Failure modes of specimens containing surface flaws under cyclic torsion

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such a torsional loading may initiate yielding at the outer radius of the shaft or in the fillets. The methods for predicting turbine-shaft fatigue life due to transient loading depent upon the mode of crack growth from an undetected crack. The most common location for the existence of a crack is the fillets or shoulders of the shaft. Specimens were designed from AISI 4340 steel with two diametrically opposed flat surfaces. Initial defect orientations of 0 deg, 45 deg and 90 deg with respect to the sepcimen axis on the fillet were studied. The specimens were subjected to cyclic torsion with zero mean torque and with a torque amplitude necessary to cause yielding at the outer radius of the specimen. When initial defects were aligned with a plane of maximum shear stress (0 deg and 90 deg), the cracks propagated along that plane. For 45-deg defects (aligned to a plane of maximum tensile stress) the crack still propagated along the plane of maximum shear. However, the number of cycles to initiate and to propagate the crack to failure for 45-deg defects were (two to three times) larger than those for 0-deg and 90-deg defects. Mode II and Mode III crack-growth rates were measured from specimens containing 0-deg and 90-deg defects. It was found that the crack-growth rate in Mode II was higher than in Mode III. However, all the specimens failed due to reduction of the net cross section, mostly attributed to Mode III crack growth. Similar results were obtained from specimens of turbine-shaft material (A469 steel), and 2024 aluminum with different rolling directions. Fatigue-crack-growth rates in Mode III were measured from circumferentially notched bar. They were found to be a unique function of ΔK _III alternating stress intensity in Mode III. It was found that the mechanism of crack growth is produced by the formation and linkage of elongated cavities at the crack tip.     

Exponential stress and strain singularity at tip of mode I growing crack in power hardening plastic material

The stress-strain distribution near the tip of a Mode I growing crack in a power hardening plastic material is reconsidered. Two types of asymptotic equations are derived and solved numerically. It is shown that when the crack tip is approached, the stress is singular of the order r^−δ, while the strain is singular of the order r^−nδ, where r is the distance measured from the crack tip. The parameter δ is a constant; it depends on the hardening exponent n being greater than one.     

Discrete dislocation simulations of the development of a continuum plastic zone ahead of a stationary Mode III crack

We present results from discrete dislocation simulations showing the development of the plastic zone in front of a Mode III crack under constant load. We find that the equilibrated zone is circular, in agreement with continuum mechanics predictions of the elastic-perfectly plastic Mode III crack. The size of the equilibrated zone scales as the square of the applied load (K_III), also in agreement with the continuum results. The zone approaches saturation exponentially, with a time that scales as K_III²/σ_p³, where σ_p is the Peierls stress. These results delineate conditions under which the classical, continuum predictions of elastic-plastic fracture mechanics are applicable.     

Crack front curvature effect on stress intensity factor of through and part-through thickness cracks

The character of the local stresses and displacements are determined for a through crack with finite radius of curvature in a finite thickness plate. Numerical results obtained from the boundary element method show that the solutions are sufficiently accurate for /a ≤ 0.03 and 0.03 ≤ /a ≤ 0.1, where and a represent, respectively, the crack front radius of curvature and crack dimension such that a is the width of a through thickness crack and the depth of a part-through crack. For /a ≤ 0.1, the asymptotic singular stress field dominates such that the Mode I stress intensity factor K₁ can be evaluated. As the crack border radius of curvature is increased for /a ≥ 0.1, the non-singular terms become significant such that K_I would no longer dominate. Other failure criteria would have to be invoked to address fracture initiation.     

Effects of material and stacking sequence on behavior of composite plates with holes

Strain distributions to failure, tensile and compressive strain-concentration factors, and strength-reduction factors were determined for glass-, boron-, and graphite-epoxy plates with holes loaded in tension. Strain gages, photoelastic coatings and moiré techniques were used. Ten variations of layup and stacking sequence were studied. The boron-epoxy composite was found to be the stiffest and strongest of the three. The graphite laminate with the highest stress concentration and the most linear strain response exhibited the highest strength-reduction factor. In all cases, the maximum strain at failure on the hole boundary was higher than the ultimate tensile-coupon strain. In general, it was found that, the higher the stress-concentration factor, the higher the strength-reduction factor. Thus, the [0/90/0/90]_s layup with a stress-concentration factor of 4.82 had a strength-reduction factor of 3.18. At the other extreme, the most flexible layup [±45/±45]_s with the lowest stress-concentration factor of 2.06 had the lowest strength-reduction factor of 1.10. Stacking sequences associated with the tensile interlaminar normal stress or high interlaminar shear stress near the boundary, resulted in laminates 10 to 20 percent weaker than corresponding alternate stacking sequences. Furthermore, it was found that stacking-sequence variations can alter the mode of failure from catastrophic to noncatastrophic.     

复合材料层合板低速冲击损伤分析的连续介质损伤力学模型

针对复合材料层合板低速冲击损伤问题,提出了一种各向异性材料连续介质损伤力学模型,模型涵盖损伤表征、损伤起始判定和损伤演化法则3 个方面. 通过材料断裂面坐标下的损伤状态变量矩阵完成损伤表征,并考虑断裂面角度的影响,建立了主轴坐标系下的材料损伤本构关系. 损伤起始由卜克(Puck) 失效准则预测,损伤演化由断裂面上的等效应变控制,服从基于材料应变能释放的线性软化行为. 模型区分了纤维损伤和基体损伤,并根据冲击载荷下层内产生多条基体裂纹继而扩展至界面形成层间裂纹(分层) 的试验观察,引入基体裂纹饱和密度参数表征层间分层. 以[0₃/45/-45]_S 和[45/0/-45/90]_4S 两种铺层的复合材料层合板为例,预测了不同冲击能量下复合材料层合板的低速冲击损伤响应参数,试验结果证明了连续介质损伤力学模型的有效性.模型在不同网格密度下的计算结果表明单元特征长度的引入可以在一定程度上降低损伤演化阶段对网格密度的依赖性.      

Analysis of dynamic mixed-mode isochromatics

The mixed-mode, elastodynamic state of stress in the neighborhood of a constant-velocity crack tip is used to generate numerically unsymmetric isochromatics. Unsymmetry associated with the third-order terms of a mixed-mode stress field, with and without the Mode II singular stress term, is also investigated. In extractingK _I from an unsymmetric isochromatic pattern, errors in the Mode I fracture parameters due to the assumed presence ofK _II in aK _I stress field were found to be significant when data are taken more than 4 mm from the crack tip. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

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.     

MIXED MODES INTERLAMINAR FRACTURE TOUGHNESS OF CFRP LAMINATES TOUGHENED WITH CNF INTERLAYER

In the present paper, the influence of carbon nanofiber on interlaminar fracture toughness of CFRP investigated using MMB(Mixed Mode Bending) tests. Vapor grown carbon fiber VGCF and VGCF-S, and multi-walled carbon nanotube MWNT-7 has been employed for the toughener of the interlayer on the CFRP laminates. In order to evaluate the fracture toughness and mixed mode ratio of it, double cantilever beam (DCB) tests, end notched fracture (ENF) tests and mixed mode bending (MMB) tests have been carried out. Boundary element analysis was applied to the CFRP model to compute the interlaminar fracture toughness, where extrapolation method was used to determine the fracture toughness and mixed mode ratio. The interlaminar fracture toughness and mixed mode ratio can be extrapolated by stress distribution in the vicinity of the crack tip of the CFRP laminate. It was found that the interlaminar fracture toughness of the CFRP laminates was improved inserting the interlayer made by carbon nanofiber especially in the region where shear mode deformation is dominant.     

The growth simulation of circular buckling-driven delamination

Some closed-form equations for the coupling problem of buckling and growth of circular delamination are derived by recourse to the moving boundary variational principle. The axisymmetric buckling of a circular delamination subjected to an equal bi-axial compression is analysed by using high-order perturbation expansion. The axisymmetric buckled delamination has the following properties : under a certain residual pressure, there exist two characteristic radii, namely the critical radius R_c and growing radius R_g; for a certain interface toughness, the blister has three configuration of stationary, stable growth and unstable growth with increasing the loads. Under a higher edge thrust, the nonaxisymmetric secondary buckling will occur on the base of axisymmetric buckling and then the toughness and the driving force of the interface crack will be different along the delamination front. So the growth of circular delamination will not be self-similar. Without any assumption regarding the delamination front, the configurations of the blister with several nonaxisymmetric buckling modes n = 2, 3, 6, 8 are simulated. The nonaxisymmetric growth process for the nonaxisymmetric buckling mode n = 2 is simulated also under a sequence of loads.     

The effects of bridging in a 3D composite on buckling, postbuckling and growth of delamination

Summary Buckling and postbuckling solutions to circular delamination constrained by transversal restoring forces, which occur extensively in stitched or woven composites with three-dimensional (3D) reinforcement, are obtained by using von Karman's geometrically nonlinear thin plate theory by means of Taylor's series expansion. The through-thickness tows are assumed to provide continuous and linear restoring tractions, opposing the deflection of the annular delaminated region adjacent to a penny-shaped crack. When the end of the delaminated layer is clamped, and the deflection is permitted in the positive direction of the z-axis only, there exists a characteristic delamination radius a _* for initial buckling. In the case that the initial delamination radius a ₀ exceeds a _*, it will consist of waves whose sizes decrease gradually, as they are apart from the delamination center with larger distances, and will usually not span the whole crack region. Therefore, buckling profiles can be divided into two types: (1) lacking contact phenomena between the delaminated layer and the base plate; (2) having contact surfaces inside the delamination region. In this paper, growth laws of buckling, postbuckling and growth of delamination at lacking contact surface are discussed. The corresponding stability of the delamination growth under fixed boundary load is studied, and the dependence of stable scope upon the fracture toughness of the composite and the elastic constant of bridging fiber is summarized. It follows from the analysis that bridging can increase the load-bearing capacity of composite structure, improve its mechanical performances and restrain the growth of delamination. Received 23 November 1998; accepted for publication on 13 January 1999     

Finite element analysis of mode III steady crack growth in anisotropic hardening materials

In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk _ss/k_c varies appreciably with the anisotropic hardening parameterM and the hardening exponentN.     

High-order asymptotic analysis for the crack in nonlinear material

Accurate high-order asymptotic analyses were carried out for Mode II plane strain crack in power hardening materials. The second-order crack tip fields have been obtained. It is found that the amplitude coefficientk ₂ of the second term of the asymptotic field is correlated to the first order field as the hardening exponentn<n ^* (n ^*≈5), but asn≥n ^*,k ₂ turns to become an independent parameter. Our results also indicated that, the second term of the asymptotic field has little influence on the near-crack-tip field and can be neglected whenn<n ^*. In fact,k ₂ directly reflects the effects of triaxiality near the crack tip, the crack geometry and the loading mode, so that besidesJ-integral it can be used as another characteristic parameter in the two-parameter criterion. The project supported by National Natural Science Foundation of China     

Plasticity aspects of interfacial fracture for polymer/glass specimens

Experimental results suggest that the interfacial fracture resistance is minimal for approximate near tip Mode I accompanied by positive and negative near tip Mode II. Finite-strain FE analysis is made for an elastic–plastic medium bonded to an ideally elastic medium with an interface crack. Small-scale plasticity conditions are invoked and examined in relation to the elastic–plastic stress distribution along the bond line. Plasticity engenders a tendency to turn near tip biaxiality towards pure Mode I regardless of the mixed-mode loading. High levels of hydrostatic stress are attained. For different mode mixities of the applied load, the dependence of the elastic–plastic normal bond stress on load level is examined. It is found that under positive Mode II loading, the normal bond stress σ_yy tends to saturate as the load level rises. This does not occur for Mode I and negative Mode II loading. In addition, deformation patterns inside the plastic zone are examined for mixed-mode situations. A displacement criterion based on the normal bond crack opening suggests a dependence of the critical load level on the extent of mixed mode. Under positive mode II fracture, traces of the ductile material are found at the top of the elastic substrate. Some of these conclusions appear to be consistent with the fracture patterns observed for LD-polyethylene/glass interfacial mixed-mode fracture.     

Pitting formation under rolling contact

The mechanism of pitting caused by rolling contact is analyzed using the fracture mechanics approach. The governing factors are the initial crack length, crack angle, contact force, friction, strain hardened layer, and the hydraulic pressure of trapped fluid acting on the crack surface. Mode I and II stress intensity and the strain energy density factors are calculated by application of the two-dimensional finite element method. The strain energy density criterion is applied to show that shallow angle crack under small rolling contact force and friction enhances the probability of pitting under the roller’s running surface. The presence of a strain hardened surface layer also tends to affect the fracture behavior. The analytical results agree well with the experimental observations.     

Anti-plane shear of kinked interface crack in bonded dissimilar anisotropic solid

Complex potentials are derived to describe the anti-plane singular shear stress fields around a kinked crack, the main portion of which is embedded along the interface of two dissimilar anisotropic elastic media. This is accomplished by formulating the problem as singular integral equations with generalized Cauchy kernels. The shear stress singularity at the kink differs from the familiar inverse square root of the local distance; it is found to influence the magnitude of the Mode III crack tip stress intensity factor, K₃. Numerical results of K₃ are obtained and displayed in graphical forms for different degree of material anisotropy and crack dimensions.     

复合材料结构的内部分层及其扩展

本文用接触观点分析了复合材料壳体结构的内部分层问题，建立了求解摩擦接触问题的有限元迭代格式，并采用释放率判据分析分层裂纹的扩展。分层裂纹前缘采用轴对称奇异单元，并了结构的大变形特性。计算表明，层间裂纹呈Ⅱ型扩展趋势。本文同时还分析了层间摩擦系数的影响，并指出分层将导致壳体结构承载能力显著下降。     

Observations on Mode I and III fracture of steel and PMMA

Considered in this work are the Mode I and III fractures of W18Cr4V steel, 60Si2Mn steel and PMMA specimens. The mixed mode critical stress intensity factor, denoted by K_1f, is shown to be greater than K_1c for Mode I. The ratio K_1f/K_1c depends on the ways in which K₁ and K₃ interact and is affected by the position of the load with reference to the crack position. Analytical and experimental results are presented and discussed in connection with the microfracture surface observed experimentally.     

Effect of yield surface vertex on crack-tip fields in mode III

An asymptotic crack-tip analysis of stress and strain fields is carried out for an antiplane shear crack (Mode III) based on a corner theory of plasticity. Because of the nonproportional loading history experienced by a material element near the crack tip in stable crack growth, classical flow theory may predict an overly stiff response of the elastic plastic solid, as is the case in plastic buckling problems. The corner theory used here accounts for this anomalous behavior. The results are compared with those of a similar analysis based on the J₂ flow theory of plasticity.     

Subcritical and fatigue crack growth in anti-plane strain state

Assuming elastic-plastic material behavior the slow growth of Mode III crack under both monotonic and pulsating loadings is considered. Rice's idea of universal R-curve is employed while the mathematical analysis is based on the one-dimensional plasticity model suggested by Kostrov and Nikitin. Motion of a quasi-static Mode III crack is studied and the stable/unstable transition points are found through application of the final stretch failure condition proposed in 1972 by Wnuk. A logarithmic formula for fatigue crack extension rate is derived. Results are compared to other well-known solutions.