晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

Micro-crack tip fracture of commercial grade aluminum under mixed mode loading

In situ tensile tests were made in a scanning electron microscope (SEM) to investigate the deformation and micro-fracture in the immediate vicinity of a micro-crack tip in commercial pure aluminum with large-size crystal. Examined are the slip line field, stress intensity factor, strain energy density factor and crack tip opening displacement (CTOD) for mixed mode loading. Blunting and sharpening effects are observed. The latter is controlled by localized slip while the former by uniformed slip of the operating slip system with the highest crack tip Schmid factor. The operating slip system depends on the crystallographic orientation of crystal containing micro-cracks.The damage and fracture take place in the blunted region and depend on the coarsening and spacing of uniformed slip lines. The mixed mode micro-crack propagates along the direction where the voids grow and coalesce into the micro-crack. The direction also depends on the orientation of the applied loading. This suggests that the formation of macro-fracture mechanics could be applied. In particular, the minimum strain energy density criterion is suitable for determining the direction of micro-crack instability in the mixed mode. The in situ data were used to yield a nearly constant critical, minimum strain energy density factor for onset of micro-cracking.     

Reevaluation of the adhesive relationship between the tire and the soil

The author proved in an earlier article that the shear diagram is not in accord with its mechanical definition. The shear stress cannot be zero at the beginning of the initial rising portion of the curve. Shearing is not an increasing loading process, rather it is a limiting case to which a finite shear stress belongs. On the other hand the sheared surface varies under the tire. There are kinematic reasons for this. Points on the tire surface describe a looped cycloid and they slip in a backward direction (opposite to the direction of travel) while contacting the soil. Thus the driving force, which points in the direction of travel, is the product of the shear stress of finite magnitude and the sheared area. The latter increases proportionally with slip. The author describes his equation which is based on the principles discussed above. He supports his theory with a numerical example.     

Study of size effects in thin films by means of a crystal plasticity theory based on DiFT

In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide given by Yefimov et al. [2004b. A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity simulations. J. Mech. Phys. Solids 52, 279-300]. In this dislocation field theory (DiFT) the transport equations for both the total dislocation density and geometrically necessary dislocation (GND) density on each slip system were obtained from the Peach-Koehler interactions through both single and pair dislocation correlations. The effect of pair correlation interactions manifested itself in the form of a back stress in addition to the external shear and the self-consistent internal stress. We here present the study of size effects in single crystalline thin films with symmetric double slip using the novel continuum theory. Two boundary value problems are analyzed: (1) stress relaxation in thin films on substrates subject to thermal loading, and (2) simple shear in constrained films. In these problems, earlier discrete dislocation simulations had shown that size effects are born out of layers of dislocations developing near constrained interfaces. These boundary layers depend on slip orientations and applied loading but are insensitive to the film thickness. We investigate the stress response to changes in controlled parameters in both problems. Comparisons with previous discrete dislocation simulations are discussed.     

Constitutive potential for ductile damaged material and void growth rate

In this paper a general formula for plastic potential including isotropic ductile damage has been presented on the basis of the thermodynamics for irreversible process and intemal variable theory. 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 results are in good agreement with the numerical results given by the cell model.     

Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal

This is a study of plastic strain localization, surface roughening and of the origin of these phenomena in polycrystals. An oligocrystal aluminum sample with a single quasi-2D layer of coarse grains is plastically deformed under uniaxial tensile loading. During deformation, the history of strain localization, surface roughening, microstructure and in-grain fragmentation is carefully recorded. Using a crystal plasticity finite element model, corresponding high-resolution simulations are conducted. A series of comparisons identifying aspects of good and of less good match between model predictions and experiments is presented. The study suggests that the grain topology and microtexture have a significant influence on the origin of strain heterogeneity. Moreover, it suggests that the final surface roughening profiles are related both to the macro strain localization and to the intra-grain interaction. Finally slip lines observed on the surface of the samples are used to probe the activation of slip systems in detail. The study concludes with an assessment of the limitations of the crystal plasticity model.     

A Dynamic-induced Direct-shear Model for Dynamic Triggering of Frictional Slip on Simulated Granular Gouges

This study presents a dynamic-induced direct-shear model to investigate the dynamic triggering of frictional slip on simulated granular gouges. An incident P-wave is generated as a shear load and a normal stress is constantly applied on the gouge layer. The shear stress accumulates in the incident stage and the frictional slip occurs in the slip stage without the effect of the reflected wave. The experimental results show a non-uniform shear stress distribution along the gouge layer, which may be induced by a shear load induced torque and by normal stress vibration along the layer. The shear stress at the trailing edge strongly affects the frictional slip along the P-wave loading direction, while the rebound stress at the leading edge propagates along the opposite direction. The frictional slip is triggered when the maximum shear stress at the trailing edge reaches a critical value. The normal stress influences the maximum shear stress at the trailing edge, the maximum slip displacement and the slip velocity. The advantages and the limitations of this model are discussed at the end.     

An experimental investigation on cyclic plastic deformation and substructures of polycrystalline copper

Cyclic deformation under proportional and nonproportional loading of a textured copper was experimentally studied, and the results were compared with those of texture-free copper with the same grain size. The texture had a great influence on the equivalent cyclic stress–strain (CSS) curves under proportional loading but insignificant influence on the CSS curves under nonproportional loading. By comparing the slip patterns on the specimen surface and dislocation substructures under proportional and nonproportional loading, the mechanism of nonproportional hardening was discussed. The slip multiplicity inherited from originally multiple-slip oriented grains plays a minor role. Nonproportional hardening is the result of enhanced activated slip systems and more uniform activation of slip systems due to the rotation of maximum shear stress under nonproportional loading. At high strain amplitudes, cells were the primary substructures for both proportional and nonproportional loading but the diameters of the cells under nonproportional loading were smaller for similar strain magnitude. A linear relationship existed between the saturation equivalent stress magnitude and the reciprocal of the diameter of the dislocation cells. Such a relationship was independent of the loading modes and texture. The saturation stress magnitude was related to the bowing stress of screw dislocations in the interior area of dislocation cells. The mechanical response was practically recoverable either when the loading magnitude was changed from a higher value to a lower value or when the loading was changed from a nonproportional loading path to a proportional loading path. However, the dislocation substructures cannot be completely recovered.     

Wrinkling of sandwich wide panels/beams based on the extended high-order sandwich panel theory: formulation, comparison with elasticity and experiments

There exist several high-order sandwich panel theories, most notably, the first to be introduced high-order sandwich panel theory (HSAPT) assumes a constant shear stress in the core. Recently, the extended high-order sandwich panel theory (EHSAPT) was introduced, its novelty being that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core, and the rotation at the centroid of the core) instead of just one (shear stress in the core) of the earlier theory. In this paper, the EHSAPT formulation for predicting the critical wrinkling load is presented for a simply supported sandwich of general asymmetric construction. The cases of (i) applying the loading just on the face sheets with a linear core assumption and (ii) applying uniform strain loading throughout the thickness of the panel and a nonlinear core assumption are examined. The results are compared with a benchmark elasticity solution. In addition, edgewise compression experiments were conducted on glass face/Nomex honeycomb core and the ensuing wrinkling point is compared with the theoretical predictions. A comparison is also made with earlier edgewise compression experiments on aluminum face/granulated-cork core reported in literature. Other wrinkling formulas that are included in the comparison are: Hoff–Mautner and the HSAPT.     

Theoretical latent hardening in crystals—I. General equations for tension and compression with application to F.C.C. crystals in tension

Equations for latent strengths in single slip, based upon the simple theory of finite distortional crystal hardening introduced by K.S. Havner and A.H. Shalaby (1977), are derived for both tensile and compression tests without restriction as to crystal class. Detailed comparisons between theoretical results and the experiments of P.J. Jackson and Z.S. Basinski (1967) on copper crystals in tension are presented. There is good qualitative agreement between theory and experiment regarding the diversity of anisotropic hardening among slip systems. Moreover, there is satisfactory quantitative agreement between the theory and the extrapolated experimental data in the stage III, large-strain range. It is suggested that further experimental investigation of latent hardening at large prestrains would be desirable.The simple theory predicts anisotropic hardening and the perpetuation of single slip in axial loading of cubic crystals initially oriented for single slip, but predicts symmetric, isotropic hardening of specimens initially oriented in positions of 4, 6 or 8-fold multiple-slip. These predictions are in general accord with experimental observations from tests of f.c.c. and b.c.c. crystals.     

Cylindrical void in a rigid-ideally plastic single crystal III: Hexagonal close-packed crystal

The analytical solution is derived for the plane strain stress field around a cylindrical void in a hexagonal close-packed single crystal with three in-plane slip systems oriented at the angle π/3 with respect to one another. The critical resolved shear stress on each slip system is assumed to be equal. The crystal is loaded by both internal pressure and a far-field equibiaxial compressive stress. The deformation field takes the form of angular sectors, called slip sectors, within which only one slip system is active; the boundaries between different sectors are radial lines. The stress fields are derived by enforcing equilibrium and a rigid, ideally plastic constitutive relationship, in the spirit of anisotropic slip line theory. The results show that each slip sector is divided into smaller regions denoted as stress sectors and the stress state valid within each stress sector is derived. It is shown that stresses are unique and are continuous within stress sectors and across stress sector boundaries, but the gradient of stresses is not continuous across the boundaries between stress sectors. The solution shows self-similarity in that the stresses over the entire domain can be determined from the stresses within a small region adjacent to the void by invoking certain scaling and symmetry properties. In addition, the stress state exhibits periodicity along logarithmic spirals which emanate from the void. The results predict that the mean value of in-plane pressure required to activate plastic deformation around a void in a single crystal can be higher than that necessary for a void in an isotropic material and is sensitive to the orientation of the slip systems relative to the void.     

A nonclassical constitutive model for crystal plasticity and its application

I.IntroductionTheresearchoncrystalplasticitycanbedatedbackto1930'sill.AherHill[=],HillandRicely]builtupaperfectsystemofthegeometryandkineticsofCrystalplasticity,itsapplicatiollbecolllesmoreandmoreattractive,especiallyintheallalysisofpolycrystallinelllaterialssubjectedtoInultiaxiallynonproportionalcyclicloading.Ithasalreadybeenrealizedthattileillll,ol'talltforthepracticalapplicationis:tofindal.ealisticalldeasilyapplicableof'ystallineconstitutiverelationandaneffectivenumericalapproach.Tilecon…     

Modelling the behaviour of polycrystalline austenitic steel with twinning-induced plasticity effect

A micromechanical model using the scale transition method in elastoviscoplasticity has been developed to describe the behaviour of those austenitic steels that display a TWIP effect. A physically based constitutive equation at the grain scale is proposed considering two inelastic strain modes: crystallographic slip and twinning. The typical organizations of microtwins observed in electron microscopy are considered, and the twin–slip as well as the twin–twin interactions are accounted for. The parameters for slip are first fitted on the uniaxial tensile response obtained at intermediate temperatures (when twinning is inhibited). Then, the parameters associated with twinning are identified using the stress–strain curve at room temperature. The simulated results in both macro and micro scales are in good agreement with experimentally obtained results.     

表层嵌贴CFRP板条-混凝土界面粘结应力模型的试验与理论研究

为研究寒冷地区饱和砂岩的冻融损伤机理,采用DMA450伺服压机,在静载100N、动载80N、波动频率5～200Hz、温度-40～40℃的条件下,进行了饱和砂岩在不同频率正弦波单轴载荷作用下杨氏模量随温度变化的实验研究,获得滞(粘)弹性的弛豫衰减,以及有衰减引起的砂岩样品微结构变化情况。结果表明：饱和砂岩的杨氏模量和弹性波速度随温度升高而降低,随频率提高而增大; -40～20℃温度范围是冻融损伤最严重的区域。同时,在三种低频条件下(1.6Hz、2.8Hz和5.0Hz)用共振法在0℃获得相变衰减峰,反映了饱和砂岩的冻胀融缩效应,其产生的应力导致了饱和砂岩的损伤。从机理来看,前者是微观缺陷的演变,长期积累会导致破坏;后者是一种物理风化作用造成的宏观损伤。本文结果可为研究寒冷地区饱和岩石冻融损伤的机理及规律提供一定的参考。     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

Modeling micro-inertia in heterogeneous materials under dynamic loading

A continuum model including micro-inertia for heterogeneous materials under dynamic loading is proposed using a micro-mechanics method. The macro strain and stress are defined as the volume averages of the strain and stress fields in the representative volume element (RVE). The macro equations of motion are derived by using Hamilton’s principle together with the strain energy density and kinetic energy density involving the micro-inertia terms. The new macro equations of motion are used to study harmonic and transient wave propagation in layered media. Using a simple linear displacement field for the RVE, the dispersion curves obtained from the present model agree with the exact solutions very well for a range of wavelengths. The present model is also applied to analyze the transient response of layered media subjected to a triangular pulse loading. Comparison is made between the results of the present model and a finite element analysis.     

Nonlocal continuum crystal plasticity with internal residual stresses

We derive a three-dimensional constitutive theory accounting for length-scale dependent internal residual stresses in crystalline materials that develop due to a non-homogeneous spatial distribution of the excess dislocation (edge and screw) density. The second-order internal stress tensor is derived using the Beltrami stress function tensor φ that is related to the Nye dislocation density tensor. The formulation is derived explicitly in a three-dimensional continuum setting for elastically isotropic materials. The internal stresses appear as additional resolved shear stresses in the crystallographic visco-plastic constitutive law for individual slip systems. Using this formulation, we investigate two boundary value problems involving single crystals under symmetric double slip. In the first problem, the response of a geometrically imperfect specimen subjected to monotonic and cyclic loading is investigated. The internal stresses affect the overall strengthening and hardening under monotonic loading, which is mediated by the severity of initial imperfections. Such imperfections are common in miniaturized specimens in the form of tapered surfaces, fillets, fabrication induced damage, etc., which may produce strong gradients in an otherwise nominally homogeneous loading condition. Under cyclic loading the asymmetry in the tensile and compressive strengths due to this internal stress is also strongly influenced by the degree of imperfection. In the second example, we consider simple shear of a single crystalline lamella from a layered specimen. The lamella exhibits strengthening with decreasing thickness and increasing lattice incompatibility with shearing direction. However, as the thickness to internal length-scale ratio becomes small the strengthening saturates due to the saturation of the internal stress.Finally, we present the extension of this approach for crystalline materials exhibiting elastic anisotropy, which essentially depends on the appropriate Green function within φ.     

A two-level micromechanical theory for a shape-memory alloy reinforced composite

A two-level micromechanical theory is developed to study the influence of the shape and volume concentration of shape-memory alloy (SMA) inclusions on the overall stress–strain behavior of a SMA-reinforced composite. The first level exists on the smaller SMA level, in which, under the action of stress, parent austenite may transform into martensite. The second level is on the larger scale consisting of the metastable SMA inclusions and an inactive polymer matrix. The evolution of martensite microstructure is evaluated from the irreversible thermodynamics, in conjunction with the micromechanics and physics of martensitic transformation. By taking martensite to exist in the form of thin plates on the micro scale and assuming SMA inclusions to be homogeneously aligned spheroids on the macro scale, the overall stress–strain behaviors of a NiTi-reinforced composite are calculated for various SMA shapes and concentrations. The results indicate that, under a tensile axial loading, martensitic transformation is easier to take place when SMA inclusions exist in the form of long fibers, but most difficult to occur when they are in the form of flat discs. In general the levels of the applied stress at which martensite transformation commences, finishes, and austenitic transformation starts, and finishes, are found to decrease with increasing aspect ratio of the SMA inclusions while the damping capacity increases with it; these properties point to the advantage of using fibrous composites for actuators or sensors under a tensile loading.     

Crystal-plasticity finite-element analysis of inelastic behavior during unloading in a magnesium alloy sheet

A crystal-plasticity finite-element analysis of the loading-unloading process under uniaxial tension of a rolled magnesium alloy sheet was carried out, and the mechanism of the inelastic response during unloading was examined, focusing on the effects of basal and nonbasal slip systems. The prismatic and basal slip systems were mainly activated during loading, but the activation of the prismatic slip systems was more dominant. Thus the overall stress level during loading was determined primarily by the prismatic slip systems. The prismatic slip systems were hardly activated during unloading because the stress level was of course lower than that during loading. On the other hand, because the strength of the basal slip systems was much lower than that of the prismatic slip systems, the basal slip systems would be easily activated under the stress level during unloading in the opposite direction when their Schmid’s resolved shear stresses changed signs because of the inhomogeneity of the material. These results indicated that one explanation for the inelastic behavior during unloading was that the basal slip systems were primarily activated owing to their low strengths compared to that of the prismatic slip systems. Numerical tests using the sheets with random orientations and with the more pronounced texture were conducted to further examine the mechanism.