numerical modeling of mixed-mode delamination fracture in ... · under the frame work of comsol...
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Numerical Modeling of Mixed-Mode Delamination Fracture in Unidirectional AS4/PEEK Composites
Viorel IONESCUa
aDepartment of Physics and Electronics, Ovidius University, Constanta, Romania
1. Abstract In this paper it was developed a Finite Element Method (FEM)
model for the simulation of interfacial failure between two plies of
an AS4/PEEK composite sample using Cohesive Zone Model (CZM),
under the frame work of Comsol Multiphysics software. Mixed
Mode Bending (MMB) method was considered here for the
numerical implementation of progressive delamination propagating
in composite specimens with pre-existing cracks. Volumetric strain
and von Mises stress at the maximum load before fracture have been
evaluated here at different ratios between mode II strain energy rate
and total strain energy rate GII/GT of 20%, 50% and 80%,
corresponding to a different delamination length a0 of the specimen:
33.7 mm, 34.1 mm and 31.4 mm, respectively.
4. Conclusions
The AS4/PEEK composite model investigated through this paper under the form of load-
displacement curve proved to be in good agreement with test results from the literature,
suggesting that the proposed numerical formulation can predict the strength of composite
structures that suffer progressive delamination.
Von Mises stress and volumetric strain have been evaluated along delamination and
damage interfaces between the two plies of the composite model at maximum load point’s
displacement before fracture: uLP1 = 8.47 mm, uLP2 = 5.24 mm and uLP3 = 4.95 mm, with
maximum stress values close to 1GPa, FPZ regions of 4.3 – 5.6 mm length and maximum
strain values between 0.0068 and 0.0088 after MMB test simulated at different GII/GT ratios.
Future work will be developed around the simulation of the interlaminar failure in
different types of unidirectional graphite/epoxy laminates (HTA/6376C, IM6/3501-6,
T300/977-2) at different nominal thickness (3.16 mm, 4.35 mm, 5.30 mm).
2. Introduction. Model set-up Composite materials in the form of a sandwich structure became
nowadays, for weight saving purposes, primary load bearing parts in
engineering applications like aircrafts, trains and ships. In aircraft
industry, thermoplastic composites like the AS4 carbon fiber
reinforced poly-ether-ether-ketone (AS4/PEEK) are used in structural
applications: leading edges, clips and brackets, and stiffened panels
[1]. Recently, AS4/PEEK composites became very attractive for
orthopedic implants, due to biocompatibility, similar modulus to bone
and ability to withstand prolonged fatigue strain [2].
As a consequence of adjacent layers separation, composite
laminates suffer delamination failure under static and fatigue
loadings, causing an important degradation of the load-bearing
property for composite structures [3].
Mixed-mode bending (MMB) test (see fig. 1) can be developed in
order to study the interlaminar fracture behavior of composite
laminates, with evaluation of critical strain energy release rate GC in
structures having initial pre-cracks [4]. MMB test combines double
cantilever beam (DCB) mode I loading and end-notch fixture (ENF)
mode II loading by evaluating total strain energy rate GT with its
mode I (GI) and mode II (GII), offering a wide range of GII/GT ratios,
starting from GII/GT = 0% (DCB) till GII/GT = 100% (ENF).
Fig. 3. Numerically predicted and experimental load-displacement curves [6] at different
mode ratios k for AS4/PEEK composite specimen
Fig. 4. Von Mises contour plots in maximum load point displacement before fracture for the
composite model simulated at different GII/GT ratios
Fig. 5. (a)Von Mises stress evolution and (b) volumetric strain variation along delamination
and damage interfaces of the model at uLP1, uLP2 and uLP3 for different GII/GT ratios
3. Results and discussions
References [1] Offringa, A., van Ingen, J.W. and Buitenhuis, A., SAMPE Journal 48 (2), 6-15 (2012). [2] Steinbergn, E. L., Rath, E., Shlaifer, A., Chechik, O., Maman, E. and Salai, M., J Mech Behav Biomed Mater. 17, 221-228 (2013). [3] Gornet, L. and Ijaz, H., Composites Part B: Engineering 42(5), 1173-1180 (2011). [4] Reeder, J.R. and Crews Jr., J.R., AIAA Journal 28(7), 1270-1276 (1990). [5] Naghipour, P., Schneider, J., Bartsch, M., Hausmann, J., & Voggenreiter, H., Engineering Fracture Mechanics, 76(18), 2821–2833 (2009). [6] Turon, A., Camanho, P. P., Costa, J. and Davila, C .G., Mechanics of Materials 38, 1072–1089, (2006).
Fig. 2. Discretization network image and geometrical features for the
beam numerical model, along with complete mesh details
Fig. 1. Schematic and loading
description of MMB test apparatus [5]
Benzeggagh and Kenane mixed – mode criterion:
η = 2.28
The beam-theory analysis:
k = 50%
Mode mixing
ratio κ :
Pm Pe
I – middle edge, II – contact pair
interface, III – cracked edge,
IV – roller edge, V – delamination
interface, VI – damage interface
L
L
The experimental MMB tests for a [90]24 unidirectional AS4/PEEK composite samples with
the fiber volume content of 60 % have been performed by A. Turon et al. [6].
2L = 102 mm, b = 25.4 mm, 2h = 3.12 mm [6]
A Fracture Process Zone (FPZ) develops at the proximity of the crack tip where inelastic
processes such as plastic deformation and micro-cracking take place and outside of this FPZ
region, the body deforms linear elastically.