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32.10.4 Yield Strength The yield strength is the nominal stress at which a material undergoes a specified permanent deformation. There are several methods to determine the yield strength, but the most reliable and consistent method is called the offset method. This approach requires that the nominal stress-strain diagram be first drawn on cartesian coordinates. A point z is placed along the strain axis at a specified distance from the origin, as shown in Figs. 32.15 and 32.16. A line parallel to the elastic modulus is drawn from Z until it intersects the nominal stress-strain curve. The value of stress corresponding to this intersection is called the yield strength by the offset method. The distance 0Z is called the offset and is expressed as percent. The most common offset is 0.2 percent, which corresponds to a nominal strain of 0.002 in/in. This is the value of offset used in Fig. 32.15 to determine the yield strength of the A40 titanium. An offset of 0.01 percent is sometimes used, and the corresponding nominal stress is called the proof strength, which is a value very close to the proportional limit. For some nonferrous materials an offset of 0.5 percent is used to determine the yield strength. Inasmuch as all methods of determining the yield strength give somewhat different values for the same material, it is important to specify what method, or what offset, was used in conducting the test.

32.10.5 Tensile Strength The tensile strength is the value of nominal stress obtained when the maximum (or ultimate) load that the tensile specimen supports is divided by the original crosssectional area of the specimen. It is shown as Su in Fig. 32.16 and is sometimes called the ultimate strength. The tensile strength is a commonly used property in engineering calculations even though the yield strength is a measure of when plastic deformation begins for a given material. The real significance of the tensile strength as a material property is that it indicates what maximum load a given part can carry in uniaxial tension without breaking. It determines the absolute maximum limit of load that a part can support.

This is fire, so mostly it will just be going up, so you will set our x and z velocities to 0:

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32.10.6 Fracture Strength The fracture strength, or breaking strength, is the value of nominal stress obtained when the load carried by a tensile specimen at the time of fracture is divided by its original cross-sectional area. The breaking strength is not used as a material property in mechanical design.

Pin # 1 5 9 10 12

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32.10.7 Reduction of Area The reduction of area is the maximum change in area of a tensile specimen divided by the original area and is usually expressed as a percent. It is designated as Ar and is calculated as follows: Ar = A0 Af (100) A0 (32.16)

where the subscripts 0 and f refer to the original area and area after fracture, respectively. The percent reduction of area and the strain at ultimate load u are the best measure of the ductility of a material.

particles.emitVolumeXRange = BBRangeMake(-30, 60); particles.emitVolumeYRange = BBRangeMake(-5, 10); particles.emitVolumeZRange = BBRangeMake(-30, 60);

32.10.8 Fracture Strain The fracture strain is the true strain at fracture of the tensile specimen. It is represented by the symbol f and is calculated from the definition of strain as given in Eq. (32.12). If the percent reduction of area Ar is known for a material, the fracture strain can be calculated from the expression f = ln 100 100 Ar (32.17)

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32.10.9 Percentage Elongation The percentage elongation is a crude measure of the ductility of a material and is obtained when the change in gauge length of a fractured tensile specimen is divided by the original gauge length and expressed as percent. Because of the ductility relationship, we express it here as De =

(100)

(32.18)

You will have it emit from a flattened spheroid:

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