Plane Stress Steady Crack Growth in a Power-Law Hardening Material

The paper reports the results from an asymptotic analysis for a crack growing quasistatically under Mode I, plane stress conditions for a power-law hardening material. The asymptotic stress and deformation velocity fields near the growing crack tip are determined, comparisons to related work are discussed and some numerical results for aluminum are included. This revised version was published online in August 2006 with corrections to the Cover Date.     

Plastic stress singularity near the tip of a V-notch

In this study, a new practical method is proposed to analyze the plastic stress singularity at a V-shaped notch tip. By dividing the domain around the notch tip into a number of wedge-shaped elements, the problem is reduced to determining the stress singularity in a wedge composed of multiple materials with different stiffness matrix. The results so obtained appear to be quite satisfactory. Based on the numerical results, the effects of the notch geometry and the hardening exponent on the singularity are discussed. In particular, an approximate expression is presented for the evaluation of the plastic stress singularity.     

Weibull Stress Solutions for 2-D Cracks in elastic and Elastic-Plastic Materials

The Weibull stress is widely used as a measure of the probability of cleavage failure. In this work analytical and semi-analytical expressions for the Weibull stress are developed in terms of the remote loading parameters, J or K, and material properties. Results are presented for sharp cracks and notches in elastic and elastic-plastic materials under plane stress and plane strain conditions. The proposed relations enable Weibull stress estimates to be obtained without the need for costly finite element analyses and provide insight into the use of the Weibull stress as a parameter for the prediction of cleavage failure of cracked bodies. The expressions have been verified using finite element techniques and good agreement has been found throughout. The results of the analyses have been used to interpret the mesh size dependence of Weibull stress values obtained from finite element calculations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Damage Field Ahead of a Tensile Crack in an Elastic-Plastic and Viscoplastic Material

This paper investigates the interaction between a macroscopic crack and microscopic damage in an elastic-plastic and viscoplastic material subjected to tensile in-plane loading. The aim is to predict the fracture conditions by accounting for void accumulation in the vicinity of the crack-tip. A power law relates the stress to the strain of the material. The damage, which invokes the growth and coalescence of microvoids, is confined to a small circular zone surrounding the crack-tip. At the onset of crack extension, the applied stress for small-scale and large-scale yielding solutions is found to be proportional to a₀ ^-1/(n+1), where 2a₀is the initial crack length and n is the strain hardening exponent of the material. For small-scale yielding, the conditions required for fatigue crack growth and steady-state creep are determined. In particular, the variations of the normalized crack length with the number of loading cycles and the time required for failure are shown for various strain hardening exponents, applied loading, and material damage parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reprint of “Cracks in inhomogeneous materials: Comprehensive assessment using the configurational forces concept”

The concept of configurational forces is applied to demonstrate the application of the concept of configurational forces in the numerical simulation of crack growth and fracture processes. It is shown, how material property variations at an interface affect the crack driving force and how the criterion of maximum dissipation is used to evaluate the direction of crack propagation. Fatigue crack growth experiments were conducted on diffusion welded bimaterial specimens consisting of a high-strength steel and soft ARMCO iron. Two cases are considered: (1) specimens with an interface perpendicular to the initial crack orientation, and (2) specimens with an inclined interface. The numerical simulation with the concept of configurational forces show that not only variations of the elastic modulus and/or the yield stress have a tremendous influence on the crack driving force, the crack growth rate, and the curvature of the crack path, but also the thermal residual stresses that resulted from a rather small difference of the coefficient of thermal expansion.     

Determination of energy release rate and mode mix in three-dimensional layered structures using plate theory

A plate theory-based method for determining energy release rates is presented for general loadings of three dimensional layered structures. Mode decomposition is performed for cases that exhibit an inverse square root singularity and for which certain other restrictions apply. Predictions for energy release rate and mode mix for typical problems are presented and verified by comparison with results obtained by three dimensional finite element analyses.     

The effect of crack surface interaction on the stress intensity factor in Mode III crack growth in round shafts

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor.The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.     

Investigate the causes of cracks in welded 310 stainless steel used in the Flare tip

The present study examines the causes of the cracks in welded 310 stainless steel that has been used in the Flare tip. According to the tests, including metallographic examination, macroscopic hardness test and scanning electron microscopic analysis, the reasons for the nucleation and growth of the cracks in the weld zone have been discussed. The results show that, because of the service temperature of Flare tip between 500 and 900 °C, and hydrocarbon gases such as methane, ethane, sour gas and carbon dioxide that are the combustion products, the component surface has been oxidized and carburized. Thus, the surface carburized oxide layer and also the subsurface damage can be fertile field for the nucleation of cracks. Likewise, the presence of sigma phases, austenite dendrites and interdendritic delta ferrite can cause a drop in toughness in the weld zone and provide fields for the crack growth in the weld zone.     

纳米材料晶粒生长理论的研究进展

实验研究表明,纳米材料的晶粒生长速率远低于传统晶粒长大理论所预测的生长速率,为解释这一异常的晶粒生长行为,研究者提出了各种理论模型。综述了纳米晶粒生长理论模型的研究现状:第一类为动力学模型,通过钉轧晶界实现延缓晶粒的生长,起钉轧晶界作用的有溶质原子、三叉晶界和第二相等;第二类是热力学模型,通过降低晶界能来降低晶粒生长的驱动力,从而实现延缓晶粒的生长,如溶质原子偏析晶界和空位注入模型等。对各种理论模型进行了描述和分析,并展望了其发展方向。     

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.     

爆破作业单位爆炸物品新型管理模式探讨

文中介绍了中介机构对爆破作业单位爆炸物品进行监管这一新型管理模式,对它的特点、依据和内容进行阐述,并以慈溪市为试点的经验探讨其可行性。实践表明对爆破作业单位爆炸物品管理引进中介服务机构管理可行,可有效防止爆破器材流失和减少爆破作业事故,符合＂安全第一,预防为主,综合治理＂的安全生产方针,可为公安机关制定防范措施和管理决策提供科学依据。     

Mode III Interlaminar Fracture Behavior of Glass Fiber Reinforced Polymer Woven Laminates at 293 to 4 K

This paper deals with mode III delamination properties of glass fiber reinforced polymer woven laminates at room temperature (293 K), liquid nitrogen temperature (77 K), gas helium temperature (20 K), and liquid helium temperature (4 K). In order to evaluate these properties, the Split Cantilever Beam (SCB) fracture test is performed. The load is applied to a test specimen through a set of identical grips in order to reduce (in some degree) the mode II loading at the free edges. A three-dimensional finite element analysis is used to study the stress and strain state of the specimens and to interpret the experimental measurements. The strain energy release rate is calculated by using the virtual crack closure technique. It is found that the strain energy release rate is dominated by the mode III component. A non-uniform distribution of the strain energy release rate along the delamination front is obtained with mode III component having maximum at the center of the delamination front, while mode II component increases towards the free edges. The strain energy release rate is also determined using the crack closure technique. A finite element analysis is also carried out to calculate the stress intensity factors for the SCB specimens. The fracture surfaces are examined by scanning electron microscopy to identify the fracture mechanisms. The most important conclusion from the present study is that at temperature lowering from 293 to 20 K the mode III fracture toughness increases, further cooling to 4 K produces a toughness decrease.     

Mode III interlaminar fracture of carbon/epoxy laminates using the edge crack torsion (ECT) test

The mode III interlaminar fracture of carbon/epoxy laminates was evaluated with the edge crack torsion (ECT) test. Three-dimensional finite element analyses were performed in order to select two specimen geometries and an experimental data reduction scheme. Test results showed considerable non-linearity before the maximum load point and a significant R-curve effect. These features prevented an accurate definition of the initiation point. Nevertheless, analyses of non-linearity zones showed two likely initiation points corresponding to G_IIIc values between 850 and 1100 J/m² for both specimen geometries. Although any of these values is realistic, the range is too broad, thus showing the limitations of the ECT test and the need for further research.     

Corrosion Fracture of Structural Metallic Materials: Effect of Electrochemical Conditions in Crack

Abstract: The work is a compressed review based on the summarised results and the original approach for study of corrosion crack growth, taking into account local electrochemical conditions in the crack tip, which was developed at the Karpenko Physico‐Mechanical Institute of NASU. The model scheme of the pre‐fracture zone in the corrosion crack tip, which can be defined by the local values of pH of solution, electrode potential of metal E and stress intensity factor K_I is proposed. For its realisation, the special method and testing equipment for corrosion crack growth study and local electrochemical measurements in the crack were developed. The variation of the electrochemical conditions in corrosion cracks was studied, and it has been found that some stabilised levels of the pH and E values can be achieved in the tip of a non‐propagating and a propagating crack under static and cyclic loading during of exposure time. On this ground, the method for forecasting of the threshold stress intensity factor K_ISCC under stress corrosion cracking was proposed using these characteristic values of pH and E. This method was also adopted for the determination of the threshold stress intensity factor K_th under corrosion fatigue. The special method for determining corrosion fatigue crack growth rate diagrams based on consideration of extreme electrochemical conditions in the crack tip was developed. It has been proven that such diagrams reflect the extreme influence of the environmental factor on corrosion fracture of material, and they may be recommended as the base for the remaining lifetime calculation of the structural elements exploited under environmental conditions.     

Multi-Scale Analysis of Fretting Fatigue in Heterogeneous Materials Using Computational Homogenization

This paper deals with modeling of the phenomenon of fretting fatigue inheterogeneous materials using the multi-scale computational homogenization techniqueand finite element analysis (FEA). The heterogeneous material for the specimens consistsof a single hole model (25% void/cell, 16% void/cell and 10% void/cell) and a four-holemodel (25% void/cell). Using a representative volume element (RVE), we try to producethe equivalent homogenized properties and work on a homogeneous specimen for thestudy of fretting fatigue. Next, the fretting fatigue contact problem is performed for 3 newcases of models that consist of a homogeneous and a heterogeneous part (single hole cell)in the contact area. The aim is to analyze the normal and shear stresses of these modelsand compare them with the results of the corresponding heterogeneous models based onthe Direct Numerical Simulation (DNS) method. Finally, by comparing thecomputational time and % deviations, we draw conclusions about the reliability andeffectiveness of the proposed method.     

Evaluation of energy release rate-based approaches for predicting delamination growth in laminated composites

A variety of energy release rate-based approaches are evaluated for their accuracy in predicting delamination growth in unidirectional and multidirectional laminated composites. To this end, a large number of unidirectional and multidirectional laminates were tested in different bending and tension configurations. In all cases, the critical energy release rate was determined from the tests in the most accurate way possible, such as by compliance calibration or the area method of data reduction. The mode mix from the tests, however, was determined by a variety of different approaches. These data were then examined to determine whether any of the approaches yielded the result that toughness was a single-valued function of mode mix. That is, for an approach to have accurate predictive capabilities, different test geometries that are predicted to be at the same mode mix must display the same toughness. It was found that variously proposed singular field-based mode mix definitions, such as the =0 approach or basing energy release rate components on a finite amount of crack extension, had relatively poor predictive capabilities. Conversely, an approach that used a previously developed crack tip element analysis and which decomposed the total energy release rate into non-classical components was found to have excellent predictive capabilities. It is postulated that this approach is more appropriate for many present-day laminated composites.     

A New Idea of Fractal-Fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models. Amongst them, the significant models of fluids and heat or mass transfer are on priority. Most recently a new idea of fractal-fractional derivative is introduced; however, it is not used for heat transfer in channel flow. In this article, we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem. More exactly, we have considered the free convection heat transfer for a Newtonian fluid. The flow is bounded between two parallel static plates. One of the plates is heated constantly. The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution. The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter. For the influence of temperature and velocity profile, it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator. Therefore, a combined approach of fractal fractional explains the memory of the function better than fractional only.