FATIGUE CRACK INITIATION LIFE PREDICTION FOR WELDED JOINTS BY LOW CYCLE FATIGUE APPROACH

Abstract— Analytical procedures based on low cycle fatigue theory are used to estimate the fatigue crack initiation life (N_i) for a cruciform welded joint in mild steel under constant amplitude tensile cyclic loading; the fatigue crack initiating at the weld toe. Effects due to welding such as residual stresses, geometrical variability and changes in material properties are handled. It is shown that for high mean stresses the discrepancies observed between the N _i estimates provided by commonly used analytical procedures exceed an order of magnitude. For the base metal (BM) the discrepancies become negligible if cyclic relaxation of notch mean stress is taken into consideration. The differences betwen the N _i estimates for heat affected zone (HAZ) material (where fatigue cracks at the weld toe usually initiate) and for BM are quantified. The applicability of HAZ material properties, estimated from hardness, to N _i prediction is evaluated.     

SOME OBSERVATIONS ON CREEP CRACK INITIATION FROM NOTCHES

Abstract— Tests have been carried out on a 1 Cr-Mo-V steel at 565°C to describe creep crack initiation in two notched geometries. From metallographic observation the initiation times were observed to be approx. 8 and 13% of rupture lives for the sharp slit and blunter notch shapes, respectively. Based on only a few tests a relationship between the initiation time t _i and the creep crack parameter J * was found to be of the form t _i( J *)^0.67= constant.     

A FATIGUE DESIGN PARAMETER FOR SPOT WELDS

Abstract— Mode I and mode II stress intensity factors for two half-spaces connected by a circular patch were used to develop a mixed-mode stress intensity factor (termed the stress index K _i) which can correlate the fatigue life of all spot weld geometries, base metals, and specimen dimensions. Empirical corrections were applied to Broek's equivalent stress intensity factor ( K _lq) to account for the weldment geometry (sheet thickness, nugget diameter, specimen width) and the effect of mean stress. The final expression, ( K _i), is a measure of the notch-root stress field in the location where crack initiation and early crack growth occur. The stress index ( k _i) should be a useful tool for spot-weld fatigue design.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

Assessment of the period to fatigue macrocrack initiation near stress concentrators by means of strain parameters

A new approach to the experimental assessment of the local strain at a stress concentrator has been presented. It is based on a procedure of notch opening displacement measurements at certain points in the vicinity of a notch related to the effective notch radius ρ _eff = ρ + d * , where ρ is the notch radius and d * is a material constant. Different stress concentrators in structural elements were modelled for a wide variation of notch radii ( ρ = 0.1–6.5 mm) and different geometries of specimens. Hence, a basic relationship, which directly relates the local strain range Δ ε* to the period of fatigue macrocrack initiation N _i has been established. Thus, by applying the value of Δ ε* , assessed from a direct measurement at the notch root, it is possible to determine the period N _i to initiate a fatigue macrocrack of length a _i = d * for some structural components of complicated geometry.     

GROWTH OF FATIGUE CRACKS EMANATING FROM NOTCHES IN SiC PARTICULATE ALUMINUM COMPOSITE

Abstract— The initiation and growth of cracks emanating from blunt notches in 6061-Al alloy reinforced with 25% particulate Sic metal matrix composite were investigated. To elucidate the role of aging condition of the matrix on the fatigue behavior, the studies were carried out at T6 and overaged conditions. The results show that the number of cycles required for initiation of fatigue cracks are not influenced with the notch severity and the aging condition of the matrix. The overaging heat treatment resulted in slower fatigue crack growth rates. The failure of the Sic particles during the fatigue process is given as the reason for the both observed initiation and crack growth characteristics. It is also shown that the growth rate of cracks emanating from blunt notches can be accurately described by an equivalent stress intensity factor range Δ K _eq. This could provide an adequate engineering method for design against fatigue failure from various stress concentrations for this composite system.     

Resistance-curve method for predicting propagation threshold of short fatigue cracks at notches

A new resistance-curve method was proposed for predicting the growth threshold of short fatigue cracks near the notch root. The resistance curve was constructed in terms of the experimentally determined threshold value of the maximum stress intensity factor which was the sum of the threshold effective stress intensity range ΔK_effth and the opening stress intensity factor K_opth The ΔK_effth value was constant, irrespective of crack length or notch geometry. The relation between K_opth and crack length was independent of notch geometry. The predicted effects of the notch-root radius and the notch depth on the propagation threshold of short fatigue cracks were compared with the experimental data obtained using center-notched specimens with various notch-root radii and single-edge notched specimens with various notch depths. Excellent agreement was obtained between predictions and experiments.     

Fatigue crack growth from sharp notches

Notch-like stress raisers occur widely in engineering components. They are preferred sites for crack initiation when the components are subjected to cyclic loadings. Thus the growth of cracks initiated from notches is very relevant to design against fatigue failures. Schematic models proposed to explain the departure of notch crack growth from linear elastic fracture mechanics predictions are briefly reviewed. Different methods of measuring crack closure are compared. It is found that the commonly employed notch-mouth clip-gauge method is not sensitive enough to detect the closure of short cracks in regions of notch plasticity. Various mechanics parameters have been claimed to be able to bring the notch crack and long crack growth rate data to a single base. In the present work on double-edge notched AISI 316 stainless steel specimens, it is found that none of them is able to correlate satisfactory all the experimental data.     

PREDICTION OF FATIGUE LIFETIME OF NOTCHED MEMBERS

Abstract— A simple model for the estimation of the total fatigue life of notched members is presented. The number of cycles to failure is estimated as the summation of the cyclic life spent in: (1) the initiation of a dominant fatigue crack at the notch root; (2) the very early growth of this crack within the notch plastic zone; (3) the subsequent fatigue crack growth in the elastic stress-strain field of the notch; and (4) the elastic stress field of the bulk material. Theoretical and experimental results are compared.     

THE SIZE OF PLASTIC ZONES AND FATIGUE CRACK GROWTH BEHAVIOUR OF THREE FORMS OF A Ti–6Al–2.5Mo–1.5Cr ALLOY

The effect of microstructure on the fatigue properties of Ti–6Al–2.5Mo–1.5Cr alloy was investigated. The experimental results for both the fatigue crack initiation and propagation behaviour, as well as the dynamic fracture toughness ( K _Id ) showed clearly that a lamellar microstructure is superior to two other structures. It was found that, as in the case of steels, the initiation and subsequent growth of cracks in the titanium specimens with a sharp notch may also occur on loading levels below the threshold values of the K factor (Δ K _th ) determined for long fatigue cracks. In addition, measurements by interferential-contrast of the plastic zone size on the surface of specimens revealed that the different rate of crack growth at identical values of Δ K in individual structural states can roughly be correlated with the size of the plastic zone. A general relationship between the fatigue crack growth rate and plastic zone size, the modulus of elasticity and the role of crack tip shielding is discussed.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

AN EXPERIMENTAL STUDY ON THE OPENING AND CLOSURE BEHAVIOUR OF FATIGUE SURFACE, CORNER AND THROUGH-THICKNESS CRACKS AT NOTCHES

Abstract— The opening and closure behaviour of surface, corner and through-thickness cracks in thin notched plates of FeE460 ( K _t= 2.5) and A15086 ( K _t= 3.4) was experimentally studied. The cracks were initiated and examined under uniaxial fully reversed constant amplitude and two-step loading. Crack opening load values were measured during crack growth in notch sections with a nonuniform stress distribution using small strain gauges glued to the specimen surface, very close to the crack tip. The results represent a comprehensive set of experimental data for crack opening load values in dependence on crack lengths a, c and load level including the influence of overloads and covering all types of cracks. The results indicate uniform relationships between crack opening load levels and all crack types. Crack opening and closure occur at nearly the same strain level, which depends on the applied load level. The crack opening load values measured at large notched specimens differ from those measured at similar smaller specimens because of the different local stress gradients.     

CRACK CLOSURE EFFECT ON CRACK GROWTH RATE AT 650°C IN DOUBLE NOTCHED SPECIMENS OF A NICKEL BASE SUPERALLOY

Abstract— Creep-fatigue tests were performed at 650°C in air on a N18 nickel base superalloy, using double notched and smooth specimens. The deformation mechanisms observed by TEM at the notch root are shown to be compatible with the constitutive set of equations used in the finite element analysis which is presented. For a given K _max at the notch root, the crack growth rate is much higher in a notched specimen than in a smooth one. This effect can be explained by a variation of the crack closure stress level with the local R ratio and the local stress. A strong accelerating effect of the R ratio, especially for negative values, is found in smooth specimens. Introducing a K _op correction in the experimental results leads to a good agreement between the measured crack growth rate plotted versus K _eff in notched and smooth samples.     

ELASTIC-PLASTIC FRACTURE MECHANICS FOR INITIATION AND PROPAGATION OF NOTCH FATIGUE CRACKS

Abstract Initiation and propagation are considered to be controlled by the extent of total plastic shear deformation φ. Crack initiation and crack propagation occur when φ, exceeds a critical threshold value which can be equated to threshold conditions determined from linear elastic fracture mechanics analyses. When a crack is in a plastically deformed zone φ_t=φ _p +φ _e . where φ _p is the component of φ _t due to notch bulk plasticity and φ _e , is the component of φ _t due to a linear elastic fracture mechanics (LEFM) analysis of the crack tip plasticity field.
When cracks initiate at notch roots φ _t > φ_th. As the crack propagates in the notch plastic zone the rate of decrease of v _p will be different from the rate of increase of φ _e and it is possible for φ _t to decrease to a level below φ_th thereby creating a non-propagating crack.     

A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non-uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024-T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.     

Investigating creep rupture and damage behaviour in notched P92 steel specimen using a microscale modelling approach

Idealized random grains separated by pseudo grain boundaries were generated by using Voronoi tessellation to simulate the polycrystalline microstructure. Combined with finite element analyses, this approach made it possible to addressing crack initiation and progressive failure due to crack growth in notched bar geometries of P92 steel at high temperature. The calculations provided good predictions for creep rupture lives of notched specimen with different notch radii and external stress. Simultaneously, irregular crack growth shape, intergranular crack mode, and wedge cracks at triple grain interaction were captured in the model. The crack initiation positions were found to be influenced by notch radius and applied stress causing high stress triaxiality at the subgrain level. Furthermore, the preferential crack growth directions were changed as the notch varied from sharp to blunt.     

THE EFFECTS OF STRESS RATIO ON THE GROWTH BEHAVIOUR OF SMALL FATIGUE CRACKS IN AN ALUMINUM ALLOY 7075-T6 (WITH SPECIAL INTEREST IN STAGE I CRACK GROWTH)

Abstract— The growth behaviour of small fatigue cracks has been investigated on aluminum alloy 7075-T6 at stress ratios R of 0, −1 and −2. The effects of stress ratio are discussed with special interest in the stage I region of small crack growth. Cracks which initiated at R =−1 and −2, grew by a stage I mechanism up to a certain depth followed by stage II crack growth. The stage I to stage II transition occurred under a constant maximum stress intensity factor which was approximately consistent with the threshold effective stress intensity range, λ K _eff,th, for large cracks. At R = 0, on the other hand, stage I crack growth was not observed because of crack initiation at inclusions. Small cracks grew more rapidly than large cracks subjected to the same nominal stress intensity ranges at all the stress ratios, and they grew below the threshold stress intensity range, λ K _th, for large cracks. Stage I cracks, in particular, showed much higher growth rates than large cracks and grew even below λ K _eff,th. It is suggested that stage II crack growth rates should be characterized in terms of an effective stress intensity range, while a micromechanics approach will be necessary to evaluate stage I crack growth rates.     

A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.