Crack Tip Region Research Articles

Three-Dimensional Characterization of Cracks in a Columnar Thermal Barrier Coating System for Gas Turbine Applications

Thermal barrier coatings (TBC) are multilayered systems comprising a metallic oxidation protection layer or so-called bond coat, a ceramic topcoat, and a thermally grown aluminum oxide developing at the interface. The coating systems fail typically by delamination cracking near this interface, which has a complex three-dimensional morphology influencing the crack path. This study combines laser shock adhesion test to introduce an artificial interfacial crack, known in size and location, and focused ion beam coupled with scanning electron microscopy 3D serial sectioning tomography. Methods for proper segmentation of cracks and adjacent materials and quantitative evaluation of the complex crack system are proposed and applied for analyzing the crack tip region. Finally, derived from the three-dimensional segmentation, a finite element model has been achieved and used for thermal analysis highlighting the crucial role of local damage on thermal conductivity of the TBC.

Modeling fatigue crack and spalling for rolling die under hot milling

AbstractIn hot milling process, rolling die is subjected to nonsteady conditions which can rise the combinations of fatigue and spalling damage mechanism. An understanding about the failure mechanism of the rolling die is essential under hot rolling process. Fatigue crack growth and spalling process are governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic‐plastic fracture mechanics, an analytical model are presented in this paper to determine the elliptical crack growth rate and spalling damage mechanism. The model includes new proposed constitutive equations for fatigue and spalling crack growth. To verify the models, finite element simulation and experimental data are considered. The results show good agreement with finite element simulation and experimental data.

Study on fracture properties of alkali-activated slag seawater coral aggregate concrete

Alkali-activated slag was first used as cementing material in seawater coral aggregate concrete (SCAC) production in this paper. It would contribute to both the environmental protection and raw materials obtained locally in island construction far away from the mainland. However, cracks would be harmful to structural durability of SCAC especially under ocean environment. Thus, the present study is mainly aimed at the fracture properties of alkali-activated slag SCAC (ASSCAC) by virtue of three-point-bending tests. Two types of slag (Types A and B) and two types of coral aggregates, namely columnar and crushed coral coarse aggregates (CCA), are considered. Besides, two beam depths of 100 mm and 150 mm are prepared and the initial notch-to-depth ratios are set from 0.1 to 0.7 for each depth. Results show that the failure modes of all the beams are fracturing of CCAs. Then an analytical approach was proposed to predict the fracture parameters of ASSCAC. The size-independent uniaxial tensile strength and fracture toughness are obtained by using the experimental maximum fracture loads and the former proves to be the maximum tensile stress at the fictitious crack-tip. Then the correlation between the maximum fracture load and the local fracture energy at crack-tip region is obtained. The size-independent fracture energy is derived based on the comparison between the analytical and experimental maximum fracture loads. The tensile strengths of ASSCAC mixed by Type A slag and crushed CCAs are larger. But the fracture toughness and fracture energy are slightly higher when the ASSCAC is made by Type B slag.

Approximation of the crack-tip field in fatigue cracks in bridge steel specimens: DIC analysis of different constraint levels

A study on the accuracy of the approximation of the displacement field around of crack tip in a sample made from bridge steel (S355) is main objective of contribution. Linear elastic fracture mechanics (LEFM) theory in framework of multi-parameter formulation, i.e. postulated by Williams is used to determine of coefficients of Williams power series terms. Over deterministic method was used to calculate the terms based on the least squares regression technique, applied on data from numerical simulation and experiment on S355 steel grades. Comparison between the stress fields (by principal stress s1 and von Mises stress sHMH) obtain from experimental measurement DIC, Hybrid method and obtain from reconstruction by using various number of Williams power terms are quantified in order to get key information around the crack tip region on bridge steel specimens.

Plastic zone evolution during fatigue crack growth: Digital image correlation coupled with finite elements method

Nonlinearities effects at the crack tip, due to the elastic-plastic material behavior, impact the crack growth rate and path. This paper is devoted to the study of the plastic zone evolution in the crack tip region. The methodology relies on coupling an elastic-plastic Finite Elements Method (FEM) model and experimental displacements measured by Digital Image Correlation (DIC). These latter are introduced as Dirichlet boundary conditions in the finite elements analysis. The considered FEM domain is constant, i.e. the same mesh with a centered crack is moved to each new crack tip position deduced from DIC. The new boundary conditions are updated and the residual stresses and plastic strains of the former computation are interpolated and actualized on the mesh shifted to the new crack tip position in order to incorporate them in the numerical model. The coupling method allowed applying experimental boundary conditions in order to be as close as possible to real experimental conditions and to observe the plasticity evolution from small to large scale yielding conditions. A fatigue test was conducted to validate the proposed approach. The identification residues are proved to be lower than those obtained with an experimental displacements projection onto Williams’ series basis, which is a method commonly used with DIC. The coupling results present an attractive similarity with Irwin’s model regardless of the crack length. Thus, the definition of the mask needed for the displacements fields projection on Williams’ model can be deduced with a reliable estimate of Irwin’s plastic radius.

High resolution crystallographic and chemical characterisation of iodine induced stress corrosion crack tips formed in irradiated and non-irradiated zirconium alloys

High resolution crystallographic and chemical analysis has been performed on iodine-induced stress corrosion crack tips taken from irradiated and non-irradiated zirconium alloys. Defuelled cladding tubes were subjected to mandrel testing and subsequent analysis of the crack tip region showed the predominance of transgranular cracking on non-basal planes for the first time in irradiated material. In a separate mandrel-tested crack tip sample, iodine was unambiguously identified in the crack tip region using both STEM-EDX and NanoSIMS. For comparison, non-irradiated C-ring samples were subjected to testing in iodine-ethanol solution, subsequent crack tip analysis showed large levels of intergranular attack and no significant iodine segregation.

A closure model for predicting crack growth under creep-fatigue loading

A strip-yield model was formulated to simulate creep-fatigue crack growth and to quantify the influence of hold time on plasticity-induced crack closure during creep-fatigue crack growth. Creep-fatigue experiments have shown that longer creep hold times result in faster crack growth rates in subsequent fatigue cycles. This model advances the idea that a decrease of plasticity-induced crack closure is experienced by the crack during fatigue loading when a longer hold time is applied each creep-fatigue cycle. Consequently, the crack tip experiences an increase in the effective stress intensity factor range causing faster growth rate during the fatigue loading. The weight function method was used to compute stress intensity factors and surface displacements for cracks embedded in a material experiencing elastic, plastic and creep deformations at elevated temperatures. It is shown that the longer the hold time, the larger the creep deformation and crack opening displacements in the near crack-tip region. In turn, this leads to a decrease in the crack-tip opening stress/load and faster crack growth rates during the subsequent fatigue cycle. The model was used to perform simulations of creep-fatigue crack growth at elevated temperatures in a nickel-base superalloy and AISI 316 austenitic steel.

Fracture resistance of textured polycrystalline Zr: A simulation study

We report the results of large-scale molecular dynamics atomistic simulations of crack propagation in of α-Zirconium. The samples studied are polycrystalline columnar grains of 11–38 nm average diameter, and different textures. The focus is on deformation mechanisms in the crack tip region and the influence of texture, grain size and temperature on the fracture propagation. We found that the [1–100] texture is the most brittle with deformation at the crack tip occurring only through twinning with almost no dislocation activity. The more ductile textures are those where dislocation mechanisms are activated. For the basal orientation we observed <a> dislocations while <c + a> dislocations are dominant for the [11–20] texture. One important observation is that crack propagation can be hindered by the presence of the grain boundaries. As a result, samples with the smallest grain sizes are the more resistant to crack propagation. As expected, higher temperatures imply easier deformation, resulting in more ductile behavior for all orientations. At room temperature and higher, crack propagation occurs mostly intra granularly. However, at 77 K the [1–100] textured sample shows crack propagation through the nucleation of micro-voids ahead of the main crack.

A structured grid based B-Spline finite elements method combining local isogeometry analysis technique for crack problems

In this paper, a structured mesh based B-Spline finite elements (BSFE) method combining the isogeometry analysis technique is developed for analyzing crack problems. The BSFE is used for the global approximation and the isogeometry analysis technique is performed on the local crack tip region which is covered by several elements around the crack tip. The geometry of the selected crack tip region is described by the B-Spline basis functions in parameter space. Meanwhile, a specific function with relevant parameters is introduced into geometry description for catching the characters of the solution around the crack tip. In addition, the B-Spline basis functions are also used as basis functions to approximate the displacement field in the local region under the parameter space. The relevant B spline basis functions used for approximation in local region are replaced by the corresponding BSFE basis functions used in the interface elements adjacent to the local region and the seamless connection between the global approximation and the local isogeometry analysis can be easily achieved. For crack problems, no enrichment functions and remeshing are needed in this new method. This newly developed method is applied to the stress analysis of 2D linear elasticity crack problems in order to investigate its performance and study parameters. Numerical results show that the present method is highly accurate and stable. The new method has a promising potential for practical applications.

The failure mechanism at adiabatic shear bands of titanium alloy: High-precision survey using precession electron diffraction and geometrically necessary dislocation density calculation

The difficulty of obtaining key information, such as the crystal orientation and geometrically necessary dislocation (GND) density distribution, from a large deformation region in an adiabatic shear band (ASB) has hindered further study of the ASB failure mechanism in titanium alloys. In this work, the crystal orientation information of the failure position and surrounding region in ASB of a Ti-5Al-2.5Cr-0.5Fe-4.5Mo-1Sn-2Zr-3Zn alloy was obtained via transmission electron microscopy (TEM) and precession electron diffraction (PED) with a high spatial resolution. The GND density distribution was calculated and the adiabatic shear failure mechanism was revealed from the collected data. ASBs (original width: ∼3–4 µm) formed in the cylinder sample during dynamic compression (strain rate: ∼3000 s−1). In the transition region at the edge of ASB, the grains were severely elongated along the direction parallel to the ASB boundaries with an average grain size on the order of μm and an average GND density of 5.5374 × 1015/m2 in the α phase. Relatively strong < 0001 > textures and weak < -12–10 > textures were observed. However, significant dynamic-recrystallization-dominated grain refinement in ASB, especially at the crack tip, resulted in many ultrafine equiaxed recrystallized grains (10 nm level) and weakened textures. The highest average GND density (8.6242 × 1015/m2, in α phase) occurred in the crack tip region. Moreover, the vicinity of the "primary microcracks" in the main crack extension line was characterized by combinations of an extremely high GND density work hardening region and a group of low GND density recrystallized grains. This indicates that cracks in the ASB were initiated by the deformation incompatibility between the antecedent recrystallization region and the surrounding high work hardening region.

Numerical model for the stress field ahead of a crack in elastoplastic regime

Damage-tolerant designs admit the pre-existence of defects and small cracks, which lead to stress redistribution in structural components. The accurate knowledge of the stress field in parts under these conditions is important for damage accumulation analysis and residual life prediction. In this work, a numerical model via finite elements is proposed to determine the stress field ahead of crack tips in a plate under cyclic loading and elastoplastic regime. The analyzed center-cracked plate simulates a M(T) specimen made of 6005-T6 extruded aluminum alloy. From the triple symmetry condition, one eighth of the plate was discretized with tetrahedral solid finite elements of quadratic order. The refinement of the mesh was concentrated around the crack tip region. The cyclic stress-strain curve of the material was experimentally obtained by strain-controlled fatigue tests. With this curve, elastic and plastic parameters have been determined, considering elastoplastic material with isotropic hardening governed by Swift’s law. Such a model differs from most usual stress analyses in cracked components, in which the possibility of hardening is not considered. Cyclic loading with ratios R = 0 and R = -1 has been applied from an initial crack of 11 mm in length. The crack growth was imposed by means of a simplified node release scheme. The results showed no significant variation in terms of the equivalent stress, but considerable differences in the equivalent plastic strain. Therefore, the compressive phase in the specimen under R = -1 contributes to increase the equivalent plastic strain, which means that the level of yielding becomes higher even when the specimen is compressed.

Localised prior strain-hardening increases the tearing resistance of ductile steel

In structural materials, ‘intrinsic’ toughening originates from plastic dissipation of strain energy at the tips of cracks. This depends on a material's microstructure and its stress–strain response. By introducing a spatially-varying distribution of prior strain-hardening into a material, we can modify the stress field which develops around a crack as it is loaded, producing an increased resistance to ductile tearing. We demonstrate this toughening effect using synchrotron X-ray diffraction and digital image correlation measurements of the crack tip region in a ductile ferritic steel. Localised strain-hardening also introduces a residual stress, but this is shown not to contribute significantly to the initiation of tearing in this material.

Effects of Temperature Variation on Mechanics Field at Crack Tip of Stress Corrosion Cracking

Creep strain near crack front zone is one of the main driving forces in nuclear structural materials of stress corrosion crack propagation. To understand the effect of temperature variation on mechanical field near crack tip of nuclear structure material in high temperature water environment, compact tensile specimen was taken as an research object and ABAQUS finite element analysis software was also adopted, the Mise stress, plastic strain and creep strain near SCC crack tip region was studied. Results show that the area of the high-stress region decreases gradually with the increasing of the creep temperature, and its declining rate was faster and faster. The effect of temperature variation on the plastic strain is not very obvious. Temperature only has an obvious effect on a small scale near crack tip. With the increase of the distance from the crack tip, the effect of temperature on creep is gradually reduced.

Three-dimensional numerical simulation of hydrogen-induced multi-field coupling behavior in cracked zircaloy cladding tubes

In the high-temperature and high-pressure irradiation environments, the multi-field coupling processes of hydrogen diffusion, hydride precipitation and mechanical deformation in Zircaloy cladding tubes occur. To simulate this hydrogen-induced complex behavior, a multi-field coupling method is developed, with the irradiation hardening effects and hydride-precipitation-induced expansion and hardening effects involved in the mechanical constitutive relation. The out-pile tests for a cracked cladding tube after irradiation are simulated, and the numerical results of the multi-fields at different temperatures are obtained and analyzed. The results indicate that: (1) the hydrostatic stress gradient is the fundamental factor to activate the hydrogen-induced multi-field coupling behavior excluding the temperature gradient; (2) in the local crack-tip region, hydrides will precipitate faster at the considered higher temperatures, which can be fundamentally attributed to the sensitivity of TSSP and hydrogen diffusion coefficient to temperature. The mechanism is partly explained for the enlarged velocity values of delayed hydride cracking (DHC) at high temperatures before crack arrest. This work lays a foundation for the future research on DHC.

Ductile and intergranular brittle fracture in a two-step quenching and partitioning steel

A two-step quenching and partitioning steel exhibits ductile fracture under uniaxial tension and unexpectedly intergranular brittle fracture in the case of pre-cracked configuration. A gradual retained austenite-to-martensite transformation because of low stress triaxiality under uniaxial tension, leads to ductile fracture with voids formation between fresh and tempered martensite resulting from the large strain partitioning and localization. When the retained austenite fast transforms to martensite in the near crack tip region because of high stress triaxiality, intergranular fracture is promoted by the high maximum principal stress level and by the formation of brittle martensite necklace along tempered martensitic packet boundaries.

Crack Propagation Analysis of Fiber-Reinforced Composite Hollow Transmission Shaft

The main purpose of this research was to investigate crack propagation resistance of shaft. Hollow transmission composite shafts were produced and their crack behavior was investigated. Glass fiber-reinforced polyester polymer composite material is used for the hollow transmission shaft of Hidasie H260 helicopter model of Dejen Aviation Engineering Complex, DAEC. The elastic engineering constants of composite transmission shaft are determined using the Classic Laminate Theory, CLT. Linear Elastic Fracture Mechanics, LEFM was used to analyze its crack propagation by taking a through-thickness central crack. The stress at the crack tip is analyzed and it was found that the glass fiber-reinforced polyester polymer composite transmission shaft has good resistance to crack propagation. FEA method was used to crack propagation analyses. The model of shaft is generated using Finite Element Method. Due to the symmetry of the problem, only a quarter part of it is modeled and analyzed. The crack-tip region was meshed using quarter point (singular) 8-node quadrilateral elements to get accurate results and the analysis used a fit of the nodal displacements in the vicinity of the crack tip. The maximum stress is at the crack tip since there is a stress concentration at sharp edges.

Higher sensitivity Digital Gradient Sensing configurations for quantitative visualization of stress gradients in transparent solids

Two modified full-field Digital Gradient Sensing (DGS) methods of higher measurement sensitivity relative to the prevailing ones are described for quantifying small angular deflections of light rays caused by stresses in transparent solids. These methods are devised by combining or altering previously proposed reflection-mode DGS (r-DGS) [1] and transmission-mode DGS (t-DGS) [2] methods. The concept involves increasing the optical path within the stressed medium by introducing an additional reflective surface behind the transparent solid, either as a separate reflector or as a rear surface reflective film deposition. The former approach is designated as t2-DGS method whose measurement sensitivity is twice that of t-DGS. The latter method results in an even higher sensitivity and is called the transmission-reflection DGS or tr-DGS method by making the back surface of a transparent planar solid reflective. The governing equations of tr-DGS are introduced first followed by a comparative demonstration of t2-DGS and tr-DGS methods by measuring the stress gradients in the crack-tip region during dynamic and static fracture experiments, respectively. Results show that tr-DGS is approx. 1.5 times more sensitive than t2-DGS, and at least three times more sensitive than t-DGS approach. Together as a family of DGS methods, these methods are used to extract the crack-tip stress intensity factors of PMMA beams under quasi-static loading conditions. The measured stress intensity factors are in good agreement with the predictions.

The Impact of Temperatures on the Stability of Rocks Surrounding a Single Fracture

Research on the influence of temperature and the accompanying stress on the stability of the rocks surrounding an underground tunnel has become ever more important. This paper constructs a geometric model of a single-fracture tunnel by combining a high-temperature underground tunnel as the object of study with an example that uses a high-temperature tunnel segment in the water diversion tunnel of a hydropower station in Xinjiang. Based on the relevant theoretical analysis, with the consideration of different working conditions, a numerical experimental analysis was conducted to determine the two-dimensional transient temperature field distribution of the tunnel rock mass by using a numerical analysis software. The experimental data was consistent with the measured data. The calculated results show the following: a. when the temperature difference is greater, the stress concentration is higher near the fracture of the surrounding rock; b. the degree of the stress concentration in the crack tip region is not positively correlated to the distance, and there is a sensitive region where the stress varies.

Advanced 3D characterisation of iodine induced stress corrosion cracks in zirconium alloys

In this study, a range of advanced techniques have been used to characterise iodine-induced stress corrosion cracks, and investigate their interaction with microstructure in zirconium alloys used as cladding material in nuclear power reactors. C-ring samples, machined from cladding tubes in a recrystallised and cold worked condition, were subjected to compressive stress while submerged in an iodine-ethanol solution to simulate stress corrosion cracks arising from pellet cladding interaction. The complex morphology of these stress corrosion cracks was imaged in 3D using X-ray computed tomography (XCT), and subsequent analysis using both 2D and 3D electron backscatter diffraction (EBSD) allowed for the interaction of these cracks with microstructure to be investigated. Intergranular cracking modes were observed to dominate in the recrystallised microstructure, resulting in cracking in the radial direction with variations on the order of the grain size. Crack propagation in the cold worked microstructure was observed to be correlated with the direction of the elongated grains, resulting in a more tangential crack path with less local variation and a microstructure potentially more susceptible to iodine-induced stress corrosion cracking. 3D-EBSD using serial sectioning allows for the determination of the full five-parameter grain boundary description, and opens up the possibility of a statistical analysis of susceptible boundaries to SCC. Nanoscale secondary ion mass spectrometry (NanoSIMS) was also used to map the chemical distribution in the crack tip region and provides possible evidence of iodine segregation ahead of the crack tip. The results provide new insight into crack propagation mechanisms in recrystallised and cold worked microstructures, and pave the way for a more mechanistic understanding of crack propagation through advanced characterisation of iodine-induced stress corrosion cracks in zirconium alloys.

Frequency characteristics of the released stress wave by propagating cracks in brittle materials

Stress waves are generated when stored energy is suddenly released from localized sources within brittle materials during the process of crack initiation and propagation. The frequency of the stress wave is related to the velocity of energy release. In this paper, the relationship between the frequency of the released stress wave and the effective elastic modulus of the medium in the crack-tip region is first investigated from the perspective of energy. Then, the relationship between the effective elastic modulus of the medium in the crack-tip region and the size of the crack source is studied. The analytical results show that the frequency of the released stress wave is inversely related to the crack size. The detected stress waves in the form of acoustic emission (AE) signals can give insights into the process of energy dissipation and emission in response to the initiation and propagation of crack. AE study of the fracture process of concrete materials under uniaxial compressive loading was performed to demonstrate the theoretical result. The inverse relationship between the frequency of the stress wave released by the propagating crack and the crack size has been verified based on experimental data in this research and from the results of AE experiments on concrete, rock, and ceramic materials performed in other researches.