Crack Motion Research Articles

Dynamic fracture instabilities in brittle crystals generated by thermal phonon emission: Experiments and atomistic calculations

Dynamic cleavage fracture experiments of brittle single crystal silicon revealed several length scales of surface and path instabilities: macroscale path selection, mesoscale crack deflection, and nanoscale surface ridges. These phenomena cannot be predicted or explained by any of the continuum mechanics based equations of motion of dynamic cracks, as presumably critical energy dissipation mechanisms are not fully accounted for in the theories. Experimentally measured maximum crack speed, always lower than the theoretical limit, is another phenomenon that is as yet not well understood.We suggest that these phenomena depend on velocity dependent and anisotropic material property that resists crack propagation. The basic approach is that the bond breaking mechanisms during dynamic crack propagation vibrate the atoms at the crack front to generate thermal phonon emission, or heat, which provides additional energy dissipation mechanisms. This energy dissipation mechanism is a material property that resists crack propagation. To evaluate this property, we combined the continuum based elastodynamic Freund equation of motion with molecular dynamics atomistic computer “experiments”.We analyzed the above experimental dynamic fracture instabilities in silicon with the obtained velocity dependent and anisotropic material property and show its importance in cleavage of brittle crystals.

Self-Oscillating Regime of Crack Propagation Induced by a Local Phase Transition at Its Tip

We report an analytical study of propagation of a straight crack with a stress-induced local phase transition at the tip. We obtain its contribution to the dynamic fracture energy in explicit form and demonstrate that it nonmonotonically depends upon the crack tip velocity. We show that its descending part gives rise to the instability of the steady propagation regime. We obtain the dynamic phase diagram and indicate those domains where self-oscillating regimes of the crack motion take place.

A new analytical formulation for contact stress and prediction of crack propagation path in rolling bodies and comparing with finite element model (FEM) results statically

Rails fracture by the growth of fatigue crack or critical crack is one of the prevalent defects in railway. The rail fracture, failure and analysis of stress should be studied to prevent rail fracture and events. In this paper, new formulation of contact stress for two rolling bodies is presented, and its results are close to the hertz stress formulation. The analysis of stress is done by Finite Element Model (FEM) and it is compared with hertz stress and new stress formulation results. Then, the analysis of stress, fracture, prediction of fracture and path of crack motion in rail and wheel are studied, statically which plays an important role in this field. The methods of analysis of stress theory fracture with numerical and FEM are compared and consequently, it was proved that these approaches have acceptable results compared with other results. So we can rely on these methods and their results. The relation between maximum displacement and maximum stress is presented, and the path of crack growth and fracture is predicted. To analyze the pressure of collection of the wheel and rail instead of elliptical contact surface, quadrant of elliptical contact surface is assumed. With this assumption, acceptable results will be attained. Key words: Rail fracture, maximum stress, Hertz’s elliptic, reformation coefficients, negative discharge energy hole, crack growth.

The Use of Atomic Force Microscopy to Study Crack Tips in Glass

This article presents a review of the application of atomic force microscopy (AFM) to crack-tip corrosion during subcritical crack growth in glass. The two principal experimental techniques used in this type of study are (1) the direct observation of crack motion by scanning the tip of a crack during crack growth and (2) the examination of fracture surfaces once the specimen has been fractured in two. The first technique has been used to demonstrate and quantify water condensation at crack tips during subcritical crack growth and is particularly useful at low crack velocities. The second technique has been used to quantify the crack-tip corrosion process and the shape of the crack tip during crack growth. In this article, we discuss experimental results showing that the environment that develops at the tips of freshly fractured glass surfaces in soda lime glass can corrode the glass surfaces near the crack tip. Soda lime silicate glass contains mobile alkali ions that will exchange with hydronium ions in solution at the crack tip, forming a highly basic solution that is corrosive to glass. Experimental evidence for such corrosion has been obtained by the atomic force microscope, which demonstrates a displacement of the two fracture surfaces near the crack tip that can be as much as 20 nm, depending on how long the crack is held open at the fatigue limit. Despite the corrosion and displacement of the crack surfaces, the crack tip itself appears to remain sharp, suggesting that the fatigue limit in soda lime silicate glass is not due to crack-tip blunting. Most likely, the fatigue limit is a consequence of ion exchange at the crack tip, in which hydronium ions in the crack-tip solution exchange with sodium ions in the glass. As hydronium ions are larger than sodium ions, this exchange process leaves a compressive stress within the fresh fracture surface of the glass that resists crack motion and results in a stress-corrosion fatigue limit, as first proposed by Bunker and Michalske. In agreement with this mechanism, no fatigue limit is observed for silica glass, which also exhibits no ion exchange. As the crack-tip solution in silica glass is only mildly acidic, pH ≈ 5, corrosion does not occur at crack tips of this glass as supported by the observation that no crack-tip displacements are observed in silica glass by AFM. As the proposed ion exchange mechanism used to explain the stress corrosion limit in glass is at variance with the belief that the fatigue limit in glass is the result of crack-tip blunting, we discuss the possibility of plastic deformation at crack tips in glass and conclude that the available experimental data does not support such a model. At the present time, chemical reaction based crack growth theories are most consistent with the body of crack growth data that is available on glass and are probably the best explanation for the phenomenon.

Crack branching in carbon steel. Fracture mechanisms

The fracture surfaces of pressure vessels made of carbon steel that form during crack branching propagation are examined by fractography. Crack branching is found to occur at a crack velocity higher than a certain critical value V > Vc. In this case, the material volume that is involved in fracture and depends on the elastoplastic properties of the material and the sample width has no time to dissipate the energy released upon crack motion via the damage mechanisms intrinsic in the material under given deformation conditions (in our case, via cracking according to intragranular cleavage).

Dynamic crack growth under Rayleigh wave

A nonuniform crack growth problem is considered for a homogeneous isotropic elastic medium subjected to the action of remote oscillatory and static loads. In the case of a plane problem, the former results in Rayleigh waves propagating toward the crack tip. For the antiplane problem the shear waves play a similar role. Under the considered conditions the crack cannot move uniformly, and if the static prestress is not sufficiently high, the crack moves interruptedly. For fracture modes I and II the established, crack speed periodic regimes are examined. For mode III a complete transient solution is derived with the periodic regime as an asymptote. Examples of the crack motion are presented. The crack speed time-period and the time-averaged crack speeds are found. The ratio of the fracture energy to the energy carried by the Rayleigh wave is derived. An issue concerning two equivalent forms of the general solution is discussed.

Morphological aspects and deterministic reconstruction of dynamical fracture surfaces in brittle materials

Linear Elastic Fracture Mechanics (LEFM) provides a quantitative description of the crack motion that agrees well with observations in brittle materials as long as the crack growth is sufficiently slow. However, several issues remain unsolved: (i) experimental observations reveal that at high velocity, the crack speed is systematically smaller than the one predicted by LEFM [1] and (ii) above a given velocity, a dynamically growing crack creates a structure of its own as evidenced from roughening of fracture surfaces at high speed [2]. The aim of this work is to present a statistical study and a deterministic reconstruction of the morphology of the fracture surfaces in Plexiglas obtained under dynamic conditions.

Ultrasound excited thermography of thickwalled steel load bearing members

Ultrasonic lockin and burst-phase thermography establish more and more as failsave NDT methods in the scope of inspection of light-weight composite structures. The methods were not fully transferred to heavy load bearing members used in constructional steelwork so far. The investigation of three massive components, a steel plate, a 3 m long hot rolled girder and an extremely thick-walled welded joint revealed the applicability of ultrasonic lockin, burst and sweep procedures. The influence of the coupling location and the thermal response behaviour of single and multiple defects are discussed. The use of differential laser vibrometry is introduced in order to examine the extent of relative motion of crack faces and to analyse the connection between mode III oscillation velocity and crack detectability.

Ultrasound excited thermography of thickwalled steel load bearing members

Ultrasonic lockin and burst-phase thermography establish more and more as failsave NDT methods in the scope of inspection of light-weight composite structures. The methods were not fully transferred to heavy load bearing members used in constructional steelwork so far. The investigation of three massive components, a steel plate, a 3 m long hot rolled girder and an extremely thick-walled welded joint revealed the applicability of ultrasonic lockin, burst and sweep procedures. The influence of the coupling location and the thermal response behaviour of single and multiple defects are discussed. The use of differential laser vibrometry is introduced in order to examine the extent of relative motion of crack faces and to analyse the connection between mode III oscillation velocity and crack detectability.

A generalized cohesive element technique for arbitrary crack motion

A computational method for arbitrary crack motion through a finite element mesh, termed as the generalized cohesive element technique, is presented. In this method, an element with an internal discontinuity is replaced by two superimposed elements with a combination of original and imaginary nodes. Conventional cohesive zone modeling, limited to crack propagation along the edges of the elements, is extended to incorporate the intra-element mixed-mode crack propagation. Proposed numerical technique has been shown to be quite accurate, robust and mesh insensitive provided the cohesive zone ahead of the crack tip is resolved adequately. A series of numerical examples is presented to demonstrate the validity and applicability of the proposed method.

Cracking sheets: Oscillatory fracture paths in thin elastic sheets

When a blunt cutting tool is forced through a thin elastic sheet that is held along its lateral boundaries, a strikingly regular wavy cut can be left behind, examples of which are presented in Fig. 1. The thin film is brittle, hence it undergoes negligible irreversible deformation besides fracture. For tools much wider than the film’s thickness, the crack tip follows a highly reproducible nonsinusoidal oscillatory path. Each single period of this path consists of two smooth curves separated by a kink, at which there is a sharp change in the direction of curvature. Propagation is primarily quasistatic, at a speed comparable to that of the cutting tool but is interrupted by periodic bursts of dynamic propagation immediately after each kink. By decreasing either the size of the cutting tool down to widths comparable to the film thickness or the tool’s speed, the crack path eventually becomes straight. These oscillatory patterns are strikingly robust and even doing the experiment by hand yields surprisingly regular patterns. In Ref. 4 we have shown that the coupling of classical theories for elastic plates and for crack propagation can be reduced to a simple set of geometrical rules which explain this experimentally observed oscillatory crack behavior in thin brittle films. This was done by following a common approach in fracture theory: calculating the elastic energy of the system while taking into account the possible large outof-plane deformations of the film induced by the cutting tool. Griffith’s criterion for crack propagation was then applied. The principal ingredient of our 2D construction is therefore the coupling between crack propagation and large out-of plane deformations in the film. Geometry is, in general, known to play an important role in the theory of elastic rods, plates, and shells but, in the tearing of thin films, geometrical considerations acquire an unprecedented level of importance. This is a compelling example where a complex crack motion is entirely ruled by geometry.

Laws of crack motion and phase-field models of fracture

Recently proposed phase-field models offer self-consistent descriptions of brittle fracture. Here, we analyze these theories in the quasistatic regime of crack propagation. We show how to derive the laws of crack motion either by using solvability conditions in a perturbative treatment for slight departure from the Griffith threshold or by generalizing the Eshelby tensor to phase-field models. The analysis provides a simple physical interpretation of the second component of the classic Eshelby integral in the limit of vanishing crack propagation velocity: it gives the elastic torque on the crack tip that is needed to balance the Herring torque arising from the anisotropic surface energy. This force-balance condition can be interpreted physically based on energetic considerations in the traditional framework of continuum fracture mechanics, in support of its general validity for real systems beyond the scope of phase-field models. The obtained law of crack motion reduces in the quasistatic limit to the principle of local symmetry in isotropic media and to the principle of maximum energy-release-rate for smooth curvilinear cracks in anisotropic media. Analytical predictions of crack paths in anisotropic media are validated by numerical simulations. Interestingly, for kinked cracks in anisotropic media, force-balance gives significantly different predictions from the principle of maximum energy-release-rate and the difference between the two criteria can be numerically tested. Simulations also show that predictions obtained from force-balance hold even if the phase-field dynamics is modified to make the failure process irreversible. Finally, the role of dissipative forces on the process zone scale as well as the extension of the results to motion of planar cracks under pure antiplane shear are discussed.

Effective rough rolling of low-alloy steel

The behavior of surface defects in continuous-cast slabs is investigated during rough rolling. A model of the change in defect shape is developed, and recommendations are made regarding the prevention of crack motion toward the strip axis.

고체추진로켓 내부에서 발생하는 동적 파괴 현상과 유체-고체 상호작용의 시뮬레이션 - Part 1 (이론적 측면)

This paper summarizes the components of an explicit aeroelastic solver developed especially for the simulation of dynamic fracture events occurring during the flight of solid propellant rockets. The numerical method combines an explicit Arbitrary Lagrangian Eulerian (ALE) version of the Cohesive Volumetric Finite Element (CVFE) scheme, used to simulate the spontaneous motion of one or more cracks propagating dynamically through a domain with regressing boundaries, and an explicit unstructured finite volume Euler code to follow the flow field during the failure event. A key feature of the algorithm is the ability to adaptively repair and expand the fluid mesh to handle the large geometrical changes associated with grain deformation and crack motion.

Numerical simulation of hydraulic fracture crack propagation

The plane problem of crack motion in an elastic medium under the pressure of a viscous fluid is considered. Under the condition of a constant fluid flow rate, the fluid is injected at the center of the crack. Contrary to other formulations of the problem, this paper attempts to take into account a possible fluid lag behind the crack tip. The resulting numerical solution is compared with a semianalytic one. It is found that the proposed numerical model can be used to predict the characteristics of a hydraulic fracture crack formed in a medium of a prescribed strength.

Determining the thermomechanical characteristics of the separation process

The crack growth condition was obtained in [1, 2] from energy considerations and holds for arbitrary nonlinearly elastic materials. This condition is reduced to determining the trajectory-independent transition from one of the shores of the mathematical cut to the other shore in the J-integral. The time when the J-integral attains the critical value corresponds to the initiation of crack motion. In the present paper, we consider the steady-state strip separation process starting from the fundamental thermodynamic relation. The strip material behavior is determined both at the stage of stable (in general, elastoplastic) loading and at the stage of Drucker unsdtable strain until the time at which the interaction between particles ceases. We single out a domain of unstable material strain, i.e., an interaction layer whose initial width is assumed to be a universal constant of the material [3]. The proposed approach permits expressing the material surface energy via the critical thermomechanical parameters (determined from the complete strain diagram) and the interaction layer thickness. We obtain expressions for the critical values of J-integrals. The critical values of J-integrals [4–6] corresponding to nonlinearly elastic and ideally plastic materials follow from general considerations. We have shown that the possibility of using J-integrals as elastoplastic separation criteria depends on the layer thickness of an irreversibly strained material. If the corresponding thickness is independent of the boundary conditions and the body geometry, then it is possible to use the value of the J-integral as a separation criterion; this corresponds to the Irwin-Orowan quasibrittle fracture approach.

Threshold Crack Speed Controls Dynamical Fracture of Silicon Single Crystals

Fracture experiments of single silicon crystals reveal that after the critical fracture load is reached, the crack speed jumps from zero to approximately 2 km/sec, indicating that crack motion at lower speeds is forbidden. This contradicts classical continuum fracture theories predicting a continuously increasing crack speed with increasing load. Here we show that this threshold crack speed may be due to a localized phase transformation of the silicon lattice from 6-membered rings to a 5-7 double ring at the crack tip.

Grain-level analysis of dynamic fragmentation of ceramics under multi-axial compression

Fragmentation of a small ceramic specimen subjected to a dynamic compressive load is analyzed numerically at the mesoscale level using a cohesive/volumetric finite element scheme. Special emphasis is placed on the effect of lateral confinement on the dynamic fragmentation process. The analysis is performed in plane strain condition and assumes intergranular crack motion. The scheme relies on Voronoi tessellation to generate the granular microstructure. A nonlinear kinematic description is used to account for the possible large deformations and/or rotations of the grains during the fracture event. A cohesive unilateral contact enforcement scheme is used to model the complex interaction between the fracture surfaces and the fragments formed. The brittle to ductile transition in the constitutive response along with the associated change in the mode of failure of this class of materials from axial splitting to shear localization are captured through detailed simulations. It is quantified together with the effect of the applied strain rate and granular microstructure on the dynamic fragmentation process. Results are in good agreement with the analytical wing crack model and experimental observations of dynamic fragmentation for this class of materials. The apparent ductility exhibited by confined ceramics is found to be associated with the suppression of lateral dilation rather than the onset of shear localization.

Supersonic crack motion in a harmonic lattice

Antiplane shear cracks in a harmonic square lattice have been studied in a molecular dynamics simulation. They can reach velocities larger than the shear wave velocity.

Steady-state motion of a mode-III crack on imperfect interfaces

Mishuris, Gennady; Movchan, N.V.; Movchan, A.B., (2006) 'Steady-state motion of a Mode-III crack on imperfect interfaces', Quarterly Journal of Mechanics and Applied Mathematics 59(4) pp.487-516 RAE2008