with antiplane moving crack

The dynamic fracture problems of the piezoelectric materials with antiplane moving crack are analysed by using function of complex variable in the paper. The results show that the coupled elastic and electric fields inside piezoelectric media depend on the speed of the crack propagation, and have singularity at the crack tip. The stress intensity factor is independent of the speed of the crack propagation, which is identical to the conclusion of purely elasticity. Moreover, independent of the electric loading, the dynamic energy release rate can be expressed by the stress intensity factor and enlarge with the increase of crack speed. High speed of the crack moving could impede the crack growth. At the same time, the crack can be propagated into either curve or bifurcation if the crack speed is higher than the critical speed.     

A mixed boundary problem for a finite internally cracked plate

A displacements and resultant forces model (see eqns 2–5, 13 and 17) for a finite internally cracked plate is proposed. This model satisfies: (a) The equilibrium and compatibility condition in the region occupied by cracked plate; (b) Stress free condition on the surface of crack; (c) Single value condition of displacements around the crack. In this model, some undetermined coefficients are contained, these coefficients are derived from outer boundary condition.

It is proved that, this model is convenient not only for the displacements or resultant forces boundary problem, but also for the mixed boundary problem. Besides this, if the boundary problem is solved, to find the value of displacements of any points in cracked body is also convenient.

Two mixed boundary problems, one for the square cracked plate (see Fig. 3), and another for circular cracked plate (see Fig. 5), are solved. The numerical results obtained are shown in Tables 1 and 2 and Figs. 4 and 6 respectively. These results can explain how the constraint affects the values of the stress intensity factor on the crack tips.     

Solutions of multiple crack problems of a circular region with free or fixed boundary condition in antiplane elasticity

Four cases of multiple crack problems in antiplane elasticity, circular region or an infinite region exterior to a circle with free or fixed boundary condition, are considered in this paper. For all these cases, the presented elementary solution is a particular solution of the circular region containing one crack. The solution consists of two parts and satisfies the following conditions: (a) The first part corresponds to a pair of longitudinal forces acting at a prescribed point on both edges of a single crack; (b) The second part corresponds to some distributed forces along both edges of the crack; (c) The elementary solution, i.e. the sum of the first and second parts, satisfies the above mentioned boundary value conditions along the circular boundary. As we have done in [1–3], the system of Fredholm integral equations for the undetermined densities of the elementary solutions can be easily estabished and the stress intensity factors at crack tips can also be evaluated.     

宏微观双尺度运动裂纹模型面内拉伸下的解析解*

研究裂纹动态扩展中宏微观因素相互作用机制与微观裂尖区的钝化效应。平面拉伸状态下,宏观主裂纹以恒定速度运动。通过一个介观约束应力过渡区,将宏观主裂纹与微观裂尖区相连接,由此建立了一个宏微观双尺度运动裂纹模型。应用弹性动力学与复变函数理论,分别在宏观与微观尺度下对该模型进行解析求解,获得了解析解。通过裂纹张开位移从宏观到微观的连续性条件与宏微观应力场协调条件,将两个不同尺度下的解相耦合,获得了计算宏微观损伤区特征长度的显式表达式。研究表明,运动裂纹的宏观应力场仍具有通常的r&;#61485;1/2的奇异性。由于微观裂尖的钝化,微观应力场奇异性的阶次有所降低,与宏观应力场相比具有弱奇异性。双尺度运动裂纹模型中,可允许裂纹运动速度达到剪切波速,解除了经典运动裂纹理论中裂纹速度不能超过Rayleigh波速的限制。数值结果表明,介观损伤过渡区与裂尖微观损伤区尺寸,及裂纹张开位移等,与裂纹运动速度、材料性质、约束应力比、裂尖钝化角度等因素有关。     

The role of stress state on hydrogen cracking in Fe-Si single crystals

While state-of-stress effects have long been known to play a major role in hydrogen embrittlement, there has been little direct evidence outside of thickness effects on threshold stress intensities. Also, there have been recent mechanisms proposed suggesting that enhanced plasticity effects may be more dominant than enhanced decohesion effects. If true, this would mandate different state of stress effects. The goal here was to settle this issue in at least one material, that being a semi-ductile, iron base single crystal. This was achieved by examining the crack initiation site under various loading and hydrogen interaction conditions in precracked Fe-3wt.%Si single crystals oriented in {001}<010> and {001}<110>. A strong dependency of hydrogen-induced cracking on the state of stress was evidenced by the consistent nature of a mid-section initiation stage and tunneling behaviour during crack propagation. This plane stress vs plane strain effect was quantified by analysing both small scale yielding and discretized dislocation computer solutions of the stress field. It was shown that the former did not provide sufficient stress and hydrogen in the local sense while the latter provided both high stress and hydrogen enrichment to cause decohesion. Finally, an assessment is made as to whether surface observations are helpful in sorting out the micromechanical aspects of cracking. This is addressed by examining surface plasticity with respect to the interior crack profile.     

Cyclic crack growth and fracture resistance of Ti-6Al-6V-2Sn as influenced by recrystallization anneal and interstitial oxygen content

This study was undertaken to determine methods for metallurgical improvement of cyclic crack growth and fracture properties in Ti-6A1-6V-2Sn. Two heats of the alloy were studied: an + β processed material containing 0.165% interstitial oxygen and β-processed material containing 0.077% interstitial oxygen. All test specimens were given a mill anneal heat treatment, in addition some specimens from each heat were given a recrystallization anneal treatment Fatigue-crack growth rates were determined using compact tension specimens and fracture toughness was determined using 1 in. dynamic tear specimens for each material/heat treatment combination. The recrystallization anneal treatment resulted in significant improvements in the fracture resistance of both materials, despite metallographic evidence that die recrystallization-annealed β-processed material did not develop a fully recrystallized structure. Improvements in cyclic crack growth resistance resulting from the recrystallization anneal treatment, per se, were modest. However, the combined effects of recrystallizalion anneal plus a reduction B interstitial oxygen content significantly improved the cyclic crack growth properties of Ti-6Al-6V-2Sn.     

Investigation of the scattering of harmonic elastic waves by two collinear symmetric cracks using non-local theory

In this paper, the scattering of harmonic waves by two collinear symmetric cracks is studied by use of non-local theory. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform is applied and a mixed boundary-value problem is formulated. The solutions are obtained by means of the Schmidt method. This method is more exact and more appropriate than Eringen's for solving this kind of problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of the incident wave.     

A fatigue crack propagation model for strain hardening materials

In this paper a crack propagation model based on Tomkins concept (dl/dN ∝ Δε_p · ω) has been developed using the theoretically developed cyclic plastic zone sizes. The crack propagation rates are found to be functions of stress intensity factor, Elber's effective stress range ratio, cyclic yield strength of material, crack length, specimen width and cyclic strain hardening exponent. Suitably grouped to give the crack growth rate in terms of five constants termed as Loading Constant, Material constant, Crack size constant, specimen Width Constant and Stress Intensity Exponent. The crack growth rates found by theory are compared with the experimental results available in literature and a good agreement is found.     

The unusual near-threshold FCG behavior of a single crystal superalloy and the resolved shear stress as the crack driving force

An investigation of the fatigue crack growth (FCG) behavior of PWA 1480 single crystal nickel base superalloy was conducted. Typical Paris region behavior was observed above a δK of 8 MPa√m. However, below that stress intensity range, the alloy exhibited highly unusual behavior. This behavior consisted of a region where the crack growth rate became essentially independent of the applied stress intensity. The transition in the FCG behavior was related to a change in the observed crack growth mechanisms. In the Paris region, fatigue failure occurred along {111} facets, however at the lower stress intensities, (001) fatigue failure was observed. A mechanism was proposed, based on barriers to dislocation motion, to explain the changes in the observed FCG behavior. The FCG data were also evaluated in terms of a recently proposed stress intensity parameter, K_rss. This parameter, based on the resolved shear stresses on the slip planes, quantified the crack driving force as well as the mode I ΔK, and at the same time was also able to predict the microscopic crack path under different stress states.     

Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media

This study is concerned with the inverse problem of calculating material distributions intending to realize prescribed apparent fracture toughness in functionally graded material (FGM) coatings around a circular hole in infinite elastic media. The incompatible eigenstrain induced in the FGM coatings after cooling from the sintering temperature, due to mismatch in the coefficients of thermal expansion, is taken into consideration. An approximation method of determining stress intensity factors is introduced for a crack in the FGM coatings in which the FGM coatings are homogenized simulating the nonhomogeneous material properties by a distribution of equivalent eigenstrain. A radial edge crack emanating from the circular hole in the homogenized coatings is considered for the case of a uniform pressure applied to the surfaces of the hole and the crack. The stress intensity factors determined for the crack in the homogenized coatings represent the approximate values of the stress intensity factors for the same crack in the FGM coatings, and are used in the inverse problem of calculating material distributions in the FGM coatings intending to realize prescribed apparent fracture toughness in the coatings. Numerical results are obtained for a TiC/Al₂O₃ FGM coating, which reveal that the apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media can be controlled within possible limits by choosing an appropriate material distribution profile in the coatings.     

Analysis of the optical method of caustics for dynamic crack propagation

In the interpretation of experimental data on dynamic crack propagation in solids obtained by means of the optical method of caustics, it has been customary to neglect the effect of material inertia on the stress distribution in the vicinity of the crack tip. In this paper, the elastodynamic crack tip stress field is used to establish the exact equations of the caustic envelope formed by the reflection of light rays from the surface of a planar solid near the tip of a propagating crack. These equations involve the instantaneous crack tip speed, the material parameters and the instantaneous dynamic stress intensity factor, and they can be used to determine the stress intensity factor for given material parameters and crack tip speed. The influence of inertial effects on stress intensity factor measurements for system parameters typical of experiments with PMMA specimens is considered. It is found that the stress intensity factor values inferred through a dynamic analysis may differ by as much as 30–40% from values based on a quasi-static analysis.     

Impact of nonlocal thin elastic plates by a cylindrical projectile

This paper is concerned with the analysis of the problem of dynamic impact of an elastic thin plate by a cylindrical projectile. The behavior of the plate material is assumed to be nonlocal elastic, and the effect of the impact is represented by a uniform velocity distribution over a circular region of the plate surface. Assuming the plate is thin, only the contributions of vertical shearing stress are considered, and the expressions of shear stress, axial displacement and the corresponding velocity components are obtained. Finally, the value of the total strain energy—crack initiation energy—for which the plastic flow will start, has been calculated and compared with experiments.     

The stress singularity of mode-i crack propagating with transonic speed

The transient problem of a mode-I centered crack propagating in an unbounded isotropic linear elastic body with the crack-tip speed larger than the S-wave speed and less than the P-wave speed is studied. The method of self-similar potentials with the function-theoretic approach has been successfully applied. Attention is focused on the stress singularity and it is found that the asymptotic solution of the stress field near the crack tips is of order , where m = 0 for the crack-tip speed equal to the P-wave as well as S-wave speeds and m = 1/2 for the crack-tip speed equal to √2 of the S-wave speed. The possibility of the mode-I crack propagating with the transonic speed is also discussed from the physical point of view, even though the problem can be solved mathematically.