A Constitutive Relation for Deformation Twinning in Body Centered Cubic Metals

Armstrong, Ronald W.; Worthington, P.J.

doi:10.1007/978-1-4615-8696-8_22

Cited by 30 publications

(24 citation statements)

References 21 publications

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“…The slip-twinning transition pressure can be obtained from the analysis presented by Meyers et al [7] for monocrystals with appropriate changes to the parameters. The slip stress is expressed by the Zerilli-Armstrong equation for BCC metals [8] and the twinning stress by the ArmstrongWorthington equation [9]. The stresses are related to the shock pressure through the Swegle-Grady equation with coefficients from Furnish [10].…”

Section: Resultsmentioning

confidence: 99%

Laser compression of nanocrystalline tantalum

Lu¹,

Maddox²,

Remington³

et al. 2012

AIP Conference Proceedings

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Abstract. Nanocrystalline tantalum was prepared by high pressure torsion from monocrystalline [100] stock, yielding a grain size of 70nm. It was subjected to laser driven compression at energy levels of ~ 350 J to ~ 850 J in the Omega facility (LLE, U. of Rochester) with corresponding pressures as high as ~ 170 GPa. The laser beam created a crater of significant depth (~ 100 µm). Transmission electron microscopy (TEM) revealed dislocations in the grains but no twins in contrast with monocrystalline tantalum. Hardness measurements were conducted and show the same trend as single crystalline tantalum. The grain size was found to increase close to the energy deposition surface due to the thermomechanical excursion.

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Section: Resultsmentioning

confidence: 99%

Laser compression of nanocrystalline tantalum

Lu¹,

Maddox²,

Remington³

et al. 2012

AIP Conference Proceedings

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show abstract

“…The slip stress is expressed by the Zerilli-Armstrong equation for BCC metals [10] and the twinning stress by the Armstrong-Worthington equation [11]. The stresses arte related to the shock pressure through the Swegle-Grady equation with coefficients from Furnish [12].…”

Section: Resultsmentioning

confidence: 99%

Laser compression of monocrystalline tantalum

Lu¹,

Maddox²,

Remington³

et al. 2012

AIP Conference Proceedings

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[111] was subjected to laser driven compression at laser energies of 350 to 685 J, generating shock amplitudes varying from 15 to 100 GPa. The laser beam, with a beam spot diameter of ~1 mm, created a crater of significant depth (~ 80 to ~ 200 μm). Twins were observed just below the crater surface (~ 42 μm) by back-scattered SEM. Transmission electron microscopy (TEM) revealed profuse mechanical twinning within a distance from the energy deposition surface of ~ 1.5 mm at 684 J compression power, corresponding to an approximate pressure of 35 GPa. The decay of the pulse through the specimens was accompanied by an attendant decrease in the density of shock-generated dislocations. Microhardness measurements were conducted on the recovered samples. The experimentally measured dislocation densities and threshold stress for twinning are compared with predictions using analyses based on the constitutive response and the similarities and differences are discussed in terms of the mechanisms of defect generation.

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“…Another highly unique characteristic of twinning, first pointed out by Armstrong and Worthington [38], is the larger grain size dependence of the twinning stress, as compared with the slip stress. For most cases, a Hall-Petch relationship is obeyed, but with a slope, k T , that is higher than the one for slip, k S :…”

Section: The Slip -Twinning Transitionmentioning

confidence: 97%

“…Similar differences are observed for BCC, FCC, and HCP metals from a number of sources. The reason for this difference is not fully understood, but Armstrong and Worthington [38] suggest that twinning is associated with microplasticity, i.e. dislocation activity occurring before the onset of generalized plastic deformation, whereas the yield stress is associated with generalized plastic deformation.…”

Section: Iron (Bcc)mentioning

confidence: 99%

Constitutive description of dynamic deformation: physically-based mechanisms

Meyers

Benson

Vöhringer

et al. 2002

Materials Science and Engineering: A

170

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The response of metals to high-strain-rate deformation is successfully described by physically-based mechanisms which incorporate dislocation dynamics, twinning, displacive (martensitic) phase transformations, grain-size, stacking fault, and solution hardening effects. Several constitutive equations for slip have emerged, the most notable being the Zerilli-Armstrong and MTS. They are based on Becker's and Seeger's concepts of dislocations overcoming obstacles through thermal activation. This approach is illustrated for tantalum and it is shown that this highly ductile metal can exhibit shear localization under low temperature and high-strain-rate deformation, as predicted from the Zerilli-Armstrong equation. A constitutive equation is also developed for deformation twinning. The temperature and strain-rate sensitivity for twinning are lower than for slip; on the other hand, its Hall-Petch slope is higher. Thus, the strain rate affects the dominating deformation mechanisms in a significant manner, which can be quantitatively described. Through this constitutive equation it is possible to define a twinning domain in the WeertmanAshby plot; this is illustrated for titanium. A constitutive description developed earlier and incorporating the grain-size dependence of yield stress is summarized and its extension to the nanocrystalline range is implemented. Computational simulations enable the prediction of work hardening as a function of grain size; the response of polycrystals is successfully modeled for the 50 nm-100 m range. The results of shock compression experiments at pulse durations of 3 -10 ns (this is two-three orders less than gas-gun experiments) are presented. They prove that the defect structure is generated at the shock front; the substructures observed are similar to the ones at much larger durations. A mechanism for dislocation generation is presented, providing a constitutive description of plastic deformation. The dislocation densities are calculated which are in agreement with observations. The threshold stress for deformation twinning in shock compression is calculated from the constitutive equations for slip, twinning, and the Swegle-Grady relationship.

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A Constitutive Relation for Deformation Twinning in Body Centered Cubic Metals

Cited by 30 publications

References 21 publications

Laser compression of nanocrystalline tantalum

Laser compression of nanocrystalline tantalum

Laser compression of monocrystalline tantalum

Constitutive description of dynamic deformation: physically-based mechanisms

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