Chapter 2

MATERIALS AND PROCESSES

35

 

 

 

 

 

 

 

2

 

(a)

(b)

 

 

 

 

F I G U R E 2 - 6

Compression Test Specimens Before and After Failure (a) Ductile Steel (b) Brittle Cast Iron The Compression Test

The tensile test machine can be run in reverse to apply a compressive load to a specimen that is a constant-diameter cylinder as shown in Figure 2-6. It is difficult to obtain a useful stress-strain curve from this test because a ductile material will yield and increase its cross-sectional area, as shown in Figure 2-6 a, eventually stalling the test machine. The ductile sample will not fracture in compression. If enough force were available from the machine, it could be crushed into a pancake shape. Most ductile materials have compressive strengths similar to their tensile strengths, and the tensile stress-strain curve is used to represent their compressive behavior as well. A material that has essentially equal tensile and compressive strengths is called an even material.

Brittle materials will fracture when compressed. A failed specimen of brittle cast iron is shown in Figure 2-6 b. Note the rough, angled fracture surface. The reason for the failure on an angled plane is discussed in Chapter 4. Brittle materials generally have much greater strength in compression than in tension. Compressive stress-strain curves can be generated, since the material fractures rather than crushes and the cross-sectional area doesn’t change appreciably. A material that has different tensile and compressive strengths is called an uneven material.

 

The Bending Test

A thin rod, as shown in Figure 2-7, is simply supported at each end as a beam and loaded transversely in the center of its length until it fails. If the material is ductile, failure is by yielding, as shown in Figure 2-7 a. If the material is brittle, the beam fractures as shown in Figure 2-7 b. Stress-strain curves are not generated from this test because the stress distribution across the cross section is not uniform. The tensile test’s – curve is used to predict failure in bending, since the bending stresses are tensile on the convex side and compressive on the concave side of the beam.

 

The Torsion Test

The shear properties of a material are more difficult to determine than its tensile properties. A specimen similar to the tensile test specimen is made with noncircular details on its ends so that it can be twisted axially to failure. Figure 2-8 shows two such samples, one of ductile steel and one of brittle cast iron. Note the painted lines along

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36

MACHINE DESIGN -

An Integrated Approach

 

 

2

 

 

 

(a)

(b)

 

F I G U R E 2 - 7

Bending Test Specimens Before and After Failure (a) Ductile Steel (b) Brittle Cast Iron

 

 

 

their lengths. The lines were originally straight in both cases. The helical twist in the

 

ductile specimen’s line after failure shows that it wound up for several revolutions be-

 

fore breaking. The brittle, torsion-test specimen’s line is still straight after failure as

 

there was no significant plastic distortion before fracture.

 

MODULUS OF RIGIDITY The stress-strain relation for pure torsion is defined by Table 2-1

Poisson’s Ratio 

Gr

=

(2.3)

 

Material

lo

Aluminum

0.34

where  is the shear stress, r is the radius of the specimen, lo is the gage length,  is the Copper

0.35

angular twist in radians, and G is the shear modulus or modulus of rigidity. G can be Iron

0.28

defined in terms of Young’s modulus E and Poisson’s ratio 

Steel

0.28

E

Magnesium

0.33

G = 2(1 + )

(2.4)

Titanium

0.34

Poisson’s ratio () is the ratio between lateral and longitudinal strain and for most metals is around 0.3 as shown in Table 2-1.

ULTIMATE SHEAR STRENGTH The breaking strength in torsion is called the ultimate shear strength or modulus of rupture Sus and is calculated from

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a)

(b)

 

F I G U R E 2 - 8

 

Torsion Test Specimens Before and After Failure (a) Ductile Steel (b) Brittle Cast Iron

 

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