PSI - Issue 42

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Niklas Ladwig et al. / Procedia Structural Integrity 42 (2022) 647–654 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

649

= tan −1 √ ⁡

(2) is defined (e.g. = 0 ° in case of pure mode I and = 90 ° in case of pure mode III loading). Our definition differs from the one made by Loh and Marzi by making use of the square root to be consistent with linear-elastic fracture mechanics (LEFM) in the limit case of linear (brittle) fracture behavior. It is further aimed to prescribe the mixed mode ratio (i.e. to keep it constant) during a test. An additional goal of the MC-DCB test is to obtain cohesive laws by an evaluation of the traction t at the crack tip in a similar way as it is well-established in single mode loading, e.g. in [10][11]. In mixed-mode loading, however, the constitutive cohesive law of the adhesive layer influences the mode partitioning as shown by Scheel et al. [12]. In the general case of coupled traction, in which the traction components depend on both (peel and shear) components of the crack opening displacement (COD)  , the (total) J-integral does not solely depend on the traction at the tip and COD, = ∫ ∙ d + ∫ ( , beam⁡deflection) d , (3) as an additional integral over the length of the fracture process zone, L FPZ , has to be considered. The latter integral vanishes in two cases: 1. = 0 2. Traction is uncoupled: ( ) , which implies = 0 if ≠ . The first case can be used as a good approximation when having stiff structural adhesive joints and cantilever-like specimens as MC-DCB. It should be emphasized that the cohesive law is the still allowed to be both coupled and path dependent. To evaluate traction in case 1, it is a further straight-forward assumption that work done by the individual traction components is related to the mode partitioning according to equation (1), = ∫ 1 d 1 and = ∫ 3 d 3 , (4) which allows the calculation of the components of traction, 1 = d d 1 and 3 = d d 3 . (5) In equations (4), (5) and in the following, the index 1 refers to the mode I component and index 3 to the mode III component of the corresponding vector. That kind of proceeding has been proposed by Loh and Marzi [8][9] as direct identification method for traction vectors. Note, that equations (3) to (5) do not require integrability of the cohesive law and therefore hold even the case of load-path dependent fracture. Nevertheless, a monotonic loading is required, since the considerations made above do not include possible impacts from effects such as plasticity and damage when unloaded.