Machinery's Handbook, 31st Edition
208 Mechanical Properties of Materials Modulus of rigidity, G (also called modulus of elasticity in shear or shear modulus ), is shear stress divided by corresponding shear strain. (Shear may be applied directly or through torsion. Strain torsion is measured in radians.) As with modulus of elasticity, this value is only meaningful within the elastic range of the material, where it is equal to the slope of the straight-line portion of the stress-strain curve. Smaller G values also are as- sociated with larger deflections, given the same stress. This value is important to consider in shaft designs where windup is a concern. Poisson’s ratio, µ, is the value of the strain transverse to the load direction, divided by the strain in the load direction. This ratio is determined when uniaxial force is applied, with tensile force having a negative sign and compressive force a positive sign. Values of Poisson’s ratio for common materials are as follows: Aluminum 0.334 Nickel silver 0.322 Beryllium copper 0.285 Phosphor bronze 0.349 Brass 0.340 Rubber 0.500 Cast iron, gray 0.211 Steel, cast 0.265 Copper 0.340 high carbon 0.295 Inconel 0.290 mild 0.303 Lead 0.431 nickel 0.291 Magnesium 0.350 Wrought iron 0.278 Monel metal 0.320 Zinc 0.331 Compressive and Shear Properties.—Compressive yield strength, S cy , and compres- sive ultimate strength , S cu , are determined from compression tests. It is common to as- sume that ultimate compressive strength is equal to ultimate tensile strength. But ductile materials in compression usually fail by excessive yielding well before they fracture; as they are weaker in shear than in tension/compression, shear failure is more likely to occur. For brittle materials, which are stronger in shear, tensile and compressive stresses are of particular concern. The properties of shear yield strength , S sy , and shear ultimate strength , S su , are deter- mined by direct shear and torsional tests. The shear yield strength of ductile materials is approximated as 0.577 times the tensile yield strength. Creep.— Continuing changes in dimensions of a stressed material over time is called creep; it varies with different materials and periods under stress, and with temperature. Creep tests may take some time, as it is necessary to apply a constant tensile load to a specimen under a selected temperature. Measurements are taken to record the resulting elongation at time periods sufficiently long for a relationship to be established. The data are then plotted as elongation against time. The load is applied to the specimen only after it has reached the testing temperature, and causes an initial elastic elongation that includes some plastic deformation if the load is above the proportional limit for the material. Some combinations of stress and temperature may cause failure of the specimen. Others show initial high rates of deformation, followed by decreasing, then constant, rates over long periods. Generally, testing times to arrive at the constant rate of deformation are over 1000 hours. Creep Rupture.— Tests for creep rupture are similar to creep tests but are prolonged until the specimen fails. Further data to be obtained from these tests include time to rupture, amount of elongation, and reduction of area. Stress-rupture tests are performed without measuring the elongation, so that no strain data are recorded, time to failure, elongation and reduction of area being sufficient. Sometimes, a V-notch is cut in the specimen to allow measurement of notch sensitivity under the testing conditions. Stress and Strain Analysis.—Stresses, deflections (strains), and loads may be charac- terized by applying strain gages or indicating coatings to the surface of a part and then subjecting it to loads simulating those encountered in service. Strain gages, available in various configurations, are attached to the part’s surface and often calibrated before use. Such gages convert tension, pressure, force, and so on into electrical resistance, which can be measured to indicate strain. Indicating coatings include brittle lacquers that crack in
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online