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Chap3_VABLE - M Vable Mechanics of Materials Mechanical...

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Mechanics of Materials: Mechanical Properties of Materials Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 3 83 M. Vable January, 2010 CHAPTER THREE MECHANICAL PROPERTIES OF MATERIALS Learning objectives 1. Understand the qualitative and quantitative descriptions of mechanical properties of materials. 2. Learn the logic of relating deformation to external forces. _______________________________________________ The ordinary wire and rubber stretch cord in Figure 3.1 have the same undeformed length and are subjected to the same loads. Yet the rubber deforms significantly more, which is why we use rubber cords to tie luggage on top of a car. As the example shows, before we can relate deformation to applied forces, we must first describe the mechanical properties of materials. In engineering, adjectives such as elastic , ductile , or tough have very specific meanings. These terms will be our qualita- tive description of materials. Our quantitative descriptions will be the equations relating stresses and strains. Together, these description form the material model (Figure 3.2). The parameters in the material models are determined by the least-square method (see Appendix B.3) to fit the best curve through experimental observations. In this chapter, we develop a simple model and learn the logic relating deformation to forces. In later chapters, we shall apply this logic to axial members, shafts, and beams and obtain formulas for stresses and deformations. 3.1 MATERIALS CHARACTERIZATION The American Society for Testing and Materials (ASTM) specifies test procedures for determining the various properties of a material. These descriptions are guidelines used by experimentalists to obtain reproducible results for material properties. In this section, we study the tension and compression tests, which allow us to determine many parameters relating stresses and strains. Figure 3.1 Material impact on deformation. Figure 3.2 Relationship of stresses and strains. Material models
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Mechanics of Materials: Mechanical Properties of Materials Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 3 84 M. Vable January, 2010 3.1.1 Tension Test In the tension test , standard specimen are placed in a tension-test machine, where they are gripped at each end and pulled in the axial direction. Figure 3.3 shows two types of standard geometry: a specimen with a rectangular cross-section and speci- men with a circular cross-section. Two marks are made in the central region, separated by the gage length L 0 . The deformation δ is movement of the two marks. For metals, such as aluminum or steel, ASTM recommends a gage length L 0 = 2 in. and diameter d 0 = 0.5 in. The nor- mal strain ε is the deformation δ divided by L 0 . The tightness of the grip, the symmetry of the grip, friction, and other local effects are assumed and are observed to die out rapidly with the increase in distance from the ends. This dissipation of local effects is further facilitated by the gradual Figure 3.3 Tension test machine and specimen. (Courtesy Professor I. Miskioglu.) d o L o + δ P P L o ε δ L o ----- = σ P A o ----- P π d o 2 4 ---------------- = = Ultimate Stress σ u Rupture
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