takes into account different failure modes involving the response of the fiber and the
matrix components to various loading conditions (the failure modes depend on which model
you use); and
can be used with damage evolution models with the following restriction: the LaRC05 model
supports damage evolution only when used with enriched elements to model discontinuities
(such as cracks) in an extended finite element method (XFEM) analysis.
Damage initiation refers to the onset of degradation at a material point. Abaqus supports two damage initiation criteria for unidirectional fiber-reinforced composites:
the Hashin criterion and the LaRC05 criterion; and the ply fabric damage initiation
criterion for bidirectional fabric-reinforced composites.
Damage is characterized by the degradation of material stiffness. It plays an important
role in the analysis of fiber-reinforced composite materials.
Unidirectional fiber-reinforced composite materials exhibit elastic-brittle behavior; that
is, damage in these materials is initiated without significant plastic deformation.
Consequently, plasticity is often neglected when modeling the behavior of these materials.
The fibers in the fiber-reinforced material are assumed to be parallel, as depicted in Figure 1.
For unidirectional fiber-reinforced composite materials, you must specify material
properties in a user-defined local coordinate system. The lamina is in the 1–2 plane, and
the local 1-direction corresponds to the fiber direction. You must specify the undamaged
material response using one of the methods for defining an orthotropic linear elastic
material (see Linear Elastic Behavior); the most convenient of which is
the method for defining an orthotropic material in plane stress (see Defining Orthotropic Elasticity in Plane Stress). However, the
material response can also be defined in terms of the engineering constants or by specifying
the elastic stiffness matrix directly.
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, and the model differentiates between tensile and compressive fiber
failure modes. The elastic undamaged response of the material must be defined using the
bilamina elasticity model (see Defining Orthotropic Elasticity in Plane Stress with Different Moduli in Tension and Compression).
matrix cracking under transverse tension and shearing; and
matrix crushing under transverse compression and shearing.
The initiation criteria have the following general forms:
Fiber tension :
Fiber compression :
Matrix tension :
Matrix compression :
In the above equations
denotes the longitudinal tensile strength;
denotes the longitudinal compressive strength;
denotes the transverse tensile strength;
denotes the transverse compressive strength;
denotes the longitudinal shear strength;
denotes the transverse shear strength;
is a coefficient that determines the contribution of the shear stress to the fiber
tensile initiation criterion; and
are components of the effective stress tensor, , that is used to evaluate the initiation criteria and which is
computed from:
where is the true stress and is the damage operator:
, , and are internal (damage) variables that characterize fiber, matrix, and
shear damage, which are derived from damage variables , , , and , corresponding to the four modes previously discussed, as follows:
Prior to any damage initiation and evolution the damage operator, , is equal to the identity matrix, so . Once damage initiation and evolution has occurred for at least one mode,
the damage operator becomes significant in the criteria for damage initiation of other modes
(see Damage Evolution and Element Removal for Fiber-Reinforced Composites for discussion of damage
evolution). The effective stress, , is intended to represent the stress acting over the damaged area that
effectively resists the internal forces.
The initiation criteria presented above can be specialized to obtain the model proposed in
Hashin and Rotem (1973) by setting and or the model proposed in Hashin (1980) by setting .
An output variable is associated with each initiation criterion (fiber tension, fiber
compression, matrix tension, matrix compression) to indicate whether the criterion has been
met. A value of 1.0 or higher indicates that the initiation criterion has been met (see
Output
for further details). If you define a damage initiation model without defining an associated
evolution law, the initiation criteria will affect only output. Thus, you can use these
criteria to evaluate the propensity of the material to undergo damage without modeling the
damage process.
Larc05 Criterion
The LaRC05 criterion (available only in Abaqus/Standard) for unidirectional fiber-reinforced composite is a three-dimensional model based on the
theory of Pinho et al. (2012). It can be applied generally to polymer-matrix
fiber-reinforced composites. It can also be used for fiber-reinforced composite lamina
similar to the Hashin criterion. The criterion considers four different damage initiation
mechanisms (matrix cracking, fiber kinking, fiber splitting, and fiber tension), as follows:
Matrix cracking:
where
The angle, , represents the orientation of a critical plane perpendicular to the local
2–3 plane. The value of is found numerically such that it maximizes .
Fiber tension :
Fiber splitting :
Fiber kinking :
In the fiber splitting and fiber kinking equations above, stresses in the
fiber-misalignment frame are computed as:
where represents the stresses in the fiber-kinking plane:
For the three fiber-failure mechanisms above, Abaqus/Standard first checks the sign of . If is positive, the fiber tension criterion, , is calculated; otherwise, for fiber splitting and kinking, stresses are
rotated to the fiber-kinking plane, and then these obtained stresses are further rotated to
the misalignment frame. During this process, the angles and are varied together until the maximum value of or is found.
In the above equations:
denotes the longitudinal tensile strength;
denotes the longitudinal compressive strength;
denotes the transverse tensile strength;
denotes the transverse compressive strength;
denotes the plane shear strength;
denotes the transverse shear strength;
denotes the fracture plane angle for pure compression (by default, =53°);
denotes the longitudinal shear friction coefficient; and
denotes the transverse shear friction coefficient.
If and are not defined, they are calculated as:
An output variable is associated with each initiation criterion (matrix cracking, fiber
kinking, fiber splitting, fiber tension) to indicate whether the criterion has been met. A
value of 1.0 or higher indicates that the initiation criterion has been met (see Output). The initiation criteria affect only output. Therefore, you can use these criteria to
evaluate the propensity of the material to undergo damage without modeling the damage
process.
Ply Fabric Criterion
The ply fabric damage initiation criterion for bidirectional fiber-reinforced composite
(available only in Abaqus/Explicit) is an anisotropic damage model based on the work of Johnson, 2001 and Sokolinsky et al., 2011. The material response along the fiber
directions is characterized with damaged elasticity. The model incorporates different
initial (undamaged) stiffness in tension and compression (see Defining Orthotropic Elasticity in Plane Stress with Different Moduli in Tension and Compression), and
differentiates between tensile and compressive fiber failure modes by activating the
corresponding damage variable depending on the stress state in the fiber directions. The
shear response is dominated by the nonlinear behavior of the matrix, which includes both
plasticity (see Plasticity Model for Bidirectional Fabric-Reinforced Composite Materials) and stiffness degradation due
to matrix microcracking.
Four different modes of damage initiation for the fibers and one for shear response of the
matrix are considered:
Fiber rupture in tension in the local 1-direction, with a damage variable ;
Fiber buckling and kinking in compression in the local 1-direction, with a damage
variable ;
Fiber rupture in tension in the local 2-direction, with a damage variable ;
Fiber buckling and kinking in compression in the local 2-direction, with a damage
variable ; and
Matrix microcracking due to shear deformation, with a damage variable .
The four fiber damage initiation criteria have the following general form:
In the above equation, an index is used to simplify notation and is used in subsequent discussions, such
that it takes the values depending on the sign of the corresponding stresses.
In the above equation:
are functions that provide initiation criteria for fiber damage and are assumed to
take the form:
where are the tensile/compressive strengths for uniaxial loading along the
fiber directions, and are effective stresses defined as:
The symbol in the equations above represents the Macaulay bracket operator,
which is defined for every as .
are damage thresholds that are initially set to one. After damage activation (), they increase with increasing damage according to:
The definition ensures that the damage thresholds are nondecreasing quantities.
The damage initiation criterion for matrix shear failure has the following form:
In the above equation:
is the matrix shear failure criterion and is assumed to take the form:
where is the shear stress for initial matrix damage, is the effective shear stress defined as , is the equivalent plastic strain due to shear deformation, and is a specified maximum value. The damage shear stress-strain
relations are computed based as discussed in Plasticity Model for Bidirectional Fabric-Reinforced Composite Materials.
is the shear damage threshold that is initially set to one. After damage activation (), it increases with increasing damage according to:
Once a particular damage initiation criterion is satisfied, the material stiffness is
degraded according to the specified damage evolution law for that criterion. For a
discussion of damage evolution, see Damage Evolution and Element Removal for Fiber-Reinforced Composites.
An output variable is associated with each initiation criterion (fiber tension in the local
1-direction, fiber compression in the local 1-direction, fiber tension in the local
2-direction, fiber compression in the local 2-direction, and matrix shear) to indicate
whether the criterion has been met. A value of 1.0 or higher indicates that the initiation
criterion has been met (for more details, see Output). If you define a damage initiation model without defining an associated
evolution law, the initiation criteria affects only output. Therefore, you can use these
criteria to evaluate the propensity of the material to undergo damage without modeling the
damage process.
Elements
The Hashin and ply fabric damage initiation criterion must be used with elements with a
plane stress formulation, which include plane stress, shell, continuum shell, and membrane
elements. The LaRC05 damage initiation criterion can be used with three-dimensional solid,
plane stress, shell, solid shell, and membrane elements.
Maximum value of the fiber tensile initiation criterion experienced during the
analysis.
HSNFCCRT
Maximum value of the fiber compressive initiation criterion experienced during the
analysis.
HSNMTCRT
Maximum value of the matrix tensile initiation criterion experienced during the
analysis.
HSNMCCRT
Maximum value of the matrix compressive initiation criterion experienced during the
analysis.
LARCMCCRT
Maximum value of the matrix cracking initiation criterion experienced during the
analysis.
LARCFKCRT
Maximum value of the fiber kinking initiation criterion experienced during the
analysis.
LARCFSCRT
Maximum value of the fiber splitting initiation criterion experienced during the
analysis.
LARCFTCRT
Maximum value of the fiber tension initiation criterion experienced during the
analysis.
PLF1TCRT
Maximum value of the fiber tensile initiation criterion in the local 1-direction
experienced during the analysis.
PLF1CCRT
Maximum value of the fiber compressive initiation criterion in the local 1-direction
experienced during the analysis.
PLF2TCRT
Maximum value of the fiber tensile initiation criterion in the local 2-direction
experienced during the analysis.
PLF2CCRT
Maximum value of the fiber compressive initiation criterion in the local 2-direction
experienced during the analysis.
PLSHRCRT
Maximum value of the matrix shear initiation criterion experienced during the
analysis.
For the variables above that indicate whether an initiation criterion in a damage mode has
been satisfied or not, a value that is less than 1.0 indicates that the criterion has not
been satisfied, while a value of 1.0 or higher indicates that the criterion has been
satisfied. If you define a damage evolution model, the maximum value of this variable does
not exceed 1.0. However, if you do not define a damage evolution model, this variable can
have values higher than 1.0, which indicates by how much the criterion has been exceeded.
References
Hashin, Z., “Failure Criteria for
Unidirectional Fiber Composites,” Journal of Applied
Mechanics, vol. 47, pp. 329–334, 1980.
Hashin, Z., and A. Rotem, “A Fatigue Criterion for
Fiber-Reinforced Materials,” Journal of Composite
Materials, vol. 7, pp. 448–464, 1973.
Johnson, A.F., “Modelling Fabric-Reinforced Composites under Impact Loads,” Composites Part A: Applied Science and Manufacturing, vol. 32, no. 9, pp. 1197–1206, 2001.
Lapczyk, I., and J. A. Hurtado, “Progressive Damage Modeling in
Fiber-Reinforced Materials,” Composites Part A:
Applied Science and Manufacturing, vol. 38, no. 11, pp. 2333–2341, 2007.
Pinho, S.T., R. Darvizeh, P. Robinson, C. Schuecker, and P. P. Camanho, “Material and Structural Response
of Polymer-Matrix Fibre-Reinforced Composites,” Journal of Composite
Materials, vol. 46, no. 19–20, pp. 2313–2341, 2012.
Sokolinsky, V.S., K. C. Indermuehle, and J. A. Hurtado, “Numerical Simulation of the Crushing Process of a Corrugated Composite Plate,” Composites Part A: Applied Science and Manufacturing, vol. 42, no. 9, pp. 1119–1126, 2011.