Computational Methods for Debonding in Composites

104 C. Schuecker and H.E. Pettermann
σnψ, andµ pl
nψ is interpolated from µ pl
12 and µpl
23 as
µ pl
nψ = µ pl
12 sin2 (ψ)+µ pl
23 cos2 (ψ) (5.7)
The general form of the plasticity law is assumed to be the same for all combinations
of fracture plane shear stresses, so n and k of Eq. (5.6) are the same as in Eqs. (5.1)
and (5.3).
To compute the plastic strain tensor in ply coordinates, the plastic strain γ pl
nψ is
split into its two components and the plastic strain tensor referenced to the inclined
fracture plane, ¯εεε pl =(0,0,0,γ pl
nl
coordinates. Since the value of γ pl
nt
the transformation leads to plastic normal strains, ε pl
22
out-of-plane shear strains, γ pl
23
,0,γ pl
nt )T (in Nye-notation), is transformed to ply
is generally non-zero for inclined fracture planes,
and εpl
33 = −εpl
22 ,aswellas
. The latter, however, cancel each other out if an equal
accumulation of plastic shear strains γ pl
nt in planes oriented at +θfp and −θfp is
assumed.
Finally, the plastic strain tensor in ply coordinates is given by
εεε pl =
�
(0,0,0,γ pl
12 ,0,0)T mode A,B
(0,ε pl
22
,ε pl
33 ,γpl
12 ,0,0)T mode C
5.2.3 Identification of Parameters for the Plasticity Model
(5.8)
There are four parameters which need to be identified in order to fully define the
plasticity model described above, i.e. n and k for the plasticity law under in-plane
simple shear (Eq. 5.1), as well as µ pl
12 and µpl
23 for the influence of normal stress
(Eqs. 5.2 and 5.5, respectively). To identify these parameters it is convenient to use
data from tests on UD laminates because then all non-linearity is related to plasticity,
according to the model assumptions.
The plasticity parameters, n and k, can be derived from experimental data of
shear tests on a UD laminate following Eq. (5.1). Ideally, n and k are determined by
curve fitting if the shear stress–shear strain curve is known. If the complete stress–
strain data is not available for a given ply material, approximations can be obtained
by choosing n in the range of n = 5−7 and computing k from the stress and strain
values at failure. As an example, the shear stress vs. plastic shear strain curve for a
glass fiber/epoxy material (see Table 5.1 for material data) is shown in Fig. 5.3, left,
using experimental data of a test on a hoop wound tube taken from [11]. The best fit
using Eq. (5.1) is obtained with parameters n = 7.2andk = 120.7 MPa (solid line).
As indicated by the dashed line for the lowest suggested value of n = 5 (resulting
in k = 150.6 MPa), a lower value of n only affects the curvature of the graph but
passes through the same end point and still yields reasonable agreement with the
experimental data.