Values Of Crack Length Research Articles

Fracture of all‐oxide ceramic composites: Crack path analysis by surface strain monitoring

AbstractCrack propagation in ceramic matrix composites is very difficult to observeand to quantify. To investigate crack formation in all‐oxide ceramic composites, single edge notched bending tests were performed including loading‐unloading cycles and online monitoring of surface deformation using digital image correlation. The crack length was calculated by the compliance method with the crack opening displacement determined optically using digital image correlation. Obtained crack length values were found to be too small considering the sample geometry. Secondly, surface strain monitoring was used to investigate the crack growth. Analysis of cyclic force‐crack opening displacement curves and the results from strain monitoring indicated no major crack growth for loads below maximum force but still a moderately decay of force after onset of cracking. Graphical analysis of the surfaces of broken samples showed crack flank lengths ranging from 3 to 6 mm. Due to highly individual crack deflection mechanisms throughout the thickness of the oxide ceramic composites, deviations between front and back of specimens are found. The results demonstrate the necessity to use individual crack length measurements of each specimen for quantitative fracture mechanical evaluation. Strain monitoring during testing was shown to be a valuable tool for online crack path investigation.

An Improved Crack Identification Method for Asphalt Concrete Pavement

The results of high-precision asphalt concrete pavement crack identification can provide help for pavement maintenance. Therefore, methods of image feature enhancement and crack identification of asphalt concrete pavement cracks are proposed. First of all, we used an industrial CCD camera mounted on a vehicle to collect an asphalt concrete pavement crack image. Then, after using the NeighShrink algorithm to denoise the acquired image, a fractional differential image enhancement algorithm was designed based on image feature blocks to enhance the image features. On this basis, crack characteristics were segmented and processed by watershed algorithm. Through crack direction identification and crack parameter extraction, crack distribution direction, crack length and width and other parameters of asphalt concrete pavement were obtained in order to achieve accurate identification of asphalt concrete pavement cracks. The experiment found that this method can effectively remove noise information from asphalt concrete crack images; after applying this method, the image entropy value of each image was improved, with a minimum improvement of 0.38 and a maximum improvement of 1.98. The time consumed by this method in identifying cracks in asphalt concrete pavement varied between 1.4 s and 2.4 s. When identifying the length of cracks in asphalt concrete pavement, the maximum deviation value was only 0.47 mm; when identifying the width of cracks in asphalt concrete pavement, the maximum deviation value was only 0.31 mm. The above results indicate that by enhancing the image features of asphalt concrete cracks, this method achieves more accurate identification results for crack distribution direction, length and width values, with high identification efficiency and good application effect.

Mode-II progressive fracture of sawn timber and timber-adhesive bond: experimental evaluation of end notched flexure (ENF) testing using DIC

The end-notched flexure (ENF) testing technique has been used in this paper to investigate the Mode II fracture behaviour of sawn timber and timber-adhesive bonds. Mode-II strain energy release rates were obtained by using classical data reduction schemes based on actual crack lengths captured using digital image correlation (DIC) technique. The compliance-based beam method (CBBM), which does not require the actual crack length measurements, was also evaluated for its suitability for Mode-II fracture of timber. Utilizing forward shear slip measurement from DIC at every millimetre of crack length, a simple yet effective and innovative technique to identify crack tip opening and to monitor crack length has been proposed herein. Three different initial notch widths were used in the current study to examine their suitability in producing reliable crack initiation and consistent bond delamination in solid timber and glued timber. The strain energy release rates calculated from the actual crack and equivalent crack length values showed similar trends in fracture resistance curves, which are commonly known as R curves, but the initial strain energy release rate (GII0) and the critical strain energy rate (GIIC) obtained from the two methods showed some discrepancies. Equivalent crack method CBBM was found to be inadequate in determining a consistent initial strain energy release rate despite producing a stable and steady fracture energy after crack initiation. Experimental results showed that Mode-II timber-adhesive bond line fracture is relatively more brittle than timber fracture, and the average critical strain energy release rate of timber-adhesive bond (GIIc) was 14% greater than that of sawn timber. Based on experimental observations, specific test criteria for ENF testing of timber structures are proposed in this paper.

Stability Enhancement and Microstructural Modification of Ni-Rich Cathodes via Halide Doping.

Elemental doping is an effective strategy to modify surface and bulk chemistry in NMC cathode materials. By adding small amounts of lithium halide salts during the calcination process, the Ni-rich NMC811 cathode is doped with Br, Cl, or F halogens. The dopant type has a significant impact on the lithiation process and heavily influences the final cathode porosity and surface morphology. Utilizing a variety of electrochemical, surface, and bulk characterization techniques, it is demonstrated that an initial content of 5 mol % LiBr or LiCl in the lithium source is effective in improving capacity retention while also providing excellent rate performance. The improvements are attributed to a substantial increase in specific surface area, the formation of a stable cathode electrolyte interface (CEI) layer, and suppressed surface reconstruction. In addition, the particle microstructure is better equipped to handle cyclic volume changes with increased values of critical crack lengths. Overall, it is demonstrated that anion doping via the addition of lithium halide salts is a facile approach toward Ni-rich NMC modification for enhanced cathode performance.

Behavior analysis of span structures with cracks during vibrations

Introduction: An important engineering task is to assess the state of span structures during their operation in various conditions and develop a methodology not only for determining the current state of the structure and its individual elements but also for predicting life cycle stages. This work is dedicated to the study of the influence of the location and crack size located in the tension region of the beam cross-section on the value of the natural oscillations frequency of the main beam of the superstructure. The article proposes a method for determining the location and parameters of crack opening in the tension region of a pin-ended beam, which is the span structure base, by analyzing several vibration frequencies. Methods: The bridge crossing beam is modeled using the Euler-Bernoulli-type flexural theory. Crack modeling was carried out using the flexibility function, with the account of the location and length of the crack. A mathematical expression is formulated to determine the location and length of an open crack in the tension region of a pin-ended beam. The MATLAB program was used for numerical studies and simulation modeling of the problem of determining the crack parameters. Results: Values of the bridge girder’s natural resonance frequency with a crack in different places along the span and different lengths of the crack in the tension region of the cross-section were obtained. The relationship between the relative crack length and the relative fundamental beam frequency with a crack for different coordinates of its location and also the relationship between the relative location and the relative fundamental beam frequency with a crack for different crack length values are constructed. These given values are proposed to be used as criterion parameters for assessing the state and possible scenarios for the further operation of the beam span. Discussion: The results obtained show that with an increase in the relative length and relative coordinate of the crack initiation site, the natural frequency decreases. Based on the study results, the conclusion was formulated that cracks in the hinged beam tension region with a relative crack length and a relative location of less than 0.1 deserve the least attention. On the other hand, it is necessary to conduct a study to assess the state of a damaged bridge beam with a relative crack location of more than 0.1 and a relative crack length of less than 0.3, and after the analysis, a decision should be made on the possible modes of further operation of the engineering structures. For span structures whose beams have cracks with a relative crack location of more than 0.1 and a relative crack length of more than 0.3, a detailed study and examination of a structure are required, with the development of recommendations for the required repair work.

A coupled phase field formulation for modelling fatigue cracking in lithium-ion battery electrode particles

Electrode particle cracking is one of the main phenomena driving battery capacity degradation. Recent phase field fracture studies have investigated particle cracking behaviour. However, only the beginning of life has been considered and effects such as damage accumulation have been neglected. Here, a multi-physics phase field fatigue model has been developed to study crack propagation in battery electrode particles undergoing hundreds of cycles. In addition, we couple our electrochemo-mechanical formulation with X-ray CT imaging to simulate fatigue cracking of realistic particle microstructures. Using this modelling framework, non-linear crack propagation behaviour is predicted, leading to the observation of an exponential increase in cracked area with cycle number. Three stages of crack growth (slow, accelerating and unstable) are observed, with phenomena such as crack initialisation at concave regions and crack coalescence having a significant contribution to the resulting fatigue crack growth rates. The critical values of C-rate, particle size and initial crack length are determined, and found to be lower than those reported in the literature using static fracture models. Therefore, this work demonstrates the importance of considering fatigue damage in battery degradation models and provides insights on the control of fatigue crack propagation to alleviate battery capacity degradation.

Mode II fracture of wood: Comparison between End-Notched Flexure and Compact Shear testing

End-Notched Flexure (ENF) and Compact Shear (CS) tests were performed on Australian Radiata Pine to quantify Mode II fracture properties in wood. Capabilities and limitations of each fracture test are compared with respect to ease of testing, underlying reduction schemes to determine Mode II fracture toughness (or strain-energy release rate), stable crack growth and mixed mode behaviour during crack growth. In particular, different reduction schemes are presented with and without the need for cumbersome crack length measurements. In contrast to CS tests, it is found that ENF tests yield stable and reliable Mode II fracture with negligible mixed-mode behaviour. Considering resistance curves, crack length measurements are only needed to determine initial fracture energy values associated with crack length values up to 20 mm while compliance-based beam theory can be used to calculate steady-state fracture energies by means of an equivalent crack length that only requires global load–displacement test data.

A study of the morphological effect of an α-Al2O3 layer on the creep life for nickel-based superalloys using microstructure-based geometrical models

A study on the role of the irregular geometry of the α-Al2O3 film during the creep rupture test was conducted on samples of DD6 Ni-based single-crystal superalloy at 980 °C/250 MPa. This study involved experimental and finite element analyses of creep-oxidation specimens. The experimental results showed that the creep rupture life of the 0.67 mm-thin samples was shorter than that of the 0.81 and 1.12 mm specimens. Microscopic examination of the oxidation-affected zones showed that the morphology of the inner α-Al2O3 layer of a 0.67 mm-thin sample was discontinuous and incomplete, and the sample (1.12 mm thick) included a continuous and complete α-Al2O3 film. Hence, the influence of different morphologies of the α-Al2O3 layer on the stress distribution was studied numerically using the ABAQUS software. The finite element modeling results showed that the maximum stress was concentrated in the blocks of a discontinuous α-Al2O3 layer, which increased the diffusion of ions and metal cations. As a result, excessive growth of the oxidation-affected zone of the thin samples and the formation of AlN particles in high density occurred. It also contributed to an increase in the surface crack growth rate in the thin wall sample, which reaches the critical value of crack length in a shorter time than thick ones. Microstructure-based modeling has provided further insight into the role of the α-Al2O3 layer morphology in the deterioration of the mechanical properties of thin creep specimens.

New insight on wheel flange/rail gauge lubrication: Effect of lasered microtexture shapes on the wear and fatigue behaviour of wheel/rail steels

Three types of differently shaped lasered microtextures (microdimples) were produced on the surface of a U75V hot-rolled rail roller with a TY-FM-20S laser marking machine. Wheel flange/rail gauge lubrication starvation tests of four kinds of rail samples running against CL60 wheel samples were carried out, and the friction properties of the wheel/rail steels were studied. The results indicate that the injection of lubricating grease dominates the friction coefficient reductions and that the lubricating effects are closely related to the shapes of the lasered microtextures; for instance, the rectangular and rhombic textures show a better lubricating effect. Furthermore, the wear rates depend on the wear mechanism of the wheel/rail steel; for example, delamination and spalling always result in severe wear while peeling results in mild wear. The materials from the rolling-sliding surface to the matrix region of the wheel/rail materials can be divided into three parts: the plastic deformation region, transition region and undeformed matrix region. The average crack length and angle values of the textured rail and coupled wheel steels are much smaller than those of the untextured rail and coupled wheel steels; thus, the textured rail and coupled wheel steels exhibit better rolling contact fatigue (RCF) resistance. The effects of the lasered microtextures shapes on the wear and fatigue damage are determined based on the fluid dynamic pressure on the microtexture. Notably, rhombic lasered microtextures can be adopted to improve the grease storage capacity, thereby reducing wear and fatigue damage.

Crack path of in-service fatigued fan titanium disk of D-18T gas-turbine engine of the aircraft An-124

The in-service fatigue fracture of the fan disk from the titanium alloy was considered and analyzed. Fatigue crack started from the cut which was produced during disk manufacturing and located along the slot for the blade. The crack path was performed by the mechanism of crack meso-tunneling with the facetted pattern relief and striation formation on the fracture surface. Based on the fractographic analysis, equivalent stress for various values of crack length was estimated. The inspection interval for reliable crack registration in the disk was provided. It was demonstrated that without cuts the disk in-service period will be not less than 15,000 flights.

Study on fracture evaluation in hydrogen environment in 316L stainless steel used in high pressure hydrogen tank

In today’s growing pollution, hydrogen fuel vehicles are an important alternative to electric vehicles. For Type-4 Hydrogen Tank, a steel boss is normally used for valve mounting. The process of hydrogen embrittlement on steel plays a detrimental role. So, studies on the effect of hydrogen embrittlement on the threaded part of 316L stainless steel boss required for fastening of the valve for the 70 MPa compressed H2 tank have been carried out. For analysis, HEDE mechanism and Paris-Erdogan Law are used. For different values of initial crack length, the critical crack lengths are obtained for a particular loading cycle. The same calculation is repeated for different loading cycles. The analysis result shows that the critical crack length increases with the number of loading cycles. The critical crack length is higher 2% to 4% if the effect of hydrogen embrittlement is taken into account. So, for high pressure hydrogen tanks it is essential to consider the effect of hydrogen embrittlement.

Development of a fracture-mechanics based fatigue testing method for epoxy/electrical steel laminates with thin adhesive layer

A fatigue fracture mechanics method was developed, implemented and used to characterize the crack kinetics of laminated electrical steel. Tests were carried out on double cantilever beam specimen based on electrical steel sheets and an epoxy adhesive layer with a thickness of just 10 µm. Two different crack length measurement methods based on optical measurement or compliance calculation were evaluated. As validation method specimens with different artificial initial crack length were used. The accuracy is limited to thin and stiff adhesives ensuring a small plastic zone size compared to the crack length. The accuracy of the crack length evaluation methods was higher for the compliance based approach meeting standard specifications at low to intermediate crack length values. The compliance based method was applied to investigate a specimen series varying the pre-curing temperature of the epoxy adhesive systematically. The fatigue tests were performed at ambient condition and 60 °C. At ambient temperature, laminates based on coated electrical steel pre-cured at low to intermediate temperatures revealed rather slow crack propagation rates in comparison to laminates made from coated steel pre-cured at 250 °C. The differences in the stable crack propagation rate of the investigated laminates at ambient conditions were up to two orders of magnitude higher. At 60 °C, the worst performance was also obtained for laminates based on coated steel sheets pre-cured at 250 °C. The failure mode was similar for laminates tested at 23 and 60 °C. While interfacial failure was ascertained for laminates based on coated steel sheets pre-cured at 190 and 250 °C, the better performing laminates made from sheets with epoxy coating pre-cured at 210 or 230 °C exhibited mainly cohesive failure. Hence, adequate pre-curing conditions are of utmost importance for the crack kinetics of adhesively bonded electrical steel.

Quantitative characterization of crack propagation behavior under the action of stage-by-stage fracturing induced by SC-CO2 fluid

The use of supercritical carbon dioxide (SC-CO2) for the fracturing of coal bodies has excellent development prospects and practicability. It alters the fissure structure of coal bodies and achieves CO2 geological sequestration. This process, which involves the mutual interaction of coal, fissures, supercritical fluid, and gas, can be subdivided into fluid-induced and phase change-induced fracturing stages. Numerical simulation of the SC-CO2 fracturing was carried out in a stagewise manner to characterize each stage's fracturing performance quantitatively. The effects exerted on the crack propagation behavior by such factors as the ground stress deviation, the permeability coefficient of coal bodies, fracturing fluid injection rate and temperature, was studied in detail for each stage. The crack morphology, length, and width of cracks induced in each stage in proportion to the total crack length and width values were determined and analyzed. The research results show that the crack length ratio of the SC-CO2 fluid-induced fracturing stage to the total crack length was 80–90%, with the remaining 10–20% corresponding to the CO2 phase change-induced fracturing stage. This indicates that cracks propagation primarily occurred at the former stage. Meanwhile, the crack width ratios were nearly the same: 40–55% for the former stage versus 45–60% for the latter stage. Thus, the crack width increased dramatically at both stages of the SC-CO2 fracturing in the coal bodies. The research findings refined the insight into the SC-CO2 fracturing mechanism in coal bodies.

The Effect of Crack Orientation on the Propagation of Cracks in Graphene Nanoplatelet Carbon Fiber-reinforced Epoxy Composites Using Digital Image Correlation

This study experimentally investigated the fracture behaviors of graphene nanoplatelet (GNP) carbon fiber-reinforced polymer (CFRP) composites for varying amounts of GNP reinforcement, crack lengths and crack orientation angles. The specimens were subjected to tensile loading, and their fracture toughness values were determined with respect to maximum damage load and crack length. To compare the results obtained from experimental data, the fracture toughness values, strain distributions and crack tip opening displacements were determined by using a Digital Image Correlation (DIC) technique from images recorded during the tests. The results showed that increasing the amount of GNP increased the fracture toughness of specimens. On the other hand, increasing the crack orientation angle decreased the fracture toughness. Increasing the crack length increased the fracture toughness values for a crack orientation angle of 30° but decreased for a crack orientation angle of 90°. DIC results were found to be compatible with the calculated results using crack length and damage stress values.

Fine granular area linked to very high cycle fatigue in martensitic and bainitic steels: Characterization by means of EBSD-dictionary indexing

In martensitic/bainitic bearing steels, non-observable critical cracks can initiate at inner inclusions well below the endurance limit (at 107 cycles), leading to very high cycle fatigue failure. The stability of these cracks is not ensured even if they have a stress intensity factor lower than the threshold for long crack propagation, strongly compromising the safety of the mechanical component. Propagation of such cracks is reported to be preceded by the formation of a fine granular area (FGA) structure. Due to the high demanding characterization and testing experimental circumstances, the crystallography of FGA is far from understood. Recent advances have come hand by hand from an experimental procedure strategy which triggers the FGA formation at predicted crack initiation sites. The novel EBSD-dictionary indexing has proven to be a powerful tool from which FGA formation acquires new value and opens the door for a systematic microstructural characterization at different crack length values.

Effect of crack propagation path on mesh stiffness of spur gears

Gear mesh stiffness is an important indicator for condition monitoring of gears as its value has been found to decrease with initiation of crack. In the current study, the effect of crack propagation path on mesh stiffness has been investigated. Elliptical cracks with different values of semi major and semi minor axes have been considered with same values of crack lengths along these paths. ANSYS 19 software along with FRANC 3D has been used to model the gears with cracks induced. Structural analysis has been performed through Mechanical APDL. The values of mesh stiffness have been found to vary significantly with change in path of crack progression.

Fracture analysis of bi-layer electrode in lithium-ion battery caused by diffusion-induced stress

An analytical model has been developed to study the fracture behavior of bi-layer electrodes in the lithium-ion battery under galvanostatic intercalation and deintercalation. The bi-layer electrode is composed of an active strip and a current collector. Crack initiation and propagation may occur when the peak tensile stress caused by diffusion exceeds the theoretical strength of the active strip. For this, solutions of concentration distribution and diffusion-induced stress are derived and the stress intensity factors at the crack tips are calculated. Numerical results show that cracks may be more easily initiated during extraction of lithium ions in the active strip since the peak tensile stress during extraction is much larger than that during insertion. Stress intensity factor decreases with increasing values of crack length, which demonstrates that crack propagation may cease when it reaches a certain length.

A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

ABSTRACTA non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

FEM simulation of welded joint geometry influence on fatigue crack growth resistance

Fatigue behaviour of welded joints is investigated, in terms of welded joint geometry and the fatigue crack position. It is based on previous work which involved numerical simulation of fatigue crack growth in a welded joint made of micro-alloyed, low-carbon pressure vessel steel P460NL1, with the main focus on fatigue crack growth rate through different welded joint regions. The goal here was to change the size of the heat affected zone, as the region in which the fatigue crack initiated, and to compare the results obtained for new crack length values with the original ones, obtained by creating numerical models based on experimental data. A number of models were created, some of which simulated the case with a bigger heat affected zone (and, consequently, a smaller crack length in the weld metal), and other which simulated the case with a smaller heat affected zone. Due to the micro-structural differences between these two welded joint regions, noticeable differences appeared in the numbers of cycles obtained for each zone with varying fatigue crack lengths, as well as in the total number of cycles for both zones through which the crack propagated.

Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.