FAILURE CRITERIA FOR COMPOSITE MATERIALS UNDER MULTIAXIAL STRESS STATES

Essam Totry 1, Carlos González 1, 2, Javier LLorca1, 2

1 Departmento de Ciencia de Materiales, Universidad Politécnica de Madrid. 2 Instituto Madrileño de Estudios Avanzados en Materiales (IMDEA-Materiales). E. T. S. de Ingenieros de Caminos. Ciudad Universitaria. 28040 – Madrid, Spain.

KEYWORDS: Failure criteria, multiaxial loading, computational micromechanics.

ABSTRACT The failure locus a fiber-reinforced composite lamina, made up of 50 vol. % of carbon fibers embedded in an epoxy matrix, is computed under multiaxial stress states involving transverse compression, in-plane and out-of-plane shear. The mechanical response was obtained by the finite element method of a representative volume element of the lamina. The actual deformation and failure mechanisms experimentally observed in the matrix, fibers and interfaces were included in the simulations through the appropriate constitutive equations. The corresponding failure loci were validated against experimental results (when available) and compared with those given by three failure criteria (Hashin, Puck and LaRC) which provide reasonable predictions in other multiaxial stress states.

SIMULATION STRATEGY The macroscopic properties of a composite lamina until failure were obtained by means of the finite element analysis of a representative volume element (RVE) of the microstructure. The three-dimensional RVE of the lamina contained a random dispersion of circular fibers (which covered 50% of the area) embedded in a matrix, as shown in Fig. 1(a). It was subjected to normal compressive stresses in the transverse direction (either σ22 or σ33) and to shear stresses perpendicular (τ23) and/or parallel to the fibers (τ12). Simulations were carried out with Abaqus/Standard within the framework of the finite deformations theory with the initial unstressed state as reference. C fibers were modelled as linear, thermo-elastic and transversally isotropic solids. The polymeric matrix was assumed to behave as an isotropic, thermo-elasto-plastic solid. Plastic deformation was governed by the Mohr-Coulumb criterion and the total matrix strain was given by the addition of the thermo-elastic and plastic strain components. In addition, decohesion was included in the simulations by means of interface elements inserted at the fiber/matrix interface. The mechanical behaviour of these elements was expressed in terms of a traction-separation law which relates the displacement jump across the interface with the traction vector acting upon it.

RESULTS AND CONCLUSIONS The RVE was subjected to different multiaxial stress states and the failure locus for each case was determined from the results of the numerical simulations. One representative example is the failure locus of the composite lamina under transverse compression (σ33) and out-of-plane

Fig. 1: (a) Representative volume element of the microstructure of the composite lamina. (b) Failure locus under transverse compression (σ33) and out-of-plane shear (τ23). shear (τ23), which is plotted in Fig. 1(b) for the materials with strong and weak interface. In the former case, the failure locus computed from the numerical simulations was consistent with the Hashin [2], Puck [3] and LaRC [4] failure criteria, in which the only experimental parameter was the strength of the composite lamina under transverse compression. The numerical simulations showed that failure took place by the localization of the plastic strain in the matrix in a shear band, whose orientation for each combination of normal and shear stresses was close to the one predicted by Puck and LaRC models. However, the three failure criteria overestimated the composite strength in shear in the composites with a weak interface, because the dominant failure mechanism in this situtation (interface decohesion) was not accounted for in the phenomenological models. Criteria to develop better and more accurate failure models were obtained from the numerical simulations for different multiaxial loading conditions.

REFERENCES

1. González C. and LLorca J., “Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: microscopic mechanisms and modeling”. Composites Science and Technology, Vol. 67, pp. 2795-2806, 2007.

2. Hashin, Z. “Failure criteria for unidirectional fiber composites”. Journal of Applied Mechanics, Vol. 47, 329-334, 1980.

3. Puck, A. and Schürmann, H., “Failure analysis of FRP laminates by means of physically-based phenomenological models”, Composites Science and Technology, Vol. 62, pp. 1663-1662, 2002.

4. Dávila, C., Camanho, P. P. and Rose, C. A.,”Failure criteria for FRP laminates”, Journal of Composite Materials, Vol. 39, 323-345, 2005.