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.     

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 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.     

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.     

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.

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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.     

Macroscopic response and microstructure evolution in viscoplastic polycrystals with pressurized pores

This paper presents a finite-strain homogenization model for the macroscopic behavior of porous polycrystals containing pressurized pores that are randomly distributed in a polycrystalline matrix. The porous polycrystal is modeled as a three-scale composite, where the pore size is taken to be much larger than the grain size, and the grains are described by single-crystal viscoplasticity. The instantaneous macroscopic response and corresponding field statistics in the material are determined using a generalization of the recently developed iterated second-order homogenization method, which employs the effective behavior of a linear comparison composite to estimate that of the nonlinear composite by means of a suitably designed variational approximation. Moreover, consistent evolution laws are derived for the pore pressure, pore geometry, and the underlying texture for the polycrystalline matrix. The model is then used to investigate porous ice polycrystals under a wide range of loading conditions. It is found that the pore pressure evolution has a strong effect on the material’s response under compressive loadings. More specifically, the macroscopic response of the porous polycrystals can be categorized into three different regimes: (i) a texture-controlled regime at low triaxialities, where the materials behave like solid polycrystals; (ii) a porosity-controlled regime at high triaxialities, where the materials behave like porous untextured materials; and (iii) a transition regime at intermediate triaxialities, where the materials exhibit a more complex behavior. This work highlights the importance of accounting for the interplay between porosity and matrix texture evolution in describing the constitutive response of porous polycrystals undergoing finite deformations.

     

The effects of residual stresses and degradation on the response of viscoplastic functionally graded materials

Functionally graded materials (FGMs), having ceramic and metallic constituents, are commonly used for extreme temperature applications. Under extreme temperature changes, the mismatches in the thermo-mechanical properties of the ceramics and metallic constituents could cause pronounced thermal stresses and could lead to degradation in the properties of the constituents. High stresses in the metallic constituent lead to plastic deformations and high tensile stresses in the ceramic constituent induce cracking. An elastic–viscoplastic micromechanical model is formulated for analyzing residual stresses and strains and degradation in ceramic–metal FGMs undergoing temperature changes due to conduction of heat. A degradation parameter that depends on the temperature and strain is introduced in order to determine the level of material degradation in the ceramics and metallic constituents. The Perzyna viscoplastic model is considered for the metallic constituent while the ceramic constituent is assumed linear elastic. The material parameters in these constituents change with the degradation. The problem leads to time-dependent coupled thermal, deformation, and degradation behaviors. The micromechanical model is implemented in a displacement based finite element (FE), which is used to determine the performance of the viscoplastic functionally graded structures subject to external thermo-mechanical stimuli.     

The Governing Parameter Method for implicit integration of viscoplastic constitutive relations for isotropic and orthotropic metals

A general algorithm of implicit stress integration in viscoplasticity, based on the governing parameter method (GPM) is briefly presented. It is assumed that the associative viscoplastic constitutive relations are governed by the Perzyna formulation with a generalization suggested by Simo and Hughes. The algorithm is first applied to isotropic metals obeying the von Mises yield condition with mixed hardening and then, to orthotropic metals with a generalized Hill's yield condition including a mixed hardening assumption. Derivation of consistent tangent moduli is presented for both viscoplastic material models. The proposed computational procedures are efficient, since they reduce the problem of stress integration to the solution of one nonlinear equation, can use large time steps and are applicable to 2-D, 3-D, shell and beam structures. The tangent elastic viscoplastic matrix provides high convergence rate in the overall equilibrium iterations. Numerical examples illustrate the main characteristics of the developed computational procedures.     

Essential work of fracture and viscoplastic response of a carbon black-filled thermoplastic elastomer

Observations are reported on a carbon black-filled thermoplastic elastomer in uniaxial cyclic tensile tests with various maximum strains and double-edge-notched-tensile (DENT) tests with various ligament widths at ambient temperature. It is shown that the stress-strain diagrams in DENT tests measured relatively far away from the ligament coincide with those in tensile cyclic tests on un-notched samples. To describe the viscoplastic response of un-notched specimens, constitutive equations are derived, and adjustable parameters are found by fitting the experimental data. It is demonstrated how the energy stored in a DENT sample under tension can be accounted for in calculations of the specific essential work of fracture.     

Shear band development in dynamic loading of a viscoplastic cylinder containing two voids

Summary We presume that plane strain state of deformation prevails when the interior of a long gun barrell or a cylindrical pressure vessel is dynamically loaded. The viscoplastic material of the body is taken to exhibit strain-rate hardening and thermal softening. Two thin ellipsoidal voids located symmetrically on the horizontal axis and near the center of the cylinder wall act as nuclei for the initiation of shear bands. We note that deformations of the cylinder are nonhomogenous even in the absence of the voids. It is therefore interesting to investigate when the bands initiate from the void tips and the interaction, if any, among them.It is found that shear bands initiate first at void tips closer to the center of the cylinder. These bands propagate faster to the inner surface of the cylinder as compared to those initiating from the other void tips which propagate towards the outer bounding surface of the cylinder. Whereas contours of constant maximum principal logarithmic strain originating from the outer void tips spread out laterally in both directions as they propagate into the cylinder, those originating from the inner void tips spread out in only one lateral direction as they propagate into the body.