Crack Tip Research Articles

Experimental study on the Mode l fracture toughness of frozen silty clay incorporating Digital image correlation

To investigate the effects of initial moisture content and temperature on the Mode I fracture toughness (KIc) of frozen silty clay, a series of three-point bending tests were conducted. Rectangular specimens with prefabricated cracks were tested, and digital image correlation (DIC) technology was employed to analyze the microscopic characteristics at the crack tip. The results indicate that the Mode I fracture toughness of frozen silty clay increases with decreasing temperature and increasing initial moisture content. Temperature governs the failure mode, with plastic failure predominantly occurring at high temperatures and brittle failure at low temperatures. Based on the load–displacement curves and DIC recordings, the macroscopic fracture process of the specimens can be categorized into three stages: elastic deformation, formation of the failure surface, and specimen failure. Additionally, the crack propagation process can be further divided into three stages: initiation and development of microcracks, transition from microcracks to macroscopic cracks, and rapid development of macroscopic cracks. These findings provide critical insights for slope stability research in cold regions and offer new perspectives for engineering design and construction in similar environments.

Anti-plane Yoffe-type crack in flexoelectric material

This work investigates the deformation and polarization fields around a finite anti-plane shear (mode III) crack growing dynamically under steady-state conditions. The leading tip of this finite crack breaks the material while the trailing tip heals it. This fast moving finite crack (referred to as a rupture “pulse” in the geophysics literature) propagates with a constant velocity and with the mechanical and the electrical fields that remain invariant with respect to an observer moving with the crack-tips. This problem belongs to the first type of steady state crack growth problems according to the classification of Freund. The “prototype” problem which refers to an isotropic, body subjected to fracture under tensile loading was first proposed and solved by Yoffe, while finite cracks (or shear pulses) were also analyzed by Freund and by Rice. In the above cases the material was assumed to be linear elastic. Our analysis extends these studies to flexoelectric materials, and it is both theoretical and numerical. It discusses the asymptotic structure of the crack-tip displacement and the polarization fields; it calculates the dynamic energy release rate and presents their dependence on crack-tip velocity. Comparisons are made to the available, classical, elasto-dynamic solutions and to the static case. The influence of the electrical properties of the material on strengthening is also analyzed. Dynamic fracture of flexoelectric materials is of relevance to both the study of earthquake source mechanics and to the analysis of the reliability of micro-electronic devices. This is because both rocks and ceramics are flexoelectric. Indeed, during earthquake rupture processes, dynamic, in-plane shear (Mode-II) and out of plane shear (Mode-III), cracks propagate along faults and exhibit both mechanical and electrical polarization signatures. At an entirely different length scale, flexoelectric ceramics are currently used as sensors and transducers and can experience dynamic shear failure along interfaces when subjected to dynamic loading (e.g. impact.). Failure by dynamic fracture can be detrimental to both their mechanical reliability and electrical functionality.

Fracture Toughness Estimate of H-Section Steel for Offshore Structure

In this study, a novel estimating equation based on the WES2808 standard was proposed to predict fracture toughness through the transition temperature of Charpy impact toughness and CTOD (Crack Tip Opening Displacement) fracture toughness. This equation was specifically developed for 460MPa class H-section steel materials used in marine structures, including the base material (BM), heat-affected zone (HAZ), and weld metal (WM). The experimental results confirmed that the proposed estimation equation accurately predicted the fracture toughness across these different material regions. These findings demonstrate the reliability and applicability of the proposed equation in estimated fracture toughness for marine structure materials, thereby contributing to improved safety and performance in harsh environmental conditions.

Analysis of Stress Corrosion Cracking Growth Rate in the Heat-Affected Zone of 316L Based on the Heterogeneity of the Mechanical Properties

The heterogeneity of the microstructure and mechanical properties of safe-end dissimilar metal welded joints (DMWJs) presents a challenge to the quantitative prediction of the stress corrosion cracking (SCC) growth rate directly from laboratory data. This study investigates the effect of the heterogeneity of the mechanical properties of the 316L-welded heat-affected zone (HAZ) in safe-end DWMJs on the SCC tip stress-strain field and the SCC growth rate. First, based on the analysis of microstructures in localized regions within the 316L-welded HAZ and the acquisition of material mechanical properties through microhardness testing, a user-defined material subroutine was developed to characterize the heterogeneous material properties within the 316L-welded HAZ. Then, using this finite element model with an inhomogeneous distribution of the mechanical properties of the material, the crack tip strain rates (CTSRs) at different locations within the 316L-welded HAZ were obtained. In conjunction with the FRI model, the SCC growth rates at various locations within the HAZ were determined. The results show that the closer to the 52Mw/316L fusion boundary within the 316L-welded HAZ, the greater the yield strength of the material and the higher the CTSR and predicted SCC growth rates at the characteristic distance.

A Versatile Microporous Design toward Toughened yet Softened Self-Healing Materials.

Realizing the full potential of self-healing materials in stretchable electronics necessitates not only low modulus to enable high adaptivity, but also high toughness to resist crack propagation. However, existing toughening strategies for soft self-healing materials have only modestly improves mechanical dissipation near the crack tip (ГD), and invariably compromise the material's inherent softness and autonomous healing capabilities. Here, a synthetic microporous architecture is demonstrated that unprecedently toughens and softens self-healing materials without impacting their intrinsic self-healing kinetics. This microporous structure spreads energy dissipation across the entire material through a bran-new dissipative mode of adaptable crack movement (ГA), which substantially increases the fracture toughness by 31.6 times, from 3.19 to 100.86 kJ m-2, and the fractocohesive length by 20.7 times, from 0.59 mm to 12.24 mm. This combination of unprecedented fracture toughness (100.86 kJ m-2) and centimeter-scale fractocohesive length (1.23 cm) surpasses all previous records for synthetic soft self-healing materials and even exceeds those of light alloys. Coupled with significantly enhanced softness (0.43 MPa) and nearly perfect autonomous self-healing efficiency (≈100%), this robust material is ideal for constructing durable kirigami electronics for wearable devices.

In-depth molecular dynamics analysis of crack evolution in polycrystalline chromium under uniaxial tensile deformation

Because of its excellent wear resistance and high hardness, chromium is widely used in coating materials. Under external load, micro-cracks on the surface of electroplated chromium coating will cause crack propagation and reduce the performance of the material. Therefore, in this study, the crack evolution process of polycrystalline chromium under uniaxial tension was studied using molecular dynamics. The effects of average grain size, strain rate, and crack location on crack propagation behavior were analyzed, which provided a scientific basis for optimizing the performance of chromium materials. The results show that cracks in polycrystalline chromium tend to fracture along grain boundaries and that stacking faults and holes are the main factors for crack propagation. As the grain size decreases, the crack passivation becomes more pronounced and the rate of crack expansion slows down. As the strain rate increases, the crystal structure of polycrystalline chromium changes more sharply, and the ultimate stress increases. At high strain rates, the direction of crack propagation changes. The degree of crack tip passivation is affected by the initial crack location, and the crack tip can be effectively passivated when it is located at the grain boundary, thus hindering crack propagation. The results of these studies reveal the influence of multiple factors on the crack propagation mechanism of polycrystalline chromium and provide theoretical guidance for the reduction of chromium coating damage.

Fatigue Failure of Alloy Grade P22 Hot Reheat Auxiliary Steam Pipe

A leak was discovered in the hot reheat auxiliary pipe. The pipe was found to have a bulging condition and a crack at the base metal area. A circumferential crack was discovered near a repair weld spot on the external surface. The failure was investigated using material characterization techniques, including in-situ replication, glow discharge spectroscopy (GDS), microhardness analysis, optical microscopy, and energy dispersive X-ray spectroscopy (EDX). Based on microstructure analysis, numerous cracks were observed to have initiated at the internal surfaces of the pipe. Most of the cracks were found on the parent metal. The cluster of cracks concentrates on the plane of 0⁰ - 180⁰. Microstructure analysis shows that the cracks are multiple, parallel, mainly transgranular, oxide-filled with branching crack tips. It is thought that the cracking is associated with fatigue and, most likely, high cyclic stress is the key contributory factor. The steam oxide cracked gradually as a result of the cyclic stress. As more metal surface was exposed, new oxide formed, causing cracks to propagate into the metal as this process was repeated due to cyclic loading.

Study on Multi-Crack Damage Evolution and Fatigue Life of Corroded Steel Wires Inside In-Service Bridge Suspenders

The parallel steel wires used in arch bridge suspenders experience random corrosion damage on their surfaces during service. Corrosion damage, including micro-cracks, pitting, and a combination of both, leads to significant stress concentration under axial loading, which affects the performance of the steel wires. The change in the stress field caused by surface damage alters the stress intensity factor at the crack tip, and the presence of adjacent crack tips significantly amplifies the stress intensity factor, thereby accelerating crack propagation. The development of small surface damages in the steel wires is difficult to control and observe through experiments. By utilizing finite element methods for simulation, it is possible to intuitively analyze the crack propagation process, the trend of stress changes at the crack tip, and the interaction between damages. Numerical simulation results based on Paris’ law indicate that corrosion pits have a certain impact on the stress intensity factor at the crack tip. The propagation process of coplanar double cracks is highly sensitive to the initial crack size and the distance between adjacent crack tips. When the crack spacing is less than the crack depth, the stress intensity factor at the adjacent crack tips exhibits significant amplification. Based on this phenomenon, the coplanar double-crack system can be simplified to a complete single crack for analysis. By comparing the fatigue life of the double-crack system with that of the equivalent single crack, the effectiveness of the simplification rule has been validated.

Fatigue Crack Growth Monitoring and Investigation on G20Mn5QT Cast Steel and Welds via Acoustic Emission

The fatigue crack growth properties of G20Mn5QT cast steel and corresponding butt welds, using compact tension specimens, were monitored and investigated via acoustic emission (AE) techniques. Fatigue crack growth is a combination of cyclic plastic deformations before the crack tip, tensile crack fractures, and shear crack fractures. The cyclic plastic deformations release the maximum amount of energy, which accounts for half of the total energy, and the second-largest number of AE signals, which are of the continuous-wave type. The tensile crack fractures release the second-largest amount of energy and the largest number of AE signals, which are of the burst-wave type. The shear crack fractures release the least amount of energy and the lowest number of AE signals, which are similar to the burst type, albeit with a relatively longer rise time and duration. Crack tip advancement can be regarded as a discontinuous process. The critical area before the crack tip brittlely ruptures when the fatigue damage caused by cyclic plastic deformations reaches critical status. The ruptures produce a large number of tensile crack fractures and rare shear crack fractures. Through fractography observation, the shear crack fractures occur probabilistically around defects caused by casting or welding, which lead to stress and strain in the local complex.

Model for predicting type Ι fatigue crack growth rate in RKE field considering stress gradient

Based on the stress–strain field at the crack tip of Rice-Kujawski-Ellyin (RKE) and considering the stress gradient effect near the crack tip of type I, a fatigue crack growth rate prediction model L-SG (RKE) for type I is proposed in this paper. Firstly, the stress gradient change value of 1 % at the crack tip is considered as the characteristic distance (stress gradient influence range), and the ratio of the equivalent stress to the far-field stress in the stress gradient influence range is defined as the stress gradient influence coefficient ρ; Secondly, the new model L-SG (RKE) is proposed to quantitatively describe the fatigue crack growth behavior by using the stress–strain field at the crack tip of RKE, and the stress gradient influence coefficient ρ is introduced, and then the crack tip passivation radius rp is defined to eliminate the crack tip singularity, and the plastic strain energy failure criterion is combined.; Finally, the prediction effect of the L-SG (RKE) model is verified by 6 metal materials and the fatigue crack growth rate test results of 2 groups of 45 steel CT specimens, and compared with the SHI-CAI (RKE) model. At the same time, based on the R2 fitting effect and the different requirements of the three stages of fatigue crack propagation, the prediction effect of the two prediction models is analyzed, and comprehensive evaluation from two aspects of safety and accuracy. The results show that the L-SG (RKE) prediction model can better reflect the actual fatigue crack propagation behavior, and can meet the requirements of practical engineering for the accuracy and safety of the prediction model. Especially, the prediction results of physical cracks in 45 steel shaft parts by this model agrees well with the experimental data.

In situ analysis of three-dimensional microcrack propagation in cross-ply laminates using synchrotron radiation X-ray computed tomography

This study utilized synchrotron radiation X-ray computed tomography to investigate the initiation and propagation of microcracks in cross-ply carbon fiber-reinforced polymer (CFRP) laminates under mechanical loading. Initially, static tensile loads were applied to detect microcracks within a ply thickness of 160 μm. The crack propagation was subsequently characterized, extending across adjacent carbon fibers and along the interfaces of individual fibers into the material's interior. The experiment was repeated with cyclic loading, where the laminates were imaged periodically. Analysis of the images revealed the presence of microcracks and provided insights into their progression from the point of initiation. Notably, microcracks exhibited the initiation toward the interior of the material rather than across the neighboring carbon fibers, whereas their propagation is more significant across the adjacent carbon fibers particularly under the static loading. Under cyclic loading, however, the crack propagation toward the interior of the material was more pronounced, implying different propagation behavior than when under static loading. These findings were also validated through the distribution of energy release rate and stress triaxiality along the crack tip calculated by finite element analysis.

Observing the crack tip behavior at the nanoscale during fracture of ceramics

Ultimately, brittle fracture involves breaking atomic bonds. However, we still lack a clear picture of what happens in the highly deformed region around a moving crack tip. Consequently, we still cannot link nanoscale phenomena with the macroscopic toughness of materials. The unsolved challenge is to observe the movement of the crack front at the nanoscale while extracting quantitative information. Here, we address this challenge by monitoring stable crack growth inside a transmission electron microscope. Our analysis demonstrates how phase transformation toughening, previously thought to be effective at the microscale and above, promotes crack deflection at the nanolevel and increases the fracture resistance. The work is a first step to help connecting the atomistic and continuous view of fracture in a way that can guide the design of the next generation of strong and tough materials demanded by technologies as diverse as healthcare, energy generation, or transport.

Effect of Thermal Load Caused by Tread Braking on Crack Propagation in Railway Wheels on Long Downhill Ramps

To investigate the propagation behavior of thermal cracks on the wheel tread under the conditions of long downhill ramps, a three-dimensional finite element model of a 1/16 wheel, including an initial thermal crack, was developed using the finite element software ANSYS 17.0. The loading scenarios considered include mechanical wheel–rail loads, both with and without the superposition of thermal wheel–brake shoe friction loads. The virtual crack closure method (VCCM) is employed to analyze the variations in stress intensity factors (SIFs) for Modes I, II, and III (KI, KII, and KIII) at the 0°, mid, and 90° positions along the crack tip. The simulation results show that temperature is a critical factor for the propagation of thermal cracks. Among the SIFs, KII (Mode II) is larger than KI (Mode I) and KIII (Mode III). Specifically, the thermal load on the wheel tread during braking contributes up to 23.83% to KII when the wheel tread reaches the martensitic phase transition temperature due to brake failure. These results are consistent with the observed radial propagation of thermal cracks in wheel treads under operational conditions.

Effect of temperature and adhesive defect on repaired structure using composite patch

In structural engineering, composite patch repairs are widely used to address cracked structures. However, their behavior under thermo-mechanical loading remains complex and less understood. This study examines the repair of a center-cracked plate subjected to both mechanical and thermo-mechanical environments, using finite element analysis in ANSYS. The repair effectiveness is evaluated using the Stress Intensity Factor (SIF) at the crack tip. Findings reveal that increased temperature substantially elevates SIF values. Boron/epoxy patches are most effective under mechanical loading, yielding the lowest SIF, while graphite/epoxy patches excel under thermo-mechanical loading due to their lower Coefficient of Thermal Expansion (CTE). Patch thickness influences SIF differently based on loading conditions; thicker patches decrease SIF under mechanical loading but increase it under thermo-mechanical loading. Furthermore, adhesive defects, particularly at the crack tip, markedly increase the risk of adhesive failure, especially under thermo-mechanical conditions. This research underscores the significant impact of temperature variations on the efficiency of structural repairs, contributing to a deeper understanding of composite patch repair performance in cracked structures.

Comparison of fracture behavior of set concretes based on natural and crushed aggregates

Abstract The studies were carried out to diagnose the effects of coarse aggregate type on the mechanical behavior of plain concretes under incremental loading. During the studies mechanical parameters including compressive strength (fcm) and splitting tensile strength (fctm), as well as fracture parameters involving critical stress intensity factor (K_Ic^S) and critical crack tip opening displacement (CTODc) were evaluated. Crushed aggregates covered: basalt (BA), granite (GT) and limestone (LM) and natural peeble gravel aggregate (GL) were used in the concrete mixtures. The composite made on pebble aggregate acted as a reference concrete, as it were, in the analysis of the test results. For better understanding of the crack initiation and propagation in concretes with different coarse aggregates, a macroscopic failure surfaces examination of the tested beams is also presented. Both of the analyzed fracture mechanics parameters, i.e. 〖 K〗_Ic^S and CTODc increased significantly in the case of concretes which were manufactured based on crushed aggregates. They amounted in comparison to concrete based on gravel aggregate at levels ranging from 20% for concrete with limestone aggregate, to over 30% for concrete with a granite aggregate, and to as much as over 70% for concrete with basalt aggregate. Moreover, a clear correlation in the changes in the obtained results between the main strength parameters and fracture mechanics parameters was observed. The fracture process in each series of concrete was: quasi-plastic in the case of gravel concrete, semi-brittle in the case of limestone concrete, and clearly brittle in the case of the concretes based on granite and basalt aggregate. The results obtained help to explain how the coarse aggregate type affects the strength parameters and fracture toughness at bending.

Experimental study on interaction characteristics of explosive cracks under confining pressure and its comparison with free boundary results

The influence of confining pressure on the dynamic fracture mechanical behavior of deep rock masses is crucial in the exploitation of deep resources and the development of underground spaces. In this study, dynamic caustics experiments were conducted using transparent epoxy resin materials to investigate the crack propagation behavior and interaction mechanisms of double cracks under confinement. The experimental results indicate that biaxial confining pressure suppresses crack propagation, interaction between double cracks, and penetration. Without confining pressure, cracks do not penetrate until the relative vertical distance ΔH between crack tips is 20 mm, whereas with confining pressure, cracks cease to penetrate when the relative vertical distance between crack tips is 10 mm; however, interaction between crack tips still exists at this point. During the crack interaction stage, both fracture toughness and propagation velocity of crack tips exhibit significant fluctuations under no confining pressure conditions, whereas under confining pressure, both decrease rapidly. Additionally, under confining pressure conditions, the fluctuation range of crack propagation direction during crack interaction is relatively small. Confining pressure rapidly reduces the degree of stress concentration at crack tips, increases the rate of energy release at crack tips, and enhances the ability of dynamic cracks to resist the influence of other crack tips or crack surfaces. Under confining pressure, continuous Rayleigh waves are typically observed at crack tips due to an imbalance between stored strain energy and the energy release rate. These waves dissipate part of the strain energy, promoting crack deflection and branching.

The Corrosion Fatigue Behavior and Mechanism of AerMet 100 Steel in 3.5% NaCl at Room Temperature.

AerMet 100 steel is a new type of double-hardened high-strength steel, which is often used as landing gear material in amphibious aircraft. In the present paper, the corrosion fatigue behavior and mechanism of AerMet 100 high-strength steel in a 3.5% NaCl solution was studied by stress-controlled fatigue tests and a series of subsequent characterizations of the fracture surface, microstructure, and cracks. The results indicated that the fatigue life of AerMet 100 high-strength steel decreased with a decrease in the stress level in a 3.5% NaCl solution, satisfying the relationship lgN = -2.69 × 10-3 σ + 6.49. The corrosion fatigue crack usually initiated from the corrosion pit and propagated across the martensitic flat noodles. Meanwhile, the corrosion fatigue crack tip was filled with Cr2O3, Fe2O3, and amorphous material; it propagated in the transgranular mode by a slip dissolution mechanism. This study provides some engineering significant for the fatigue performance of AerMet 100 steel in a 3.5% NaCl solution.

Effect of Coarse Aggregate Type on the Fracture Toughness of Ordinary Concrete

This research work aims to compare the strength and fracture mechanics properties of plain concretes, obtained from different coarse aggregates. During the study, mechanical parameters including compressive strength (fcm) and splitting tensile strength (fctm), as well as fracture parameters involving critical stress intensity factor (KIcS) and critical crack tip opening displacement (CTODc) were evaluated. The effect of the aggregates used on the brittleness of the concretes was also analyzed. For better understanding of the crack initiation and propagation in concretes with different coarse aggregates, a macroscopic failure surfaces examination of the tested beams is also presented. Crushed aggregates covered were basalt (BA), granite (GT), and limestone (LM), and natural peeble gravel aggregate (GL) were used in the concrete mixtures. Fracture toughness tests were performed on an MTS 810 testing machine. Due to the high strength of the rock material, the rough surface of the aggregate grains, and good bonding in the ITZ area between the aggregate and the paste, the concretes with crushed aggregates exhibited high fracture toughness. Both of the analyzed fracture mechanics parameters, i.e., KIcS and CTODc, increased significantly in the case of concretes which were manufactured with crushed aggregates. They amounted, in comparison to concrete based on gravel aggregate, to levels ranging from 20% for concrete with limestone aggregate to over 30% for concrete with a granite aggregate, and to as much as over 70% for concrete with basalt aggregate. On the other hand, the concrete with gravel aggregate showed the lowest fracture toughness because of the smooth surface of the aggregate grains and poor bonding between the aggregate and the cement paste. However, the fracture process in each series of concrete was quasi-plastic in the case of gravel concrete, semi-brittle in the case of limestone concrete, and clearly brittle in the case of the concretes based on granite and basalt aggregates. The results obtained help to explain how the coarse aggregate type affects the strength parameters and fracture toughness at bending.

Crack Growth Analytical Model Considering the Crack Growth Resistance Parameter Due to the Unloading Process

Crack growth analysis is essential for probabilistic damage tolerance assessment of aeroengine life-limited parts. Traditional crack growth models directly establish the stress ratio–crack growth rate or crack opening stress relationship and focus less on changes in the crack tip stress field and its influence, so the resolution and accuracy of maneuvering flight load spectral analysis are limited. To improve the accuracy and convenience of analysis, a parameter considering the effect of unloading amount on crack propagation resistance is proposed, and the corresponding analytical model is established. The corresponding process for acquiring the model parameters through the constant amplitude test data of a Ti-6AL-4V compact tension specimen is presented. Six kinds of flight load spectra with inserted load pairs with different stress ratios and repetition times are tested to verify the accuracy of the proposed model. All the deviations between the proposed model and test life results are less than 10%, which demonstrates the superiority of the proposed model over the crack closure and Walker-based models in addressing relevant loading spectra. The proposed analytical model provides new insights for the safety of aeroengine life-limited parts.

An adaptive acceleration scheme for phase-field fatigue computations

Abstract Phase-field models of fatigue are capable of reproducing the main phenomenology of fatigue behavior. However, phase-field computations in the high-cycle fatigue regime are prohibitively expensive due to the need to resolve spatially the small length scale inherent to phase-field models and temporally the loading history for several millions of cycles. As a remedy, we propose a fully adaptive acceleration scheme based on the cycle jump technique, where the cycle-by-cycle resolution of an appropriately determined number of cycles is skipped while predicting the local system evolution during the jump. The novelty of our approach is a cycle-jump criterion to determine the appropriate cycle-jump size based on a target increment of a global variable which monitors the advancement of fatigue. We propose the definition and meaning of this variable for three general stages of the fatigue life. In comparison to existing acceleration techniques, our approach needs no parameters and bounds for the cycle-jump size, and it works independently of the material, specimen or loading conditions. Since one of the monitoring variables is the fatigue crack length, we introduce an accurate, flexible and efficient method for its computation, which overcomes the issues of conventional crack tip tracking algorithms and enables the consideration of several cracks evolving at the same time. The performance of the proposed acceleration scheme is demonstrated with representative numerical examples, which show a speedup reaching up to four orders of magnitude in the high-cycle fatigue regime with consistently high accuracy. Graphical abstract