The interaction of two collinear cracks in a rectangular superconductor slab under an electromagnetic force

The interaction of two collinear cracks is obtained for a type-II superconducting under electromagnetic force. Fracture analysis is performed by means of finite element method and the magnetic behavior of superconductor is described by the critical-state Bean model. The stress intensity factors at the crack tips can be obtained and discussed for decreasing field after zero-field cooling. It is revealed that the stress intensity factor decreases as applied field increases. The crack-tip stress intensity factors decrease when the distance between the two collinear cracks increases and the superconductors with smaller crack has more remarkable shielding effect than those with larger cracks.     

Thermal stress cleaving of silicon wafer by pulsed Nd：YAG laser

The applied laser energy absorbed in a local area in laser thermal stress cleaving of brittle materials using a controlled fracture technique produces tensile thermal stress that causes the material to separate along the moving direction of the laser beam. The material separation is similar to crack extension, but the fracture growth is controllable. Using heat transfer theory, we establish a three-dimensional （3D） mathematical thermoelastic calculational model containing a pre-existing crack for a two-point pulsed Nd：YAG laser cleaving silicon wafer. The temperature field and thermal stress field in the silicon wafer are obtained by using the finite element method （FEM）. The distribution of the tensile stress and changes in stress intensity factor around the crack tip are analyzed during the pulse duration. Meanwhile, the mechanism of crack propagation is investigated by analyzing the development of the thermal stress field during the cleaving process.     

Thermal shock fracture of piezoelectric materials

This paper deals with a case study for the piezoelectric materials suddenly exposed to an environmental medium of different temperature. The problem is idealized to a plate containing an edge crack or an embedded crack. The stress and electric displacement histories in an uncracked plate are calculated. These stresses and electric displacements are then added to the crack surface tractions and electric displacements with opposite sign to formulate a mixed boundary value problem. The cracking problem is thus reduced to a singular integral equation of Cauchy type, which is then solved numerically. Both impermeable crack assumption and permeable crack assumption are considered. The results for stress and electric displacement intensity factors are computed as a function of normalized time and crack size. Lower bound solutions are obtained for the maximum thermal shock that the material can sustain without catastrophic failure according to the two distinct criteria: (i) The maximum local tensile stress equals the tensile strength of the medium. (ii) The maximum stress intensity factor for the pre-existing representative crack equals the fracture toughness of the medium. The parameters that control the transient thermal stress and electric displacement are also identified. The method can be used to explore susceptibility to thermal fracture in piezoelectric materials containing pre-cracks.     

Analysis of composite material interface crack face contact and friction effects using a new node-pairs contact algorithm

A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem(e.g., resistant coating and thermal barrier coatings) subjected to complicated load conditions.To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors(SIFs) and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors K?IIfor the friction coefficient decrease by 16% when f changes from 1 to 0.     

Peeling stress analysis for an inhomogeneous high-Tc superconductor with a discontinuous interface at the substrate

This paper presents an analysis of a superconductor–substrate system to calculate the peeling stress of a high temperature superconductor (HTS) when the temperature decreases from ambient to operating conditions (cryogenic temperatures). Firstly, the values for the material properties of the inhomogeneous high temperature superconductor (HTS) were obtained by fitting a second order polynomial to the experimental data. It is assumed that the material properties of the inhomogeneous HTS vary with varying height coordinate and temperature. Then, through the proposed graded finite element method, the coupled thermo-mechanical equations were solved numerically. The numerical results show that the thermal stress generated in the inhomogeneous HTS is larger on a SiTiO₃ substrate than on a MgO substrate. The maximum thermal stresses, i.e., the peeling stresses, occur near the bottom corner of the inhomogeneous HTS and may induce fracture behavior at the bi-material interface. The inhomogeneous HTS cools at a slower pace than the homogeneous HTS from the room temperature to the operating temperature. It is also shown that the magnitude of the peeling stress for a homogeneous HTS is larger than that for an inhomogeneous HTS. It is intended that the model presented here be useful to researchers who are interested in the mechanical properties of an inhomogeneous HTS.     

Fracture Analysis in Orthotropic Thermoelasticity Using Extended Finite Element Method

In this paper, a method for extracting stress intensity factors (SIFs) in orthotropic thermoelasticity fracture by the extended finite element method (XFEM) and interaction integral method is presented. The proposed method is utilized in linear elastic crack problems. The numerical results of the SIFs are presented and compared with those obtained using boundary element method (BEM). The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.     

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten‐step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.     

碳纤维布补强梁裂尖奇异性的光学焦散线实验研究

通过光学焦散线方法对碳纤维布加固含裂纹梁进行三点弯荷载下的静荷载和冲击实验,研究了其断裂特性。在静态实验研究中,记录了不同载荷状态下裂纹的焦散斑光学图像,计算了与之对应的裂纹尖端的应力强度因子,分析了试件在粘贴加固不同长度的碳纤维布情况下焦散斑和应力强度因子演化规律。在动态实验中,记录了裂纹扩展的过程和在此过程中不同时刻的焦散斑和裂纹扩展的路线。通过各瞬间的焦散斑图像,分析裂纹的扩展长度及速度,并得到各时刻的动态应力强度因子。     

The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model

The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter C→0. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H. We found an excellent agreement between the exact solutions and asymptotic solutions when H is very small.     

Strength evaluation of brittle ceramics with surface defects subjected to thermal shock

The thermal shock strength of a ceramic material plate with a semi-elliptical surface crack is evaluated in this paper. The thermal stress distribution at the plate without crack is expressed by a polynomial form. The calculated thermal stresses are used to obtain the thermal stress intensity factors of semi-elliptical surface cracks using the geometric functions. Variations of thermal stress intensity factor with crack depth and time are obtained. For the strength evaluation of the material, crack growth analysis is conducted. In addition, the thermal shock resistance of the ceramic material plate is evaluated by the stress-based failure criterion and the toughness-based failure criterion. The critical temperature at which crack propagation starts is obtained. Applicability of the two failure criteria in thermal shock resistance evaluation of ceramic is identified and the importance of the semi-elliptical surface defects on the thermal shock resistance behaviour of ceramic materials is justified.     

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.     

A model of a belt chamber cracking based on crack profiles calculations

Abstract

The problem of a Belt chamber matrix cracking is presented. The influence of crack surface quality on the effective values of near crack tip stress is discussed. It is shown that under working conditions of the vessel, the existing shear friction between upper and lower crack surfaces caused by crack surface roughness can prevent the crack surface sliding displacement. Therefore, the control variable for matrix cracking is the value of stress intensity factor K_I corresponding to normal node of loading only. The calculations are performed by finite element method within the range of linear elastic fracture mechanics.     

Effect of thermal stresses on chip-free diode laser cutting of glass

In laser cleaving of brittle materials using controlled fracture technique, thermal stresses are used to induce a crack and the material is separated along the cutting path by extending this crack. In this study, a glass sheet is stressed thermally using a 808-940 nm diode laser radiation. One of the problems in laser cutting of glass with controlled fracture technique is the cut deviation at the leading and the trailing edges of the glass sheet. In order to avoid this damage it is necessary to understand the stress distributions which control crack propagation. A study is conducted here to analyse the cut deviation problem of glass by examining the stress fields during diode laser cutting of soda-lime glass sheets. Optical microscope photographs of the breaking surface are obtained to examine the surface quality and cut path deviation while the latter is explained from the results of the stress fields which are obtained from a finite element simulation.     

Investigation on periodic cracking of elastic film/substrate system by the extended finite element method

Multiple cracking behavior in a thin elastic film bonded to a thick elastic substrate is investigated by the extended finite element method. Stress and stress intensity factor are obtained using a periodic finite element model for the cracked film/substrate system. The influences of various parameters including crack length, film thickness, periodic crack spacing, and relative stiffness of the substrate on the stress and stress intensity factor are discussed in detail. It is demonstrated that the effects of geometric parameters are more sensitive than that of material property. In particular, the crack spacing has a saturation value due to interactions of neighboring cracks and relief of tensile stress in the film. The film/substrate couple with multiple periodic cracks can exhibit a positive potential in improving the durability of the film/substrate system.     

Dynamic caustics and its applications

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.     

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level T _z (z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and T _z (z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.     

Graded finite element simulation of thermal stress in inhomogeneous high-Tc superconductor

YBa₂Cu₃O_y is an orthotropic material with different material properties in a, b and c directions, such as Young’s modulus, coefficient of thermal expansion (CTE), and thermal conductivity. It is assumed that the material properties of inhomogeneous high temperature superconductor (HTS) vary with different height coordinate and temperature. A model is presented in this paper to calculate the thermal stress of inhomogeneous HTS when temperature decreases from ambient to operating conditions (cryogenic temperatures). By fitting a second order polynomial to the experimental data, value of the material properties of inhomogeneous HTS can be obtained. Then, through the proposed graded finite element method, the coupled thermo-mechanical equations were solved numerically. The numerical results show that the temperature profiles distribute the function of time after soaking. It is notable that the temperature profile reaches steady in a very short period of time, so the thermal stress suddenly increases to a very high level for a bulk superconductor. It is also shown that the closer to the sample internal region it is, the larger the heat fluxes are. Besides, the maximum tensile stresses, i.e. the peeling stresses, occur near bottom corner of inhomogeneous HTS. It is intended that the model presented in this paper could be useful to researchers who are interested in mechanical properties of inhomogeneous HTS.     

Failure analysis of threaded end closures

Abstract

Procedures for the load, stress and fracture mechanics analysis of threaded end closures are reviewed. The limitations of some procedures for determining crack tip stress intensity factors for severe stress gradients are outlined.     

Nanoindentation and nanoscratch behaviors of Ag/Ni multilayers

The hardness, elastic modulus and scratch behaviors of Ag/Ni mulitlayers deposited by evaporation have been carried out by nanoindentation and nanoscratch. It has been found that the hardness (H) increases, while the modulus (E) decreases, that is to say an increase of H/E as the periodicity decreases. Many mechanisms are included in nanoscratch, including initial elastic contact, plowing and fracture stage, in each multilayer. Coefficient of friction during plowing decreases with the decrease of the periodicity, which can be ascribed to decreasing material pile-up due to the increase of H/E. Elastic recovery after scratching also increases as the periodicity decreases because of the increase of H/E, which leads to improved wear resistance. The fracture stage will be postponed with decreasing periodicity, which also leads to better wear behavior.     

Dynamic analysis of a geared rotor system considering a slant crack on the shaft

The vibration problems associated with geared systems have been the focus of research in recent years. As the torque is mainly transmitted by the geared system, a slant crack is more likely to appear on the gear shaft. Due to the slant crack and its breathing mechanism, the dynamic behavior of cracked geared system would differ distinctly with that of uncracked system. Relatively less work is reported on slant crack in the geared rotor system during the past research. Thus, the dynamic analysis of a geared rotor-bearing system with a breathing slant crack is performed in the paper. The finite element model of a geared rotor with slant crack is presented. Based on fracture mechanics, the flexibility matrix for the slant crack is derived that accounts for the additional stress intensity factors. Three methods for whirling analysis, parametric instability analysis and steady-state response analysis are introduced. Then, by taking a widely used one-stage geared rotor-bearing system as an example, the whirling frequencies of the equivalent time-invariant system, two types of instability regions and steady-state response under the excitations of unbalance forces and tooth transmission errors, are computed numerically. The effects of crack depth, position and type (transverse or slant) on the system dynamic behaviors are considered in the discussion. The comparative study with slant cracked geared rotor is carried out to explore distinctive features in their modal, parametric instability and frequency response behaviors.