Dislocation-mechanics-based constitutive relations for material dynamics calculations

Zerilli, Frank J.; Armstrong, Ronald W.

doi:10.1063/1.338024

Cited by 1,699 publications

(796 citation statements)

References 17 publications

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“…We therefore evaluate a number of models which are best suited to the regime of interest to us. This regime consists of strain-rates between 10 3 /s and 10 6 /s and temperatures between 230 K and 800 K. We have observed that the combined effect of high temperature and high strain-rates has been glossed over in most other similar works (for example Zerilli and Armstrong (1987); Johnson and Holmquist (1988); Zocher et al (2000)). Hence we examine the temperature dependence of plastic deformation at high strain-rates in some detail in this paper.…”

Section: Introductionmentioning

confidence: 54%

“…These models are the Johnson-Cook model (Johnson and Cook (1983)), the Steinberg-Cochran-Guinan-Lund model (Steinberg et al (1980); Steinberg and Lund (1989)), the Zerilli-Armstrong model (Zerilli and Armstrong (1987)), the Mechanical Threshold Stress model (Follansbee and Kocks (1988)), and the Preston-Tonks-Wallace model (Preston et al (2003)). We also evaluate the associated shear modulus models of Varshni (1970), Steinberg et al (1980), and Nadal and Le Poac (2003).…”

Section: Introductionmentioning

confidence: 99%

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Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature

Zhang

Shim

2010

Acta Materialia

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Phenomenological plastic flow stress models are used extensively in the simulation of large deformations of metals at high strain-rates and high temperatures. Several such models exist and it is difficult to determine the applicability of any single model to the particular problem at hand. Ideally, the models are based on the underlying (subgrid) physics and therefore do not need to be recalibrated for every regime of application. In this work we compare the Johnson-Cook, Steinberg-Cochran-Guinan-Lund, Zerilli-Armstrong, Mechanical Threshold Stress, and Preston-Tonks-Wallace plasticity models. We use OFHC copper as the comparison material because it is well characterized. First, we determine parameters for the specific heat model, the equation of state, shear modulus models, and melt temperature models. These models are evaluated and their range of applicability is identified. We then compare the flow stresses predicted by the five flow stress models with experimental data for annealed OFHC copper and quantify modeling errors. Next, Taylor impact tests are simulated, comparison metrics are identified, and the flow stress models are evaluated on the basis of these metrics. The material point method is used for these computations. We observe that the all the models are quite accurate at low temperatures and any of these models could be used in simulations. However, at high temperatures and under high-strain-rate conditions, their accuracy can vary significantly.

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Section: Introductionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature

Zhang

Shim

2010

Acta Materialia

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“…Those proposed by Cowper and Symonds [5] and Johnson and Cook [6] are empirical, and in that due to Zhao [7], an extension of the Tanimura formulation [47], temperature effects are not included. Zerilli and Armstrong [9] proposed a constitutive relation coupled with temperature and with some background of materials science. Next, a comparison between some of these constitutive relations for sheet steel ES is performed, Fig.…”

Section: Thermoviscoplastic Modelingmentioning

confidence: 99%

Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

et al. 2005

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It is well known that a specimen for impact testing must be optimized in terms of its dimensions. The main reason is to reduce strain gradients due to the effects of elastic plastic wave propagation. On the other hand, when a split Hopkinson bar in tension is applied, the net displacement of the specimen ends is very limited, usually from 2.0 to 3.0 mm. Thus, to reach a maximum strain of 0.5 the specimen length must be reduced in dimensions from 4.0 to 6.0 mm. Consequently, small diameters or lateral dimensions and lengths must be applied to assure one dimensional deformation. Such small lengths substantially perturb the determination of real material behavior. So the main motivation of this study was to perform a systematic analysis, numerical and analytical, to find differences in the behavior of short and long specimens loaded in impact tension. The finite element code ABAQUS/Explicit has been used to simulate several spec imen lengths from 10 to 40 mm submitted to impact velocities ranging from 10 to 100 m/s.Keywords: Constitutive relation; Dynamic tension; Normalization; Plastic instability; Numerical simulations Thermoviscoplastic modelingTo study the dynamic processes of plastic deformation in sheet metals, a well defined constitutive relation has earlier been proposed. Several processes of fast deformation have been previously studied by applying that relation: perforation [1], double shear by direct impact [2], the Taylor test and fast tension test [3]. With the constitutive relation, Eq. (1), the effect of temperature and strain rate on the flow stress can be studied and analyzed. It is clear that the adiabatic increase of temperature has a substantial effect on the flow stress and it induces a decrease in the ultimate tensile stress. In order to describe precisely the behavior of materials at high strain rates and temperatures, the equivalent stress r needs to be taken as the sum of two components r l and r * which are, respectively, the internal and the effective stress. The first component is directly related to the strain hardening of the material and the second defines the contribution due to the thermal activation (a combination of temperature and strain rate). The constitutive relation can be written in terms of equivalent scalar quantities:where e p is the equivalent plastic strain, T is the absolute temperature, E 0 is the YoungÕs modulus at T 0 K and E(T) is the evolution of the modulus as a function of temperature. Eq. (1) is based to some extent on physical considerations [2]. The explicit expressions for both stress components are given below:where Bð _ e p ; T Þ and nð _ e p ; T Þ are the modulus of plasticity and the strain hardening exponent, respectively. These quantities, defined by Eqs. (3) and (5), respectively, take into account the experimental observations that the strain hardening itself depends on temperature and strain rate.

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“…Based on the intrinsic characteristics of dislocation and microstructure, Zerilli and Armstrong [30] made the athermal stress to Hall-Petch relationship for FCC metal. Jiang et al [24] developed the Hall-Petch relationship associated with the dislocation pile-up theory and flow stress-grain size relationship as:…”

Section: Constitutive Modellingmentioning

confidence: 99%

Influences of temperature and grain size on the material deformability in microforming process

Jiang

Zhao

et al. 2016

Int J Mater Form

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This paper investigated the influences of temperature and grain size on the deformability of pure copper in micro compression process. Based on the dislocation theory, a constitutive model was proposed taking into account the influences of forming temperature, Hall-Petch relationship and surface layer model. Vacuum heat treatment was employed to obtain various grain sizes of cylindrical workpieces, and then laser heating method was applied to heat workpieces during microforming process. Finite element (FE) simulation was also performed, with simulated values agreed well with the experimental results in terms of metal flow stress. Both the FE simulated and experimental results indicate that forming temperature and grain size have a significant influence on the accuracy of the produced product shape and metal flow behaviour in microforming due to the inhomogeneity within the deformed material. The mechanical behaviour of the material is found to be more sensitive to forming temperature when the workpieces are constituted of fine grains. experimental results indicate that forming temperature and grain size have a significant influence on the accuracy of the produced product shape and metal flow behaviour in microforming due to the inhomogeneity within the deformed material. The mechanical behaviour of the material is found to be more sensitive to forming temperature when the workpieces are constituted of fine grains.

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Dislocation-mechanics-based constitutive relations for material dynamics calculations

Cited by 1,699 publications

References 17 publications

Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature

Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature

Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

Influences of temperature and grain size on the material deformability in microforming process

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