The initial tangent modulus is usually used when no straight portion exists on the stress versus strain diagram. Figure 1 shows that the initial tangent modulus is taken by the slope of a tangent to the stress-strain curve through the origin. However, there is little practical importance to using the initial tangent modulus since it is only valid for very low stresses.

Figure 1

The tangent modulus can be taken at any point on the stress-strain curve. Figure 2 shows that the tangent modulus is represented by the slope of the tangent to any point on the curve. The accuracy in calculating the tangent modulus is somewhat limited because the tangent is usually drawn by hand.

Figure 2

The secant modulus represents the actual deformation at a selected point. Figure 3 shows that the secant modulus is drawn from the origin to any point on the stress-strain curve. This method is most widely used because there are no uncertainties in determining its value from the diagram.

Figure 3