An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystal...An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.展开更多
Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a comp...Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.展开更多
By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill＇s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs＇ mode...By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill＇s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs＇ model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function （ODF）, and the single BCC crystal＇s plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor＇s model in order to compare the expression with that of the macroscopic yield function.展开更多
Ingot metallurgy (IM) aluminum has long been the subject and attracted the attention of many metallurgists and textural researchers of materials. Due to the introduction of large amounts of ex situ interfaces, however...Ingot metallurgy (IM) aluminum has long been the subject and attracted the attention of many metallurgists and textural researchers of materials. Due to the introduction of large amounts of ex situ interfaces, however, the textures in powder metallurgy (PM) processed aluminum has been rarely reported. In this article, a pure aluminum plate was prepared via PM route. The starting billet was first produced with uni-axially cold compaction and flat hot-extrusion and then followed by cold rolling processes. The hot-extruded and cold rolling deformation textures of the pure PM aluminum at 50%, 80% and 90% cold rolling reductions were studied by orientation distribution functions (ODFs) analysis. The finite element polycrystal model (FEPM) was finally utilized to simulate the cold rolling textural evolution at various stages of cold rolling. In FEPM simulation, the initial hot-extruded textures were taken into account as inputs. The results showed that typical β-fiber texture formed in pure PM aluminum with the cold rolling reduction increased till 80%, and there was not much change after excessive cold rolling deformation. Homogeneous slip is not the only deformation mode in PM processed pure aluminum plate at over 80% cold rolling reduction. The experimental results were qualitatively in good agreement with the simulated ones.展开更多
Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiation-induced defects such as vacancies,interstiti...Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiation-induced defects such as vacancies,interstitials and dislocation loops,etc.In this paper,we develop an elastic-viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored.At the microscopic grain scale,we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop,which facilitates the analysis of the defect loop evolutions and dislocation-defect interactions.At the macroscopic polycrystal scale,the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties.Based on the proposed model,we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops,and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors.At the polycrystalline scale,numerical results for pure Fe match well with the irradiation experiment data.The model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan bowing.The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.展开更多
A mesoscale model of plastic deformation of ferritic stainless steels （FSSs） is formulated by combining a crystal plasticity finite element model with 3D cellular automaton algorithm. The actual grain orientations o...A mesoscale model of plastic deformation of ferritic stainless steels （FSSs） is formulated by combining a crystal plasticity finite element model with 3D cellular automaton algorithm. The actual grain orientations of FSS cold rolling and annealing sheet have been detected by electron backscatter diffraction and selected to be assigned to the polycrystal model. The simulation results have been validated by comparing the calculated true stress-strain response with the experimental one. For the lack of considering the interactions of dislocations with impurities, there are no upper and lower yield points in the simulation stress-strain curves. However, the calculated yield strength and the stress-strain response after yielding agree well with the real material. The local stress and strain fields show inhomogeneous at mesoscale. The plastic deformations of the grains with typical orientations have been characterized. The analysis reveals that the grains with fiber texture show higher thickness reduction ratio as compared to others. The deformation behaviors of the grains in polycrystal are not only related to the orientations but also to the interactions from adjacent grains.展开更多
基金The project supported by the National Natural Science Foundation of China(10562004)the Oversea Returning Grant of China.
文摘An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.
基金the National Natural Science Foundation of China(10562004,10662004)the Natural Science Foundation of Jiangxi of China(0512021)+1 种基金the Science Foundation of Jiangxi Educational Department of China([2006]3)the Foundation of Train
文摘Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.
基金Project supported by the National Natural Science Foundation of China (No. 10562004) the Natural Science Foundation of Jiangxi (Nos.0450035 and 0512021) the Science Foundation of Jiangxi Educational Department (No.[2006]3) the Oversea Returned Scholars Grant of China.
文摘By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill＇s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs＇ model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function （ODF）, and the single BCC crystal＇s plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor＇s model in order to compare the expression with that of the macroscopic yield function.
文摘Ingot metallurgy (IM) aluminum has long been the subject and attracted the attention of many metallurgists and textural researchers of materials. Due to the introduction of large amounts of ex situ interfaces, however, the textures in powder metallurgy (PM) processed aluminum has been rarely reported. In this article, a pure aluminum plate was prepared via PM route. The starting billet was first produced with uni-axially cold compaction and flat hot-extrusion and then followed by cold rolling processes. The hot-extruded and cold rolling deformation textures of the pure PM aluminum at 50%, 80% and 90% cold rolling reductions were studied by orientation distribution functions (ODFs) analysis. The finite element polycrystal model (FEPM) was finally utilized to simulate the cold rolling textural evolution at various stages of cold rolling. In FEPM simulation, the initial hot-extruded textures were taken into account as inputs. The results showed that typical β-fiber texture formed in pure PM aluminum with the cold rolling reduction increased till 80%, and there was not much change after excessive cold rolling deformation. Homogeneous slip is not the only deformation mode in PM processed pure aluminum plate at over 80% cold rolling reduction. The experimental results were qualitatively in good agreement with the simulated ones.
基金support provided by the Major State Basic Research Development Program of China(Grant 2011CB013101)the National Natural Science Foundation of China(NSFC)(Grants 11225208 and 91226202)+2 种基金support from the key subject "Computational Solid Mechanics" of the China Academy of Engineering Physicsthe support provided by the Shanghai Eastern-Scholar Planby the State Key Laboratory for Mechanical Behavior of Materials
文摘Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiation-induced defects such as vacancies,interstitials and dislocation loops,etc.In this paper,we develop an elastic-viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored.At the microscopic grain scale,we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop,which facilitates the analysis of the defect loop evolutions and dislocation-defect interactions.At the macroscopic polycrystal scale,the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties.Based on the proposed model,we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops,and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors.At the polycrystalline scale,numerical results for pure Fe match well with the irradiation experiment data.The model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan bowing.The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.
基金supported by the National Natural Science Foundation of China(No.51604058)the Fundamental Research Funds for the Central Universities of China+1 种基金the Scientific Research Fund of Liaoning Provincial Education Department under Grant No.L2015120the Open Research Fund from the State Key Laboratory of Rolling and Automation,Northeastern University,China
文摘A mesoscale model of plastic deformation of ferritic stainless steels （FSSs） is formulated by combining a crystal plasticity finite element model with 3D cellular automaton algorithm. The actual grain orientations of FSS cold rolling and annealing sheet have been detected by electron backscatter diffraction and selected to be assigned to the polycrystal model. The simulation results have been validated by comparing the calculated true stress-strain response with the experimental one. For the lack of considering the interactions of dislocations with impurities, there are no upper and lower yield points in the simulation stress-strain curves. However, the calculated yield strength and the stress-strain response after yielding agree well with the real material. The local stress and strain fields show inhomogeneous at mesoscale. The plastic deformations of the grains with typical orientations have been characterized. The analysis reveals that the grains with fiber texture show higher thickness reduction ratio as compared to others. The deformation behaviors of the grains in polycrystal are not only related to the orientations but also to the interactions from adjacent grains.
