Calculation of yield strength from the stress-strain curve

Yield strength is one of the important parameters for the analysis and design of structural components like members, beams and bars etc. It is basically the stress under which complete plastic deformation takes place and a component in a structural system acts as a yield point. A common way to calculate yield strength is from the stress-strain curve. While figuring out how to calculate yield strength from stress strain curve may seem complicated to a beginner,  taking time to understand it is absolutely important because you will be using this methodology regularly in your career. So let’s get started:

First step: Calculating Young’s modulus

the linear elastic part of the stress-strain curve is used to find Young’s modulus.   Hence within the elastic region, the slope of the linear part within the stress-strain curve refers to Young’s modulus. If you are doing the calculations in an Excel sheet then you can use a slope function which would return the slope of the linear regression line that passes through the given data points. You can also use a two-point slope question to find Young’s modulus between two points. While the two answers may differ you can choose either of the results

Second step:  Calculating the 0.2 offset stress-strain values

in this step, you need to offset all the strain values by a factor of 0.2 per cent which equates to 0.002 strain. You can do this by adding 0.002 to every strain value. Once you do this you get a series of 0.2% offset strain values.

The next part of this step is calculating the 0.2% offset stress value. For doing this you need to multiply all the strain values with Young’s modulus. As a result of this multiplication, you will get a linear behaviour for the stress line and it should be parallel to the elastic part of the curve. Hence essentially you would have created a linear behaviour for all stress-strain points after this just like in step one you need to calculate the 0.2% offset stress value for every point of stress value. .

Third step: Plotting the stress strain curve with 0.2% offset

after having completed steps one and two you will have a list of 0.2% offset stress data and 0.2% offset strain data. You should use these data points to plot a graph. The result would be a straight line which would be parallel to the linear elastic region of the original stress-strain curve.

The intersection point of the stress-strain curve with this newly formed straight line will give you the 0.2% offset yield strength value. The typical convention is to mark this point with a green dot. The stress value that corresponds to this intersection point on the Y axis is the 0.2% offset yield stress.