The effect of contact stress intensity factors on fatigue crack propagation

Using the technique of Dimensional Analysis the phenomenon of crack closure is modelled using the concept of a contact stress intensity factor Kc. For constant amplitude loading, a simple expression, Kc_max = g(R) ΔK, is obtained without making idealized assumptions concerning crack tip behaviour. Further, by assuming that crack closure arises from the interaction of residual plasticity in the wake of the crack and crack tip compressive stresses, the function g(R) is shown to be constant for non-workhardening materials. This implies that any dependency of Kc_max on R must be attributed to the workhardening characteristic of the material. With Kc known, an “effective” stress intensity factor Ke may be calculated and incorporated into a crack growth law of the form da/dn = f(ΔKe). From analysis, it can be deduced that for a workhardening material, Kc_max will decrease as R increases and the effective stress intensity factor will increase. This means that the fatigue crack propagation rate will increase with R, in accordance with experimental observations.     

Crack bifurcation in laminar ceramics having large compressive stress

Crack bifurcation is observed in laminar ceramics that contain large residual compressive stress. In such composites, alternating material layers have tensile and compressive residual stress, due to thermal expansion mismatch or other sources. The compressive stress ensures that crack growth leading to failure in the laminar system is mediated by threshold strength, but, in some cases, it also leads to bifurcation of the propagating flaw. The phenomenon of bifurcation takes place when the crack tip is propagating in the compressive layer, and occurs typically at a distance equal to a few laminate thicknesses below the free surface and beyond. The observation of this phenomenon is usually associated with the presence of edge cracking in the compressive layers of the laminar ceramic, although it can also occur in the absence of such edge cracks. In the few cases where bifurcation occurs without edge cracks, the residual stresses and layer thicknesses are close to the condition in which edge cracks will occur. In addition, in this case the bifurcation is confined to near the specimen free surface, and below the bifurcation plane, the cracks are straight. The energy release rates for the straight and bifurcated cracks are calculated from the results of finite element computations and compared. When edge cracking is ignored, the crack is simulated as a through-thickness crack in an infinite body, and the energy release rate is used to predict crack deviation and bifurcation. Based on this, the finite element model successfully predicts bifurcation in only one material combination that was investigated in experiments. However, the experimental bifurcation takes place in two additional material combinations. When the effect of edge cracking is incorporated into the finite element simulations, the energy release rate calculations successfully predict the phenomenon of bifurcation in three material combinations, as observed in the experiments. Since no edge cracks are present in the fourth material combination tested experimentally, its lack of bifurcations is automatically predicted by the model. The presence of edge cracking, or its incipience, is thus concluded to be critical to the occurrence of crack bifurcation in laminar ceramic composites.     

短裂纹闭合的尺寸效应分析

对循环荷作用下缺口根部静态短裂纹和扩展短裂纹的闭合现象进行了弹塑性有限元分析。考虑不同应力水平和应力比，尤其是零－压载荷对短裂纹的作用。在此基础上提出分析长，短裂纹闭合尺寸效应的修正模型。与实验结果相比，本文模型对短裂纹的闭合预测甚好。     

An interacting micro-crack damage model for failure of brittle materials under compression

A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.     

Note on arc crack experiencing slip

Under certain loading conditions a crack surface may undergo partial sliding (slip). Such slip may be triggered by non-uniformity of frictional characteristics along the crack surface, variability of applied stresses or curvilinearity of a crack path. In the present work we study the influence of a curvilinear shape of a crack on slip evolution. The analysis is carried out for the case of a two-dimensional circular arc crack. Initiation and propagation of a slip zone is investigated based on the criterion that the shear stress intensity factor vanishes at endpoints of the slip zone. Two case scenarios are studied: first, when slip is attributed to the non-uniform distribution of a coefficient of friction and, second, when slip is initiated by the far field compressive loads. The curvilinear effects are estimated by comparing the obtained solutions with the ones for a straight crack. Analytical expressions for the stress intensity factors (SIFs) derived in this work may also present certain interest of their own.     

利用焦耳效应提高含裂纹金属构件抗裂性能问题的研究

设一无限大金属薄板中含有一个线裂纹,对金属板施加恒定的电流场,在两个裂尖处产生的热量远远大于其余地方产生的热量,可简化成两个点热源．经求解得到了问题的解析解,包括裂纹尖端附近区域温度、应力、应变、应变能密度因子的解析表达式．计算结果表明,裂纹尖端处的材料发生熔化而形成一个焊点,裂纹尖端明显纯化,可抑制裂纹的进一步扩展,提高含裂纹金属构件的抗裂性能．     

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.     

Thermal fracture of macrocrack with closure as influenced by microcracks

The fracture stability of macrocracks under uniform heat flux is analyzed to include the effect of a system of microcracks. The interaction of cracks leads to full or partial closure of crack surfaces. The boundary problem is stated and a solution is obtained. The domains where microcracks are closed and/or affect partial closing of the macrocrack are found. Evaluated is the macrocrack tip stress intensity factor accounting for closure.     

Prediction models of fatigue crack closure and growth under random loading

The effects of plastic zones both in front of and behind crack tip on crack closure have been analysed. The total residual deformations of crack surfaces involve two parts, that is, the amount of plastic blunting of crack tip and the residual deformation in the wake of the tip. This paper presents a fatigue crack closure model in which the influences of compressive load on closure stress are discussed. The model is applied to random loading conditions by the assumption of limited memory properties. The fatigue lives are predicted using the proposed crack growth model for CCT plane stress specimen cut from 2219-T851 aluminum alloy under flight spectrum loadings, and the prediction values agree with the test results.The project was supported by the natural science foundation of China.     

受弯脱层层板后屈曲有限元分析

脱层是复合材料层板结构中主要的缺陷形式之一。当脱层层板受到压力载荷的作用会造成脱层的局部屈曲和扩展,从而使结构的强度和刚度大为降低。含脱层层板的弯曲问题包含了脱层的压缩问题,却比压缩问题更加复杂。本文对含穿透脱层层板在纯弯载荷作用下的后屈曲问题进行了基于一阶剪切层板理论的几何非线性有限元分析,运用虚裂纹闭合技术求解了纯弯载荷作用下的脱层尖端的能量释放率各型分量,并用脱层扩展判据求解了脱层起始扩展载荷。     

Shape variation of a three-dimensional planar crack

Investigated are the integral and local properties of the solutions for the three-dimensional elastostatic problem of a Mode I crack whose shape can vary. Results are obtained by specifying the first and second order variations of integral functionals on crack surface displacements. Constraints are invoked such that the opening crack is either unable to resist tensile stresses or its partial closure take place. Extermal properties are established for the crack with the unknown free boundary. A gradient type procedure is used for determining the crack opening domain. Discussed also is the energetic treatment of the crack problem.     

Delamination effects on cracked steel members reinforced by prestressed composite patch

Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce crack closure effect. Moreover, it modifies the crack geometry by bridging the crack lips and reduces the stress range at crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A debond crack in the adhesive–plate interface was observed by optical technique. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique. A parametric analysis is performed in order to investigate the influence of some design parameters such as the composite patch Young’s modulus, the adhesive thickness and the pretension level on the adhesive–plate interface debond.     

疲劳裂纹闭合研究的进展

本文阐述了疲劳裂纹闭合的四种诱发机制,介绍了疲劳裂纹闭合现象测量的几种方法并结合作者的工作进行了评述.文中详细地介绍和探讨了材料、应力比、试样几何尺寸、环境及载荷谱等因素对裂纹闭合现象的影响,指出了目前研究工作中存在的问题.并对今后开展研究工作的方向提出了看法.     

Errors in crack closure measurements caused by flexure test fixture support effects

Flexural tests are sometimes used for the evaluation of fatigue and fracture properties, especially for thin cross sections such as plate material where compact tension speciments cannot be used, or where material thicness is limited in the direction required for data generation. The method is also useful for evaluation of crack closure provided the force transfer occurs correctly. This paper shows how the influence of incorrect test fixture supports, which are outside the standard testing arrangement for such test specimens, can affect the force-displacement curves as evidenced using the backface strain method. The results show that incorrect test fixture supports may cause deviations in the force-displacement trace as an artifact of the testing conditions. This effect can severely influence crack closure measurements. The effect was also modeled with finite element analysis.     

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique,the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface.Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable.The results can be reduced to the well-known solutio...     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

THERMAL STRESS FIELD WHEN CRACK ARREST IN AN AXIAL SYMMETRY METAL DIE USING ELECTROMAGNETIC HEATING

In order to solve the thermal stress field around crack tip in metal die when crack prevention using electromagnetic heating, a metal die with a half-embedded round crack was selected as the study object. The complex function method was used as a basis for the theoretical model of the space crack prevention in metal dies using electromagnetic heating. The crack arrest was accomplished by a pulse current discharge through the inner and outer. The theoretical analysis results show that the temperature around the crack tip rises instantly above the melting point of the metal. Small welded joints are formed at a small sphere near the crack tip inside the metal die by metal melting as a result of the heat concentration effect when the current pulse discharged. The thermal compressive stress field appears around the crack tip at the moment. The research results show that the crack prevention using electromagnetic heating can decrease the stress concentration and forms a compressive stress area around the crack tip, and also prevents the main crack from propagating further, and the goal of crack preventing can be reached.     

DYNAMIC BEHAVIOR OF TWO COLLINEAR PERMEABLE CRACKS IN A PIEZOELECTRIC LAYER BONDED TO TWO HALF SPACES

IntroductionIn the fracture mechanics studies for piezoelectric materials,differently electricboundary conditions at the crack surfaces have been proposed by many researchers.Forexample,for the sake of analytical simplification,the assumption that the cra…     

单边裂纹通电瞬间裂尖处应力场的复变函数解

本文应用复变函数中的Schwarz-Christoffel变换方法，在具单边裂纹的导电薄板通电瞬间温度场复变函数解的基础上，推导出用复变函数表示的应力场的表达式，并且给出算例，通过理论计算得知；当对具有单边裂纹的导电薄板通入适当密度的电流时，裂尖处温度急剧升高并熔化便裂尖变钝。同时，在裂尖周围形成了有利于遏制裂纹扩展的压应力场，有效地防止了裂纹沿其主方向和其它方向延伸。从理论上证明了电磁热效应在裂尖处产生高温形成焊口的同时，压应力场的形成是遏制裂纹扩展的主要因素之一。理论计算结果与实验结果比较吻合，为这一止裂方法的应用打下了理论基础。     

Cracked elastic layer under compressive mechanical loads

We consider boundary value problem in which an elastic layer containing a finite length crack is under compressive loading. The crack is parallel to the layer surfaces and the contact between crack surfaces are either frictionless or with adhesive friction or Coulomb friction.Based on fourier integral transformation techniques the solution of the formulated problems is reduced to the solution of a singular integral equation, then, using Chebyshev’s orthogonal polynomials, to an infinite system of linear algebraic equations. The regularity of these equations is established. The expressions for stress and displacement components in the elastic layer are presented. Based on the developed analytical algorithm, extensive numerical investigations have been conducted.The results of these investigations are illustrated graphically, exposing some novel qualitative and quantitative knowledge about the stress field in the cracked layer and their dependence on geometric and applied loading parameters. It can be seen from this study that the crack tip stress field has a mode II type singularity.