### A combination of analysis programs simulates the stochastic nature of fiber breakage in composites.

The Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) is core technology in a software suite called ImMAC, developed at NASA’s John Glenn Research Center. An abbreviation for Integrated Multiscale Micromechanics Analysis Code, ImMAC is used in the design and analysis of advanced composite structures.

The MAC/GMC component of the software performs rapid, standalone analysis of composite materials and laminates based on non-FEA (finite element analysis) micromechanics methods. The GMC approach determines the effective response of composite materials and laminates based on the arrangement and properties of the constituent materials, rather than on the finite element method.

New ImMAC software called FEA Micromechanics Analysis Code (FEAMAC) now couples the efficient micromechanics capabilities of MAC/GMC with the ABAQUS finite element code from ABAQUS. Through FEAMAC, the coupled software enables linear and nonlinear multiscale analysis of composite structures using micromechanics to simulate fiber and matrix behavior.FEAMAC calls a MAC/GMC library directly from ABAQUS to represent the composite material at each integration point in the finite element model, and at each loading increment and iteration. The coupled software thereby simulates the stochastic nature of fiber breakage in composites by incorporating an appropriate FEA damage and failure model that operates on the level of the fiber. Recently, FEAMAC was used to perform a progressive failure analysis of a titanium matrix composite tensile test specimen. Part of the challenge was to identify the techniques needed to model the statistical nature of the problem properly.

Two simulations were performed. First, fiber strength in the specimen was allowed to vary randomly at the level of the local finite element only. Next, fiber strength was allowed to vary globally across the entire composite structure. Including the effects of fiberstrength variability globally across all scales resulted in a more realistic simulation. In particular, it was observed that failure initiation in a composite part does not necessarily occur at the location of highest structural stress.The test specimen simulated was a longitudinally reinforced SiC/Ti metal matrix composite, commonly referred to as a “dogbone” specimen. The ABAQUS model of the specimen was meshed with 300 C3D8 elements and boundary conditions were applied, including tensile displacement loading at a rate of 3 × 10-4 in/s. FEAMAC was used to model the composite material occupying each element via a GMC repeating unit cell (RUC). For longitudinal loading, the simplest composite RUC (i.e., a 2 × 2, consisting of 4 sub-cells), was sufficient to capture the material response of a SiC/Ti composite at each integration point of each element of the ABAQUS mesh. Because each finite element contains eight integration points, the MAC/GMC micromechanics code is called 2,400 times per iteration per increment during the simulation.

Elastic and viscoplastic material properties were defined for the SiC fiber and Ti matrix, respectively. Finally, parameters were entered in FEAMAC for the stochastic Curtin fiber failure model, which predicts fiber stiffness degradation due to damage and failure.

For the first simulation, the same Curtin model parameters were assigned to all elements in the specimen. This means the fiber failure process was stochastic locally but did not vary across the entire composite structure. Figure 1 shows the progression of fiber failure as the simulated tensile test proceeds. In physical tests of SiC/Ti specimens, one typically observes failure within the gauge section. In the simulation, however, failure initiated at the transition to the gauge section. Also, the fiber failure progressed through the specimen very quickly.

In the second simulation, to account for global fiber-strength variability in real-life dogbone specimens, the Curtin model parameters were distributed randomly across the specimen geometry (see Figure 2). In essence, by providing different elements with different values of this parameter, the elements were allowed to damage and fail at different fiber stress levels.

This time, failure initiated within the gauge section, and subsequent failure, did not progress as rapidly. Global loading continued for 0.6 seconds before the fibers in another weak element failed. After one other adjacent element failed, the established failure path was arrested due to the presence of a stronger element. It took 2.64 seconds of additional global loading before further failures occurred.

In a FEAMAC multiscale stochastic analysis of the progressive failure of a SiC/Ti specimen, accounting for statistics only at the micro scale leads to inaccurate failure predictions. Spatially randomizing the fiber-strength statistics throughout the specimen enables realistic gauge section failure and predicts significantly lower specimen tensile strength, along with more progressive failure.

The multiscale FEAMAC framework circumvents the need for complex, multiaxial, anisotropic damage and constitutive models that are required to operate on the macro scale for nonlinear analysis of composite structures.

*This article was written by Steven M. Arnold of NASA’s John Glenn Research Center and Brett A. Bednarcyk of the Ohio Aerospace Institute, using software from ABAQUS, Inc. For more information about the ImMAC software suite from NASA Glenn Research Center, visit www.grc.nasa.gov/WWW/LPB/mac. To access the full white paper on this application, visit http://info.hotims.com/10964-121.*