A computational methodology for predicting the initiation and propagation of failures in laminated matrix/fiber composite-material structures has been developed. The methodology follows the progressive-failure approach, in which it is recognized that a laminated composite structure can develop local failures or exhibit such local damage as matrix cracks, fiber breakage, fiber/matrix debonds, and delaminations under normal operating conditions, and that such damage can contribute to the eventual failure of the structure. The ability to predict the initiation and growth of such damage is essential for predicting the performances of composite structures and developing reliable, safe designs that exploit the advantages offered by composite materials.
In this and other progressive-failure-analysis methodologies, a typical analysis involves a multistep iterative procedure in which the load on a mathematically modeled structure is increased in small steps. At each load step, a nonlinear analysis is performed until a converged solution (representing an equilibrium state) is obtained, assuming no changes in the mathematical submodels of the component materials of the structure. Then using the equilibrium state, the stresses within each lamina are determined from the nonlinear-analysis solution. These stresses are compared with allowable stresses for the affected materials and used to determine failure according to certain failure criteria.
If a failure criterion indicates failure of a lamina, then the mathematically modeled properties of the lamina are changed according to a mathematical submodel of degradation of the affected material properties. When this happens, the initial nonlinear solution no longer corresponds to an equilibrium state, and it becomes necessary to re-establish equilibrium, using the modified lamina properties for the failed lamina while maintaining the current load level. This iterative process of obtaining nonlinear equilibrium solutions each time a local material submodel is changed is continued until no additional lamina failures are detected. However, in this progressive failure methodology, small load step sizes were used instead of the iterative process of obtaining equilibrium solutions to minimize the effect of not establishing equilibrium at the same load level. The load step is then incremented and the foregoing analysis repeated until catastrophic failure of the structure is detected.
The present progressive-failure-analysis methodology includes the use of C1 (slope-continuous) shell finite elements from classical lamination theory for calculation of in-plane stresses. The failure criteria used in this methodology include the maximum-strain criterion, Hashin's criterion (a stress-based criterion that predicts failures in tensile and compressive fiber and matrix modes), and Christensen's criterion (a strain-based criterion that distinguishes between fiber failures and fiber/matrix-interaction failures). The material-degradation model used in this methodology includes several options; the best option in each case depends on the choice of failure criterion and on the nature of the composite material (e.g., unidirectional composite vs. fabric composite).
The methodology is implemented by computer code that has been incorporated into the Computational Mechanics Testbed (COMET) program, which is a general-purpose finite-element-analysis program. As thus augmented, COMET can predict the damage and response of a laminated composite structures from initial loading to final failure.
The methodology and its various failure criteria and material-degradation submodels were compared and assessed by performing analyses of several laminated composite structures. The results from these computations were found to be well correlated with available test data (see figure), except in structures in which interlaminar stresses are suspected of being large enough to cause certain failure mechanisms (such as debonding or delaminations) that are not modeled in this methodology.
This work was done by David W. Sleight of Langley Research Center. L-17660