Quantitative correlation between geometric parameters and stress concentration of corrosion pits

Pitting corrosion damage often occurs in aluminum alloy structures and can significantly reduce the service life of structures and cause structural failures. In this research, three-dimensional corrosion pit morphology of 7075-T6 aluminum alloy was observed with the Sensofar PLμ confocal imaging profiler and scanning electron microscope. According to the corrosion pit morphology, we systematically investigated the quantitative correlation between the stress state and geometric features of a corrosion pit idealized as a semi-ellipsoidal pit. It is found that the stress concentration factor (SCF) increases with R_s (the ratio of pit width to length) and R_d (the ratio of pit depth to half-length). The maximum possible SCF is independent of R_d and increases linearly with R_s. The SCF of a rotated pit increases with the orientation angle in a cos²θ relation when R_s < 1.0. The empirical equations are also proposed to correlate the SCF to R_s, R_d and θ.     

Prediction of stress concentration factor of corrosion pits on buried pipes by least squares support vector machine

Concentrated working stress of a corrosion pit is known to be an important factor inducing the deterioration and consequently the breakage of a buried pipe. In this paper, we investigate the stress concentration factors (SCFs) of isolated elliptical corrosion pits using 3-D finite element analyses. The elliptical pits are fully characterized by their 3-D geometries, i.e., major and minor diameters and pit depth via a series of parametric studies of finite element pipe models. This is to quantify the effect of geometric variations of the pits on SCF. Realizing the fact that the 3-D finite element analysis is computationally intensive, efficient statistically predictive models have been developed based on least squares support vector machine (LS-SVM) realized in a ubiquitous spreadsheet platform. This approach shows very close predictions of SCF to the numerical findings for elliptical corrosion patterns on buried pipes. Particularly, two typical kernel functions have been adopted to cross validate the excellent performance of the LS-SVM method in SCF prediction of corroded pipes.     

CRACK NUCLEATION AND PROPAGATION IN BLADE STEEL MATERIAL

Stress corrosion cracking and corrosion fatigue of 12 Cr steel in sodium chloride solution has been investigated. Tests have been performed in air at room temperature and in aqueous solution with 22% NaCl at 80°C. The influence of corrosion pits on crack nucleation has been investigated. On fracture surfaces tested in environment (22% NaCl solution), crack initiation was observed in correspondence with corrosion pits; in this case fatigue life can be described using a fracture mechanics approach. The ΔK value for crack nucleation from a pit in rotating bending fatigue tests is very low in air (about 3 MPa√m). The results of slow strain rate tests on smooth specimens show that there is a threshold stress intensity, K_ISCC, of about 15 MPa√m and a plateau in stress corrosion crack growth rate of about 10^-5mm/s.     

Prediction of corrosion fatigue lives of aluminium alloy on the basis of corrosion pit growth law

Tension‐compression and rotating‐bending fatigue tests were carried out using aluminium alloy 2024‐T3, in 3% NaCl solution. The corrosion pit growth characteristics, and also the fatigue crack initiation and propagation behaviour were investigated in detail. The results obtained are summarized as follows: (i) Most of corrosion fatigue life (60–80%) is occupied with a period of corrosion pit growth at low‐stress amplitude. The corrosion pit growth law can be expressed as functions of stress amplitude σ_a and an elapsed time t. (ii) The critical stress intensity factor for crack initiation from the corrosion pit was determined as 0.25 . This value is the same as the threshold stress intensity factor range for crack propagation. (iii) Corrosion fatigue life can be estimated on the basis of corrosion pit growth law and crack propagation law. The estimated fatigue lives agree well with the experimental data.     

CORROSION FATIGUE FRACTURE BEHAVIOUR OF A SiC WHISKERALUMINIUM MATRIX COMPOSITE UNDER COMBINED TENSIONTORSION LOADING

We describe an investigation into the fatigue fracture behaviour under combined tension–torsion loading of a SiC whisker-reinforced A6061 aluminium alloy fabricated by a squeeze casting process. Special attention was paid to the environmental effects on fatigue fracture behaviour. Tests were conducted on both the composite and its unreinforced matrix material, A6061-T6, under load-controlled conditions with a constant value of the combined stress ratio, α = τ_max /σ_max in laboratory air or in a 3.5% NaCl solution at the free corrosion potential. The corrosion fatigue strength of both the matrix and composite was less in the solution than in air. The dominating mechanical factor that determined the fatigue strength in air was either the maximum principal stress or the von Mises-type equivalent stress, depending on the combined stress ratio. However, in the 3.5% NaCl solution, the corrosion fatigue strength of both materials was determined by the maximum principal stress, irrespective of the combined stress ratio. In the case of the matrix material, crack initiation occurred by a brittle facet normal to the principal stress due to hydrogen embrittlement. However, in the composite material, the crack was initiated not at the brittle facet, but at a corrosion pit formed on the specimen surface. At the bottom of the pit, a crack normal to the principal stress was nucleated and propagated, resulting in final failure. Pitting corrosion was nucleated at an early stage of fatigue life, i.e. about 1% of total fatigue life. However, crack initiation at the bottom of a pit was close to the terminal stage, i.e. about 70% or more of total fatigue life. The dominating factor which determined crack initiation at a pit was the Mode I stress intensity factor obtained by assuming the pit to be a sharp crack. Initiation and propagation due to pitting corrosion and crack growth were closely examined, and the fatigue fracture mechanisms and influence of the 3.5% NaCl solution on fatigue strength of the composite and matrix under combined tension–torsion loading were examined in detail.     

Effect of biaxial loads on elastic-plastic <Emphasis Type="Italic">J</Emphasis> and crack tip constraint for cracked plates: finite element study

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.     

FATIGUE CRACK GROWTH FROM TWO-DIMENSIONAL SURFACE DEFECTS

Abstract The growth of semi-elliptical cracks emanating from single surface defects under cyclic bending loading conditions has been investigated. Experiments to determine crack shape development during fatigue have been conducted on specimens containing spark-machined starter defects of various shapes and sizes. The results appear to indicate that the size and shape of the initial starter defect only affects the developing crack shape until the crack depth is approximately 20% of the specimen thickness; upon reaching this depth, all crack shapes (independent of initial size and shape) appear to be very similar. A mathematical model, based on the Newman and Raju stress intensity solution for semi-elliptical cracks, has been utilised to predict effectively the shape of the cracks developing from the various single starter defects with aspect (a/c) ratios as large as 3.     

Fatigue crack formation and growth from localized corrosion in Al-Zn-Mg-Cu

The effect of precorrosion on the fatigue life of aluminum alloy 7075-T6511 was measured, physical characteristics of corrosion topography plus fatigue damage were established by microscopy, and a corrosion modified equivalent initial flaw size (CM-EIFS) was established using fracture mechanics modeling. Fatigue life is reduced by clustered corrosion pits on the L-S surface from laboratory-EXCO exposure. Cracks initiate from pits clustered as a semi-elliptical surface micronotch rather than the deepest pits, consistent with shape-dependent stress intensity. Marker band analysis establishes that the number of cycles to form a crack about a pit cluster can be a significant fraction of total fatigue life. The CM-EIFS, back-calculated from fracture mechanics analysis of measured fatigue life, equals measured initiating-pit cluster size provided that important inputs are provided; such favorable comparison validates this approach to corrosion-fatigue interaction. Calculated CM-EIFS provides a metric to characterize alloy corrosion damage, and can be used to forward-model the effects of stress and loading environment on fatigue life distribution, critical for efficient alloy development. Use in prognosis of the fatigue performance of a service-corroded surface is hindered by uncertain non-destructive characterization of corrosion topography.     

FATIGUE ANALYSIS OF SURFACE CRACKS AT FILLET WELDED TOES

This paper reports a study of fatigue crack growth and coalescing behaviour at semi-elliptical cracks in the stress concentration region of steel plates with fillet shoulders or fillet welds. Fatigue tests were carried out on machined plate specimens with a fillet geometry similar to a fillet welded joint. These specimens were notched and precracked to provide single and multiple coplanar semi-elliptical surface cracks at the fillet toe region. Finite element stress analysis results were used to obtain approximate Mk factors (i.e.: stress concentration magnification factors) for the fillet toe geometry with a semi-elliptical surface crack. An analytical model was developed to simulate crack shape development and growth to failure in the case of multiple coplanar semi-elliptical cracks. In this model, a simple crack coalescing procedure is applied to merge coplanar cracks when they meet by recharacterising the coplanar cracks into a single semi-elliptical crack. Alternative crack growth laws were investigated and comparisons made between actual and predicted shape developments and lives.     

Stress corrosion cracking of maraging steel weldments

Abstract

The stress corrosion characteristics of 18 wt-%Ni (MDN-250) maraging steel and its weldments made under different welding conditions have been investigated. The threshold stress intensity factor K _ISCC in stress corrosion conditions has been determined in 3.5 wt-%NaCl environment for the base metal and weldments. The fractured surfaces were analysed to study the types of fracture during stress corrosion cracking in base and weld metals. Fracture toughness tests were carried out and the results obtained from these tests have been compared with K _ISCC values.     

CONSIDERATIONS OF ALLOWABLE STRESS OF CORROSION FATIGUE (FOCUSED ON THE INFLUENCE OF PITTING)

Abstract— Long life corrosion fatigue behaviour is discussed. The importance of (i) quantification of corrosion pit depth (or surface roughness caused by corrosion) as a function of service period and (ii) corrosion pit modelling is emphasized. Extreme value statistics is useful for corrosion pit depth quantification. It is demonstrated that a corrosion pit can be treated as an elliptical crack with the same depth and surface length as a pit. From these considerations, a method for determination of a reasonable allowable stress in corrosion fatigue is proposed. Finally, an example of an allowable stress is given, i.e. the allowable stresses of a real machine component under rotating bending stress are determined from estimation curves of pit depth together with corrosion fatigue crack growth data.     

Threshold stress intensity factor and crack growth rate for stress corrosion cracking of simulated heat affected zone in caustic solution

The threshold stress intensity factor for stress corrosion cracking (K_Iscc) of the simulated heat affected zone (HAZ) of mild steel in caustic solution has been determined using circumferential notch tensile (CNT) technique. The HAZ microstructure produced upon manual metal arc welding of grade 250 steel was simulated over a length of 35 mm of CNT specimens, using a thermo-mechanical simulator. Inter- and trans-granular stress corrosion cracking has been confirmed using a scanning electron microscope. The results presented here validate the ability of CNT technique for the determination of K_Iscc of HAZ and Base metal. Crack growth rates have also been determined using CNT technique. Further, the effect of microstructures on K_Iscc and crack growth rate is discussed in the present study. The determined K_Iscc of Base metal and simulated heat affected zone in 30% caustic solution is 24 and 45 MPa m^1/2, respectively.     

Corrosion Fracture of Structural Metallic Materials: Effect of Electrochemical Conditions in Crack

Abstract: The work is a compressed review based on the summarised results and the original approach for study of corrosion crack growth, taking into account local electrochemical conditions in the crack tip, which was developed at the Karpenko Physico‐Mechanical Institute of NASU. The model scheme of the pre‐fracture zone in the corrosion crack tip, which can be defined by the local values of pH of solution, electrode potential of metal E and stress intensity factor K_I is proposed. For its realisation, the special method and testing equipment for corrosion crack growth study and local electrochemical measurements in the crack were developed. The variation of the electrochemical conditions in corrosion cracks was studied, and it has been found that some stabilised levels of the pH and E values can be achieved in the tip of a non‐propagating and a propagating crack under static and cyclic loading during of exposure time. On this ground, the method for forecasting of the threshold stress intensity factor K_ISCC under stress corrosion cracking was proposed using these characteristic values of pH and E. This method was also adopted for the determination of the threshold stress intensity factor K_th under corrosion fatigue. The special method for determining corrosion fatigue crack growth rate diagrams based on consideration of extreme electrochemical conditions in the crack tip was developed. It has been proven that such diagrams reflect the extreme influence of the environmental factor on corrosion fracture of material, and they may be recommended as the base for the remaining lifetime calculation of the structural elements exploited under environmental conditions.     

Three‐dimensional stress concentrations at circular pin holes in clearance‐fit lugs

The influences of thickness and bonding clearance on stress concentration factors (SCFs) at circular holes in pin‐loaded straight lugs are systematically investigated using the finite element method. The three‐dimensional effect on stress concentration at pin hole is strong when the thickness B of lug is higher than the radius R of pin hole. The maximum tensional SCF K_max normalized by its corresponding plane stress solution K_p–σ increases with increasing B/R when B/R is higher than 2 for all of r/R (the radius of pin to that of lug), and also increases with decreasing r/R for a given B/R. It is also found that the plane stress SCF K_p–σ nearly remains a constant when r/R < 0.98, but is strongly sensitive to r/R and increases by 30% with r/R changing from 0.98 to 1. On the other hand, the friction coefficient, Young's modulus and the load level have also influences on stress concentrations, which should not be neglected in design of structures. An empirical formula of the maximum SCF is obtained for convenience of engineering applications.     

ESTIMATIONS OF STRESS INTENSITY FACTORS FOR SMALL CRACKS AT NOTCHES

This paper presents a simple method for determining the stress intensity factors for small notch-emanating cracks. The proposed method is based on similarities between elastic notch-tip stress fields described by two parameters; the stress concentration factor K₁, and the notch-tip radius ρ. The method developed here is rather general, and can be used for a variety of central and edge notches with through-thickness of semi-elliptical cracks. The predicted values are in good agreement with the available numerical data.     

Stress intensity factors for a wide range of long-deep semi-elliptical surface cracks, partly through-wall cracks and fully through-wall cracks in tubular members

To calculate the rate of fatigue crack growth in tubular members, one approach is to make use of the fracture mechanics based Paris law. Stress intensity factors (SIF) of the cracked tubular members are prerequisite for such calculations. In this paper, stress intensity factors for circumferential deep semi-elliptical surface crack (a/t > 0.8), semi-elliptical partly through-wall crack and fully through-wall crack cracks in tubular members subjected to axial tension are presented. The work has produced a comprehensive set of equations for stress intensity factors as a function of a/T, c/πR and R/T for deep surface cracks. For the partly through-wall cracks and fully through-wall cracks, two sets of bounding stress intensity factor equations were produced based on which all stress intensity factors within the range of parameters can be obtained by interpolation.     

Stress intensity factors of an elliptical crack or a semi-elliptical crack subject to tension

This paper is concerned with the analysis of stress intensity factors of a semi-infinite body with an elliptical or a semi-elliptical crack subject to tension. Analysis is based on the body force method [1] which has been applied to the various plane stress problems. In this paper the method is extended to three-dimensional problems. The numerical calculations are performed for various shapes and configurations of ellipses and the results are in agreement with the two-dimensional cases by M. Isida asb/a→0. The stress intensity factor of a semi-elliptical crack in a plate of finite width is also discussed.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Stress-intensity factors for semi-elliptical surface cracks in welded joints

A method for calculating stress intensity factors for edge and surface cracks in weldments has been presented. The weight function method was applied and appropriate weight functions have been derived using the Petroski-Achenbach crack opening displacement expression. The derived weight functions account for both the global weldment geometry and the weld profile characterised by the weld angle.Finally analysis of several parameters such as the type of loading, crack aspect ratio, weld angle and weld toe radius have been carried out assessing their effect on the stress intensity factor.The calculated stress intensity factors were verified against available finite element data.Very close agreement was achieved between the finite element data and the weight function based calculations.

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Résumé On présente une méthode de calcul des facteurs d'intensité de contraintes dans le cas de fissures de bord et de surface dans des soudures. On applique la méthode des fonctions pondérales et, en utilisant l'expression du COD proposée par Petroski et Achenbach, on tire les fonctions pondérales appropriées, qui tiennent compte de la géométrie générale de la soudure et du profil du joint, caractérisé par l'angle à la racine. Enfin, on a procédé à l'analyse de divers paramètres tels que le type de sollicitation, l'aspect de la fissure, l'angle et le rayon du congé à la racine, en vue de déterminer leur effet sur le facteur d'intensité des contraintes.On vérifie les facteurs d'intensité de contraintes par rapport aux données par éléments finis qui sont disponibles. On obtient un accord très proche entre les données numériques venant des éléments finis et les calculs basés sur les fonctions pondérales.

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Notation a crack length for an edge crack or depth for a semi-elliptical surface crack - c half crack length for semi-elliptical surface crack - E modulus of elasticity - F, F(a/t) geometric stress intensity correction factor - F, F,(a/t) geometric correction factor for the reference stress intensity factor - F ^x _sf geometric stress intensity factor for an edge crack emanating from an angular corner in a semi-finite plate with a step - F ⁹⁰ _sf geometric stress intensity correction factor for a crack emanating from the right angle corner ( = 90°) in a semi-finite plate with a step - G(a/t) parameter of the crack opening displacement function - H generalised modulus of elasticityH = E — for plane stressH = E/(1 —v ²) — for plane strain - h weld leg length (or the step thickness) - I ₁ (a), I ₂ (a), I ₃ (a) parameters of the crack opening displacement function - K stress intensity factor - K _r reference stress intensity factor corresponding to the local reference stress _r(x) and nominal stressS _r - K ^p _e stress intensity factor for an edge crack in a flat plate - K ^w _e stress intensity factor for an edge crack in a weldment - K ^p _s stress intensity factor for a semi-elliptical surface crack in a flat plate - K ^w _s stress intensity factor for a semi-elliptical surface crack in a weldment - m(x, a) weight function - m(x, a, a) weight function for an edge crack emanating from an angular corner in a finite thickness plate with a step or weight function for an edge crack in a T-butt welded joint - m _B (x, a) Bueckner's weight function for an edge crack in a flat plate - m _s (x, a, c) weight function for a semi-elliptical surface crack in a flat plate - Q= /2 elliptical integral of second kind for a circular crack     

Stress concentration effects of undercut defect and reinforcement metal in butt welded joint

In the present study, stress distribution of butt welded joints with various amounts of reinforcement metal and undercut defect has been investigated under uniaxial tension for a full penetration by systematically conducting a series of two-dimensional finite element (FE) models. The FE analysis indicated that the amount of reinforcement metal in weld zone has an important effect on stress distribution. For 120° of the reinforcement angle that designating reinforcement metal in weld joint, and 0.5 mm of toe radius, the value of stress concentration factor (SCF) exceeds 3.3σ₀. The analyses show that SCF takes much higher values in both low reinforcement angle and ratio of toe radius to plate thickness (R/t). As for joints with undercut defects, it is concluded that severity of SCF is mainly controlled by the ratio of depth to radius of undercut (h/r) and width (W). In addition to undercut defect, the presence of reinforcement metal, SCF noticeably increases with decreasing the reinforcement angle; it attains maximum value (7.4σ₀) for h/r = 5 and W = 3 mm. However, for the joints having wider undercut defects, the influence of reinforcement metal on SCF is found to be relatively lower; SCF is 6.7σ₀ for W = 6 mm. Finally, an attempt has been made to construct simple relationships among the SCF of the weld joint, reinforcement angle, undercut defect and dimensionless parameters defining weld toe detail.