The limitations of using one-parameter to describe the crack-tip fields have prompted investigators to consider better descriptions of the crack tip fields. The two-parameter descriptions, such as J-Q theory, have bee...The limitations of using one-parameter to describe the crack-tip fields have prompted investigators to consider better descriptions of the crack tip fields. The two-parameter descriptions, such as J-Q theory, have been an important development in this field. But under the consideration of plane strain and three-dimensional problem, the effects of the out-of-plane stress can not be neglected In this paper, effects of the in-plane constraint as well as the out-of-plane constraint are studied by aid of the finite element method on the plane strain condition. It is obvious that both the in-plane constraint (Q factor) and the out-of-plane constraint (Tz = σzz/(σxx + σyy) ) affect the crack tip fields.Several important features of the out-of-plane constraint are described out based on the simulation results. At the end of this paper, a three-parameter formulation is proposed, in which both the in-plane constraint and the out-of-plane constraint are considered. Comparing with the results of the FEM numerical simulation, the three-parameter description can provide a better prediction near the crack tip.展开更多
Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are o...Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.展开更多
Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tz...Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.展开更多
In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantiti...In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantities and criterion equation which deduces these conserved quantities are presented.This result establishes the theory basis for further researches on conservation laws of Tzénoff equations of the higher-order nonholonomic constraint system.展开更多
Plane strain elastic-plastic finite element analyses are used tostudy the stress, strain fields around a straight crack in powerhardening plastic material. Center crack panel (CCP), single edgecrack panel (SECP) and d...Plane strain elastic-plastic finite element analyses are used tostudy the stress, strain fields around a straight crack in powerhardening plastic material. Center crack panel (CCP), single edgecrack panel (SECP) and double edge crack panel (DECP) tensionspecimens are analyzed with various crack lengths. Two localconstraint parameters, i.e. in-plane stress ratio T_x andout-of-plane constraint T_z are an- alyzed, which are defined astangential stress dividing normal (open) stress and out-of-planestress dividing the sum of tangential stress and normal stressrespectively.展开更多
The theoretical solutions are obtained for the three-dimensional(3-D)stress field in an infinite isotropic elastic plate with a through-the-thickness circular hole subjected to shear load at far field by using Kane an...The theoretical solutions are obtained for the three-dimensional(3-D)stress field in an infinite isotropic elastic plate with a through-the-thickness circular hole subjected to shear load at far field by using Kane and Mindlin′s assumption based on the stress function method.Based on the present solutions,the characteristics of 3-D stress field are analyzed and the emphasis is placed on the effects of the plate thickness and Poisson′s ratio on the deviation of the present 3-D in-plane stress from the related plane stress solutions,the stress concentration and the out-of-plane constraint.The present solutions show that the stress concentration factor reaches its peak value of about 8.9% which is higher than that of the plane stress solutions.As expected,the out-of-plane stress constraint factor can reach 1on the surface of the hole when the plate is a very thick one.展开更多
文摘The limitations of using one-parameter to describe the crack-tip fields have prompted investigators to consider better descriptions of the crack tip fields. The two-parameter descriptions, such as J-Q theory, have been an important development in this field. But under the consideration of plane strain and three-dimensional problem, the effects of the out-of-plane stress can not be neglected In this paper, effects of the in-plane constraint as well as the out-of-plane constraint are studied by aid of the finite element method on the plane strain condition. It is obvious that both the in-plane constraint (Q factor) and the out-of-plane constraint (Tz = σzz/(σxx + σyy) ) affect the crack tip fields.Several important features of the out-of-plane constraint are described out based on the simulation results. At the end of this paper, a three-parameter formulation is proposed, in which both the in-plane constraint and the out-of-plane constraint are considered. Comparing with the results of the FEM numerical simulation, the three-parameter description can provide a better prediction near the crack tip.
基金The project supported by the National Natural Science Foundation of China （50275073）
文摘Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.
基金National Natural Science Foundation of China under Grant No.10672143
文摘Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.
基金Project supported by the National Natural Science Foundation of China(Grant No.10972127)
文摘In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantities and criterion equation which deduces these conserved quantities are presented.This result establishes the theory basis for further researches on conservation laws of Tzénoff equations of the higher-order nonholonomic constraint system.
基金the National Foundation of Distinguished Young Scientists of China(No.59625510)
文摘Plane strain elastic-plastic finite element analyses are used tostudy the stress, strain fields around a straight crack in powerhardening plastic material. Center crack panel (CCP), single edgecrack panel (SECP) and double edge crack panel (DECP) tensionspecimens are analyzed with various crack lengths. Two localconstraint parameters, i.e. in-plane stress ratio T_x andout-of-plane constraint T_z are an- alyzed, which are defined astangential stress dividing normal (open) stress and out-of-planestress dividing the sum of tangential stress and normal stressrespectively.
基金Supported by the National Natural Science Foundation of China(11372269,10902057)
文摘The theoretical solutions are obtained for the three-dimensional(3-D)stress field in an infinite isotropic elastic plate with a through-the-thickness circular hole subjected to shear load at far field by using Kane and Mindlin′s assumption based on the stress function method.Based on the present solutions,the characteristics of 3-D stress field are analyzed and the emphasis is placed on the effects of the plate thickness and Poisson′s ratio on the deviation of the present 3-D in-plane stress from the related plane stress solutions,the stress concentration and the out-of-plane constraint.The present solutions show that the stress concentration factor reaches its peak value of about 8.9% which is higher than that of the plane stress solutions.As expected,the out-of-plane stress constraint factor can reach 1on the surface of the hole when the plate is a very thick one.
