Stress Intensity Factor Distribution Research Articles

A closed form expression of stress intensity factor for an arbitrarily shaped planar crack in 3-D under tensile loading

A closed-form equation was developed in this work to quantify the stress intensity factor (SIF) along an arbitrarily shaped planar crack under mode-I loading by substituting the ellipse-related parameters in Irwin’s solution with geometry-related parameters fi of the crack. This allowed incorporation of the local crack curvature effect on SIF at each discrete point along the crack front and its relative weighted contribution to SIF of the neighboring crack point i, where either stress concentration or shielding took place, into computation of the SIF distribution along the crack front. Good agreement was obtained between the KI values derived in the current work and previous numerical simulation-based studies. The current method could capture the KI distributions for surface and embedded cracks having the same shape, with their maximum values being consistent with Murakami’s area method. This solution of KI allows for highly efficient calculation of ΔKI for quantification of the 3D growth behaviors of a fatigue crack with a complex shape, paving the way for studying the statistical nature of short fatigue crack growth.

SIF formula based on exact SIF distribution for semi‐elliptical surface cracks subjected to mode I, II, III uniform loading

AbstractThe stress intensity factor (SIF) distribution of a semi‐elliptical surface crack is often used for evaluating the fatigue strength of structures. Virtually exact distributions of SIFs can be provided along the crack front by solving the hypersingular integral equation of the body force method. In this paper, to create a very accurate SIF variation formula, the elliptical crack SIF solutions , , are used and the SIF ratios , , are mainly focused. Paying attention to the corner point singularity, by applying the least squares method to the ratio , in the whole range of parametric angle , and formulas can be proposed. Instead, formula can be proposed by applying the method of least squares to the ratio of in the range but applying directly to in the range . In this way, all of formulas proposed in this paper provide the SIFs with better than 1.0% accuracy.

Crack propagation analysis of slewing bearings in wind turbines applying a modified sub-model technology

As slewing bearings in wind turbines are exposed to complex operational environments, they are prone to crack initiation, propagation and evolution that can lead to contact fatigue problems. Reliable crack extension prediction is a critical requirement. With the goal of obtaining more accurate crack characteristics, this study proposes a crack initiated contact finite element model (CI-CFEM) targeted at the raceway of slewing bearings by introducing a modified sub-model. In the application of the global finite element model (G-FEM) to the slewing bearing system, the rolling displacements of the ball and the boundary displacements are employed in CI-CFEM to take account of external ring deformations and the support conditions. The crack is embedded using FRANC3D, and the stress intensity factor distribution and propagation characteristics of the crack front are investigated. Furthermore, the effect of external load and the design parameters of the slewing bearing on crack propagation are explored, providing insight for optimizing the design of slewing bearings to extend service life. The results reveal that changing external loads and bearing parameters are an effective means of retarding crack propagation rate, while have relatively minor influence on crack growth angle.

Study on the influence of shot peening strengthening before shot peen forming on 2024-T351 aluminum alloy fatigue crack growth rate

It is sparse and inconclusive that research on the subject whether the fatigue life of the structure will be reduced by shot peening strengthening before shot peen forming (S + F), and this study investigates accordingly. First, the crack growth rate test of the machine-processing plate and shot peening strengthening before shot peen forming plate demonstrate that both plates’ final crack growth rate and length are similar. However, the test shows the “fluctuation phenomenon” of crack growth rate and the “intersection phenomenon” in the Paris curve. This study is based on a self-developed simulation plugin for crack growth paths. The results verify that “fluctuation” causes the differential distribution of the overall stress intensity factor in the strengthened (4.5% increase compared to machine-processing) and formed (9.8% decrease compared to machine-processing) crater areas of the shot peening strengthening before shot peen forming plate. Comparing to the full coverage strengthening area, the forming area (only 30% coverage) in the early stage of growth as well as the gain amplitude of the residual stress in the late stage of growth gradually decrease and tend to be the same as that of the machine-processing, as validated by the “intersection phenomenon”.

Stress intensity factor of a cracked molar restored with different materials and designs: A 3D-FEA

ObjectiveThis work used 3D finite element analysis (FEA) to analyze and directly compare the stress intensity factor (SIF) and stress distribution at the crack tip of identical cracked tooth models restored with different materials and crown parameters. MethodsA 3D model of the cracked tooth was generated. Then, we applied 25 restorative models, including three parameters (shoulder height, width, and degree of polymerization), five restorative materials (GC, IPS, LU, ZC, VE), and two combinations of types of cement (RMGIC and GIC). An occlusal load of 800N was applied to the spherical part along the longitudinal axis. The stress distribution of the preparation and the SIF of the crack tip was analyzed. ResultsThe crack tip SIF was minimal for a shoulder height offset of 0.8 mm (P = 0.032), a shoulder width of 0.6 mm (P = 0.045), a crown material of ZC (P < 2e-16), and a cement material of RMGIC (P < 0.05), respectively. In contrast, the effect of different polymerization degrees on SIF was insignificant (P = 0.95). ConclusionOur results suggest that the selection of a larger modulus of elasticity (MOE) material for the crown, the preparation of a smaller shoulder width within a safe range, a reasonable increase in the crown length, and the selection of adhesive materials with high fracture toughness are favorable methods to prevent further crack extension.

Safety margin determination of the nuclear power plant reactor pressure vessel with taking into account warm pre-stress effect

In case for nuclear power plants long-term service operation over their design life, it is necessary to calculate reactor pressure vessel (RPV) strength and durability acknowledgment (static strength, strength under cyclic and seismic loads, brittle fracture resistance (BFR) include) the as one of the most important NPP structure. Usually, according to the brittle strength assessment, RPV resource is determined, that is, time of its subsequent safe operation. The purpose of this work is assessed BFR RPV at potential emergency accidents (EA) using the Ukrainian warm pre-stress approach. The calculated thermohydrodynamic parameters at EA were used to calculate the stress-strain state of the developed reactor finite element (FE) model. For researching, the most indicative scenarios were selected: where reactor is cooled at a high pressure. In RPV FE model cracks are modeled at the most dangerous places - welds and nozzle. Stress intensity factor (SIF) distribution along crack front and temperature for the most dangerous accidents in terms of BFR are presented in figures. Brittle strength condition is ensured during the nuclear power plants service operation for up to 60 years, which is more than 1.5 times more than the oldest Ukrainian power plant with VVER-1000. For some emergency accidents, warm pre-stress really significantly increased RPV safety margin, but for the most dangerous accidents, the results are the same as without taking into account WPS.

Multiple crack growth simulation for lap-joints based on three-dimensional finite element analysis

PurposeThe fuselage riveted lap-joints are susceptible to multiple site damage (MSD) and should be considered in damage tolerance analysis. This paper aims to investigate the stress intensity factor (SIF) and crack growth simulation for lap-joints based on three-dimensional (3D) finite element analysis.Design/methodology/approachThe 3D finite element model of lap-joints is established by detailed representation of rivets and considering the rivet clamping force and friction. Numerical study is conducted to investigate the SIF distribution along the thickness direction and the effect of clamping force. A predictive method for the cracks propagation of MSD is then developed, in which an integral mean is adopted to quantify the SIF at crack tips, and the crack closure effect is considered. For comparison, a fatigue test of a lap-joint with MSD cracks is conducted to determine the cracks growth live and measure the cracks growth.FindingsThe numerical study shows that the through-thickness crack at riveted hole in lap-joints can be treated as mode I crack. The distribution of SIF along the thickness direction is inconstant and nonmonotonic. Besides, the increase in clamping force will lead to more frictional load transfer at the faying surfaces. The multiple crack growth simulation results agreed well with the experimental data.Originality/valueThe novelty of this work is that the SIF distribution along the thickness direction and the MSD cracks growth simulation for lap-joints are investigated by 3D finite element analysis, which can reflect the secondary bending, rivet clamping, contact and friction in lap-joints.

Assesment of the temperature loading influence on crack resistance of a tank with a semi-eliptical crack

Reservoir parks are the main place of storage of petroleum products. There has been a tendency transition to the use of larger tanks in recent years, which is economically justified. However, it is leads to fire risk increase to accumulate large quantities of petroleum products. Tank fire is one of the most dangerous emergency event, which can lead not only to significant material damage but also to ecological human losses in case of spreading of fire to other tanks. To ensure safety and test the bearing capacity in these conditions determination of the stress-strain state in such tanks must be performed taking into account the temperature load. If there is an initial crack in the tank wall the assessment of crack resistance should be performed. In a previous work the authors determined the stress intensity factor (SIF) distribution along the semi-elliptical crack front in the RVS-5000 tank under hydrostatic pressure. The estimation of a stress-strain state of a steel vertical tank with an initial semi-elliptical crack under the thermal loading is performed in this article. It is suppoused that the part of wall of the tank, located closest to the fire epicenter, is heated unevenly in height: from 300 degrees at the top to 200 degrees at the bottom. On the other part of the tank the temperature reaches 70 degrees. The temperature within wall thickness is considered constant. Given the asymmetric nature of the temperature distribution, a discrete model was developed for the entire tank. After determining the stress-strained state in the whole tank under hydrostatic pressure and temperature load, a fragment with a semi-elliptical crack was calculated separately. The stresses determined from the calculation of the whole tank are used like an external load, applied on fragment boundaries. The difference of results of direct and energetic method of SIF calculation are in the range of 5%. Taking into account the temperature loading leads to an increase in the SIF values by about 20 % in comparison to the results of the calculation only under hydrostatic pressure.

PLA-based 3D printed porous scaffolds under mixed-mode I/III loading

Additive manufacturing technologies, due to their unique manufacturing features, have been viewed as a potential alternative to the conventional production of medical implants. Biomechanical structures, however, are susceptible to crack growth under constant loading conditions, which can occur due to mixed-modes of loadings. Here, the effects of mixed-mode I/III loading conditions on 3D printed porous scaffolds were investigated. Different design parameters like pore size and geometry were analyzed. Numerical analysis was utilized to explore the stress intensity factor distribution under various loading conditions. Results revealed that the size, shape, density, and pattern of pores had critical impacts on mechanical strength.

Fatigue crack propagation for an aircraft compressor under input data variability

The quantification of all the uncertainty sources affecting the phenomenon of fatigue crack-growth is essential to enhance competitiveness in designing more high-performance products, e.g. aircraft engines. This work reports crack propagation simulations for a first-stage compressor of a turbo-fan engine, by considering the impact on life prediction accuracy given by geometrical tolerances, material variability and actual rotational speed. Crack-growth simulations were developed by Finite Element Method (FEM) considering the variability of the fillet radius between blades and disk, so as to derive the distribution of Stress Intensity Factors (SIF) along the crack size as a function of both fillet radius and rotational speed. Consequently, a NASGRO formulation, calibrated on Ti6Al4V test data, was implemented in a MATLAB routine in a stochastic way so as to derive the residual life predictions for the component. Statistical evaluations were made and the contributes of all the considered uncertainty sources were compared and classified.

Mixed mode surface crack growth in aluminium alloys under complex stress state

In this study fatigue crack growth tests were carried out on hollow cylindrical specimens, made of D16T and B95AT aluminum alloys (analogue of 2024 and 7075 aluminum), with initial external semi-elliptical surface cracks and undergoing complex stress state. The crack growth behavior of aforementioned materials was studied under cyclic axial tension, pure torsion and combined tension+torsion fatigue loading. Optical microscope measurements and the crack mouth opening displacement (CMOD) method were respectively used to monitor crack length and calculate crack depth. The experimental crack front positions were highlighted by using a beach mark procedure during the tests. The stress strain field along the crack front of semi-elliptical cracks in the cylindrical hollow specimens was assessed by Finite Element Method (FEM) analysis. The stress intensity factors (SIFs) were calculated by the 3D M-integral approach and the distributions of equivalent elastic SIFs along the crack front were used for crack growth rate assessment under mixed mode conditions. As a result, the fracture resistance parameters of aluminum alloys under complex stress state were presented. The simulation of cracks propagation turned out to be consistent with experimental results.

Stress intensity factors in the specimen with a surface semi-elliptical defect

In this work, equations for stress intensity factors calculating in the specimen with a surface semi-elliptical defect in order to interpret experimental data of the surface crack growth rate tests at elevated temperatures were obtained. In the commercial finite element code ANSYS 3D finite element models with surface flaws for the range of the relative crack depth b/t = 0.1…0.7 and the aspect ratio b/a = 0.3…1 were generated. For these ratios stress intensity factors were calculated based on the finite element method. For the same configurations of semi-elliptical crack fronts using Murakami's stress intensity factors handbook stress intensity factors were calculated. It has been established that the results of numerical calculations and the Murakami's handbook have a similar pattern of the stress intensity factors distribution. For the stress intensity factors calculating in the specimen with a surface semi-elliptical crack to the Murakami's handbook specimen geometry-dependent stress intensity factor functions a correction function was added. The results allow to interpret the experimental data of the surface crack growth rate tests of the specimen at elevated temperatures.

The Crack Growth in the Imitation Model of a GTE Turbine Disk under Operating Loading Conditions

The paper presents the experimental results of growing surface cracks in the turbine disk of a gas turbine engine (GTE) under cyclic tension at room and elevated temperatures. The geometry of the imitation model of the GTE turbine disk with a stress concentration zone in the form of a bolt hole was justified. In order to ensure the similarity of the initial damage of the imitation model and the GTE turbine disc in the plane of symmetry of the stress concentration zone, a semi-elliptical notch was made. The loading conditions of the imitation model were developed based on results of a comparative stress-strain state (SSS) analysis of the stress concentration zone of the imitation model and the GTE turbine disc. As a result of the fatigue test of the imitation model at room and elevated temperatures, the experimental positions and sizes of the crack fronts with respect to the drop potential signal on the crack edges were obtained. The fixed positions and sizes of the crack fronts were used as the basis for the numerical calculation of the fracture resistance parameters. For the numerical studies, ten three-dimensional finite element models with different positions and sizes of the crack fronts were considered. The numerical calculation results based on the finite element method were used to determine the distributions of the elastic stress intensity factors along each crack front. The crack growth rate characteristics both on the free surface and at the deepest point of the crack front were obtained at room and elevated temperature conditions. A technique for the automation tests that simulate the block-type loading of the disk material at elevated temperatures was proposed.

Crack growth in rotor P2M steel at elevated temperature

The paper presents a comprehensive computational and experimental study of the crack growth rate during the creep-fatigue interaction in compact specimens of P2M steel at a temperature of 550 °C. The theoretical part of the study consisted in the formulation of the fracture resistance parameters through the classical and new constitutive equations of the cracked body state taking into account the accumulation of damage. Numerical calculations included the determination of the stress-strain state fields for the conditions of elasticity, plasticity, and creep, as well as the distributions of nonlinear stress intensity factors and the C*-integral along the crack length and along the crack front for each tested compact specimen. The interpretation of the experimental results for specimens of the same shape in plan but different thicknesses is given in terms of elastic and nonlinear stress intensity factors, taking into account the accumulation of creep damage. It was found that the crack growth rate under the fatigue and creep interaction increases monotonically as the crack size increases in comparison with harmonic fatigue by an order of magnitude or more on specimens of the same geometry. Taking into account the damage through the creep stress intensity factors causes differences in the cyclic fracture diagrams. The superposition of fatigue and creep contributions in terms of load holding time shows an order of magnitude increase in the total crack growth rate compared to the interpretation of the experimental data in terms of pure creep.

Three-dimensional mixed-mode stress intensity factors for deflected external surface cracks in thin and midsize-thick-walled spherical pressure vessels

Normalized three-dimensional mixed-mode stress intensity factor (SIF) distributions are presented for deflected external surface cracks in thin- and midsize-thick-walled spherical pressure vessels. With an aim to build a library of SIF solutions, values of the governing parameters of the problem, namely crack deflection angle, normalized crack depth and crack shape aspect ratio, are changed within their practical ranges. The obtained results show that for a given case, increasing the deflection angle yields a decrease in mode-I SIFs and increases in mode-II and mode-III SIFs. It is also observed that as the normalized crack depth increases, SIFs generally increase along the crack front. The results also show that magnitudes of the normalized mixed mode stress intensity factors at the depth location for midsize-thick-walled vessels are lower than those of thin-walled spherical vessels. The crack deflection angle has the highest effect among all parameters, emphasizing the importance of this study. It is concluded that the presented SIF solutions can be used to assess damage tolerance of a spherical vessel with a deflected external surface crack.

Extended finite element simulation on Tensile, fracture toughness and fatigue crack growth behaviour of additively manufactured Ti6Al4V alloy

The mechanical properties such as tensile, fracture toughness, and fatigue properties of Additive Manufacturing (AM) fabricated Ti6Al4V alloy is critically crucial for structural applications. The in-house developed MATLAB-based extended finite elements method (XFEM) model has been utilized to analyse experimental results of fatigue, fracture, and tensile properties of AM fabricated Ti6Al4V alloy, to avoid expensive and destructive mechanical characterisation. The XFEM model was first used to validate the single edge cracked sample of laser powder bed fusion (LPBF) processed Ti6Al4V alloy for fatigue crack growth rate (FCGR). The XFEM simulation study was further extended to analyse fatigue life of center and double-side cracked specimens, as well as for evaluating fracture toughness KIC upon accounting potential crack initiation site. The model has also been developed to predict FCGR of edge cracked specimen under mixed-mode loading conditions. The critical stress intensity factor (SIF) and stress distribution map in the crack vicinity of the C(T) specimen were modelled through FEA Abaqus package to estimate the fracture toughness of Ti alloy. A similar XFEM approach was used to analyse the tensile properties of Ti alloy to predict its fracture behaviour through the center cracked specimen taken at the tensile gauge section. The strengthening mechanisms contributing to Ti alloy's static and dynamic properties are elucidated through microstructural characteristics of LPBF processed Ti6Al4V alloy reported in the literature.

Fatigue and creep-fatigue crack growth in aviation turbine disk simulation models under variable amplitude loading

This study analyzes the simulation model configuration and its loading conditions in fatigue and subsequent crack growth tests. Following the simulation principles, a full-size 3D finite element analysis of a representative GTE turbine disc was performed. With the aim of reproducing the simulation model, the in-service critical zone of both the stress–strain state and damage accumulation is studied. Based on the parametric computations, the block type loading conditions of the simulation models are determined and verified. Experimental study of the surface crack growth rate in the simulation model under harmonic and block loading at elevated temperature is performed for the fatigue and creep-fatigue interaction conditions. To interpret the experimental data, we calculate the nonlinear stress intensity factor distributions along the semielliptical crack front for flaws growing on the inner surface of the hole in the simulation model using numerical procedures. It is found that in terms of the nonlinear fracture resistance parameters, the sections of the fatigue fracture diagrams form one common curve representing the previous and subsequent increasing stages of block loading in pure fatigue and creep-fatigue interaction loading conditions. The possibility of using the proposed simulation model, tested under variable amplitude loading, to assess the structural integrity of GTE turbine disks is discussed.

Effect of Pitting Corrosion on the Stress Intensity Factor Magnitude and Distribution

Effect of Pitting Corrosion on the Stress Intensity Factor Magnitude and Distribution

Determination of crack resistance of a tank with elliptical crack

The occurrence of crack-like defects is a common phenomenon in the operation of vertical steel tanks (VST). Such defects can occur both at the beginning of the operation of the tanks, which may be associated with a violation of the manufacture conditions or the installation procedures of the tank elements and during operation. Over time, such defects increase significantly and turn into cracks. Existing regulations prohibit the operation of VST with cracks. At the same time, the organization that operates the tank does not always have the opportunity to perform repairs immediately. There are cases of trouble-free operation of tanks with non-through surface cracks at the stage of sustainable growth, which are confirmed by model calculations are known from practical experience. The analysis of crack resistance of the VST-5000 tank with a semi-elliptical crack under the action of hydrostatic pressure is carried out in the work. The level of filling the tank with petroleum products is 95% of its height. The semi-elliptical crack is located on outside surface of the wall panel in lower row of cladding. Determination of crack resistance of a tank with a crack is performed on the basis of stress intensity factors (SIF). Direct and energy methods were used to SIF calculation. Determination of the stress-strain state is performed on the basis of the semi-analytical finite element method (SFEM). The SIF distribution along the crack front obtained using SFEM by both direct and energy methods almost coincides and agrees well with the values of SIF calculated by the direct method when using three-dimensional FEM. The obtained values of SIF differ along the crack front by 50%: the minimum value of SIF acquires at the point of the front, which is located on the outer surface of the tank, the maximum one - at the point of the front inside the wall that is furthest from the outer surface. The obtained results show the quite uneven SIF distribution along the crack front, so that the calculation of such problems requires the spatial setting of problem.

Convenient and accurate formulas for stress intensity factor distribution of semi-elliptical surface crack

In this paper, the stress intensity factor (SIF) formula [Formula: see text] along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution [Formula: see text] is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio [Formula: see text]/[Formula: see text] is focused considering the exact solution [Formula: see text] of an elliptical crack. By applying the least squares method to the ratio [Formula: see text]/[Formula: see text], accurate and convenient formula is proposed. The proposed formulas may provide the accurate SIF distributions for the aspect ratio [Formula: see text]–4 better than 0.2% accuracy.