A simple mathematical theory of finite distortional latent hardening in single crystals

A simple (one-parameter) hardening law is proposed which accounts for the perpetuation of finite single slip, beyond the symmetry line, in the tensile test of f. c. c. crystals and reduces to Taylor’s rule at infinitesimal strain. This new law emerges as the simplest case of a general mathematical theory of finite deformation of elastic-plastic crystals. The fully anisotropic finite-distortional hardening of latent slip systems predicted by the simple theory is in qualitative agreement with experiment.

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Latent hardening in single crystals - I. Theory and experiments

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1991.0127 ◽

1991 ◽

Vol 435 (1893) ◽

pp. 1-19 ◽

Cited By ~ 92

Keyword(s):

Single Crystals ◽

Creep Behaviour ◽

Time Dependent ◽

Slip Systems ◽

Initial Yield Stress ◽

History Of ◽

Latent Hardening ◽

Physical Phenomena ◽

Theory And Experiments ◽

Flow Theory Of Plasticity

Accurate measurements of the initial yield stress on previously latent slip systems as well as a reinterpretation of widely reported experimental observations have led to a new description of single crystal hardening within the framework of the incremental (flow) theory of plasticity. Slip interactions and the history of slips are essential in explaining well-known physical phenomena such as stage II deformation and latent hardening. Guidelines for deriving the set of instantaneous hardening moduli are given in terms of inequality restrictions. Although time-independent behaviour is assumed throughout the present study, these restrictions are expected to apply as well to time-dependent creep behaviour at low to intermediate temperatures. In Part II, a complete constitutive theory is developed with analytical forms given for the instantaneous hardening moduli.

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Further Investigation of a New Hardening Law in Crystal Plasticity

Journal of Applied Mechanics ◽

10.1115/1.3424352 ◽

1978 ◽

Vol 45 (3) ◽

pp. 500-506 ◽

Cited By ~ 24

Author(s):

K. S. Havner ◽

A. H. Shalaby

Keyword(s):

Face Centered Cubic ◽

Slip Systems ◽

Anisotropic Hardening ◽

Active System ◽

Cubic Crystals ◽

Hardening Law ◽

Crystallographic Symmetry ◽

Latent Hardening ◽

Face Centered

A simple theory of latent hardening in crystals, recently proposed by the authors [1], is applied to the determination of anisotropic hardening in slip systems of face-centered cubic crystals in the tensile test, based upon a parabolic resolved-shear-stress versus slip curve in the active system. The theory predicts the generally observed continuation of finite single slip beyond the crystallographic symmetry line. Moreover, the predicted diversity of finite distortional hardening among latent slip systems is in qualitative agreement with experiment.

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Room-temperature deformation of single crystals of ZrB2 and TiB2 with the hexagonal AlB2 structure investigated by micropillar compression

Scientific Reports ◽

10.1038/s41598-021-93693-9 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Zhenghao Chen ◽

Bhaskar Paul ◽

Sanjib Majumdar ◽

Norihiko L. Okamoto ◽

Kyosuke Kishida ◽

...

Keyword(s):

Single Crystals ◽

Plastic Flow ◽

Room Temperature ◽

Resolve Shear Stress ◽

Temperature Deformation ◽

Slip Systems ◽

Compression Tests ◽

Plastic Deformation Behavior ◽

Bulk Single Crystals ◽

Micropillar Compression

AbstractThe plastic deformation behavior of single crystals of two transition-metal diborides, ZrB2 and TiB2 with the AlB2 structure has been investigated at room temperature as a function of crystal orientation and specimen size by micropillar compression tests. Although plastic flow is not observed at all for their bulk single crystals at room temperature, plastic flow is successfully observed at room temperature by the operation of slip on {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 3> in ZrB2 and by the operation of slip on {1$${\bar{1}}$$ 1 ¯ 00}<0001> and {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 0> in TiB2. Critical resolve shear stress values at room temperature are very high, exceeding 1 GPa for all observed slip systems; 3.01 GPa for {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 3> slip in ZrB2 and 1.72 GPa and 5.17 GPa, respectively for {1$${\bar{1}}$$ 1 ¯ 00}<0001> and {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 0> slip in TiB2. The identified operative slip systems and their CRSS values are discussed in comparison with those identified in the corresponding bulk single crystals at high temperatures and those inferred from micro-hardness anisotropy in the early studies.

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A N. Bourbaki Type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

Georgian Mathematical Journal ◽

10.1515/gmj.1999.179 ◽

1999 ◽

Vol 6 (2) ◽

pp. 179-190

Author(s):

SH. Pkhakadze

Keyword(s):

General Theory ◽

Mathematical Theory ◽

General Mathematical Theory

Abstract A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory .

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