A review on the strain rate dependency of the dynamic viscoplastic response of FCC metals

The response of structures and materials subject to impulsive loads remains a field of intense research. The dynamic loading and temperature increase affect the material’s mechanical/failure response. For example, strains due to explosive blast will increase at rates from 10² to 10⁴ s⁻¹, leading to regimes of elastic/plastic wave propagation, plane stress and adiabatic deformations. Few constitutive models consider high strain rate effects, however some constitutive approaches that were developed and tested at low strain rate regimes will also be addressed here due to their relevance. Specific reference will be made to strain rate regimes close to 10⁴ s⁻¹, where shock waves may develop. The paper focuses on constitutive models for polycrystalline face-centred-cubic (FCC) metals since their behaviour under high strain rate regimes is not yet fully understood mostly due to path loading dependency. Reference is also made to aluminium alloys since they are widely used in virtually all fields of industry and in armour and protective structures and systems. A basic review of the main theoretical aspects that constitute the basis for most of the constitutive models described is also presented and the main features of each model are thoroughly discussed.     

Pressure-shear stress wave analysis in plate impact experiments

Numerical results are presented for the combined longitudinal and shear wave propagation in an elastic-viscoplastic solid as it occurs in high strain-rate plate impact experiments. Special attention is paid to the initial stage of the impact experiment and the effects of the specimen thickness, elastic impedances of flyer-anvil plates, and viscoplastic properties of materials on the time to reach a homogenous stress and deformation state within a specimen. The simple interpretation of experimental results which assumes a homogenous stress and deformation state within a specimen is found in general to be valid only at a much later time after impact. It is recommended that the measurement of the stress wave profiles should be made at the back face of the specimen rather than at its impact face, and that a pressure-shear stress wave analysis of the plate impact experiment should be performed to evaluate the inertial effects on the early part of experimental recordings. The comparison between measured stress wave profiles and the numerical simulation of the experiment provides a critical assessment of advanced viscoplastic models developed for applications under impact loading.     

An experimental method to validate viscoplastic constitutive equations in the dynamic response of plates

In the present paper measured and simulated vibrations of viscoplastic plates under impulsive loadings are compared to each other. The aim is to determine how accurately the measured deformations can be calculated by the chosen constitutive and structural theories. A first-order shear deformation shell theory assuming small strains and moderate rotations as well as viscoplastic laws are used. In the experimental part of this study short time measurement techniques are applied to shock tubes in order to record fast loading processes and plate deformations.     

Instrumented anvil-on-rod impact experiments for validating constitutive strength model for simulating transient dynamic deformation response of metals

Instrumented anvil-on-rod impact experiments were performed to access the applicability of this approach for validating a constitutive strength model for dynamic, transient-state deformation and elastic–plastic wave interactions in vanadium, 21-6-9 stainless steel, titanium, and Ti–6Al–4V. In addition to soft-catching the impacted rod-shaped samples, their transient deformation states were captured by high-speed imaging, and velocity interferometry was used to record the sample back (free) surface velocity and monitor elastic–plastic wave interactions. Simulations utilizing AUTODYN-2D hydrocode with Steinberg–Guinan constitutive equation were used to generate simulated free surface velocity traces and final/transient deformation profiles for comparisons with experiments. The simulations were observed to under-predict the radial strain for bcc vanadium and fcc steel, but over-predict the radial strain for hcp titanium and Ti–6Al–4V. The correlations illustrate the applicability of the instrumented anvil-on-rod impact test as a method for providing robust model validation based on the entire deformation event, and not just the final deformed state.     

A viscoplastic constitutive model for dynamic fracture

The use of a viscoplastic approach to dynamic fracture prediction is proposed with the aim of producing a model which is applicable to ductile situations. A numerical (finite-element) approach is adopted with specially developed joint elements being used to simulate behaviour within the fracture-process zone. Results are presented for an expanding edge-crack problem. Experimental results are used to calibrate the numerical model by determining the material-specimen parameters under dynamic-fracturing conditions. Detailed results are presented for both LEFM and nonlinear fracture-mechanics approaches.     

波浪冲击作用下核电站防浪堤动力响应的数值模拟

基于多物质ALE方法,利用带阻尼罚函数实现波浪与防浪堤结构间耦合作用,模拟波浪冲击作用下防浪堤结构及流体三维动态响应过程,所得结果与物理模型试验结果一致性较好。讨论挡浪墙表面波压力分布及挡浪墙所承受最大水平推力及结构动态响应对波浪冲击系数影响。结果表明,前挡浪墙静水面位置与后挡浪墙底部波压力较大;后墙承受波浪水平推力较大;结构动态响应会增强波浪的冲击作用。仿真结果可作为防浪堤强度设计重要依据及控制越浪量设计参考。     

A theoretical description of large viscoplastic shear deformation in metals

In this work, a new 3-dimensional viscoplastic model based on a previous plasticity theory is presented. The proposed constitutive model anticipates the contribution of the main features of plastic behavior, such as yielding, rate effect, isotropic and kinematic hardening, through a new approximation of the constitutive equation with a viscoplastic term, as well as a new consideration of the functional form of the rate of plastic deformation. A high accuracy simulation of shear experimental data at various rates and temperatures for a variety of materials, as well as the sign inversion of normal stress has been postulated.     

坍塌触地冲击荷载作用下地铁车站动力响应分析及其安全性评价

建筑物拆除时坍塌触地的冲击作用必然会对地下结构造成影响。采用现场试验和数值模拟相结合的方法探讨了坍塌触地冲击作用对邻近地铁车站的影响。基于某高架桥单跨足尺试验结果分析桥面整体塌落触地振动作用下地下管线的动力响应,并基于试验数据和经验公式验证数值分析方法的合理性;利用验证后的数值方法进行关键影响因素的参数分析,基于计算分析结果建议了评价指标和阈值,考虑塌落物体积、高度、数量等关键影响因素,对各因素下车站结构的振动响应规律及其安全性进行了评价。研究结果表明:(1)坍塌触地引起的振动以竖向振动为主;(2)所采用的数值分析方法是合理可行的;(3)坍塌触地引起的振动对邻近地铁车站的影响不容忽视,特别是在塌落物质量较大或有多个塌落物时,而这些是实际情况中较为常见的。     

泥石流冲击荷载下拦挡坝的动力响应分析

选取典型的泥石流冲击荷载,把钢筋混凝土拦挡坝简化成悬臂梁,建立其动力偏微分方程,运用数学物理方程中的变量分离法和结构动力学中的振型叠加法求得动力偏微分方程的解析解,最后根据材料力学得到相应的应力以及应变。算例分析表明解析解是可靠的,且在拦挡坝的坝顶处有最大的位移,为实际工程力学计算提供一种思路。       

Temperature rise in a viscoplastic material during dynamic crack growth

Dynamic steady-state crack growth has been analyzed under mode I plane stress, small-scale yielding conditions using a finite element procedure. A Perzyna type viscoplastic constitutive equation has been employed in this analysis. The viscoplastic work rate is converted into heat input and the temperature distribution is determined by solving the governing conduction/convection equation also by a finite element method. The Stream-line Upwinding Petrov-Galerkin formulation has been employed for this purpose because of the high Péclet number that results in such a type of analysis. The effect of strain rate sensitivity and crack speed on the temperature distribution near the crack tip is examined.     

冲击荷载下单层球面网壳动力响应分析与试验研究

为分析带下部支承结构的Kiewitt-6型单层球面网壳在冲击荷载下动力响应,在ANSYS/LS-DYNA中建立钢管柱支承的单层球面网壳数值分析模型,据冲击响应特点,总结四种响应模式,研究冲击能量、冲击位置、环梁刚度对上部网壳动力响应影响。进行钢管柱支承的单层球壳模型冲击试验,测量、分析结构的动应力、动位移及加速度,研究冲击柱破坏模式。结果表明,四种响应模式以冲击柱破坏模式(轻微损伤、局部凹陷、压弯破坏、剪切破坏)为典型特征;除响应模式4,网壳动力响应随冲击能量增大而增大;柱中为最不利冲击位置;环梁刚度增大,网壳动力响应减小;有限元分析结果与实测结果吻合较好,验证数值计算方法的正确性。     

On the dynamic fracture of structural metals

Some fundamental aspects of dynamic crack growth in structural steels are presented and discussed. The discussion takes the form of a direct comparison of experimental results to elastic-plastic analyses, and attempts to clarify the role of material inertia and plasticity in the dynamic crack growth process. In addition the relation of crack growth criteria to micromechanical void growth models is considered.Potential problems in the analysis of data obtained by either direct optical measurements or numerical simulations of crack growth are presented. It is demonstrated that large errors in the velocity records caused by stress wave effects are a main source of uncertainty in the interpretation of experimental results.

---

Résumé On présente et on discute certains aspects fondamentaux de la croissance dynamique d'une fissure dans des aciers de construction. La discussion prend la forme d'une comparaison directe des résultats expérimentaux à l'analyse élasto-plastique et tente de clarifier le rôle de l'inertie et de la plasticité du matériau dans le processus de croissance dynamique d'une fissure. On considère en outre la relation qui les critères de la croissance d'une fissure aux modèles micro-mécaniques de croissance des lacunes.On présente les problèmes potentiels que peuvent surgir dans l'analyse des données obtenues par des mesures directes optiques ou par des simulations numériques de la croissance d'une fissure. On démontre que des erreurs importantes dans les enregistrements de vitesse causées par des effets d'onde de contrainte sont la source principale d'incertitudes dans l'interprétation des résultats expérimentaux.

     

水下爆炸冲击下码头结构动力响应的数值模拟

为探究水下爆炸冲击对码头结构的结构损伤,开展爆炸荷载下高桩码头结构的数值模拟分析。基于ALE多物质流固耦合法,建立了码头结构的水下爆炸Lagrange-Euler全耦合模型,基于Cole经验公式,验证了模拟的可靠性,研究了起爆距离、起爆深度以及TNT当量对码头结构动力响应特性的影响规律。结果表明,在水下爆炸冲击荷载作用下,所有桩柱产生不同程度损伤,码头端部的第一根桩柱底部基岩区域以及与横梁相连的基岩区域塑形损伤破坏较为严重;当TNT炸药的起爆距离较小时,桩柱上的反射波要强于水底面的反射波,并会与之相抵消,作用在桩柱上的反射稀疏波会随之削弱;在其他条件相同的情况下,当起爆点到自由水面的距离与起爆点至基础底面距离之差的绝对值越大时,爆炸荷载作用于码头结构上的压力峰值会显著增大。     

Numerical simulation method for elastic-plastic dynamic response for hypervelocity impact phenomena

This study presents a time-dependent numerical method for impact in planar or cylindrical symmetry. We use Eulerian finite-difference scheme, Tilloston's Metallic Equation of state, von Mises Yield criterion, for calculating the large deformation of elastic-plastic high velocity impact. Failure, cavitation and melting of solids are accounted for. The present model treats the formation and evolution of a crater, the deformation of the projectile and the deformation and dynamical response of the target. A two-stage gas gun was employed to experimentally study the phenomena of hypervelocity impact. Good agreement is obtained between the present computational results and craters obtained in experiments of polyethylene/aluminium impacts. The relation of crater shape and penetration depth to dynamic parameters of the projectile and the target is discussed. The Multi Purpose Graphics System (MPGS) is used to describe the calculation results with color graphics.