Micropolar crystal plasticity simulation of particle strengthening

Abstract

The yield and work hardening behavior of a small-scale initial-boundary value problem involving dislocation plasticity in an idealized particle strengthened system is investigated using micropolar single crystal plasticity and is compared with results for the same problem from dislocation dynamics simulations. A micropolar single crystal is a work-conjugate higher-order continuum that treats the lattice rotations as generalized displacements, and supports couple stresses that are work-conjugate to the lattice torsioncurvature, leading to a non-symmetric Cauchy stress. The resolved skew-symmetric component of the Cauchy stress tensor results in slip system level kinematic hardening during heterogeneous deformation that depends on gradients of lattice torsion-curvature. The scale-dependent mechanical response of the micropolar single crystal is dictated both by energetic (higher-order elastic constants) and dissipative (plastic torsion-curvature) intrinsic material length scales. We show that the micropolar model captures essential details of the average stress-strain behavior predicted by discrete dislocation dynamics and of the cumulative slip and dislocation density fields predicted by statistical dislocation dynamics.

A strengthening model of particle-matrix interaction based on an axisymmetric strain gradient plasticity analysis

“…The looping mechanism suggested by Orowan (1948) and the analytical solution introduced by Friedel (1964) for the cutting mechanism are both pioneering works within this approach. In recent years, more sophisticated methods have been used to study precipitation hardening, such as crystal plasticity (Ohashi (2004), Wulfinghoff and Böhlke (2015), Mayeur and McDowell (2015)) or dislocation dynamics (Chang et al (2012), Monnet (2015), Hu and Curtin (2021)).…”

Thermodynamic theory of crystal plasticity: Formulation and application to polycrystal fcc copper

“…With an eye towards greater abilities to predict the deformation response of metallic materials, there has been a systematic drive towards greater physical basis of continuum crystal models. Although dislocation motion is inherently discrete at the length scale of the Burgers vector, there have been many critical advances in continuum dislocation mechanics theories Parks, 1999, 2002;Gurtin, 2000;Gurtin and Needleman, 2005;Acharya et al, 2004;Anand et al, 2005;Busso and McClintock, 1996;Busso et al, 2000;Aifantis, 1992;Hutchinson, 1993, 1997;Zhu et al, 1995;Gerken and Dawson, 2008;Mayeur et al, 2011;Mayeur and McDowell, 2015) employing high level dislocation mechanics representations. More recently, theories for advanced representation of dislocation interaction and reactions have been formed and quantified using techniques of molecular dynamics and discrete dislocation dynamics (e.g., Kubin, 2013;Bulatov and Cai, 2007;Zepeda-Ruiz et al, 2017).…”

Thermomechanical conversion in metals: dislocation plasticity model evaluation of the Taylor-Quinney coefficient

“…Quantifying the stored energy of cold work will not only require accurate description of the mechanics of dislocation motion and interaction [22,23], but must also be done within a framework of thermodynamic consistency [24,25,26] to enable connection with experiment. A great deal of progress has been made over the years to represent the complex mechanics of dislocations within a continuum context [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. These important advancements in theory have been greatly facilitated by large-scale dislocation physics simulations to enable the study of details not yet available experimentally [e.g., 42,43,44,45,46,47,48,49,50,51].…”