MSE2160 Problem Set 5 Chapters 8 and 9: Deformation and Failure, due electronically via Canvas on Wednesday, March 20th 1. (a) Show, for a tensile test, that %CW = (+++) * 100 if there is no change in specimen volume during the deformation process (i.e., Aolo = Aala). (b) Using the result of part a, compute the percent cold work experienced by naval brass (the stress-strain behavior of which is shown below) when a stress of 400 MPa is applied. Stress (MPa) 500 Tensile strength 450 MPa (65,000 psi) 400 103 psi 300 MPa 40 70 60 40 40 Stress (10³ psi) 50 30 200- 200 Yield strength 30 250 MPa (36,000 psi) 20 100 20 10 100 0 0.10 0.20 Strain 0.005 0 0.30 0.40 10 2. The average grain diameter for a brass material was measured as a function of time at 650 °C and data was collected. After 30 minutes, the grain size was 3.9x102 mm and after 90 minutes the grain size was 6.6x102 mm. a. What was the initial grain size? b. What is the grain size after 150 minutes? c. If the initial yield strength is 160 MPa and the coefficient ky is 12 MPa-mm¹², what are the yield strengths after 30, 90, and 150 minutes? d. If we wait a very long time at 650 °C, what will be the yield strength of this brass material? 3. A wing component of an aircraft is fabricated from an aluminum alloy that has a plane strain fracture toughness of 40 MPa-m1/2. It has been determined that fracture occurs at a stress of 365 MPa when the maximum internal crack length is 2.5 mm. a. Over time, it was found that cracks grow to a maximum length of 4 mm. Compute the stress level at which fracture will occur. b. If we wish to utilize this component at a stress level of 500 MPa with an engineering safety factor of 4, what will be the maximum internal crack length we can allow? 4. A tensile specimen was found to have a surface crack with a depth of 0.4 mm and radius of curvature of 0.1 mm. a. Compute the magnitude of stress at the tip of the crack when the externally applied stress σ is 100 MPa. b. If this specimen is made of an aluminum alloy with a yield strength of 345 MPa, what will happen to the crack? c. Using a factor of safety of 3, what will the radius of curvature at tip of the crack need to be in order to ensure no deformation will occur near the crack?