Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material ...Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material was put forward. The effects of shear modulus and Poisson＇s ratio of the matrix material and attaching material on eigen-values were analyzed. A generalized expression for calculating/（i of the perpendicular V-notch of bi-materials was obtained by means of stress extrapolation. Effects of notch depth, notch angle and Poisson＇s ratio of materials on the singular stress field near the tip of the V-notch were analyzed systematically with numerical simulations. As an example, a finite plate with double edge notches under uniaxial uniform tension was calculated by the method presented and the influence of the notch angle and Poisson＇s ratio on the stress singularity near the tip of notch was obtained.展开更多
The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notc...The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notch angles β is obtained. The angulardistributions of stress for several cases are plotted. Theself-similarity behavior between the higher order terms is noticed.It is found that the terms with higher Order can be neglected for theV-notch angle β>45°.展开更多
The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic material...The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.展开更多
A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched s...A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used. However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modem materials would require more experiments to infer material dependent parameters in the local fracture model.展开更多
The aim of this study is to determine the complete elastic–plastic stress asymptotic solutions at the plane V-notch tip with the two edges being clamped–clamped,free-clamped and free-friction.Firstly,the displacemen...The aim of this study is to determine the complete elastic–plastic stress asymptotic solutions at the plane V-notch tip with the two edges being clamped–clamped,free-clamped and free-friction.Firstly,the displacement and stress fields around the notch tip are expressed as asymptotic expansions,and then,these asymptotic expansions are substituted into the displacement–strain relation and the equilibrium equations to establish the ordinary differential equations(ODEs).Finally,the interpolating matrix method is employed to solve the eigenvalue problem of the ODEs,and consequently,the leading-order and higher-order stress and displacement eigen-solutions at the notch tip are obtained.Numerical examples demonstrate that the presented method has the advantages of great versatility and high accuracy.展开更多
The stress intensity factor (SIF) at the V-notch tip of a single-edge-notched polymethyl methacrylate plate was measured by the digital gradient sensing (DGS) method. First, the displacement fields near the V-notch ti...The stress intensity factor (SIF) at the V-notch tip of a single-edge-notched polymethyl methacrylate plate was measured by the digital gradient sensing (DGS) method. First, the displacement fields near the V-notch tip of the specimen were recorded using digital image correlation under three-point bending. Second, the stress gradient function of the V-notch tip with unknown SIF was deduced from the Williams series expansion for singular elastic stress fields. Finally, the relationship between the stress gradient and the angular deflection around the V-notch tip was established according to the photoelastic effect. Combined with the theory of linear elastic fracture mechanics, it was derived that the angular deflection of each point can be expressed with the unknown SIF. Considering the unavoidable effects of rigid-body translation and rotation in the experiments, the new angular deflection control equation was derived based on the traditional angular deflection control equation. The SIF was obtained by the least square method. The experimental values calculated by the new control equation were compared with the analytical values. The result shows that the DGS method can accurately measure the SIF at the V-notch tip, which effectively improves the accuracy of SIF.展开更多
基金supported by the Ministry of Education of China(No.208152)Gansu Natural Science Foundation(No.3ZS061-A52-47).
文摘Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material was put forward. The effects of shear modulus and Poisson＇s ratio of the matrix material and attaching material on eigen-values were analyzed. A generalized expression for calculating/（i of the perpendicular V-notch of bi-materials was obtained by means of stress extrapolation. Effects of notch depth, notch angle and Poisson＇s ratio of materials on the singular stress field near the tip of the V-notch were analyzed systematically with numerical simulations. As an example, a finite plate with double edge notches under uniaxial uniform tension was calculated by the method presented and the influence of the notch angle and Poisson＇s ratio on the stress singularity near the tip of notch was obtained.
基金the National Natural Science Foundation of China (Nos.10132010 and 10072033).
文摘The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notch angles β is obtained. The angulardistributions of stress for several cases are plotted. Theself-similarity behavior between the higher order terms is noticed.It is found that the terms with higher Order can be neglected for theV-notch angle β>45°.
基金Project supported by the National Natural Science Foundation of China(Nos.12172048 and 12027901)the National Science and Technology Major Project of China(Nos.2019-Ⅶ-0007-0147 and 2017-Ⅵ-0020-0093)。
文摘The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.
文摘A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used. However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modem materials would require more experiments to infer material dependent parameters in the local fracture model.
基金This work was supported by the National Natural Science Foundation of China(No.11772114)the doctoral initiative fund(No.2020QDZ08).
文摘The aim of this study is to determine the complete elastic–plastic stress asymptotic solutions at the plane V-notch tip with the two edges being clamped–clamped,free-clamped and free-friction.Firstly,the displacement and stress fields around the notch tip are expressed as asymptotic expansions,and then,these asymptotic expansions are substituted into the displacement–strain relation and the equilibrium equations to establish the ordinary differential equations(ODEs).Finally,the interpolating matrix method is employed to solve the eigenvalue problem of the ODEs,and consequently,the leading-order and higher-order stress and displacement eigen-solutions at the notch tip are obtained.Numerical examples demonstrate that the presented method has the advantages of great versatility and high accuracy.
基金the National Basic Research Program of China (under Grant No. 14118683)China Postdoctoral Science Foundation (under Grant No. 2014M552548XB)the National Natural Science Foundation of China (under Grant. No. 11402103).
文摘The stress intensity factor (SIF) at the V-notch tip of a single-edge-notched polymethyl methacrylate plate was measured by the digital gradient sensing (DGS) method. First, the displacement fields near the V-notch tip of the specimen were recorded using digital image correlation under three-point bending. Second, the stress gradient function of the V-notch tip with unknown SIF was deduced from the Williams series expansion for singular elastic stress fields. Finally, the relationship between the stress gradient and the angular deflection around the V-notch tip was established according to the photoelastic effect. Combined with the theory of linear elastic fracture mechanics, it was derived that the angular deflection of each point can be expressed with the unknown SIF. Considering the unavoidable effects of rigid-body translation and rotation in the experiments, the new angular deflection control equation was derived based on the traditional angular deflection control equation. The SIF was obtained by the least square method. The experimental values calculated by the new control equation were compared with the analytical values. The result shows that the DGS method can accurately measure the SIF at the V-notch tip, which effectively improves the accuracy of SIF.
