Shock viscosity and the prediction of shock wave rise times

Swegle, J. W.; Grady, D. E.

doi:10.1063/1.336184

Cited by 374 publications

(250 citation statements)

References 17 publications

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“…It is known that different metals have different threshold pressures for the initiation of twinning; it has been established by Murr [96] that for FCC metals this pressure is a function of the SFE. The analysis requires the use of the Swegle-Grady [97] equation and the procedure is delineated in Ref. [98].…”

Section: Discussionmentioning

confidence: 99%

The onset of twinning in metals: a constitutive description

Vöhringer²,

2001

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Abstract-A constitutive approach is developed that predicts the critical stress for twinning as a function of external (temperature, strain rate) and internal (grain size, stacking-fault energy) parameters. Plastic deformation by slip and twinning are considered as competitive mechanisms. The twinning stress is equated to the slip stress based on the plastic flow by thermally assisted movement of dislocations over obstacles, which leads to successful prediction of the slip-twinning transition. The model is applied to body centered cubic, face centered cubic, and hexagonal metals and alloys: Fe, Cu, brasses, and Ti, respectively. A constitutive expression for the twinning stress in BCC metals is developed using dislocation emission from a source and the formation of pile-ups, as rate-controlling mechanism. Employing an Eshelby-type analysis, the critical size of twin nucleus and twinning stress are correlated to the twin-boundary energy, which is directly related to the stacking-fault energy (SFE) for FCC metals. The effects of grain size and SFE are examined and the results indicate that the grain-scale pile-ups are not the source of the stress concentrations giving rise to twinning in FCC metals. The constitutive description of the slip-twinning transition are incorporated into the Weertman-Ashby deformation mechanism maps, thereby enabling the introduction of a twinning domain. This is illustrated for titanium with a grain size of 100 µm. 

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Section: Discussionmentioning

confidence: 99%

The onset of twinning in metals: a constitutive description

Vöhringer²,

2001

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“…It is necessary to note that the actual strain rate in the penetrating process is hardly measured, therefore the parameter D 0 in the constitutive equations was chosen only by trial calculations. In this paper the trial calculations were performed in the assessed range of 10 5 s À1 according to Zukas et al (1982), Swegle and Grady (1985), Anderson and Walker (1991) and the parameter D 0 for each material was chosen as shown in Table 3.…”

Section: Calculation Examplementioning

confidence: 99%

The application of B–P constitutive equations in finite element analysis of high velocity impact

Song

Zhang

Duowang³

2001

International Journal of Solids and Structures

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We present in this paper the application of B±P constitutive equations in ®nite element analysis of high velocity impact. The impact process carries out in so quick time that the heat-conducting can be neglected and meanwhile, the functions of temperature in equations need to be replaced by functions of plastic work. The material constants in the revised equations can be determined by comparison of the one-dimensional calculations with the experiments of Hopkinson bar. It can be seen from the comparison of the calculation with the experiment of a tungsten alloy projectile impacting a three-layer plate that the B±P constitutive equations in that the functions of temperature were replaced by the functions of plastic work can be used to analysis of high velocity impact. Ó

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“…According to the Hall-Petch law, it results in increase of the conventional yield strength. Increase of strain rate to some critical values (∼ 10 7 s −1 ) causes fast growth of dislocation density and formation of twins, which can be aggregated as packages consisting of tens of parallel micro twins [11,16]. In this case, the stationary yield strength grows much quicker than during slow (static) deformation, approaching its limiting value.…”

Section: Introductionmentioning

confidence: 99%

Development of wide-range constitutive equations for calculations of high-rate deformation of metals

Raevsky¹,

Aprelkov²,

Ignatova³

et al. 2010

EPJ Web of Conferences

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Abstract. For development of models of strength and compressibility of metals in wide range of pressures (up to several megabar) and strain ratesε ∼ 1 ÷ 10 8 s −1 , the method of dynamic tests is used. Since direct measurement of strength is impossible under complicated intensive high-rate loading, a formal model is created at first, and then it is updated basing on comparison with many experiments, which are sensitive to shear strength. Elastic-plastic, viscous-elastic-plastic and relaxation integral models became nowadays most commonly used. The basic unsolved problems in simulation of high-rate deformation of metals are mentioned in the paper.

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Shock viscosity and the prediction of shock wave rise times

Cited by 374 publications

References 17 publications

The onset of twinning in metals: a constitutive description

The onset of twinning in metals: a constitutive description

The application of B–P constitutive equations in finite element analysis of high velocity impact

Development of wide-range constitutive equations for calculations of high-rate deformation of metals

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