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ENGR 3450 Spring, 2012 Homework Department of Materials Science and Engineering

HOMEWORK #5, Spring 2012

Electronic & Atomic Structure; Bonding

Out of 10 points (+6 possible), Due March 8th

, 2012

PROBLEM #1 (2 points):

Mechanical Properties, Callister and Rethwisch, Chapter 7

(Callister 7.1)Using mechanics-of-materials principles (i.e., equations of mechanical equilibrium applied to afree-body diagram), derive Equations 7.4a and 7.4b.

PROBLEM #2 (2 points):

Mechanical Properties, Callister and Rethwisch, Chapter 7

(Callister 7.6)Consider a cylindrical titanium wire 3.0 mm (0.12 in.) in diameter and 2.5 X 10

4mm (1000 in.)

long. Calculate its elongation when a load of 500 N (112 lbf) is applied. Assume that thedeformation is totally elastic. (Take Youngs modulus for Ti as 107 x 10

12Pa )

PROBLEM #3 (2 points):

Mechanical Properties, Callister and Rethwisch, Chapter 7(Similar to Callister 7.44)

The following true stresses produce the corresponding true plastic strains for a brass alloy:

True Stress (psi) True Strain

50,000 0.10

63,625 0.25

What true stress is necessary to produce a true plastic strain of 0.19? Calculate the error in thestress value if you have used the linear interpolation to get this result.

PROBLEM #4 (2 points):Mechanical Properties, Callister and Rethwisch, Chapter 7(Callister 7.3)

A specimen of aluminum having a rectangular cross section 10 mm X 12.7 mm (0.4 in. X 0.5 in.)is pulled in tension with 35,500 N (8000 lb f) force, producing only elastic deformation. Calculate

the resulting strain. (Take Youngs modulus for Al as 69 x 1012

Pa)

PROBLEM #5 (2 points):

Mechanical Properties, Callister and Rethwisch, Chapter 7

a) Define the term hardness as a mechanical property of the material.b) Explain the advantages of performing hardness tests. State some commonly used

hardness testing techniques.

PROBLEM #6 (6 points):

Mechanical Properties, Callister and Rethwisch, Chapter 7

The following data were obtained during the tension test of a low- carbon steel with a specimen

having a 12 mm diameter and a 50 mm gage length.Yield point, 24.8 kN; breaking load, 27.2 kN; final gage length, 72.8 mm; final diameter 6.3 mm.

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ENGR 3450 Spring, 2012 Homework Department of Materials Science and Engineering

Load (kN) Elongation (mm) Load (kN) Elongation (mm)

2.0 0.0041 25.2 0.51

4.0 0.0082 28.0 1.526.0 0.0132 30.0 2.03

8.0 0.0183 34.0 3.05

10.0 0.0226 38.4 4.5712.0 0.0267 40.0 6.6014.0 0.0310 40.4 7.62

16.0 0.0351 40.8 12.718.0 0.0391 40.2 14.7

20.0 0.0445 38.6 15.722.0 0.0485 36.4 17.8

24.0 0.0518 32.4 19.3

a) Plot the engineering stress- strain curve.b) Determine the proportional limit, modulus of elasticity, yield point at strain offset of0.002, tensile strength, fracture stress, modulus of resilience and approximate ductility in

percent elongation.c) Plot the true- stress true- strain curve up to maximum load.d) Explain what other considerations have to be taken into account to plot the true- stress

true- strain curve beyond the maximum load.