Problem 1 (Problem 3.5 from the textbook) In a tensile test on a steel specimen,

Question

Problem 1 (Problem 3.5 from the textbook) In a tensile test on a steel specimen, true strain = 0.11 at a stress of 245 MPa. When true stress = 340 MPa, true strain = 0.31. Determine the strength coefficient and the strain-hardening exponent in the flow curve equation. Problem 2 A bending test is used on an experimental cemented carbide material. Based on previous testing of the material, its transverse rupture strength = 1000 MPa, what is the anticipated load at which the specimen is likely to fail, given that its width = 15 mm, thickness = 7.5 mm, and length = 50 mm? Problem 3 A batch of annealed steel has just been received from the vendor. It is supposed to have a tensile strength in the range 60,000 - 70,000 lb/in2. A Brinell hardness test in the receiving department yields a value of HB = 118. (a) Does the steel meet the specification on tensile strength? (b) Estimate the yield strength of the material.

Explanation / Answer

Here is the solution for problem # 1. Please post all other problems separately.

Solution#1

Using relation = K n

For first case, when = 245 MPa and = 0.11 above relation becomes

(245 MPa) = K (0.11)n     ............................ (1)

For second case, when = 340 MPa and = 0.31 above relation becomes

(340 MPa) = K (0.31)n     ............................ (2)

Dividing equation (1) by (2) we get

(245 / 340) = (0.11 / 0.31)n

0.7206 = (0.3548)n

ln(0.7206) = n ln(0.3548)

n = 0.316

Using this value of n in equation (1)

(245) = K (0.11)0.316

K = 492.14

strength coefficient = K = 492.14

strain-hardening exponent = n = 0.316

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