A three dimensional rate-dependent crystal plasticity model is applied to study the influence of crystal orientation and grain boundary on the void growth and coalescence. The 3D computational model is a unit cell inc...A three dimensional rate-dependent crystal plasticity model is applied to study the influence of crystal orientation and grain boundary on the void growth and coalescence. The 3D computational model is a unit cell including one sphere void or two sphere voids. The results of three different orientations for single crystal and bicrystals are compared. It is found that crystallographic orientation has noticeable influences on the void growth directionvoid shape, and void coalescence of single crystal. The void growth rate of bicrystals depends on the crystallographic orientations and grain boundary direction.展开更多
The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the R...The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages: the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.展开更多
In this paper a general formula for plastic potential including isotropic ductile damage has been present ed on the basis of the thermodynamics for irreversible process and internal variable the- ory.With this formula...In this paper a general formula for plastic potential including isotropic ductile damage has been present ed on the basis of the thermodynamics for irreversible process and internal variable the- ory.With this formula the mass conservation law is satisfied and it also contains a series of unknow coefficients which are the function of macro equivalent stress and the average micro equivalent stress and an unknown function which is the function of two generalized forces. The approximate yield surface equation for isotropically damaged materials is developed.Using this equation the void growth rate is calculated for nonlinear material containing voids.The present re- sults are in good agreement with the numerical results given by the cell model.展开更多
Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plan...Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results.展开更多
The relationship between fracture toughness VGC and critical void growth RC/RO was studied for ten kinds of Steel. The macroscopic fracture toughness VGC was determined by using notched tensile specimens. and the micr...The relationship between fracture toughness VGC and critical void growth RC/RO was studied for ten kinds of Steel. The macroscopic fracture toughness VGC was determined by using notched tensile specimens. and the microscopic parameters of critical void growth ratio RC/RO were quantitatively measured under SEM. Then, the coefhcient C in the relation VGC = C In(RC/RO) proposed in author's past work was specifically explored. The correlation of C with tensile proderty parameter φ=σyδ/(Eφn) was presented for the Steel investigated, and the effects of low temperature on C were also discussed. Results show that the coefficient C is linearly related to the parameter and insensitive to low temperature.展开更多
The problem of void growth and interaction is of importance to understanding the mechanics of failure in metals exhibiting ductility. In this work, the growth and interaction of voids in 6061-T6 aluminum were studied ...The problem of void growth and interaction is of importance to understanding the mechanics of failure in metals exhibiting ductility. In this work, the growth and interaction of voids in 6061-T6 aluminum were studied experimentally. Specifically, holes of varying numbers and relative placement were investigated for their normalized area growth with applied displacement. Flat dog-bone specimens were carefully drilled in their gauge area with no (zero) holes, one hole, and two holes (arranged vertically or horizontally) for experimentation after polishing. The growth of holes, captured by video recordings, exhibited exponential behavior and was influenced greatly by the number and arrangement of holes with the horizontal voids growing the fastest and the vertical ones growing the slowest. Also, the ensuring deformation of the sample was studied using load-displacement curves, pictography and videography, SEM imaging and Atomic Force Microscopy (AFM). The methods revealed that although the major part failure is due to large crack formation, it was preceded by intense dislocation slip activity and the formation of micro cavities. Also, the AFM quantified the three-dimensional nature of crystal or grain deformation and how it is greatly influenced by distance and location from the hole. Lastly, theoretical understanding of hole growth was offered.展开更多
Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjec...Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjected to uniaxial tension strain with one-void and two-void at the centered grain boundary were employed to analyze the effect of specimen size, temperature and applied strain rate on the stress-strain response, incipient yield strength and macroscopic effective Young's modulus. The evolutions of dislocations, twin bands and void shapes under different specimen sizes were also presented. The obtained results show that, regardless of the void numbers, the specimen sizes, temperature, the applied strain rate had significant influence on the void shape evolution, stress-strain curve and incipient yield strength, while negligible effects on the macroscopic effective Young's modulus except for the temperature. Moreover, the voids growth rate along the grain boundary was also found to be associated with the specimen sizes.展开更多
In this paper, the strain energy function proposed by Shang and Cheng was generalized by introducing a nonlinear term. Void formation and growth in the interior of a sphere composed of compressible hyper-elastic mater...In this paper, the strain energy function proposed by Shang and Cheng was generalized by introducing a nonlinear term. Void formation and growth in the interior of a sphere composed of compressible hyper-elastic material, subjected to a prescribed uniform displacement, was examined. A parametric cavitated bifurcation solution for the radial deformed function was obtained. Stability of the solution of the cavitated bifurcation equation was discussed. With the appearance of a cavity, an interesting feature of the radial deformation near the deformed cavity wall is the transition from extension to compression.展开更多
The finite deformation and stress analyses for a rectangular plate with a center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper. An approximati...The finite deformation and stress analyses for a rectangular plate with a center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper. An approximation solution was obtained from the minimum potential energy principle. The numerical results for the growth of the cavitation and stresses along the edge of the cavitation were discussed. In addition, the stress concentration phenomenon was considered.展开更多
In this paper, a new model to describe the dynamic ductile fracture is proposed. The constitutive relation of the elastic-viscoplastic matrix has an overstress form given by previous authors. A dynamic loading surface...In this paper, a new model to describe the dynamic ductile fracture is proposed. The constitutive relation of the elastic-viscoplastic matrix has an overstress form given by previous authors. A dynamic loading surface at constant equivalent strain rate(with the volumetric part also taken into account) is derived and an approximate expression for this dynamic loading surface is suggested. In the case where the porous material element is subjected to spherically symmetric tension, the Carroll-Holt’s model and Johnson’s model are recovered; and in the case where the strain rate sensitivity of the material tends to zero, the Gurson’s model is recovered. Moreover, the normality condition of the plastic strain rate for the dynamic loading surface is discussed, and it is shown that the normality rule is no longer valid in general. Finally, comparisons of this model with the models recently proposed by Pan, Saje and Needleman as well as by Perzyna are also presented.展开更多
In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the voi...In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelusticannular plate and its approximate solution is obtained from the minimum potentialenergy principle. The growth of the cavitation iS also nunterically computed andanalysed.展开更多
The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility...The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.展开更多
The influence of crystallographic orientation on the void growth in FCC crystals was numerically simulated with 3D crystal plasticity finite element by using a 3D unit cell including a spherical void,and the rate-depe...The influence of crystallographic orientation on the void growth in FCC crystals was numerically simulated with 3D crystal plasticity finite element by using a 3D unit cell including a spherical void,and the rate-dependent crystal plasticity theory was implemented as a user material subroutine.The results of the simulations show that crystallographic orientation has significant influence on the growth behavior of the void.Different active slip systems of the regions around the void cause the discontinuity in lattice rotation around the void,and the corner-like region is formed.In the case of the void located at grain boundary,large heterogeneous deformation occurs between the two grains,and the equivalent plastic deformation along grain boundary near the void in the case of θ=45°(θ is the angle between grain boundary direction and X-axis) is larger than the others.Large difference of orientation factor of the two grains leads to large equivalent plastic deformation along grain boundary,and the unit cell is more likely to fail by intergranular fracture.展开更多
The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extensio...The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared.展开更多
A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as void...A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution(rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.展开更多
基金supported by National Natural Science Foundation of China(No.50575143)the Research Fund for the Doctoral Program of Higher Educa-tion (No.20040248005)
文摘A three dimensional rate-dependent crystal plasticity model is applied to study the influence of crystal orientation and grain boundary on the void growth and coalescence. The 3D computational model is a unit cell including one sphere void or two sphere voids. The results of three different orientations for single crystal and bicrystals are compared. It is found that crystallographic orientation has noticeable influences on the void growth directionvoid shape, and void coalescence of single crystal. The void growth rate of bicrystals depends on the crystallographic orientations and grain boundary direction.
基金the National Natural Science Foundation of China(No.10572110).
文摘The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages: the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.
文摘In this paper a general formula for plastic potential including isotropic ductile damage has been present ed on the basis of the thermodynamics for irreversible process and internal variable the- ory.With this formula the mass conservation law is satisfied and it also contains a series of unknow coefficients which are the function of macro equivalent stress and the average micro equivalent stress and an unknown function which is the function of two generalized forces. The approximate yield surface equation for isotropically damaged materials is developed.Using this equation the void growth rate is calculated for nonlinear material containing voids.The present re- sults are in good agreement with the numerical results given by the cell model.
基金This paper is jointly supported by the National Natural Science Foundation of China (19872064)the Chinese Academy of Sciences (KJ951-1-201)the Laboratory for Nonlinear Mechanics of Continuous Media of the Institute of Mechanics
文摘Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results.
文摘The relationship between fracture toughness VGC and critical void growth RC/RO was studied for ten kinds of Steel. The macroscopic fracture toughness VGC was determined by using notched tensile specimens. and the microscopic parameters of critical void growth ratio RC/RO were quantitatively measured under SEM. Then, the coefhcient C in the relation VGC = C In(RC/RO) proposed in author's past work was specifically explored. The correlation of C with tensile proderty parameter φ=σyδ/(Eφn) was presented for the Steel investigated, and the effects of low temperature on C were also discussed. Results show that the coefficient C is linearly related to the parameter and insensitive to low temperature.
文摘The problem of void growth and interaction is of importance to understanding the mechanics of failure in metals exhibiting ductility. In this work, the growth and interaction of voids in 6061-T6 aluminum were studied experimentally. Specifically, holes of varying numbers and relative placement were investigated for their normalized area growth with applied displacement. Flat dog-bone specimens were carefully drilled in their gauge area with no (zero) holes, one hole, and two holes (arranged vertically or horizontally) for experimentation after polishing. The growth of holes, captured by video recordings, exhibited exponential behavior and was influenced greatly by the number and arrangement of holes with the horizontal voids growing the fastest and the vertical ones growing the slowest. Also, the ensuring deformation of the sample was studied using load-displacement curves, pictography and videography, SEM imaging and Atomic Force Microscopy (AFM). The methods revealed that although the major part failure is due to large crack formation, it was preceded by intense dislocation slip activity and the formation of micro cavities. Also, the AFM quantified the three-dimensional nature of crystal or grain deformation and how it is greatly influenced by distance and location from the hole. Lastly, theoretical understanding of hole growth was offered.
基金supported by the Open Foundation of State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology (Grant No. KFJJ11-0Y)the National Basic Research Program of China (Grant No. 2010CB631005)the National Natural Science Foundation of China (Grant Nos. 11172148 and 51071094)
文摘Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjected to uniaxial tension strain with one-void and two-void at the centered grain boundary were employed to analyze the effect of specimen size, temperature and applied strain rate on the stress-strain response, incipient yield strength and macroscopic effective Young's modulus. The evolutions of dislocations, twin bands and void shapes under different specimen sizes were also presented. The obtained results show that, regardless of the void numbers, the specimen sizes, temperature, the applied strain rate had significant influence on the void shape evolution, stress-strain curve and incipient yield strength, while negligible effects on the macroscopic effective Young's modulus except for the temperature. Moreover, the voids growth rate along the grain boundary was also found to be associated with the specimen sizes.
文摘In this paper, the strain energy function proposed by Shang and Cheng was generalized by introducing a nonlinear term. Void formation and growth in the interior of a sphere composed of compressible hyper-elastic material, subjected to a prescribed uniform displacement, was examined. A parametric cavitated bifurcation solution for the radial deformed function was obtained. Stability of the solution of the cavitated bifurcation equation was discussed. With the appearance of a cavity, an interesting feature of the radial deformation near the deformed cavity wall is the transition from extension to compression.
文摘The finite deformation and stress analyses for a rectangular plate with a center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper. An approximation solution was obtained from the minimum potential energy principle. The numerical results for the growth of the cavitation and stresses along the edge of the cavitation were discussed. In addition, the stress concentration phenomenon was considered.
基金Project supported by the National Natural Science Foundation of China and Chou Peiyuan's Science Foundation of Peking University.
文摘In this paper, a new model to describe the dynamic ductile fracture is proposed. The constitutive relation of the elastic-viscoplastic matrix has an overstress form given by previous authors. A dynamic loading surface at constant equivalent strain rate(with the volumetric part also taken into account) is derived and an approximate expression for this dynamic loading surface is suggested. In the case where the porous material element is subjected to spherically symmetric tension, the Carroll-Holt’s model and Johnson’s model are recovered; and in the case where the strain rate sensitivity of the material tends to zero, the Gurson’s model is recovered. Moreover, the normality condition of the plastic strain rate for the dynamic loading surface is discussed, and it is shown that the normality rule is no longer valid in general. Finally, comparisons of this model with the models recently proposed by Pan, Saje and Needleman as well as by Perzyna are also presented.
文摘In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelusticannular plate and its approximate solution is obtained from the minimum potentialenergy principle. The growth of the cavitation iS also nunterically computed andanalysed.
文摘The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.
基金Project(2005CB623706) supported by the Major State Basic Research Development Program of China
文摘The influence of crystallographic orientation on the void growth in FCC crystals was numerically simulated with 3D crystal plasticity finite element by using a 3D unit cell including a spherical void,and the rate-dependent crystal plasticity theory was implemented as a user material subroutine.The results of the simulations show that crystallographic orientation has significant influence on the growth behavior of the void.Different active slip systems of the regions around the void cause the discontinuity in lattice rotation around the void,and the corner-like region is formed.In the case of the void located at grain boundary,large heterogeneous deformation occurs between the two grains,and the equivalent plastic deformation along grain boundary near the void in the case of θ=45°(θ is the angle between grain boundary direction and X-axis) is larger than the others.Large difference of orientation factor of the two grains leads to large equivalent plastic deformation along grain boundary,and the unit cell is more likely to fail by intergranular fracture.
文摘The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared.
基金support of this work by the National Science Foundation (CMMI Award no.1932975)。
文摘A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution(rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.