Prediction of notch sensitivity effects in fatigue and in environmentally assisted cracking (original) (raw)
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Short crack threshold estimates to predict notch sensitivity factors in fatigue
International Journal of Fatigue, 2007
The notch sensitivity factor q can be associated with the presence of non-propagating fatigue cracks at the notch root. Such cracks are present when the nominal stress range Dr n is between Dr 0 /K t and Dr 0 /K f , where Dr 0 is the fatigue limit, K t is the geometric and K f is the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the propagation behavior of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value DK th of the stress intensity range and the crack size a for very small cracks. Most of these expressions are based on length parameters, estimated from DK th and Dr 0 , resulting in a modified stress intensity range able to reproduce most of the behavior shown in the Kitagawa-Takahashi plot. Peterson or Topper-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of DK th (a) estimate. In this work, a generalization version of El Haddad-Topper-Smith's equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for K f and therefore for q. It is found that the q estimates obtained from this generalization, besides providing a sound physical basis for the notch sensitivity concept, better correlate with experimental data from the literature.
Is notch sensitivity a stress analysis problem.PDF
Semi-empirical notch sensitivity factors q have been widely used to properly account for notch effects in fatigue design for a long time. However, the intrinsically empirical nature of this old concept can be avoided by modeling it using sound mechanical concepts that properly consider the influence of notch tip stress gradients on the growth behavior of mechanically short cracks. Moreover, this model requires only wellestablished mechanical properties, as it has no need for data-fitting or similar ill-defined empirical parameters. In this way, the q value can now be calculated considering the characteristics of the notch geometry and of the loading, as well as the basic mechanical properties of the material, such as its fatigue limit and crack propagation threshold, if the problem is fatigue, or its equivalent resistances to crack initiation and to crack propagation under corrosion conditions, if the problem is environmentally assisted or stress corrosion cracking. Predictions based on this purely mechanical model have been validated by proper tests both in the fatigue and in the SCC cases, indicating that notch sensitivity can indeed be treated as a stress analysis problem.
Estimation of Notch Sensitivity and Size Effect on Fatigue Resistance
Procedia Engineering, 2013
This paper addresses the problem of high cycle fatigue resistance associated to notches and the role of short crack propagation in the fatigue notch sensitivity quantified by the notch factor k f . An integrated fracture mechanics approach is proposed to estimate the fatigue notch sensitivity, by including the effect of both blunt and sharp notches. Whether fatigue strength at a given life is controlled by crack initiation (very blunt notches, k f = k t ), by microstructuraly short cracks (blunt notches, k f < k t ), or by mechanically short crack propagation (sharp notches, k f << k t ), depends on the stress concentration k t , the notch length D and the material threshold to crack initiation eR , to short crack propagation K th and to long crack propagation K thR . The approach includes the prediction of the fatigue crack propagation threshold for short cracks, previously developed to analyze the short crack behavior in metallic materials with or without blunt notches, and is integrated adding the influence of sharp notches and accounting for the controlling parameters. It estimates the fatigue resistance of the component by comparing the threshold for fatigue crack propagation as a function of crack length, K th , with the applied K for the given configuration. Estimations for results reported in published bibliography are presented. The proposed fracture mechanics approach allows accounting for the effects of notch acuity, notch size and intrinsic material fatigue properties on fatigue notch sensitivity. It opens the door to a new simple method for predicting fatigue notch sensitivity and fatigue strength of components with geometric concentrators by using parameters that can be easily measured or estimated, without the necessity of any fitting parameter.
In this work, short cracks emanating from circular holes are studied. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for the fatigue stress concentration factor K f and therefore the notch sensitivity q. A generalization of El Haddad-Topper-Smith's parameter, which better correlates with experimental crack propagation data from the literature, is presented.
Fatigue notch factor and short crack propagation
Engineering Fracture Mechanics, 2008
This paper addresses the problem of high cycle fatigue at notches and the role of short crack propagation in the fatigue notch factor k f. Ahead of a V-notched feature, the stress field is characterized by two parameters, i.e. the stress concentration factor k t and the normalized notch stress intensity factor k n. Whether fatigue strength at a given life is controlled by crack initiation (k f = k t) or by short crack propagation (k f < k t) depends on k t , k n and the material resistances to crack initiation and to short crack propagation. The analysis accounts for the effects of notch acuity, notch size, material and fatigue life on the fatigue notch factor k f. It opens the door to a new method for predicting fatigue life using two S-N curves for a given material; one being measured from a smooth specimen, the other from a severe V-notch.
NOTCH SENSITIVITY FACTOR PREDICTIONS BASED ON SHORT CRACK THRESHOLD ESTIMATES
In this work, cracks emanating from circular holes are studied using finite elements. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for the fatigue stress concentration factor K f and therefore the notch sensitivity q. A generalization of El Haddad-Topper-Smith's parameter, which better correlates with experimental crack propagation data from the literature, is presented. It is found that the q estimates obtained from this generalization better correlate with Peterson's experimental crack initiation data.
International Journal of Fatigue, 2020
Classical fatigue limit prediction models and material-dependent characteristic length parameters for notched components are critically reviewed before a modified stress gradient based approach is proposed to integrate the non-propagation behavior of microstructurally small crack. Assuming fatigue limit (strength) as a general function of root surface stress and stress gradient defined over a characteristic length, an effective stress parameter is derived to characterize the resistance of a notch to fatigue limit (high cycle fatigue) loading. The model is validated by comparing with reviewed models through a large amount of test data. Physical interpretation and perspectives on the model are also discussed.
CRACK TIP PLASTICITY AND THE EFFECT OF STRESS RATIO ON EARLY NOTCH FATIGUE CRACK GROWTH RATES
This paper aims at investigating the ability of a previously proposed parameter to correlate the behaviour of a physical short mode I stage II crack initiated at and growing from the root of a notch due to constant amplitude cyclic load at different stress ratios. The parameter combined the extents of both monotonic and cyclic crack tip plasticity and a length-dependent crack resistance term. Low carbon steel plates having a single un-cracked U-shaped notch were tested under constant amplitude axial stresses. Four tests were performed at four stress ratios such that the applied maximum stress was kept the same. Each test was simulated with a cyclic elastic-plastic two-dimensional finite element analysis. The development of monotonic and cyclic plasticity accommodated at the tip of a mode I physical short crack artificially advancing from the notch root was traced. The numerical results demonstrated the capability of the proposed parameter in reflecting the effect of stress ratio and notch contribution on the observed fatigue crack growth rates.
Fatigue <html_ent glyph="@amp;" ascii="&"/> Fracture of Engineering Materials and Structures, 2000
The theoretical foundation of a micromechanical model that accounts for the fatigue crack growth threshold conditions at notches was described in Part I of this study. Strictly speaking, the proposed formulation is restricted to the analysis of a component with an elliptical notch under antiplane stress. In this section of the study, the expressions derived in Part I are generalized for application to axial stress states and non-elliptical notch geometries. The procedure is validated by comparing the model's predictions with reported experimental results.
A Crack Closure Model for Predicting the Threshold Stresses of Notches
Fatigue & Fracture of Engineering Materials and Structures, 1993
A model is proposed to estimate the threshold stress range of a notched component. The model considers the variation of crack closure with crack length in the presence of a notch. The threshold stress range was found from the condition that the minimum value of effective threshold stress intensity range of a crack emanating from a notch equals the effective threshold stress intensity range of a "long" crack. The effects of notch depth, of notch acuity, of notch and specimen type, of load ratio, and of material properties on the threshold stresses were considered. Experimental data reported in the literature were used to assess the validity of the model. It was found that the model correctly predicts the behavior of cracks in notched components. NOMENCLATURE D = Notch depth: for edge notch, D is the full notch length, and for centered notch D is half of notch length E = Elastic modulus H = Plastic modulus K,, K, = Fatigue notch factor at the threshold condition (gross and net-section) 4, Km = Gross and net-section elastic stress concentration factor AK = Stress intensity factor range