Onset of Propagation of Planar Cracks in Heterogeneous Media

Abstract

The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along the crack front which is non-monotonic in time due to the elastic waves in the medium. In the quasistatic limit with instantaneous stress transfer, the crack front exhibits dynamic critical phenomenon, with a second order like transition from a pinned to a moving phase as the applied load is increased through a critical value. At criticality, the crack-front is self-affine, with a roughness exponent $\zeta =0.34\pm 0.02$. The dynamic exponent $z$ is found to be equal to $0.74\pm 0.03$ and the correlation length exponent $\nu =1.52\pm 0.02$. These results are in good agreement with those obtained from an epsilon expansion. Sound-travel time delays in the stress transfer do not change the static exponents but the dynamic exponent $z$ becomes exactly one. Real elastic waves, however, lead to overshoots in the stresses above their eventual static value when one part of the crack front moves forward. Simplified models of these stress overshoots are used to show that overshoots are relevant at the depinning transition leading to a decrease in the critical load and an apparent jump in the velocity of the crack front directly to a non-zero value. In finite systems, the velocity also shows hysteretic behaviour as a function of the loading. These results suggest a first order like transition. Possible implications for real tensile cracks are discussed.

51 pages + 20 figure

Cited by in corpus (40)

• Statistical Models of Fracture
• Bulk Metallic Glasses Deform via Slip Avalanches
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• An extremal model for amorphous media plasticity
• Roughness at the depinning threshold for a long-range elastic string
• Can crack front waves explain the roughness of cracks ?
• Width distribution of contact lines on a disordered substrate
• Depinning transition of dislocation assemblies: pileup and low-angle grain boundary
• Crack roughness and avalanche precursors in the random fuse model
• Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone
• Effective toughness of heterogeneous brittle materials
• The roughness of stylolites: Implications of 3D high resolution topography measurements
• Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media
• Depinning with dynamic stress overshoots: Mean field theory
• Quantitative prediction of effective toughness at random heterogeneous interfaces
• A New Criterion for Crack Formation in Disordered Materials
• Depinning exponents of the driven long-range elastic string
• Higher correlations, universal distributions and finite size scaling in the field theory of depinning
• Creep motion of elastic interfaces driven in a disordered landscape
• Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior
• Roughness of moving elastic lines - crack and wetting fronts
• Material independent crack arrest statistics
• The cooperative effect of load and disorder in thermally activated rupture of a two-dimensional random fuse network
• Roughness of Crack Interfaces in Two-Dimensional Beam Lattices
• Models of plastic depinning of driven disordered systems
• One-Way Hysteresis in the Depinning Transition
• Dynamical Inequality in Growth Models
• Stability and roughness of tensile cracks in disordered materials
• Depinning in a two-layer model of plastic flow
• Distribution of velocities and acceleration for a particle in Brownian correlated disorder: inertial case
• On the critical region of long-range depinning transitions
• Scaling theory for the statistics of slip at frictional interfaces
• Energy dissipation statistics in the random fuse model
• Reply to Comment on "Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone"
• Role of the sample thickness in planar crack propagation
• Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface
• On the Self-Affine Roughness of a Crack Front in Heterogeneous Media
• Depinning and flow of a vortex line in an uniaxial random medium
• Dynamic crack growth along heterogeneous planar interfaces: interaction with unidimensional strips
• Depinning free of the elastic approximation