Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-07 GTBL042-Callister-v2 August 9, 2007 13:52

Summary • 233

Solution

The first step in this design process is to decide on a factor of safety,N, which then

allows determination of a working stress according to Equation 7.29. In addition,

to ensure that the apparatus will be safe to operate, we also want to minimize any

elastic deflection of the rods during testing; therefore, a relatively conservative

factor of safety is to be used, sayN=5. Thus, the working stressσwis just

σw=

σy

N

=

310 MPa

5

=62 MPa (9000 psi)

From the definition of stress, Equation 7.1,

A 0 =

(

d

2

) 2

π=

F

σw

wheredis the rod diameter andFis the applied force; furthermore, each of the

two rods must support half of the total force or 110,000 N (25,000 psi). Solving for

dleads to

d= 2

√

F

πσw

= 2

√

110,000 N

π(62× 106 N/m^2 )

= 4. 75 × 10 −^2 m= 47 .5mm(1.87 in.)

Therefore, the diameter of each of the two rods should be 47.5 mm or 1.87 in.

SUMMARY

Concepts of Stress and Strain

Stress–Strain Behavior

Elastic Properties of Materials

True Stress and Strain

A number of the important mechanical properties of materials have been discussed

in this chapter. Concepts of stress and strain were first introduced. Stress is a mea-

sure of an applied mechanical load or force, normalized to take into account cross-

sectional area. Two different stress parameters were defined—engineering stress and

true stress. Strain represents the amount of deformation induced by a stress; both

engineering and true strains are used.

Some of the mechanical characteristics of metals can be ascertained by simple

stress–strain tests. There are four test types: tension, compression, torsion, and shear.

Tensile are the most common. A material that is stressed first undergoes elastic, or

nonpermanent, deformation, wherein stress and strain are proportional. The constant

of proportionality is the modulus of elasticity for tension and compression, and is the

shear modulus when the stress is shear. Poisson’s ratio represents the negative ratio

of transverse and longitudinal strains.