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.     

Plastic collapse of general frames

A structural theory is presented for the large static plastic deformation of space frames composed of thin walled members. Displacements comparable to the overall structural dimensions are contemplated. The frame is considered to consist of an arbitrary number of beam elements connected at node points. The analysis assumes that plastic deformation is confined to idealized hinges located at the node points. As a basis for a general frame computer program, the equations for a beam element are derived as a relationship between appropriate generalized force and deformation rates. The structural constitutive theory employed for the plastic hinge includes biaxial bending, torsion, and axial extension. It accounts for reduction in the load carrying capacity of the hinge due to local deformation. Predicted force-deformation curves for a space frame are in good agreement with experimental results.     

A finite deformation theory of strain gradient plasticity

Plastic deformation exhibits strong size dependence at the micron scale, as observed in micro-torsion, bending, and indentation experiments. Classical plasticity theories, which possess no internal material lengths, cannot explain this size dependence. Based on dislocation mechanics, strain gradient plasticity theories have been developed for micron-scale applications. These theories, however, have been limited to infinitesimal deformation, even though the micro-scale experiments involve rather large strains and rotations. In this paper, we propose a finite deformation theory of strain gradient plasticity. The kinematics relations (including strain gradients), equilibrium equations, and constitutive laws are expressed in the reference configuration. The finite deformation strain gradient theory is used to model micro-indentation with results agreeing very well with the experimental data. We show that the finite deformation effect is not very significant for modeling micro-indentation experiments.     

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.     

A dislocation density based strain gradient model

Strain gradients play a vital role in the prediction of size-effects in the deformation behavior of metals at the micrometer scale. At this scale the behavior of metals strongly depends on the dislocation distribution. In this paper, a dislocation density based strain gradient model is developed aiming at predictions of size-effects for structural components at this scale. For this model, the characteristic length is identified as the average distance of dislocation motion, which is deformation dependant and can be determined experimentally. The response of the model is compared to the strain gradient plasticity model of Huang et al. [Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H., 2004. A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 20, 753–782]. It is shown that the present strain gradient model, which only requires a physically measurable length-scale, can successfully predict size effects for a bar with an applied body force and for void growth.     

Transformation-induced plasticity in high-temperature shape memory alloys: a one-dimensional continuum model

A constitutive model based on isotropic plasticity consideration ispresented in this work to model the thermo-mechanical behavior ofhigh-temperature shape memory alloys. In high-temperature shapememory alloys (HTSMAs), both martensitic transformation andrate-dependent plasticity (creep) occur simultaneously at hightemperatures. Furthermore, transformation-induced plasticity isanother deformation mechanism during martensitic transformation. Allthese phenomena are considered as dissipative processes to model themechanical behavior of HTSMAs in this study. The constitutive modelwas implemented for one-dimensional cases, and the results have beencompared with experimental data from thermal cycling test foractuator applications.     

Large strain elasto-plastic model of paper and corrugated board

An anisotropic elasto-plastic constitutive model of paper material is presented. It is formulated in a spatial setting in which anisotropic properties are accounted for by use of structural variables. A multiplicative split of the deformation gradient is employed to introduce plasticity. A similar approach is used to model the plastic deformation of the substructure. The yield surface adopted is based on the Tsai–Wu failure criterion, used previously to model failure of paper material. A non-associated plasticity theory is employed to calibrate the model to experimental data. It turns out that a multi-axial loading situation is needed to calibrate the model and here a biaxial tension test is audited. The model was implemented into a finite element environment and the creasing process of a corrugated board panel is investigated.     

Failure analysis of stainless steel at elevated temperatures

In this paper, particular emphasis has been put on gathering information on the phenomena that take place at the crack tip of a crack propagating at 1100°F. Since the experimental program was directed toward studying crack propagation in tubing, the tests were conducted on rings.From the experimentally obtained data and from the correlation with the theoretically predicted values, the following picture emerges for the fracture behavior with full plasticity present. There is a region surrounding the crack tip where very large plastic deformations take place. This region is surrounded by a much larger region where the loading is nearly proportional and the behavior can be predicted well by the results of the deformation theory of plasticity and the theory of singularity fields. As the crack propagation initiates, there is a drastic change in the crack-tip configuration. The crack tip does not blunt and a fairly sharp crack-tip region is observed. The crack tip carries a large deformation field of a far more localized nature than that observed at the initiation of the crack growth.Paper was presented at 1978 SESA Spring Meeting held in Wichita, KS on May 14–19.     

A model of fracture in reinforced concrete arches based on lumped damage mechanics

A simplified model of cracking and damage in RC circular elements is proposed. The model can be used for the structural assessment of arches and rings. The constitutive equations are based on lumped damage mechanics which is an adaptation of fracture and continuum damage mechanics to the theory of frames with plastic hinges. An arch element is assumed to be the assemblage of an elastic circular component and two inelastic hinges where the main inelastic effects, plastic yielding of the longitudinal reinforcement and concrete cracking, are concentrated. Deformations in the elastic part are assumed to be small but the model may include some geometrically nonlinear effects due to large displacements or rotations of the hinges. The numerical examples presented in the paper show that the model describes correctly the global behavior of two structures including the softening phase.     

Mechanism-based strain gradient Drucker–Prager elastoplasticity for pressure-sensitive materials

Modeling strain gradient plasticity effects has achieved considerable success in recent years. However, incorporating the full mechanisms of the pressure-sensitive yielding and the size dependence of plastic deformation still remains an open challenge. In this work, a mechanism-based stain gradient (MSG) plasticity theory for pressure sensitive materials with a variable material length-scale parameter is presented. The flow theory of MSG plasticity based on the Drucker–Prager yield function is established following the same hierarchical framework of MSG plasticity proposed by Gao et al., 1999, Huang et al., 2000 and Qiu et al. (2003) in order to link the strain gradient plasticity theory on the mesoscale to the Taylor dislocation model on the micro-scale. The incremental constitutive relation based on the associated flow rule is derived for the Drucker–Prager yield function on the micro-scale, including the higher-order stress introduced as the thermodynamic conjugate of strain gradient at the mesoscale. The proposed theory successfully predicts the experimental results. The numerical results show that when the pressure-sensitivity index defined by the Drucker–Prager yield function takes different values, the material response curves are different and the material strength increases with the increase of pressure-sensitivity index. It proves that this procedure is able to represent the material behavior of pressure-sensitive materials such as geomaterials, polymeric materials, metallic foams and metallic glass.     

Finite deformation analysis of mechanism-based strain gradient plasticity: torsion and crack tip field

A finite deformation theory of mechanism-based strain gradient (MSG) plasticity is developed in this paper based on the Taylor dislocation model. The theory ensures the proper decomposition of deformation in order to exclude the volumetric deformation from the strain gradient tensor since the latter represents the density of geometrically necessary dislocations. The solution for a thin cylinder under large torsion is obtained. The numerical method is used to investigate the finite deformation crack tip field in MSG plasticity. It is established that the stress level around a crack tip in MSG plasticity is significantly higher than its counterpart (i.e. HRR field) in classical plasticity.     

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation

Nanoindentation experiments have shown that microstructural inhomogeneities across the surface of gold thin films lead to position-dependent nanoindentation behavior [Phys. Rev. B (2002), to be submitted]. The rationale for such behavior was based on the availability of dislocation sources at the grain boundary for initiating plasticity. In order to verify or refute this theory, a computational approach has been pursued. Here, a simulation study of the initial stages of indentation using the embedded atom method (EAM) is presented. First, the principles of the EAM are given, and a comparison is made between atomistic simulations and continuum models for elastic deformation. Then, the mechanism of dislocation nucleation in single crystalline gold is analyzed, and the effects of elastic anisotropy are considered. Finally, a systematic study of the indentation response in the proximity of a high angle, high sigma (low symmetry) grain boundary is presented; indentation behavior is simulated for varying indenter positions relative to the boundary. The results indicate that high angle grain boundaries are a ready source of dislocations in indentation-induced deformation.     

Study of the Elastoplastic Deformation of Hardened Metals under Static Loading in View of Their Structure. The Case of a Complex Stress State

A generalization is made of the results of experimental investigations into the elastoplastic deformation of initially isotropic structural materials with a stable and metastable structure loaded along rectilinear and slightly curved paths. It is revealed and physically substantiated why some hypothesis of plastic theory, which are valid for materials with a stable structure, are not fulfilled for deformationally unstable metals. It is indicated how much the study results can be used in calculations and to improve the technology of manufacturing thin-walled shell structural elements by optimizing their strength, plasticity, and crack resistance     

非经典大变形弹塑性本构方程及其算法研究

本文介绍了作者提出的非经典大变形弹塑性木构方程的增量形式，发展了相应的有限元分析方法。由于不采用屈服面的概念及相应的流动规律与加载准则，与传统的算法相比，本文提出的算法不仅简化了计算过程，而且改善了收敛速度和计算精度。作为验证和应用的例子，分析了圆柱试件的大变形拉伸颈缩过程和短圆柱的镦粗过程。与实验结果的比较证明了所发展方法的有效性。     

Multiaxial yield behavior of 1100 aluminum following various magnitudes of prestrain

The multiaxial yield and flow behavior of metals has been of interest for many years. Recently, the experimental work of Phillips & Lee [1979], Shiratori et al. [1979] and Ohashi [1982] has been quite notable in this field. These authors have concentrated their efforts in measuring yield loci after small to moderate prestrains (≤0.06). In this paper we discuss small strain yield loci we have measured after prestrains between 0.03 and 0.05 in torsion. These experiments on 1100 aluminum are in general agreement with the literature. They show a translation, distortion and expansion of the yield loci. A rounded nose forms in the direction of prestrain with the yield locus flattering opposite the prestrain. We observed that the distortions change to match the strain direction after very small reversals in prestrain.The subsequent yield locus has also been measured after a large torsional prestrain of γ=0.5. Using a 5 × 10^?6 offset criterion for yielding, the shape, distortion and translation of the yield locus was very similar to that found after the smaller prestrains. In addition a large-strain yield locus, using a back extrapolation technique, was determined for the same sample. This yield locus exhibited close to von Mises isotropic expansion. The observed deviations, while slight are extremely important. They match those predicted by a polycrystal slip model. Thus, the small-strain yield locus, after a large prestrain, appears to be determined largely from dislocation considerations only, where as the large-strain yield locus is determined by the developing texture. Finally, aluminum sheet was deformed by rolling to larger prestrains ?^{von Mises} = 0.5, 1.0, 1.5, 2.0 and 2.5 and subsequently tested in plane strain compression. Two types of compression experiments were done, one such that there was no deformation mode change from rolling, the other rotating the direction of zero strain by 90° producing a stress path change. The large strain yield and flow behavior of these experiments was again predicted using the relaxed constraint polycrystal model of Kocks & Canova [1981]. For these very large prestrains the experiments and texture theory differ. Micrstructural observations have shown the presence of micro-shear bands which resulted from the rolling prestrain. We speculate that these features are responsible for the deviation from crystal plasticity theory.We believe that this work points to several operative mechanisms of deformation. Small-strain yielding (5 × 10^?6) appears to be controlled purely by dislocation mechanisms and interactions even after relatively large prestrains. Large-strain yielding, on the other hand, is controlled by texture after moderate prestrains (at least to γ = 0.5). After large prestrains, obtained by rolling, the experiments deviate from texture based predictions. This is possibly the result of microstructural deformation mechanisms, for example micro-shear bands, playing a role in the deformation process.     

A constitutive model for active–passive transition of muscle fibers

In this paper, we examine the transition of striated muscles between active and passive states. New experimental data of a muscle performing such a transition are provided, allowing for a new model to be developed to capture this mechanical behavior. Specifically, a strain energy function is formulated using the theory of transient networks, introducing an intermediate, stress-free configuration for the active muscle fibers. Additionally, energy dissipation occurring during the unloading is accounted for by specifying a pseudo-energy function. The general three-dimensional case is specialized to uniaxial deformation for comparison with test data, from which material parameters are determined. Finally, numerical results are presented, demonstrating the model's ability to capture the mechanical behavior with changing stimulus.     

Experiments and modeling of carbon nanotube-based NEMS devices

In this paper, carbon nanotube-based nanoelectromechanical systems (NEMS) are nanofabricated and tested. In-situ scanning electron microscopy measurements of the deflection of the cantilever under electrostatic actuation are reported. In particular, a cantilever nanotube suspended over an electrode (nanoswitch), or two symmetric cantilever nanotubes (nanotweezers), from which a differential in electrical potential is imposed, are studied. The finite deformation regime investigated here is the first of its kind. An analytical model based on the energy method in both small deformation and finite kinematics (large deformation) regimes is used to interpret the measurements. The theory overcomes limitations of prior analysis reported in the literature towards the prediction of the structural behavior of NEMS. Some of the simplifying hypotheses have been removed. Furthermore, the theory takes into account the cylindrical shape of the deflected nanotube in the evaluation of its electrical capacitance, the influence of the van der Waals forces as well as finite kinematics. In addition, tip charge concentration and a quantum correction of the electrical capacitance are also considered. The energy-based method is used to predict the structural behavior and instability of the nanotube, corresponding to the on/off states of the nanoswitch, or to the open/close states of the nanotweezers—at the so-called pull-in voltage. Accuracy of the derived formulas is assessed by comparison of the theoretical prediction and experimental data in both small deformation and finite kinematics regimes. The results reported in this work are particularly useful in the characterization of the electromechanical properties of nanotubes as well as in the optimal design of nanotube-based NEMS devices.     

含冷却孔镍基合金次级取向效应的应变梯度晶体塑性有限元研究

单晶镍基合金具有优异的耐高温、高强、高韧等性能, 这些力学性能受制造过程引入的次级取向和冷却孔的影响. 已有研究大多关注单孔薄板的变形机理和力学性能, 而工程中应用的往往是多孔薄板, 当前亟需阐明多孔的塑性滑移带变形机理、次级取向效应以及冷却孔引起的应变梯度效应. 文章采用基于位错机制的非局部晶体塑性本构模型对含冷却孔镍基单晶薄板的单拉变形进行了数值模拟. 此模型基于塑性滑移梯度与几何必需位错的关系引入了位错流动项, 因此可有效刻画非均匀变形过程中的应变梯度效应. 为了全面揭示含孔镍基薄板的次级取向效应, 系统研究了[100]和[110]取向(两种次级取向)下镍基薄板的单拉变形行为, 并重点探究了在两种次级取向下冷却孔数量对薄板塑性行为的影响. 此外, 还分析了镍基合金板变形过程中各个滑移系上分切应力变化、主导滑移系开动以及几何必需位错密度的演化过程, 并讨论了塑性滑移量及其分布特征对不同次级取向镍基合金板强度的影响. 研究表明, 单孔和多孔的[110]薄板抗拉强度均低于[100]薄板, 多孔薄板的塑性变形过程比单孔薄板更为复杂且受次级取向影响更大, 并且发生滑移梯度位置主要位于冷却孔附近以及塑性滑移带区域. 研究结果可为工程中镍基合金的设计和服役提供理论指导.