Test MethodTheoretical and experimental analysis of carbon epoxy asymmetric dcb specimens to characterize mixed mode fracture toughness
Introduction
Delamination is a complex process where more than one failure mode is usually present giving rise to a mixed mode mechanism. There are several experimental methods documented in the literature in order to determine the mixed mode fracture toughness in laminated composites. The procedure most widely used is the MMB method (Mixed Mode Bending) [1], [2], [3], [4] (Fig. 1). This test method allows the calculation of GI and GII as the test configuration controls the mode I/mode II load percentage at the crack tip. Nevertheless, the required test fixtures are somewhat complex.
ADCB test is an interesting alternative to the MMB test. This test configuration is similar to the DCB (Double Cantilever Beam) tests. Nevertheless, in ADCB samples the crack plane is out of the laminate midplane and so a mixed mode load state is present at the crack tip (Fig. 2, Fig. 3).
The analytical procedures developed in the ASTM D 5528-01 standard that allows the calculation of G in DCB tests are no longer valid to analyze ADCB specimens. In this test configuration, the position of the crack plane controls the mode I and mode II load level at the crack tip.
There are some analytical expressions developed in the literature to compute G, GI and GII [5]. Mangalgiri et al. [6] were the first to apply the ADCB test to study mixed mode fracture. Other studies based on ADCB specimens can be found in references [7], [8], [9], [10]. Ducept et al. [11] carried out experimental tests on ADCB glass fibre reinforced epoxy composite samples and compared these results with analytical and numerical results. Bennati et al. [12] developed an enhanced beam theory model for the ADCB test based on the experimental work developed by Ducept et al. [11].
In this work, they were carried out ADCB tests on two different unidirectional carbon epoxy laminates: AS4/8552 and AS4/3501. The Hexcel 3501 matrix is an epoxy resin modified to improve toughness. Different approaches were used in order to compute the energy release rate. The specimens were modelled by means of FE analysis. On the other hand, an analytical method (based on the Modified Beam Theory) and an empirical formulation (based on FEM studies) were developed to calculate G, GI and GII. Finally, both numerical and analytical approaches were compared.
Section snippets
The modified beam theory (MBT) for asymmetric specimens
The ASTM Standard D 5528-01 [13] describes the Double Cantilever Beam (DCB) mode I fracture test. One of the data reduction methods proposed in the standard for the calculation of G is the Modified Beam Theory (MBT).
This theory, for samples with the crack placed on the midplane, is based on the stress analysis of a perfectly built-in double cantilever beam:where I is the moment of inertia. The energy release rate is then given by:where C is the compliance defined as δ/P.
FEM analysis of the ADCB specimen
FE modelling is a useful tool to analyze fracture mechanisms [14]. FEM software allows a direct calculation of the elastic energy of the system for a given load state. Therefore, Gc can be calculated by computing the change in the elastic energy of the system before and after the crack extension (Energy Variation Method). This method is quite simple to apply but only allows the calculation of the global value of G. This procedure does not allow the calculation of GI and GII. The mode I and mode
Empirical formulation
In order to determine an empirical expression, multiple sample configurations with different crack positions h2 (Fig. 3) were analyzed by means of the FE Method.
From these results, an empirical equation was derived that fits the numerical results and allows the calculation of GI/G and GII/G (where G = GI + GII). FEM calculations were performed by means of the Two Step Extension Method described below.
Fig. 4 shows the plot of GI/G and GII/G versus α.
From the plot in Fig. 4, we can write:
Materials
Two 6 mm thick unidirectional AS4 carbon fibre reinforced epoxy laminates were used in this study. One of the laminates was produced with a Hexcel 8552 epoxy matrix and the other with a tougher modified epoxy matrix (Hexcel 3501-6). A non-adherent insert was placed in the laminates during lamination in order to produce an artificial delamination to initiate the crack. The structure of both laminates was 6/d/26.
The mechanical properties of the laminates are shown in Table 1.
Experimental results
Five specimens of each material were tested in a MTS testing machine with a 10 kN max. load cell at a speed was 0.5 mm/min. Table 2 shows the obtained results (S.D.: standard deviation) where:
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a0: initial crack length.
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h: total thickness.
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B: width.
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Pc: critical load.
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δc: critical displacement.
Finite element analysis
The ADCB specimens were modelled by means of an ANSYS® FEM package. Four node 2D solid elements with two degrees of freedom at each node (translations in the nodal x and y directions) were used to build the FE
Conclusions
The ADCB test constitutes an alternative configuration to the MMB test to produce a mixed mode load state at the crack tip. This test configuration is as simple as pure mode I tests.
In this paper, two different CFRP laminates were tested: AS4/8552 and AS4/3501. The Hexcel 3501 matrix is an epoxy resin modified to improve toughness properties. Nevertheless, the energy release rate (G) found for the AS4/8552 laminate was slightly higher.
In order to calculate G, GI and GII values two procedures
References (19)
- et al.
Mixed mode fracture toughness of GFRP composites
Composite Structures
(2006) - et al.
A mixed-mode failure criterion derived from tests on symmetric and asymmetric specimens
Composites Science and Technology
(1999) - et al.
An enhanced beam-theory model of the asymmetric double cantilever beam (ADCB) test for composite laminates
Composites Science and Technology
(2009) - et al.
Fractography and failure mechanisms in static mode I and mode II delamination testing of unidirectional carbon reinforced composites
Polymer Testing
(2009) - et al.
Finite element calculation of stress intensity factors by a modified crack closure integral
Engineering Fracture Mechanics
(1977) - J.H. Crews Jr., J.R. Reeder, A mixed-mode bending apparatus for delamination testing. NASA Technical Memorandum 100662,...
- et al.
The mixed-mode bending method for delamination testing
AIAA Journal
(1990) - et al.
Redesign of the mixed-mode bending delamination test to reduce nonlinear effects
Journal of Composites Technology and Research
(1992) Mixed mode I-mode II interlaminar fracture t of unidirectional fibre reinforced polymer matrix composites
ASTM International
(2001)
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