Numerical Modeling of Mixed-Mode Delamination Fracture in ... · under the frame work of Comsol...

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.