Mechanical Properties of Materials, Exercises of Mechanics

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Mechanical Properties of Materials

Mechanics of materials 4. Mechanical Properties of Materials 4.1/23 Mechanical Properties of Materials Important Points A conventional stress-strain diagram is important in engineering since it provides a means for obtaining data about a material’s tensile or compressive strength without regard for the material’s physical size or shape. Engineering stress and strain are calculated using the original cross-sectional area and gauge length of the specimen. A ductile material, such as mild steel, has four distinct behaviors as it is loaded. They are elastic behavior, yielding, strain hardening, and necking. A material is linear elastic if the stress is proportional to the strain within the elastic region. This behavior is described by Hooke’s law, o = Ee, where the modulus of elasticity E is the slope of the line. Important points on the stress-strain diagram are the proportional limit, elastic limit, yield stress, ultimate stress, and fracture stress. The ductility of a material can be specified by the specimen’s percent elongation or the percent reduction in area. Ifa material does not have a distinct yield point, a yield strength can be specified using a graphical procedure such as the offset method. Brittle materials, such as gray cast iron, have very little or no yielding and so they can fracture suddenly. Strain hardening is used to establish a higher yield point for a material. This is done by straining the material beyond the elastic limit, then releasing the load. The modulus of elasticity remains the same; however, the material’s ductility decreases. Strain energy is energy stored in a material due to its deformation. This energy per unit volume is called strain-energy density. If it is measured up to the proportional limit, it is referred to as the modulus of resilience, and if it is measured up to the point of fracture, it is called the modulus of toughness. It can be determined from the area under the o—e diagram. R. C. Hibbeler, Mechanics Of Materials, 8" Edition, Pearson Prentice Hall, 2011.