In some materials, the stress at which the material changes from elastic to plastic behavior is not easily detected. In this case, the offset yield strength is determined. A line is constructed parallel to the initial portion of the stress-strain curve but offset by 0.002 in/in (0.2%) from the origin. The 0.2% offset yield strength is the stress at which the constructed line intersects the stress-strain curve as shown:
Determination of the yield strength using the offset method
The yield strength, corresponding to the yield point, is often defined by an offset method. Line AB is drawn at a slope equal to Young's modulus. Point A corresponds to a definite or stated amount of permanent set, usually 0.2 percent of the original gauge length, although 0.01, 0.1, and 0.5 are occasionally used.
In the case of aluminum and of many other ductile materials, the onset of yield is not characterized by a horizontal portion of the stress-strain curve. Instead, the stress keeps increasing—although not linearly—until the ultimate strength is reached. Necking then begins, leading eventually to rupture. For such materials, the yield strength σy can be defined by the offset method. The yield strength at 0.2% offset, for example, is obtained by drawing through the point of the horizontal axis of abscissa ε = 0.2% (or ε = 0.002), a line parallel to the initial straight-line portion of the stress-strain diagram. The stress σy corresponding to the point y obtained in this fashion is defined as the yield strength at 0.2% offset.
A standard measure of the ductility of a material is its percent elongation, which is defined as:
Percent elongation = 100
Lb − L0
L0
where L0 and Lb denote, respectively, the initial length of the tensile test specimen and its final length at rupture corresponding to the breaking strength. The specified minimum elongation for a 2-in gage length for commonly used steels with yield strength up to 50 ksi is 21%. Note that this means that the average strain at rupture should be at least 0.21 in/in.
Another measure of ductility which is sometimes used is the percent reduction in area, defined as
Percent reduction in area = 100
A0 − Ab
A0
where A0 and Ab denote, respectively, the initial cross-sectional area of the specimen and its minimum cross-sectional area at rupture corresponding to the breaking strength. For structural steel, percent reductions in area of 60 to 70 percent are common.
