PSI - Issue 28

M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1601–1620 M.Z. Sadeghi et al./ Structural Integrity Procedia 00 (2019) 000–000

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such as delamination (Ducept et al., 2000). Based on the determined G C values in respective modes, a fracture envelope could be ascertained. This fracture behaviour is formulated by a failure locus or damage criterion based on the presence of these mode interactions. A comprehensive overview of various fracture envelopes is provided in (Bui, 2011). Energy-based envelopes are preferred over the displacement-based envelopes since these envelopes combine shear and tension (Ridha et al., 2011). Fracture envelopes considered in this study are concerned with their applicability for numerical simulation in Abaqus FE software (Abaqus Analysis User's Manual (6.9), 2009). Abaqus provides fracture evolution in terms of power-law and Benzeggagh - Kenane (B-K) law (Benzeggagh and Kenane, 1996). By changing the power-law index which is a material property (Nunes et al., 2019), one can obtain interaction and non-interaction modes. However, BK law is incapable of reproducing a non-interaction fracture locus (Bui, 2011). Numerous studies have been performed to evaluate the Power law-based envelope, the most popular based on index values ranging (1/2,1,3/2 and 2) (Campilho et al., 2013; Campilho et al., 2012; Loureiro et al., 2020; Nunes et al., 2019; Sadeghi et al., 2020). In these studies, single lap bending (SLB) (Loureiro et al., 2020), Semicircular bend (SCB) (Ajdani et al., 2020), asymmetric tapered DCB (ATDCB) (Nunes et al., 2019) was employed to determine the mixed mode fracture toughness of the adhesive. While SLB could assess a mode mixity up to 41%, asymmetric tapered DCB would assess up to 20%. However, such a test would limit the fracture toughness evaluation to a particular mode mixity (Santos and Campilho, 2017) and hence the locus of failure described by various failure envelopes is not ascertained. The power-law formulation is given below: � G � G �� �  � �� G �� G ��� �  � � (1) The simplest case of this law of the form (  =  ) is available in the commercial FEM package Abaqus. However, in the case of certain materials, the Power-law would take the form as in Equation (2) (Bui, 2011). However, the Power law of this form is not discussed further in this paper since the Abaqus FE package does not provide an option to simulate this envelope: � G � G ∗ �� �  � �� G �� G ∗ ��� �  � � (2) where G * IC = G * IC (G I , G II ) and G * IIC = G * IIC (G I , G II ) . Another fracture envelope criterion available in Abaqus is the BK law. In this envelope, a strong coupling between the mode exists through the mixed mode ratio. In this case, the law represents without the need for characterisation tests can be replaced by MMB test for various mode mixities, thereby replacing Mode-I and Mode-II tests. The B-K law formulation (Benzeggagh and Kenane, 1996) is given by: G �� � �G ��� � G �� � � G �� G � � G �� � � � G �� (3) where � �� � � �� �� is defined as the mixed-mode ratio. This law accounts for interaction between various modes of fracture which is like the loading condition of an SLJ. However, the limitation of this law would its inability to predict the non-interaction fracture mode – a case of power law where  =  = 1. This can be attributed to the basic assumption in its formulation which assumes mode dependence (Bui, 2011). In this work, full fracture envelope for two-component epoxy adhesive Araldite 2015 by using two data reduction methods namely J-integral and ECLM were determined under mixed-mode loading. The mode-mixity was achieved by carrying out a Double cantilever beam (DCB) and Mixed-mode bending (MMB) tests with different adhesive layer thickness. To validate the accuracy of the developed fracture envelopes for the adhesive, the determined Gc were used for simulation of single lap joints (SLJ) with different bondline thickness.