Elsevier

Polymer Testing

Volume 29, Issue 6, September 2010, Pages 766-770
Polymer Testing

Test Method
Theoretical and experimental analysis of carbon epoxy asymmetric dcb specimens to characterize mixed mode fracture toughness

https://doi.org/10.1016/j.polymertesting.2010.04.001Get rights and content

Abstract

The Asymmetric DCB test (ADCB) is an alternative configuration to the MMB test (Mixed Mode Bending) to produce a mixed mode load state at the crack tip. In this test, the crack plane is out of the laminate midplane. This test configuration is as simple as pure mode I tests. Nevertheless, the mixed mode load state at the crack tip cannot be controlled by means of the test fixtures and so GI and GII are not easily calculated. In this test configuration, the position of the crack plane controls the percentage of mode I and mode II load at the crack tip.

In this paper, unidirectional carbon epoxy ADCB samples have been used to study the mixed mode load state at the crack tip from different points of view: experimental, numerical and analytical procedures.

The MBT method has been adapted to allow the calculation of G in ADCB samples. Also, an empirical procedure has been proposed in order to calculate GI and GII.

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The analytical procedures developed in the ASTM D 5528-01 standard that allows the calculation of G in DCB tests are no longer valid to analyze ADCB specimens.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:δ=2Pa33EIwhere I is the moment of inertia. The energy release rate is then given by:G=P22BdCdawhere 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:GIIG=f(α)

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:

  • a0: initial crack length.

  • h: total thickness.

  • B: width.

  • Pc: critical load.

  • 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

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