Maximum Stress Intensity Factor Research Articles

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.

Stress corrosion cracking in fuel-grade ethanol: The role of the testing methodology

The increase in fuel-grade ethanol (FGE) consumption demands efficient and safe storage and transportation. However, depending on the raw material used for ethanol production, stress corrosion cracking (SCC) might be a major concern. This work evaluated the API 5L X70 steel susceptibility to SCC in simulated fuel-grade ethanol (SFGE), corn, and sugar cane FGE. The maximum stress intensity factor (Kmax.) was determined from KR curves, and the stress intensity factor threshold for environment-assisted cracking (KEAC) was obtained from the direct current electric potential difference (DCEPD) versus load-line displacement (LLD) curves. The results showed that Kmax. was weakly affected by the environment (different variants of ethanol), although brittle fracture comprising cleavage-like features, intergranular facets, and secondary cracks was observed for SFGE and corn FGE. Under the specific set of testing conditions adopted here, the parameter KEAC was effective in showing that the API 5L X70 steel is quite sensitive to SCC in SFGE and corn FGE, and not susceptible to this progressive cracking process in sugar cane FGE.

Experimental Study of VHCF Fractographic Features of Conventionally and Additively Manufactured Steels

Materials produced by additive manufacturing (AM) have been extremely related to literature. However, there is still unconsolidated knowledge about the fatigue life and respective mechanisms of initiation of cracks predominant in the VHCF regime for these materials. What has been observed in materials produced by conventional routes is that fatigue cracks tend to nucleate from intrinsic defects of the material located internally or in subsurface regions. The change in the evolution process of fatigue cracks leads to the formation of a characteristic morphology on the fracture surface, known as “fish-eye”. Another widespread aspect observed on the fracture surfaces is the formation of a fine granular area (FGA) nearby the initiation sites. This work aims to investigate the mechanisms of crack nucleation in VHCF of two distinct materials: conventional steel, DIN 34CrNiMo6 and AISI 316L stainless steel produced by L-DED. The ultrasonic tests were carried out at a frequency of 20±0,5 kHz and R= -1. The S-N curves were obtained and fracture surfaces were analyzed, fish-eye and FGA formation was verified. FGA sizes were compared to values estimated by empirical equations. FGA and fish-eye sizes were related to stress amplitude and maximum stress intensity factor (SIF).

Very high cycle fatigue of high carbon chromium bearing steel at high compressive mean stresses

Very high cycle fatigue (VHCF) of high carbon chromium bearing steel 100Cr6 (SAE52100; JISSUJ2) is investigated with ultrasonic fatigue testing for compressive mean stresses with minimum stresses σmin at compressive yield stress σCY, for σmin = 0.59σCY, and for load ratio R = −1. Fatigue limits are found for σmin = σCY and for σmin = 0.59σCY, whereas no fatigue limit below 109 cycles exists at R = −1. Cracks leading to VHCF failures exclusively start at interior inclusions. Considering inclusions as cracks, the maximum stress intensity factor of a load cycle being below the effective threshold stress intensity factor determines the fatigue limit.

Fracture mechanics analysis of a closure head of a PWR reactor pressure vessel LEFM-based SIF

In this study, fracture mechanics analysis of a closure head of a PWR reactor pressure vessel has been performed under accidental conditions. For the purpose, a wide range of elliptical surface cracks starting from minute cracks to worst-case cracks was postulated at the highest stress concentration locations of the head. The analyzed accidental conditions are small break loss of coolant accident (SB-LOCA) and Rancho-Seco transient (RST). The maximum linear elastic fracture mechanics-based stress intensity factors of the worst-case crack ‘a = 0.25 th; a = 0.33 c’ under SB-LOCA and RST are 104.37 MPa√m and 137.12 MPa√m respectively, which are less than the fracture toughness value of the material i.e. 155.6 MPa√m. Hence, the accidental conditions do not threaten the structural integrity of the proposed closure head.

Pre-cyclic-loading-enhanced Stage-1b stress corrosion crack growth of pipeline steels

The influence of prior cyclic loading on Stage-1b stress corrosion cracking (SCC) growth of X52 pipeline steels was investigated. Results showed that Stage-1b SCC growth was observed for pre-cyclically-loaded specimens under subsequent cyclic loading at the maximum stress intensity factor of 16 MPa m0.5 rather than those without pre-cyclic-loading. Large magnitude of prior stress cycles favored the SCC crack growth and its transition. Intergranular attack by static corrosion contributed marginally to the Stage-1b crack growth. Prior cyclic loading plus heat treatment facilitated strain-aging-assisted SCC crack growth. Removal of the plastically deformed regions before re-coating could reduce the cracking susceptibility.

Analytical fracture parameters of two unequal collinear interface cracks in an orthotropic bimaterial

This paper presents an analytical solution for the fracture parameters of two unequal collinear interface cracks (UCIC) in an infinite orthotropic or isotropic bimaterial subject to in-plane loading. The analytical expressions for the stress intensity factors (SIF), Jk-integrals and crack opening displacements of two UCIC in an infinite orthotropic bimaterial plate are derived using the complex variable method and evaluated in conjunction with the Jacobian elliptic functions and elliptic integrals. The presented theory is verified using the boundary element method. The results show that the fracture parameters are greatly influenced by mismatch of the engineering constants and proximity of the cracks. The inner tip of the longer crack always experiences the maximum SIFs and Jk values. These fracture parameters will increase exponentially when the distance between the cracks inner tips decreases. This study provides a baseline for the verification of future numerical and experimental studies of two UCIC which is not currently available in the SIFs handbooks.

A new effective stress intensity factor approach to determine thickness-independent fatigue crack growth rate curves

In this paper, it is experimentally demonstrated that the use of standardised methods to characterise the crack growth rate curves of metallic materials conforms to thickness-dependent results. To correct that dependency, the contribution of the stress intensity factor and crack closure on the effective stress intensity factor range is assessed by comparing analytical and numerical alternatives of calculation, which consider crack shapes experimentally determined. The findings reveal that (i) the crack closure is a thickness-independent edge effect, which allow developing analytical equations to determine the crack closure distribution along the thickness, and that (ii) the distribution of the effective stress intensity factor range is more influenced by crack closure than the maximum stress intensity factor. With the aim of obtaining a superposition of fatigue crack growth curves from different specimen thicknesses, an approach to calculate thickness-independent effective stress intensity factor range (ΔKeff,TI) is proposed and demonstrated.

Initiation and Fracture Characteristics of Different Width Cracks of Concretes under Compressional Loading

A stress concentration at a crack tip may cause fracture initiation even under low-stress conditions. The maximum axial stress theory meets the challenges of explaining the fracture propagation of a non-closed fracture of cracked concretes under compressional loading. Uniaxial loading tests of single-crack concrete specimens were carried out and a numerical simulation of fracture propagation under uniaxial compression was performed. The radial shear stress criterion for a mode-II fracture is proposed to examine the stress intensity factor (SIF) of the pre-crack specimens under compressional loading. When the maximum radial shear stress at the crack tip is larger than the maximum axial tensile stress, and the maximum dimensionless SIFs can satisfy frθmax/fθmax > 1 and frθmax/fθmax > KIIC/KIC (fθmax=KIe/σyπa and frθmax=KIIe/σyπa are maximum dimensionless mode-I and mode-II SIFs, respectively), the crack will extend along the direction of the maximum radial shear stress. The influence of the single-crack angle and width on the mechanical properties of the specimens was examined. The experimental and numerical results indicate that the existence of cracks can considerably weaken the strength of the specimen. The distribution and width of the cracks had a significant effect on the specimen strength. The strength of the concrete specimen initially decreased and then increased with increasing fracture angle. The failure mechanism and rupture angle of pre-crack brittle material while considering crack width will be discovered.

Closed-Form Stress Intensity Factor Solutions for Circumferential and Axial Surface Cracks With Large Aspect Ratios in Pipes

Abstract The ASME Boiler and Pressure Vessel Code Section XI prescribes the stress intensity factor solutions at the surface and deepest points for a semi-elliptical crack. The ASME Code Section XI, however, provides no solutions for a crack with a large aspect ratio, that is a crack in which the crack depth a is larger than the half-length c. The difficulty in treating the crack with a large aspect ratio relates to the position of the maximum stress intensity factor, which appears at neither the surface point nor the deepest point. In this paper, we investigate the influence of the stress intensity factor at the maximum point for circumferential and axial inside surface cracks with a large aspect ratio in a cylinder. First, we obtain the influence coefficients Gi for the stress intensity factor at the surface point, the deepest point, and the maximum point by finite element analysis, and developed a series of closed-form Gi solutions. Three geometrical factors are considered as parameters affecting the influence coefficients Gi: aspect ratio (a/ℓ = 0.5, 1.0, 2.0, and 4.0), crack depth ratio (a/t = 0.01, 0.1, 0.2, 0.2, 0.4, 0.6, and 0.8), and radius to thickness ratio (Ri/t = 2, 5, 10, 20, 40, and 80). Finally, we propose methods for evaluating the stress intensity factor for a crack with a large aspect ratio in a manner that characterizes the influence of the solutions at the maximum point.

Distribution of the through-thickness effective stress intensity factor range and its influence on fatigue crack growth rate curves

This paper focuses on an analysis of the through-thickness distribution of the effective stress intensity factor range of compact tension specimens, aiming to improve the characterisation of fatigue crack growth rate propagation curves. The maximum stress intensity factor and opening load are evaluated by standard analytical methods and three-dimensional numerical models for various crack lengths and crack front shapes to assess the relevance of considering real crack shapes. The findings reveal that standard procedures attributes only one value of velocity and one value of the fracture parameter for the entire front, whereas numerical methods report different values for both parameters along the thickness. Three-dimensional response surfaces are modelled and validated to estimate the fracture parameters, showing an incongruity in the use of fatigue crack growth rate curves obtained by standard two-dimensional procedures to assess the 3D crack growth.

Defect-induced asymmetrical mechanical behavior in shape memory zirconia: A phase-field investigation

An elastoplastic phase-field model is used to investigate the deformation mechanisms of yttria stabilized tetragonal zirconia in presence of defects. A remarkable tension-compression asymmetry is detected. A higher strength and a lower degree of transformation are observed in compression than in tension. Also, deformation mechanism is asymmetric depending on the crystal orientation. For some cases (other cases), phase transformation is absent in tension (in compression), while both transformation and plasticity are present in compression (in tension). Such tension-compression asymmetry is attributed to activation of different monoclinic variants with different Eigen strain tensors in tension versus compression. Results also reveal a higher degree of transformation and plasticity with lower onset stresses as the void size increases. Elliptic voids exhibit a directional effect with a maximum stress intensity factor of 5.6 MPa m1/2 when the long semi-axis is diagonally oriented with respect to the loading direction, and this prediction is comparable to experiments.

Slow fatigue crack growth in 2024-T3 and Ti-6Al-4V at low and ultrasonic frequency

Abstract Fatigue crack growth in 2024-T3 has been studied in ambient air and in vacuum at load ratios R = –1, R = 0.05 and R = 0.5 using ultrasonic equipment (cycling frequency 20 kHz) and servo-hydraulic equipment (20 Hz). In vacuum, no strain rate influences were found and similar growth rates and threshold stress intensities were measured at both frequencies. In ambient air, threshold stress intensities were similar at 20 Hz and 20 kHz and were 53 –62% of the respective values measured in vacuum. Above threshold, fatigue crack growth rates at ultrasonic frequency are slower (at R = –1) or similar (at R = 0.5) to growth rates at 20 Hz. Ultrasonic fracture mechanics tests in Ti-6Al-4V at load ratios R = 0.1, R = 0.5 and R = 0.8 in ambient air delivered threshold values similar to cycling frequency 50 Hz, whereas growth rates above threshold are approximately a factor of 3 higher at 20 kHz. The compressive part of a load cycle under fully reversed loading condition causes additional fatigue damage, and the maximum stress intensity factor at threshold is lower at R = –1 than at R = 0.05 or R = 0.1.