Crack Motion Research Articles

Experimental study on opto-acoustic nonlinear frequency-mixing technique with separated basic temperature

Different from the traditional frequency-mixing technique which employs a contacting transducer, the laser-induced acoustic nonlinear frequency-mixing detection technique utilizes a laser source to instigate crack motion and generate acoustic waves. Thus, apart from the temperature oscillation induced by the pump laser, the “basic temperature” originating from the probe laser can also influence the crack. This additional variable complicates the contact state of the crack, yielding a more diverse range of nonlinear acoustic signal attributes. In light of this, our study enhances the conventional opto-acoustic nonlinear frequency mixing experimental setup by integrating an independent heating laser beam. This modification isolates the impact of the “basic temperature” on crack width while also dialing down the probe laser power to mitigate its thermal effects. To amplify the sensitivity of crack detection, we deliberated on the optimal laser source parameters for this setup. Consequently, our revamped system, paired with fine-tuned parameters, captures nonlinear acoustic signals with an enriched feature set. This investigation can provide support for the non-contact opto-acoustic nonlinear frequency mixing technique in the detection and evaluation of micro-cracks.

Finite element implementation of Field Crack Mechanics for brittle and ductile fracture

In this work, a Finite Element (FE) implementation of a Field Crack Mechanics (FCM) model is presented for the first time. The implementation includes general boundary conditions and application to bulk plasticity as well. The current numerical investigation adopts the standard Galerkin finite element formulation to solve the equation of linear momentum balance and finite difference framework for crack evolution. Our preliminary investigation includes the modes-I and II loading conditions, where their respective normal stress fields are compared against their analytical counterparts. The fundamental questions in classical fracture mechanics, e.g. the existence of threshold stress for the crack to move, and various stages associated with the crack propagation are investigated. Additionally, this study explores two distinct strain energy functions based on the crack surface normal and hydrostatic deviatoric energy split. Crack irreversibility is a natural phenomenon in the FCM model, and it does not require satisfying any extra irreversibility constraints. The model shows good agreement against literature and analytical framework. The current FCM implementation also recovers the basic notion of fracture propagation which satisfies both energy and stress criterion. The study also explores the crack motion under the effect of plasticity in ductile materials. The results thus obtained for both brittle and ductile fracture cases are consistent with the predictions of classical fracture mechanics. The current implementation of the FCM effectively demonstrates stable crack propagation, eliminating the requirement for surfing boundary conditions.

Frictional weakening leads to unconventional singularities during dynamic rupture propagation

Earthquakes i.e. frictional ruptures, are commonly described by singular solutions of shear crack motions. These solutions assume a square root singularity order around the rupture tip and a constant shear stress value behind it, implying scale-independent edge-localized energy. However, recent observations of large-scale thermal weakening accompanied by decreasing shear stress potentially affecting the singularity order can challenge this assumption. In this study, we replicate earthquakes in a laboratory setting by conducting stick-slip experiments on PMMA samples under normal stress ranging from 1 to 4 MPa. Strain gauges rosettes, located near the frictional interface, are used to analyze each rupture event, enabling the investigation of shear stress evolution, slip velocity, and material displacement as a function of distance from the rupture tip. Our analysis of the rupture dynamics provides compelling experimental evidence of frictional rupture driven by enhanced thermal weakening. The observed rupture fronts exhibit unconventional singularity orders and display slip-dependent breakdown work (on-fault dissipated energy). Moreover, these findings elucidate the challenges associated with a priori estimating the energy budget controlling the velocity and final extent of a seismic rupture, when thermal weakening is activated during seismic slip.

FRACTURE ANALYSIS AND SHIELDING EFFECTS IN ADVANCED MATERIALS

Due to their ability to interconnect electrical and mechanical domains, piezoelectric materials are increasingly finding applications in advanced electromechanical systems. Notably, magneto-electric composites like BaTiO3-CoFe2O4 have emerged as vital materials for the next generation of devices. Exploring this realm is a complex and significant endeavor, demanding the attention of the scientific community and further research. Over recent decades, the scope of formulating and executing computational models for continuous media has substantially broadened, encompassing a diverse array of material properties and fields in computational models. This article centers on the utilization of asymptotic analysis as a mathematical tool for constructing approximate equations and assessing the relevance of various hypotheses. It delves into the utilization of the perturbation method, pioneered by Kagadiy T. S. and others, to tackle two-dimensional contact problems in electropelasticity, particularly in the context of materials with linear anisotropy. The extensive applicability of this asymptotic approach underscores its efficacy in simplifying intricate problems by breaking them down into a sequence of boundary problem resolutions grounded in the theory of potentials. The collaborative effort of the authors in this research underscores that employing the mentioned method opens up avenues for formulating pertinent boundary problems for the fundamental equations. This, in turn, allows for the representation of the initial electropelasticity problem as a superposition of more manageable boundary problems. While mechanical and electrical components can be treated separately, they still interact via boundary conditions. To conduct a numerical analysis, the article examines scenarios where one crack surface slides parallel to the crack front against another and selects relevant materials with known characteristics. Calculations reveal that, even in the absence of mechanical load, crack surfaces undergo relative sliding due to non-zero electrical or magnetic fields. The study of the shielding effect, which mitigates crack motion by altering magnetic field distribution, holds particular significance. This effect reduces the overall stress intensity factor and impedes crack propagation. Conducting such a comprehensive analysis is pivotal for comprehending and foretelling the strength and reliability of structural components composed of piezoelectric and piezomagnetic materials. It is imperative to conduct a thorough examination of the mechanisms governing their failure.

Synergistic strengthening-toughening effect of SiCp(CNT) hybrid reinforcements on Mg-compensated SiCp(CNT)/Al–Zn–Mg–Cu composites

In this study, SiCp(CNT) hybrid reinforcements were prepared by in-situ growth of CNTs on the SiCp surface by chemical vapor deposition (CVD) process. The yield strength (YS) and ultimate tensile strength (UTS) of SiCp(CNT)/7075Al were significantly improved by compensating Mg into the SiCp(CNT)/7075Al composites. The results showed that the SiCp(0.5CNT)/7075Al–Mg composites exhibited the best balance of strength and ductility at a Mg compensation of 1.0 wt %, not only the UTS (∼651 MPa) was higher than that of SiCp/7075Al-1.0 Mg, but also the elongation (3.5 %) was improved by more than 20 %. This is attributed to the fact that the Mg compensation can effectively improve the aging precipitation behavior of the interfacial micro-zones of SiCp(CNT)/7075Al–Mg, allowing it to be effectively strengthened and thus to transfer the load adequately and give full play to the strengthening effect of the SiCp(CNT) hybrid reinforcement. In addition, the toughness of the SiCp(CNT)/7075Al composites was significantly higher than that of SiCp/7075Al with or without the compensation of Mg. Further studies showed that the toughening mechanism of CNTs is divided into the following three main points: (1) the introduction of CNTs can effectively strengthens the interfacial micro-zones, thus retarding the crack initiation. And CNTs can redirect the motion of cracks through the initiation of daughter cracks; (2) the bridging, pull-out and fracture of CNTs can cause the composites to consume more energy during deformation; (3) the introduction of CNTs can effectively prolong the crack propagation path and make the deformation around SiCp more uniform.

Tensile cracks can shatter classical speed limits.

Brittle materials fail by means of rapid cracks. Classical fracture mechanics describes the motion of tensile cracks that dissipate released elastic energy within a point-like zone at their tips. Within this framework, a "classical" tensile crack cannot exceed the Rayleigh wave speed, [Formula: see text]. Using brittle neo-hookean materials, we experimentally demonstrate the existence of "supershear" tensile cracks that exceed shear wave speeds, [Formula: see text]. Supershear cracks smoothly accelerate beyond [Formula: see text], to speeds that could approach dilatation wave speeds. Supershear dynamics are governed by different principles than those guiding "classical" cracks; this fracture mode is excited at critical (material dependent) applied strains. This nonclassical mode of tensile fracture represents a fundamental shift in our understanding of the fracture process.

A dissipation informed peridynamic model for dynamic brittle fracture

In this paper, we propose a dissipation informed peridynamic (PD) model for dynamic brittle fracture. The viscosity is introduced in for dissipation compensation to recover the physical mechanism of fracture. The general type of deformation in solids is considered and the bulk viscosity force state is nonlocally constructed from the bond level as a minimum variation of conventional PD. Rather than adjusting the artificial coefficient, the signal processing method, i.e. the wavelet method is employed for viscosity evolution. With the wavelet method, the spurious stress waves can be identified and the dissipation deficiency can be naturally quantified. The proposed model is then verified by a rigorous validation simulation against the experiment results, which is still missing in the PD literature. The real loading condition is modeled to reproduce the ‘quasi-steady-state crack propagation’ problem and twenty different cases are included to cover the whole fracture stage. The results demonstrate that the model is capable to recover the physical mechanism and capture the dynamic brittle fracture. New insights into the dynamic brittle fracture are also gained by investigating the viscosity effect and deriving the crack motion equation.

Calibration and uniqueness analysis of microparameters for DEM cohesive granular material

The differential evolution (DE) algorithm was deployed to calibrate microparameters of the DEM cohesive granular material. 4 macroparameters, namely, uniaxial compressive strength, direct tensile strength, Young’s modulus and Poisson’s ratio, can be calibrated to high accuracy. The best calibration accuracy could reach the sum of relative errors REsum < 0.1%. Most calibrations can be achieved with REsum < 5% within hours or REsum < 1% within 2 days. Based on the calibrated results, microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material: (1) microparameters effective modulus, tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth, (2) microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress, and (3) microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour. Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study. The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.

Effective Toughness of Heterogeneous Materials with Rate-Dependent Fracture Energy.

We investigate the dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of the rate dependency of the fracture energy and the inertia of the medium, which allows the crack to cross a fracture energy discontinuity at a constant energy release rate. This discontinuous dynamics and the rate dependence cause higher effective toughness, which governs the coarse-grained behavior of these cracks.

Back-analysis of Donghekou landslide using improved DDA considering joint roughness degradation

Currently, the dynamic behavior of high-speed long-runout landslides triggered by earthquakes remains unclear due to the complexity of such phenomena. Degradation in the shear strength of rock masses is considered a primary factor contributing to the high velocities and long runout distances of these landslides. In this study, the strength degradation induced by changes in rock joint morphology is analyzed considering a numerical model of the Donghekou landslide, by using discontinuous deformation analysis (DDA). First, an exponential joint roughness degradation function (i.e., JRCm) that depends on displacement is incorporated with the nonlinear Barton–Bandis (B–B) shear strength criterion, and this modified B–B criterion is combined with the DDA. Moreover, a virtual joint is introduced in the DDA to model the propagation of cracks in intact rock masses, in order to simulate the dynamic phenomenon of earthquake-induced landslides. Subsequently, this improved DDA (IDDA) is validated via simulations of a shear test and a sliding block over an inclined plane. Finally, the IDDA is employed to simulate the Donghekou landslide, which was induced by the 2008 Wenchuan earthquake in China. Furthermore, the entire dynamic process of the landslide, including crack propagation, instability, initiation, and motion, is depicted. The simulated deposit patterns obtained via the IDDA are in good agreement with the results of field investigations. The simulation results also prove that the IDDA can reflect key movement behaviors of Donghekou landslide and that the degradation of rock joints significantly influences the long runout distance and high velocity of sliding mass.

Shear failure in supported two-dimensional nanosheet van der Waals thin films

Liquid-phase deposition of exfoliated 2D nanosheets is the basis for emerging technologies that include writable electronic inks, molecular barriers, selective membranes, and protective coatings against fouling or corrosion. These nanosheet thin films have complex internal structures that are discontinuous assemblies of irregularly tiled micron-scale sheets held together by van der Waals (vdW) forces. On stiff substrates, nanosheet vdW films are stable to many common stresses, but can fail by internal delamination under shear stress associated with handling or abrasion. This “re-exfoliation” pathway is an intrinsic feature of stacked vdW films and can limit nanosheet-based technologies. Here we investigate the shear stability of graphene oxide and MoSe2 nanosheet vdW films through lap shear experiments on polymer-nanosheet-polymer laminates. These sandwich laminate structures fail in mixed cohesive and interfacial mode with critical shear forces from 40 to 140 kPa and fracture energies ranging from 0.2 to 6 J/m2. Surprisingly these energies are higher than delamination energies reported for smooth peeling of ordered stacks of continuous 2D sheets, which we propose is due to energy dissipation and chaotic crack motion during nanosheet film disassembly at the crack tip. Experiment results also show that film thickness plays a key role in determining critical shear force (maximum load before failure) and dissipated energy for different nanosheet vdW films. Using a mechanical model with an edge crack in the thin nanosheet film, we propose a shear-to-tensile failure mode transition to explain a maximum in critical shear force for graphene oxide films but not MoSe2 films. This transition reflects a weakening of the substrate confinement effect and increasing rotational deformation near the film edge as the film thickness increases. For graphene oxide, the critical shear force can be increased by electrostatic cross-linking achieved through interlayer incorporation of metal cations. These results have important implications for the stability of functional devices that employ 2D nanosheet coatings.

On the Mathematical Modeling of Loading High-Speed Material at the Department of Physical Mechanics, St. Petersburg State University

The issues of studying shock-wave processes in structural materials are relevant; however, it is difficult, expensive, and sometimes even impossible to perform field studies. Therefore, all research on this topic is reduced to various options for modeling the processes rapidly loading materials under laboratory conditions. In the paper, we consider the following areas of the mathematical modeling of high-speed material loading at the Department of Physical Mechanics, St. Petersburg State University: modeling of shock-loaded media using the dynamics of dislocations, modeling the high-speed loading of media with allowance for relaxation phenomena in the near-surface region, modeling the propagation of a short elastoplastic pulse in a medium under the impact of a weak magnetic field, construction of mathematical models of deformation and destruction of thin metal rings by the magnetic-pulse method, and simulation of crack motion under short-term pulse loading.

Research on crack monitoring at the trailing edge of landslides based on image processing

Currently, the frequency of landslides is increasing. Scientific monitoring methods are playing an essential role in effectively reducing landslide disasters. This paper proposes a method for identifying the cracks at the trailing edge of a landslide (TEL) based on image processing technology and adopts the custom interval median comparison algorithm (IMCA) to calculate the crack motion parameters. First, we perform a series of processes on the TEL images, including image preprocessing, Otsu’s algorithm processing, and Canny edge detection processing, to identify the outline of the TEL. Then, we propose using the azimuth and displacement to characterize the motion of the cracks and using the IMCA to calculate the changes before and after motion of any two groups of cracks. Finally, we design a computer program using a free and open-source widget toolkit (named QT platform) based on the calculation model that corresponds to the proposed method, and we apply the crack monitoring test to a 3D simulation model, a gravel model, a soil model, and a collapsed body of the Panzhihua Airport landslide in southwestern China. From the results, it can be assessed that the method can identify the outline of the TEL and calculate the azimuth and displacement of two crack curves before and after motion. These two parameters can describe the movement of the trailing edge cracks of the monitored landslide. Thus, this method can be used in early warning system for landslide hazards.

Dynamic fracture development in a multiply cracked solid

We have been studying the collective, global behaviour of multiple cracks in solid materials and its connection with each individual, local crack motion. Here, by using a high-speed digital video camera, we examine fracture evolution in a two-dimensional, initially linear elastic rectangular polycarbonate specimen where sets of cracks are prepared and uniaxial tensile strain with a prescribed constant rate is externally applied. We trace local fracture development around every individual crack, and simultaneously, we obtain global stress-strain curves and physical properties like tensile strength of the specimens. By knowing the global characteristics, then, we concentrate our attention to more local, secondary and further fractures caused by the extending main or primary fracture and reversely its influence on the global nature of the multiply cracked specimens. For various different distribution patterns and values of density of initial cracks, we observe the dynamic evolution of the primary fracture and the fracture-induced waves, as well as the generation of the subsidiary fracture. We find that after a total split of the specimen into two by the propagation of the primary fracture, the secondary fracture may be initiated and propagated at a distance from the primary fracture. That is, fracture propagation may jump in multiply cracked solids even without additional external loading. Moreover, in our observations, the secondary fracture moves into the direction opposite to the primary one, and is once arrested and then resumes its propagation with some delay. The secondary and further fractures, or a cluster of fractures, are obviously not owing to additional external energy, but by dynamic waves produced upon enlargement of the primary fracture. The development of the secondary and further fractures in a specimen may be concealed in the global stress-strain relation but may rather appear in a global pattern of dynamic wave radiation such as doublet or a cluster of ruptures in the solid Earth, namely, earthquakes.

In situ TEM observations of high-strain-rate deformation and fracture in pure copper

Abstract The plastic deformation of polycrystalline metals at high strain rates is controlled by the way defects (dislocations and twins) nucleate, propagate, and interact in the microstructure. To-date, the role of these defects has been estimated based on dynamic mechanical measurements coupled with ex situ investigations of the deformed microstructure. However, such investigations are fundamentally limited in their ability to characterize transient mechanisms. Here, we present for the first time direct, experimental observations of the nucleation, motion, and interaction of defects and cracks during deformation of pure copper at strain rates between 103 and 104 s−1. These observations are enabled by coupling a custom-built in situ high-rate straining stage with nanosecond-resolution dynamic transmission electron microscopy. The results show that while twins play only a minor role in the deformation of copper at quasi-static strain rates, the twin nucleation rate increases markedly at high strain rates. The preferred nucleation sites for twins also change, and the new twin interfaces become preferential paths for crack propagation, facilitating fracture through the original grains.

Effect of crack interaction on dynamic behavior of rockunder impact

<p indent="0mm">Rock contains numerous cracks, which will interact mutually under the action of external loads. This research based on the wing crack model, the interaction of Mode I cracks is considered for square and hexagonal configurations of crack distribution, and the effect of crack interaction on rock dynamic behavior is studied. Using crack motion equation and loading equation, the effect of crack concentration on dynamic deformation and fracture is investigated numerically. Numerical results show that, the greater the crack density is, the more intensive the crack interaction is, the lower the failure strength is, and the greater the inertia-induced additional axial stress is.

Crack growth in heterogeneous brittle solids: intermittency, crackling and induced seismicity.

Crack growth is the basic mechanism leading to the failure of brittle materials. Engineering addresses this problem within the framework of continuum mechanics, which links deterministically the crack motion to the applied loading. Such an idealization, however, fails in several situations and in particular cannot capture the highly erratic (earthquake-like) dynamics sometimes observed in slowly fracturing heterogeneous solids. Here, we examine this problem by means of innovative experiments of crack growth in artificial rocks of controlled microstructure. The dynamical events are analysed at both global and local scales, from the time fluctuation of the spatially averaged crack speed and the induced acoustic emission, respectively. Their statistics are characterized and compared with the predictions of a recent approach mapping fracture onset to the depinning of an elastic interface. Finally, the overall time-size organization of the events is characterized to shed light on the mechanisms underlying the scaling laws observed in seismology.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Numerical simulation of two-dimensional problems of creep crack growth with material damage consideration

Approach for numerical simulation of the process of the creep crack growth taking into account the hidden material damage is proposed. The approach is based on the application of finite element creep modeling, accompanied by damage. For calculations, the FEM Creep software package is used. Using the proposed algorithm for rebuilding the grid with the removal of the destroyed elements, the current picture of deformation and fracture is analyzed. This takes into account the growing level of damage during the crack motion in each element. Numerical fracture simulation data are used to determine the constants in the differential creep fracture propagation equation. As an example, the creep fracture of planar specimens with sharp notches in their plane is considered. The material of the specimens is a high-temperature nickel-based alloy EI 867 at a temperature of 950 °C. Calculations are carried out for different values of the load. For different times, finite element grids with remote elements are shown. Graphs of the dependence of crack length on time are built. Comparison of numerical and calculated data obtained with the motion equation of a crack shows their acceptable coincidence. The possibility of using the proposed approach for obtaining constants in the equation of crack motion as an alternative to the existing experimental one is discussed.

Features of destruction of a ferrite-martensitic composite

The behavior of a crack in steel with the structure of a ferriticmartensitic composite is studied. The modes of heat treatment for obtaining a composite structure with alternating layers of ferrite and martensite are given. The kinetics of crack development during cyclic tests was studied. The obtained data show that the rate of development of the crack in the material with the structure of the composite is substantially lower than for the usual sorbite structure. It is shown that the frontal growth of the crack in the composite is carried out with “stops”, on which the matrix deforms and its stratification occurs in the direction normal to the front of the crack motion.

Numerical analysis of the influence of liquid on propagation of a rolling contact fatigue crack

Numerical investigations of the propagation of rolling contact fatigue crack filled by the liquid have been conducted. Two models of fluid – crack interaction have been considered. In the first model called “hydrostatic” the assumption of incompressible, inviscid and weightless liquid was accepted. It was also assumed that due to the wheel load the trapped liquid could not get outside the crack and its volume remained constant until the rising pressure would open up the crack mouth again. On this assumption the analysis has a steady-state character. In the second model it has been assumed that the crack is filled by the viscous, incompressible fluid and the fluid motion as well as the resulting pressure distribution can be represented by one-dimensional form of the Reynolds equation. The method for solving the problem of the coupled motion of liquid and crack faces has been developed and series of calculation were made. The method has been employed for the predicting of crack deformation in the course of wheel rolling.