PSI - Issue 13

Christopher Schmandt et al. / Procedia Structural Integrity 13 (2018) 799–805 C. Schmandt, S. Marzi / Structural Integrity Procedia 230 (2018) ECF22 5 were found as adequate to describe increasing fracture energy J c and cohesive strength σ 0 at higher loading rates. Thereby, 〈 〉 denotes Macauley brackets. v j marks the inflection point in the J c - v -curve. v 0 = 0.1 µm/s is the lowest investigated crack opening velocity and was chosen as lower bound for v influencing σ 0 . J qs and σ qs are lower bounds for fracture energy and cohesive strength at static loading conditions. This model behavior is important, concerning that neither fracture energy nor cohesive strength must fall below zero in the static limit case. If v increases towards infinity, J c increases to its upper bound 2 J qs , σ 0 tends to infinity as well, but much slower than v , because there are no experimental data available that would justify an upper plateau for cohesive strength. σ dyn is a scaling factor determining the slope of the model function. Although an infinite cohesive strength is nonphysical, the chosen model should be appropriate to roughly estimate cohesive strength under loading rates outside the investigated range. The model parameters J qs = (7.9 ± 0.75) kJ/m 2 and v j = (1.9 ± 1.88) µm/s were found as well as σ qs = (5.4 ± 0.30) N/m 2 and σ dyn = (0.2 ± 0.07) N/m 2 , using the results of all v -controlled tests as supporting points for fit generation. Regarding the 95% confidence bounds for v j , the trustworthiness of the fitting result is insufficient, and a reliable value cannot be specified accurately, although the resulting J c - v -approach looks satisfactorily and a value for v j in between 1 µm/s and 10 µm/s is expected. The observed effects of increasing mode I fracture energy and cohesive strength at higher loading rates as well as a thereby nearly constant cohesive stiffness were also shown by Schmandt and Marzi (2018) for a low modulus hyperelastic adhesive. May et al. (2015) found an increasing cohesive strength and a rising of J c up to a plateau value as well for an epoxy adhesive regarding peel loading at higher strain rates. The observed processes of crack growing are described in Fig. 4 (a) by showing J -time-curves for monotonic loaded specimens at various constant crosshead velocities. The crosshead velocities are chosen in a way that the resulting crack opening velocities, which are approximately one order of magnitude below v ch due to beam bending, are quite similar to the previously investigated range. The highest tested v ch of 10.0 mm/s even yields crack opening velocities near 1.0 mm/s, which is above the investigated v -range. The curve for v ch of 0.1 mm/s is exemplarily compared to pictures recorded from specimen’s edge to describe observed crack propagation processes in Fig. 4 (b). At the beginning of monotonic loading, the inserted pre-crack gets visible (picture 1). When increasing the loading, distinctive necking occurs in the adhesive layer prior to crack propagation (picture 2). 803

Fig. 4. (a) J over time for various controlled v ch ; (b) Pictures recorded from specimen’s edge while crack was propagating.

At this point, subcritical crack propagation starts before reaching maximum of J , which was observed independent of crosshead velocity v ch for all tests. The effect of a propagating crack within rising J was noticed by Loh and Marzi (2018) as well for a low modulus hyperelastic adhesive performing mode I, mode III and mixed mode tests with constant mode ratio. When reaching maximum of J (picture 3), crack propagation rate is suddenly increasing, and crack growth gets overcritical, which was likewise observed independent of crosshead velocity v ch