Finite compressibility and strain hardening in elasto-plastic models of amorphous matter.
ORAL
Abstract
We study a mesoscopic elasto-plastic model of amorphous matter with varying dimensionless compression modulus, K/μ, where K and μ are the compression and shear moduli.
We study both cyclic shear with amplitude Γ and forward steady shear.
In cyclic shear, the terminal behavior is, in order of increasing Γ: i) trivially elastic, ii) hysteretic but with microscopically reversible limit cycles, iii) diffusive with no return to previously visited configurations.
We show that the the transition between i) and ii) at the onset point Γ_0 is determined by the so-called Eshelby back stress, σ_0, which depends on the Poisson ratio.
The result is that systems which are more compressible, with smaller K/μ, are effectively harder with a higher value of Γ_0 and a correspondingly larger regime of purely elastic behavior in cyclic loading.
In forward shear, we show that σ_0 plays a similar role where lower K/μ results in a higher value of the steady state flow stress, σ_y.
We show how increasing K/μ results in an increase in the amplitude of the stress redistribution after a local yielding event without resulting in a change in the net stress relaxation from the event and discuss how this is related to the assumptions which go into mean-field descriptions of amorphous solids.
Another striking feature of the model is the emergence of a complex hardening behavior in the absence of any microspcopic ad-hoc hardening parameters or rules.
In particular, we observe a transition between a kinematic and an isotropic hardening behavior precisely at the shear cycling amplitude Γ_0 associated with the hysteresis transition.
The enhanced plastic response for incompressible systems is also seen in amorphous alloys where it is usually attributed to excess free volume, while in the present model, it arises simply as a consequence of the dependence of the Eshelby backstress on the Poisson ratio.
Our results should have important implications for amorphous metallic alloys or other glassy systems (such as colloidal glasses, emulsions, etc.) where K/μ can vary with composition, age, quench procedure, or mechanical processing history.
We study both cyclic shear with amplitude Γ and forward steady shear.
In cyclic shear, the terminal behavior is, in order of increasing Γ: i) trivially elastic, ii) hysteretic but with microscopically reversible limit cycles, iii) diffusive with no return to previously visited configurations.
We show that the the transition between i) and ii) at the onset point Γ_0 is determined by the so-called Eshelby back stress, σ_0, which depends on the Poisson ratio.
The result is that systems which are more compressible, with smaller K/μ, are effectively harder with a higher value of Γ_0 and a correspondingly larger regime of purely elastic behavior in cyclic loading.
In forward shear, we show that σ_0 plays a similar role where lower K/μ results in a higher value of the steady state flow stress, σ_y.
We show how increasing K/μ results in an increase in the amplitude of the stress redistribution after a local yielding event without resulting in a change in the net stress relaxation from the event and discuss how this is related to the assumptions which go into mean-field descriptions of amorphous solids.
Another striking feature of the model is the emergence of a complex hardening behavior in the absence of any microspcopic ad-hoc hardening parameters or rules.
In particular, we observe a transition between a kinematic and an isotropic hardening behavior precisely at the shear cycling amplitude Γ_0 associated with the hysteresis transition.
The enhanced plastic response for incompressible systems is also seen in amorphous alloys where it is usually attributed to excess free volume, while in the present model, it arises simply as a consequence of the dependence of the Eshelby backstress on the Poisson ratio.
Our results should have important implications for amorphous metallic alloys or other glassy systems (such as colloidal glasses, emulsions, etc.) where K/μ can vary with composition, age, quench procedure, or mechanical processing history.
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Presenters
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Craig E Maloney
- Northeastern University