Kink band and shear band localization in anisotropic perfectly plastic solids

Nizolek, Thomas J.; Pollock, Tresa M.; McMeeking, Robert M.

doi:10.1016/j.jmps.2020.104183

Title: Kink band and shear band localization in anisotropic perfectly plastic solids

Journal Article · Wed Oct 28 00:00:00 EDT 2020 · Journal of the Mechanics and Physics of Solids

DOI:https://doi.org/10.1016/j.jmps.2020.104183· OSTI ID:1772459

^[1]; Pollock, Tresa M. ^[2]; McMeeking, Robert M. ^[3]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of California, Santa Barbara, CA (United States)
Univ. of California, Santa Barbara, CA (United States)
Univ. of California, Santa Barbara, CA (United States); Univ. of Aberdeen, Scotland (United Kingdom); Leibniz Inst. for New Materials (INM), Saarbrucken (Germany)

Shear-driven strain localization has been observed in a wide variety of materials and may take the form of shear bands or kink bands. Based on observations of kink bands in plastically anisotropic metallic nanolaminates and single crystal metals, here we posit that, for the specific case of isochoric deformation, the kinematics of kink band formation are indistinguishable from those of plane strain shear band formation. The only distinction between shear bands and kink bands in these systems would then be that kink bands ‘lock up’ at a particular value of material rotation while shear bands may progress to arbitrarily high strains. In order to investigate whether strong material anisotropy is sufficient to arrest shear localization at a geometry that matches the classic kink band geometry, we model the development of a band of simple shear within an anisotropic perfectly plastic material. The resulting analytical model provides the stress state needed to maintain the kinematics of simple shear as a function of material anisotropy, deformation band orientation, and shear strain (or equivalently, material rotation). It is found that plastic anisotropy can promote either kink band or shear band formation depending on the loading orientation. When the deviatoric stress is positive parallel to the plane of anisotropy, shear localization may progress without bound and a shear band is produced. When the deviatoric stress is negative parallel to the plane of anisotropy, shear localization is arrested after a certain material rotation, resulting in a kink band. Examination of the requisite applied stress state during kink band formation provides an explanation for the experimentally-observed ‘lock up’ geometry. Solutions for the band boundary inclination angle are obtained and used to provide bounds on permissible band angles for both shear bands and kink bands.

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Research Organization:: Texas A & M Univ., College Station, TX (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003857; 20200182DR; 89233218CNA000001

OSTI ID:: 1772459

Alternate ID(s):: OSTI ID: 1699471; OSTI ID: 1776118

Report Number(s):: LA-UR-20-25448; TRN: US2206968

Journal Information:: Journal of the Mechanics and Physics of Solids, Vol. 146; ISSN 0022-5096

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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