A metal sample is constrained on one side by a rigid substrate. A uniform compressive stress...

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A metal sample is constrained on one side by a rigid substrate. A uniform compressive stress of zz is applied to the material, as shown in Problem- Figure 2.1. x Z Material Substrate Problem-Figure 2.1: Material with substrate of consideration. Assume that the contact between the material and the substrate is frictionless. However, this time, the stress zz is significant enough that the material undergoes plastic deformation. For the sake of simplicity, assume that this material is an isotropic, linear-elastic material, with moduli {E, v}, and elastic-perfectly plastic, with a yield stress 0. Problem 2.1 (6 points) Compute the stress tensor in the initial, linear-elastic state. Problem 2.2 (4 points) Compute the stress deviator, o dev ME 108 Problem Set 6 2 of 3 Do not distribute outside of course [2022-2023 Term 2 (Spring)] ME 108 (Mechanical Behavior of Engineering Materials) Problem Set 6 Dingyi Sun UC Berkeley Assigned: Friday, March 3, 2023 | Due: 11:59 pm, Friday, March 10, 2023 Problem 2.3 (8 points) Derive the yield condition of the material assuming a Mises criterion. Problem 2.4 (8 points) Derive the yield condition of the material assuming a Tresca criterion. Assume that |v| < 1. Problem 2.5 (4 points) Suppose that our material of interest is cast iron A536 (65-45-12). What is the numerical value of the stress zz required to induce plasticity in each yield criterion? Look up the elastic moduli and yield stress as needed. A metal sample is constrained on one side by a rigid substrate. A uniform compressive stress of zz is applied to the material, as shown in Problem- Figure 2.1. x Z Material Substrate Problem-Figure 2.1: Material with substrate of consideration. Assume that the contact between the material and the substrate is frictionless. However, this time, the stress zz is significant enough that the material undergoes plastic deformation. For the sake of simplicity, assume that this material is an isotropic, linear-elastic material, with moduli {E, v}, and elastic-perfectly plastic, with a yield stress 0. Problem 2.1 (6 points) Compute the stress tensor in the initial, linear-elastic state. Problem 2.2 (4 points) Compute the stress deviator, o dev ME 108 Problem Set 6 2 of 3 Do not distribute outside of course [2022-2023 Term 2 (Spring)] ME 108 (Mechanical Behavior of Engineering Materials) Problem Set 6 Dingyi Sun UC Berkeley Assigned: Friday, March 3, 2023 | Due: 11:59 pm, Friday, March 10, 2023 Problem 2.3 (8 points) Derive the yield condition of the material assuming a Mises criterion. Problem 2.4 (8 points) Derive the yield condition of the material assuming a Tresca criterion. Assume that |v| < 1. Problem 2.5 (4 points) Suppose that our material of interest is cast iron A536 (65-45-12). What is the numerical value of the stress zz required to induce plasticity in each yield criterion? Look up the elastic moduli and yield stress as needed.