Change In Crack Length Research Articles

Numerical study of phase space analysis for the development of subsurface crack detection method using pulsed eddy current

Root-deck cracks, a prominent form of subsurface damage observed in orthotropic steel decks (OSDs), pose significant challenges to maintaining structural integrity. Early detection of these cracks is crucial to prevent further deterioration. This paper introduces novel and robust techniques for processing response signals obtained from the Pulsed Eddy Current Technique (PECT) using phase space analysis. The proposed methods aim to improve sensitivity and noise handling capabilities by employing an appropriate damage index derived from comprehensive phase space analysis, enabling effective detection of subsurface cracks in OSDs. A numerical study demonstrates the effectiveness of the proposed methods in detecting crack length change as small as 1 mm from the bottom of a 12 mm steel plate, with the Change in Phase Space Topology (CPST) identified as a suitable damage index. Furthermore, the newly proposed signal processing techniques allow for a more comprehensive interpretation of response signals for subsurface damage detection, encapsulating the extent of damage within a single value, even in the presence of small crack lengths near the bottom of the steel plate and noise. As a result, the proposed methods overcome the limitations of conventional approaches and offer promising prospects for enhanced subsurface crack detection in OSDs.

On the Response of Chondrites to Diurnal Temperature Change—Experimental Simulation of Asteroidal Surface Conditions

AbstractThermal fatigue is a process that degrades rocks and pebbles exposed to space by diurnal cycling. We simulate the diurnal temperature variation at 1 AU of 5 mm‐sized sample cubes using an evacuated cryostat, allowing conditions that are closer to those expected in space. Sample cubes of ordinary, CV, CM2, and C2 chondrites were investigated using scanning electron microscopy and microcomputed tomography scans. In contrast to previous work, the ordinary and CV chondrite samples did not show any cracking. The CM2 chondrites respond with the formation and extension of cracks. Pre‐existing cracks present in the C2 chondrite Tagish Lake closed in the course of cycling to different degrees, which has not been reported before in the context of thermal fatigue driven rock breakdown. Most changes in crack length occur in the initial ∼20 cycles indicating a rapid buildup of strain followed by a rapid release by the formation and extension of cracks when exposed to diurnal temperature variation. The overall cracking rate is comparable to that of previous work on CM2 chondrites and in 15%–20% of the observed cracking occasions they are associated with fine‐grained rims around chondrules implying that the comminution of CM‐like rocks and pebbles is controlled by the abundance of chondrules (and other coarse‐grained components) and their rims. We propose that thermal fatigue‐driven comminution of rocks and especially pebbles on asteroids under the here studied conditions is controlled by the abundance of hydrated minerals. This, in turn, can result in different abundances and natures of finer‐grained material on asteroid surfaces.

Kaji Teoritis Pengaruh Variasi Letak Retak Terhadap Perambatan Retak Dengan Pendekatan Double Cantilever Beam (DCB)

One of the causes of structural failure is the presence of defects in the form of cracks that appear during the manufacturing or usage process of the structure. The propagation of cracks in the structure greatly depends on the value of the energy released rate possessed by the defective structure. Therefore, it is necessary to calculate the energy released rate of a structure that has a crack. One simple approach is the double cantilever beam (DCB) method. The DCB approach is derived from the change in strain energy with respect to the change in crack length. In this study, variations in crack length and crack location will be analyzed using the DCB approach and compared with the Finite Element Method (FEM) approach. It can be concluded that the calculation of strain energy can be performed using the cantilever beam approach, where the results do not significantly differ from the FEM calculations. Additionally, the strain energy is heavily influenced by the length of the beam, as longer beams result in a significant increase in strain energy (cubic relationship). The value of Energy Released Rate (ERR) is highly influenced by the crack length; a longer initial crack length leads to a quadratic increase in the Energy Released Rate (ERR). Furthermore, the value of Energy Released Rate (ERR) is also affected by the crack location; the closer the crack is to the surface of the beam, the higher the Energy Released Rate (ERR) will be.

Evaluation of nonlinear interface areas in a multiple scattering medium by Nonlinear Coda Wave Interferometry (NCWI): Experimental studies

This paper aims to investigate the application of the Nonlinear Coda Wave Interferometry (NCWI) method in evaluating the nonlinear interface areas in highly heterogeneous materials. An experimental protocol is proposed for quantitatively analyzing the nonlinear interface effects in a multiple scattering medium. The experimental design involves a perforated aluminum plate with a surface ratio of circular voids equal to 17.63%, some of which are threaded to accommodate screws. The nonlinear contacts between the screws and the perforated plate are highlighted by a strong pump wave and investigated using the coda waves. Drawing upon prior numerical simulation findings (Chen et al., 2021), it is anticipated that the CWI observables (namely, the relative variation of coda wave velocity θ and the remnant decorrelation coefficient Kd) will be proportional to the change in crack length within the heterogeneous medium. In this study, the change in crack length through numerical simulation can be simulated by considering the different nonlinear interface areas between the screws and the perforated aluminum plate in the experimental design. Experimental findings demonstrate that the CWI observables are proportional to the nonlinear interface areas, which essentially aligns with previous numerical simulation results. In this paper, suggestions for refining the experimental setup are provided. This guidance is instrumental for further conducting quantitative research on nonlinear interface effects in complex media.

Plane and axisymmetric problems of an interfacial crack in a power-law graded material

Plane and axisymmetric problems of interfacial cracks in a power-law graded infinite medium are examined. It is shown that the models are governed by integral equations of Mellin’s convolution type whose kernels are expressed through the hypergeometric function. Exact solutions are derived by the method of orthogonal Jacobi polynomials in a series form and by the Wiener–Hopf method by quadratures. Mode-I stress intensity factors and the associated weight functions for power-law graded materials in the plane and axisymmetric cases are introduced and evaluated. It is shown that, although the displacement jump and the normal traction component have power singularities at the crack tip different from 1/2, the strain energy variation is proportional to the crack length change as in the case of homogeneous materials. A Griffith-type criterion of crack propagation in power-law graded materials is proposed and results of numerical tests are reported.

A new digital surface crack image monitoring technology for coal failure

AbstractThe experimental study on the variation law of coal fracture and stress was carried out in the laboratory and engineering fields, respectively. A multiparameter monitoring system including electromagnetic radiation and a high‐speed camera was built, and three stress paths, uniaxial compression, cyclic loading, and graded loading, were used to monitor the dynamic expansion process of surface cracks during uniaxial compression failure of coal specimens. Through the quantitative analysis of the electromagnetic radiation signal in the crack propagation process, it is found that the electromagnetic radiation and the stress change trend are consistent, and the electromagnetic radiation signal is ahead of the failure of coal‐generating rock mass 1–2 s. The surface crack changes after the peak value of electromagnetic radiation and presents a stepwise growth trend, crack length changes on the millisecond time scale, and the crack propagation speed is about 2000 mm/s. The surface cracks appear when the stress reaches a certain degree, and the propagation of the principal cracks is consistent with the failure of the specimen. The electromagnetic radiation value of the coal mass from static period to dynamic is analyzed by using electromagnetic radiation at the engineering site, and it was found that the electromagnetic radiation is consistent with the stress distribution of the mining face. Through normalization, the variation rule of electromagnetic radiation in laboratory and engineering sites is similar, but the peak value of electromagnetic radiation in engineering sites is more significant. Therefore, electromagnetic radiation has a good monitoring effect on the stress distribution and cracks propagation of underground coal mining working faces, which could guide the layout of underground drilling.

Nanoscale crack propagation in clay with water adsorption through reactive MD modeling

AbstractThe atomic‐scale cracking mechanism in clay is vital in discovering the cracking mechanism of clay at the continuum scale in that clay is a nanomaterial. In this article, we investigate mechanisms of modes I and II crack propagations in pyrophyllite and Ca‐montmorillonite with water adsorption through reactive molecular dynamics (MD) with a bond‐order force field. Clay water adsorption is considered by adding water molecules to the clay surface. During the equilibration stage, water adsorption could cause bending deformation of the predefined edge crack region. The relatively small orientating angle of water molecules indicates the formation of hydrogen bonds in the crack propagation process. The peak number density of adsorbed water decreases with the increasing strains. The atomistic structure evolution of the crack tip under loading is analyzed to interpret the nanoscale crack propagation mechanism. The numerical results show that the crack tip first gets blunted with a significant increase in the radius of the curvature of the crack tip and a slight change in crack length. The crack tip blunting is studied by tracking the crack tip opening distance and O–Si–O angle in the tetrahedral Si–O cell in modes I and II cracks. We compare bond‐breaking behaviors between Al–O and Si–O. It is found that Si–O bond breaking is primarily responsible for crack propagation. The critical stress intensity factor and critical energy release rate are determined from MD simulation results.

Quantification of the effect of pump wave amplitude on crack breathing for the Nonlinear Coda Wave Interferometry

In civil engineering, an emerging ultrasonic approach based on Code Wave Interferometry (CWI), called Nonlinear Coda Wave Interferometry (NCWI) has been developed to detect microcracks in cementitious materials that cannot be detectedby conventional ultrasonic methods. NCWI uses a high amplitude low frequency (LF) nonlinear pump wave to generate a nonlinear clapping effect at microcracks that can be detected by a high frequency (HF) probe wave. The imaging of cracks inside heterougeneous materials using NCWI requires the inversion technique, which is constitued by model space and data space, in which conatains model parameters and data parameters respectively. In the frame of inversion with NCWI, the model parameter used is the scatetring cross section of a crack sigmaD, and the experimental parameter is the decorrelation coefficient Kd. Knowing that sigmaD depends on the pump wave amplitude. Therefore, in order to introduce NCWI in inversion, the relationship between the pump wave and sigmaD is needed, which is the goal of this study. The dynamic pump wave generates clapping effect at crack tips, the probe wave frequencies are higher than the pump waves’ by an order of magnitude, hence the effect of pump wave on the coda wave is rather averaged. Previous study showed that this clapping effect is equivalent to a single crack length change dL, dL can be related to an equivalent static stress sigma0 which produces the same dL in quasi-static regime, which is equivalent to the dynamic pump wave. Therefore, a relation can be established between sigma0 and sigmaD. This introduces NCWI into the inverison. Then, the theoretical estimation of Kd can be achieved by the simulation of NCWI using 2D Spectral Element Method (SEM2D), combining with the relationship between sigma0 and sigmaD, which can be used later on in the inversion for the crack imaging.

Analysis of fatigue crack propagation mechanism of Ni3Al under supergravity at atomic size

Mechanisms of fatigue crack propagation of Ni3Al alloy under supergravity are studied by the molecular dynamics method. The initial model of the crack is a [100](010) crack in Ni3Al. Changes in the microstructure evolution, crack growth rate, and stress intensity factor of [100](010) crack are compared and analyzed without and with supergravity. The results show that the deformation mechanisms of the crack tip are slip bands along the a/6[112] direction by dislocation analysis in the absence of supergravity cyclic loading; after adding to supergravity, the mechanisms of crack propagation have changed, multiple voids are formed at the crack tip, and the dislocation lines also grow faster, which cause severe damage to the internal structure of the [100](010) crack in Ni3Al. By tracking the changes in crack length and width, it is found that the supergravity accelerates the growth of crack length and width and reduces the stress intensity factor threshold. Finally, the crack propagation rate increases under supergravity conditions.

Evaluation of the fatigue properties for the long-term service asphalt pavement using the semi-circular bending tests and stereo digital image correlation technique

Reliable assessment of the fatigue resistance of asphalt pavement with a long-term service is critically crucial for the rational formulation of original pavement utilization strategies in reconstruction and expansion projects. Currently, the pavement performance evaluation indicators are mainly used to guide pavement preventive maintenance, and its applicability in reconstruction and expansion projects of the freeway is limited. This paper aims to propose an evaluation method of fatigue resistance of asphalt concrete utilizing semi-circular bending (SCB) tests and stereo digital image correlation (stereo-DIC) techniques. A total of 27 asphalt concrete cores were drilled from the three freeways (K84, K124, and K165) with a service life of more than 20 years, and the SCB specimens were produced to conduct the SCB fracture and fatigue tests. During the SCB test, the stereo-DIC technique was employed to monitor the evolution process of the strain distribution and crack length for the specimens. K-dimension tree neighbor-searching algorithm (K-d tree algorithm) was used to effectively measure the change of crack length corresponding to each fatigue load cycle. Meanwhile, the strain threshold of asphalt concrete crack initiation was determined by the bilinear softening cohesive zone model (CZM) to ensure the accuracy of the crack length calculated by the K-d tree algorithm. Furthermore, the relationship between crack growth rate and stress intensity, which was used to fit the Paris law parameters, was determined. The CZM and DIC results indicated that the strain threshold of asphalt concrete crack should be set as 2000 με when using the K-d tree algorithm to determine the crack length. With the stress ratio increase, the Paris law parameter A increased wavily, and the parameter n decreased steadily, while the threshold of the stress intensity factor increased steadily. The Paris law master curves could characterize the fatigue performance of various road sections at a wide load range. The residual fatigue life of K84, K124, K165 the road sections were 2.13E + 08, 3.57E + 08, and 1.02E + 07, respectively.

Influence of cracks and voids on the responses of composites

In this paper, numerical study on influence of parameters related to cracks and voids on the responses of the composites under tension, compression, and shear deformation is conducted by extended finite element method (XFEM). Under tension, the maximum stress of composites changes less than 5% when crack orientation, fiber orientation, and void distance change. The maximum averaged stress could differ by 10% when the crack location and crack length change. In the multi-crack composites, there is difference by 10% in maximum stress due to relative crack location. Under shear deformation, crack orientation affects the maximum averaged shear stress significantly when compared to the same composites under tension. The difference of maximum averaged shear stress is more than 15% when fiber orientation changes. The void distance results in 5% difference on the maximum stress of composites. In the multi-crack composites, the relative crack location could result in 10% difference in maximum averaged shear stress. Crack length also could result in significant difference in maximum stress of composites under shear deformation. Under tension and shear deformation, one crack is always the dominant crack and its propagation path determines the strength of the multi-crack composites. Unlike in tension and shear deformation, single crack in the composites under compression doesn’t result in the failure of composites even when the strain is 0.03. That is, no geometric buckling occurs for the single crack composite under compression. Noticeable crack propagation starts in multi-crack composites under geometric buckling, which result from the existence of multi-cracks and their interaction in the composites.

Numerical parametric study of Nonlinear Coda Wave Interferometry sensitivity to microcrack size in a multiple scattering medium

This paper reports a numerical study of the sensitivity and applicability of the Nonlinear Coda Wave Interferometry (NCWI) method in a heterogeneous material with a localized microcracked zone. We model the influence of a strong pump wave on the localized microcracked zone as a small average increase in the length of each crack. Further probing of this microcracked zone with a multiply scattered ultrasonic wave induces small changes to the coda-type signal, which are quantified with coda wave interferometry. A parametric sensitivity study of the CWI observables with respect to the changes in crack length is established via numerical simulations of the problem using a 2D spectral element method (SEM2D). The stretching of the signal, proportional to the relative variation in effective velocity, is found to be linearly proportional to the global change in crack length, while the other CWI parameter, the remnant decorrelation coefficient, is found to be quadratically proportional to the crack length change. The NCWI method is shown to be relevant for the detection of different damaged material states in complex solids. The reported numerical results are especially significant in the context of quantitative nondestructive evaluation of micro-damage level of a heterogeneous materials using nonlinear ultrasound signals.

Numerical Simulation of Cracks in Automotive Coatings Under Mechanical and Thermal Loading Using Element Free Galerkin Method

ABSTRACT The work presented in this paper aims to delve into the applications of Element Free Galerkin Method (EFGM) which is a type of Meshless Method (MM) to the area of Automobile Engineering. EFGM is implemented to detect a change in the material property at the interface of the coating along with the identification of crack. Simulation of centre crack in coatings has been reported for the first time using EFGM. Simulations with change in crack inclination angle, change in crack length are reported. Multiple cracks are reported in the form of collinear cracks, coplanar cracks and the effect of their presence on primary crack has been discussed. This work involves the study which leads to understanding the effect of temperature on the stress fields of the cracks present in coatings. Variations of the temperature field parallel to crack and perpendicular crack shows enticing results. The effect of variation in materials properties of coating and substrate is discussed. The work reveals the nature of crack severity in automobile coatings. Various conditions depicted in this work enhance the understanding of researches in comprehending the effect of thermal load in coated materials.

The effects of microstructural properties and temperature on the mechanical behavior of Nextel 720 composite fibers: A novel multiscale model

A novel multiscale technique called the Bridging Cell Method (BCM) was used to model the mechanical behavior of Nextel 720 composite fibers across a range of temperatures. The previously validated room temperature Nextel BCM was used as a benchmark, and a temperature-dependent formulation was employed to account for the temperature effect. The model was tested under uniaxial tensile loads ranging from room temperature to 1700 K. The results were evaluated in terms of ultimate tensile strength (UTS), elasticity, and failure strain. The temperature-dependent Nextel BCM was validated via experimental data obtained from the literature. The high-temperature drop in composite's strength was predicted by the Nextel BCM. This was the result of implementing the fibers' microstructural evolution into the model, caused by phase transformation occurring at higher temperatures. The model was further validated with the fracture resistance variations of the composite that resulted from changes in crack length. The fracture behavior of the fibers at room and high temperatures were tested, by applying inter- and intra-granular cracks. Finally, the effect of grain alignment with respect to the applied load was investigated. The results show that the Nextel BCM is capable of predicting Nextel 720 composite's mechanical behavior across a range of temperatures.

Failure Mechanism and Acoustic Emission Characteristics of Rock Specimen with Edge Crack Under Uniaxial Compression

There are many cracks in rock mass which have a significant influence on the stability of rock engineering. Most of current researches on the failure mechanism of cracked rock are mainly focused on the internal cracks. However, edge cracks around underground openings are common in many engineering fields. Understanding the failure mechanism of rock with edge cracks is essential to assess the stability of underground structures. Rock failure is closely related to the cracking processes and acoustic emission characteristics is deemed as an effective means of monitoring the cracking processes of rock. In this study, a series of numerical simulations utilizing particle flow software PFC2D were performed to investigate the influence of the length and position of edge crack on the failure mechanism and acoustic emission characteristics of rock specimens with edge cracks under uniaxial compression. The results show that: the strength of specimens is sensitive to the change of crack length and position; the directions of crack propagation in each specimen is in good agreement, the different crack tip position and the specimen boundary lead to different failure modes; the influence of crack length on acoustic emission is greater than that of crack position.

COMPUTER SIMULATION OF COMBINED SPLITTING FORCE: STRAIN LOADING OF DOUBLE-BEAM SAMPLES

The purpose of this work is to study possible schemes of loading double-cantilever beam (DCB) specimens to replenish the arsenal of the methods used in their testing. Mathematical analysis of ten different modes of specimen loading is carried out for different methods of immobilizing and loading of the cantilever including splitting force, deformational and combined loading. Analytical expressions for the stress intensity factor (SIF), as well as the dependence of the beam spread angle θ (rotation angle of the beam head) on the crack length are derived. Those dependences form a basis for developing the methods for measuring the dynamics of the crack length changes during testing. The energy approach is used in determination of the stress intensity factors. The classical scheme of force loading of the DCB specimen by a pair of forces is supplemented with a loading scheme with two pairs of forces applied to different cross sections. A modification of the DCB specimen by rigid binding of the ends of its consoles when each shoulder of the specimen is considered a singly statically indeterminable beam and DCB specimen becomes a double-beam specimen is also considered. The possibility of rearranging the sections of the load application and position of the rigid support-link is also studied. The deformational loading is simulated by inserting a wedge in one or two sites along the specimen length. The wedge effect is modeled by a preset deformation in one of the sections and binding of the specimen consoles in the other. Formulas of the stress intensity factor for the DCB specimen asymmetric with respect to the crack propagation line upon pure force loading by the forces applied in one section are presented. References to the reports on experimental implementation of a number of proposed and considered load configurations are presented.

Crack propagation in graphene

The crack initiation and growth mechanisms in an 2D graphene lattice structure are studied based on molecular dynamics simulations. Crack growth in an initial edge crack model in the arm-chair and the zig-zag lattice configurations of graphene are considered. Influence of the time steps on the post yielding behaviour of graphene is studied. Based on the results, a time step of 0.1 fs is recommended for consistent and accurate simulation of crack propagation. Effect of temperature on the crack propagation in graphene is also studied, considering adiabatic and isothermal conditions. Total energy and stress fields are analyzed. A systematic study of the bond stretching and bond reorientation phenomena is performed, which shows that the crack propagates after significant bond elongation and rotation in graphene. Variation of the crack speed with the change in crack length is estimated.

Effects of loading and sample geometry on acoustic emission generation during fatigue crack growth: Implications for structural health monitoring

The reliability of traditional non-destructive methods for crack detection is well understood and characterised using Probability of Detection (POD) curves. Structural Health Monitoring (SHM) techniques in contrast remain largely unquantified. The performance of the Acoustic Emission (AE) technique for damage detection and location in potential SHM applications is underpinned by the intensity of AE signal generation from the damage site. In this paper, factors influencing the rates of emission of Acoustic Emission (AE) signals from propagating fatigue cracks were investigated. Fatigue cracks were grown in specimens made from 2014 T6 aluminium sheet while observing the effects of changes in crack length, loading spectrum and sample geometry on rates of acoustic emission. Significant variation was found in the rates of AE signal generation during crack progression from initiation to final failure with a number of distinct phases identified in that progression implying different failure mechanisms operating at particular stages in the failure process. A new ‘probability of hit’ method for quantifying crack detecting capability using AE is also presented.

Sound Radiation Response of a Rectangular Plate Having a Side Crack of Arbitrary Length, Orientation, and Position

Here, sound radiation characteristics of a rectangular plate having a side crack of different crack lengths, orientations, and positions are studied considering clamped boundary conditions. First, a free and forced vibration response analysis of a cracked plate is done using the Ritz method. Orthogonal polynomials are used for faster convergence and some corner functions are used to generate the effect of a crack. Radiated sound power and radiation efficiency of the cracked plate are computed by the quadruple integration. A convergence test of radiation efficiency is carried out to fix the number of polynomials and corner functions in the analysis. It is found that the radiation efficiency and radiated sound power computed by the Ritz method are close to the same obtained from the boundary element method (BEM). The natural frequencies computed using the Ritz method are also found to be close to that obtained from the finite element method (FEM). The radiation efficiency curves of different modes are shown for a change in crack length, orientation and position. Finally, the variations of normalized sound power are shown to be due to a change in the crack parameters.

Detection and Monitoring of Fatigue Cracks in Metallic Structures Using Acoustic Emission: Routes to Quantification of Probability of Detection

The performance and reliability of Structural Health Monitoring (SHM) techniques remain largely unquantified. This is in contrast to the probability of detection (POD) and sensitivity of manual non destructive inspection methods which are well characterised. In this study factors influencing the rates of emission of Acoustic Emission (AE) signals from propagating fatigue cracks were investigated. Fatigue crack growth experiments were performed in 2014 T6 aluminium sheet to observe the effects of changes in crack length, loading spectrum and sample geometry on rates of emission and the probability of detecting and locating the fatigue crack. Significant variation was found in the rates of AE signal generation during crack progression from initiation to final failure. AE signals at any point in the failure process were found to result from different failure mechanisms operating at particular stages in the failure process.