It is an accepted fact that the dislocation accumulation on grain boundaries and at other interphase boundaries leads to plastic strain accumulation. So does any empirical relationship exist between plastic strain and dislocation density?
I have calculated the plastic strain using crystal plasticity simulations, and based on these results, I want to calculate the dislocation density using an empirical relation.
The relationship between plastic strain (also known as plastic deformation) and dislocation density is typically described by the well-known empirical relationship known as the "Kocks-Mecking relationship" or the "Ludwik-Hollomon equation." This relationship is widely used to model the flow stress in metals during plastic deformation, particularly in the context of strain hardening.
The Kocks-Mecking relationship is given as follows:
σ = K * ε^n
where: σ is the flow stress (true stress) of the material, ε is the plastic strain, K is the strength coefficient, and n is the strain-hardening exponent.
The strain-hardening exponent (n) characterizes the rate at which the material hardens as it undergoes plastic deformation. It is related to the dislocation density generated in the material during plastic deformation. The value of n depends on the specific material and its microstructure. For most metals, n typically falls in the range of 0.1 to 0.5.
A basic correlation is that flow stress varies as the square-root of dislocation density, if deformation is primarily sustained by dislocation glide. Flow stress is related to the exponent of strain, through constitutive equations like Kocks-Mecking, as mentioned by Krishna Kant Pandey
Since this exponent is often close to 0.5, the plastic strain and dislocation density are often (approximately) linearly related.
All of this is very coarse approximation; the empirical correlations would be altered by a number of complicating factors- temperature being an obvious one.
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