Kinematic hardening 1 We have a linearly elastic linearly von Mises/Prager kinematic hardening plastic continuum with - yield strength s and - plastic hardening constant c(k). (1) The material is first subjected to a uniaxial load where 11 increases from 0 to 1.5. (2) After reaching , the material is unloaded. (3) Thereafter the material is loaded uniaxially in the e2 direction: o Compute at which plastic flow now begins. Kinematic hardening 2 A metal sheet is manufactured from a linearly elastic linearly von Mises/Prager kinematic hardening plastic material. Material properties: - elastic modulus E, - Poisson’s numb - yield strength and - plastic hardening constant c(k). The sheet is loaded in a sequence of three steps: (1) A first loading in biaxial tension: where increases from 0 to . (2) Thereafter the sheet is unloaded (3) Finally, the sheet is loaded in uniaxial compression , where decreases from 0. Compute at which plastic flow starts during load step (3). Kinematic hardening 3 A linearly elastic linearly kinematically von Mises/Prager hardening plastic material (yield strength and plastic hardening constant ) is used for manufacturing a circular rod with radius a. The rod is first loaded in uniaxial tension up to a plastic strain . After that it is unloaded. Finally a torque is applied. How large can this torque be before plastic flow begins?
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