Daughter Crack Research Articles

Phase-field simulation and coupled criterion link echelon cracks to internal length in antiplane shear

This paper provides a comprehensive numerical analysis of daughter crack localization in pure antiplane shear. Although antiplane shear fracture is important in various industrial applications, understanding the morphology of the resulting fragmentation remains challenging. The paper develops innovative phase-field models to induce the facets using a small spatial variation in the toughness field and examines the impact of numerical and material parameters on the newly formed daughter cracks’ shape and spacing. Through meticulous comparison to the coupled criterion, the paper reveals a compelling connection between the internal length-scale of damage regularization, Irwin’s length and the facet crack spacing. Furthermore, the effect of Poisson’s ratio on the crack form and spacing is investigated: the results reveal a significant influence and showcase comparable initiation distances between the numerical simulations and experimental measurements in pure antiplane loading.

Sub-Rayleigh to supershear transition of dynamic mode-II cracks

The Sub-Rayleigh to supershear transition is commonly accepted to be governed by the Burridge-Andrews mechanism. Such a mechanism predicts the direct nucleation of a secondary intersonic crack (daughter crack), which is triggered ahead of the main crack front due to a developing shear stress peak. Yet, some research shows that the supershear transition is not always accompanied by a daughter crack. And to our knowledge, mother-daughter crack pairs are rarely reported with visual observations. By conducting numerical experiments for pre-strained PMMA plates, the mother-daughter crack mechanism is successfully observed in phase-field fracture modeling for the first time. On this basis, both the supershear transition with and without the daughter crack are discussed in terms of the stress field and prestress level. Our results reveal a critical prestress level, below which no supershear transition can be accomplished from the Sub-Rayleigh crack propagation. Furthermore, we also presented the criteria for predicting the occurrence of daughter crack through systematic simulations.

Transition from sub-Rayleigh anticrack to supershear crack propagation in snow avalanches

Snow slab avalanches, characterized by a distinct, broad fracture line, are released following anticrack propagation in highly porous weak snow layers buried below cohesive slabs. The anticrack mechanism is driven by the volumetric collapse of the weak layer, which leads to the closure of crack faces and to the onset of frictional contact. Here, on the basis of snow fracture experiments, full-scale avalanche measurements and numerical simulations, we report the existence of a transition from sub-Rayleigh anticrack to supershear crack propagation. This transition follows the Burridge–Andrews mechanism, in which a supershear daughter crack nucleates ahead of the main fracture front and eventually propagates faster than the shear wave speed. Furthermore, we show that the supershear propagation regime can exist even if the shear-to-normal stress ratio is lower than the static friction coefficient as a result of the loss of frictional resistance during collapse. This finding shows that snow slab avalanches have fundamental similarities with strike-slip earthquakes.

Supershear Rupture, Daughter Cracks, and the Definition of Rupture Velocity

AbstractRupture velocity is a fundamental feature of earthquake behavior. How rupture velocity is defined can therefore affect our understanding of earthquake physics. Based on dynamic rupture simulations, we compare the tangent and average rupture velocities calculated via one‐ and two‐dimensional gradients. Two strike‐slip scenarios with free‐surface‐induced supershear ruptures are presented within a homogeneous and a depth‐dependent stress regime, respectively. Although both scenarios produce a daughter crack that propagate over the seismogenic depth, in the depth‐dependent case the 1D and 2D rupture velocities capture different features: A 1D horizontal gradient measurement implies a supershear rupture, while a 2D gradient measurement reveals sub‐Rayleigh rupture propagation everywhere except very close to the free surface. A large area on the fault with the 1D horizontal tangent rupture velocity does not necessarily produce an observable Mach front, which arises the importance of rupture velocity definitions in supershear analysis.

The effects of sediments on supershear rupture

The effects of sediments on supershear rupture have been discussed. Two sediment models with different media properties have opposite effects on supershear rupture. The rupture accelerates into supershear more easily if the sediment is thin in the model with a relatively low wave velocity. In contrast, the supershear rupture transition occurs more easily if the sediment is thick in the model with a relatively high wave velocity. Supershear is first triggered at the lower boundary of the sediment if the initial stress is sufficiently high. Otherwise, supershear is prevented or triggered at the free surface if the initial stress is relatively low. A deep hypocenter favors supershear rupture. The very long supershear transition distance in some cases may explain the extremely long supershear transition distance in the 2001 Kunlunshan earthquake. We also investigate the effects of the depth-dependent stress on the supershear rupture and find that similar results are concluded. Besides, a daughter crack is triggered but propagates in a subshear regime in some cases. A multi-layered sediment model makes it easier to trigger supershear rupture in relative high-velocity sediment but harder in relatively low-velocity sediment. Our results provide a possible explanation for the rarity of supershear earthquakes in nature.

The Sustainability of Free‐Surface‐Induced Supershear Rupture on Strike‐Slip Faults

AbstractWhile prior numerical simulations indicate that the Earth's free surface can induce supershear propagation on strike‐slip faults, copious observations of strike‐slip earthquakes have produced only a few instances of such supershear rupture. Our dynamic rupture simulations with varying initial normal stresses and fault strengths show that free‐surface‐induced supershear rupture on strike‐slip faults may return to sub‐Rayleigh speed as the rupture progresses. Such a phenomenon is defined as unsustained free‐surface‐induced supershear rupture, indicating that a rupture on a strike‐slip fault, even if it encounters the free surface, may not generate supershear rupture that is sustained long enough to be observable. The shape of the rupture front contour on the fault may also lead to a false impression about the rupture velocity, since the daughter crack may also propagate at sub‐Rayleigh speed, with near‐field fault‐perpendicular ground motion. Shallower hypocenter depths increase the likelihood of an unsustained free‐surface‐induced supershear rupture.

Twin induced fracture toughness in SiCW/SiC composites processed by spark plasma sintering

The twin boundaries (TBs) was responsible for 30% and 26% enhancement in the fracture toughness of 10% and 20% SiCW/SiC composites spark plasma sintered at 1800 °C, respectively. Crack deflection at TBs, and daughter crack formation at the twin zone were found to be the responsible mechanisms for twin toughening.

Dynamic mode II crack growth along an interface between an elastic solid and a plastic solid

Dynamic crack growth is analyzed numerically for a planar bimaterial block with an initial edge crack subject to mode II impact loading along the side of the block. The crack is constrained to grow along a weak interface directly ahead of the initial crack tip. A cohesive constitutive relation, that relates tractions and displacement jumps, is specified across the weak interface. The normal traction along the interface is taken to be a linear function of the normal displacement across the interface while the shear traction is taken to be a nonlinear function with the shear traction approaching zero for large displacement jumps, thus allowing mode II crack propagation. The material on the impact side of the interface is taken to be a linear elastic (actually hypoelastic) solid while the material on the other side of the interface is taken to be an isotropically hardening elastic-viscoplastic solid. Both plastically incompressible and plastically compressible solids are considered. Results are presented for the effects of plastic deformation on the evolution of near crack tip fields, on the crack speed history, and on the tractions that develop at the interface. The effects of various parameter variations are also explored. It is found that plasticity can result in tensile normal tractions developing on the interface in the crack tip vicinity and that the transition to an intersonic crack speed via a daughter crack mechanism can take place in the presence of small amounts of plastic straining.

The effects of barriers on supershear rupture

AbstractA barrier may induce a supershear rupture transition in some cases, whereas it may prevent the further propagation of a supershear rupture in other cases. We investigate the effects of a barrier on the supershear rupture propagation on a planar fault in a 3‐D half‐space. Our results show that the effect of a barrier on supershear is strongly dependent on its size, strength, and location. For larger sizes, shallower buried depths, and relatively higher strengths, the barrier tends to prevent supershear propagation more strongly. When the barrier is located on the free surface and near the critical distance, it prevents the further propagation of supershear rupture. If a barrier is located far from the critical distance, the first supershear daughter crack is slowed down and a new supershear daughter crack is generated after the rupture front passes through the barrier. This mechanism greatly lengthens the supershear transition distance.

Spatiotemporal properties of Sub-Rayleigh and supershear rupture velocity fields: Theory and experiments

Fundamental spatiotemporal field properties and particle velocity waveform signatures of sub-Rayleigh and supershear ruptures were experimentally investigated through a series of laboratory earthquake experiments. We appeal to dynamic rupture theory to extract and highlight previously unnoticed aspects and results, which are of direct relevance to our new experiments. Kinematic relationships derived from both singular and non-singular solutions are applied to analyze and interpret various features observed in these experiments.A strong correspondence is demonstrated between particle velocity records obtained in lab experiments and synthetic particle velocity waveform profiles derived from theory. Predicted temporal profiles, sense of particle motion, and amplitude decay properties of sub-Rayleigh and supershear particle velocity waveforms are experimentally verified. In a particular set of supershear rupture experiments, the fault-normal (FN) and fault-parallel (FP) velocity waveforms were simultaneously recorded at fixed, off-fault field points as a shear Mach front swept these locations. Particle velocity records collected over a broad range of stable supershear rupture speeds validate the predicted scaling relationship δu̇1s/δu̇2s=Vr2/Cs2−1=βs, between the FP (δu1ṡ) and the FN (δu2ṡ) velocity jumps propagated by a shear Mach front. Additional experimental findings include detailed rupture speed measurements of sub-Rayleigh and supershear ruptures and the observation of a supershear daughter crack with vanishing shear Mach front.Previously unappreciated scaling relations between particle velocity field components, attributed to dilatational and shear waves, are also developed and experimentally verified. In particular, the FP velocity jump δu1ṡ(x1,x2) propagated by the shear Mach front, and the sliding speed δu̇1(x1,0+), measured at a field point positioned extremely close to the frictional fault plane, are shown to obey a speed-dependent scaling relationship given by δu̇1s/δu̇1+=1−2Cs2Vr2, which was gleaned from a non-singular, steady state velocity field solution.

A study of frictional contact in dynamic fracture along bimaterial interfaces

We investigate numerically the dynamic in-plane propagation of a centered crack along bimaterial interfaces using a spectral formulation of the elastodynamic boundary integral equations. Particular attention is given to the effect of contact zones at the subsonic/intersonic transition. In a single set-up, we simulate and describe the different phenomenon observed experimentally (distinct natures of contact zones, unfavorable velocity range, asymmetric crack propagation). We show that different behaviors are observed as function of the crack propagation direction, i.e., with respect to the particle displacements of the compliant material. When the crack propagates in the same direction, the propagation velocities between $$c_\mathrm{R}$$ and $$c_\mathrm{s}$$ are forbidden and the subsonic/intersonic transition occurs with the nucleation of a daughter crack in front of the main rupture. The intersonic stress field at the crack front is compressive due to the material mismatch and a contact zone appears behind the tip. In the opposite direction, a smooth subsonic/intersonic transition occurs although crack face closure (in normal direction) is observed for speeds between $$c_\mathrm{s}$$ and $$\sqrt{2}c_\mathrm{s}$$ . In this regime, a Rayleigh disturbance is generated at the crack surface causing a contact zone which detaches from the tip. Using a contact model governed by a regularized Coulomb law, we provide a quantitative evaluation of the influence of friction on the effective fracture toughness. Finally, we show the applicability of our analysis to the description of different bimaterial situations as well as the single-material set-up.

Theoretical Study of the Conditions and the Mechanism of Shear Crack Acceleration towards the Longitudinal Wave Velocity

The question about physically admissible velocity of dynamic crack growth is of significance to safety engineering as well as to earthquake dynamics. Recent researches including numerical simulations, experimental observations and the analysis of strong earthquakes have shown a possibility of propagation of shear cracks in supershear regime, namely at velocities comparable with dilatational wave speed. The present paper is devoted to the theoretical (numerical) study of some fundamental aspects of this problem. It is shown that development of a sub Raleigh shear crack is connected with a vortex traveling ahead of the crack tip at a shear wave velocity. The stress concentration area ahead of the crack tip revealed by different authors (Burridge, Andrews, Geubelle, Rosakis and others) is connected with this vortex. Acceleration of a shear crack towards the longitudinal wave velocity is concerned with formation of a daughter crack by the mechanism of shearing (the daughter crack is formed in the center of vortex). Analysis of sub Raleigh to intersonic transition has shown that development of shear cracks is self-similar and depends on dimensionless parameters.

Arcan-Richard Specimens: Is there a Pure Shear Mode?

Traditionally, applications of fracture mechanics have been mainly focused on cracks growing under the opening or mode I mechanism (three point bend specimen, middle tension specimen, crack tension specimen, etc.). When investigating instability under mixed mode loading conditions, three different alternatives can be envisaged consisting of: a) machining a hole in standard specimens, b) creating a crack oriented under a given angle, and c) using non-standard Arcan-Richard specimens. In this work, finite element calculations are performed to analyze the initial values of the fracture parameters in Arcan-Richard specimens. First, the influence of the normal stress mode to the shear stress mode ratio is analyzed, then the effect of the constraint level is discussed, and finally, the initial propagation angle of the daughter crack is derived.

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113–2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent −1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Toughening by nano-scaled twin boundaries in nanocrystals

Joint enhancement on strength and toughness provides a cutting-edge research frontier for metals and alloys. Conventional strengthening methods typically lead to suppressed ductility and fracture toughness. In this study, large-scale atomic simulation on the fracture process is performed featuring nanocrystals embedded with nano-scaled twin boundaries (TBs). Four toughening mechanisms by nano-scaled TBs are identified: (i) crack blunting through dislocation accommodation along the nano-scaled TBs; (ii) crack deflection in a manner of intragranular propagation; (iii) daughter crack formation along the nano-scaled TBs that further enhances the toughness and (iv) curved TB planes owing to an excessive pileup of geometrically necessary dislocations. These toughening mechanisms jointly dictate the mechanical behavior of nano-structured materials, and provide insights into the application of nano-scaled TBs with an aim to simultaneously obtain enhanced strength and toughness. New approaches to introduce these coherent internal defects into the nanostructure of crystalline materials are also proposed.

Analysis of supershear transition regimes in rupture experiments: the effect of nucleation conditions and friction parameters

SUMMARY We consider the effect of the rupture initiation procedure on supershear transition of Mode II ruptures on interfaces governed by linear slip-weakening friction. Our study is motivated by recent experiments, which demonstrated the transition of spontaneous ruptures from sub-Rayleigh to supershear speeds in the laboratory. In these works the experiments were analysed using the Burridge–Andrews model of supershear transition, in which a supershear daughter crack is nucleated in front of the main mother rupture. It was concluded that the critical slip of the linear slip-weakening formulation needs to be pressure-dependent for a good match with experiments. However, the dynamic rupture initiation mechanism in the experiments was conceptually different from the quasi-static one adopted in the numerical work used for comparison. Here, our goal is to determine the effect of the nucleation by numerically modelling the experiments using a rupture initiation procedure that captures the dynamic nature of the wire explosion mechanism used in the experiments. We find parameter regimes that match the experimentally observed transition distances for the entire range of experimental conditions. Our simulations show that the dynamic rupture initiation procedure significantly affects the resulting transition distances, shortening them by about 30–50 per cent compared to those predicted through the quasi-static rupture initiation process. Moreover, for some cases, the dynamic initiation procedure changes the very mode of transition, causing a direct supershear transition at the tip of the main rupture instead of the mother–daughter mechanism. We find reasonable parameter regimes which match experimentally determined transition distances with both direct supershear transition at the rupture tip and the Burridge–Andrews (mother– daughter) mechanism, using both pressure-independent and pressure-dependent critical slip. The results show that there are trade-offs between the parameters of the rupture initiation procedure and the properties of interface friction. This underscores the importance of quantifying experimental parameters for proper interpretation of the experiments and highlights the importance of the rupture initiation procedure, in simulations of both experiments and real-life earthquake events.

Conditions governing the occurrence of supershear ruptures under slip‐weakening friction

A general theory for transitions between sub‐Rayleigh and intersonic rupture speeds is developed for faults governed by slip‐weakening friction. The transition occurs when stresses moving at intersonic speeds ahead of expanding or accelerating sub‐Rayleigh ruptures exceed the peak strength of the fault, initiating slip within a daughter crack. Upon reaching a critical nucleation length, the daughter crack becomes dynamically unstable, expanding into a self‐sustaining intersonic rupture. This mechanism holds in both two and three dimensions. On faults with uniform properties, the seismic S ratio [S = (τp − τ0)/(τ0 − τr)], a measure of the initial loading stress, τ0, relative to the peak and residual strengths, τp and τr, respectively, must be smaller than some critical value for the transition to occur. The maximum S value for unbounded faults in three dimensions is 1.19, smaller than the value of 1.77 that Andrews (1985) has shown to govern the transition in two dimensions. The supershear transition length (i.e., how far the rupture propagates before reaching intersonic speeds) is proportional to a length scale arising from the friction law governing the nucleation and stability of the daughter crack. A sufficiently narrow fault width suppresses the transition; the critical width is approximately 0.8 times the transition length on an unbounded fault. The transition length is highly sensitive to the form of the slip‐weakening law even when the associated fracture energies are identical. Heterogeneous propagation, in the form of abrupt accelerations or increases in stress‐release rate, induces stress‐wave radiation that can trigger transient bursts of intersonic propagation.

Transition of mode II cracks from sub-Rayleigh to intersonic speeds in the presence of favorable heterogeneity

Understanding sub-Rayleigh-to-intersonic transition of mode II cracks is a fundamental problem in fracture mechanics with important practical implications for earthquake dynamics and seismic radiation. In the Burridge–Andrews mechanism, an intersonic daughter crack nucleates, for sufficiently high prestress, at the shear stress peak traveling with the shear wave speed in front of the main crack. We find that sub-Rayleigh-to-intersonic transition and sustained intersonic propagation occurs in a number of other models that subject developing cracks to intersonic loading fields. We consider a spontaneously expanding sub-Rayleigh crack (or main crack) which advances, along a planar interface with linear slip-weakening friction, towards a place of favorable heterogeneity, such as a preexisting subcritical crack or a small patch of higher prestress (similar behavior is expected for a small patch of lower static strength). For a range of model parameters, a secondary dynamic crack nucleates at the heterogeneity and acquires intersonic speeds due to the intersonic stress field propagating in front of the main crack. Transition to intersonic speeds occurs directly at the tip of the secondary crack, with the tip accelerating rapidly to values numerically equal to the Rayleigh wave speed and then abruptly jumping to an intersonic speed. Models with favorable heterogeneity achieve intersonic transition and propagation for much lower prestress levels than the ones implied by the Burridge–Andrews mechanism and have transition distances that depend on the position of heterogeneity. We investigate the dependence of intersonic transition and subsequent crack propagation on model parameters and discuss implications for earthquake dynamics.

Data-driven feature modeling, recognition and analysis in a discovery of supersonic cracks in multimillion-atom simulations

This paper presents a new, automated image- and feature-based pipeline of analysis algorithms to elucidate and quantify a discovery regarding supersonic cracks made using large-scale molecular dynamics computations. The first computational confirmation of supersonic cracks was made in recent years, along with the discovery of a two-step, discrete process of increasing crack velocity through the nucleation of a transonic daughter crack and the later nucleation of a supersonic granddaughter crack. This discovery was facilitated by the work presented here. The algorithm pipeline includes modeling, recognition and motion analysis of both the front most crack tips and the more subtle secondary wavefronts from the slower ancestor cracks. The algorithms employed include line extraction from Canny edge maps, feature modeling based on physical properties, and subsequent tracking of primary and secondary wavefronts. The model embeds anticipated propagation properties (physics-based framework) and adapts to changes in the data for unexpected aspects (data-driven modeling). This process is completely automated; it runs in real time on three different 834-frame sequences using 40 250 MHz processors. Results supporting the discovery of the two-step transition to supersonic crack propagation in bilayer materials are presented in terms of both feature tracking and velocity analysis.

Implementation aspects of the bridging scale method and application to intersonic crack propagation

AbstractThe major purpose of this work is to investigate the performance of the bridging scale method (BSM), a multiscale simulation framework for the dynamic, concurrent coupling of atomistics to continua, in capturing shear‐dominant failure. The shear‐dominant failure process considered in this work is intersonic crack propagation along a weak plane in an elastic material, similar to the seminal molecular dynamics (MD) simulations by Abraham and Gao (Phys. Rev. Lett. 2000; 84(14):3113–3116). We show that the BSM simulations accurately capture the essential physics of the intersonic crack propagation, including the formation of a daughter crack and the sudden acceleration of the crack to a velocity exceeding the material shear wave speed. It is also demonstrated that the non‐reflecting boundary condition can adequately dissipate the strongly localized wave formed by the Mach cone after the crack accelerates beyond the material shear wave speed. Finally, we provide the algorithm for our implementation of the BSM, as well as the code used to determine the damping kernels via a newly adopted technique which is less expensive than previous methods. Copyright © 2007 John Wiley & Sons, Ltd.