A method of computational simulation of progressive fracture in composite-material (matrix/fiber) structural components has been developed. This method does not involve stress-intensity factors or fracture toughnesses. Instead, it involves consideration of the mechanics of the composite from the microscopic (matrix and fiber) constituent level through the subply and ply scales to the structural scale, while using probabilistic techniques to account for uncertainties in such variables as properties of materials, fabrication variables, dimensions, and loads.
The methodology for step-by-step simulation of fracture in a variety of generic composite-material components has been incorporated into the Composite Durability Structural Analysis (CODSTRAN) computer program. CODSTRAN quantifies damage states at all scales except structural by use of the mechanics of composites; the degradation of structural behavior is quantified by use of a finite-element technique in which the damaged part of a structure is treated as not contributing to resistance to load. The integration of composite-mechanics and finite-element techniques makes it possible to describe the relationship formally between local conditions (including local damage) and global structural behavior. The criteria for initiation, growth, accumulation, and propagation of damage are examined at each scale and integrated (synthesized) upward through the various scales from microscopic (local) to macroscopic (global). The effects of changes at the global scale (e.g., changes in loading or support conditions) on damage and stress at the local scale are tracked. Overall, global structural equilibrium is maintained by tracking local-to-global and global-to-local effects until convergence is achieved.
The foregoing integrated microscopic-to-macroscopic-mechanics approach is further integrated with the probabilistic approach in the Integrated Probabilistic Assessment of Composite Structures (IPACS) computer program. The resulting overall integrated approach was described previously in "Probabilistic Analysis of Composite-Material Structures" (LEW-16092) NASA Tech Briefs, Vol. 21, No. 2 (February 1997), page 58. IPACS starts by defining uncertainties in the properties at the microscopic constituent level. The uncertainties are then propagated to, and combined with, the uncertainties at the next higher scale; that is, subply, then ply, then laminate, then structure (see figure). The uncertainties in the fabrication variables, dimensions, and other variables are carried through the same hierarchy. Consequently, one can obtain probability-density functions (PDFs) and cumulative distribution functions (CDFs) that characterize the responses of structure at all scales from microscopic to macroscopic. One can also obtain sensitivities of structural responses to uncertainties in design variables.
This method has been demonstrated by applying it to a bolted joint in a laminated composite panel under an edge load (see figure). The results showed that the most effective way to reduce end displacement fracture is to control both the load and the ply thickness. The cumulative probability for longitudinal stress in all plies was found to be most sensitive to the load; in the plies with longitudinal fibers, it was very sensitive to ply thickness. The cumulative probability for transverse stress was found to be most sensitive to the coefficient of thermal expansion of the matrix material. The fiber volume ratio and fiber transverse modulus were both found to contribute significantly to the cumulative probability for the transverse stresses in all plies.
This work was done by C. C. Chamis of Lewis Research Center; S. N. Singhal of NYMA, Inc.; and L. Minnetyan of Clarkson University. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Materials category, or circle no. 122on the TSP Order Card in this issue to receive a copy by mail ($5 charge).
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