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2
/ = C
F I G U R E 2 - 24
Strength Plotted Against Density for Engineering Materials (From Fig. 4-4, p. 39 in M. F. Ashby, Materials Selection in Mechanical Design, 2ed, Butterworth-Heinemann 1999, with permission)
reported strengths are the ultimate tensile strength Sut and the tensile yield strength Sy. The Sut indicates the largest stress that the material will accept before fracture, and Sy indicates the stress beyond which the material will take a permanent set. Many materials have compressive strengths about equal to their tensile strengths and are called even materials. Most wrought metals are in the even category. Some materials have significantly different compressive and tensile strengths and these are called uneven materials. Cast metals are usually in the uneven category, with compressive strengths much greater than their tensile strengths. The shear strengths of even materials tend
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MACHINE DESIGN -
An Integrated Approach
to be about half their tensile strengths, while shear strengths of uneven materials tend to be between their tensile and compressive strengths.
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One or more of these strengths may be of interest when the loading is static. If the material is ductile, then Sy is the usual criterion of failure, as a ductile material is capable of significant distortion before fracture. If the material is brittle, as are most cast materials, then the Sut is a more interesting parameter, because the material will fracture before any significant yielding distortion takes place. Yield strength values are nevertheless reported for brittle materials, but are usually calculated based on an arbitrary, small value of strain rather than on any measured yielding of the specimen. Chapter 5
deals with the mechanisms of material failure for both ductile and brittle materials in more detail than does this chapter.
The tensile test is the most common measure of these static strength parameters.
The stress-strain curve (–) generated in this test is shown in Figure 2-2. The so-called engineering – curve differs from the true – curve due to the reduction in area of a ductile test specimen during the failure process. Nevertheless, the engineering – curve is the standard used to compare materials, since the true – curve is more difficult to generate.
The slope of the – curve in the elastic range, called Young’s modulus or the modulus of elasticity E, is a very important parameter as it defines the material’s stiffness or resistance to elastic deflection under load. If you are designing to control deflections as well as stresses, the value of E may be of more interest than the material’s strength. While various alloys of a given base material may vary markedly in terms of their strengths, they will have essentially the same E. If deflection is the prime concern, a low-strength alloy is as good as a high-strength one of the same base material.
When the loading on the part varies with time it is called dynamic or fatigue loading. Then the static strengths do not give a good indication of failure. Instead, the fatigue strength is of more interest. This strength parameter is measured by subjecting a specimen to dynamic loading until it fails. Both the magnitude of the stress and the number of cycles of stress at failure are reported as the strength criterion. The fatigue strength of a given material will always be lower than its static strength, and often is less than half its Sut. Chapter 6 deals with the phenomenon of fatigue failure of materials in more detail than does this chapter.
Other material parameters of interest to the machine designer are resilience, which is the ability to absorb energy without permanent deformation, and toughness or the ability to absorb energy without fracturing (but with permanent deformation). Homogeneity is the uniformity of a material throughout its volume. Many engineering materials, especially metals, can be assumed to be macroscopically homogeneous even though at a microscopic level they are often heterogeneous. Isotropism means having properties that are the same regardless of direction within the material. Many engineering materials are reasonably isotropic in the macro and are assumed so for engineering purposes. However, other useful engineering materials such as wood and composites are neither homogeneous nor isotropic and their strengths must be measured separately in different directions. Hardness is important in wear resistance and is also related to strength. Heat treatment, both through and surface, as well as cold working can increase the hardness and strength of some materials.