A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall-Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or materials that contain unequal grain size distributions. These deficiencies can be overcome by incorporating both grain size and orientation characteristics into crystal plasticity theory. Homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for high purity α-titanium are recovered through orientation imaging microscopy coupled with the chord length distribution. A comparison between the new method and the traditional viscoplastic Taylor approach is made by evaluating yield surface plots.
","abstract_html":"<p>A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall-Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or materials that contain unequal grain size distributions. These deficiencies can be overcome by incorporating both grain size and orientation characteristics into crystal plasticity theory. Homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for high purity α-titanium are recovered through orientation imaging microscopy coupled with the chord length distribution. A comparison between the new method and the traditional viscoplastic Taylor approach is made by evaluating yield surface plots.</p>","abstract_has_math":false,"creators":["Fromm, Bradley S."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:29:03Z","subjects":["texture","strength","grain size","viscoplasticity","yield surface","titanium","Mechanical Engineering"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/1275","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Fromm, Bradley S."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-12-21T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["texture","strength","grain size","viscoplasticity","yield surface","titanium","Mechanical Engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/1275","https://scholarsarchive.byu.edu/context/etd/article/2274/viewcontent/ETD_CISOPTR_1279.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ira A. Fulton College of Engineering and Technology; Mechanical Engineering"]},{"key":"dc:description.abstract","label":"Abstract","values":["A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall-Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or materials that contain unequal grain size distributions. These deficiencies can be overcome by incorporating both grain size and orientation characteristics into crystal plasticity theory. Homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for high purity α-titanium are recovered through orientation imaging microscopy coupled with the chord length distribution. A comparison between the new method and the traditional viscoplastic Taylor approach is made by evaluating yield surface plots.
"]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Incorporating Grain Size Effects in Taylor Crystal Plasticity"]}]}],"canonical_facts":{"dc:creator":["Fromm, Bradley S."],"dc:date":["2007-12-21T08:00:00Z"],"dc:description":["Ira A. Fulton College of Engineering and Technology; Mechanical Engineering"],"dc:description.abstract":["A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall-Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or materials that contain unequal grain size distributions. These deficiencies can be overcome by incorporating both grain size and orientation characteristics into crystal plasticity theory. Homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for high purity α-titanium are recovered through orientation imaging microscopy coupled with the chord length distribution. A comparison between the new method and the traditional viscoplastic Taylor approach is made by evaluating yield surface plots.
"],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/1275","https://scholarsarchive.byu.edu/context/etd/article/2274/viewcontent/ETD_CISOPTR_1279.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["texture","strength","grain size","viscoplasticity","yield surface","titanium","Mechanical Engineering"],"dc:title":["Incorporating Grain Size Effects in Taylor Crystal Plasticity"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:29:03Z"}