MAT 33 - Fall 2016 Homework #6 Due: 10/24/2016 1.) A cylindrical specimen of some metal alloy 12mm in diameter is stressed elastically in tension. A force of 26,500N produces a reduction in specimen diameter of 8.5 x 10-3 mm. Calculate Poisson's ratio for this material if its Modulus of Elasticity is 115GPa. 2). A copper bar of 9mm square section is subjected to a tensile load that increases its length from 90 to 92mm. The value of Poisson's ratio for copper is 0.323. Calculate the new dimensions of the bar. 3.) The flexural strength and associated volume fraction porosity for two specimens of the same ceramic material are as follows. Porosity (%) flexural strength fs (MPa) 180 10 140 15 (i) Calculate the flexural strength for the non-porous material. (ii) Calculate the flexural strength for 18 vol% porosity? (iii) At what vol% porosity would be the flexural strength for this material be 90MPa? 4.) A three point bend test was performed on MgO sample with a circular cross section with a radius of 5 mm; the specimen fractured at a load of 2200 N when the distance between the support points was 45 mm. Another test is to be performed on a specimen of this same material with a same length of 45 mm, but one that has a square cross-section with a length of 6 mm on each edge. At what load would you expect this specimen to fracture if the support point separation is maintained at 45 mm? 5.) A cylindrical specimen of aluminum having a diameter of 22.5 mm and a gauge length of 50.800 mm is pulled in tension. Use the load-elongation characteristics shown in the following table to complete parts (a) through (h). Load (N) Length (mm) 0 50.800 7,330 50.851 15,100 50.902 23,100 50.952 30,400 51.003 34,400 51.054 38,400 51.308 41,300 51.816 44,800 52.832 46,200 53.848 47,300 54.864 47,500 55.880 46,100 56.896 44,800 57.658 42,600 58.420 36,400 Fracture 59.182 Fracture a.) Plot the data as engineering stress versus engineering strain (recommend to use software, e.g. Excel) b.) Calculate the modulus of elasticity c.) Determine the yield strength at a strain offset of 0.002 d.) Determine the tensile strength of this alloy e.) What is the ductility in % elongation? f.) Compute the modulus of resilience g.) Determine the true stress and true strain at the tensile strength h.) This material is used for the expecting load of 20,000 N. Determine the minimum required diameter assuming a factor of safety 3