J integral applications for short fatigue cracks at notches

Elastic and elastic-plastic fracture mechanics solutions are modified to predict the behaviour of short cracks. An effective crack length, l ₀ is introduced into the solutions for both the linear elastic stress intensity factor and the J integral. Crack growth results for short cracks, in both elastic and plastic strain fields of unnotched specimens, when interpreted in terms of the modified solutions, show excellent agreement with elastic long crack data. The modified J integral solutions are extended to plastically strained notches, and the solutions obtained are tested in the correlation of data for growth of sort cracks near notches of varying severity with data for long crack under elastic loading. Although constant stress amplitude tests of these notches gave crack growth rate versus crack length curves which varied from monotonically increasing for blunt notches, to an initial decrease followed by an increase of sharp notches, all the data fell within the long crack data when correlated by the J integral solutions. Conversely, these solutions can be used to predict elastic and inelastic short crack growth curves for notches of various severities.

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Résumé On a modifié les solutions de mécanique de rupture élastique et élastoplastique afin de prédire le comportement de fissures courtes. On a introduit une longueur effective de fissure l ₀ dans les solutions donuant le facteur d'intensité de contrainte linéaire élastique et l'intégrale J. Les résultats de croissance de fissure dans le cas de fissures courtes dans des éprouvettes non entaillées soumises à des champs de déformation élastique ou plastique, font état d'un excellent accord avec les données afférant à des fissures longues en condition élastique, lorsqu'ils sont interprétés sous forme de solutions modifiées. Les solutions des intégrales J sont extrapolées aux cas des entailles sollicitées dans le domaine plastique, et les solutions obtenues sont éprouvées dans une corrélation des données de croissance de fissures courtes au voisinage d'une entaille de sévérités diverses, avec les données de croissance de fissures longues sous mise en charge élastique.Les essais à amplitude de contrainte constante sur ces entailles conduisent à une vitesse de croissance qui, en fonction de la longuer de fissure, varie d'un accroissement régulier dans le cas d'entailles arrondies, à une diminution suivie d'un accroissement, dans le cas d'entailles aiguës. Ce nonobstant, toutes les données se sont révélées similaires aux données pour de longues fissures, lorsque l'on établit la corrélation des solutions des intégrales J.Complémentairement, ces solutions peuvent être utilisées pour prédire les courbes de croissance des fissures courtes élastique et inélastique, dans le cas d'entailles de sévérités différentes.

     

Propagation of fatigue cracks from notches

Abstract

The traditional design approaches to fatigue at notches, based on stress level–endurance relationships, are briefly reviewed. It is shown, by considering crack propagation from notches and invoking a change in control mode from notch plasticity to crack-tip plasticity, that a critical stress condition can be obtained which must be exceeded if the crack is to propagate to failure. The traditional techniques are then reinterpreted and explained by this propagation method. An example is given of crack growth from a sharp defect at a weld toe. It is shown that the integration of an elastic fracture mechanics growth law can reproduce stress range–cycles to failure data for this situation. There are, however, complexities of stress analysis and crack shape. A simple treatment of residual stresses affecting the threshold and slow–growth regimes, shows some promise as a technique for accounting for residual stresses.

MST/70     

SIF and threshold for small cracks at small notches under torsion

The basic approach to the problem of torsional fatigue strength of pieces containing defects is based on the stress concentration factor concept. However, experiments have shown that the torsional fatigue limit of specimens containing small holes is controlled by the threshold condition for small cracks emanating from small notches. Therefore, the ratio of torsional to bending fatigue limit ( τ _w / σ _w ) for specimens containing small defects must be studied from the viewpoint of fracture mechanics.
The scope of this paper is to address the calculation of the stress intensity factor for a small crack emanating from a three-dimensional hole under a biaxial state of stress by using the weight function method and to apply it to the fatigue limit prediction. The results obtained are in good agreement with experimental results on specimens with defects.     

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.     

Estimations of the T-stress for small cracks at notches

The T-stress is increasingly being recognized as an important additional stress field characterizing parameter in the analyses of cracked bodies. Using T-stress as the constraint parameter, the framework of failure assessments including the constraint effect has been established; and the effect of T-stress on fatigue crack propagation rate has been investigated by several researchers. In this paper, a simple method for determining the T-stress for small notch-emanating cracks is presented. First, the background on the T-stress calculation using the superposition principle and the similarities between the elastic notch-tip stress fields described by two parameters: the stress concentration factor (K_t) and the notch-tip radius (ρ), are summarized. Then, the method of estimating T-stress for both short and long cracks at the notches is presented. The method is used to predict T-stress solutions for cracks emanating from an internal hole in a wide plate, and cracks emanating from an U-shaped edge notch in a finite thickness plate. The results are compared to the T-stress results in the literature, and the T-stresses solutions obtained from finite element analysis. Excellent agreements have been achieved for small cracks. The method presented here can be used for a variety of notch crack geometries and loading conditions.     

A micromechanical approach to fatigue in small notches*

The present work shows the application to small notches of a micromechanical model which describes the growth of a short crack across the steep stress gradient generated at the root of a notch. The model, based on the theory of distributed dislocations, takes into account the interaction between short cracks and material barriers such as grain boundaries. The term ‘small notches’ refers in this paper to stress raisers the size of which is of the same order as the characteristic microstructural unit of the material. Typical examples are superficial scratches, corrosion pits, inclusions or pores. Comparisons between predicted fatigue limits and experimental results reported in the literature for different materials containing small artificial defects are shown and discussed.     

The measurement of fatigue cracks at spot-welds

Current fabrication changes in the automotive industry have stimulated interest in fatigue avoidance at spot-welded joints. Basic endurance data are available only for specific specimen types; a generalized fracture mechanics approach has been impeded by lack of crack propagation data. This paper describes a direct current potential difference technique for the continuous measurement of crack dimensions in spot-welded mild steel specimens under fatigue loadings. Initial results indicate that macrocrack propagation is the dominant fatigue mechanism for specimens with lives of the order 2 × 10⁶ cycles.     

Nd-Dy-Fe-Co-B磁体的环境加速腐蚀行为研究

研究了不同成分的烧结Nd-Fe-B磁体在恒定湿热和高压加速腐蚀环境中的腐蚀行为,对其腐蚀形貌进行宏观观察和扫描电镜微观观察,讨论了合金成分及不同腐蚀试验条件对磁体磁通损失的影响.研究结果表明,以重稀土元素Dy部分取代Nd,及微量添加Co元素等,能明显提高烧结Nd-Fe-B磁体的耐湿热腐蚀性能.在恒定湿热和高压加速腐蚀两...     

On a model of small fatigue cracks

A simple model is proposed, which allows one to explain and describe quantitatively the peculiarities of the kinetics of small fatigue cracks growth. The characteristics of material microstructure are introduced into consideration explicitly as well as those of the fields of microstress induced by the material microstructure.     

Description of behavior of short fatigue cracks

The Article was received in the German language. Authorized translation by S. Ya.     

Mechanisms of growth of small fatigue cracks in torsion

Strength of Materials -     

Internal stress effects on fatigue crack initiation at notches

In this paper the effects of the internal stresses on crack initiation at notches is investigated. Internal stresses are induced by applying two pre-loading cycles at a given load ratio, R = S_MIN/S_MAX, to the ‘virgin’ notched specimen. After pre-loading, blocks of 10⁶ cycles with a constant nominal stress range, ΔS, slightly larger than the nominal threshold stress range, ΔS_th, are applied with increasing minimum stress, S_MIN, in each subsequent block until a crack initiates. The lowest S_MIN above which a crack initiates is recorded as S_IN. The process is repeated for a wide range of positive and negative load ratios in order to obtain S_IN/S_MAX vs. load ratio curve. This curve for positive load ratios surprisingly resembles the K_PR/K_MAX plot reported in the literature for a cracked specimen. The results are explained in terms of compressive internal stress and the associated local clamping action at the notch cyclic plastic zone. Both the analytical and finite element calculations show a fairly good agreement with the experimental results.     

Roles of precipitates on corrosion fatigue crack growth of high-strength steels in corrosive environments

The effect of microstructures on resistance to corrosion fatigue cracking and fracture surface morphology for age-hardened steels were investigated in a 3.5% NaCl aqueous solution under a cathodic potential of –0.85 V (Ag/AgCl). The free corrosion was about –0.63 V (Ag/AgCl). The resistance to corrosion fatigue cracking of materials containing coherent precipitates in the matrix (underaged conditions) was less than that of materials containing incoherent precipitates (reheated conditions) at equal strength levels. Accelerated fatigue crack growth rates of the underaged material in the aqueous solution were followed by cracking along prior-austenite grain boundaries, due to hydrogen embrittlement, while the overaged material did not show accelerated fatigue crack growth rates and had fracture surfaces similar to those in air. The difference in the fracture surfaces of both materials in air and in the aqueous solution was considered to depend on the ease of diffusion of hydrogen to the prior-austenite grain boundaries. It is concluded that incoherent precipitates in the matrix made hydrogen accumulation at prior-austenite grain boundaries much slower than for coherent precipitates.     

Propagation of short fatigue cracks from notches in a Ni base superalloy: experiments and modelling

A notched specimen containing a semicircular slot (0.1 mm deep) was designed to simulate the growth of three-dimensional short cracks under a stress concentration. Fatigue tests were performed on N18 superalloy at 650 °C with trapezoidal loading cycles. A high-resolution optical measurement technique proved to be capable of detecting half-surface crack increments as small as 10 μm, and the potential drop method was found to be inappropriate for very small crack lengths. The stress intensity factor, Δ K , was calculated using a weight functions method. Non-uniform stress fields were determined by FEM modelling using elasto-viscoplastic constitutive equations. The plasticity-induced crack closure effect was calculated within the specimen using viscoplastic FEM modelling. The prediction of crack aspect ratio was used to investigate differences of closure along the crack front. The role of notch plasticity on these differences is discussed. Using these calculations, it is shown that the apparent differences between the growth behaviour of short and long cracks can be largely accounted for.     

A surface acoustic wave technique for monitoring the growth behavior of small surface fatigue cracks

The theory of Kino and Auld which relates the reflection coefficient of acoustic waves from a crack to its size is summarized. A scattering model is evaluated from this theory concerning the reflection of surface acoustic waves (SAW) from a small surface fatigue crack at a frequency such that the crack depth is much smaller than the acoustic wavelength. Acoustic predictions of crack depth are compared to postfracture measurements of depth for small surface cracks in Pyrex glass, 7075-T651 aluminum, and 4340 steel. Additionally, the minimum detectable crack depth as limited by the acoustic noise level is determined for several typical aluminum and steel alloys. The utility of SAW reflection coefficient measurements for inferring crack depth, crack growth, and crack opening behaviorin situ during fatigue cycling is discussed.     

Behaviour of fatigue cracks emanating from circular notches in Ti-6Al-4V under bending

This paper is aimed at evaluating the behaviour of small cracks emanating from notches in the Ti‐6Al‐4V alloy. Pulsating four point bending tests were performed at a nominal stress ratio of 0.1 and a frequency of 15 Hz on prismatic specimens with a central hole. The conditions of initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 56.6 and 100% of the 0.2% yield stress of the material. Microstructural effects were discussed. To this purpose a specific device based on the ‘in situ’ detection of cracks by photomicroscopy was developed. Corresponding results were analysed quantitatively considering the effect of the yielded region at the notch tip by elastic–plastic finite element modelling. Furthermore, information regarding the sites of fatigue crack initiation and propagation path were discussed on the basis of careful fractographic analysis of the specimens. The importance of the two phase α, β microstructure on the material damage was highlighted and correlated to the observed oscillations in the crack growth rate. Mechanically and microstructurally long cracks were correlated by linear‐elastic fracture mechanics.