Equation icon  Hall-Petch relationship

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Resource type: Equation
Description: Hall-Petch relationship illustrates the relationship between yield strength and grain size. Only holds down to ≈ 10nm grain size after which plastic deformation uses a different mechanism and yield strength decreases.

TeX format: \sigma_y =\sigma_0 + {k_y \over \sqrt{d}}

σy {\sigma_y} = yield stress (Pa){Pa}
σ0 {\sigma_0} = material constant (Pa){Pa}
ky {k_y }= strengthening coefficient (Pa.m½){Pa.m^{1/2}}
d {d}= grain diameter (m){m}

Keywords: Hall-Petch • grain size • grain • yield strength • yield stress • plastic deformation • grain boundary
Categories: Science approaches
Science approaches > Structure, bonding & defects > Grain boundaries
Science approaches > Strengthening mechanisms > Grain size hardening
Science approaches > Strengthening mechanisms > Recovery, recrystallisation & grain growth
Processes > Shaping > Deformation > Rolling
Processes > Shaping > Deformation > Sheet forming
Properties > Mechanical & thermal > Yield strength
Created by: The University of Liverpool
License: This resource is released under the Creative Commons Attribution license (2.0 UK: England & Wales).
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Date created: 02 July 2010
Date added: 04 August 2010
Resource ID: 3182