Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

Microbranching instability in phase-field modelling of dynamic brittle fracture

“…By increasing the loading for W = 5 mm, we confirm that the crack surface becomes increasingly z-invariant with the same quasi-periodic microbranching regime. Contrary to [20], we did not observe a strong difference in terms of critical speed associated with branching compared to the 2D simulations of [19]. Interestingly, the crack branching speeds have always been observed to be higher than the theoretical minimal speed of 0.52c R necessary for the propagation of branched cracks found in [24].…”

“…The fully damaged zone increases with crack advance, as in 2D simulations, which can be associated to an increasing local damage dissipation rate Γ, identified with an apparent fracture energy (see [19]). We computed this quantity for different two-dimensional slices along the z-direction and at different propagation times.…”

“…The modelling of the I+III mixed-mode instability using such an approach has, for instance, shown very promising results [15,16]. Regarding the branching process, a large majority of works concentrated on two-dimensional simulations and, usually, were only able to reproduce macroscopic branching [17][18][19]. In [20], microbranching has been obtained in 3D computations using a Ginzburg-Landau phase-field model after perturbing the initial crack front and relatively good agreement of the fractographic patterns with experimental observations has been obtained.…”

“…A recent study on the crack branching phenomenon in a two-dimensional pre-strained plate configuration [19] has revealed that single crack propagation is characterized by a progressive widening of the damaged band associated to an increase of the energy release rate. Macroscopic branching has been observed to occur when the energy release rate exceeds a critical value close to 2G c , as initially argued by Eshelby [21].…”

“…The pre-strain loading consists in fixed vertical displacements of intensity ±∆U on the top and bottom boundaries, both horizontal displacements are free and all other boundaries are stress-free. Unless stated otherwise, the default values are W = 1 mm, l 0 = 0.04 mm and ∆U = 0.06 mm, default material properties are close to PMMA (see [19]). For this specific prestrained plate setting, the initially stored elastic energy per unit length along the x-direction is Ψ = 2(∆U ) 2 E/H.…”