MATERIALS ENGINEERING CONCEPTS - Materials for Civil and Construction Engineers - page 11

Elastic
limit

0.5% extension
yield strength

0.2% offset
yield strength

Proportional
limit

Strain, % Strain, %

0.2% 0.5%

(a) (b)

FIGURE 1.7 Methods for estimating yield stress: (a) offset method and
(b) extension method.

Figure 1.7(a) demonstrates three concepts of the stress-strain behavior
of elastoplastic materials. The lowest point shown on the diagram is the
proportional limit , defined as the transition point between linear and nonlinear
behavior. The second point is the elastic limit , which is the transition be-
tween elastic and plastic behavior. However, most materials do not display
an abrupt change in behavior from elastic to plastic. Rather, there is a grad-
ual, almost imperceptible transition between the behaviors, making it diffi-
cult to locate an exact transition point (Polowski and Ripling 1966). For this
reason, arbitrary methods such as the offset and the extension methods, are
used to identify the elastic limit, thereby defining the yield stress (yield
strength) . In the offset method, a specified offset is measured on the abscis-
sa, and a line with a slope equal to the initial tangent modulus is drawn
through this point. The point where this line intersects the stress-strain
curve is the offset yield stress of the material, as seen in Figure 1.7(a). Dif-
ferent offsets are used for different materials (Table 1.2). The extension yield

T ABLE 1.2 Offset Values Typically Used to Determine Yield Stress

Corresponding

Material Stress Condition Offset (%) Strain

Steel Tension 0.20 0.0020

Wood Compression

parallel to grain 0.05 0.0005

Gray cast iron Tension 0.05 0.0005

Concrete Compression 0.02 0.0002

Aluminum alloys Tension 0.20 0.0020

Brass and bronze Tension 0.35 0.0035