Fracture analysis of semi-circular and semi-circular-bend geometries

A fracture mechanics analysis of the semi-circular (SC) and semi-circular-bend (SCB) fracture geometries is presented. The weight function method is implemented to obtain wide ranging stress intensity factor (SIF) and crack opening displacement (COD) expressions. This study has as its basis a finite element analysis of the semi-circular disk (SC) subjected to a reference loading case. The latter is required to determine both the associated reference stress intensity factor and the weight function for the base-edge-cracked semi-circular geometry. With this information, SIF and COD expressions for the full range of crack lengths are obtained. The special cases of the SC subject to a concentrated crack mouth loading and the SCB are analyzed in detail. The weight function for the SCB is fully developed, with an accurate expression for the SIF and and a numerical result for the crack mouth opening displacement (CMOD). The latter wide ranging expressions can, in turn, be applied as a reference solution. From this weight function approach, SIF's and COD's for the SC and SCB subject to any other loading can be obtained.     

Effect of thickness on fracture criterion in general yielding fracture mechanics

In this research work, the effect of thickness on fracture criterion is studied for extra deep drawn (EDD) steel sheets. Experimental results are generated on fracture toughness of EDD steel sheets using compact tension specimens and a ‘maximum load’ as a fracture criterion. Critical crack tip opening displacement (CTOD) is found with the help of three methods: plastic hinge model (PHM), crack flank opening angle (CFOA) and finite element model (FEM). The fracture toughness is found to increase with increase in thickness of specimens. The fracture behaviour exhibited characteristics of general yielding fracture mechanics.     

Effect of Hydrogen on Plastic Deformation near Crack-tipof A537 Steel in 3.5%NaCl Solution

A computerized digital speckle-intederometry system was set up to study in-situ the influence of cathodic hydrogen charging on the crack opening displacement and on the plastic strain distribution at corrosion fatigue crack tip for the singIe-edge notched plate specimens of structural steel in 3.5%NaCl solution with an applied potential of -1400 mV (SCE). Meanwhile, the mono-directional tension tests with smooth specimens were pedermed in both air and 3.5%NaCl solution under the hydrogen charging conditions. The fracture sudece morphology from corrosion fatigue and tension was examined by SEM. The experimental results show that the existence of hydrogen in crack tip material caused an increase of both yield strength and hardening exponent and a decrease of plastic zone size at the corrosion fatigue crack tip.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

A mathematical approach of fracture macromechanics for strain-softening material

A new mathematical fictitious crack model is proposed to analyse the stable crack propagation in elastic-softening materials, and a possible load-displacement diagram is obtained for a simple tension specimen. By using the complex variable and the weight integral method, the effective crack is divided into two parts: the real crack and the fictitious crack. The proposed model is based on the theory of elasticity, to represent the character of the fracture process zone (or microcracked zone), in which the crack tip opening displacement (CTOD) is taken as a fracture (or crack propagation) criteria.     

Process zone analysis for the single-edge notched specimen: Part I. Process zone size and crack profile

A systematic analysis of the process zone is presented. Relations among the process zone size, load and crack opening displacement (COD) are derived using the weight function method and a power function closing pressure distribution in the process zone. These relations are specialized and used to study the behaviour of the single-edge notched (SEN) specimen loaded in tension and in bending. This study shows that the method presented here may be successfully used to analyze the fracture of finite-size specimens.     

A study of continuous filament reinforced aluminum matrix composites

Some principal results of the research work on metal matrix composites at Beijing Institute of Aeronautical Materials, concerning CVD-produced continuous B and SiC filaments reinforced aluminum and its alloys, are summarized. The processing, fiber degradation, interface, mechanical properties and fracture behavior of the composites are discussed.Abbreviations CVD chemical vapor deposition - MMCs metal matrix composites - ROM rule of mixtures     

A wide range weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Stress intensity factors may be determined by the weight function method. A weight function for the single edge cracked geometry with clamped ends is developed and verified in this paper. It is based on analytical forms for the reference stress intensity factor and crack mouth opening displacement. The analytical forms are shown to be valid, by comparison with finite element results, over a wide range of crack depths and plate aspect ratios. Use of the analytical form enables the weight function to be calculated for any plate aspect ratio without the need for preliminary finite element analysis. Stress intensity factors and crack mouth opening displacements, predicted using this weight function, correlated well with finite element results for non-uniform crack surface stress distributions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fatigue life prediction of fiber reinforced concrete under flexural load

This paper presents a semi-analytical method to predict fatigue behavior in flexure of fiber reinforced concrete (FRC) based on the equilibrium of force in the critical cracked section. The model relies on the cyclic bridging law, the so-called stress–crack width relationship under cyclic tensile load as the fundamental constitutive relationship in tension. The numerical results in terms of fatigue crack length and crack mouth opening displacement as a function of load cycles are obtained for given maximum and minimum flexure load levels. Good correlation between experiments and the model predictions is found. Furthermore, the minimum load effect on the fatigue life of beams under bending load, which has been studied experimentally in the past, is simulated and a mechanism-based explanation is provided in theory. This basic analysis leads to the conclusion that the fatigue performance in flexure of FRC materials is strongly influenced by the cyclic stress–crack width relationship within the fracture zone. The optimum fatigue behavior of FRC structures in bending can be achieved by optimising the bond properties of aggregate–matrix and fiber–matrix interfaces.     

混凝土裂缝扩展过程中裂尖张开口位移(CTOD)与裂缝嘴张开口位移(CMOD)的变化关系分析

裂缝尖端张开口位移(CTOD)和裂缝嘴张开口位移(CMOD)是衡量裂缝张开程度的两个指标.该文进行了楔入式紧凑拉伸混凝土断裂试验,研究了在裂缝扩展的整个过程中裂缝尖端张开口位移和裂缝嘴张开口位移之间的关系.发现,裂缝尖端张开口位移和裂缝嘴张开口位移关系曲线可以用三线性模型来描述,两个转折点与裂缝的起裂和临界失稳扩展相对...     

Probabilistic analysis of the uncertainty in the fatigue capacity of welded joints

This paper presents the results of a study of the uncertainty in the fatigue capacity (constant amplitude fatigue life) of welded steel joints, due to uncertainties related to geometrical and material parameters.An efficient method of probabilistic fracture mechanics analysis is described and applied. A linearelastic fracture mechanics model and the Paris-Erdogan law of crack propagation were adopted. Stressintensity factors were evaluated by employing an influence function method, which is very cost-effective. The main parameters were treated as stochastic variables. Data for weld and crack geometry of the non-load carrying fillet weld cruciform joint selected as the example joint in the study, were recorded from specimens. Other data were compiled from the literature. The uncertainties associated with the basic variables were transformed into a measure of uncertainty of the fatigue capacity by employing the Monte Carlo simulation technique. The relative contributions to the uncertainty in the fatigue capacity from the various factors were also compared.The $\text{S-N}$ data established analytically compared fairly well with test data obtained with 42 specimens. The probabilistic fracture mechanics analysis provided a sufficient sample of data to allow a test of analytical probability distributions to the fatigue life. The fit of two- and three-parameter lognormal and Weibull distributions was examined. Only the three-parameter lognormal pdf passed the chi-square test on the 5% confidence level.     

Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes

The notched beam specimens have been commonly used in concrete fracture. In this study, the splitting-cube specimens, which have some advantages - compactness and lightness - compared to the beams, were analyzed for the effective crack models: two-parameter model and size effect model. The linear elastic fracture mechanics formulas of the cube specimens namely the stress intensity factor, the crack mouth opening displacement, and the crack opening displacement profile were first determined for different load-distributed widths using the finite element method. Subsequently, four series of experimental studies on cubic, cylindrical, and beam specimens were performed. The statistical investigations indicated that the results of the split-cube tests look viable and very promising.     

Effect of combined loading on cracks in graphite/epoxy composites

Moiré Interferometry technique has been used to study the effect of combined loading on crack displacement in graphite epoxy plates. Specimens with central cracks of various orientations were subjected to uniaxial tensile loads. Thus, the cracks were under biaxial-stress fields, mode I (tension stress) and mode II (sliding stress). The obtained fringe patterns represented contours of constant-in-plane displacements. Based on these fringe patterns, two types of displacements were determined at the crack center, crack opening displacement (COD) and crack shearing displacement (CSD). The effect of combined loading on COD and CSD as well as the behavior of the material under these conditions was investigated in more detail. Experimental data were compared with the linear elastic fracture mechanics (LEFM) solution.     

Fracture analysis of base-edge-cracked reverse-tapered plates

This paper presents a fracture mechanics analysis of the base-edge-cracked reverse-tapered (RT) fracture geometry. Motivation for this study was the use of this test geometry in Phase 1 of a recently completed joint-industry-agency project entitled Large-Scale Ice Fracture Experiments. Underlying the choice of the RT fracture geometry for Phase 1 was the desirability of achieving crack propagation in a controlled and stable manner; such control would allow a number of observations to be made on one testpiece. Reverse tapering greatly improves not only crack growth stability but also crack path stability. The weight function method was used to provide accurate wide-ranging stress intensity factor (SIF), crack face displacement (COD) and crack opening area (COA) expressions for the RT subject to any loading. The required weight function was obtained through a finite element analysis of this geometry subject to a reference load case which determined the associated stress intensity factor and crack opening displacements. The Wu and Carlsson procedure was followed. A key modification to the latter procedure facilitated the attainment of the reference CMOD for all crack lengths, including the zero ligament limit; this was achieved by considering an additional reference solution. This modification is general in nature and could be pursued whenever the reference CMOD is not known analytically. An analytical solution for the crack opening area (COA) was also achieved for the special case of concentrated loading at the crack mouth. This solution can be applied to any geometry where the reference CMOD expression is known.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.     

混凝土/花岗岩界面Ⅰ-Ⅱ复合型动态断裂试验研究

为研究混凝土/岩石界面在复合型应力条件下的动态断裂性能,考虑四种应变率(10-5~10-2 s-1)及三种模态(21.8°,41.7°和60.3°)工况,对混凝土/花岗岩复合试件进行了四点剪切试验,获得了荷载与裂缝张开位移及裂缝剪切位移的关系曲线;结合界面力学理论和结构动力分析得到了界面Ⅰ型和Ⅱ型动态应力强度因子,据此得到并分析了断裂韧度、应变能释放率的率相关性及模态比相关性。结果表明:在所研究的应变率和模态角范围内,同一时刻的裂缝张开位移均大于裂缝剪切位移;Ⅰ型和Ⅱ型断裂韧度均随应变率的提高而增加,Ⅰ型断裂韧度随模态角的增大而减小,Ⅱ型断裂韧度随模态角的增大而增加;应变能释放率随应变率和模态角的增加均呈现出增长趋势。     

A general solution procedure for fracture mechanics weight function evalution based on the boundary element method

This paper reports on the development of an efficient and accurate means for the direct computation of crack surface weight functions for two dimensional fracture mechanics analysis. Weight functions are mathematical representations which can be used to efficiently calculate stress intensity factors for a variety of crack loading and boundary conditions. The method is inherently capable of handling mixed-mode problems. The weight function capability is especially important for problems of fatigue crack growth modeling where the efficient calculation of stress intensity factors is crucial.The basis of the new formulation and numerical solution method is the boundary element method (BEM), as implemented for two dimensional fracture mechanics analysis. The paper will review the analytical formulation of the new BEM, the numerical solution algorithm, and a limited number of validation examples.     

A fracture mechanics approach to high temperature fatigue crack growth in Udimet 700

Crack growth behavior under high temperature fatigue in Udimet 700 has been analyzed using both linear and non-linear elastic fracture mechanics concepts. It is shown that crack growth data for various loads in a compact tension specimen correlate well with the stress intensity factor, even at temperatures as high as 850°C. Using these results, a self consistent procedure has been developed for the determination of the $\text{J-}\text{integral}$ parameter under load-controlled fatigue and is shown to be compatible with data based on the stress intensity factor. The spread in the crack growth data is smaller in terms of $\text{J-}\text{integral}$ as compared to stress intensity or crack opening displacement parameters. Also based on a detailed fractographic analysis, it is suggested that the micromechanism of crack growth in Stages I and II is the environmentally assisted cleavage process, whereas in Stage III creep assisted crack growth processes are superimposed on the cleavage mode of crack growth. Effects of stress and temperature on the fatigue crack growth behavior of the Udimet alloy are discussed in detail.     

Boundary element analysis of three‐dimensional cracks in anisotropic solids

This paper presents a boundary element analysis of linear elastic fracture mechanics in three‐dimensional cracks of anisotropic solids. The method is a single‐domain based, thus it can model the solids with multiple interacting cracks or damage. In addition, the method can apply the fracture analysis in both bounded and unbounded anisotropic media and the stress intensity factors (SIFs) can be deduced directly from the boundary element solutions. The present boundary element formulation is based on a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. While the former is collocated exclusively on the uncracked boundary, the latter is discretized only on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (COD) (i.e. displacement discontinuity, or dislocation) is treated as a unknown quantity on the crack surface. This formulation possesses the advantages of both the traditional displacement boundary element method (BEM) and the displacement discontinuity (or dislocation) method, and thus eliminates the deficiency associated with the BEMs in modelling fracture behaviour of the solids. Special crack‐front elements are introduced to capture the crack‐tip behaviour. Numerical examples of stress intensity factors (SIFs) calculation are given for transversely isotropic orthotropic and anisotropic solids. For a penny‐shaped or a square‐shaped crack located in the plane of isotropy, the SIFs obtained with the present formulation are in very good agreement with existing closed‐form solutions and numerical results. For the crack not aligned with the plane of isotropy or in an anisotropic solid under remote pure tension, mixed mode fracture behavior occurs due to the material anisotropy and SIFs strongly depend on material anisotropy. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of crack closure on the experimentally measured characteristics of cyclic crack-growth resistance of steels

On the basis of the proposed approach and an original procedure for determination of the current value of crack tip opening displacement, we obtain new characteristics of cyclic crack-growth resistance for which the effect of crack closure disappears. We experimentally discovered a phenomenon of natural pulsations of crack closure with constantly decreasing amplitude and duration of pulses to the minimum stress intensity factor K _min in a cycle for any positive asymmetry of cycles. We construct a model of damped pulsations of crack closure depending on the maximum stress intensity factor K _max in a cycle and asymmetry of cycles. This model is used to show that the kinetic diagrams of fatigue fracture are invariant for any positive asymmetry of cycles within the limits of the presence of the effect of crack closure. The observed effect of asymmetry quantitatively takes into account the range of pulsating stress intensity factors of crack closure ΔK _cl ^op in the range of stress intensity factors ΔK in a cycle. Practical experience shows that the procedure for quantitative investigation of the kinetics of growth of fatigue cracks extensively used in linear fracture mechanics and based on analysis of the coefficients of crack opening displacement U and γ and functional dependences of the stress intensity factor of crack opening displacement K_op on k _max is inconsistent. We propose a new experimental approach to the qualitative analysis of the kinetics of growth of fatigue cracks based on evaluation of the effect of crack closure and expressed in terms of the effective range of stress intensity factors ΔK_eff in the case of its simple determination from the kinetic diagrams of fatigue fracture together with K_op. We hope that the accumulated experimental data and the proposed model of damping pulsations of crack closure will lay a foundation for a new understanding of the natural resistance of materials to fracture under cyclic loading. Scientific and Engineering Center of Materials-Science Support of the Production and Certification of Equipment of Nuclear Power Plants at the Institute for Problems of Strength of the National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 161 – 171, March – April, 1998.