Small Surface Cracks Research Articles

Rough surface rolling contact fatigue crack stress intensity factor calculation for modern rail steels

For premium grades (and rail surface treatments such as ‘laser cladding’) there is little plastic damage expected during typical operating conditions, and smooth surface contact models predict a long life. However, damage still develops, including rolling contact fatigue, affecting premium steels from multiple suppliers. A model is described predicting stress intensity factors and indicative crack growth rates for cracks driven by surface roughness stresses. Accompanying field data quantify the asperity separation and tip radii for rails from metro, mixed traffic and a freight line in ground or unground conditions. The results predict that in rough surface contact small surface cracks (50–100 μm, exceeding microstructural dimensions) can grow faster than crack removal by wear, even when smooth surface models predict no growth. The model has application in identifying how rail grinding marks or wheel roughness may be an important factor in determining rail life through raised stresses at the rail surface (leading to wear), and increased stress intensities and growth rates for incipient cracks.

Stress intensity factor analysis for mixed-mode fracture behavior of inclined semi-elliptical surface crack in stiffened plate under tension load

This study aims to investigate the mixed-mode fracture behavior of stiffened plates with inclined semi-elliptical surface cracks (ISSCs). For this purpose, a new numerical model is developed for the fracture analysis using FRANC 3D in combination with ABAQUS. Normalized stress intensity factors (SIFs) are used to analyze the fracture behavior at the surface and deepest points of the surface crack. Additionally, an arrest parameter ψ is proposed to quantify the level of crack arrest under mixed-mode conditions. Then, a thorough investigation is conducted to examine the fracture behavior of stiffened plates with ISSCs, focusing on the effects of aspect ratio, relative depth, spacing ratio, stiffness coefficient, crack angle, and loading mode. The findings indicate that the restraint effect of stiffeners on the fracture of large surface cracks is significantly stronger compared to small surface cracks. It is also identified that the restraint effect is more pronounced at the surface point than at the deepest point. Finally, a set of novel formulas is derived to evaluate the mixed-mode SIFs in stiffened plates through statistical analysis of the results.

Experimental Analysis of Drying Kinetics and Quality Aspects of Convection-Dried Cathodes at Laboratory Scale

The evaporation of N-Methyl-2-Pyrrolidone (NMP) solvent during the large-scale production of LiNixMn1−x−yCoyO2 (NMC) cathodes usually occurs in convection ovens. This paper aims to close the gap between the industrial convection drying method and the conventional vacuum oven typically used at the laboratory scale. Multiple studies focus on modeling convection dryers to reduce energy consumption, but few have studied their impact on the cathode quality experimentally and compared them to vacuum-dried cathodes. A convection oven designed for LIB electrode drying was developed to investigate the influence of drying kinetics on the formation of small electrode surface cracks (<1400 μm2) and binder migration. The drying kinetics were revealed through thermogravimetric analysis (TGA) at drying temperatures of 50 and 100 °C and hot air velocities of 0.5 and 1 m/s. Even at these relatively low drying rates, structural differences were detected when comparing the two drying methods, illustrating the importance of implementing drying conditions that represent the industry process in laboratories. Surface cracking increased with drying rates, and cathodes with multiple cracks after calendering obtained a higher discharge capacity at discharge currents >C/2. An alternative surface analysis with less sample preparation was sufficient for determining the relative change in binder migration.

Fracture-based shape optimization built upon the topological derivative

In Silva et al. (2011) and Alidoost et al. (2020), the authors developed an approximation of the energy release rate field associated with a small edge or surface crack at any boundary location and with any orientation using the topological derivative. The approximation is computationally attractive because it requires only a single analysis on the non-cracked domain in contrast with conventional boundary-element and finite-element-based methods, which require a separate and costlier analysis for each crack length-location-orientation combination. In this work, a shape optimization scheme for fracture-resistant structures is developed using the energy release rate approximation. In the gradient-based optimization scheme, the domain and its boundary are defined implicitly using level-set functions. The level-set functions of arbitrary geometries are constructed using Boolean operations from the level-set functions of simple primitives. This geometrical representation has the dual advantage of (i) allowing shapes to intersect and/or separate during the optimization and (ii) simplifying the computation of the shape sensitivities.

Fatigue Crack Initiation and Propagation Relation of Notched Specimens with Welded Joint Characteristics

This study focuses on predicting the fatigue life of notched specimens with geometries and microstructure representative of welded joints. It employs 26 series of fatigue tests on welded and non-welded specimens containing notches located in different material zones, including the parent material, weld metal, and heat-affected zone. Overall, 351 test samples made of six structural steels are included in the present evaluation. For each individual specimen, the stress concentration factor, as well as the stress distribution in the notched section, was determined for subsequent fracture mechanics calculation. The latter is employed to estimate the fraction of fatigue life associated with crack propagation, starting from a small surface crack until fracture. It was shown that the total fatigue life can be realistically predicted by means of fracture mechanics calculations, whereas estimates of the fatigue life until macroscopic crack initiation are subject to numerous uncertainties. Furthermore, methods of statistical data analyses are applied to explore correlations between the S–N curves and the notch acuity characterized by the notch radius, opening angle, and the stress concentration factor. In particular, a strong correlation is observed between the notch acuity and the slope of the S–N curves.

Modes I-II-III stress intensity factors of a semi-elliptical surface crack at a round bar under torsion loading by FEM and DBEM

The corner point singularity of surface cracks by finite element method (FEM) has become a numerical concern decades ago. The literature showed that the stress intensity factors (SIFs) at the corner points were often excluded. Further, most SIFs were reported for larger ratios of the crack depth over cylinder diameter. This paper presents the SIFs (Modes I, II and III) of a semi-elliptical surface crack at a solid round bar under torsion. The tetrahedral and hexahedral elements were used in the finite element modelling. The effects of the loading mode and the crack aspect ratio on the corner point singularity were discussed. The tetrahedral meshing was generally observed to be more suitable for modelling relatively small surface cracks, particularly in respect to the corner point singularity. For all loading modes, the SIFs away from the corner points of using the tetrahedral meshing were found to have fairly good agreement with those by dual boundary element method (DBEM).

Study of the Crack Propagation Property in Very-long Life Regime in Vacuum Environment of High Strength Steel

In general, high-strength steel is known to occur an internally initiated fatigue fracture called "Fish-eye failure" in the very long life region. In addition, the fatigue life of a fish-eye failure is dominated by the ODA (Optically Dark Area) that forms around the fracture origin. Therefore, it is necessary to elucidate the formative mechanism of ODA in order to predict the fatigue life of fish eye failure. Besides, it has been reported that small surface cracks propagate at extremely low speeds below the lattice spacing in a vacuum simulating the interior of high-strength steel. However, it has not been confirmed that the growth of these small cracks forms ODA. In this study, fatigue tests were conducted from a very short crack to a long crack, which corresponds to internal failure in the very long life region, instead of the fatigue tests with a relatively long crack of around 150 μm that have been conducted so far. The results of intermittent observation of the growth behavior and the relationship between the crack growth rate, stress intensity factor, and maximum stress suggest that small cracks grow and form ODAs.

A Bi-grating laser acoustic spectrum method for small surface-breaking crack imaging and depth evaluation

The Laser ultrasonic testing method is effective for the location and evaluation of small surface-breaking cracks. This paper presents a bi-grating laser acoustic spectrum method for precise evaluation and imaging of surface cracks. With a bi-grating laser source, the reflection and transmission coefficient of the SAWs at the crack can be directly obtained with a single measurement by monitoring the amplitude ratio of the two frequency SAW in the frequency domain. It provides a self-reference method with good reliability, high SNR, and high resolution. Simulation results show that the surface crack can be precisely positioned from the ultrasonic reflection/transmission coefficient, and the characteristic parameter increases linearly with the surface crack depth when crack depth is smaller than the wavelength of the surface wave. Moreover, the feasibility and capability of the method are verified by experiment validation. The ultrasonic reflection/transmission coefficient is taken to obtain the C-scan imaging. The experimental results show that the proposed method is effective to locate and evaluate the small surface crack depth, and promising in the in-situ detection and imaging for surface cracks.

원자로 내부구조물 균열개시 민감도에 미치는 영향인자 고찰

To safely operate domestic nuclear power plants approaching the end of their design life, the material degradation management strategy of the components is important. Among studies conducted to improve the soundness of nuclear reactor components, research methods for understanding the degradation of reactor internals and preparing management strategies were surveyed. Since the IGSCC (Intergranular Stress Corrosion Cracking) initiation and propagation process is associated with metal dissolution at the crack tip, crack initiation sensitivity was decreased in the hydrogenated water with decreased crack sensitivity but occurrence of small surface cracks increased. A stress of 50 to 55% of the yield strength of the irradiated materials was required to cause IASCC (Irradiation Assisted Stress Corrosion Cracking) failure at the end of the reactor operating life. In the threshold-stress analysis, IASCC cracks were not expected to occur until the end of life at a stress of less than 62% of the investigated yield strength, and the IASCC critical dose was determined to be 4 dpa (Displacement Per Atom). The stainless steel surface oxide was composed of an internal Cr-rich spinel oxide and an external Fe and Ni-rich oxide, regardless of the dose and applied strain level.

Crack growth models for multiaxial fatigue in a ship’s propeller shaft

A premature fatigue failure of a large intermediate propeller shaft in a shuttle tanker is discussed and analyzed. The short fatigue life consists mainly of a crack growth phase. Life predictions are carried out by crack growth modelling based on engineering fracture mechanics. The purpose of the present investigation is to identify the most likely loading modes based on the evolution of the crack propagation. A Linear Elastic Fracture Mechanics Model (LEFM) is applied with the stress intensity factor range entering the Paris law as a key parameter. Existing formulas for the geometry functions are supplemented by more detailed stress intensity factor calculations pertaining to small semi-elliptical surface cracks subjected to stress mode I. Enhanced geometry functions are proposed as a function of the relative crack depth and the crack shape aspect ratio. The ability of the fracture mechanics model to reconstruct the observed crack path and crack shape development is emphasized. Various loading modes and multi-axial stress states are applied to pursue the observed crack behavior. The observed semi-elliptical crack shapes and the shift in crack planes are included in the analysis.

Crack growth in fillet welded steel joints subjected to membrane and bending loading modes

The present paper presents the results from extensive studies of the fatigue damage evolution in fillet welded steel joints subjected to Constant Amplitude (CA) stress under membrane and bending loading modes. The welded joints in question are F class details (category 71) with plate thicknesses ranging from 25 to 32 mm. The steel quality is a medium strength carbon manganese steel. Crack growth histories for the shallow semi-elliptical shaped cracks emanating from the weld toe are obtained by an Alternating Current Potential Drop (ACPD) technique. These growth histories are presented in detail and modelled by Linear Elastic Facture Mechanics (LEFM). The calculations follow the recent recommendations found in rules and regulations based on different formats of the Paris law. The uncertainties related to a multiple cracks situation and the variability in the weld toe geometry are discussed. The measured crack growth was modelled from an initial crack depth of 0.1 mm to final fracture. The recommended rule-based parametric formulas for the Stress Intensity Factor Range (SIFR) for small surface cracks at the weld notch are examined and supplemented by results from finite element modelling. Recommendations are given on how to make decision regarding uncertainties related to a correct characterization of the local weld toe geometry and the crack coalescence. Finally, an attempt is made to capture the influence of the applied stress ratio R and the applicability of a threshold value for the SIFR is discussed.

Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

AbstractThe topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

Growth Rate of Small Surface-Cracks in Age Hardening Cu-Ni-Si Alloy under Cyclic Stressing

Stress-controlled fatigue tests were conducted on round-bar specimens to understand the fatigue behavior of precipitate-strengthened Cu–6Ni–1.5Si alloy. The cracks were initiated at the grain boundaries, followed by growth along the crystallographic slip planes in the adjacent grains. The crack growth data of plain specimens exhibited a large scatter, resulting in a difficulty of the measurement of crack growth rate. To evaluate the small-crack growth rate of the alloy, the plain specimens with a small blind hole as the crack starter were fatigued. The crack growth rate of small cracks from the hole was uniquely determined by a term σanl and the material constant, n, was 5.3. The term σanl with n = 5.3 was applied to the plain specimen, showing good applicability of the term to small cracks in the plain specimen.

Study on wear and RCF performance of repaired damage railway wheels: Assessing laser cladding to repair local defects on wheels

Sometimes, railway wheels cannot be re-turned and have to be discarded far before its time in service due to local defects and severe wear. Laser cladding which deposits a surface layer of a repair material may be an approach to repair wheels locally. In this study, cladding materials are deposited at a small section of wheel surfaces in order to repair wheels with local defects. 316L, 410, and 420 stainless steel were used as cladding materials on wheel discs while rail discs are unclad. Twin-disc tests were performed to study wear and rolling contact fatigue (RCF) behaviours of clad wheels. Results indicate that adhesion coefficients do not have notable difference between clad and unclad discs. All three clad wheel discs have slightly lower wear rates compared to the unclad wheel discs. The wear rates decrease with increased hardness of the clad materials. Plastic deformation and ratcheting is found on the surface of unclad samples/zones. Only small surface cracks can be found. Deep cracks are found at the boundary between clad and unclad zones leading to a large chunk of material loss. The cracks may be initiated from where maximum shear stress presents below the surface and further propagate along the boundary due to the difference in deformation between clad and unclad materials.

Steering and in situ monitoring of drying phenomena during film fabrication

During film fabrication, the phenomena of crack formation and delamination are often observed, dramatically hindering the discovery and characterization of new materials for energy applications. In this work, we report on a novel approach to fully steer the drying parameters or “knobs” that are commonly used during electrode manufacture. It allows us to precisely in situ control and monitor the solvent-specific evaporation rates that affect the development of suspension composition during drying. We managed to control the capillary stress inside the layer by precisely controlling the selectivity of solvent evaporation. Large cracks result when the surface tension increases over time and layer delamination occurs. When using an n-propanol/water system, critical crack formation is achieved when water is enriched by decreasing the gas exchange during drying or preloading the gas phase with water vapor. High gas exchange rates inhibit the water’s enrichment, and therefore, only small surface cracks develop. The experiments also surprisingly indicate that the drying temperature has no significant effect on crack formation. These results are of fundamental meaning for the future development of electrodes as the drying step has a high impact on the products specification and now can be ultimately controlled. The future development of electrodes will surely benefit from this achievement in the controlled fabrication of films for a variety of applications.

Application of configurational mechanics in characterizing contact fatigue life and its crack propagation: a numerical lattice-based approach

A numerical lattice-based approach equipped with a brittle erosion algorithm and material forces in the context of LEFM and configurational mechanics is introduced to analyze contact fatigue life and crack propagation of brittle solids under low amplitude cyclic loading using the classical Paris’s law. Material force vectors at lattice nodes were employed in identifying potential crack path in high-cycle fatigue applications. A 2D plane strain pad-substrate system with contact formulations under constant compression and cyclic sinusoidal shear with constant amplitude was considered to investigate fatigue crack’s growth rate and its shape in the substrate, made of hydrided brittle Zircaloy-4 used in nuclear industry. The capability of the lattice in predicting the crack extension path using the material force vectors at the crack tip is verified by comparing with analytical solutions for a centered crack domain under pure shear and direct tension loading, and also for an initial small surface crack for the contact fatigue pad-substrate system. Obtaining the total fatigue life by assuming a failure value for the crack length and confirming the Paris’ law crack growth, the lattice results demonstrate that the fatigue crack path in the substrate is a curved trajectory which gradually reduces as the fatigue crack tip grows deeper into the substrate. Having simple constitutive formulation and straightforward erosion algorithm, this approach together with configurational mechanics implications can be employed in analyzing fretting fatigue problems.

소성가공에 따른 STS 304L재의 초음파피로시험시 작은 표면균열의 거동에 관한 파괴역학적 연구

소성가공에 따른 STS 304L재의 초음파피로시험시 작은 표면균열의 거동에 관한 파괴역학적 연구

Study on Fatigue Design Method of an Engine Component Produced by Flake Graphite Cast Iron for Different Loading Modes and Mean Stresses

In order to improve reliability of an automotive engine, a fatigue design method was studied based on the fatigue mechanisms in flake graphite cast iron. In the present study, fatigue test specimens were cut from an actual engine component. The material used showed nonlinear behavior in stress–strain relationship from lower stress level during tensile testing. Rotating bending fatigue testing and axial load fatigue testing were performed. Fatigue crack initiation and propagation behavior were observed during the fatigue tests by a replication technique. Fatigue cracking initiated from the tip of flake graphite in early stage of the total fatigue life when the applied stress was higher than the fatigue limit. On the other hand, fatigue cracking was not observed in the specimen tested with applied stress below the fatigue limit. The threshold stress intensity factor obtained with a small surface crack was lower than that obtained with a through-thickness crack. Fatigue limits under various loading conditions such as bending loading and axial loading were predicted well based on fracture mechanics using the $$ \sqrt {\text{area}} $$ parameter. Threshold stress intensity factor for a small surface crack and the maximum graphite size assumed as an initial crack were used for the prediction. Axial load fatigue tests with different stress ratios were performed. The fatigue limit diagram obtained by the fatigue tests did not follow the modified Goodman relation. On the other hand, fatigue limits prediction based on fracture mechanics approach showed good agreement with fatigue limit obtained with fatigue tests in a wider range of mean stresses σmean varying from − 150 to 50 MPa, in negative stress ratio. In case of σmean higher than 50 MPa, in a positive stress ratio, a smaller effect of stress ratio in the fatigue limit diagram was observed. It was considered that this phenomenon could be explained by the lower effect on the crack closure in a small surface crack initiated from the tip of graphite flake and also influence of local plastic behavior of the matrix around the tip of graphite flake. It can be summarized that the fracture mechanics approach is an effective way to predict fatigue limits of an engine component produced by flake cast iron in different loading conditions and in wider range of mean stress conditions.

Failure Assessment for the High‐Strength Pipelines with Constant‐Depth Circumferential Surface Cracks

In the oil and gas transportation system over long distance, application of high‐strength pipeline steels can efficiently reduce construction and operation cost by increasing operational pressure and reducing the pipe wall thickness. Failure assessment is an important issue in the design, construction, and maintenance of the pipelines. The small circumferential surface cracks with constant depth in the welded pipelines are of practical interest. This work provides an engineering estimation procedure based upon the GE/EPRI method to determine the J‐integral for the thin‐walled pipelines with small constant‐depth circumferential surface cracks subject to tension and bending loads. The values of elastic influence functions for stress intensity factor and plastic influence functions for fully plastic J‐integral estimation are derived in tabulated forms through a series of three‐dimensional finite element calculations for different crack geometries and material properties. To check confidence of the J‐estimation solution in practical application, J‐integral values obtained from detailed finite element (FE) analyses are compared with those estimated from the new influence functions. Excellent agreement of FE results with the proposed J‐estimation solutions for both tension and bending loads indicates that the new solutions can be applied for accurate structural integrity assessment of high‐strength pipelines with constant‐depth circumferential surface cracks.

Improved J Estimation by GE/EPRI Method for the Thin-Walled Pipes With Small Constant-Depth Circumferential Surface Cracks

Application of thin-walled high strength steel has become a trend in the oil and gas transportation system over long distance. Failure assessment is an important issue in the construction and maintenance of the pipelines. This work provides an engineering estimation procedure to determine the J-integral for the thin-walled pipes with small constant-depth circumferential surface cracks subject to the tensile loading based upon the General Electric/Electric Power Research (GE/EPRI) method. The values of elastic influence functions for stress intensity factor and plastic influence functions for fully plastic J-integral are derived in tabulated forms through a series of three-dimensional (3D) finite element (FE) calculations for a wide range of crack geometries and material properties. Furthermore, the fit equations for elastic and plastic influence functions are developed, where the effects of crack geometries are explicitly revealed. The new influence functions lead to an efficient J estimation and can be well applied for structural integrity assessment of thin-walled pipes with small constant-depth circumferential surface cracks under tension.