1971 journal article

A discrete model for the prediction of subsequent yield surfaces in polycrystalline plasticity

International Journal of Solids and Structures, 7, 719–730.

By: K. Havner n

co-author countries: United States of America 🇺🇸
Source: NC State University Libraries
Added: August 6, 2018

A discrete model suitable for the analysis of polycrystalline aggregate response under macroscopically uniform, quasi-static loading is developed, with particular emphasis on the characteristics of subsequent yield surfaces in stress or strain space. Internal stress and deformation states are determined from approximating, piecewise linear infinitesimal displacement fields within crystal grains, based upon broadly defined constitutive behavior which permits inclusion of cubic or hexagonal crystal anisotropy and relatively general hardening laws over crystallographic slip systems. Appropriate aggregate matrices are established as symmetric, positivedefinite, and internal fields corresponding to the solution of the discrete model are proved to be unique. It is further shown that the final calculation of incremental crystal shears can be posed as a quadratic programming problem. Oпpeдeляeтcя диcкpeтнaя мoдeль, пpигoднaя для aнaдизa пoBeдeния пoликpиcтaлличecкoгo зaпoлнитeля пoд Bлияниeм мaкpocкoпичecки oднopoднoй, кBaзиcтaмичecкoй нaгpyзки, co cпeциaльным yчeтoм чapaктepиcтик пoBepчнocтeй тeчeния B пpocтpaнcтBe нaпpяжeний и дeфopмaции. Bнyтpeнниe нaпpяжeния и дeфopмaции oпpeдeляютcя пyтeм пpиближeния кycoчныч, линeйныч, инфинитeзимaльныч пoлeй дeфopмaций c кpиcтaлличecкими зepнaми, нa ocнoBe шиpoкo oпpeдeлeннoгo кoнcтцтyтиBнoгo пoBeдeния, кoтopoe дaeт Boзмoжнocть Bключить кyбичecкyю или гeкcaгoнaльнyю кpиcтaлличecкyю aнизoтpoпию и cooтBecтBeннo oбшиe зaкoны yпpoчнeния для кpиcтaлличecкич cиcтeм cкoльeнмя. BыBoдятcя cooтBecтByющиe мaтpицц зaпoлнитeля B кaчecтBe cиммeтpичecкцч и пoлoжитeльнo oпpeдeлeнныч. Bнyтpeнниe пoля, cooтBecтByющиe peшeнию диcкpeтнoй мoдeли, oкaзыBaютcя eдинcтBeнными. Дaлee yкaзaнo, чтo ocтaтoчнoe peшeниe для пpиpaщeния cдBигoB кpиcтaллoB мoжнo paccмaтpиBaть B кaчecтBe зaдaчи кBaдpaтaчeoкoиo пpoгpaммиpoBaния.