UDK 678.6/.7:620.18
Original scientific article/Izvirni znanstveni članek
ISSN 1580-2949 MTAEC9, 42(3)171(2008)
NUMERICAL AND EXPERIMENTAL ANALYSES OF THE DELAMINATION OF CROSS-PLY LAMINATES
NUMERIČNA IN EKSPERIMENTALNA ANALIZA DELAMINACIJE V KRIŽNIH PLOŠČATIH LAMINATIH
Robert Zemcik, Vladislav Laš
University of West Bohemia in Pilsen, Department of Mechanics, Univerzitni 22, 306 14, Plzen, Czech Republic
zemcik@kme.zcu.cz
Prejem rokopisa — received: 2007-09-20; sprejem za objavo - accepted for publication: 2008-01-16
This article focuses on a numerical and experimental investigation of the delamination of cross-ply FRP laminates. The tested samples were cut from plates [0/90/90/0] made of unidirectional carbon-epoxy prepregs in a vacuum autoclave. The experimental tests were performed on precracked double-cantilever beam samples according to ASTM standards with Mode-I loading. The load-displacement relations were recorded during the test and the crack length was measured optically with a digital camera. The corresponding numerical simulations were performed in the finite-element code MSC.Marc. The goal was to assess the critical value of the energy-release rate G, which was chosen as the interlaminar fracture toughness. The simulation used the equality between the energy-release rate and the J-integral for the elastic case.
Keywords: composite, cross-ply, beam, delamination, experiment, simulation
V delu obravnavamo numerično in eksperimentalno raziskavo delaminacije v križnih ploščatih FRP-laminatih. Preizkušanci so bili odrezani iz plošč [0/90/90/0], ki so bile izdelane v avtoklavu iz surovcev ogljikovo vlakno-epoksi. Preizkusi so bili izvršeni na vnaprej razpokanih dvojno vpetih nosilcih skladno z ASTM-standardi z obremnitvijo Mode 1. Odnos obremenitev - pomik je bil ugotovljen med preskusom, dolžina razpoke pa se je merila optično z digitalno kamero. Za numerično simulacijo je bila uporabljena metoda končnih elementov s kodo MSC.Marc. Cilj je bil določiti kritično vrednost hitrosti sprostitve energije G, ki je bila opredeljena kot interlaminarna žilavost loma. V simulaciji je uporabljena enakost med hitrostjo sprostitve energije in J-integralom za primer elastičnosti.
Ključne besede: kompoziti, križna plošča, nosilec, delaminacija, eksperiment, simulacija
1 INTRODUCTION
One of the key damage mechanisms in laminates is the origin and propagation of a failure or a crack between individual layers; this is known as delamination and it must be considered in the design of a laminated structure. Delamination can be caused by imperfections during the manufacturing process or due to static and dynamic loads. The existence of delamination in a composite material degrades its stiffness and in certain cases it can degrade the stability to a critical level. The dangerous factor is the propagation of the delamination, which is influenced by the geometrical parameters, the material characteristics and the loading type. Both types of propagation can be present: slow and stable as well as fast and unstable.
In this investigation we have looked at a numerical simulation of the delamination of a laminated specimen made of unidirectional fiber-reinforced composite layers. This follows on from the work started in 1. The aim is to design a numerical model for the simulation of crack propagation. An important parameter used in such analyses is the critical value of the energy-release rate (Gc).
The majority of studies investigating the delami-nation on laminated structures use either the critical value of energy-release rate Gc2-4 or the stress-intensity
factor Kc 5 as the interlaminar fracture toughness. The early studies were focused mainly on the experimental procedures and analytical solutions. These were later followed by studies dealing with numerical simulations based on a finite-element analysis and introducing new, special element types for the modeling of the delami-nation 6-8.
It is known that the critical value of Gc as calculated according to the ASTM standard 9 does not behave as a constant. The critical value changes during the prescribed test by as much as tens of percent. Therefore, it is questionable as to which value should be chosen, for instance, for the numerical simulation.
In this work the value of Gc is assessed by experimental measurements on a Mode-I delamination specimen. The analysis was performed on a cross-ply laminate manufactured from unidirectional plies reinforced with carbon fibers in an epoxy resin. It is known 10 that in the case of linear stress-strain behavior there is equality between G and the value of the J-integral (J). Therefore, it was possible to substitute the evaluation of the decisive parameter Gc with the calculation of Jc in the numerical simulations. The numerical calculations are carried out using the finite-element method in MSC.Marc.
The difference between the experimentally and numerically obtained dependencies of force vs. displace-
Materiali in tehnologije / Materials and technology 42 (2008) 4, 171-174
171
R. ZEMČlK, v. LAS: NUMERICAL AND EXPERIMENTAL ANALYSES OF THE DELAMINATION
ment for the critical value Gc is presented. The basic material parameters (elasticity constants) used in the simulations were identified in previous studies 1112, where the damage and failure of specimens made of the same material are investigated.
2 EXPERIMENT
Firstly, an experimental assessment of the interlaminar toughness for Mode-I delamination was carried out according to the standard ASTM D 5528-01 9. The specimens used were rectangular strips denoted as DCB (Double Cantilever Beam) having dimensions l x b = (160 x 19.7) mm (see Figure 1). Each specimen was cut out using a water jet from a 4.6-mm-thick laminated cross-ply composite plate with a lay-up [0/90/90/0], whereas the middle part was 0.3 mm thick (see Figure 2). The plate was manufactured from epoxy prepregs reinforced with continuous Toray T600SC carbon fibers using autoclave technology. A non-adhesive aluminum foil, which served as the initial crack, was inserted into the midplane of the plate (i.e., between the 90 degree plies) during manufacture (see Figures 1 and 4). The thickness of the foil was 11 pm.
The experiment was performed on the Zwick/Roell Z050 testing machine. The opening force was applied using two piano hinges bonded on the lower and upper surfaces of the specimen (see Figures 1 and 3). During the testing process the dependence of the opening force F vs. the transverse (or load point) displacement d was recorded (see Figure 3). The crack propagation with time (crack length a) was inspected optically using a digital camera (Canon EOS 400D, Sigma 105/2.8 EX DG MACRO) every 10 s (resolution approximately 20 px/mm). The optical measurement also served as a verification of the transverse displacement values, which might differ, in general, from the grip movement, as recorded by the testing machine, due to its imperfect rigidity. The delamination process had a slow and stable character up to the final rupture. The speed of the grip movement was 10 mm/min.
The major problems identified during the experiments were the inhomogeneity of the initial crack zone
Figure 2: Material lay-up (showing the part without the foil) Slika 2: Zlog materiala (prikazan je del brez folije)
Figure 3: DCB specimen experimental setup
Slika 3: DCB-vzorec z eksperimentalno postavitvijo
Figure 4: Crack surfaces of the fractured DCB specimen Slika 4: Površina razpok pretrganega DCB-vzorca
(the end of the foil) and the so-called fiber bridging between the upper and lower parts of the specimen (see Figure 5). The bridging of fibers occurs in composite specimens within the unidirectional layers, as in this case.
3 ESTIMATION OF THE ENERGY-RELEASE RATE
The energy-release rate G is defined mathematically, in general, as
g=-1dU
b da
(1)
Figure 1: DCB specimen with attached piano hinges and inserted foil Slika 1: DCB-vzorec s pritrjenim šarnirom in z vstavljeno folijo
where dU is the differential increase in the strain energy, da is the differential increase in the delami-nation (or crack) length, and b is the specimen width. Concerning the investigated Mode I for the DCB specimen, the corresponding energy-release rate GI can be expressed using the Euler-Bernoulli theory of beams as 3,13
172
Materiali in tehnologije / Materials and technology 42 (2008) 4, 171-174
R. ZEMČlK, v. LAS: NUMERICAL AND EXPERIMENTAL ANALYSES OF THE DELAMINATION
Figure 5: Sequence of photographs showing the fiber-bridging progress
Slika 5: Sekvenca posnetkov, ki prikazuje napredovanje vlaknate premostitve
G i =
F2 a2 bEI
G i =
2ba
(3)
obtained for both types of specimens are shown in Table 1. Equation (2) can be corrected in a similar way.
4 NUMERICAL SIMULATION
The numerical simulation was performed using the finite-element method in the MSC.Marc system. In this case the analysis was solved as a plane-strain problem. The geometry was modeled using 4-node rectangular elements. The [0/90/90/0] lay-up was meshed with 8/2/2/8 layers of elements in the thickness direction and 600 elements along the length. A different model was prepared for each crack length a.
The equality between the values of the energy-release rate and the J-integral in the case of the elastic analysis was used in the simulations. MSC.Marc calculates the J-integral using the DeLorenzi method 14.
The material is assumed to be homogeneous, linearly elastic, and orthotropic, and to have the following elasticity constants: longitudinal Young's modulus El = 110000 MPa, transverse modulus Et = 7700 MPa, Poisson's ratio Vlt = 0.28 and shear modulus Glt = 4500 MPa, which were identified previously 1112.
The critical values of the energy-release rate and the parameter A were calculated using (4) in order to best characterise the averaged experimental dependency in Figure 6. The hypothetical delamination curves for the interval 0.1 < Gfc <1.5 kJ/m2 are shown in the graph together with the optimum curve corresponding to the values displayed in Table 1. The reconstructed load-displacement curve from the FEA is compared with the experiment.
(2) Table 1: Measured and calculated parameters of the DCB specimen
where EI is the bending stiffness, i.e., the sum of the Young's moduli in the axial direction multiplied by the inertia moments for all the plies (see Figure 1).
There are several possible ways of calculating the strain-energy release (or eventually the interlaminar fracture toughness) according to the ASTM standard 9. One way is the so-called Modified Beam Theory (MBT) method. The energy-release rate in this case is calculated as
3 FÔ
Initial crack length /mm	a0	62
Crack-length correction /mm	|A|	5.12
Critical energy-release rate /(kJ/m2)	Gic	1.373
Since the beam is not perfectly built-in (a certain amount of rotation can occur at the crack front, i.e., where a clamped condition is assumed), a correction can be applied, which assumes that the delamination is larger by the amount . Hence, the crack length is (a+ ) and the corrected energy-release rate is then given by
G = 3 FÔ	(4)
1 = 2b(a + |A)|
where the value of A is calculated according to the procedure given in the standard 9 and the values
Figure 6: Load-displacement curves for the DCB specimen Slika 6: Krivulje obremenitev - pomik za DCB-vzorec
Materiali in tehnologije / Materials and technology 42 (2008) 4, 171-174
173
R. ZEMČlK, v. LAS: NUMERICAL AND EXPERIMENTAL ANALYSES OF THE DELAMINATION
5 CONCLUSIONS
An experimental investigation of low-speed Mode-I delamination was carried out on carbon-fiber-reinforced epoxy specimens in order to estimate the critical energy-release rate value Gfc. The double-cantilever beam specimens with a cross-ply lay-up were manufactured with inserted aluminum foil serving as an initial crack. The critical energy-release-rate value was determined using the Euler-Bernoulli theory and the ASTM standard from the averaged experimental data. A numerical model was created in the FEA code MSC.Marc for the simulation of the experiment. The model took advantage of the equality between the energy-release rate and the J-integral in the case of an elastic material. The load-displacement dependency was reconstructed and compared with the experimental results. It is clear that it is possible to consider the critical energy-release rate value as the interlaminar fracture toughness in the case of the delamination of a composite with transversely oriented fibers.
Acknowledgement
This work was supported by the research project GA AV IAA200760611 and research project MSM 4977751303.
6 REFERENCES
1V. Las, R. Zemcik, P. Mest'anek: Numerical simulation of composite delamination with the support of experiment. Acta Mechanica Slovaca, 1 (2006), 303-308
2M. Hojo et al.: Mode I delamination fatigue properties of inter-layer-toughened CF/epoxy laminates. Composite Science and Technology, 66 (2006), 665-675 3T. Kusaka et al.: Rate dependence of Mode I fracture behaviour in carbon-fibre/epoxy composite laminates. Composites Science and Technology, 58 (1998), 591-602 4 A. B. Pereira, A. B. Morais: Mode I interlaminar fracture of carbon/epoxy multidirectional laminates. Composites Science and Technology, 64 (2004) 2261-2270 5W. T. Chow, S. N. Atluri: Stress intensity factors at the fracture parameters of delaminations crack growth in composite laminates. Composites Part B, 28B (1997), 375-384 6R. Borst, J. J. C. Remmers: Computational modelling of delami-
nation. Composites Science and Technolgy, 66 (2006), 713-722 7 C. H. Roche, M. L. Accorsi: A new finite element for global modelling of delaminations in laminated beams. Finite Elements in Analysis and Design, 31 (1998), 165-177 8F. Shen, K. H. Lee, T. E. Tay: Modeling delamination growth in laminated composites. Composites Science and Technology, 61 (2001) 1239-1251 9 ASTM D5528-01, Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites, Annual Book of ASTM Standard, 2002, 249-260
10D. P. Miannay: Fracture mechanics, Springer, 1998
11	R. Zemcik, V. Las: Identification of composite material properties using progressive failure analysis. Proc. of Computational mechanics 2005, Nectiny, 2005, 695-700
12	R. Zemcik, V. Las: Numerical simulation of damage in fiber-reinforced composites and comparison with experiment. Proc. of 22nd Danubia-Adria symposium on experimental methods in solid mechanics, Monticelli Terme, Parma, 2005, 174—175
13	M.-S. Sohn, X-Z Hu: Comparative study of dynamic and static delamination behaviour of carbon fibre/epoxy composite laminates. Composites, 26 (1995), 849-858
14	MSC.Marc Volume A: Theory and user information, Version 2005. MSC.Software Corporation, 2004
174
Materiali in tehnologije / Materials and technology 42 (2008) 4, 171-174