Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

We propose a new approach to the experimental estimation of local strains at the tip of a concentrator. The approach is based on the measurement of displacement of certain points in the vicinity of the tip of a notch, which is further associated with the effective radius of the notch. Various concentrators in structures are simulated within a wide range of variation in radii of notches (ρ=0.1−6.5mm) and in the geometry of specimens. We establish the main dependences between the value of the range of local strains Δɛ^* and the periodN _i prior to the nucleation of a fatigue macrocrack. Thus, by using the experimental quantity Δɛ^*, we can estimate the periodN _i prior to the nucleation of a fatigue crack of lengtha _i=d^* for structural elements of a complicated geometry. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv. Vol. 34, No. 3, pp. 55–66, May–June, 1998.     

Fatigue strength of laser beam welded automotive components made of thin steel sheets considering size effects

The applicability of and the quality of assessment using the nominal stress, structural stress and notch stress approaches for calculating the fatigue strength of laserbeam welded components made of thin steel sheets has been investigated. For this purpose, the fatigue lives of a longitudinal carrier, an injector and two tube-flange specimens have been determined by tests under constant amplitude loading. Fatigue cracks initiated at sharp root notches on all of these components. While the nominal stress is derived by theory of structural mechanics, the determination of structural and notch stresses is performed using 3D finite element models and solid elements. The structural stress is derived by an extrapolation of surface stress to the fatigue critical notch and the notch stresses by rounding the sharp root notch with a reference radius of r_ref = 0.05 mm. For all of the concepts used, the endurable stresses have been compared to the design SN-curves recommended by the International Institute of Welding (IIW).On comparing the quality of assessment of the different concepts, the notch stress approach shows the highest scatter. The highest endurable notch stresses occur in specimens with crack initiation at weld ends. These specimens have a very small highly loaded weld length. The lowest endurable stresses are determined for specimens with a long, equally loaded weld. The reason for these findings can be explained by statistical size effects. For an improved fatigue assessment, an easily applicable method is introduced, which takes into account the highly stressed weld length.     

Effects of external operating environments on fatigue of heat‐exchanger copper tubes

The purpose of this study is to analyze the effects of surface defects (eg, notches) and external environment conditions (eg, operating temperature, the number of re‐weldings) on the static strength and fatigue of C1220T‐O copper tubes used in the heat exchangers of air conditioners. Instead of using standardized specimens, as is done in general rotary bending fatigue tests, special specimens were fabricated in this study by inserting metal plugs on both ends of the copper tubes to perform fatigue tests on the actual tube product, and then the fatigue characteristics were evaluated using stress‐life (S‐N) curves. Regarding the welding conditions (maximum 1000°C and 10 seconds), the grain size grew (grain size number decreased), and the hardness decreased as the number of re‐weldings increased. The effects of the operating temperatures on the fatigue life were examined at a room temperature of 25°C and a heat exchanger operating temperature of 125°C, resulting in the same fatigue limit (70.21 MPa) at both room and operating temperatures. However, the fatigue limit of 37.46 MPa measured in the notched specimens (radius of 3 mm, depth of 0.2 mm) was lower than that obtained from those without notches. The material constant (1.07) used in the Peterson equation was then computed from the fatigue notch factor (1.87 = 70.21/37.46), and the stress concentration factor (2.18) of the notched tube specimens was obtained from the structural analysis. This material constant can be used to predict a decrease in the fatigue limit over varying notch sizes in copper tubes (C1220T‐O).     

Study of influence of notch root radius on fracture behaviour of extra deep drawn steel sheets

Fracture tests are carried out on extra deep drawn steel CT specimens containing notches with different values of notch root radius (ρ= 0.07–0.75 mm). Experimental findings clearly show a critical notch root radius (ρ_c) below which the fracture toughness remains independent of ρ and above which it varies linearly with ρ. The 3D finite element analysis shows that the location of maximum stress level causing crack initiation is in the vicinity of notch tip. The maximum stress level is independent of ρ; however, its location is shifted away from notch tip along unbroken ligament length with increase in ρ.     

Fatigue strength of notched specimens made of 40CrMoV13.9 under multiaxial loading

The work deals with multiaxial fatigue strength of notched round bars made of 40CrMoV13.9 steel and tested under combined tension and torsion loading, both in-phase and out-of-phase. The axis-symmetric V-notches present a constant notch root radius, 1 mm, and a notch opening angle of 90°; the notch root radius is equal to 4 mm in the semi-circular notches where the strength in the high cycle fatigue regime is usually controlled by the theoretical stress concentration factor, being the notch root radius large enough to result in a notch sensitivity index equals to unity. In both geometries the diameter of the net transverse area is 12 mm.The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than 120 new fatigue data are summarised in the present work, corresponding to a one-year of testing programme.All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

Fracture toughness and hydrogen embrittlement of pipes with notches

A technique for experimental determination of fracture toughness and hydrogen embrittlement of pipes made of API 5L X52 steel is described. The tests were performed using arc-shaped specimens with a notch cut out from pipes under the conditions of a three-point bend. The fracture toughness was determined in terms of the J-integral and the stress intensity factor at the notch tip. The value of K _ρ,c was established using the volumetric method based on the experimentally measured critical load and the results of the FEM calculation of the distribution of elastic-plastic stresses ahead of the notch tip, and J _ρ,c was determined using the method of separable functions. The effect of hydrogen embrittlement was studied using electrolytically prehydrogenated 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.     

Fatigue cracks emanating from sharp notches in high-strength aluminium alloys: The effect of loading direction, kinking, notch geometry and microstructure

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches was investigated. To this purpose, an experimental campaign has been conducted on Al-7075–T651 specimens carrying notches with aperture angles of 45°, 90°, and 135°. In order to investigate the role of microstructure texture, specimens were extracted from the plates with the main axis either in the longitudinal rolling direction (L-samples) or in the transversal direction (T-samples), or 45° inclined with respect to both directions (LT-samples). The effect of stress amplitude was investigated by performing tests at two load levels. Three loading directions θ = 0°, 45° and 90° were considered. Some specimens experienced pure Mode I loading condition, whereas the remaining ones were subjected to combined Mode I and Mode II loading condition. The crack deflection induced by the variation in loading direction was determined by measuring the kinking angle. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors (SIF) of straight cracks were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. On the contrary, a finite element model has been built up to derive the SIFs at the tip of the kinked cracks. The influence of K_II on the crack propagation was discussed on the basis of theoretical and semi-empirical models. It has been found that (i) the crack initiation at the notch root occurred in mixed mode conditions, (ii) a decreasing Mode II component with growing crack length was observed under initial loading direction θ₀ = 45° and θ₀ = 90°, (iii) a crack deflection was observed after 45° rotation of the initial loading direction; a good prediction of the kinking angle was obtained using the maximum tangential stress criterion, and (iv) a fairly good rationalization of all the collected crack growth rate data is obtained if the driving force for crack propagation is expressed in terms of K_I.     

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G _I and G _II using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = − 1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G _I since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.     

Fatigue strength of sharp V-notched specimens made of ductile cast iron

In the present, the high cycle fatigue strength of notched ductile cast iron is investigated. Experimental tests under axial loading, has been carried out on sharp V-notched specimens taken from heavy section casting considering nominal load ratios (R = 0). All specimens, taken from a heavy section casting, are characterized by a notch tip radius less than 0.1 mm, a notch depth of 10 mm and a notch opening angle = 90°. In order to evaluate the influence of chunky graphite morphology on fatigue life, fatigue tests were carried out also on a second set of specimens without that microstructural defect.Metallurgical analyses were performed on all the samples and some important microstructural parameters (nodule count and nodularity rating, among others) were measured and compared. It was found that a mean content of 40% of chunky graphite in the microstructure (with respect to total graphite content) does not influence significantly the fatigue strength properties of the analysed cast iron.     

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.     

Life fatigue estimation of welding seams based on notch strains

When based on structural stress acting on shell elements, the stress simulation for welding seams on thin sheets provides no sufficient correlation with damages occurring during real component tests under operational load.The calculation technique on hand is based on the analysis of the operational strength behavior of crucial positions such as toe notches and root notches. The notches are fictitiously rounded with radii of 0.05 mm. The notch root stress reduced by the support effect (especially the microstructural support effect) has proved to be an appropriate stress criterion.In order to verify the universality of the method for other welding seam geometries as well, the fatigue strength behavior of H-specimen was not only simulated for MAG-welding seams but also for laser welding seams and spot welding.The fatigue life estimation was carried out in accordance with the critical plane method and by using the P_SWT–stress-cycle curve. The Miner rule was used as hypothesis of damage accumulation.     

Generalised Neuber concept of fictitious notch rounding

The microsupport effect at sharp notches subjected to high-cycle fatigue can be described according to Neuber by averaging the maximum notch stress in a small material volume (microsupport length ρ^*) at the notch root (radius ρ). The averaged stress may be expressed by the maximum stress of a corresponding notch of an enlarged, fictitious radius, ρ_f = ρ + sρ^*, where s is the microsupport factor. The status of Neuber’s concept within his general theory of notch stresses is reviewed, followed by more recent theoretical and application-relevant developments. The theoretical developments refer to the notch angle dependency of the support factor, to its value for pointed versus rounded notches and to in-plane shear loading with out-of-bisector crack propagation. The application developments refer to the fatigue assessment of welded joints.     

Size effect in beams with rounded-tip V-notch

Stresses and strains in a beam with a single-edge rounded-tip V-notch subjected to bending were analyzed by the method of finite elements by using nonconforming quadrilateral elements under the assumption that the material is linearly elastic. We studied the influence of the depth of the notcha, its radius of curvature ρ, the angle of the notch ω, and the height of the beamh on the stress intensity factorK _t . It is established that the relative depth of the notch ζ=a/h causes practically no influence if the notch angle ω lies within the range 0°–135°. The influence of the notch rapidly weakens as the relative radius of curvature ρ _d =ρ/h increases from 0.01 to 1.0 and becomes insignificant for ρ _d ≤ 1. For small ρ _d (ρ _d ≤ 1), the quantityK _t attains its maximum value provided that ζ lies within the range 0.1–0.3. As the height of the beam increases, the quantityK _t first remains practically constant, then increases, and finally, ash infinitely increases, approaches a certain constant value. Dipartimento di Ingegneria Civile, Universita di Parma Viale delle Scienze, 43100 Parma, Italy. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 73–79, May–June, 1996.     

Multi-axial fatigue behaviour of a severely notched carbon steel

The paper deals with multi-axial fatigue strength of notched specimens made of C40 carbon steel (normalised state), subjected to combined tension and torsion loading, both in-phase and out-of-phase (Φ=0 and 90°). V-notched specimens have been tested under two nominal load ratios, R=−1 and 0, while keeping constant and equal to the unity the biaxiality ratio, λ=σ_a/τ_a. All specimens have the same geometry, with notch tip radius and depth equal to 0.5 and 4 mm, respectively, while the V-notch angle is equal to 90°. The results determined are discussed together with those deduced under pure tension or torsion loading on plain and notched specimens as well as on small shafts with shoulders. The application of an energy-based approach allows all the fatigue data obtained from the notched specimens to be summarised in a single scatter band, in terms of the total strain energy density evaluated at the notch tip against cycles to failure.     

A study on the combined effect of notch and fretting on the fatigue life behaviour of Al 7075-T6

In this study, an investigation was conducted on the fatigue performance of Al 7075-T6 plates in the presence of stress raisers (notch, fretting, and a combination of notch and fretting). Fretting situation was induced on the surface of the aluminium plate through steel contacting pads under two different clamping forces of 2 kN and 5.6 kN. The fatigue tests revealed a more dominant effect from stress concentrators originating from geometrical discontinuities such as the tested notch compared to the fretting wear conditions. Therefore, no noticeable differences were found between the fatigue lives of the notched specimens and the combined notch and fretting condition. A finite element stress analyses of the notched model under the contacting fretting pads agreed with the experimental results. The stress distribution at the clamped area introduced tensile stresses at the edge of the contact region, however, the stress at the notch tip was observed to be higher when an axial tensile load was applied to the end of the plate. Fractographic analyses confirmed the presence of cracks initiating from the fretting damaged surface for most of the combined notch and fretting fatigue test specimens particularly at the high cycle fatigue (HCF) zone.     

Fatigue crack growth of filament wound GRP pipes with a surface crack under cyclic internal pressure

In this study, fatigue damage behavior of (±75₃) filament wound composite pipes with a surface crack under alternating internal pressure was investigated. The specimens were tested at room temperature and exposed to open ended fatigue tests in which the pipe can be deformed freely in the axial direction. The tests were carried out in accordance with the ASTM D-2992 standard. The alternating internal pressure was generated by conventional hydraulic oil. The low cycle tests were performed with 0.42 Hz frequency and R = 0.05 stress ratio. Glass reinforced polymer pipes (GRP) are made of E-glass/epoxy and have (±75₃) configuration. Surface cracks were machined in the axial direction of the pipes which have depth-to-thickness ratios a/t = 0.25–0.38–0.50 and depth to length ratio of a/c = 0.2. Tests were performed at three different loads of 50%, 40%, and 30% of ultimate hoop stress strength of unnotched pipes. The failure behavior of GRP pipes during the test was observed and fatigue test results were presented by means of (S–N) curves and delamination damage zone area-cycle (A–N) curves.     

Multiaxial fatigue of V‐notched steel specimens: a non‐conventional application of the local energy method

The paper deals with the multi‐axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V‐notched specimens were subjected to combined tension and torsion loading, both in‐phase and out‐of‐phase, under two nominal load ratios, R=?1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τ_a/σ_a. The notch geometry of all axi‐symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V‐notch angle of 90° and a net section diameter of 12 mm. The results from multi‐axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non‐propagating cracks measured from some run‐out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V‐notch tip. The control volume is found to be dependent on the loading mode.     

A unified model of initiation and growth of fatigue macrocracks. part 3. stage of growth of a macrocrack

From a common viewpoint, fatigue fracture of materials is simulated by the process of initiation of an initial macrorack of lengtha _i =d ^* (d ^* is the constant of the material), which is successively (stepwise) repeated at the stage of its growth. As a result, the diagram “range of local stresses-period of initiation of an initial macrocrack” or ”range of local strains-period of initiation of an initial macrocrack,” which was determined for notched specimens, can be used for the construction of the diagram “growth rate of a macrocrack-range of the stress intensity factor” or “growth rate of a macrocrack-range of local strains,” respectively, if the crack is presented as a sharp notch with effective rounded radius ρ_eff=d ^* of the tip. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 5–14, May–June, 1999.