PSI - Issue 13

Lukas Loh et al. / Procedia Structural Integrity 13 (2018) 1318–1323 Author name / Structural Integrity Procedia 00 (2018) 000–000

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I and III. Thereby, arbitrary mode-mixities of modes I + III can be obtained, since the corresponding loadings of both modes are not mutually dependent. Due to calculation of current energy release rate (ERR) during test procedure, testing machine can be controlled on particular contributions of ERR. By means of that, test is denoted by mixed mode-controlled DCB (MC-DCB) test. In this work, fracture behavior of an elastic-plastic adhesive, SikaPower R -498, has been examined under several mode mixities I + III. The following section briefly depicts the evaluation method of ERR regarding boundary conditions of MC-DCB specimens and shows the experimental setup. In section 3, results of di ff erent mode-mixities are presented and afterwards compared to results of mixed-mode I + II tests from literature. This section describes test conditions of performed MC-DCB tests and gives an overview on corresponding eval uations methods. A detailed description of test procedure, especially regarding test control, can be found in Loh and Marzi, (2018). As depicted in Fig.1 a), the MC-DCB specimen is loaded by axial forces 1 F y and 2 F y as well as moments 1 M y and 2 M y for introducing mode I or mode III loading, respectively. Since lateral forces are constructively avoided by clamping equipment, 1 F y = 2 F y = F y and 1 M y = 2 M y = M y . Due to clamping conditions of MC-DCB test, unintended external loadings additionally act on the specimen. These loadings are denoted artificial loadings and are displayed in high lighted gray in Fig.1 a). Taking into account that local rotations around z-axes θ of upper adherend at the position of load introduction are unlocked, the moment 1 M z vanishes. For determining energy release rate, J -integral by Rice (1968) was used. J has been given with J = S   Wdy − t · ∂δ t ∂ x dS   , (1) where W being the strain energy density, t is the traction vector and δ t the corresponding displacement vector acting on an arbitrary path S containing the crack tip as shown in Fig.1 a). As illustrated, x and y are coordinates, whereby crack propagation occurs in x -direction. Furthermore, ERR is in equilibrium with contributions of J from external loads, since J vanishes along a closed path. Considering external loadings of MC-DCB specimen in Fig. 1a), their contributions to J -integral can be defined as follows: Since mode I loading is almost completely evoked by F y , while mode III loading occurs only due to moment M y , corresponding intended contributions to J are given by where b describes the specimen width, E is the Young’s modulus of adherends material and I y represents the second moment of area around y-axis. However, the unintended (artificial) contributions are denoted by J I ∗ = 1 M 2 x + 2 M 2 x 2 b 1 GI t , describing a contribution to J from an ”out-of-plane mode I”-loading and J I + II = 2 M 2 x 2 b 1 EI z is producing an additional mixed-mode I + II contribution. The shear-modulus of adherends material is given by G and the torsional second mo ment of area is denoted by I t . Consequently, J equals the sum of J = J I + J III + J I ∗ + J i + II . To obtain prescribed I + III mode-mixities, artificial contributions J I ∗ and J I + II need to be negligible. This has been verified for di ff erent mode mixities in the subsequent section. Furthermore, the mixed-mode-ratio has been defined with χ = tan − 1 ( J III / J I ). In this work, several mixed-mode-ratios of constant and variable mode-mixities have been investigated, as depicted in Table 1. Besides of test series with mixed-mode-ratios χ = 90 ◦ , χ = 0 ◦ and χ I − III describing pure mode III loading, pure mode I loading and a superimposition in row of both modes with an angle / displacement test-control, all test series of constant mode-mixity have been conducted under control of J I . For these tests, an angular-velocity of ˙ α = 0 . 01 ◦ / s 2. Methods and experimental setup J I = F y θ b and J III = M 2 y 2 b 1 EI y , (2)