Summary
At any generic state, the tangent moduli and compliances of a metal crystal are derived in terms of its elastic moduli and compliances, and its physical slip system hardening modulih ij. The structure ofh ij is explored in conjunction with a mixed hardening law. It is found that the latent hardening moduli (h ij,i≠j) are related to the active hardening moduli (h ij,i+j) through the latent hardening coefficients, and that each active hardening modulus is composed of the selfhardening, single slip modulush and the latent structural-change hardening modulih ′ij . The theory is supplemented with some suggested functions forh andh ′ij , suitable for metal forming analysis. The derived constitutive relations are finally applied to calculate the tensile stress-strain relations of aluminum and zinc crystals under finite strains.
Zusammenfassung
Für jeden beliebigen Zustand werden die Tangentenmoduli und die Nachgiebigkeiten von Metallkristallen in Termen ihrer elastischen Moduli und der Nachgiebigkeiten und ihrer Verfestigungsmoduli des physikalischen Gleitsystemsh ij hergeleitet. Die Bauart vonh ij wird in Verbindung mit einem gemischten Verfestigungsgesetz erforscht. Es wird gefunden, daß die verborgenen Verfestigungsmoduli (h ij i≠j) auf die aktiven Verfestigungsmoduli (h ij,i+j) durch verborgene Verfestigungskoeffizienten bezogen werden können und daß jeder aktive Verfestigungsmodul sich aus dem Modulh der Einzelgleitung und dem verborgenen Strukturänderungsverfestigungsmodulh ′ij zusammensetzt. Die Theorie wird durch einige fürh undh ′ij vorgeschlagenen Funktionen, geeignet für die Analyse von Metallumformung, ergänzt. Die hergeleiteten Werkstoffgleichungen werden abschließend angewendet zur Berechnung von Zugspannungs-Verzerrungsbeziehungen von Aluminium und Zinkkristallen unter endlichen Verzerrungen.
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Weng, G.J. Constitutive relations of metal crystals at arbitrary strain. Acta Mechanica 41, 217–232 (1981). https://doi.org/10.1007/BF01177349
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DOI: https://doi.org/10.1007/BF01177349