弹、塑性轮盘塑性区的实验应力换算

介绍一种弹、塑性状态轮盘的实验应力换算新方法．其优点是在迭代运算过程中无需反复利用拉伸曲线求割线模量E’,大大简化计算工作．     

A finite deformation theory of higher-order gradient crystal plasticity

For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation (GND) densities supplement the conventional theory within a non-work-conjugate framework in which there is no need to introduce higher-order microscopic stresses that would be work-conjugate to slip rate gradients. We discuss its connection to a work-conjugate type of finite deformation gradient crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution for the small deformation theory. As in a previous formulation for small deformation, the present formulation applies to the context of multiple and three-dimensional slip deformations.     

基于多弹簧模型的空间梁柱单元(I):理论模型

引入多轴应力状态下的塑性应力-应变关系理论,在单元模型中考虑了弹塑性区域剪切变形对单元的弹塑性刚度影响,推导了考虑剪切变形弹塑性刚度影响的多弹簧模型的空间梁柱单元刚度矩阵,为整体钢框架结构的弹塑性动力分析奠定了单元基础。     

饱水对煤层顶板砂岩单轴压缩破坏能量影响的分析

为研究饱水对砂岩力学参数和能量特征的影响,利用RMT-150B岩石力学系统对煤层顶板砂岩自然和饱水试样进行单轴压缩试验。试验结果表明:饱水对砂岩试样的强度和变形参数均有不同程度的影响,软化系数为0.79,弹性模量降幅为5.25%,变形模量降幅为5.92%;饱水后砂岩试样峰值前吸收能量、可释放弹性能和耗散能均有不同程度降低,吸收能量降幅36.8%,可释放弹性能降幅为34.4%,耗散能降幅为57.7%;饱水后砂岩储蓄能量的能力有较大减弱,脆性减弱,塑性明显增强;饱水砂岩试样压缩过程中积蓄可释放能难以使试样滑移破坏,仍需要吸收部分能量使试样逐步失稳破坏;饱水对砂岩试样压缩过程吸收能量、可释放能量比例关系的影响较小,而对耗散能比例关系的影响较大;自然状态下砂岩试样峰值前相同应变条件下吸收能量、可释放能均明显高于饱水试样对应能量值;深部巷道位置确定和支护设计时应充分考虑水对巷道围岩弱化的影响,对于完整坚硬围岩采用高压注水软化可有效防止冲击地压发生和减缓灾害程度。     

On the evolution of lattice deformation in austenitic stainless steels—The role of work hardening at finite strains

In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.     

Method of calculating the fields of residual stresses and plastic strains in cylindrical specimens with allowance for surface hardening anisotropy

A mathematical model is proposed for calculating the stress-strain state of a cylindrical specimen, which arises as a result of plastic surface hardening leading to material deformation anisotropy. The model adequacy is verified through comparisons with experimental data for cylindrical specimens made of 30KhGSA and St. 45 steels. A method of identifying model parameters on the basis of results of a fundamental experiment is developed. Good agreement of the calculated and experimental data is demonstrated.     

Strain-stress relation in macromolecular microsphere composite hydrogel

This paper investigates the strain-stress relation for the macromolecular microsphere composite (MMC) hydrogel. The novel point is to present the strain-stress model, which is based on the microscopic mixed entropy set up in the previous work and the Flory-Rehner elastic energy. Then, the numerical result of the strain-stress model is shown, which is completely consistent with the chemical experiment. Moreover, the theoretical relation of the strain-stress depends on the microscopic parameters of the MMC hydrogel. Therefore, it is a way to investigate the relation of macroscopic properties and microscopic structures of soft matters. This approach can be extended to other soft matters.     

Multiscale modeling of the plasticity in an aluminum single crystal

This paper describes a numerical, hierarchical multiscale modeling methodology involving two distinct bridges over three different length scales that predicts the work hardening of face centered cubic crystals in the absence of physical experiments. This methodology builds a clear bridging approach connecting nano-, micro- and meso-scales. In this methodology, molecular dynamics simulations (nanoscale) are performed to generate mobilities for dislocations. A discrete dislocations numerical tool (microscale) then uses the mobility data obtained from the molecular dynamics simulations to determine the work hardening. The second bridge occurs as the material parameters in a slip system hardening law employed in crystal plasticity models (mesoscale) are determined by the dislocation dynamics simulation results. The material parameters are computed using a correlation procedure based on both the functional form of the hardening law and the internal elastic stress/plastic shear strain fields computed from discrete dislocations. This multiscale bridging methodology was validated by using a crystal plasticity model to predict the mechanical response of an aluminum single crystal deformed under uniaxial compressive loading along the [4 2 1] direction. The computed strain-stress response agrees well with the experimental data.     

Defect substructure and local internal stresses inherent in plastic flow at mesolevel

This paper is concerned with the characteristics of defect substructures associated with plastic flow at the mesolevel. The important features are high curvature of the crystal lattice such that the local internal stress could reach the theoretical shear strength of the crystal and high stress gradient up to G/5 μm⁻¹ giving rise to stress moments. The foregoing is characteristics of the deformation of high-strength materials.     

Influence of Physically Nonlinear Deformation on Short-Term Microdamage of a Laminar Material

The structural theory of short-term damage is generalized to the case where the undamaged components of an N-component laminar composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for an N-component laminar composite with porous components whose skeleton deforms nonlinearly. Microvolumes of the composite components meet the Huber–Mises failure criterion. Damaged microvolume balance equations are derived for the physically nonlinear materials of the composite components. Together with the equations relating macrostresses and macrostrains of the laminar composite with porous nonlinear components, they constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. For a two-component laminar composite, algorithms for calculating the microdamage–macrostrain relationship and plotting deformation curves are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardening component and do not in the linearly elastic component     

Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2

A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.     

Progressing step by step and integrating calculation of overcritical deformation of spherical shallow shells

In this paper, the problem of second buckling of the spherical shallow shell is calculated by use of the method of progressing step by step and integrating. The result is more exact than that of first approximate analysis for over-critical deformation of spherical shallow shell. It has been solved that the solution of second approximate analysis in this problem can’t be found. The calculating example in this paper shows that the solution of progressing step by step and integrating converges to second approximate solution.     

A Simplified Model for Calculating Hydrodynamic Lubrication Film Thickness in Elastoplastic Line Contacts

The present paper proposes a simplified model for calculating hydrodynamic lubrication film thickness in elastoplastic line contacts. According to the Saint-Venant’s principle, the pressure in the contact is taken as uniformly distributed, this gives the contact surface elastic deformations in the inlet zone far away from the contact center close to real ones while gives those close to the contact center greater than real ones. This treatment is validated for hydrodynamic lubricated elastic contacts for relatively light loads and high rolling speeds. It gives the film thickness at the contact center a little higher than that calculated based on the real elastic model. The treatment is extended to a hydrodynamic lubricated elastoplastic line contact. The contact surfaces in the inlet zone are assumed as elastic and their deformations are calculated based on the uniform pressure distribution in the elastoplastic contact area. An inlet zone analysis is taken for obtaining the calculating equation of the hydrodynamic film thickness at the contact center. The equation overestimates the central film thickness but gives a satisfactory film thickness prediction for the heavy load which gives significant plastic deformations in the elastoplastic contact. It is found that when the load is lighter than 0.6 w _pc , the contact can be taken as elastic when calculating the central film thickness, while when the load is heavier than 0.6 w _pc , the contact can be taken as fully plastic; Here w _pc is the critical load for the contact fully plastic deformation. The plastic deformation in an elastoplastic line contact is found to reduce the hydrodynamic lubrication film thickness in the contact. This reduction is greater for higher rolling speeds and heavier loads. However, it is significantly dropped with increasing surface hardness.     

Nano-Indentation Hardness and Strain Hardening of Silicon,Sodium Chloride and Tungsten Crystals

Background

A previous review of micro- and nano-indentation hardness tests and their analyses gave emphasis to obtaining measurements of continuous nano-indentation load, P, versus, depth, h, recordings that monitor the full elastic–plastic deformation behavior of a localized crystal volume [1].

Objective

Attention is given to determining the complete, indentation-based, elastic–plastic deformation properties of the local volume, including the initial crystal elastic deformation behavior and, especially to evaluation of post pop-in plastic strain hardening.

Method

Stress–strain calculations are presented for an initial Hertzian elastic loading and follow-on crystal micro- and nano-scale plastic deformation responses [2].

Results

Applied load, P, dependencies on contact diameters, d_i, of silicon crystals are compiled on the basis of elastic, plastic and cracking predictions, giving indication at the lowest P values of an indentation size effect (ISE) for the crystal hardness. Elastic–plastic stress–strain curves are presented for sodium chloride and tungsten crystals. The hardness and strain hardening calculations also demonstrate an influence of the ISE.

Conclusions

The exceptional plastic strain hardening behaviors scale dimensionally with corresponding dislocation interactions and sessile reactions within the very localized plastic indentation zones. There is usefulness in determining elastic modulus values from the initial loading record. Micro- and nano-scale dislocation interactions/reactions account for the high stress and strain hardening levels as well as the occurrence of an ISE.

     

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Lightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843–1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip 〈c + a〉 versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.     

Numerical modeling of formability of extruded magnesium alloy tubes

In this paper, a constitutive framework based on a rate-dependent crystal plasticity theory is employed to simulate the large strain deformation phenomena in hexagonal closed-packed (HCP) metals such as magnesium. The new framework is incorporated into in-house codes. Simulations are performed using the new crystal plasticity model in which crystallographic slip and deformation twinning are the principal deformation mechanisms. Simulations of various stress states (uniaxial tension, uniaxial compression and the so-called ring hoop tension test) for the magnesium alloy AM30 are performed and the results are compared with experimental observations of specimens deformed at 200 °C. Numerical simulations of forming limit diagrams (FLDs) are also performed using the Marciniak–Kuczynski (M–K) approach. With this formulation, the effects of crystallographic slip and deformation twinning on the FLD can be assessed.     

Duality in constitutive formulation of finite-strain elastoplasticity based on F=FeFp and F=FF decompositions

A constitutive theory for large elastic–plastic deformations is presented by employing F=F^pF^e decomposition of the total deformation gradient. A duality in constitutive formulation based on this and the well-known Lee's decomposition F=F_eF_p is established for isotropic polycrystalline and single crystal plasticity.     

悬索桥主缆过三定点的精确线形数值解析计算方法

系统阐述了悬索桥分段悬链线理论及其基本方程,对变化刚度迭代法计算主缆线形进行了深入分析,发现了其不收敛的情况。对此,提出主缆过三定点的精确线形E-M解析计算方法,通过主缆平衡方程分别推导出末点和中间点标高与主缆左端水平和竖向分力H和V的解析关系式,得出综合考虑末点和中间点标高误差影响的H和V的修正迭代式。算例验证与有限元方法吻合较好,在吊索索力极不均匀的情况下,E-M计算方法仍能有效满足主缆线形过三定点的要求,收敛速度快精度高。     

有限变形下单晶变温本构模型

本文构造了单晶热弹粘塑性的本构模型,模拟材料在不同温度下的力学行为。该模型以晶体热运动学作为分析变形的基础,即考虑温度变化情况下总体变形梯度的乘式分解,建立温度影响下的以弹性变形梯度为基本变量的控制方程来描述单晶材料的变形,算法采用隐式积分方法来求解控制方程以保证计算的稳定性。模型能反映单晶材料变形过程中温度对应力-应变响应的影响。     

Evolution of defect substructure of metal alloys at microscopic and mesoscopic level under torsion

Transmission electron microscopy was used to investigate the reorientation of crystal lattice during the formation of ultrafine-grained (UFG) copper, nickel, and an alloy of Ni–18% Al–8% Cr–1% Zr–0.15% B (at.%) under severe plastic deformation by equal-channel angular (ECA) pressing and twisting at a high quasi-hydrostatic pressure. The crystal lattice was found to transform into a UFG state; it is fragmented at the nano-, micro-, and mesoscale levels. Possible mechanisms for the reorientation of the crystal lattice under deformation at the micro- and mesoscale level are discussed.