Machinery's Handbook, 31st Edition
Mechanical Properties of Materials
207
(1)
(2)
(3)
Yield Point
Ultimate Strength Elastic Limit Proportional Limit
Ultimate Strength Elastic Limit
Yield Strength
Proportional Limit
Strain
Strain
Strain
Offset
Fig. 1. Stress-Strain Curves In the SI, the unit of stress is the pascal (Pa), the newton per meter squared (N/m 2 ). The megapascal (newtons per millimeter squared) is often an appropriate sub- multiple for use in practice. Proportional limit is the point on a stress-strain curve at which it begins to deviate from the straight-line relationship between stress and strain. Prior to this point, the curve has a constant slope equal to the modulus of elasticity for that material. Elastic limit is the maximum tensile stress to which a test specimen may be subjected and still return to its original length upon release of the load. A material is said to be stressed within the elastic region when the working stress does not exceed the elastic limit, and to be stressed in the plastic region when the working stress does exceed the elastic limit. The elastic limit for steel is for all practical purposes the same as its proportional limit. Yield point is a point on the stress-strain curve at which there is a sudden increase in strain without a corresponding increase in stress. While not all materials have a yield point, for those that do, this point tends to occur at or near the onset of plastic or permanent deformation. Modern standards may refer to this as upper yield strength . Yield strength, S y , is the stress associated with a specified small amount of permanent strain. Ideally, this is the maximum stress that can be applied with no permanent de- formation of the material; in practice, it is not easily measurable. When a material does not have a clearly defined upper yield strength (yield point), an offset yield strength may be defined instead, as illustrated in Fig. 1 (3). In such cases, yield strength is the stress value on the stress-strain curve corresponding to a defined amount of permanent set or strain, usually 0.1%, 0.2%, or 0.5% of the original dimension. A line drawn parallel to the elastic range curve (with slope equal to the modulus of elasticity) intersects the X-axis at the target strain. The intersection of the stress-strain curve with that offset line is the offset yield point (again 0.2%). Yield strength data for various materials are given in tables starting on pages 388 , 390 , 418 , 419 , 421 , 423 , 427 , 510 , 512 , 516 , 525 , 526 , 531 , 532 , 536 , 544 , 546 , 547 , and elsewhere. Ultimate tensile strength, S u (also called ultimate strength ), is the maximum stress value obtained in a tensile test for a given material. This value has significance in designs with brittle materials; design calculations for ductile materials use yield strength instead. Modulus of elasticity, E (also called Young’s modulus ), is a measurement of the elasticity of a given material. Calculated according to Hooke’s law by dividing stress by the corre- sponding strain within a material’s elastic range, this value is equal to the slope of the linear portion of the stress-strain curve. Smaller E values indicate larger deflections under a given stress. Young’s modulus has significant implications for parts in use, as well as those being machined or processed. Some representative values of Young’s modulus in both US cus- tomary and metric units are as follows: Material Young’s Modulus Material Young’s Modulus 10 6 psi 10 9 Pa 10 6 psi 10 9 Pa Aluminum, cast, pure 9 62.1 Magnesium, AZ80A-T5 6.5 44.8 Aluminum, wrought, 2014-T6 10.6 73.1 Titanium, pure 15.5 106.9 Beryllium copper 19 131 Titanium, alloy, 5 Al, 2.5 Sn 17 117.2 Brass, naval 15 103.4 Steel for bridges and buildings, ASTM A7-61T, all shapes 29 199.9 Bronze, phosphor, ASTM B159 15 103.4 Cast iron, malleable 26 179.3 Steel, castings, high strength, for structural purposes, ASTM A148-60 29 199.9 Cast iron, nodular 23.5 162
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