Review the details of fatigue damage for unidirectional materials, woven materials, and damage propagation.
Eq. 61 presents the fundamental equation used to determine the cycles required to initiate a crack within the matrix constituent of a polymer matrix composite. Once the lowest number of cycles is determined, the consequences of a fatigue failure must be enforced for the material such that loading may realistically distribute within the composite structure.
Keeping with previous sections (Phenomenology of Composite Fatigue and Kinetic Theory of Fracture), we identify two failure modes: transverse (off-axis) and longitudinal (on-axis). Coupling Eqs. 61, 45, and 46 can be used to compute the cycles to failure for both longitudinal and transverse cracking. The number of cycles to failure for the material point in question is always taken as the minimum cycles to failure between the two. The type of failure predicted (e.g. longitudinal or transverse) dictates the type of damage imposed on the material.
Woven materials can exhibit damage in a multitude of combinations. For simplicity, we identify damage due to fatigue loadings as transverse cracking in fill/warp bundles and longitudinal cracking in fill/warp bundles.
Transverse cracking within tows is identified through the static failure criteria presented earlier (Matrix Constituent Failure Criterion). The static matrix failure criterion is continually evaluated as the fatigue loading is imposed on the structure and as damage accumulates during the fatigue analysis. Further Eq. 61 is coupled with Eq. 40 to determine the minimum cycles to failure to initiate a longitudinal crack. Damage of the lamina is continuously updated to reflect the amount of damage (transverse cracking in tow(s) and/or longitudinal cracking in tow(s)) present.
We identify the damage states within unidirectional and woven lamina in accordance with those presented earlier (Damage States in Composite Materials). Anytime a transverse crack is predicted to occur within a lamina (or tow), the matrix constituent properties are reduced orthotropically so that the load carrying capability in the longitudinal direction is not affected by the transverse cracks. Similarly, anytime a longitudinal crack is predicted to occur in a lamina (or tow) the matrix material properties are reduced to those above, and the fiber properties are reduced to near zero to simulate near zero load carrying capability of the lamina (or tow).