Thermomechanics of Cosserat medium: modeling adiabatic shear bands in metals

Abstract

During most metal manufacturing processes, the medium deforms by generating large quantities of plastic strain at relatively high strain rates, inevitably inducing rises in temperature. Metals characterized by low thermal conductivity properties might locally retain high temperatures, consequently undergoing thermal softening. The classical balance laws governing the continuum equilibrium show severe mesh sensitivity if they were numerically discretized through Finite Element Methods. Furthermore, the plastic deformation tends to localize in narrow areas whose characteristic length is comparable to grain size, thereby requiring the adoption of theories able to predict sizeeffects. In this manuscript we demonstrate that the Cosserat medium is able to overcome these issues related to manufacturing processes simulation. We first provide a thermodynamically-consistent description of the Cosserat medium, and then we propose a method to calibrate the two additional characteristic lengths introduced by the Cosserat medium description by enriching the model with the TANH stress flow rule under adiabatic conditions.

A micropolar isotropic plasticity formulation for non‐associated flow rule and softening featuring multiple classical yield criteria

“…Tensors of the first, second, third and fourth orders will be referred to in the compact representation using bold letters of any case, but for the purpose of clarity, the order will be distinguished, similarly to Russo et al 7 ,. using a combination of bars and tildes below the letter.…”

“…Eringen 17 ), however, since an energy approach is adopted in the coming sections, this is also used for their formulation, by applying the Green's theorem to the work rate (similarly to e.g. Russo et al 7 …”

“…It should be noted that whilst the spherical component of the strain tensor is indeed not associated to distortion, the principal diagonal terms of the curvature tensors account for the rate of variation along one axis of the component along the same axis of the rotation vector of the micro‐volumes , that is, they define a torsional curvature (e.g. Russo et al 7 …”

“…Many available constitutive models for the Cosserat continuum are independent of the Lode's angle and the adopted yield and plastic potential surfaces have a circular deviatoric section, for example, those defined by the von Mises and the Drucker‐Prager criteria (e.g. Altenbach and Eremeyev 6 , Russo et al., 7 Sabet and De Borst 4 ). However for many applications, such as those in the geotechnical domain, that is too much of a crude assumption, which, depending on how parameters are calibrated, results in excessively unconservative or overconservative predictions.…”

A multifield continuum model for the description of the response of microporous/microcracked composite materials

“…We particularly focus on multiscale approaches and, among the latter kind of non-local models, continua with affine microstructure [42] or continua with configurational forces [43], as [44,45,46]. In all non local models, there are internal length scales, and the microstructure is revealed by the dispersive character of propagating waves, which results in a frequency-dependent wave propagation speed and consequent space and time distorsion of a non-monochromatic propagating disturbance [20,21,45,47,48,49,50].…”