PSI - Issue 2_A

Timothy Crump et al. / Procedia Structural Integrity 2 (2016) 381–388 Crump / Structural Integrity Procedia 409 (2016) 000–000

385

5

The solution for a steady-state sharp crack in a DCB is described by a nonlinear differential equation: ܽሷ ൌ ଵ ଶ ௔ሶ మ ௔ ൅ ଵ ସ ଴ହ ఘ ா ஺ ூ ௔ ଵ య െ ଷ ଵ ହ ଶ ధ ୻௔ బ మ ఘ஺ (10) When solving this and making it equal to nΓ to account for some bluntness of the crack tip (such as cohesive zone characteristic length l c ), where ݊ is a bluntness factor, Eqn.(10) can be reduced to find the equilibrium point of crack arrest length at ܽሷ ൌ ܽሶ ൌ Ͳ to approximately be: ܽ ൌ ܽ ଴ ݊ భ ర (13) From this, the estimated arrest length region should be 37 - 41mm away from the initial notch for a static loaded crack (cohesive zone bluntness). 3.1 Homolite-100 2D DCB The stress plot results in 2D can be found in Fig.5 for 3 points in the crack propagation: before initiation, just before the first stress wave interaction and the final arrest location at 40mm which is nearer the blunt crack arrest length approximation from Eqn (13). The crack propagation speed is in line with the observed experimental speed and the corrected analytical solution which takes into account reflected wave interaction with the crack tip as can be seen in Fig.6(a).

(a)

(b)

(c)

Fig. 5. (a) Warped stress plot of initial notched DCB; (b) propagating crack just before first reflected wave interaction; (c) final arrested crack