Problem

Using the data in Problem 7.29 and Equations 7.15, 7.16, and 7.18a, generate a true stress...

Using the data in Problem 7.29 and Equations 7.15, 7.16, and 7.18a, generate a true stress–true strain plot for aluminum. Equation 7.18a becomes invalid past the point at which necking begins; therefore, measured diameters are given in the following table for the last four data points, which should be used in true stress computations.

Load		Length		Diameter
N	lbf	mm	in.	mm	in.
46,100	10,400	56.896	2.240	11.71	0.461
44,800	10,100	57.658	2.270	11.26	0.443
42,600	9,600	58.420	2.300	10.62	0.418
36,400	8,200	59.182	2.330	9.40	0.370

(7.15)

(7.16)

(7.18a)

Problem 7.29

A cylindrical specimen of aluminum having a diameter of 0.505 in. (12.8 mm) and a gauge length of 2.000 in. (50.800 mm) is pulled in tension. Use the load–elongation characteristics shown in the following table to complete parts (a) through (f).

Load		Length
N	lbf	mm	in.
0	0	50.800	2.000
7,330	1,650	50.851	2.002
15,100	3,400	50.902	2.004
23,100	5,200	50.952	2.006
30,400	6,850	51.003	2.008
34,400	7,750	51.054	2.010
38,400	8,650	51.308	2.020
41,300	9,300	51.816	2.040
44,800	10,100	52.832	2.080
46,200	10,400	53.848	2.120
47,300	10,650	54.864	2.160
47,500	10,700	55.880	2.200
46,100	10,400	56.896	2.240
44,800	10,100	57.658	2.270
42,600	9,600	58.420	2.300
36,400	8,200	59.182	2.330
Fracture

(a) Plot the data as engineering stress versus engineering strain.
(b) Compute 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 approximate ductility, in percent elongation?
(f) Compute the modulus of resilience.