Question

PROBLEM # | A TENSILE TEST WAS PERFORMED ON A SAMPLE OF INITIAL LENGTH = 2.00" AND INITIAL DIAMETER = 0.500" GIVEN THE FOLLOWING DATA, CONSTRUCT THE STRESS - STRAIN DIAGRAM UP TO WHERE P : 12,700 LBS. SHOW THE PROPORTIONAL LIMIT AND DE TERMINE THE MODULUS OF ELASTICITY. Load Deformation Load Deformation (lb) (in.) (lb). (in.) 1,500 3,100 4,700 6,200 8,000 9,500 11,000 12,000 12,300 12,500 12,700 12,700 12,500 0.0004 0.0010 0.0016 0.0022 0.0026 0.0032 0.0035 0.0041 0.0051 0.0071 0.0100 0.0131 0.0150 12,300 12,200 12,000 13,000 15,000 16,000 17,500 19,000 19,600 20,100 20,100 18,700 17,200 16,400 0.0170 0.0200 0.0275 0.0330 0.0400 0.0500 0.0680 0.1080 0.1510 0.2010 0.2600 0.3300 0.4100 0.4500 (fracture)

Answer 1

"Given Data: - Initial length = 2"" Initial diameter = 0.500"" Initial Area = pi/4 times (0.5)^2 = 0.19634 in^2 To find: - Stress- strain diagram: - Step-1: - we need to calculate strain for each individual load and Reformation: - Load (lb) = 0, Reformation (in) = 0 sigma = 0/A = Strain (E) = Reformation/Initial length = 0 Load (lb) = 1500, Reformation (in) = 0.0004 Load (lb) = 15000.19634 = 7639.44_epsilon = 0.004/2 = 0.0002 Load (lb) = 3100, Reformation (in) = 0.0010 sigma = 3100/0.19634 = 15788.94 lb/in^2_ epsilon = 0.0010/2 = 0.0005 Load (lb) = 4700, Reformation (in) = 0.0016 sigma = 4700/0.19634 = 23938 lb/in^2 epsilon = 0.0016/2 = 0.0008 Load (lb) = 6200 Reformation (in) = 0.0022 sigma = 6200/0.19634 = 31577.87 lb/in^2 epsilon = 0.0022/2 = 0.001 Load (lb) = 8000, Reformation (in) = 0.0026 sigma = 8000/0.19634 = 40745.65 lb/in^2, epsilon = 0.0026/2 = 0.0013 Load (lb) = 9500, Reformation (in) = 0.0032 sigma = 9560/0.19634 = 48385.45 lb/in^2 epsilon = 0.0032/2 = 0.0016 "

Answer 2

"Given Data: - Initial length = 2"" Initial diameter = 0.500"" Initial Area = pi/4 times (0.5)^2 = 0.19634 in^2 To find: - Stress- strain diagram: - Step-1: - we need to calculate strain for each individual load and Reformation: - Load (lb) = 0, Reformation (in) = 0 sigma = 0/A = Strain (E) = Reformation/Initial length = 0 Load (lb) = 1500, Reformation (in) = 0.0004 Load (lb) = 15000.19634 = 7639.44_epsilon = 0.004/2 = 0.0002 Load (lb) = 3100, Reformation (in) = 0.0010 sigma = 3100/0.19634 = 15788.94 lb/in^2_ epsilon = 0.0010/2 = 0.0005 Load (lb) = 4700, Reformation (in) = 0.0016 sigma = 4700/0.19634 = 23938 lb/in^2 epsilon = 0.0016/2 = 0.0008 Load (lb) = 6200 Reformation (in) = 0.0022 sigma = 6200/0.19634 = 31577.87 lb/in^2 epsilon = 0.0022/2 = 0.001 Load (lb) = 8000, Reformation (in) = 0.0026 sigma = 8000/0.19634 = 40745.65 lb/in^2, epsilon = 0.0026/2 = 0.0013 Load (lb) = 9500, Reformation (in) = 0.0032 sigma = 9560/0.19634 = 48385.45 lb/in^2 epsilon = 0.0032/2 = 0.0016 "