Maximum Stress Intensity Factor Research Articles

Cross-Crack Interaction and Initiation Mechanism Under Hydro-Mechanical Coupling

In this paper, the equation for computing the maximum Stress Intensity Factor (SIF) of cross-crack under hydraulic-mechanical coupling was derived by the dislocation method and the integral equation, and the influence of cross-crack geometric parameters (branch-crack length, pinch angle, inclination angle) on the interacting SIF was analyzed, and its influence law was obtained. Using the maximum shear and tensile SIF ratio criterion as a basis, the fracture criterion of hydraulic-mechanical coupling cross-crack was established, and the initiation process of hydraulic-mechanical coupled red sandstone cross-crack was predicted (including the cross-crack initiation angle, initiation load, and initiation mechanism). Results showed that for cross-crack with the inclination angle fixed ([Formula: see text]), [Formula: see text] of crack tip C decreases slowly. For cross-crack with change of [Formula: see text]. [Formula: see text] of crack tip A increases, and crack tip C decreases with [Formula: see text]. For the cross-crack hydraulic-mechanical coupling test, as the cross-crack angle [Formula: see text] grows, the fracture initiation stress first reduces before increasing. Initiation mechanisms are Mode I fracture and initiation angles are usually negative. The hydraulic-mechanical coupling cross-crack initiation criterion is validated by the experimental findings, which align with the expected outcomes.

In situ observation of fatigue crack propagation in soda‐lime glass with initial crack and residual stress induced by Vickers indentation under four‐point bending

AbstractThe present study examined the four‐point bending fatigue properties of glass with an initial crack and residual stress induced by Vickers indentation. The fatigue properties of glass with an initial crack are influenced by the residual stress induced by Vickers indentation. Regardless of the presence of residual stress, the failure time under static fatigue is shorter than that under cyclic fatigue. In the region of a small crack, the fatigue crack aspect ratio for glass is smaller than that for metallic materials. The crack growth rate in glass with an initial crack initially decreases and then increases with an increase in the maximum stress intensity factor, Kmax. To investigate the effect of residual stress on the fatigue crack propagation behavior of soda‐lime glass, the in situ observation of fatigue crack propagation was conducted. Crack closure occurs in glass in which tensile residual stress induced by Vickers indentation was released by annealing.

Finite Element Analysis Study of Buried Crack Defects in B-Sleeve Fillet Welds

Finite Element Analysis Study of Buried Crack Defects in B-Sleeve Fillet Welds

Optimization of physico-mechanical and erosive wear properties of single/multilayer – coated granite filled aluminum alloy composites

Abstract In the present research, uncoated and coated (CrN/SiN–CrN) granite dust reinforced aluminum alloy (AA 1050, AA 5083) composites samples were fabricated using stir casting and their physical, mechanical and slurry erosion behavior were assessed. The study reveal a persistent increase in void content, hardness, impact strength and stress intensity factor for both uncoated and coated alloy with the inclusion of reinforcement. In contrast, flexural strength and corrosion rate decrease continuously with increased granite content and also with the corresponding coating. Multilayer coated 5083 aluminum alloy composite with 6 wt.% granite particle shows maximum hardness, impact strength and stress intensity factor and minimum slurry erosion rate. The entropy method was applied to the operating parameter to rank the fabricated composites. The performance of each operating parameter is determined using the VIKOR (Vise Kriterijumska Optimizacija Kompromisno Resenje) optimization method. The optimal formulation based on Performance-Defining Attributes (PDAs) is observed for multilayer-coated 6 wt.% granite particulate reinforced 5083 aluminum alloy composites.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

Fatigue performance of laser powder bed fusion manufactured TiB2/AlSi10Mg composite: Experimental investigation and fracture mechanics-based life prediction model for defect tolerance analysis

The fatigue performance of AlSi10Mg composites decorated with nano-TiB2 particles fabricated through laser powder bed fusion (LPBF) was first experimentally investigated at room temperature and it exhibited superior fatigue resistance compared with other LPBF AlSi10Mg alloys and other reinforced AlSi10Mg composites. Then the fractography was examined and a fracture mechanics-based life prediction method was proposed to correlate the critical defect information (size and location) and fatigue life. To assess the crack growth driving force for critical defects, we employed Murakami's concept of the maximum stress intensity factor (SIF). The modification was made to include the effect of specimen cross-sectional geometry and initiation location since Murakami’s method would underestimate the maximum SIF in some cases. Meanwhile, the process of small crack propagation was also considered in modeling, and a unified model to describe crack arrest, small crack growth, and long crack growth was established. By inputting information about defect size and location and external loading conditions, the fatigue life could be evaluated and our results demonstrated good estimation within the [1/4,2] scatter band. Furthermore, an unbroken specimen subjected to the highest external loading was examined using X-ray computed tomography (CT) to characterize the defect population. By incorporating the CT statistical results into our life prediction model, outcomes such as non-propagating cracks or small crack growth without leading to ultimate failure could be obtained, which was consistent with CT findings. Concurrently, CT analysis revealed that the detrimental effect of large inner defects could be less significant than that of small surface defects. Therefore, we propose a novel strategy that combines defect size and location to enhance defect tolerance in additive manufacturing (AM) materials.

A new method for predicting multi-crack fracture mechanism in the finite plate of red sandstone

A novel theoretical approach was put forth to forecast multi-crack propagation trajectories in a finite plate. First, a weighted residual approach and complex function are used to create the formula for computing the maximum (stress intensity factor) SIF of multi-crack in the finite plate. And then, three cracks were then chosen as a model for computation to determine how the plate size affects the SIF. The formula of multi-branch crack in finite plate is derived and the crack initiation and propagation criterion of multi-crack in finite plate was established. Finally, the propagation paths of three cracked red sandstone in a finite plate were predicted and verified by the uniaxial compression test. It demonstrates that the SIF of multiple cracks in a finite plate is consistently larger than that of an infinite plate. Under the uniaxial compression test, the first crack initiation point is often A2 or B2, and each specimen’s first crack initiation time increases and subsequently reduces when the relative horizontal spacing (Ds’) of cracks varies. The crack initiation stress increases and the unstable stress first increases and then decreases with Ds’. The total crack extension length initially goes down and then goes up. All of the fracture initiation and propagation mechanisms are Mode I. The effectiveness of the multi-crack propagation theory in finite plates is established by the good agreement between predicted and test findings.

Fatigue life prediction of AA2524 thin plate strengthened using compound laser heating and laser shot peening method

AA2524 is a aluminum alloy based on damage tolerance design, and it is mainly used for the manufacturing of aircraft skins. Aircraft skins often occur fatigue failure due to harsh working conditions. To improve the fatigue resistance of aircraft skins and to accurately predict the fatigue life of AA2524 compact tension (CT) samples. The compound strengthening method of lsear heating (LH) and lsear shot peening (LSP) is proposed to improve the fatigue life of AA2524 in this paper. Considering the effect of stress ratio (R), residual stress (RS), stress intensity factor range (ΔK), and maximum stress intensity factor (Kmax) on the fatigue crack growth rate (FCGR), the fatigue life of CT samples was predicted applying artificial neural networks, support vector regression models. The results show that laser heating and laser shot peening can obviously improve the fatigue life by 30.703% at R = 0.1 and 4.701% at R = 0.5, compared with base materials. The neural networks have better fatigue life prediction ability, and the fit coefficients for the neural networks predicting fatigue life reach 0.97, which is better than that of Walker model (0.91). The prediction value for ANN model is 75,462 cycles, the magnitude for SVR model is 78,234 cycles, and the experimental value is 74,204 cycles. The deviation are 1.7% and 5.43%, respectively. Meanwhile, the effect of R on the FCGR of AA2524 is closely associated with the crack closure effect.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

Analytical prediction of fatigue resistance of additively manufactured aluminium alloy based on Murakami method

This research is devoted to analyze the stress state and fatigue strength of two specimens made by a newly developed high-strength aluminium alloy produced by the wire arc additive manufacturing (WAAM) process. The relationship between fatigue strength and flaw size was calculated based on the root squared area – a parameter by conventional Murakami’s equation which is a widely used analytical approach for predicting fatigue resistance in metallic materials. The research involves the metallographic preparation process on two aluminum alloy labeled HS-Al-A and HS-Al-B followed by Vickers hardness measurement. Further, the image of the observed pores was processed and dimensioned using an open-sourced software ImageJ by considering pixels and actual distance as well as by defining image threshold value for measuring pore sizes. The analytical approach is conducted in order to describe the maximum stress intensity factor Kmax at the crack front and to assess the fatigue strength σFS. As final results, specimen A has an average pore area of ≈65 µm with Kmax of 333.75 MPa∙√m and σFS of 137 MPa, while specimen B has an average pore area of ≈42 µm with Kmax of 325.13 MPa∙√m and σFS of 153 MPa. Overall, this research allows the formulation of a method for estimating fatigue strength of large defects leading to a conclusion that flaws can influence the fatigue resistance of the material so that the bigger the flaw size is, the lower σFS and the higher the Kmax.

Methods for calculating aerodynamics inside high-speed railway tunnel lining cracks and predicating stress intensity factors

PurposeThis study aims to propose a series of numerical and surrogate models to investigate the aerodynamic pressure inside cracks in high-speed railway tunnel linings and to predict the stress intensity factors (SIFs) at the crack tip.Design/methodology/approachA computational fluid dynamics (CFD) model is used to calculate the aerodynamic pressure exerted on two cracked surfaces. The simulation uses the viscous unsteady κ-ε turbulence model. Using this CFD model, the spatial and temporal distribution of aerodynamic pressure inside longitudinal, oblique and circumferential cracks are analyzed. The mechanism behind the pressure variation in tunnel lining cracks is revealed by the air density field. Furthermore, a response surface model (RSM) is proposed to predict the maximum SIF at the crack tip of circumferential cracks and analyze its influential parameters.FindingsThe initial compression wave amplifies and oscillates in cracks in tunnel linings, resulting from an increase in air density at the crack front. The maximum pressure in the circumferential crack is 2.27 and 1.76 times higher than that in the longitudinal and oblique cracks, respectively. The RSM accurately predicts the SIF at the crack tip of circumferential cracks. The SIF at the crack tip is most affected by variations in train velocities, followed by the depth and length of the cracks.Originality/valueThe mechanism behind the variation of aerodynamic pressure in tunnel lining cracks is revealed. In addition, a reliable surrogate model is proposed to predict the mechanical response of the crack tip under aerodynamic pressures.

Stress Intensity Factor Solutions for Eccentric Annular External Cracks in Notched Round Bars under Tensile Loading

In this paper, stress intensity factor (SIF) solutions of eccentric annular external cracks in elliptical notched round bars under tension loading have been obtained from 3D finite element analysis, along with their relation to the energy release rate obtained with the J-integral contour. The analysis variables have been the ligament diameter, its eccentricity, and the elliptical notch aspect ratio. The maximum SIF increases with the ligament eccentricity, the presence of the notch (compared to when the bar is smooth), and the elliptical notch axial semi-axis (for the same notch depth); it decreases with the ligament diameter. For external cracks, eccentricity induces bending of the bar subjected to tensile loading, which can produce partial and full contact of the crack surface, relevant phenomena in terms of the SIF value at the different points of the crack front.

Effective elastic properties of three-dimensional multiple crack problems with the isogeometric boundary element parallel fast direct solver

We propose an isogeometric boundary element (IGABEM) parallel fast direct solver based on OpenMP to solve three-dimensional multiple crack problems. In this paper, the orderly and randomly distributed cracks are studied to observe the influence of the multiple crack interaction on the effective elastic properties. This paper designs the parallel implementation of the matrix low rank approximation and the matrix assembly for the hierarchical off-diagonal low rank (HODLR) matrix. In the matrix low rank approximation, we propose the m-n tree to improve the accelerated hybrid algorithm to balance the CPU performance and memory usage. The numerical results show that the effective elastic properties can respond to the strong interaction to a certain extent, but the maximum stress intensity factors (SIFs) of multiple cracks still need to be calculated to diagnose the possible crack initiation points. On the other hand, the numerical results also show that the IGABEM parallel fast direct solver can greatly improve the computational efficiency on the premise of ensuring the computational accuracy.

Effect of different loading conditions on corrosion fatigue crack growth rate of a nickel-based alloy in supercritical water

Advanced ultra-supercritical (A-USC) technology improves the initial steam temperature to 650 °C and more. In such an extremely corrosive medium environment, metallic materials are susceptible to corrosion fatigue. In the present study, the aim is to evaluate the effect of maximum stress intensity factor (Kmax), stress ratio (R), waveform, frequency, and holding time (th) on the corrosion fatigue cracking behavior of C-HRA-2 (a candidate nickel-based alloy for A-USC units) in supercritical water (650 °C/25 MPa). The results show that with the increase of Kmax, the corrosion fatigue crack growth rate (CFCGR) increases and satisfies the exponential relationship. The decrease in R and frequency both cause the rise of CFCGR, which satisfies the logarithmic linear relationship. Sinusoidal and triangular wave loading have no significant effect on the CFCGR. Trapezoidal wave with th has a larger CFCGR while with the rise in th, the CFCGR increases. The crack propagation path is straight, perpendicular to the loading direction, and secondary cracks are also observed. Transgranular and intergranular mixed fractures occurred during continuous loading. The proportion of intergranular fracture increases significantly as holding time is applied. The corrosion fatigue crack growth of C-HRA-2 in supercritical water can be explained by dynamic embrittlement mechanism.

Effects of orientation on fatigue crack propagation of Ni3Al under super-gravity by molecular dynamics simulation

The effects of orientation on fatigue crack propagation of Ni3Al alloys under the super-gravity condition were studied by using the molecular dynamics method. The research found that the crack initiation and propagation mechanisms were different for different orientation crack models: the [001](010) crack germinated in the form of blunting damage and voids and the [1̄10](110) crack began initiation as blunting damage and slip bands. For the [112̄](111) crack, the initiation mechanisms of the crack were the same as the [1̄10](110) crack. In the crack propagation stage, the main deformation mechanisms of all crack models were slip bands, but the slip directions were different: the [001](010) crack and [112̄](111) crack presented ductile cracking and the [1̄10](110) crack presented brittleness fracture. Then, the crack growth rate and stress intensity factor were also analyzed under the super-gravity condition. The results showed that the [112̄](111) crack had the slowest growth rate compared to other two cracks under the super-gravity condition, and the [112̄](111) crack had the maximum stress intensity factor variable at initiation, but the variation tendency of stress intensity factors was slowest for the [112̄](111) crack under the super-gravity condition.

Effect of eccentric loading on fatigue cracking mode and characteristics of diaphragm-to-rib welded joints in steel bridge deck

The non-uniformly distributed wheel loads in orthotropic bridge decks will cause its lower components to be eccentrically loaded. By conducting numerical simulation, field measurement and fatigue tests of diaphragm-to-rib welded joints (DU), the crack-growth characteristics under eccentric loading were analyzed and compared with that under symmetric loading, through which the warning crack length for maintenance and an evaluating method for crack-growth rates were proposed. The result demonstrates that the eccentrically loaded side (ES) of DU will crack ahead of non-eccentric side (NES) with a larger growth angle. The crack performs the same three-stage features of fast-slow-rapid growth under eccentric loading with demarcations of 27 mm and 70 mm, which are obviously larger than that under symmetric loading. The weld toe on NES will be particularly prone to fatigue cracking once the crack on ES enters the third rapid-growth stage. The new initiated crack on NES will own the same growth rate as ES. The demarcation 70 mm shall be taken as the warning length for crack maintenance to avoid cracking on the other side. It is appliable to evaluate the crack-growth rate of DU by Paris formula and the maximum stress intensity factor obtained by K I and K II of mixed mode cracks.

On the strain energy release rate and fatigue crack growth rate in metallic alloys

The field of fracture mechanics started with Griffith’s energy concept for brittle fracture in 1920. In 1963, Paris et al. used a fracture mechanics’ parameter to introduce an equation for the fatigue crack growth rate in ductile materials and this equation is now commonly known as the ‘Paris law’. However, the Paris law and the semi-empirical models that followed ever since do not fully account for the main intrinsic and extrinsic properties involved with fatigue crack growth in metallic alloys. In contrast, here a dimensionally correct fatigue crack growth rate equation is introduced that is based on the original crack driving force as introduced by Griffith and the presence of plasticity in a metal to withstand crack propagation. In particular it is shown that the fatigue crack growth rate shows a power law relationship with the cyclic strain energy release rate over the maximum stress intensity factor. The new description corrects for the ratio between the minimum and maximum stress in a cycle during constant amplitude loading and for crack growth retardation under variable amplitude loading. The method has been successfully applied to variable amplitude crack growth with spectra that are representative of different fatigue dominated aircraft locations. As such, it allows for accurate predictions of variable amplitude fatigue crack growth life in aerospace structures.

Fracture mechanics analysis of a closure head of a PWR reactor pressure vessel the effect of bolt pre-load and thermal stresses

The effect of the bolt pre-load and thermal stresses in addition to pressure stresses on the structural integrity of a closure head of an RPV is presented here. The trends of the stress intensity factors (SIFs) of the surface cracks have been investigated under the combined effects of the loading conditions. A contradictory behavior of the surface cracks at the inside and outside locations of the head is observed due to thermal stresses, while the bolt pre-load decreases the integrity of the head at both locations. The maximum SIFs of the analyzed cracks are also found well below the material’s fracture toughness.

Effect of temperature and medium environment on corrosion fatigue behavior of Inconel 625

AbstractInconel 625 is a nickel‐based alloy with exceptional creep and corrosion resistance properties. It has emerged as a candidate material for operational and structural use in critical and supercritical power generation plants. Supercritical power plants work at high temperatures, pressure and in an erosive environment that makes metallic materials more vulnerable to corrosion fatigue. This study aimed to evaluate the fatigue crack growth rate (FCGR) at elevated temperatures (550–650°C) in a steam and supercritical water environment. All the experiments were performed at a water oxygen level of 8000 ppb. A cyclic stress of 1 Hz frequency and sine waveform was applied for the test. A 0.6 stress ratio was applied with a maximum stress intensity factor of 32 MPa√m. A direct current potential drop method was applied to detect the crack growth rate (CGR). For the given parameters, fractographic analysis validated the role of corrosion‐fatigue interaction as the primary source of variation in the FCGR. Results revealed that the CGR was enhanced with a rise in temperature under all test environments. The influencing mechanism of temperature on CGR was also discussed.

Quantitative estimation of contribution of pore size and the distance between nearest neighbour pores on high cycle fatigue (HCF) crack initiation in Ti-6Al-4V MIM-sintered materials

The fatigue damages due to pores of MIM-sintered Ti64 were investigated using the synchrotron X-ray CT imaging. The effect of pores on the fatigue strength limits was analysed independently from that of grain size by introducing the fatigue limit ratio RF. The pores near to the maximum-stress area were identified by elastic FEM. The maximum stress intensity factor KI-max at the edge of the identified pores showed a negative correlation with RF. Moreover, the initial cleavage in the crack was influenced by the mutual interference of both stress fields by the proximity of the identified pore and its adjacent pores.