Module 4: Plane Stress Constitutive Equations
  Lecture 15: Lamina Engineering Constants
 


Transverse Modulus:

Consider an off-axis lamina subjected to in-plane transverse loading as shown in Figure 4.4. Thus, for this loading condition we have  and
.

Figure 4.4: Off axis lamina loaded in traction along y direction

Let us define the transverse modulus as

(4.69)

Thus, from Equation (4.5) for the above loading, we can write

(4.70)

If we express  using engineering constants, we get

(4.71)

From this expression, we can see that the modulus  when  and  when . The variation of the modulus  with fibre orientation for AS4/3501-6 Epoxy material is shown in Figure 4.5. The variation of the modulus , similar to the variation of , for both positive and negative fibre orientations is identical in nature. Further, it can be observed that the curve for  is shifted by  to that of .

Figure 4.5: Variation of transverse modulus with fibre orientation for AS4/3501-6 Epoxy

Other Poisson’s Ratio:

The other Poisson’s ratio  can be obtained from the loading condition given in Figure 4.4. Let us define this Poisson’s ratio as

(4.72)

Thus, using Equation (4.5) for this loading, it becomes

(4.73)

which can be written using engineering constants as

(4.74)

The fibre orientation dependence of axial Poisson’s ratio and the other Poisson’s ratio for AS4/3501-6 Epoxy is shown in Figure 4.6.

Figure 4.6: Variation of Poisson's ratios with fibre orientation