PSI - Issue 43

Stanislav Žák et al. / Procedia Structural Integrity 43 (2023) 23 – 28 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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In addition to complex approach in eq. (3), the mode-mixity in eq. (2) is influenced by the phase factor ω which is a function of the Dundurs parameters. While the phase factor is usually assumed to equal its value for α = β = 0, hence ω = 52.1° according to (Suo and Hutchinson, 1990), recent research (Žák et al., 2022) showed that modern material combinations leads to vastly different ω -values, leading to significant changes in computed mode-mixity angles. Since the adhesion energy is originally treated as a function of the mode-mixity angle, hence Γ ( Ψ ), and numerous empirical (see e.g. works by (Cordill et al., 2004; Hutchinson and Suo, 1992)) or theoretical (see e.g. works by (Banks-Sills and Ashkenazi, 2000; Charalambides et al., 1992) interfacial fracture criteria are constructed by fitting a function through experimentally obtained Γ ( Ψ )-values, a proper characterization and implementation of the elastic mismatch influence must be used. The presented work aims to investigate and show the impact of the false use of ω = 5 2.1° a ssumption and the errors introduced by it when evaluating the interface fracture criteria and practical work of adhesion Γ I (see a summary by (Volinsky et al., 2002)) based on the buckling-induced delamination of thin films. 2. Methods 2.1. Model for ω(α, β) function As mentioned in the introduction section, the mode-mixity angle Ψ is dependent on the elastic material properties mismatch through the phase factor ω . Therefore, our previous research (Žák et al., 2022) aimed at numerical modelling of possible α and β parameters combinations for case according to Fig. 1 using the finite element modelling. Evaluation of the SIFs and usage of eqs. (2) and (3) for each model (defined by the specific α and β values) led to fitted polynomial ω ( α , β ) function, therefore, correct ω - and Ψ -values ca be evaluated: 2.2. Fracture criteria The adhesion energy of a thin film-substrate system is always dependent on the mode-mixity angle Ψ . There are many semi-empirical approaches to describe the mixed-mode fracture criteria. Since the mode-mixity angle Ψ is directly influenced by the elastic mismatch of the interface, these criteria can change when the correct ω -value is used. In order to demonstrate this effect, these fracture criteria are used in relation to experimental results. In the Table 1, the G I, c stands for mode I critical crack driving force (equivalent to the practical work of adhesion Γ I ), Ψ 0 is the phase shift and λ is a parameter describing the mode II involvement in the fracture process whereas for purely brittle interfaces λ = 1 and Γ ( Ψ ) = G I, c and for other cases λ ∈ (0; 1): Table 1. Fracture criteria used for evaluation of experimental results with correct ω -values. Criterion introduced (and used) by Identifier Expression (Hutchinson and Suo, 1992) H-S (Cordill et al., 2004; Hutchinson and Suo, 1992) C-H-S (Banks-Sills and Ashkenazi, 2000; Charalambides et al., 1992) BS-A-Ch 2.3. Experimental data For application of evaluated changes in Γ ( Ψ ) due to new approach for ω, three sets of experimentally measured data were used – buckled Mo thin film on polyimide (PI) and two different depositions of Mo-Cu bi-layer on glass substrate. All Γ ( Ψ ) values were evaluated using eqs. (1) - (3) from the direct profile height measurements of buckles by Confocal Laser Scanning Microscopy (CLSM) method with Olympus OLS 4100 LEXT microscope. 3 4 5 3 52.466 10.510 1.403 9.477 10.298 48.786 6.444 5.943          = +  −  +  +  −  −  +   ( ) ( )   1 2 2 I, c 1 1 sin G  −   = + −  ( ) ( )    2 I, c 1 tan 1 G    = + −  ( ) ( )   2 I, c 0 1 tan G   = +  −  . (4)