Young's Modulus

• Young's Modulus is the slope of the elastic portion of the stress-strain curve for the material being analyzed. Engineers develop stress-strain curves by performing repeated tests on material samples and compiling the data. Calculating Young's Modulus (E) is as simple as reading a stress and strain value from the graph and dividing the stress by the strain.
  
  

Stress Equation

• Stress (sigma) is related to strain (epsilon) through the following equation:
  
  sigma = E*(epsilon)
  
  This relationship is only valid in regions where Hooke's Law is valid. Hooke's Law states that a restorative force is present in an elastic material that is proportional to the distance the material has been stretched. Since yield stress is the point where plastic deformation occurs, it marks the end of the elastic range. Use this equation to estimate a yield stress value.
  
  

The 0.2% Offset Rule

• The most common engineering approximation for yield stress is the 0.2 percent offset rule. To apply this rule, assume that yield strain is 0.2 percent, and multiply by Young's Modulus for your material:
  
  sigma = 0.002*E
  
  To distinguish this approximation from other calculations, engineers sometimes call this the "offset yield stress."
  
  

Von Mises Criteria

• The offset method is valid for uniaxial applications, but some applications require biaxial analysis. For these problems, use the Von Mises criteria:
  
  (sigma1 - sigma2)^2 + sigma1^2 + sigma2^2 = 2*sigma(y)^2
  
  sigma1 = x-direction max shear stress
  sigma2 = y-direction max shear stress
  sigma(y) = yield stress