Principles And Practices Of Manufacturing Processes Homework 2 - Assignment

Homework 2 Problem 1 (14 points) During the tensile loading for a metallic material sample in the cylindrical shape, “necking” occurs at a true strain of ε = 0.16. The material strain hardening index is n = 0.16, and the strength coefficient is K = 300 MPa. The cylindrical sample initial diameter is 10 mm. (1) What is the tensile force (loading) in the unit of Newton that can generate necking in the sample. (2) Assume the sample fracture occurs at a true strain of ε = 0.2, what is the toughness of the material? Problem 2 (10 points): In a tensile test, the initial length of the sample testing portion is L 0 = 20 mm, and the sample initial cross sectional area is A0 = 25 mm2. Table 1 below shows the engineering stress - engineering strain relation obtained from the test before the material reaches the necking point. Please convert the engineering stress – engineering strain relation to the true stress – true strain relation in Table 2. Table 1 Engineering stress (MPa) Engineering strain 320 440 0.07 0.12 Table 2 True stress (MPa) True strain Problem 3 (12 points): A metal workpiece in the cylindrical shape (where the original diameter is 20 mm and original height is 60 mm) is compressed at a high temperature of 500 K to a smaller height by a hydraulic press that operates at v = 30 mm/s. It is assumed that m = 0.05 and C = 200 MPa. The friction effect is neglected. Please determine the pressing force needed if the workpiece is compressed to (1) 45 mm, and (2) 30 mm Problem 4 (4 points): For a low carbon steel sample, its Brinell hardness number is BHN = 110.