Multiscale modelling of the induced plastic anisotropy in bcc metals

This paper presents a new framework to predict the qualitative and quantitative variation in local plastic anisotropy due to crystallographic texture in body-centered cubic polycrystals. A multiscale model was developed to examine the contribution of mesoscopic and local microscopic behaviour to the macroscopic constitutive response of bcc metals during deformation. The model integrated a dislocation-based hardening scheme and a Taylor-based crystal plasticity formulation into the subroutine of an explicit dynamic FEM code (LS-DYNA). Numerical analyses using this model were able to predict not only correct grain rotation during deformation, but variations in plastic anisotropy due to initial crystallographic orientation. Optimal results were obtained when {1 1 0}〈1 1 1〉, {1 1 2}〈1 1 1〉, and {1 2 3}〈1 1 1〉 slip systems were considered to be potentially active. The predicted material heterogeneity can be utilised for research involving any texture-dependent work hardening behaviour, such as surface roughening.     

弹性、弹塑性材料显式模拟计算中的准静态加载速度研究

摘 要：动力学显式算法采用时间积分原理,其较静力学隐式算法在强非线性问题中的适用性更广。为将此方法应用到岩土等非线性材料的计算中,考虑到显式算法中动能的影响会导致结果波动,分析动力学显式算法在模拟计算中的准静态加载速度的选取十分必要,如何在缩短模拟消耗时间与结果准确性之间寻求平衡是本文研究重点。研究中提出以加载-位移曲线的波动比来评价准静态计算效果,首先开展弹性材料的平面应变模拟试验以分析弹模、密度、泊松比、围压4个参数对准静态加载速度取值的影响,结果表明：弹模、泊松比、围压的增大会提高准静态加载速度;密度的增大则会减小准静态加载速度。通过对各影响因素与准静态加载速度的相关性分析给出了准静态加载速度取值的经验公式。最后,选取能够反映砂土复杂力学特性的弹塑性本构模型,开展其平面应变模拟试验,对比分析准静态加载速度经验公式在弹性材料与弹塑性材料中的适用性差异,并提出应用建议公式。     

干燥和饱和混凝土动态力学特性及其机理

采用分离式Hopkinson杆装置,对混凝土进行干燥和饱和状态下的SHPB实验,并与准静态实验进行对比。结果表明：干燥和饱和混凝土均具有明显的应变率效应,中等应变率条件下的应力应变曲线上升段比准静态的曲线陡;饱和混凝土动态强度提高的幅度接近干燥混凝土的2倍,具有更强的应变率敏感性;存在一个应变率临界值,仅当应变率大于临界值时,饱和混凝土的动态强度才大于干燥混凝土的的动态强度;基于实验结果,给出了不同饱和度混凝土强度与应变率的关系。

     

High strain-rate behavior of ice under uniaxial compression

In the present study, a modified split Hopkinson pressure bar (SHPB) is employed to investigate the dynamic response of ice under uniaxial compression in the range of strain rates from 60 to 1400 s^?1 and at initial test temperatures of ?10 and ?30 °C. The compressive strength of ice shows positive strain-rate sensitivity over the range of strain rates employed; a slight influence of ice microstructure is observed, but it is much less than that reported previously for ice deformation under quasi-static loading conditions [Schulson, E.M., IIiescu, D., Frott, A., 2005. Characterization of ice for return-to-flight of the space shuttle. Part 1 – Hard ice. NASA CR-2005-213643-Part 1]. Specimen thickness, within the range studied, was found to have little or no effect on the peak (failure) strength of ice, while lowering the test temperature from ?10 to ?30 °C had a considerable effect, with ice behaving stronger at the lower test temperature. Moreover, unlike in the case of uniaxial quasi-static compression of ice, the effect of specimen end-constraint during the high rate compression was found to be negligible. One important result of these experiments, which may have important implications in modeling ice impacts, involves the post “peak-stress” behavior of the ice in that the ice samples do not catastrophically lose their load carrying capacity even after the attainment of peak stress during dynamic compression. This residual (tail) strength of the damaged/fragmented ice is sizable, and in some cases is larger than the quasi-static compression strength reported for ice. Moreover, this residual strength is observed to be dependent on sample thickness and the strain rate, being higher for thinner samples and at higher strain-rates during dynamic compression.     

Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg–Landau theory

A finite element approach is suggested for the modeling of multivariant stress-induced martensitic phase transitions (PTs) in elastic materials at the nanoscale for the 2-D and 3-D cases, for quasi-static and dynamic formulations. The approach is based on the phase-field theory, which includes the Ginzburg–Landau equations with an advanced thermodynamic potential that captures the main features of macroscopic stress–strain curves. The model consists of a coupled system of the Ginzburg–Landau equations and the static or dynamic elasticity equations, and it describes evolution of distributions of austenite and different martensitic variants in terms of corresponding order parameters. The suggested explicit finite element algorithm allows decoupling of the Ginzburg–Landau and elasticity equations for small time increments. Based on the developed phase-field approach, the simulation of the microstructure evolution for cubic-tetragonal martensitic PT in a NiAl alloy is presented for quasi-statics (i.e., without inertial forces) and dynamic formulations in the 2-D and 3-D cases. The numerical results show the significant influence of inertial effects on microstructure evolution in single- and polycrystalline samples, even for the traditional problem of relaxation of initial perturbations to stationary microstructure.     

A variational formulation for the incremental homogenization of elasto-plastic composites

This work addresses the micro–macro modeling of composites having elasto-plastic constituents. A new model is proposed to compute the effective stress–strain relation along arbitrary loading paths. The proposed model is based on an incremental variational principle (Ortiz, M., Stainier, L., 1999. The variational formulation of viscoplastic constitutive updates. Comput. Methods Appl. Mech. Eng. 171, 419–444) according to which the local stress–strain relation derives from a single incremental potential at each time step. The effective incremental potential of the composite is then estimated based on a linear comparison composite (LCC) with an effective behavior computed using available schemes in linear elasticity. Algorithmic elegance of the time-integration of J₂ elasto-plasticity is exploited in order to define the LCC. In particular, the elastic predictor strain is used explicitly. The method yields a homogenized yield criterion and radial return equation for each phase, as well as a homogenized plastic flow rule. The predictive capabilities of the proposed method are assessed against reference full-field finite element results for several particle-reinforced composites.     

Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fcc mechanisms of metals

Combination of physically based constitutive models for body centered cubic (bcc) and face centered cubic (fcc) metals developed recently by the authors [Voyiadjis, G.Z., Abed, F.H., 2005. Microstructural based models for bcc and fcc metals with temperature and strain rate dependency. Mech. Mater. 37, 355–378] are used in modeling the plastic deformation of AL-6XN stainless steel over a wide range of strain rates between 0.001 and 8300 s⁻¹ at temperatures from 77 to 1000 K. The concept of thermal activation analysis as well as the dislocation interaction mechanism is used in developing the plastic flow model for both the isothermal and adiabatic plastic deformation. In addition, the experimental observations of AL-6XN conducted by Nemat-Nasser et al. [Nemat-Nasser, S., Guo, W., Kihl, D., 2001. Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures, J. Mech. Phys. Solids 49, 1823–1846] are utilized in understanding the underlying deformation mechanisms. The plastic flow is considered in the range of temperatures and strain rates where diffusion and creep are not dominant, i.e., the plastic deformation is attributed to the motion of dislocations only. The modeling of the true stress–true strain curves for AL-6XN stainless steel is achieved using the classical secant modulus for the case of unidirectional deformation. The model parameters are obtained using the experimental results of three strain rates (0.001, 0.1, and 3500 s⁻¹). Good agreement is obtained between the experimental results and the model predictions. Moreover, the independency of the present model to the experiments used in the modeling is verified by comparing the theoretical results to an independent set of experimental data at the strain rate of 8300 s⁻¹ and various initial temperatures. Good correlation is observed between the model predictions and the experimental observations.     

PMMA材料的动态压缩力学特性及应变率相关本构模型研究

利用INSTRON万能试验机和分离式Hopkinson压杆(SHPB)对PMMA试件在较宽应变率范围内进行了单轴压缩实验,研究加载应变率对PMMA材料力学性能的影响.利用扫描电子显微镜对回收的试样进行了显微观察,重点分析不同加载应变率下PMMA的微观损伤破坏模式.结果表明:随着应变率的增大,PMMA的流动应力显著地增加,且冲击加载条件下,峰值应力的应变率敏感性明显高于准静态;在准静态加载条件下,PMMA试样呈现明显的延性破坏特征,在动态加载条件下则表现为脆性破坏.最后,对PMMA材料的ZWT粘弹性本构模型参数进行了拟合,拟合结果与实验结果吻合较好,表明该本构模型能够较好地描述较宽应变率范围内PMMA材料的应力应变关系.     

Characterization of Polyurethane Rubber at High Deformation Rates

Polyurethane rubber materials have widespread usage in large-deformation energy absorption and dissipation applications. Accurate design modeling with these materials requires an appropriate constitutive material model that accounts for both static (low strain rate) and dynamic (high strain rate) responses. A common modeling approach is the use of hyper-viscoelastic formulations, which couple quasi-static hyperelastic with dynamic viscoelastic responses and describe the material response over a range of deformation rates. In this work the effectiveness of two models, the Modified Quasi-Linear Viscoelastic and Non-Linear Hyper-Viscoelastic, are investigated to describe the high-rate behaviour of two different grades of polyurethane rubber. From quasi-static, uniaxial compression tests, a Rivlin hyperelastic formulation was found to describe the low-rate response well. High-rate, uniaxial compressions test were performed using a Polymeric Split Hopkinson Pressure Bar (PSHPB), supported by high-speed photography. In general, it was found that the Modified Quasi-Linear Viscoelastic model did not fit the experimental data well due to its limited non-linear terms, while the Non-Linear Hyper-Viscoelastic provided very good agreement.     

Effects of strain rate and moisture content on the behaviour of sand under one-dimensional compression

The influence of strain rate and moisture content on the behaviour of a quartz sand was assessed using high-pressure quasi-static (10^?3 s^?1) and high-strain rate (10³ s^?1) experiments under uniaxial strain. Quasi-static compression to axial stresses of 800 MPa was carried out alongside split Hopkinson pressure bar (SHPB) experiments to 400 MPa, where in each case lateral deformation of the specimen was prevented using a steel test box or ring, and lateral stresses were recorded. A significant increase in constrained modulus was observed between strain rates of 10^?3s^?1 and 10³s^?1, however a consistently lower Poisson’s ratio in the dynamic tests minimised changes in bulk modulus. The reduction in Poissons ratio suggests that the stiffening of the sand in the SHPB tests is due to additional inertial confinement rather than an inherent strain-rate dependence. In the quasi-static tests the specimens behaved less stiffly with increasing moisture content, while in the dynamic tests the addition of water had little effect on the overall stiffness, causing the quasi-static and dynamic series to diverge with increasing moisture content.     

On the Plastic Wave Propagation Along the Specimen Length in SHPB Test

To observe the plastic wave propagation, an experimental setup is designed with a SHPB facility and a high speed digital camera. Two types of OFHC copper were selected as specimen materials: in the cold work condition and after total annealing, which represent non strain hardening and strain hardening material respectively. The rise time of incident impulse in the SHPB test is relevant to bar’s radius. A maximum allowable specimen length and a maximum allowable impact velocity (MAIV) of striker are proposed for the SHPB test. The propagation of plastic waves is observed along specimen length at the beginning of specimen’s plastic deformation in SHPB test. However, for both types of material, no plastic wave motion is caught along specimen length for large plastic strain level. Side confinement effect of friction is found to be significant, even with lubricant in the experiment.     

Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling

The elastic–plastic behaviors of three body-centered cubic metals, tantalum, tantalum alloy with 2.5% tungsten, and AerMet 100 steel, are presented over a wide range of strains (15%), strain rates (10⁻⁶–10⁴ s⁻¹) and temperatures (77–600°F). Johnson-Cook and Zerilli-Armstrong models were found inadequate to describe the observations. A new viscoplastic model is proposed based on these experimental results. The proposed constitutive model gives good correlations with these experimental results and strain-rate jump experiments. In the next paper (Liang, R., Khan A.S., 2000. Behaviors of three BCC metals during non-proportional multi-axial loadings and predictions using a recently proposed model. International Journal of Plasticity, in press), multi-axial loading results on these materials and comparison with the proposed model will be presented.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

宽应变率范围下2A16-T4铝合金动态力学性能

为了研究2A16-T4铝合金的动态力学性能,利用电子万能试验机、高速液压伺服试验机及霍普金森压杆(SHPB)装置进行常温下准静态、中应变率和高应变率的动态力学性能实验,得到不同应变率下的应力应变曲线,基于修正的Johnson-Cook本构模型对它进行拟合,并分析材料中应变率力学特性对模型应变率敏感参量的影响。结果表明:2A16-T4铝合金在应变率10-4~102 s-1范围内应变率敏感性较弱,而在102~103 s-1范围内应变率敏感性较强,且应变率强化效应随塑性应变的增大而减小;同时,在10-4~103 s-1范围内具有较强的应变硬化效应,且应变硬化效应随应变率的增大而减小;此外,修正Johnson-Cook本构模型的拟合结果与实验结果吻合很好,能够很好表征材料的动态力学行为,且考虑材料中应变率力学特性可提高本构模型参量的准确性。     

Stabilized interface methods for mechanical joints: Physics-based models and variationally consistent embedding

This paper presents the application of a new method for interfacial modeling utilizing a merger of continuous Galerkin and discontinuous Galerkin concepts to simulate the behavior of mechanical joints. The interfacial flux terms arising naturally from the discontinuous Galerkin treatment provide a mechanism to embed friction models in a variationally consistent fashion. Due to the unbiased implementation of the interface, facilitated by avoiding the master–slave concept, the deformation of the two interacting surfaces conforms to the local material and geometric attributes of the surfaces. This results in a better preservation of physics in interface mechanics. Additionally, the method is incorporated into a Variational Multiscale framework that comes equipped with a built-in error estimation module, providing numerical estimation of convergence and distinguishing discretization errors from modeling errors. A series of quasi-static numerical simulations of a lap joint under fretting conditions are conducted to compare the performance of two friction models: (i) classical Coulomb friction model and (ii) physics-based multiscale model. Hysteresis study of a three-dimensional double-bolted lap joint for the two friction models is also presented and the computed results are shown to be consistent between conforming and nonconforming meshes.     

基于统一强度理论的岩石弹塑性本构模型及其数值实现

基于弹塑性力学理论,以统一强度准则为屈服准则,建立了考虑硬化/软化行为和应变率效应的岩石弹塑性本构模型;采用Fortran语言通过LS-DYNA的用户自定义材料接口(Umat)对该弹塑性本构模型进行编程,并把该程序生成求解器以达到对该模型进行应用的目的;通过岩石的单轴压缩实验和SHPB实验对所建的弹塑性本构模型进行验证,结果表明,该弹塑性本构模型能够反映岩石在准静态和动态下的力学行为。     

脆性颗粒材料的应变率效应机理研究

利用分离式Hopkinson压杆（SHPB）,对干燥石英砂进行了被动围压下的动态压缩实验,发现石英砂表现出了明显应变率效应。通过激光粒度分析测量了动静态压缩后的试件的级配曲线,发现同一应力水平下准静态压缩比动态压缩后的试件的颗粒破碎量更大。而通过拟合相对破碎率与外力功之间的关系,发现准静态压缩在颗粒破碎方面能量利用率更高也即破碎效率更高,而这正是脆性颗粒材料应变率效应的本质原因。     

CoCrFeNiAlx系高熵合金的动态力学性能和本构关系

高熵合金,以其独特的合金设计和优异的综合性能,成为当下材料研究的热点。本文利用高真空电弧熔炼法成功制备出了CoCrFeNiAl_x（x=0, 0.6, 1）系高熵合金,并通过分离式霍普金森压杆对其进行一系列不同应变速率下的动态压缩试验。通过X射线、扫描电镜和透射电镜分析,深入探索了该合金系的晶体结构、微观组织和变形特征。最后,利用修正后的Johnson-Cook (J-C)本构模型,获得了该体系高熵合金的动态本构关系。     

Multiscale modeling of strain-hardening cementitious composites

This research involves the multiscale characterization of strain-hardening cementitious composites under tensile loading. The sensitivity of cracking behavior to fiber dispersion is studied using a special form of lattice model, in which each fiber is explicitly represented. It is shown that the nonlocal modeling of fiber bridging forces is essential for obtaining realistic patterns of crack development and strain-hardening behavior. Crack count and crack size are simulated for progressively larger levels of tensile strain. The influence of fiber dispersion is clearly evident: regions with significantly fewer fibers act as defects, reducing strength and strain capacity of the material.