Dislocation based strain gradient plasticity model for prediction of length scale dependent initial yield strength

• Many experimental studies have shown a plastic strengthening effect for structural length scales approaching microstructural dimensions. Both increases in initial yield strength and strain hardening have been observed. Over the last 30 years different strain gradient plasticity (SGP) theories have been developed in order to capture these length scale dependences. However, up to now no generally accepted theory has emerged. In the present presentation, focus is directed into a physically based SGP model for initiation of plastic deformation.The plastic behavior is governed by a dissipative part that primarily controls the hardening at moderate plastic strains and an energetic part that is of importance for the initiation of plastic flow. It is shown that a model based on the self-energies of dislocations can be translated into an internal free energy in terms of plastic strain gradients. Similarly, the dissipative part of the model is based on the Taylor model, which also gives a direct connection to dislocation theory.In this way, a physical connection is made between the SGP framework and dislocation mechanics. It is shown that the same length scale emerges for both the energetic and the dissipative part of the model. Apart from a non-dimensional factor of the order of unity, the length scale can be defined as the Burgers vector divided by the strain for initiation of plastic deformation.When the structural length scale approaches this microstructural length scale, strengthening effects result. The three-dimensional SGP model is specialized to the simple load cases of tensile tension with a passivation layer that prohibits plastic deformation on the surfaces as well as pure bending with free and fixed boundary conditions for plastic strain. Simulations of initial yield stress for varying thicknesses are compared to experimental observations reported in the literature. It is shown that the model in a good way can capture the length scale dependences. Also upper bound solutions are presented for a spherical void in an infinite volume as well as torsion of a cylindrical rod. The model is as well applied to derive a prediction for the Hall-Petch effect.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

Nyckelord

strain gradient plasticity

Hållfasthetslära

Solid Mechanics

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