Computational Methods for Debonding in Composites

102 C. Schuecker and H.E. Pettermann
5.2 Plasticity Model
The plasticity model proposed here is a phenomenological approach based on the
assumption that plastic deformation occurs in the form of shear bands with a specific
orientation. As mentioned previously, experimental results of a study into the
micromechanics of PMC failure mechanisms suggest that the shear bands are precursors
of later cracks [3]. It is therefore assumed further that the shear bands
develop in planes that have the same orientation as the fracture plane which is predicted
here by Puck’s action plane failure criterion for plane stress states (Puck 2D)
[17, 20, 23].
According to Puck, fracture occurs in a plane that is parallel to the fiber orientation
and defined by a fracture plane angle, θfp, as depicted in Fig. 5.2, left.
The fracture plane is perpendicular to the laminate plane (i.e. θfp = 0) in the case
of combined transverse tensile stresses and in-plane shear (mode A) or moderate
transverse compression with in-plane shear (mode B). For combinations of high
transverse compressive stresses with shear, the fracture plane angle is non-zero
(mode C) and can be computed analytically [17,20,23]. For example, uniaxial transverse
compression of epoxy matrix composites typically leads to a predicted fracture
plane angle of approximately θfp = 50 ◦ −56 ◦ , which agrees well with experimental
findings [3,17,20] and results of micromechanical models [9]. In light of the considerations
put forth above, the plasticity law is formulated with respect to the predicted
fracture plane.
5.2.1 Plastic Strain for θθθ fp = 0 (Puck Modes A and B)
In a perpendicular plane, θfp = 0, the only shear stress component under plane
stress conditions is σ12. The relation of shear stress and plastic shear strain for in-
plane simple shear, γ pl
12 (σ12,σ22 = 0), can be derived from experimental data and
described by any suitable analytical expression. Here, a power law,
1
3
γ12 = γ el pl σ12
12 + γ12 = +
G12
t
l
n
2
θ fp
� �
σ12
n
k
sf
p
l
snn
s ny
sln
t
y
snt
n
(5.1)
Fig. 5.2 Definition of fracture plane and corresponding coordinate system, l-n-t, with regard to the
ply coordinate system, 1-2-3, by fracture plane angle, θfp (left); tractions on the fracture plane for
θfp �= 0(right)