Failure Analysis

For each panel, failure of the spar was tested using the Tsai-Wu criterion, explained in Reference [5]. As mentioned above, the spar is expected to carry seven times the hover loads without failing. Because the loads for propeller mode are much less than the loads in helicopter mode; only operation in helicopter mode is checked for failure.

To test for failure, we first employ classical lamination theory to determine the strains in the spar. The spar is subjected to seven times the blade loading in hover. The spar's axial load corresponds to the axial load of the beam, $N_x$. In fact, the loads have the same symbol in the two theories. However, in classical lamination theory, $N_x$ is force per unit length; thus the beam $N_x$ must be divided by the breadth of the spar (equivalently, the airfoil thickness) to be used for the strength test. The in-plane shear of the spar corresponds to $Q_z$ of the beam, except that, once again, it must be divided by the spar's breadth. Although $Q_y$ relates to out-of-plane shear in the spar, we expect the spar to carry very little of the shear force in the $y$-direction, and so we ignore it.

Using classical lamination theory, the forces on the spar yield the mid-plane strains and curvatures. These, in turn, yield the local strains. And from the local strains, we get local stresses, which are rotated to yield principal stresses. The Tsai-Wu criterion is applied using the principal stresses. In testing for local failure, the outer surface of each ply in the spar was tested.