The surface cracking behavior in air plasma sprayed thermal barrier coating system incorporating interface roughness effect

The objective of this work is to understand the effect of interface roughness on the strain energy release rate and surface cracking behavior in air plasma sprayed thermal barrier coating system. This is achieved by a parameter investigation of the interfacial shapes, in which the extended finite element method (XFEM) and periodic boundary condition are used. Predictions for the stress field and driving force of multiple surface cracks in the film/substrate system are presented. It is seen that the interface roughness has significant effects on the strain energy release rate, the interfacial stress distribution, and the crack propagation patterns. One can see the completely different distributions of stress and strain energy release rate in the regions of convex and concave asperities of the substrate. Variation of the interface asperity is responsible for the oscillatory characteristics of strain energy release rate, which can cause the local arrest of surface cracks. It is concluded that artificially created rough interface can enhance the durability of film/substrate system with multiple cracks.     

Effect of periodic surface cracks on the interfacial fracture of thermal barrier coating system

Periodic surface cracks and interfacial debonding in thermal barrier coating (TBC) system may be induced during cooling process. The objective of this work is to investigate the effect of periodic surface cracks on the interfacial fracture of TBC system. The finite element method (FEM) incorporating cohesive zone model is used in analysis. It is found that surface crack spacing has significant effect on the initiation and propagation of short interface crack. Three different regions are identified for describing the effect of surface crack spacing. In Region I the interface crack driving force is dramatically reduced due to high surface crack density. In this case, the initiation of interfacial delamination can be delayed. Region II applies as the surface crack spacing is moderate. Analysis of this transition zone brings to the definition of normalized critical surface crack spacing. Region III arises for sufficient large surface crack spacing. In this case, the interface crack driving force reaches a steady state, where the effects of adjacent surface cracks are relatively insignificant and can be ignored. It can be concluded that an appropriately high surface crack density can enhance the durability of TBC system.     

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.     

柔性基周期性厚度梯度薄膜的应变效应

可控的表面微结构在柔性电子、仿生器件和能源材料等方面均具有重要的应用价值.本文采用编织铜网作为掩模板,利用磁控溅射技术在柔性聚二甲基硅氧烷(PDMS)基底上制备具有周期分布的厚度梯度金属银薄膜,研究了薄膜在单轴压缩/拉伸过程中的形貌演化规律.实验发现,在单轴机械载荷作用下,银薄膜表面将形成相互垂直的条纹褶皱和多重裂纹.膜厚的梯度变化调制了薄膜的面内应力分布,导致褶皱在膜厚较小处率先形成,并逐渐扩展到膜厚较大区域,而裂纹则基本限定在膜厚较小区域.基于应力理论和有限元计算,对周期性厚度梯度薄膜的褶皱和裂纹的形貌特征、演化行为和物理机制进行了深入分析.该研究将有助于加深对非均匀薄膜体系的应变效应的理解,并有望通过梯度薄膜的结构设计在柔性电子等领域获得应用.     

Simulated caustic patterns for dynamic crack growth in a plate based on a three-dimensional numerical analysis

The rapid growth of a through-the-thickness crack in a nominally elastic plate under Mode I conditions is considered, with emphasis on the three-dimensional aspects of the elastodynamic crack growth process. For points near the crack edge, the assumptions on stress state consistent with plane stress analysis are not valid, and the possibility of an inertial effect associated with rapid lateral contraction must be considered. The steady crack growth process is analyzed here by means of the finite element method, and the degree to which the local fields are described by plane stress analysis is established. In addition, synthetic shadow spot patterns are generated from the numerical three-dimensional solutions. The inferred values of stress intensity factor are compared with the values of the corresponding plane stress dynamic stress intensity factor.     

Effect of microcracking on electric-field-induced stress intensity factors in dielectric ceramics

This paper gives a quantitative analysis of the effect of near-tip microcracks on electric-field-induced stress intensity factors in isotropic elastic dielectrics. Nucleation of the microcracks is assumed to be governed by the electric-field-induced mean stress or the maximum normal stress. Based on the solutions for the effect of a single microcrack on the local electric field at the main crack, simple formulae are derived for the electric-field-induced stress intensity factors in the presence of the microcracks. It is found that the relative change in the stress intensity factor due to the microcracks for a conducting crack is equal and opposite to that for an insulating crack provided that the distribution of microcrack orientations is random. In particular, the microcracking zone is found to amplify the electric-field-induced stress intensity factor in some cases, especially for stationary insulating cracks, while the microcracking zone wake has an antishielding effect for sufficiently grown conducting cracks. These results are in sharp contrast with the well-known toughening effects of microcracks in elastic media under pure mechanical loads. This is attributed to the fact that the interaction between the microcracks and the main crack in elastic dielectrics under electrical loading is governed essentially by electrostatics, while the shape of the microcracking zone is determined by the electric field induced elastic stress field.     

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.     

Thermoelastic behavior of a thermoelectric thin-film attached to an infinite elastic substrate

Abstract

This paper examines the thermoelectric behaviour of a thermoelectric thin film bonded to an elastic substrate. A calculation model for thermoelectric thin films is developed based on the singular integral equation method. The interface shear stress is found to exhibit singular behaviour at the ends of the films. Numerical results for the thermal stress distribution in the film and the film/substrate interface are obtained. Effects of film thickness and the substrate to film stiffness ratio on the stress of the film and the stress intensity factor of the interface are identified. The effects of interface electricity conductivity and the elastic–plastic deformation of the film are discussed.     

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.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

Basic solution of four parallel non-symmetric permeable Mode-III cracks in a piezoelectric/piezomagnetic composite plane

The interaction of four parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic composite plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through a Fourier transform into four pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relationships among the electric displacement, magnetic flux and stress fields near the crack tips were obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding effect is present in piezoelectric/piezomagnetic composites.     

Modeling of thermomechanical fracture of functionally graded materials with respect to multiple crack interaction

Different aspects of thermomechanical fracture of functionally graded materials (FGMs) are considered. Among them are the crack interaction problems in a functionally graded coating on a homogeneous substrate (FGM/H). The interaction between systems of edge cracks is investigated, as well as, how this mutual interaction influences the fracture process and the formation of crack patterns. The problem is formulated with respect to singular integral equations which are referred to the boundary equation methods. The FGM properties are modeled by exponential functions. The main fracture characteristics are calculated, namely, the stress intensity factors, the angles of deviation of the cracks from their initial propagation direction and the critical stresses when the crack starts to propagate. The last two characteristics are calculated using an appropriate fracture criterion. The problem contains different parameters, such as the geometry (location and orientation of cracks, their lengths, and the width of the FGM layer) and material parameters, i.e. the inhomogeneity parameters of elastic and thermal coefficients of the functionally graded material. The influence of these parameters on the thermo-mechanical fracture of FGM/H is investigated. As examples the following real material combinations are discussed: TiC/SiC, Al₂O₃/MoSi₂, MoSi₂/SiC, ZrO₂/nickel and ZrO₂/steel.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

Simulation of the interface characterization of thin film on substrate system by bending creep tests

In the present paper, the finite element simulation of the bending creep tests of the thin film on substrate system is carried out. The purpose of the investigation is to understand the creep stress characterization of the thin film on substrate system with the three points bending creep test method, which plays an important role in the bending creep testing characterization, so as to provide some foundation on determination of interface properties of the thin film on substrate system by a bending creep testing. Finite element results shows that the influences of the thickness of thin film and the modulus ratio of thin film to substrate on stress distribution are important.     

Oscillating cracks in glassy films on silicon substrates

Cracks that propagate with near-perfect sinusoidal form are reported in amorphous silicon-rich silica films deposited onto (001) silicon substrates by plasma-enhanced chemical vapour deposition and subjected to thermal annealing. The cracks are shown to result from high tensile stresses that develop in the film during thermal annealing at temperatures in the range up to 700°C, a process shown to be correlated with the loss of hydrogen from the films. Two distinct modes of crack propagation are reported: straight cracks that propagate along directions parallel to [100] cube-edge directions in the substrate, and oscillating cracks that propagate with sinusoidal form parallel to [110] diagonal directions. Sections through the cracks show that the oscillating cracks have a complex three-dimensional structure that extends through the glassy film and into the underlying silicon substrate. This involves a correlated oscillation between the crystallographic orientation of the crack in the surface plane and that of the crack extension into the substrate. Whereas a complete theoretical treatment of this behaviour would be extremely complicated, a simple theory is developed to demonstrate that an oscillating crack has a minimum energy per unit length for a particular wavelength and amplitude that depends upon the physical parameters of both film and substrate. The energy at this minimum is shown to be lower than that of a straight crack for certain parameter ranges so that the oscillating geometry is preferred.     

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.     

熔石英亚表面缺陷附近光强分布的数值模拟

熔石英亚表面缺陷对光场的调制是导致激光辐照场破坏的主要因素。采用有限元方法对熔石英亚表面缺陷（平面和锥形划痕）周围的光强分布进行了数值模拟。结果表明：划痕形状、几何尺寸、方位角、光的入射角等是影响划痕周围光强分布的主要因素;前表面划痕对光强的增强效果比后表面弱;在理想形状的划痕截面和表面同时发生内全反射时,平面划痕周围的光强增强效果明显。锥形划痕周围的光强分布为正确解释交叉划痕的夹角平分线附近的损伤提供了理论依据。     

熔石英亚表面缺陷附近光强分布的数值模拟

 熔石英亚表面缺陷对光场的调制是导致激光辐照场破坏的主要因素。采用有限元方法对熔石英亚表面缺陷（平面和锥形划痕）周围的光强分布进行了数值模拟。结果表明：划痕形状、几何尺寸、方位角、光的入射角等是影响划痕周围光强分布的主要因素;前表面划痕对光强的增强效果比后表面弱;在理想形状的划痕截面和表面同时发生内全反射时,平面划痕周围的光强增强效果明显。锥形划痕周围的光强分布为正确解释交叉划痕的夹角平分线附近的损伤提供了理论依据。     

ANALYSIS OF THE RESPONSE OF A CRACKED JEFFCOTT ROTOR TO AXIAL EXCITATION

The coupling of lateral and longitudinal vibrations due to the presence of transverse surface crack in a rotor is explored. Steady state unbalance response of a Jeffcott rotor with a single centrally situated crack subjected to periodic axial impulses is studied. Partial opening of crack is considered and the stress intensity factor at the crack tip is used to decide the extent of crack opening. A crack in a rotor is known to introduce coupling between lateral and longitudinal vibrations. Therefore, lateral vibration response of a cracked rotor to axial impulses is studied in detail. Spectral analysis of response to periodic multiple axial impulses shows the presence of rotor bending natural frequency as well as side bands around impulse excitation frequency and its harmonics due to modulations caused by rotor running frequency. It is concluded that the above approach can prove to be a useful tool in detecting cracks in rotors.     

The interaction and the surface crack of single-crystal silicon induced by a millisecond laser

When the silicon material is irradiated by laser, it absorbs the laser energy leading to the temperature rise and the thermal stress. The damage effect includes melting, vaporation and thermal stress damage. Once the thermal stress exceeds the stress strength the crack will initiate. The silicon surface cracks induced by a millisecond laser are investigated. The experimental results show that three types of cracks are generated including cleavage crack, radial crack and circumferential crack. The cleavage crack is located within the laser spot. The radial crack and circumferential crack are located outside the laser spot. A two-dimensional spatial axisymmetric model of silicon irradiated by a 1064 nm millisecond laser is established. To assess what stresses generate and explain the generation mechanism of the different cracks, the thermal stress fields during laser irradiation and the cooling process are obtained using finite element method. The radial stress and hoop stress within the laser spot are tensile stress after the laser irradiation. The temperature in the center is the highest but the thermal stress in the center is not always highest during the laser irradiation. The cleavage cracks are induced by the tensile stress after the laser irradiation. The radial crack and the circumferential crack are generated during the laser irradiation.