铝单晶体潜在硬化的指向性行为研究

应用高纯铝单晶体，采用偏离弹性线法定义其在潜在滑移系统在屈服应力，研究了潜在滑移系在正负两个滑移方向上的屈服及应变硬化行为。结果表明，潜在滑移系负行为的差异要远远小于动滑移系的Ｂａｕｓｃｈｉｎｇｅｒ效应，其正负方向的屈服应力一般均等于或略小于预应变时的最大分切应力，大大高于动滑移系的负向屈服应力，潜在滑移系和原始滑移系的相对取向及预应变的大小对单晶体潜在移系在潜在硬化的影响不大，但对其起始过渡区应     

单晶体塑性滑移有限变形下的应力计算

为了探讨和发展单晶金属材料的非弹性有限变形分析方法,提出一种单晶体各向异性弹塑性分析的计算格式.该方法是一种以初始构形为变形计算参考构形的描述方法,它对单晶体塑性构形的演化用增量计算以跟随加载路径,而在应力计算时在卸载构形的基础上用Hencky对数弹性应变来计算总量的应力以保证计算的稳定和收敛;通过求解满足瞬时屈服条件和应力与弹性应变关系的广义胡克定律的非线性方程组来搜索激活滑移系.     

Anisotropic hardening in single crystals and the plasticity of polycrystals

Based on the dislocation structures developed during plastic deformation, an anisotropic hardening law is developed to describe the latent hardening behavior of slip systems under multislip. This theory incorporates the concept of isotropic hardening, kinematic hardening, and the two-parameter representation; it automatically includes the strength differential between the forward and reversed slips and between the acute and obtuse cross slips. The self-hardening modulus of a slip system is found to be “associated” with the latent hardening law involved, and, based on some experimental evidence, two specific sets of self-hardening modulus are suggested. An important feature of this associated modulus is that the slip system with a soft latent hardening (e.g., the reversed system with a Bauschinge effect) will have an enhanced self-hardening modulus. This newly developed hardening law, together with its associated latent hardening moduli, is then applied to examine the strain-hardening behavior of a polycrystal. Although crystals with a stronger latent hardening will, in general, also lead to a stranger strain-hardening for the polycrystal, the stress-strain behavior of the polycrystal using the kinematic hardening law of single crystals is found to be not necessarily softer than that using the isotropic hardening law. Within the range of experimentally measured latent hardening ratio of slip systems, the anisotropic theory is also used to calculate the motion of yield surface of a polycrystal. The general results, employing four selected types of anisotropic hardening, all show the essential features of experimental observations by Phillips and his co-workers. The application is highlighted with a reasonably successful quantitative modeling of initial and subsequent yield surfaces of an aluminum.     

A crystal plasticity model for strain-path changes in metals

A model is proposed that deals with the transient mechanical anisotropy during strain-path changes in metals. The basic mechanism is assumed to be latent hardening or softening of the slip systems, dependent on if they are active or passive during deformation, reflecting microstructural mechanisms that depend on the deformation mode rather than on the crystallography. The new model captures the experimentally observed behaviour of cross hardening in agreement with experiments for an AA3103 aluminium alloy. Generic results for strain reversals qualitatively agree with two types of behaviour reported in the literature – with or without a plateau on the stress–strain curve. The influence of the model parameters is studied through detailed calculations of the response of three selected parameter combinations, including the evolution of yield surface sections subsequent to 10% pre-strain. The mathematical complexity is kept to a minimum by avoiding explicit predictions related directly to underpinning microstructural changes. The starting point of the model is a combination of conventional texture and work hardening approaches, where an adapted full-constraints Taylor theory and a simple single-crystal work-hardening model for monotonic strain are used. However, the framework of the model is not restricted to these particular models.     

Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure

The anisotropic plastic deformation behavior of extruded 5000 series aluminum alloy tubes, A5154-H112, of 76 mm outer diameter and 3.9 mm wall thickness is investigated, using a servo-controlled tension-internal pressure testing machine. This machine is capable of applying arbitrary stress or strain paths to a tubular specimen using an electrical, closed-loop control system. Detailed measurements were made of the initial yield locus, contours of plastic work for different levels of work-hardening, and the directions of the incremental plastic strain vectors for both linear and combined stress paths. It is found that the measured work contours constructed in the principal stress space are similar in shape, and that the directions of the incremental plastic strain vectors remain almost constant at constant stress ratios. The work-hardening behavior predicted using Hosford's or the Yld2000-2d yield functions under the assumption of isotropic hardening agrees closely with the observations for both linear and combined stress paths. The material is thus found to work-harden almost isotropically. Both yield functions are effective phenomenological plasticity models for predicting the anisotropic plastic deformation behavior of the material.     

A modified model for simulating latent hardening during the plastic deformation of rate-dependent FCC polycrystals

A strain hardening model for the plastic deformation of rate-dependent FCC crystals is proposed based on experimental observations previously reported for single crystals. This model, which is an extension of that employed by et al. [1983], includes both the self-hardening and latent hardening of the slip systems. The differential hardening of the latent systems is assumed to arise from the interaction between glide dislocations and forests. With this hardening model and a rate-sensitive crystal plasticity theory, the deformation behavior of FCC polycrystals can be predicted from the deformation response of the constituent single crystals. As examples, the uniaxial tensile behaviour of pure aluminum and copper polycrystals is simulated using the extended model, and the results are compared with published experimental data. The effects of latent hardening on polycrystal deformation, especially on flow stress and the formation of tensile textures, are discussed.     

Constitutive modelling of anisotropic creep deformation in single crystal blade alloys SRR99 and CMSX-4

A damage mechanics based model has been developed to model stress rupture and creep behaviour of the first and second generation single crystal superalloys SRR99 and CMSX-4. In this article the creep behaviour of CMSX-4 in several different orientations at 950°C is simulated using finite elements, these simulations are compared with the results of creep tests. In order that the effects of rotation and specimen bending can be accounted for in the analysis the entire creep specimen is modelled. The FE program ABAQUS has been used and the slip system model is written using a User MATerial subroutine (UMAT). EBSD (electron back scattered diffraction) measurements of the lattice rotations occurring during creep indicate that the active slip systems at 950°C are the <101>{111} and <112>{111} systems, our simulations show that the creep results can be explained by activating these two families of slip system. There is strong microstructural evidence that the significant components of the hardening matrix should be those causing self and latent hardening of the <101>{111} systems and latent hardening by the <101>{111} systems on the <112>{111} systems.     

A semi-implicit integration scheme for rate independent finite crystal plasticity

An efficient new numerical integration scheme is presented for rate independent crystal plasticity theory. A key feature of this approach is the ability to identify active slip systems prior to determining their shearing rate. Options are described for various cases of slip system hardening, including self hardening and latent hardening. Alternatives for the constitutive update are explored, including hyperelasticity based on the multiplicative decomposition of the deformation gradient as well as application of the consistency condition in a much more efficient hypoelastic formulation. Several conclusions are drawn concerning the influences of elastic and plastic properties on the activation of slip systems and their subsequent shearing rates. Key among these is the fact that, once activated, shearing rates are independent of the levels of shear flow resistance on the slip systems, provided that the plastic hardening moduli are much less in magnitude than the elastic moduli, as is usually the case. Determination of active slip systems and their shearing rates depend on the degree of elastic anisotropy of the crystal, but not on the magnitude of elastic stiffness.     

Comparisons of crystal hardening laws in multiple slip

This paper brings together and concisely reviews results from recent analytical investigations on single crystals (variously done alone or with students) in which predictions from different theoretical hardening laws are contrasted and compared with experimental studies. Finitely deforming f.c.c. crystals in both constrained and unconstrained multiple-slip configurations are considered. Four crystal hardening laws are given prominence. Two of these belong to a class of theories in which the physical hardening moduli relating rates-of-change of critical strengths (in the 24 crystallographically equivalent slip systems) to slip-rates are taken as symmetric. These are G.I. Taylor's classic isotropic hardening rule (proposed in 1923), which is almost universally adopted in the metallurgical literature for various approximate analyses of single and poly-crystal deformation, and a 2-parameter modification of Taylor's rule that has an empirical basis in the qualitative features of experimentally determined latent hardening in single slip. The other two hardening laws featured here belong to a class of theories that were introduced in 1977 by this author. This class requires the above moduli to be nonsymmetric and explicity dependent upon the current stress state in such a manner that the following consequences are assured. (1) The deformation-dependent hardening of latent slip systems necessarily develops anisotropically if there is relative rotation of gross material and underlying crystal lattice. (2) The theories admit self-adjoint boundary value problems for crystalline aggregates, hence a variational formulation. (The fact that symmetric physical hardening moduli do not permit variational formulations of polycrystalline problems was shown at the 1972 Warsaw Symposium.) The two members of this class considered here are the original (and simplest p possible) theory of rotation-dependent anisotropy, which was proposed by this author in 1977 and commonly has been referred to as the “simple theory,” and a modification of this theory introduced in 1982 by Peirce, Asaro and Needleman that lies between Taylor's rule and the simple theory in its predictions for finitely deforming f.c.c. crystals. (In a series of five papers during 1977–1979, the simple theory was shown to universally account for the experimental phenomenon of “overshooting” in single slip in both f.c.c. and b.c.c. crystals.) Theoretical results from the various hardening rules are contrasted and compared with finite strain experiments in the metallurgical literature. Both tensile-loaded crystals in 4, 6 and 8-fold symmetry orientations and compressively loaded crystals under conditions of channel die constraint are treated. A postulate of minimum plastic work introduced in 1981 plays a prominent role in the theoretical analyses, in many cases providing a unique solution to the slip system inequalities and deformation constraints (where applicable). The rather remarkable ability of the simple theory to reconcile diverse qualitative features of both constrained and unconstrained finited deformation of f.c.c. crystals is demonstrated. Finally, conditions for total loading (all systems active) in 6-fold symmetry are investigated, and certain concepts regarding the selection of active systems under prescribed straining are critically assessed.     

Shakedown theory for elastic plastic kinematic hardening bodies

Shakedown static and kinematic theorems for elastic–plastic (generally nonlinear) kinematic hardening solids are derived in classical (path-independence) spirit with new constructions. The generally plastic-deformation-history-dependent hardening curve is assumed to be limited by the initial yield stress and ultimate yield strength, and to obey a positive hysteresis postulate for closed plastic cycles, but else can be arbitrary and unspecified. The theorems reveal that the shakedown of structures is not affected by the particular form of the hardening curve, but just by the initial and ultimate yield stresses. While the ultimate yield strength is clearly defined macroscopically and attached to the incremental collapse mode with unbounded plastic deformations, the initial yield stress, which is responsible for the bounded cyclic plasticity collapse mode, should not be taken as the convenient one at a fixed amount of plastic deformation (0.2%), but is suggested to be taken as low as the fatigue limit to preserve the classical load-history-independence spirit of the shakedown theorems. Otherwise, for our pragmatic application purpose, it may be given empirical values between the low fatigue limit and high ultimate yield stresses according to particular loading processes considered, which may range anywhere between the high-cycle and low-cycle ones. The theorems appear as simple as those of Melan and Koiter for perfect plasticity but applied to the much larger class of more realistic kinematic hardening materials.     

Theoretical latent hardening in crystals—II. BCC crystals in tension and compression

The general latent hardening law of single slip derived in the first paper of this series (Havner, Baker and Vause, 1979) is applied to an analysis of “overshooting” phenomena in bcc crystals in tension and compression. This new law, which predicts anisotropic hardening of latent slip systems, is based upon the simple theory of finite distortional crystal hardening introduced by Havner and Shalaby (1977).Because of historical ambiguities regarding identification of the slip plane in bcc metals, parallel analyses are presented corresponding to two separate criteria: (i) slip on {110}, {112} and {123} crystallographic planes only; and (ii) slip on the plane of maximum resolved shear stress containing a 〈111〉 direction. It is established that the new hardening law is a theory of “overshooting” in bcc crystals according to either identification of the slip plane.A qualitative comparison between theoretical results and two experimental papers on Fe crystals is included. The general difficulties in making comparisons with the experimental literature on finite distortional latent hardening are briefly discussed.     

Rate-independent crystalline and polycrystalline plasticity,application to FCC materials

This paper deals with the simulation of the mechanical response and texture evolution of cubic crystals and polycrystals for a rate-independent elastic–plastic constitutive law. No viscous effects are considered. An algorithm is introduced to treat the difficult case of multi-surface plasticity. This algorithm allows the computation of the mechanical response of a single crystal. The corresponding yield surface is made of the intersection of several hyper-planes in the stress space. The problem of the multiplicity of the slip systems is solved thanks to a pseudo-inversion method. Self and latent hardening are taken into account. In order to compute the response of a polycrystal, a Taylor homogenization scheme is used. The stress–strain response of single crystals and polycrystals is computed for various loading cases. The texture evolution predicted for compression, plane strain compression and simple shear are compared with the results given by a visco-plastic polycrystalline model.     

Void growth and coalescence in single crystals

Void growth and coalescence in single crystals are investigated using crystal plasticity based 3D finite element calculations. A unit cell involving a single spherical void and fully periodic boundary conditions is deformed under constant macroscopic stress triaxiality. Simulations are performed for different values of the stress triaxiality, for different crystal orientations, and for low and high work-hardening capacity. Under low stress triaxiality, the void shape evolution, void growth, and strain at the onset of coalescence are strongly dependent on the crystal orientation, while under high stress triaxiality, only the void growth rate is affected by the crystal orientation. These effects lead to significant variations in the ductility defined as the strain at the onset of coalescence. An attempt is made to predict the onset of coalescence using two different versions of the Thomason void coalescence criterion, initially developed in the framework of isotropic perfect plasticity. The first version is based on a mean effective yield stress of the matrix and involves a fitting parameter to properly take into account material strain hardening. The second version of the Thomason criterion is based on a local value of the effective yield stress in the ligament between the voids, with no fitting parameter. The first version is accurate to within 20% relative error for most cases, and often more accurate. The second version provides the same level of accuracy except for one crystal orientation. Such a predictive coalescence criterion constitutes an important ingredient towards the development of a full constitutive model for porous single crystals.     

Hardening evolution of AZ31B Mg sheet

The monotonic and cyclic mechanical behavior of O-temper AZ31B Mg sheet was measured in large-strain tension/compression and simple shear. Metallography, acoustic emission (AE), and texture measurements revealed twinning during in-plane compression and untwinning upon subsequent tension, producing asymmetric yield and hardening evolution. A working model of deformation mechanisms consistent with the results and with the literature was constructed on the basis of predominantly basal slip for initial tension, twinning for initial compression, and untwinning for tension following compression. The activation stress for twinning is larger than that for untwinning, presumably because of the need for nucleation. Increased accumulated hardening increases the twin nucleation stress, but has little effect on the untwinning stress. Multiple-cycle deformation tends to saturate, with larger strain cycles saturating more slowly. A novel analysis based on saturated cycling was used to estimate the relative magnitude of hardening effects related to twinning. For a 4% strain range, the obstacle strength of twins to slip is 3 MPa, approximately 1/3 the magnitude of textural hardening caused by twin formation (10 MPa). The difference in activation stress of twinning versus untwinning (11 MPa) is of the same magnitude as textural hardening.     

Finite deformation solution of a dynamic problem of combined compressive and shear loading for an elastic-plastic half-space

A self-similar problem involving combined compressive and shear loading of a non work-hardening elastic-plastic half-space is solved, for large deformations, within the framework proposed earlier by J.R. Willis (1969). The thermodynamic system, which was left open in the general framework, is taken to be that proposed recently by G.W. Swan and C.K. Thornhill (1974). Results are presented for oblique loading of a block of low carbon steel. For an imposed normal velocity of the order of 1,100 m s^?1, a smooth shear wave behind the shock that is formed is possible only for small transverse velocities, perhaps no greater than 14 m s^?1, depending upon the value assumed for the yield stress. Larger transverse velocities would give rise to a thin layer of intense shear near the surface of the block, whose study would require allowance for both work-hardening and temperature-dependent yield stress.     

K0超固结结构性黏土的本构模型

K₀固结黏土在自然界广泛分布, 其通常同时具有超固结性与天然结构性, 而K₀超固结性又与K₀正常固结性质存在很大差异. 为了有效的描述K₀超固结性质, 在结构性模型基础上, 做了如下三点改进, 使得原模型拓展为同时考虑K₀超固结特性与天然结构性影响的本构模型. (1)引入相对应力比来描述屈服面, 并引入初始各向异性转轴参量ξ来表达初始各向异性对屈服面在p-q空间的位置影响. (2)基于给定的屈服面方程, 推导得到变相应力比参量, 并将变相应力比引入到统一硬化参数中, 利用统一硬化参数可以有效描述初始各向异性固结黏土在剪切加载下的剪缩与剪胀, 应变硬化及软化现象. (3)引入反映结构性胶结强度性质的胶结参量p_e, 并给出p_e随塑性偏应变的衰减演化方程, 利用胶结参量可描述结构性黏土的剪胀特性. 预测与试验结果对比表明, 所提的K₀超固结结构性模型可有效描述K₀超固结黏土的刚度提高效应, 黏土的包辛格效应, 结构性黏土胶结强度的损失现象以及结构性黏土的应变软化现象. 证明了所提模型的适用性以及合理性.      

Theoretical analysis of the channel die compression test—I. General considerations and finite deformation of F.C.C. crystals in stable lattice orientations

An extensive theoretical investigation of f.c.c. crystals under [110] loading in the channel die compression test is presented. Two lattice orientations known from experiment to be stable relative to the channel axes, through large deformations, are investigated for each of four hardening laws. These are Taylor's classical isotropic hardening rule, a 2-parameter empirical rule from the metallurgical literature, the “simple theory” of anisotropic latent hardening(Havner and Shalaby, Proc. R. Soc. A 358,47 (1977)), and a modification of the simple theory proposed by pfirce et al., Acta Met.30, 1087 (1982). Predictions of active systems, equal multiple-slip and consequent lattice stability, finite shape change, and lateral constraint stress are the same for all theories, corresponding to minimum rate of plastic work, and are in general agreement with experiments on copper crystals by Wonsiewicz and Chin, Met. Trans.1, 2715 (1970) and Wonsiewiczet al., Met. Trans.2, 2093 (1971). The predictions of latent hardening differ among the theories, however, depending upon whether there is relative rotation of material and lattice. The potential significance of experimental studies of latent hardening in these particular stable lattice orientations is emphasized.     

Comparison of the work-hardening of metallic sheets using tensile and shear strain paths

This work deals with the characterization of the kinematic work-hardening of a bake-hardening steel. A shear test device has been designed and its use for the characterization of the work-hardening of sheet metals is described. Two main results are presented. Firstly, a local strain measurement, based on the following of three dots drawn on the gauge area, gives the evolution of the strain tensor eigenvalues during the test. It is shown, by comparing the theoretical kinematics of simple shear with a slightly perturbated one, that the strain state is close to the ideal one in the center of the gauge area. Secondly, reversal of the shear direction is performed after several prestrain and the evolution of the kinematic work-hardening with the equivalent plastic strain has been identified using an anisotropic elasto-viscoplastic model of Hill 1948 type. Isotropic and kinematic contributions of the work-hardening are also calculated from loading–unloading tensile tests and are compared to those obtained from the simple shear tests. The results show a discrepancy between both identification for the isotropic and the kinematic hardening. However, they are in agreement concerning the evolution of the global work-hardening.