Oscillatory and tip-splitting instabilities in 2D dynamic fracture: The roles of intrinsic material length and time scales
Section snippets
Background and motivation
Materials failure, which is mainly mediated by crack propagation, is an intrinsically complex phenomenon that couples dynamic processes at length and time scales that are separated by many orders of magnitude, giving rise to a wealth of emergent behaviors. Crack initiation and dynamics are of prime fundamental and practical importance, and have been intensively studied in the last few decades (Freund, 1998, Broberg, 1999). Despite some significant progress, our understanding of many basic
A nonlinear phase-field approach to dynamic fracture: resolving physically-relevant, intrinsic material length scales
The nonlinear phase-field approach to dynamic fracture, to be employed in this paper, has been introduced in quite some detail in Chen et al. (2017) and studied in Chen et al. (2017) and Lubomirsky et al. (2018). Its presentation is repeated here for completeness, and in order to further highlight its physical content and potential utility. This phase-field approach is a Lagrangian field theory that is designed to incorporate the intrinsic material length scales and , and to allow for high
The oscillatory instability: The limit, supercritical Hopf bifurcation and independence of
One of the major achievements of the phase-field approach presented in the previous section is related to the high-velocity 2D oscillatory instability, shown in Fig. 1a–b and briefly discussed earlier in Section 1. To apply the phase-field framework to a given physical problem, one needs to specify the relevant elastic strain energy density functional , the degradation functions , and , the system’s geometry and the applied boundary conditions. As the 2D oscillatory
The ultra-high velocity tip-splitting instability: Relations to the wave-speed inside the dissipation zone
As discussed above in relation to Figs. 1c,f and 2c, upon increasing the driving force for fracture, cracks are predicted to accelerate faster and to yet higher velocities, and feature a tip-splitting instability, either after the onset of oscillations or even prior to it. This behavior is supported by experiments, cf. Fig. 1d. The observation of tip-split crack states, together with the previously discussed oscillatory crack states, allow one to construct a comprehensive phase diagram
Discussion and concluding remarks
In this paper, we used phase-field simulations to investigate the role of intrinsic material length and time scales on the emergence of oscillatory and tip-splitting instabilities in 2D dynamic fracture. The two basic length scales, which are absent in LEFM, include the scale of the dissipation zone where elastic energy is transformed irreversibly into new fracture surfaces and a nonlinear length that is a measure of the distance from the crack tip at which elastic nonlinearity becomes
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research was supported by a grant from the United States-Israel Binational Science Foundation (BSF, Grant No. 2018603), Jerusalem, Israel, and the United States National Science Foundation (NSF, Grant No. 1827343). E.B. also acknowledges support from the Ben May Center for Chemical Theory and Computation and the Harold Perlman Family .
References (60)
- et al.
Solidification microstructures and solid-state parallels: Recent developments, future directions
Acta Mater.
(2009) Some multistep methods for use in molecular dynamics calculations
J. Comput. Phys.
(1976)- et al.
The 1/r singularity in weakly nonlinear fracture mechanics
J. Mech. Phys. Solids
(2009) - et al.
Numerical experiments in revisited brittle fracture
J. Mech. Phys. Solids
(2000) - et al.
A time-discrete model for dynamic fracture based on crack regularization
Int. J. Fract.
(2011) - et al.
Instability in dynamic fracture
Phys. Rep.
(1999) - et al.
A phase-field formulation for dynamic cohesive fracture
Comput. Methods Appl. Mech. Engrg.
(2019) - et al.
Laws of crack motion and phase-field models of fracture
J. Mech. Phys. Solids
(2009) - et al.
Integrating the equations of motion
J. Mol. Biol.
(1983) - et al.
Evaluation of variational phase-field models for dynamic brittle fracture
Eng. Fract. Mech.
(2020)
Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory
Int. J. Plast.
Computer simulation studies of the liquid state
Comput. Phys. Comm.
A review on phase-field models of brittle fracture and a new fast hybrid formulation
Comput. Mech.
Phase-field modeling of ductile fracture
Comput. Mech.
Continuum field description of crack propagation
Phys. Rev. Lett.
Microbranching instability in phase-field modelling of dynamic brittle fracture
Appl. Phys. Lett.
Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms
Int. J. Fract.
Dynamic crack tip equation of motion: High-speed oscillatory instability
Phys. Rev. Lett.
Autonomy and singularity in dynamic fracture
Phys. Rev. E
Dynamics of simple cracks
Annu. Rev. Condens. Matter Phys.
The dynamics of rapid fracture: instabilities, nonlinearities and length scales
Rep. Progr. Phys.
Weakly nonlinear theory of dynamic fracture
Phys. Rev. Lett.
The variational approach to fracture
J. Elasticity
Morphogenesis and propagation of complex cracks induced by thermal shocks
Phys. Rev. Lett.
Cracks and Fracture
Instability in dynamic fracture and the failure of the classical theory of cracks
Nat. Phys.
Crack front segmentation and facet coarsening in mixed-mode fracture
Phys. Rev. Lett.
Thermal fracture as a framework for quasi-static crack propagation
Int. J. Fract.
Fracture in mode i using a conserved phase-field model
Phys. Rev. E
Recent developments in dynamic fracture: some perspectives
Int. J. Fract.
Cited by (0)
- 1
Equal contribution.