Low‐cycle fatigue/high‐cycle fatigue interactions in notched Ti‐6Al‐4V*

Combined low‐cycle fatigue/high‐cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V‐notched cylindrical Ti–6Al–4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10⁷ cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K_t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10⁶ cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity‐induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.     

A simple method to analyse the notch sensitivity of specimens in fatigue tests

A simple method to analyse the notch sensitivity of specimens in fatigue tests is presented. The parameter m, which can be used to measure the notch sensitivity, the nominal stress and the stress concentration factor (K_t) are used to establish the method. In order to verify the feasibility of the method, notch fatigue test results from our group and literatures were collected. The results reveal that an optimal value of parameter m does exist for each material. Life predictions indicated that the model is able to describe the life evolution for notched specimens under high cycle fatigue and low cycle fatigue tests. Because the geometry effect is accounted for K_t, the method is suitable for the conditions when the notch geometries and the absolute dimensions are similar to the tested specimens.     

A three-dimensional graphical aid to analyze fatigue crack nucleation and propagation phases under fatigue limit conditions

A three-dimensional diagram is presented in which the fatigue limit of notched components is plotted as a function of the notch stress concentration factor K _t and the ² a/a ₀ ratio, , a and a ₀ being a shape factor, the notch depth and the El Haddad–Smith–Topper length parameter, respectively. Intersections with the planes normal to the axes allow the display of the different influence of crack nucleation and propagation on the fatigue limit of notched components.     

The effect of notch geometry on critical distance high cycle fatigue predictions

A critical distance method for predicting the fatigue limit stresses of notched specimens was implemented for notched specimens with a wide range of notch dimensions. Circumferentially notched cylindrical specimens (k_t=1.97–4.07) taken from Ti–6Al–4V forged plate were cycled to failure (R=0.1 and 0.5) using a step loading method for estimating the 10⁶ cycle fatigue limit stresses. These experimental data were used in combination with finite element solutions for all specimen geometries to determine a ‘critical distance’, a quantity or parameter determined from the stress distribution surrounding the notch in combination with fatigue limit stress data from unnotched specimens. A unique parameter was not found for all of the specimen geometries. However, predictions for the fatigue limit stresses of the larger notch geometries may be made with some amount of accuracy using a single value of the critical distance parameter, while reasonable predictions for the specimens with the smallest notch dimensions may be made upon the recognition of an apparent size effect.     

Prediction of fatigue limit reliability of high strength steel with deep notch under mean stress <Emphasis Type="Italic">σ</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> = 0

Because a fatigue limit of high strength steel with Vickers hardness H _V > 400 is scattered, it is difficult to predict the fatigue limit for S-N curve experimentally. The authors have proposed a nondestructive method for predicting the fatigue limit reliability of plain specimen of the high strength steel by the stress-strength model which consists of “statistical characteristics of hardness of a matrix under a small indentation load” and “statistical characteristics of hardness required for non-propagations of fatigue cracks from microstructural defects in a material”. In this paper, a nondestructive method for predicting the fatigue limit reliability of notched specimen of the high strength steel with microstructural defects such as non-metallic inclusions and pits from characteristics of a stress field near a notch, statistical characteristics of Vickers hardness and defect size is proposed. Especially, the method is applied to a structure with a deep notch under a mean stress σ _m = 0. Then, fatigue tests were carried out on the notched specimens of quenched-tempered 0.5% carbon steels with H _V ≃ 600 changing a notch root radius under a constant notch depth, and the validity of the prediction method is examined by comparing predicted results to experimental ones.     

Fatigue notch sensitivity of steel blunt-notched specimens

The notch sensitivity of three steels with similar plain fatigue limits was analysed and modelled. The analysis was made by using a model previously derived which estimated the fatigue limit of blunt notched components by means of the parameter k_td defined as the stress concentration introduced by the notch at a distance d from the notch root surface equal to the distance between microstructural barriers. The analyses show how the first two or three microstructural barriers define the fatigue limit and the fatigue notch sensitivity of blunt notched specimens.     

Notched fatigue testing of Inconel 718 prepared by selective laser melting

Selective laser melting (SLM) was used to prepare notched high‐cycle fatigue test specimens made from nickel‐based superalloy Inconel 718. Samples were designed to have 1 of 3 different notch geometries, including V notches with K_t of 2.2 or 3.1, a U notch with K_t of 2.0, and were printed in either vertical or horizontal orientations. Samples were tested with as‐printed dimensions and surfaces after heat treatment, but a separate set of SLM samples were printed as plates and machined to final dimensions comporting to the V‐notch specimen with K_t = 3.1. High‐cycle fatigue testing showed that machined SLM specimens behaved similar to wrought Inconel 718 plate specimens, but testing with as‐produced surfaces led to a decrease in fatigue life. The explanation for this difference is based on approximations of linear elastic fracture mechanics solutions for short cracks emanating from notch roots, with intrinsic surface features of SLM materials serving as the cracks. Analysis of the actual notch geometries after SLM fabrication indicates that stress intensity in the presence of these features plays a prominent role in determining number of cycles before fatigue crack initiation and propagation occurs.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

Influence of notch geometry on the estimation of the stress intensity factor threshold by considering the Theory of Critical Distances

Recently the Theory of Critical Distances was applied to estimate the threshold stress intensity factor, ΔK_th, as an alternative to standard fracture mechanics tests. This strategy requires only a linear-elastic Finite Element Analysis (FEA) around the notch vicinity and fatigue limit data from notched and smooth specimens, usually available in the literature, or at least easier and cheaper to produce and test than fracture mechanics cracked specimens necessary in ΔK_th experiments. The aim of this work is to revisit this numerical–experimental strategy and to assess the effect of notch geometry in the predictive methodology in order to evaluate its domain of validity mainly, but not only, in terms of notch root radius bluntness. A wide range of experimental data for different metallic alloys and types of notches were selected to validate the analysis. The results showed that only fatigue data from notch root radii, normalized with respect to the net cross section of the specimen, smaller or equal to 0.01 can provide estimates of ΔK_th within an error interval about 20%.     

Effect of notch on fatigue behaviour of a directionally solidified superalloy at high temperature

The effect of notch types and stress concentration factors (K_t) on low cycle fatigue life and cracking of the DZ125 directionally solidified superalloy has been experimentally investigated. Single‐edge notched specimens with V and U type geometries were tested at 850 °C with stress ratio R = 0.1. High temperature in situ optical method was used to observe crack initiation and short crack propagation. Scanning electron microscope observation of fracture was used to analyse the failure mechanism. The results reveal that fatigue resistance decreases with K_t increasing from 1.76 to 4.35. The ratcheting is found to be affected by both K_t and the nominal stress from the displacement–force curve. In situ observations indicate that the cracking does not occur at the notch apex but at the location where the max principal stress or Hill's stress is the highest. According to the scanning electron microscope observations, the failure of the notched specimens strongly depends on the anisotropy microstructures.     

Foreword – Materialwissenschaft und Werkstofftechnik 10/2011

Load controlled fatigue tests were performed up to 10⁷ cycles on flat notched specimens (K_t = 2.5) under constant amplitude and variable amplitude loadings with and without periodical overloads. Two materials are studied: a ferritic‐bainitic steel and a cast aluminium alloy. These materials have a very different cyclic behaviour: the steel exhibits cyclic strain softening whereas the Al alloy shows cyclic strain hardening. The fatigue tests show that, for the steel, periodical overload applications reduce significantly the fatigue life for fully reversed load ratio (R_σ = –1), while they have no influence under pulsating loading (R_σ = 0). For the Al alloy overloads have an effect (fatigue life decreasing) only for variable amplitude loadings. The detrimental effect of overloads on the steel is due to ratcheting at the notch root which evolution is overload's dependent.     

钙钠玻璃的循环疲劳强度预测

本文提出了一种表征及预测钙钠玻璃光滑和缺口试件在不同载荷条件下疲劳强度的通用方法．因钙钠玻璃中不存在有效的裂纹屏蔽机制,循环载荷在钙销玻璃中不会造成明显的附加损伤,亚临界裂纹扩展受应力腐蚀机制控制,循环疲劳寿命与加载频率无关．缺口试件的缺口疲劳系数Kf与其应力集中系数Kt近似相等．采用文中定义的等效应力做为力学参量,可将光滑及缺口试件在不同加载条件下的SPT图归一化．     

NON-DAMAGING NOTCHES IN FATIGUE*

The fact that very small notches (cavities, holes, scratches, etc.) have no effect on the fatigue limit of metallic materials is well known. This paper presents both a qualitative explanation for the existence of non-damaging notches and a quantitative derivation of their critical sizes. The condition for a notch (characterized by the stress concentration factor K_t and the notch root radius ρ) to be non-damaging in a metallic material (characterized by a critical crack size l₀) is (K²_t? 1)ρ≤ 4.5 l₀. The critical crack size can be expressed with good approximation in terms of the threshold stress intensity for fatigue crack growth and the plain fatigue limit. Therefore the above relation can be applied for an engineering evaluation of non-damaging notches. Test results obtained for copper and a pressure vessel steel demonstrate the applicability of the proposed method.     

Fatigue limit prediction of notched components using short crack growth theory and an asymptotic interpolation method

Mechanical components have stress risers, such as notchs, corners, welding toes and holes. These geometries cause stress concentrations in the component and reduce the fatigue strength and life of the structure. Fatigue crack usually initiates at and propagates from these locations. Traditional fatigue analysis of notched specimens is done using an empirical formula and a fitted fatigue notch factor, which is experimentally expensive and lacks physical meaning. A general methodology for fatigue limit prediction of notched specimens is proposed in this paper. First, an asymptotic interpolation method is proposed to estimate the stress intensity factor (SIF) for cracks at the notch root. Both edge notched and center notched components with finite dimension correction are included into the proposed method. The small crack correction is included in the proposed asymptotic solution using El Haddad’s fictitious crack length. Fatigue limit of the notched specimen is estimated using the proposed stress intensity factor solution when the realistic crack length is approaching zero. A wide range of experimental data are collected and used to validate the proposed methodology. The relationship between the proposed methodology and the traditionally used fatigue notch factor approach is discussed.     

NOTCH SIZE EFFECT IN FATIGUE

Abstract— The notch size effect (i.e. the decrease of the notched fatigue limit with increasing notch size for the same stress concentration factor) was quantitatively derived by describing the threshold conditions for the propagation of a short semi-elliptical crack nucleated at the notch root. A close relation between the Kitagawa—Takahashi diagram for the short crack threshold stress and the dependence of the notched fatigue limit on the notch size was shown. The derived relation for the notch size effect was experimentally verified for several specimen/notch geometries in the cases of pressure vessel steel and copper.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Local limit loads in components with competing failure locations

The plastic limit load is an important feature of the S‐N curve. The classical way of plastic limit load calculation using elastic‐ideal plastic material behaviour is restricted to one location of the component. Complex components normally have several fatigue critical locations, for all of them the local plastic limit loads has to be determined. By the classical way the plastic limit load can be evaluated only for one of them. A new method is presented. The local plastic notch factor K_p and the corresponding plastic limit loads are calculated applying Neuber's rule to FE calculations with plastic hardening material. The new method is validated on the basis of six different notched specimens. The need and capability is exemplarily shown on a specimen with two competing failure locations.     

Short crack threshold estimates to predict notch sensitivity factors in fatigue

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 Δσ_n is between Δσ₀/K_t and Δσ₀/K_f, where Δσ₀ 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 ΔK_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 ΔK_th and Δσ₀, 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 ΔK_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.     

Dauerschwingfestigkeit und zyklisches Werkstoffverhalten

Fatigue Limit and Cyclic Material Behaviour Fatigue tests to determine the fatigue limit are very timeconsuming. Therefore a lot of possibilities have been proposed to estimate the fatigue limit, especially the so-called correlation formulae. This paper shows for carbon and low alloy steel, that the correlation between fatigue limit σ_W (unnotched specimen, tension-compression, mean-stress equal zero) and cyclic yield strength R′_p0.2 is better than between fatigue limit and static tensile strength R_m or static yield strength R_p0,2. An additional improvement of this correlation is possible by fixing the fatigue limit on the level of the cyclic stress for a plastic strain amplitude ε_{a, p} = 0,026%. These results are based on 24 test series taken from the data collection [7].