Crack Growth Direction Research Articles

Mechanism and modeling of fatigue crack initiation and propagation in the directionally solidified CM186 LC blade of a gas turbine engine

First-stage blades of gas turbines are elements positioned after the combustion chamber and are responsible for extracting energy from high temperature and high pressure gas. One of the common problems of mechanical components, particularly gas turbine blades, is fatigue cracking which usually occurs under variable loading due to the start and shutdown process and vibrations. Low-cycle fatigues are caused by the stress induced by high centrifugal force due to high rotational speed and thermal loads triggered by temperature gradients in startup and shutdown of gas turbine, as well as operation at critical environmental conditions. The present study aimed at presenting the mechanism and modeling of fatigue crack initiation and propagation in CM186 LC directional solidified material of a first-stage gas turbine blade. To investigate the crack initiation point, a finite element study was carried out using ABAQUS software package. The stress distribution of the blade was calculated in accordance with engine conditions and the fatigue crack growth was then predicted by using ZENCRACK fracture mechanics code. Moreover, the Paris model was used in this study to estimate the fatigue life. The stress intensity factors (KI & KII) of individual mode and fracture mechanics quantities were calculated from CTOD and J-Integral methods, followed by the computation of crack growth direction on the basis of maximum energy release rate criterion.

Analysis of fatigue crack growth under mixed mode (I + II) loading conditions in rail steel using CTS specimen

The paper is focused on the investigation of fatigue crack growth in rail steel. Mode I and its combination with mode II are one of the frequent reason for rail failures. Therefore, mode I and mixed-mode (I + II) experiments were carried out in order to obtain the fatigue crack growth curves for typical rail steel. In experimental campaign were used CTS (Compact Tension Shear) specimens. The Stress Intensity Factors (SIF) were determined for all load cases using Finite Element Method (FEM) with developed and automated Authors’ tool ABAQUS environment. During the experimental and numerical study, the impact of different elastic mixity level on fatigue crack growth rates and fatigue crack growth directions has been discussed. As it is noticeable the decrease of the mode I domination (under mixed-mode loading condition) caused an increase of the specimen fatigue lifetime. This observation was also discussed in the light of the detailed fatigue crack paths study using Scanning Electron Microscope (SEM).

Numerical investigation of creep crack growth in plastically graded materials using C(t) and XFEM

In this work, a numerical methodology is proposed to predict the creep response and creep crack growth for functionally graded material/plastically graded material in the extended finite element method framework. The stress relaxation and redistribution as a result of creep are incorporated into the analysis of graded material. The Ct-integral (which includes all creep stages from small-scale creep to extensive creep) based relation analogous to Paris Law is employed to calculate the creep crack growth rate. The numerical difficulties faced at the time of simulation, such as strain-energy rate density derivative and maintaining plastic/creep irreversibility during crack growth are well addressed in this paper. The strain-energy rate density derivative is evaluated by the surface approximation. The plastic/creep irreversibility is maintained by the appropriate data transfer and null step analysis scheme. The crack growth direction is decided by the maximum circumferential stress criterion. The proposed methodology is first validated with the experimental results for homogeneous material and later on, it is implemented to calculate the crack growth for various cases of gradation. The capabilities of the present scheme are demonstrated by performing the mixed-mode crack growth simulations at the specimen and component level.

Modes I and II stress intensity factors of semi-circular bend specimen computed for two-phase aggregate/mastic asphalt mixtures

The cracking behavior of asphalt mixtures in the shape of angled edge crack semi-circular bend (SCB) specimens created by the generation and packing algorithm was investigated numerically. Using extensive two-dimensional finite element analyses, the effects of crack length and crack inclination angle, elastic modulus of aggregates and mastic parts, Poisson’s ratios of aggregates and mastic parts, shape of aggregates, distribution pattern for the aggregates inside the asphalt mastic, crack tip location, and air void distribution on geometry factors (YI and YII) were investigated. It was shown that the crack tip location has a significant effect on the magnitude and sign of geometry factors but the shape of aggregates had no sound influence on both modes I and II stress intensity factors. Geometry factors obtained from heterogeneous modeling (i.e. two-phase aggregate/mastic asphalt mixture) when the crack tip is located inside the aggregates were greater than those obtained from homogeneous model. On the other hand, if the crack tip is located inside the mastic part, the geometry factors will be smaller than the homogeneous SCB model. The crack growth path was predicted using the maximum tensile stress criterion. It was shown that the aggregates could change the crack growth path locally; however, the general direction of crack growth in heterogeneous and homogeneous modeling is the same.

Effect of TiB Orientation on Near-Threshold Fatigue Crack Propagation in TiB-Reinforced Ti-3Al-2.5V Matrix Composites Treated with Heat Extrusion.

TiB-reinforced Ti-3Al-2.5V matrix composites, in which TiB whiskers are oriented parallel to the direction of heat extrusion, were fabricated via mechanical alloying and hot isostatic pressing (HIP). To investigate the near-threshold fatigue crack propagation in TiB-reinforced Ti-3Al-2.5V matrix composites, stress intensity factor K-decreasing tests were conducted for disk-shaped compact specimens having two different orientations of TiB whiskers at force ratios from 0.1 to 0.8 under ambient conditions. The crack growth rates, da/dN, for the composites incorporating TiB whiskers oriented perpendicular to the direction of crack growth were constantly lower than those obtained in the case where the orientation was parallel at the same stress intensity range ΔK, while the threshold stress intensity range, ΔKth, was higher. This effect can be explained by the increase in the degree of roughness-induced crack closure resulting from the perpendicular TiB, because fatigue cracks preferentially propagated across the boundaries between the matrix and the TiB in certain regions. In contrast, the effective threshold stress intensity range, ΔKeff,th, for composites was unaffected by the TiB orientation at low force ratios.

Fault dip variations related to elastic layering

Summary In this paper we model the crack growth in an elastic medium constituted by two welded half-spaces with different rigidities. We implement a 2D Boundary Element Method (BEM) computing shear and normal tractions acting on the crack and the slip accommodating stress drop from an arbitrary initial configuration to a final frictional configuration. The direction of crack growth follows the criterion of maximum energy release (strain and gravitational energy) provided that it overcomes the surface fracture energy and the work dissipated by friction. The energetic criterion leads to estimates of the dip angle of seismic faults depending on the amplitude of the initial stress and it includes the classical Anderson's results as a particular case. Moreover, in presence of a sharp rigidity contrast, the direction of crack growth is strongly deflected. The model simulates non-planar, complex, fault geometries, as in the case of detachment and listric faults and it explains the increase of dip angles for both normal and reverse faults, when they enter soft sedimentary layers.

Three-dimensional dynamic numerical simulation of a Brazilian disc of concrete with variation of dip angle of parallel double slits

In order to study the influence of the change of the inclination angle of parallel double slits on concrete disk under dynamic load, we establish a three-dimensional dynamic numerical model of the flattened Brazilian disc by using finite element method. Non-uniform distribution of concrete materials has been realized in the model by adopting Weibull statistical theory. Moreover, we study the effect of variation of dip angle of parallel double slits on crack propagation pattern under stress wave, and obtain both diagrams of the complete failure process and acoustic emission of crack initiation, propagation and penetration. The results show that the failure of the specimen is cleavage and the direction of new crack growth is consistent with that of the dynamic load, the acoustic emission activity decreases with the increase of the dip angle of the prefabricated slits; the bigger the dip angle of prefabricated parallel double slits is, the bigger the peak load is, and the less the accumulated energy of acoustic emission is, the less likely the specimen is to be damaged.

Crack deflection in short fiber reinforced composites: Theory and experiment

AbstractIn the past decades different crack growth and crack deflection criteria have been proposed, e.g. the maximum hoop stress criterion [1], the minimum strain energy density criterion [2] or the maximum energy release rate criterion [3]. These criteria were extended concerning phenomena such as crack path instability [4,5] and the anisotropy of fracture parameters [4]. Another approach for the prediction of crack growth and deflection angle is based on the Jk‐integral [6], assuming the crack to grow into the direction of the J‐vector [7]. The resulting deflection angles coincide well with those from other criteria in the case of small mixed‐mode ratios KII/KI or deflection angles, respectively. One challenge is the accurate calculation of the second coordinate J2 [8] and the appropriateness of this approach has been shown [9]. Nevertheless, in the cases of anisotropic crack resistance parameters, large mode‐II loading or unstable crack paths, the classical J‐vector criterion fails.In this paper, an extended J‐vector criterion is introduced providing the crack growth direction in the case of anisotropic fracture parameters and elastic constants [9,10]. The theory is validated by experimental results for different anisotropy ratios and orientations.

Fatigue Life Behavior of Laser Shock Peened Duplex Stainless Steel with Different Samples Geometry

Two different stress raiser geometries (fillets and notched) were treated by laser shock peening (LSP) in order to analyze the effect of sample geometry on fatigue behavior of 2205 duplex stainless steel (DSS). The LSP treatment was carried through Nd : YAG pulsed laser with 1064 nm wavelength, 10 Hz frequency, and 0.85 J/pulse. Experimental and MEF simulation results of residual stress distribution after LSP were assessed by hole drilling method and ABAQUS/EXPLICIT software, respectively. The fatigue tests (tensile-tensile axial stress) were realized with stress ratio of R = 0.1 and 20 Hz. A good comparison of residual stress simulation and experimental data was observed. The results reveal that the fatigue life is increased by LSP treatment in the notched samples, while it decreases in the fillet samples. This is related to the residual stress distribution after LSP that is generated in each geometry type. In addition, the fatigue crack growth direction is changed according to geometry type. Both the propagation direction of fatigue crack and the anisotropy of this steel results detrimental in fillet samples, decreasing the number of cycles to the fatigue crack initiation. It is demonstrated that the LSP effect on fatigue performance is influenced by the specimen geometry.

Thermo-electro-mechanical fatigue crack growth simulation in piezoelectric solids using XFEM approach

Cracks and multiple voids resulting from manufacturing processes interact with each other and severely affect the fracture phenomenon of piezoelectric components. These geometrical discontinuities degrade the service performance and lower the reliability of the piezoelectric devices. Therefore, the present work predicts fatigue-cracking behavior of piezo-electric structures in existence of multiple geometrical discontinuities under cyclic thermal-electrical-mechanical loads using extended finite element method (XFEM). Thermal interaction integrals approach and Stroh formalism are applied for estimating stress intensity factors (SIFs). Modified hoop SIF criterion has been utilized to predict crack growth direction under quasi-static fatigue loading conditions.

Finite Element Analysis of Creep Crack Initiation in Functionally Graded Materials with Crack Parallel to the Gradient

With the advances in material synthesis technologies, functionally graded materials (FGMs) are developed to use in high temperature structurals due to the excellent high temperature mechanical properties. To facilitate wide use of FGMs in high temperature structures, finite element method (FEM) was used in this paper to investigate effects of creep resistant properties gradients on creep crack initiation (CCI) in FGMs, with crack parallel to the gradient. Results indicated that when creep resistant properties increased in the crack growth direction, CCI was retarded by creep properties gradients. However, CCI was accelerated by creep properties gradients when creep resistant properties decreased in the crack growth direction. CCI position occurred in the two symmetric slanted planes of the initial crack, regardless of the gradient variation of creep resistant properties.

Fracture and fatigue of the surface layer of layered media due to adhesive sliding contact

Layer cracking in a layered medium consisting of an elastic-perfectly plastic half-space (substrate) and a relatively stiff, elastic surface layer in adhesive sliding contact with a rigid asperity was analyzed with the finite element method using linear elastic fracture mechanics. The directions of tensile and shear mode fracture were determined from the maximum tensile and shear stress intensity factors (SIFs), respectively, whereas the directions of tensile and shear mode fatigue crack growth were determined from the maximum range of tensile and shear SIFs, respectively. The effects of asperity position, interfacial adhesion (Maugis parameter), crack depth, asperity interaction distance, layer thickness, and material properties of the elastic layer and the elastic-plastic substrate on fracture and fatigue crack growth in the layer are interpreted in the context of simulation results. It is shown that the propensity for fracture and fatigue in the layer is enhanced with increasing asperity interaction distance and Maugis parameter and decreasing crack depth and layer thickness. The numerical results of this study reveal that, for similar tensile and shear fracture toughness, layer fracture in adhesive sliding contact predominantly occurs by the out-of-plane tensile mode of fracture, whereas fatigue crack growth in the layer is a manifestation of the in-plane shear and out-of-plane tensile modes of fatigue crack growth.

Prediction of a Crack Growth Trajectory with Allowance for the Angular Distribution of the Small Components of the Tangential Stresses at a Crack Tip

Abstract—To determine a crack growth direction, we propose to take into account constant T-stresses and the higher-order terms in the expansion of the stress field at a crack tip by representing them as a function of the angular distribution of T-stresses. A modified criterion is suggested for determining a crack growth direction using the maximum tangential stresses with allowance for the angular distribution of T-stresses at a crack tip.

A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation

Abstract The numerical manifold method (NMM) can be viewed as an inherent continuous-discontinuous numerical method, which is based on two cover systems including mathematical and physical covers. Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants. Therefore, higher-order NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy. In addition, it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics. Thus, some other enriched local approximations are introduced to model the stress singularity at the crack tip. Generally, higher-order NMM, especially first-order NMM wherein local approximations are first-order polynomials, has the linear dependence problems as other partition of unit (PUM) based numerical methods does. To overcome this problem, an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method (FEM), which has no linear dependence issue. Meanwhile, the stresses at the nodes of mathematical mesh (the nodal stresses in FEM) are continuous and the degrees of freedom defined on the physical patches are physically meaningful. Next, the extended NMM is employed to solve multiple crack propagation problems. It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation. Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM. The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions. Thus the effectiveness and correctness of the developed NMM have been validated.

Extended finite element method and anisotropic damage plasticity for modelling crack propagation in concrete

In this article, a new algorithm is developed for predicting crack initiation and growth direction in 3D solid concrete. The algorithm combines the anisotropic damage-plasticity model used for simulation of concrete material degradation (crack) and irreversible plastic deformation and the eXtended Finite Element Method (X-FEM). The Voyiadjis local anisotropic damage-plasticity model is expressed in a non-local form to prevent strain and damage localization in damaged points. Also, a new crack propagation direction criterion based on second order damage tensor of anisotropic damage, containing different material degradation components in different directions is proposed for 3D problems. Computational algorithms with an elastic predictor and plastic and damage corrector returning map are also developed. Finally, three numerical examples are solved and results of crack propagation paths predicted by the proposed algorithm are compared with available experimental data and those of other numerical simulations. It is shown that the results from the proposed method are in better agreement with experimental data compared to other reported numerical methods.

X-ray characterization of the micromechanical response ahead of a propagating small fatigue crack in a Ni-based superalloy

The small fatigue crack (SFC) growth regime in polycrystalline alloys is complex due to the heterogeneity in the local micromechanical fields, which result in high variability in crack propagation directions and growth rates. In this study, we employ a suite of techniques, based on high-energy synchrotron-based X-ray experiments that allow us to track a nucleated crack, propagating through the bulk of a Ni-based superalloy specimen during cyclic loading. Absorption contrast tomography is used to resolve the intricate 3D crack morphology and spatial position of the crack front. Initial near-field high-energy X-ray diffraction microscopy (HEDM) is used for high-resolution characterization of the grain structure, elucidating grain orientations, shapes, and boundaries. Cyclic loading is periodically interrupted to conduct far-field HEDM to determine the centroid position, average orientation, and average lattice strain tensor for each grain within the volume of interest. Reciprocal space analysis is used to further examine the deformation state of grains that plasticize in the vicinity of the crack. Analysis of the local micromechanical state in the grains ahead of the crack front is used to rationalize the advancing small crack path and growth rate. Specifically, the most active slip system in a grain, determined by the maximum resolved shear stress, aligns with the crack growth direction; and the degree of microplasticity ahead of the crack tip helps to identify directions for potential occurrences of crack arrest or propagation. The findings suggest that both the slip system level stresses and microplasticity events within grains are necessary to get a complete description of the SFC progression. Further, this detailed dataset, produced by a suite of X-ray characterization techniques, can provide the necessary validation, at the appropriate length-scale, for SFC models.

Significant enhancement of fracture toughness and mechanical properties of epoxy resin using CTBN‐grafted epoxidized linseed oil

ABSTRACTCarboxyl‐terminated poly(acrylonitrile‐co‐butadiene) (CTBN)‐grafted epoxidized linseed oil (ELO) (CTBN‐g‐ELO) was synthesized and used as an effective toughener to simultaneously enhance the mechanical properties and fracture toughness of epoxy resin (EP). The ELO was fabricated from linseed oil via epoxidation processing. The characteristics of the ELO and CTBN‐g‐ELO, such as the average molecular weight and chemical structure, were determined using gel permeation chromatography, proton nuclear magnetic resonance, and Fourier transform infrared spectroscopy. The effects of the CTBN‐g‐ELO loading on the characteristics of the EP were investigated in detail. The test results indicated that by adding 15 phr CTBN‐g‐ELO, the tensile strength, impact strength, and critical stress intensity factor (KIC) were significantly increased, by approximately 23.62, 91.8, and 33.8%, respectively, compared with pristine EP. The glass‐transition temperature (Tg) and storage modulus, which were examined via dynamic mechanical thermal analysis and differential scanning calorimetry, respectively, exhibited decreasing trends. Scanning electron microscopy revealed that the CTBN‐g‐ELO existed as spherical particles in the EP, helping to stop the crack growth and change the crack growth directions. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci.2020,137, 48276.

Evaluation of the intergranular crack growth resistance of ultrafine grained tungsten materials

The brittleness of tungsten at room temperature represents a severe challenge particularly for structural applications. Tungsten composites, consisting of foils or wires, overcome this low ductility by utilizing the remarkable mechanical properties of ultrafine grained tungsten materials. A comprehensive understanding of the fracture behaviour of these ultrafine grained tungsten materials is therefore essential for a further development of high performance structural composites. However, the dimensions of specimens used for classical fracture toughness experiments are not applicable to test all important crack growth directions in the case of thin foils and wires, especially, in the direction of the presumably lowest fracture toughness, which is along their characteristically elongated microstructure. Femtosecond laser processing allows to fabricate micro single leg bending specimens, which enable to properly evaluate the fracture toughness in this orientation. The fracture toughness value at crack initiation found for the foil is 2.4 MPam, whereas for the wire a value of 5.3 MPam was determined. In both cases the results are significantly below the values reported for other orientations. This strongly anisotropic fracture behaviour is responsible for the reduced brittle to ductile transition temperature and the delamination induced toughening for crack orientations perpendicular to the elongated ultrafine grained structure. The distinct difference of the fracture toughness at crack initiation and the R-curve between wire and foil specimens could be primarily explained by the morphologies of the fracture surfaces, exhibiting significantly different roughnesses of the evolving crack paths.

Characterization of Microstructures and Fatigue Properties for Dual-Phase Pipeline Steels by Gleeble Simulation of Heat-Affected Zone.

To increase transmission efficiency and reduce operation cost, dual-phase (DP) steels have been considered for pipeline applications. Welding has to be involved in such applications, which would cause a localized alteration of materials and cause many potential fatigue issues to arise under cyclic loading. In this work, the fatigue crack propagation and fatigue life of simulated heat-affected zone (HAZ) were examined. Results indicate that when the maximum stress is at the same magnitude, the fatigue life at a peak temperature of 1050 °C is very close to that of a peak temperature of 850 °C, and both of them are higher than that of a peak temperature of 1350 °C. The changes in da/dN with ΔK for HAZ subregions are attributed to the variation of crack path and fracture mode during the crack propagation. The fatigue cracks may propagate along the bainite lath preferentially in coarse-grained HAZ (CGHAZ), and the prior austenite grain boundaries can change the crack growth direction. A considerable amount of highly misoriented grain boundaries in fine-grained HAZ (FGHAZ) and intercritical-grained HAZ (ICHAZ) increase the crack growth resistance. The difference of fatigue crack propagation behavior in HAZ subregions between actual and simulated welded joints was also discussed.

An experimental study of the translaminar fracture toughnesses in composites for different crack growth directions, parallel and transverse to the fiber direction

This work studies how the direction of crack propagation affects the translaminar fracture toughness in composites. In particular, this work focuses on propagation mode-I toughness. The two extreme cases are analyzed: crack propagating in the direction either parallel or perpendicular to the fibers (always without breaking fibers). To evaluate the effect of the direction of crack propagation, an experimental campaign was carried out by two new cracked Three Point Bending (TPB) specimens specially developed for this purpose. Using these specimens, the fracture toughness was measured for different directions of the crack propagation. In addition, a set of standard Double Cantilever Beam (DCB) specimens (corresponding to the longitudinal interlaminar fracture toughness) were tested for the sake of comparison. The results show that the translaminar fracture toughness is higher when the crack grows parallel to the fiber direction than when it grows perpendicular. In both cases, the fracture toughness is higher than that measured for the longitudinal interlaminar growth using DCB specimens. The physical reasons for these experimental results are discussed.