Microstructure and mechanical properties of copper subjected to high pressure torsion

Experiments were conducted on copper subjected to High Pressure Torsion to investigate the evolution of microstructure and microhardness with shear strain, gamma. Observations have been carried out in the longitudinal section for a proper demonstration of the structure morphology. An elongated dislocation cell/subgrain structure was observed at relatively low strain level. With increasing strain, the elongated subgrains transformed into elongated grains and finally into equiaxed grains with high angle grain boundaries. Measurements showed the hardness increases with increasing gamma then tends to saturations when gamma >5. The variation tendency of microhardness with gamma can be simulated by Voce-type equation.

Torsion fracture behavior of drawn pearlitic steel wires with different heat treatments

In this paper, torsion fracture behavior of drawn pearlitic steel wires with different heat treatments was investigated. Samples with different heat treatments was investigated. Samples with different heat treatment conditions were subjected to torsion and tensile tests. The shear strain along the torsion sample after fracture was measured. Fracture surface of wires was examined by Scanning Electron Microscopy. In addition, the method of Differential Scanning Calorimetry was used to characterize the thermodynamic process in the heat treatment. A numerical simulation via finite element method on temperature field evolution for the wire during heat treatment process was performed. The results show that both strain aging and recovery process occur in the material within the temperature range between room temperature and 435 degrees C. It was shown that the ductility measured by the number of twists drops at short heating times and recovers after further heating in the lead bath of 435 degrees C. On the other hand, the strenght of the wire increases at short heating times and decreases after further heating. The microstructure inhomogeneity due to short period of heat treatment, coupled with the gradient characteristics of shear deformation during torsion results in localized shear deformation of the wire. In this situation, shear cracks nucleate between lamella and the wire breaks with low number of twists.

Influence of processing temperature on microstructure and microhardness of copper subjected to high-pressure torsion

Cu samples were subjected to high-pressure torsion (HPT) with up to 6 turns at room temperature (RT) and liquid nitrogen temperature (LNT), respectively. The effects of temperature on grain refinement and microhardness variation were investigated. For the samples after HPT processing at RT, the grain size reduced from 43 mu m to 265 nm, and the Vickers microhardness increased from HV52 to HV140. However, for the samples after HPT processing at LNT, the value of microhardness reached its maximum of HV150 near the center of the sample and it decreased to HV80 at the periphery region. Microstructure observations revealed that HPT straining at LNT induced lamellar structures with thickness less than 100 nm appearing near the central region of the sample, but further deformation induced an inhomogeneous distribution of grain sizes, with submicrometer-sized grains embedded inside micrometer-sized grains. The submicrometer-sized grains with high dislocation density indicated their nonequilibrium nature. On the contrary, the micrometer-sized grains were nearly free of dislocation, without obvious deformation trace remaining in them. These images demonstrated that the appearance of micrometer-sized grains is the result of abnormal grain growth of the deformed fine grains.

Applications of generalized torsion angles in studies on quantitative structure-activity relationship

In this article, generalized torsion angles of derivatives of 1-[(2-hydroxyethoxy)methy1]-6(phenylthio)thymine(HEPT) were calculated, which include abundant three dimensional information of molecules. Molecular similarity matrix was built based on the calculated generalized torsion angles. These similarities were taken as the new variables, and the new variables were selected by using Leaps-and-Bounds regression analysis. Multiple regression analysis and neural networks were performed, and the satisfactory results were achieved by using the neural networks.

Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

A new hardening law for strain gradient plasticity

A new hardening law of the strain gradient theory is proposed in this paper, which retains the essential structure of the incremental version of conventional J(2) deformation theory and obeys thermodynamic restrictions. The key feature of the new proposal is that the term of strain gradient plasticity is represented as an internal variable to increase the tangent modulus. This feature which is in contrast to several proposed theories, allows the problem of incremental equilibrium equations to be stated without higher-order stress, higher-order strain rates or extra boundary conditions. The general idea is presented and compared with the theory given by Fleck and Hutchinson (Adv. in Appl. Mech. (1997) 295). The new hardening law is demonstrated by two experimental tests i.e. thin wire torsion and ultra-thin beam bending tests. The present theoretical results agree well with the experiment results.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

An anisotropic elastic-plastic constitutive model for single and polycrystalline metals. II—Experiments and predictions concerning thin-walled tubular OFHC copper

Predictions based on an anisotropic elastic-plastic constitutive model proposed in the first part of this paper are compared with the experimental stress and strain data on OHFC copper under first torsion to about 13% and partial unloading, and then tension-torsion to about 10% along eight different loading paths. This paper also describes the deformation and stress of the thin-walled tubular specimen under finite deformation, the numerical implementation of the model, and the detailed procedure for determining the material parameters in the model. Finally, the model is extended to a general representation of the multiple directors, and the elastic-viscoplastic extension of the constitutive model is considered.

Formation of adiabatic shear band in metal matrix composites

A modified single-pulse loading split Hopkinson torsion bar (SSHTB) is introduced to investigate adiabatic shear banding behavior in SiCp particle reinforced 2024 Al composites in this work. The experimental results showed that formation of adiabatic shear band in the composite with smaller particles is more readily observed than that in the composite with larger particles. To characterize this size-dependent deformation localization behavior of particle reinforced metal matrix composites (MMCp), a strain gradient dependent shear instability analysis was performed. The result demonstrated that high strain gradient provides a deriving force for the formation of adiabatic shear banding in MMCp. (C) 2004 Elsevier Ltd. All rights reserved.

Microstructural evolution and formation of nanocrystalline intermetallic compound during surface mechanical attrition treatment of cobalt

Nanocrystalline intermetallic Co3Fe7 was produced on the surface of cobalt via surface mechanical attrition (SMA). Deformationinduced diffusion entailed the formation of a series of solid solutions. Phase transitions occurred depending on the atomic fraction of Fe in the surface solid solutions: from hexagonal close-packed (<4% Fe) to face-centered cubic (fcc) (4-11% Fe), and from fcc to body-centered cubic (>11% Fe). Nanoscale compositional probing suggested significantly higher Fe contents at grain boundaries and triple junctions than grain interiors. Short-circuit diffusion along grain boundaries and triple junctions dominate in the nanocrystalline intermetallic compound. Stacking faults contribute significantly to diffusion. Diffusion enhancement due to high-rate deformation in SMA was analyzed by regarding dislocations as solute-pumping channels, and the creation of excess vacancies. Non-equilibrium, atomic level alloying can then be ascribed to deformation-induced intermixing of constituent species. The formation mechanism of nanocrystalline intermetallic grains on the SMA surface can be thought of as a consequence of numerous nucleation events and limited growth. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Study of three elastic-plastic constitutive models by non-proportional finite deformations of OFHC copper

Experimental stress-strain data of OFHC copper first under torsion to 13% and then under torsion-tension to about 10% are used to study the characteristics of three elastic-plastic constitutive models: Chaboche's super-positional nonlinear model, Dafalias and Popov's two surface model and Watanabe and Atluri's version of the endochronic model. The three models, originally oriented for infinitesimal deformation, have been extended for finite deformation. The results show (a) the Mises-type yield surface used in the three models brings about significant departure of the predictions from the experimental data; (b) Chaboche's and Dafalias' models are easier than Watanabe and Atluri's model in determining the material parameters in them, and (c) Chaboche's and Watanabe & Atluri's models produce almost the same prediction to the data, while Dafalias' model cannot accurately predict the plastic deformations when a loading path changes in its direction. Copyright (C) 1996 Elsevier Science Ltd

高压扭转铜试样的微观组织与压缩性能

通过高压扭转对铜试样施加不同程度的变形，研究了样品扭转面（ND面）和纵截面（TD面）上微观组织特征．对ND面，在较小的剪应变下，原始晶粒形貌模糊，晶粒内部形成等轴状的位错胞及亚晶结构；随变形量的增大，亚晶间取向差及亚晶内部的位错密度增大，最后形成亚微米尺度的等轴晶粒．对TD面，变形初期原始晶粒被拉长，晶粒内部为位错墙分割成的层状结构，层内为拉长的位错胞；随变形程度的增大，拉长晶粒的宽度减小，与剪切方向的夹角减小，晶内层状组织间距减小，并逐渐演化成拉长的亚晶组织；进一步增大变形，晶粒拉长痕迹消失，变形组织与ND面相似，为等轴状亚微米晶粒．压缩实验表明，经16圈扭转后，整个试样上的压缩性能基本均匀，σ0．2达到385MPa，应变率敏感性指数增大至0．021．

高压扭转致纯铜晶粒细化及与应变的关系

设计并加工了在材料试验机上使用的高压扭转夹持装置，并用装置获得了不同扭转变形量的纯铜试样．使用电子背散射衍射技术测量了处理后试样品粒尺寸沿径向的分布．对比分析了晶粒细化程度和应变量的关系，提出了一个描述晶粒细化的简单剪切球模型．结果表明，晶粒细化程度随着应变量的增大而增强，平均晶粒尺寸为原始平均尺寸的1／50．当剪切应变小于10对，晶粒尺寸随着剪切应变的增大迅速变小；当剪切应变大于10对，晶粒尺寸的变化趋于缓慢，晶粒细化程度与Stuwe等效应变之间有幂函数关系．依据简单剪切球形晶粒的模型，得到了晶粒细化程度随剪切应变增大而增强的规律，并与实验数据的变化趋势一致。

限定型高压扭转过程变形研究

文章制备了一套限定型高压扭转（HPT）设备。采用HPT处理纯铜试样，对比处理前后试样几何尺寸，观察试样与砧头之间的相对滑动，结果表明，HPT处理前后试样厚度变化小于5％，试样端面和模具不发生相对滑动。用量纲分析和有限元方法分析试样的变形，得到切应变和厚度／直径、压力／材料弹性模量以及模具侧面的摩擦状况相关；直径8mm厚0．86mm纯铜试样上r〈3．2mm区域的变形可以用纯扭转来描述。