# How to Calculate 0.2 Offset Yield Strength: Formulae with Examples

The yield point or yield strength of a material is defined in materials science and engineering as the stress at which a material begins to deform plastically. Offset Yield Strength is the arbitrary estimate of elastic limit.

It is the point of stress that corresponds to the point of intersection of a stress-strain diagram and a line parallel to the straight line portion of the diagram. ‘Offset’ is expressed in terms of strain (often 0.2%) and refers to the distance between the origin of the stress-strain diagram, and the point of intersection of the parallel line and the 0 stress axis. Offset yield strength is the engineering stress at which, by convention, it is considered that plastic elongation of the specimen has commenced.

The yield stress is not clearly defined in most materials. It is often difficult to precisely define yielding due to the wide variety of stress–strain curves exhibited by real materials. In addition, there are several possible ways to define yielding.  Thus, a standard has been developed to determine its most expected value. The common practice is to prepare a parallel line to the initial elastic region starting at 0.002 strain. This 0.002 strain point is often termed as the 2% offset strain point. The intersection of this new line with the stress-strain curve then defines the yield strength.

Thus, it is the stress required to produce a small-specified amount of plastic deformation and denotes how much the specimen will be deformed after loading and unloading. The yield strength found by offset method is generally used for specification and design purposes because it avoids the practical difficulties of measuring the proportional limit or elastic limit. The offset yield strength is usually specified in USA as a strain of 0.2 percent (e = 0.002). It is the stress at which the stress-strain curve for axial loading deviates by a strain of 0.2% from the linear-elastic line.

Tables for Material Strength have variety of different stress values. Ultimate stress, whether it is of compression, tension, bending or shearing is the highest value of stress that a material can withstand. Yield Stress as we have known earlier signifies the stress value where plastic deformation occurs, is difficult to foretell. The most common process of engineering approximation for yield stress is the 0.2 percent offset rule. To calculate under the.2% Offset Rule, the yield strains is assumed as 0.2 percent and multiply the same by Young’s Modulus for the material under consideration. The 0.2% (0.002) is a value of strain, which is arbitrary, but it covers somewhat the uncertainty of when a given material actually departs from the purely linear (elastic) relationship between stress and strain.

If you have a Load (y-axis) vs. Displacement (x-axis) curve, yield strength will be calculated as per Load vs. Displacement curve in the following way:

Let L= Length, then Strain ε = (L – Lo)/ Lo, where Lo = Original Length (usually the Gauge Length). Also, the Displacement, d, is given by (L – Lo), so strain ε = d/Lo.

Similar the stress, σ, is just the Load / Force, F divided by area A, i.e. σ = F/A, where A is constant until the specimen reaches UTS or Ultimate Tensile Strength, which corresponds to the Limit of uniform elongation, and necking begins.

Now back to Length/ displacement

with ε = (L – Lo)/Lo, one rewrites the equation as ε = L/Lo – 1, and reorganizing the terms, L= Lo (1+ε),

so the Length equivalent to the strain offset of 0.002 is just L= Lo X 1.002, or d (0.002) = 0.002 Lo.

The difference in yield strength is usually attributed to the differential microstructures, resulted from the different heat-treating parameters used by the heat treatment providers rather than metal defects or composition. It is the outcome of austenitizing temperature, soaking time, tempering temperature and quenching control resulting differences in micro structural variations, the size and distribution of carbides and grain size and especially in the mixture of phases