Semi-elliptical Surface Crack Research Articles

The Effects of Residual Stress Distribution and Component Geometry on the Stress Intensity Factor of Surface Cracks

The stress intensity factor estimated by the appropriate modeling of components is essential for the evaluation of crack growth behavior in stress corrosion cracking. For the appropriate modeling of a welded component with a crack, it is important to understand the effects of residual stress distribution and the geometry of the component on the stress intensity factor of the surface crack. In this study, the stress intensity factors of surface cracks under two assumed residual stress fields were calculated. As residual stress field, a bending type stress field (tension-compression) and a self-equilibrating stress field (tension-compression-tension) through the thickness were assumed, respectively. The geometries of the components were plate and piping. The assumed surface cracks for those evaluations were a long crack in the surface direction and a semi-elliptical surface crack. In addition, crack growth evaluations were conducted to clarify the effects of residual stress distribution and the geometry of the component. Here, the crack growth evaluation means simulating increments of crack depth and length using crack growth properties and stress intensity factors. The effects of residual stress distribution and component geometry on the stress intensity factor of surface cracks and the appropriate modeling of cracked components are discussed by comparing the stress intensity factors and the crack growth evaluations for surface cracks under residual stress fields.

Mixed Mode 3D Stress Fields and Crack Front Singularities for Surface Flaw

The elastic-plastic stress fields and mode mixity parameters for semi-elliptical surface cracks on biaxial loaded plates have been investigated using detailed three-dimensional finite element calculations. Different degrees of mode mixity are given by combinations of the far-field stress level, biaxial stress ratio and inclined crack angle. For a wide range of crack inclination angles, elastic-plastic stress fields along the crack front for both semi-circular and semi-elliptical surface cracks being subjected to remote biaxial loading have been obtained. For both crack geometry types, it was demonstrated that, in the vicinity of the corner, the behavior stress fields differ from the stress component distributions at the deepest point on the crack front. This phenomenon is due to the free surface effect. Combining analytical solutions and 3D finite element calculations, the elastic crack tip singularity for a surface semi-elliptical crack has been investigated on a biaxially loaded plate. The distributions of singularity exponents have been obtained along the crack front for three main cases of mixed-mode loading.

S042011 SiCウイスカー強化Si_3N_4複合セラミックスの亀裂治癒現象について([S04201]セラミックスおよびセラミックス系複合材料(1))

SiC whisker reinforced Si_3N_4 composite was used for studying crack healing behavior. The semi-elliptical surface cracks with the length of 200μm, 600μm, 3mm were introduced on the specimens using Vickers hardness indenter. The cracked specimens were heat-treated at 1000℃, 1100℃, 1200℃ and 1300℃ for 1 hour in air. Bending strength was measured at room temperature in air by three point bending test system. Bending strength of cracked specimen reduced to about 50% of that of smooth specimen. However, bending strength of some pre-cracked and heat treated specimens recovered completely up to that of smooth specimen.

影響関数法による任意分布応力場における表面き裂の応力拡大係数と疲労き裂進展評価手法の開発

We present an evaluation method of the crack growth rate and behavior for a semi-elliptical surface crack in a plate subjected to arbitrarily stress distribution. To calculate stress intensity factors, the influence coefficients were developed on the basis of the influence function method with the finite element method. Although the arbitrarily stress distribution such as weld residual stress on the crack surface are difficult to approximate by using a polynomial formula, the stress intensity factor could be calculated by direct mapping of arbitrary stress field obtained from doing finite element analysis of the crack surface. To determine whether the evaluation method based on the influence function method was valid, fatigue crack growth tests were conducted for flat plates with a semi-elliptical surface crack. Flat plate specimens had a distributed residual stress by the non-filler welding before the fatigue crack growth tests. The results of a comparison of estimations and the tests show that both the growth rate and behavior agreed well. From the calculated stress intensity factors based on the influence function method, the asymmetrical crack growth rates and behaviors can be calculated quickly.

Modified Stress Intensity Factor Equations for Semi-Elliptical Surface Cracks in Finite Thickness and width Plates

Weld defects and severe variation of shape near the welds cause high stress concentration at weld toes or weld roots. This high stress concentration reduces fatigue lives of welded structures. A stress intensity factor (SIF) which includes this effect increases the accuracy of fatigue lives prediction. A magnification factor is commonly used to multiply the SIF of semi-elliptical surface cracks to account for the stress concentration effect in welded connections. Yamada and Hirt model is one of these methods. Comparison between Yamada & Hirt SIF equations and Newman & Raju SIF equations are applied to SIF of semi-elliptical surface cracks. The results suggest that Yamada & Hirt SIF equations are valid when the crack aspect ratio is less than 0.6. New empirical SIF equations are developed based on Yamada & Hirt SIF equations. The newly derived SIF equations are verified by comparing with experimental data.

Elastic-Plastic Analysis of Surface Crack in Round Bars under Torsion

An elastic-plastic finite element analysis (FEA) is used to determine the J-integral around the crack front of 3-dimensional semi-elliptical surface crack in a round bar under torsion loading. Crack geometries are based on the experimental observation. The present model is validated using the SIF under bending loading since no suitable SIF for torsion is available. Lack of numerical solution of elastic and plastic stress parameters under torsion are found. The FE J values are normalized by dividing with the estimation J value using a reference stress method. It is found that higher J values are obtained for deep cracks and the maximum J changed from the deepest point along the crack front to the outer point at the free surface when a/D > 0.2. J values can be estimated for all type of crack geometries under consideration with a correction factor, h1.

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi-elliptical surface cracks in a bearing steel was investigated under cyclic shear-mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear-mode crack growth in the longitudinal direction of cylindrical specimens. Non-propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔKIIth and ΔKIIIth, were estimated from the shape and dimensions of non-propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔKIIth and ΔKIIIth.

Linear and non-linear analyses for semi-elliptical surface cracks in pipes under bending

In this paper, the J integral was calculated for semi-elliptical surface cracks in pipes under bending using three-dimensional finite element analysis. The computations were performed for elastic and elastic-plastic behaviours. For the elastic case, the numerical results allowed the extrapolation of shape functions for analytical determination of the J integral. The results are in a good agreement with those in the literature if the ratio between the radius and the thickness of the pipe ( R/ t) is from 1 to 10. The analysis was extended to values of the ratio R/ t higher than 10. For the elastic-plastic, the numerical results are in good agreement with the analytical solution found in the literature for thick pipes ( R/ t ≥ 10). The effect of the ratio R/ t becomes sensible when the ratio of the applied moment to the moment of reference ( M/Mo r) exceeds 0.9.

Effect of specimen geometry on fatigue crack growth rates for the railway axle material EA4T

This paper presents experimental results on fatigue crack growth propagation for the EA4T steel widely employed in the manufacturing of railway axles. Apart from standard M(T) and C(T) specimens, the investigations include bending tests on cylindrical bars and rectangular plates containing semi-elliptical surface cracks, geometries representative of surface flaws in components. The results give an evidence of the crack growth rate dependency upon the geometry and loading conditions of cracked specimens. The paper also concludes that fatigue crack growth rates correlate with crack tip plasticity, even within low and middle stress intensity factor ranges. Some remarks are provided with respect to the significance of the results for assessing residual lives of railway axles under in-service conditions.

Stress Intensity Factors for Surface Semi-Elliptical Crack in Cylindrical Specimen under Combined Torsion and Axial Compression

Some authors proposed to combine a torsional loading of cylindrical specimens with surface semi-elliptical cracks (the principal axes along the axial direction) with superimposed static axial compression in order to eliminate kinking or branching of shear cracks from the shear plane. To authors’ knowledge, however, no precise numerical analysis of such a loading configuration is currently available. The aim of this article is to calculate stress intensity factors KI, KII and KIII along the semi-elliptical crack front using the ANSYS code. The problem is solved for a semi-circular crack front and various crack inclination angles. The results reveal that the compressive loading cannot eliminate the branching process. The inclination of the crack plane induces a rather high opening mode which means that the microscopically tortuous fatigue cracks observed in experiments grew under mixed-mode I+II+III.

Mechanism analysis of thermal shock properties for ZrB 2-20%SiCp-10%AlN ultra-high temperature ceramic with the surface defects

An indentation–quenching test was used to characterize thermal shock properties of ZrB 2-20%SiCp-10%AlN ceramic with surface defects that arisen from Vickers indentation. It showed that the thermal shock resistance was affected by the length of pre-crack and the thickness of specimen. The critical temperature difference was up to 550 °C and the residual strength approached to a constant in this paper. Thermal stress intensity factor ( K I) was investigated at temperature of 550 °C by the semi-elliptical surface crack physical model, and it indicated that K I ascended firstly and descended afterwards. The crack propagation behavior was characterized by calculating the difference between the crack resistance and K I. The main influencing factors for K I were also discussed and analyzed here.

Empirical Stress Intensity Factors for Surface Cracks under Rolling Contact Fatigue

This article contains empirical equations for the K I , K II , and K III stress intensity factors (SIFs) for semi-elliptical surface cracks for brittle materials subjected to rolling contact fatigue (RCF) as a function of the contact patch diameter, angle of crack to the surface, max pressure, position along the crack front, and aspect ratio of the crack. The equations were developed from SIFs calculated by parametric three-dimensional (3D) finite element analysis (FEA) for a range of contact patch radii (1b, 2b, and 3b) and angles of the crack to the surface (0°, 45°, and 60°). Calculating mixed-mode SIFs for surface cracks subject to RCF using 3D FEA is computationally complex because of extreme mesh refinement required at multiple levels to capture steep stress gradients. The comprehensive empirical curve fits presented are accurate to within 0.5% of FE simulations and are useful for component design where contact-initiated surface fatigue damage is important such as in gears, roller bearings, and railway wheels. The results are of particular relevance to hybrid silicon nitride ball bearings, which are susceptible to failure from fatigue spalls emanating from preexisting surface cracks, due to crack growth driven by RCF (G. Levesque and N. K. Arakere, An investigation of partial cone cracks in silicon nitride balls. International Journal of Solids and Structures, 2008, 45:6301–6315).

CRACK-HEALING BEHAVIOR AND BENDING STRENGTH PROPERTIES OF SiC CERAMICS BASED ON THE TYPE OF ADDITIVE SiO2 EMPLOYED

Silicon carbide ( SiC ) exhibits good strength at high temperatures and resistance to radioactivity. However, it has poor fracture toughness. The ability to heal cracks represents a very desirable means of overcoming this weakness. This study focuses on the crack-healing behavior and bending strength of SiC ceramics to which sintering additives have been added. Optimized crack-healing condition was found to be 1hr at an atmospheric level of 1100 °C. The maximum crack size that can be healed at the optimized condition was a semi-elliptical surface crack of 450 µm in diameter. Si oxide was revealed to be the principle material involved in crack-healing.

Compliance-Based Assessment of Stress Intensity Factor in Cracked Plates with Finite Boundary Restraint: Application to Thermal Shock Part I

The evaluation of mode I stress intensity factor associated with the creep-free thermal shock (TS) of finite length elastically/thermoelastically restrained cracked plates is a problem of interest. Among existing evaluation methodologies, the mechanical weight function approach is often perceived to be an optimal compromise between simplicity and accuracy for evaluation. However, to confidently apply the mechanical weight function methodology in such circumstances requires the derivation of different weight functions for each potential boundary restraint configuration, i.e., free, flexible or rigid boundary conditions. In this article, the traditional mechanical weight function philosophy is complimented with an elastic compliance analysis, enabling the mechanical weight function and geometry factors for an equivalent semi-infinite cracked plate to be used to evaluate associated with finite length elastically/thermoelastically restrained cracked plates. The need for deriving different weight functions is therefore removed and the proposed Compliance Adjusted Weight Function (CAWF) approach becomes more “user-friendly”. The targeted cracked plates are assumed to exhibit an exterior through-the-thickness edge crack or an exterior through-the-thickness semi-elliptical surface crack.

T-Stress solutions for a semi-elliptical axial surface crack in a cylinder subjected to mode-I non-uniform stress distributions

Abstract This paper presents the T -stress solutions ( T 11 and T 33 ) for semi-elliptical axial surface cracks in a cylinder subjected to mode-I non-uniform stress on the crack surface. Two cylindrical geometries with inner radius ( R i ) to wall thickness ( t ) ratios R i / t = 5 and 10 were considered. The T -stresses were applied along the crack front for normalized crack depth values a / t of 0.2, 0.4 and 0.5 and aspect ratios a / c of 0.2, 0.4, 0.6 and 1.0. Three stress distribution; uniform, linear and parabolic were applied to the crack face. In addition to these solutions, concrete formulation of the superposition principle is given for the T 33 -stress, which is known as an elastic parameter that describes the out-of-plane crack tip constraint effect. Then, the validity of the formulation was shown through application of our T -stress solutions to the problem of an axial semi-elliptical surface crack in a cylinder subjected to internal pressure, and checking that the principle of superposition holds for the problem.

Fatigue life prediction of semi-elliptical surface crack in 14MnNbq bridge steel

The fatigue life prediction of semi-elliptical surface crack in 14MnNbq bridge steel is discussed in this paper. The FCG rates under different stress ratios R as well as FCG behavior under tensile and bending loading conditions are investigated experimentally. Moreover, an approach to predict surface crack growth is discussed, and the advantage of the approach is that the data used in the prediction is obtained from the testing of through-thickness cracks. The effects of crack closure on predictions are also considered and the data corrected by crack closure of through-thickness crack is used. Comparison results show that the corrected prediction with consideration of crack closure provides much better predictions than the normal ones. And reasonable agreement is obtained between the predicted and experimental results.

User friendly assessment of stress intensity factor in thermal shocked cracked structures with finite boundary restraint

Evaluation of thermal shock stress intensity factors is a problem of interest in many industries. Many structures experiencing thermal shock can be accurately idealised to comprise finite length elastically/thermo-elastically restrained plates and finite length elastically/thermo-elastically restrained hollow cylinders. This article describes how a ‘user-friendly‘ Compliance Adjusted Weight Function (CAWF) approach can be used to assess mode I stress intensity factor associated with the creep-free thermal shock of such structure with edge and semi-elliptical surface cracks. Based upon a mechanical weight function philosophy, the CAWF approach utilises a mechanical weight function analysis, available mechanical weight functions/geometry factors attributed to an equivalent semi-infinite cracked structure, a crack-free finite element analysis and an elastic Line-Spring analysis of compliance. The need for deriving different weight functions at each configuration of boundary restraint is therefore removed and the results of several verification exercises highlight that the CAWF approach is suitable for estimates within 5–10% of benchmark fracture mechanics finite element values. This suitability of the CAWF approach is valid for a wide range of cracked plate configurations, cracked hollow cylinder configurations and boundary restraint. An exception to this suitability is observed when examining semi-elliptical surface crack configurations and a free or near free boundary restraint condition. Adjustments to correction for this ‘free boundary effect’ are discussed elsewhere.

Mechanism of factory-roof formation

Factory-roof (F-R) patterns produced by cyclic torsion loading of V-notched cylindrical steel specimens were investigated by means of experimental and theoretical methods. A three-dimensional model of F-R patterns was constructed by means of stereophotogrammetry in the scanning electron microscope and the basic geometrical rules of F-R formation were identified. The theoretical analysis revealed that the F-R initiates by elementary mode I branches of semi-elliptical surface cracks growing under mixed-mode II + III. The exact positions of such branches were analytically determined in terms of the maximum synergy of mode II and mode III loadings. An increasing density of the semi-elliptical surface cracks results in the refinement and the size reduction of F-R patterns. This effect, along with strong wear damage, explains the fact that the F-R patterns are usually not observed in the low-cycle fatigue region.

Crack-healing behavior of Si 3N 4/SiC composite under stress and low oxygen pressure

The crack-healing behavior of Si 3N 4/SiC composite under constant stress and low oxygen partial pressure was investigated. A semi-elliptical surface crack with a length of about 100 μm was introduced at the center of the tensile surface by the indentation method. The specimens were crack-healed at 1200 °C for 5 h under tensile stress ( σ app. = 200–300 MPa) and under low oxygen partial pressure and air ( P O 2 = 50 – 21 000 Pa ). The threshold constant stress for crack-healing was defined as 200 MPa in oxygen partial pressure over 500 Pa. The bending strengths of crack-healed specimens under tensile stress in P O 2 ≥ 500 Pa showed almost the same value as a healed smooth specimen, and most specimens fractured outside the crack-healed zone. From these results, we conclude that crack-healing can be achieved under stress in low oxygen pressure and can lengthen lifetime and increase reliability in Si 3N 4/SiC composite ceramic.

Enhancement of J estimation for typical nuclear pipes with a circumferential surface crack under tensile load

This paper is to report enhancement of engineering J estimation for semi-elliptical surface cracks under tensile load. Firstly, limitation of the sole solution suggested by Zahoor is shown for reliable structural integrity assessment of thin-walled nuclear pipes. An improved solution is then developed based on extensive 3D FE analyses employing deformation plasticity theory for typical nuclear piping materials. It takes over the structure of the existing solution but provides new tabulated plastic influence functions to cover a wide range of pipe geometry and crack shape. Furthermore, to facilitate easy prediction of the plastic influence function, an alternative simple equation is also developed by using a statistical response surface method. The proposed H1 values can be used for elastic-plastic fracture analyses of thin-walled pipes with a circumferential surface crack subjected to tensile loading.