Notch Size Effect Research Articles

Empirical Correlation of Specimen Size Effects in Charpy Impact Properties of 11Cr-0.5Mo-2W, V, Nb Ferritic-Martensitic Stainless Steel

An effect of specimen size on the Charpy impact property was evaluated in the ferritic-martensitic 11Cr-0.5Mo-2W, Nb, V stainless steel (PNC-FMS). The upper shelf energy (USE) is expressed by the power law equation as USE[J]=m(Bb) n where m is the material constant (m=0.277 in PNC-FMS), B[mm] is the specimen thickness and b[mm] is the ligament size. The normalizing exponent n was empirically derived using the USE of the full size specimen as n=1.38×10–3USEfull+1.20. The n value varies in the range of 1.2 to 1.7, which is affected by the fracture volume below the notch. The PNC-FMS wrapper takes n=1.42. The ductile-to-brittle transition temperature (DBTT) of PNC-FMS is correlated as DBTT=115(log10 BKt)—158 using an elastic stress concentration factor Kt that represents the effects of notch size, e.g. notch depth, notch root radius and notch angle.

Notch size effects on high cycle fatigue limit stress of Udimet 720

Notch size effects on the high cycle fatigue (HCF) limit stress of Ni-base superalloy Udimet 720 were investigated on cylindrical specimens with three notch sizes of the same stress concentration factor K t=2.74. The HCF limit stress corresponding to a life of 10 6 cycles was experimentally determined at a stress ratio of 0.1 and a frequency of 25 Hz at room temperature. The stresses were calculated using finite element analysis (FEA) and the specimens analyzed using scanning electron microscopy (SEM). Test results show that at the same K t value, notch size can slightly affect the HCF limit stress of U720 when notch root plasticity occurs. FEA and SEM results reveal that the notch size effects are influenced by a complicated combination of the stress and plastic strain fields at the notch tip, the nominal stress, and the effects of prior plastic deformation on fatigue crack initiation.

Comment on “Notch Size Effects in the Fatigue Limit of Steel” by M. Makkonen [Int J Fatigue 25 (2003) 17–26

Comment on “Notch Size Effects in the Fatigue Limit of Steel” by M. Makkonen [Int J Fatigue 25 (2003) 17–26

Response to comments by Prof. Taylor on “Notch Size Effects in the Fatigue Limit of Steel” by M. Makkonen [Int J Fatigue 25 (2003) 17–26

Response to comments by Prof. Taylor on “Notch Size Effects in the Fatigue Limit of Steel” by M. Makkonen [Int J Fatigue 25 (2003) 17–26

Notch size effects in the fatigue limit of steel

The fatigue behaviour of grooved test specimens has been investigated in this paper. It is shown that there are two kinds of size effects connected to notches: statistical size effect and geometric size effect. The statistical size effect is calculated based on the distribution of the maximum depth of initiated cracks in specimens with varying stress area. The geometric size effect depends on the stress gradient and can be estimated with the help of the linear elastic fracture mechanics. It is concluded that the notch size effect in blunt notches can be explained with those two factors. When the notch gets sharper, after certain limit the magnitude of the plastic portion of the strain starts to play an important role in the fatigue crack initiation, and the fatigue limit is lower than that predicted by statistical and geometric size effects. Another estimation method shall be used to that kind of notches.

On crack-growth resistance curve fitting for ceramics

K R -curves of crack growth resistance were studied for a particulate ceramic-metal composite in the system lanthanium chromite–chromium in the temperature range 20 to 1100°C. It is shown that the K R -curves can be described satisfactory by an exponential function. With the use of this function, the similarity of the crack-growth resistance curves for the specimens tested at different temperatures can be demonstrated. The notch-size effect can also be minimized if the K R -curves are normalized with respect to crack length, the normalizing factor being the parameter l of the exponential function. A possible background in the framework of the model of the crack-face bridging by frictional ligaments in a wake zone is proposed.

Size effects in concrete fracture: Part I, experimental setup and observations

This paper presents an experimental investigation on the influence of microstructural parameters, such as aggregate size, and macroscopic parameters, such as specimen dimensions, on brittle fracture. Maximum aggregate size was used as a representative parameter of aggregate distribution in agreement with ASTM C 136 standards. Six groups of geometrically similar concrete specimens with various dimensions and aggregate sizes were prepared. Similarity of the specimens was strictly maintained by scaling the specimen dimensions from one group to another by a factor of two starting from a specimen size of (width × total depth × thickness) 105×105×12.5 mm to 1680×1680×200 mm. Two separate sets of removable pre-cast notches were designed to determine the effect of initial notch size. A considerable effort was devoted to the design of the loading fixture to have a reproducible crack initiation and controlled crack growth. Several loading fixtures were evaluated prior to selection of the one used in the experimental program. Quasi-static splitting cyclic loading in edge cleavage configuration was applied. A servo-hydraulic Instron machine was used for testing. The fracture process was monitored by optical and acoustic imaging techniques. Three forms of comparisons of the test results with respect to the specimen and aggregate sizes were adopted. The first corresponded to the various specimen sizes cast with the same maximum aggregate size. The second comparison was based on the geometrically identical specimens cast with various maximum aggregate sizes. The third form of comparison dealt with complete geometrical similarity, i.e., all dimensionless geometrical characteristics including specimen thickness to maximum aggregate size ratio were identical. Results from this study indicated that as the specimen size decreases, the envelope becomes larger within the first and third forms of comparison. In the second form of comparison, i.e., geometrically identical specimens cast with various maximum aggregate sizes, the area under the envelope was greater as the maximum aggregate size increased. The existence of a trend in dimensionless critical load-CMOD envelopes despite the apparent geometrical and physical similarity of the test conditions is the direct indication of a scale effect, i.e., the modified fracture energy, $$\overline {G_F } $$ indicates the existence of a strong scale effect: $$\overline {G_F } $$ increases with the specimen dimensions as well as maximum aggregate size.

Influence of stress state on high cycle fatigue of notched Ti-6Al-4V specimens

The high cycle fatigue (HCF) notch size effect is investigated for Ti-6Al-4V flat dogbone specimens with two notch sizes, each having an elastic stress concentration factor of K t=2.72. Points were generated on a constant life Haigh diagram using a step-loading technique. The notch size effect is compared with previous results obtained from circumferentially notched cylindrical specimens in terms of the biaxial state of stress at the notch root and von Mises effective stress. Within the range of dimensions tested, there is limited dependence of the fatigue limit upon the notch root radius. Stresses at the notch root and the fatigue notch factor are examined as a function of uniaxial stress, effective stress, notch plasticity, and notch root radius.

Notch size effects in HCF behavior of Ti–6Al–4V

The high cycle fatigue (HCF) behavior of Ti–6Al–4V is investigated for cylindrical specimens having three sizes of geometrically similar circumferential V-notches, each with an elastic stress concentration factor, K t , of approximately 2.78. A step loading technique for obtaining a point on a constant life (10 6 cycles) Haigh diagram from a single test specimen was implemented. Tests were performed at stress ratios of R=0.1, 0.5, and 0.8 for specimens machined from two different product forms of Ti–6Al–4V, bar and plate forgings. Results indicate that while there is a definite notch size effect in the Ti–6Al–4V bar within the range of notch sizes tested, little or no such effect exists in the plate.

FATIGUE LIMIT OF BLUNT‐NOTCHED COMPONENTS

The position and effective resistance of microstructural barriers and their relation to the fatigue strength of blunt‐notched specimens are analysed and modelled for three low‐carbon steel microstructures. A relationship for the notch size effect on the basis of the experimental evidence that the fatigue limit (both plain and notched) represents the threshold stress for the propagation of the nucleated microstructurally short cracks, was derived. The derived relationship characterizes the fatigue notch sensitivity by means of the parameter ktd 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, and was experimentally verified for two notch geometries in three microstructures: ferrite, ferrite–bainite and bainite–martensite.

An experimental study of the effect of a flaw at a notch root on the fatigue life of cast Al 319

Smooth and notched specimens of a 319 cast aluminum alloy containing casting defects were fatigue tested in the as cast and hipped conditions. Hipping is a process in which the material is subjected to a high pressure at high temperature to eliminate flaws and then slowly cooled. The materials were tested under fully reversed constant amplitude loading and under a variable amplitude load history consisting of underloads followed by constant amplitude small cycles. The stress ratio and the number of constant amplitude small cycles following an underload were adjusted so that the crack did not close and remained fully open for all the small cycles. Three notch sizes of 1.0 mm, 3.0 mm and 6.0 mm in diameter, with a natural flaw at the center of the notch root, were examined under constant and variable amplitude loading. In another series of tests the natural flaws in the as cast material were modeled in the hipped material by a notch made with a circular drill at the notch root. The fatigue lives observed showed the following: 1. A notch size effect is observed for notched as cast and hipped Al 319 specimens having a 0.6 mm diameter flaw at notch root under constant and variable amplitude loading. The fatigue limit stress ranges for hipped Al 319 under constant amplitude loading were 117 MPa, 90 MPa, and 80 MPa for 1.0 mm, 3.0 mm, and 6.0 mm diameter edge notches respectively. The corresponding values under variable amplitude loading were 25 MPa, 18 MPa, and 8 MPa. 2. The effect of natural flaws or casting defects, on fatigue strength, in the 319 cast aluminum alloy can be modeled by a drilled hole of the same size. A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behavior of the cast aluminum material under variable amplitude loading. In calculating the fatigue life of the cast aluminum, the flaw was modeled by a spherical cavity having the same diameter as the natural flaw. The size and location of the flaw at the notch root were varied to examine their effect on fatigue life. Fatigue life predictions were in good agreement with the experimental results.

The influence of variable amplitude loading on crack closure and notch fatigue behaviour

Smooth and notched 1045 steel specimens were tested under constant amplitude, R = −1 loading and under a variable amplitude load history consisting of periodic overloads followed by high R-ratio small cycles. The notched specimens exhibited a notch size effect under constant amplitude loading, but the effect was reduced in the long life region (defined as a fatigue life > 10 7 cycles) under the variable amplitude load history. A crack growth model that followed crack closure changes on a cycle-by-cycle basis adequately predicted fatigue life for the periodically overloaded notched specimens.

Evaluations of effective crack growth and residual strength of fibre-reinforced metal laminates with a sharp notch

The main objective of this study was to evaluate the residual strength of fibre-reinforced metal laminates with a sharp notch by means of an effective crack growth model (ECGM). Damage is assumed to be initiated when the local normal stress ahead of the notch tip reaches the tensile strength of the composite and the yield strength of metal layers, respectively. The damage in constituent materials was modelled by fictitious cracks with cohesive stress acting on the crack surfaces, and the damage growth was simulated by extension of the fictitious cracks and reduction of the cohesive stress with crack opening. The apparent fracture energy of composite layers and fracture toughness of metal layers was used to define the relationships between the tensile/yield strength and the critical crack opening. On the basis of global equilibrium, an iterative technique was developed to evaluate the applied load required to produce the damage growth. The residual strength of notched fibre-reinforced metal laminates was defined by instability of the applied load with damage growth. The effect of notch size on the residual strength evaluation was studied and the stress redistribution with damage growth was discussed. The residual strength simulated from ECGM correlated well with experimental data in the literature for the various ARALL laminates with a centre crack. The results indicate that stable crack growth occurs in both aluminium and composite layers before unstable fracture of the whole laminate.

Strength and Damage Mechanisms of Notched Two-Dimensional Triaxial Braided Textile Composites and Tape Equivalents Under Tension

The unnotched and notched (open hole) tensile strength and failure mechanisms of two-dimensional (2D) triaxial braided composites were examined. The effect of notch size and notch position were investigated. Damage initiation and propagation in notched and unnotched coupons were also examined. Four different fiber architectures were considered; braid angle, yarn and braider size, and percentage of longitudinal yarns, and braider angle varied. Tape laminates equivalent to textile composites were also constructed for comparison. Unnotched tape equivalents were stronger than braided textiles but exhibited greater notch sensitivity. Notched textiles and tape equivalents have roughly the same strength at large notch sizes. Two common damage mechanisms were found: braider yarn cracking and near notch longitudinal yarn splitting. Cracking was found to initiate in braider yarns in unnotched and notched coupons, and propagate in the direction of the braider yarns until failure. Longitudinal yarn splitting occurred in three of four architectures that were longitudinally fiber dominated. Damage initiation stress decreased with increasing braid angle.

On the variability of strength to toughness ratio in zirconia-alumina composites

In his review of available flexure strength/fracture toughness (S/K~c) results for ceramic matrix composites, Rice [1] found it useful to relate the S/KI~ ratio of these materials to their microstructures, in particular to the volume fraction of the dispersed phase. In some gr0ups of composites, more detailed analysis of S/Klc plots turned out to be difficult due to significant scatter of the data, as shown in Fig. 1 for ZTA materials. The main reason for this scatter is believed to be the fact that different researchers used different measuring techniques and sample sizes for determination of mechanical properties, in particular the fracture toughness. The technique of measuring fracture toughness was shown to affect the calculated S/KIo values in at least one systematically analysed case of non-transformation toughened particulate composite [2]. In ZTA materials the most significant differences are known to appear between the fracture toughness values measured by single edge-notched beam (SENB), indentation fracture (IF) and indentation strength in bending (ISB) techniques [3-5], not only due to the effects of notch size and shape [4], but also due to mostly undefined local notch/indent tip transformation in non-annealed samples [5]. Rice suggested in his analysis [1] that to some extent the variability of

Notch fatigue behaviour as influenced by periodic overloads

The fatigue behaviour of centre-notched specimens of a 2024-T351 aluminium alloy is examined under a variable-amplitude loading sequence consisting of a periodic compression-tension overload of yield magnitude followed by smaller high stress ratio cycles. It is found that the effects of both overloads and notches can act simultaneously to reduce severely the fatigue strength of notched specimens and that the notch-size effect that is typically observed under constant-amplitude loading is reduced by periodic overloading. This is attributed to the absence of crack closure in the loading sequence examined. A crack growth model is developed to predict the fatigue life of notched specimens subjected to periodic overloads.

Effect of Notch and Grain Size on the Fatigue Strength of Cast Stainless Steel.

Rotating bending fatigue tests were carried out on the notched specimens of cast stainless steels. We prepared fine and coarse grain size materials in order to investigate the effect of grain size on the notched fatigue strength. The main results are summarized as follows : (1) The notch radii of the branch point ρ0 are nearly 0.3 mm, independent of grain size. (2) The master curves of Ktσw2 vs 1/ρ of the two materials are nearly equal, but the master curve of Ktσw1 vs 1/ρ of fine-grain-size material is somewhat higher than that of coarse-grain-size material. (3) When the notch radius is larger than about 2.5 mm, the notched fatigue strength of cast stainless steels decreases by the effect of a microshrinkage cavity.

Effect of Notch on Failure of Two-Dimensional ±45° Triaxial Braided Textile Composite Materials

The unnotched and notched (open hole) tensile strength and failure mechanisms of two-dimensional (2-D) triaxial braided composites are examined. The effects of notch size and notch position within the macroscopically nonhomogeneous textile material are investigated. Damage initiation and propagation in notched and unnotched coupons are also examined. Two different fiber architectures are considered, both of similar braid geometry but one with larger longitudinal yarns (approximately six times) and larger percent of longitudinal yarns (approximately four times). The 2-D braided coupons exhibited notch and notch position sensitivity that were architecture dependent. Notch sensitivity occurred in coupons with notch size greater than the unit cell size and increased with hole diameter. Results suggested notch position sensitivity in one of the architectures tested. Cracking was found to initiate in braider yarns in unnotched and notched coupons, and to propagate in the direction of the braider yarns until failure. Fracture occurred along the braider yarn in both architectures but differed in size and appearance, suggesting architectural influences on damage mechanisms. Our results show the damage initiation and propagation is most likely to occur within the braider yarns.

Notch-size effects in fatigue based on surface strain redistribution and crack closure

A fracture mechanics solution for the stress range at the fatigue limit and the depth of non-propagating cracks in smooth and notched specimens is presented. The solution is based on the non-uniformity of strains at the surface of a specimen and on the development of crack closure. Surface grains oriented for easy slip experience an inherent microstructurally dependent strain concentration, which decays with depth into the material at a rate that is inversely proportional to the grain size. For cracks in smooth specimens the threshold stress range is separated into a crack opening stress component and an intrinsic stress component. The latter is the stress range that is just sufficient to grow a fully open crack and it is estimated by considering the near-surface strain concentration for a variety of crack depths. The crack opening stress range is added to the intrinsic component to obtain the nominal threshold stress range as a function of crack depth. The maximum threshold stress range defines the fatigue limit of the specimen. For notched specimens a geometrical strain concentration is considered in addition to the inherent strain concentration. The predicted fatigue limits agree well with the observed values for a variety of notch sizes and stress ratios in the aluminium alloy 2024-T351. The proposed solution also offers a prediction for the depth of non-propagating cracks wa both smooth and notched specimens. In the latter, the depth of non-propagating cracks was found to be dependent on the notch radius and the stress level. The predictions of non-propagating crack depths agree with the experimental data for the aluminium alloy BSL65.

Features of mechanics of quasi-brittle crack propagation in concrete

Physical observations of crack propagation in concrete are discussed in the present paper. Based on these physical observations, different models proposed for mode I fracture of concrete are examined. In the past, verification of validity of fracture models has always been difficult. It is proposed that notch sensitivity and size effect be used as criteria to evaluate the validity of fracture models. In addition, a successful model should also satisfy a ‘portability’ condition, namely the model should be applicable to structures of an arbitrary geometry. Discussion on the effects of different loading conditions, i.e. mixed-mode loading conditions and different loading rates, on the fracture process in concrete is also presented.