About Damage and Failure for Fiber-Reinforced Composites

Unidirectional fiber-reinforced composite materials exhibit elastic-brittle behavior; damage in these materials is initiated without significant plastic deformation. Consequently, plasticity is often neglected when modeling behavior of these materials. You must specify material properties in a user-defined local coordinate system, with the local 1-direction aligned with the fiber direction, as shown in Figure 1. You can use any of the available methods to define orthotropic elastic behavior to define the undamaged response.

Figure 1. Unidirectional lamina.

For bidirectional fabric-reinforced composite materials, the shear response is dominated by the nonlinear behavior of the matrix, which includes both plasticity and stiffness degradation due to matrix microcracking. The fiber directions are assumed to be orthogonal. You must specify material properties in a user-defined local coordinate system, with the local 1-direction and 2-direction aligned with the fiber directions, as shown in Figure 2. The material response along the fiber directions is characterized with damaged elasticity. The model incorporates different initial (undamaged) stiffness in tension and compression and differentiates between tensile and compressive fiber failure modes. Therefore, you must use bilamina elasticity to define the undamaged response (see Defining Orthotropic Elasticity in Plane Stress with Different Moduli in Tension and Compression).

Figure 2. Bidirectional fabric.

Abaqus offers the following damage initiation criteria for unidirectional fiber-reinforced composites:

• Hashin model, based on the work of Matzenmiller et al. (1995), Hashin and Rotem (1973), Hashin (1980), and Camanho and Davila (2002).

• LaRC05 model (available only in Abaqus/Standard), based on the work of Pinho et al. (2012).

Abaqus offers the following damage initiation criterion for bidirectional fabric-reinforced composites:

• Ply fabric model (available only in Abaqus/Explicit), based on the work of Johnson (2001) and Sokolinsky et al. (2011).

These models include initiation criteria for various failure mechanisms commonly observed in fiber-reinforced composites, such as fiber fracture in tension, fiber buckling/kinking under compression, and matrix cracking/crushing under tension/compression. These criteria are discussed in Damage Initiation for Fiber-Reinforced Composites.

Once a particular damage initiation criterion is satisfied, the material stiffness is degraded according to the specified damage evolution law for that criterion. In the absence of a damage evolution law, the material stiffness is not degraded.

The damage evolution law describes the rate of degradation of the material stiffness once the corresponding initiation criterion is reached. At any given time during the analysis, the stress tensor in the material is given by:

where ${\mathbf{C}}_{\mathbf{d}}$ is the damaged elasticity matrix. Abaqus assumes that the degradation of the stiffness of the fiber and matrix components can be expressed in terms of three scalar damage variables that reflect the current states of fiber, matrix, and shear damages, respectively. The evolution of the elasticity matrix due to damage is discussed in more detail in Damage Evolution and Element Removal for Fiber-Reinforced Composites; that section also discusses:

• options for treating severe damage (Maximum Degradation and Choice of Element Removal); and

• viscous regularization (Viscous Regularization).

The LaRC05 damage initiation model supports damage evolution only when used with enriched elements to model discontinuities (such as cracks) in an extended finite element method (XFEM) analysis. For more information, see Modeling Discontinuities as an Enriched Feature Using the Extended Finite Element Method.