Creep properties of a U‐type notch plate in Ni‐based superalloy

In the present investigation, the effect of notch on creep rupture behavior and creep rupture life of a Ni‐based superalloy has been assessed by performing creep tests on smooth and U‐notched plate specimen under 0°C. The finite element analysis coupled with continuum damage mechanics are carried out to understand the stress distribution across the notch throat and the creep damage evolution under multi‐axial stress state. The creep rupture life of U‐notched specimen is much larger than that of plane plate specimen under the same stress condition, indicating that there is a strengthening effect on notch specimen. Creep rupture life increases with increasing the notch radius, the smaller notch radius can induce the creep rupture easier. The effect of notch on the creep damage is also studied. It is found that the location of the maximum creep damage and the maximum equivalent creep strain initiates first at the notch root and gradually moves to the inside as the notch radius increases.     

Effect of notch root radius on tensile behaviour of 316L(N) stainless steel

Abstract

Type 316L(N) stainless steel (SS) is used as the major structural material for high temperature components of sodium cooled fast reactors. The influence of notch root radius on the tensile behaviour of 316L(N) SS under multi-axial stress state was investigated. Double U-notches with five different kinds of notch geometry were incorporated symmetrically into the tensile testing specimens by changing the notch root radius while keeping the gross diameter, net diameter and notch depth as the same for all the notches. The notch root radius was varied as 0·25, 0·5, 1·25, 2·5 and 5 mm. Tensile tests were carried out on the notched specimens at room temperature (298 K) and at 923 K at a constant strain rate of 3×10^?3 s^?1. The tensile strength and yield strength of notched specimen of 316L(N) SS increased with decrease in notch radius at both the temperatures and the notch severity was less pronounced at high temperature. The fractured notch surface was analysed using scanning electron microscope and unfractured notch was sliced along the axis and observed under optical microscope. Finite element analysis was performed on the models of notched specimens with various notch root radii. These results showed that Von Mises equivalent stress which was derived from triaxial stresses decreased with decrease in notch radius. The shift of location of peak values of maximum principal stress and hydrostatic stress towards the axis of the specimen, leading to formation of cracks, occurred at a lower nominal stress when the notch radius was increased.     

Investigation of blunting line and evaluation of fracture toughness under mixed mode I/III loading in commercially pure titanium

Abstract

The blunting line and fracture toughness in commercially pure titanium under mode I and mixed mode I/III loading was studied. A modified compact tension geometry was used for determining the blunting line as well as mixed mode I/III fracture toughness. The results showed that the constraint factor m in the blunting line equation under mode I loading was 1.84. Also, there was no effect of notch root radius on the slope of the blunting line. The blunting line slope under mixed mode I/III loading was found to be lower than that under mode I loading and agreed with empirical correlations. The fracture toughness under mode I loading was found to be higher for specimens with larger notch root radius. However, notch root independent fracture toughness could be obtained from blunt notch specimen tests using stretch zone width measurements. The fracture toughness was found to decrease with increasing mode III loading.     

Effect of notch root radius on fracture toughness of polycrystalline cubic boron nitride

The fracture toughness of five grades of polycrystalline cubic boron nitride (PCBN) has been determined using Single Edge V-Notched Beam specimens. Both coarse and fine grade materials were considered, containing CBN grain sizes of between 1 μm and 22 μm. The influence of notch root radius on the measured fracture toughness was examined. The notch root radius was found to have a major effect for materials with smaller CBN grain sizes while only a small effect was noted for the material with large CBN grain sizes. A simple analytical model was developed to explain the effect of the notch root radius on the fracture toughness and was found to agree well with experiment for all the materials tested. It was shown that the effect of notch root radius is directly linked to the size of the CBN grain. It is proposed that this effect results from the interaction between the microstructure and the stress field around the notch tip.     

Effect of an asymmetrical V-notch on the load carrying capacity of eccentrically loaded columns

In this paper theoretical and experimental investigations have been carried out to determine the effect of an asymmetrical V-shaped notch on the load carrying capacity of eccentrically loaded columns. The depth of the notch was kept constant whereas the notch angle, notch root radius; eccentricity of loading and length of the column was varied. It has been concluded that an asymmetrically placed V-notch decreases the load carrying capacity of the column. The load carrying capacity is not affected appreciably upto a notch angle of approx. 90°, but beyond 90° it increases. The load carrying capacity of the column also increases as the notch root radius increases but it decreases as the eccentricity of load and slenderness ratio increase.     

Asymptotic characterisation of nearly-sharp notch root stress fields

A solution procedure is developed for characterising the stress state at the root of a notionally sharp notch, but possessing a small root radius, using two nested asymptotic solutions: an outer asymptote representing a sharp semi-infinite V-notch and an inner solution representing a semi-infinite rounded notch. The two asymptotes are matched to each other remote from the notch root, and to an example finite notch using a generalised stress intensity factor. It follows that the characteristic, singular, sharp-notch field diverges from the rounded-notch solution very near the root. On the other hand, the notch in a finite body diverges from the sharp semi-infinite notch in the far field. Providing that the notch root radius is sufficiently small, it follows that there is an intermediate field where the singular field does characterise the behaviour of the finite radiused notch, and this is quantified.Note that this topic has also been investigated in the very recent literature by Gomez and Elices (2004) for brittle components, using the same analytical frame presented here     

Effect of notch root radius on fracture toughness of Ti–18Al–8Nb alloy

Abstract

The effect of notch root radius on the mode I fracture toughness of Ti–18Al–8Nb alloy in beta solution treated and water quenched condition was investigated. The apparent fracture toughness K _IA was found to be independent of the notch root radius below a critical notch root radius ρ ₀ and subsequently increase linearly with the square root of notch root radius ρ^1/2 beyond ρ ₀. The critical notch root radius in this alloy was found to be ～50 μm. The results were explained on the basis of strain controlled fracture model.     

Effect of notch root radius on the initiation and propagation of fatigue cracks

Under the conditions of constant nominal applied stress, increasing notch root radius causes an increase in the number of cycles to initiate a fatigue crack at a notch root. An explanation of the effect is given in terms of the effective stress concentration factor of the notch. Data are presented which indicate that variations in notch root radius may cause changes in the crack growth rate during the initial stages of propagation from a notch.     

A generalised notch stress intensity factor for U-notched components loaded under mixed mode

A novel notch stress intensity factor (NSIF) for U-notched specimens loaded under mixed mode is examined in this article. The concept is based on the averaged strain energy density criterion, or alternatively on the cohesive zone model, as well as the equivalent local mode approach. To a certain extent, it is a generalisation of Glinka’s NSIF for mode I, where σ_tip is replaced by σ_max.The applicability of a fracture criterion based on this new NSIF is checked against 171 fracture tests with PMMA (at −60 °C) performed on U-notched specimens, with different notch root radii and loaded under mixed mode. The asymptotic behaviour of the new NSIF as the notch becomes a crack (when the notch root radius tends to zero) or when the notch disappears (when the notch root radius tends to infinity) is also discussed.     

Study on creep mechanical behaviour of P92 steel under multiaxial stress state

The creep mechanical behaviour of P92 steel at 650°C has been studied by experimental research and finite element analysis. During the creep of P92 steel, there existed the notched strengthening effect, which was influenced by the shapes of the notch and the nominal stress. Under the condition of the same notch depth, the creep life enhancement factor increased with decreasing notched radius or the increase of stress. The multiaxial stress caused by the notch effect had a significant influence on the evolution of the microstructure and resulted in a transforming tendency from ductile to brittle at the root of the notch. The fracture position varied with the shapes of the notch: the U shaped notch started to fracture at the root of the notch, while the C shaped notch in the centre of the specimen. The creep process of notched specimens was simulated by embedding Kachanov–Rabotnov creep damage constitutive model into the interface program of finite element software. The result showed that damage distribution of notched specimens varied during the process of creep. The maximum damage location at the end of creep depended on the notch shape: with larger notch radius the maximum damage location was in the centre, while smaller radius of notch specimens was near the notch root, which was consistent with the analysis of the fracture morphology.     

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.     

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

The Notch Stress Intensity Factors (NSIFs) quantify the intensities of the asymptotic linear elastic stress distributions of sharp (zero radius) V-shaped notches. When the notch tip radius is different from zero, the singular sharp-notch field diverges from the rounded-notch solution in the close neighborhood of the notch tip. Nevertheless the NSIFs might continue to be parameters governing fracture if the notch root radius is small enough. Otherwise they can be seen simply as stress field parameters useful in quantifying the stress distributions ahead of the specific notch. Taking advantage of some analytical formulations which are able to describe stress distributions ahead of parabolic, hyperbolic and V-shaped notches with end holes, the paper discusses the form and the significance of the NSIFs with reference to in-plane shear loading, considering explicitly the role played by the notch opening angle and the notch tip radius. These parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case to which they should naturally tend for decreasing values of the notch radius.     

The relationship between crack tip opening displacement,local strain and specimen geometry

A method is described whereby values of crack tip opening displacement (COD) can be measured at any section of a pre-cracked or slotted specimen. The relationship between COD and the degree of transverse strain at the notch root of a Charpy specimen has been investigated. A specimen will show some portion in plane strain up to a COD of about one twenty-fifth of the thickness. Transverse contraction results in smaller COD values, for a particular clip gauge displacement, at the outside than at the specimen midsection. An equation is presented relating COD to longitudinal notch root strain for Charpy specimens with root radius 0.002 in. COD and notch root strain are found to be not directly proportional. This finding is discussed in relation to the concept of a “miniature tensile specimen” at the notch root. The effect of specimen geometry on the value of COD at fracture initiation, (COD)_c, has been investigated. Neither a change in specimen thickness nor a change from a fatigue pre-crack to a 0.002 in. root radius notch has been found to significantly affect (COD)_c. The material used in this research was, for the most part, a low alloy pressure vessel steel, A533B.     

Fracture Toughness Test with a Sharp Notch Introduced by Focussed Ion Beam

The validity of fracture toughness data obtained from tests with V-notched bending bars is affected by the notch root radius and the presence of R-curve behavior. A macroscopic test specimen has been developed that contains a notch introduced by focused ion beam machining. This produces a notch root radius of less than 0.1 μm, so that notch effects can be ignored for most ceramics. Also, due to the very small notch depths the influence of a rising R-curve should be very close to that of natural cracks. First tests, carried out on a Ce-doped zirconia ceramic resulted in a toughness of K _Ic ≈ 5.9 MPa√m.     

Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.     

陶瓷材料断裂韧性与缺口半径 Ⅱ 断裂韧性估算方法

在陶瓷材料裂纹尖端存在一个断裂过程区，当断裂过程区内平均应力达到断裂强度时，裂纹扩展。本文由理论推导结合实验数据，得到了新断裂过程区的大小是平均晶粒直径的四倍。并由平均应力断裂模型，给出了陶瓷材料断裂韧性和缺口半径及平均晶粒直径之间的关系式，由此关系式可以用宽缺口试件测出的断裂韧性去估算陶瓷材料的本质断裂韧性。     

The influence of manganese addition on mechanical properties of commercial Al‐4Mg casting alloys

The aim of this study was to investigate the mechanical properties of Al‐Mg‐Si alloys aged to peak hardness with different dispersoid volume fraction. It was found that the tensile strength increases with dispersoid content, for alloys having similar ductility. The effect of an increasingly triaxial stress state on a fracture strain above mentioned alloys were measured using a series of notched tensile specimens whose notch root radius of curvature was changed. The alloy ductility was found to increase with dispersoid content and root radius and to decrease with increased stress triaxiality. The fracture toughness of these alloys was determined as a function of dispersoid content and notch root radius of curvature. It was observed that the fracture toughness increased as the dispersoid content and the notch root radius increased. scanning electron microscope analysis of the fracture surfaces revealed that fracture mechanism was transgranular fracture with dimples formation. It is argued that optimum mechanical properties in these alloys can be achieved at about 0.5 % Mn content.     

EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS

Generally, fracture toughness and fracture stress of ceramics depend on crack length, notch root radius and grain size. These three parameters are most important when assessing the integrity of structural ceramic members and developing high-performance ceramics. A new failure criterion called the process zone size failure criterion, has been proposed based on the existence of a crack-tip process zone. Using this criterion, it is shown that theoretical values are in good agreement with many test results quoted from many papers. It is concluded that this failure criterion is useful when evaluating crack length and notch root radius problems. The effect of grain size on both the fracture toughness and on the toughening mechanism is also considered.     

Dynamic fracture toughness testing of epoxy resin filled with sio2 particles

The fracture behavior of epoxy resin used as one of electrical insulation materials is generally brittle compared with that of metals. Therefore, when epoxy resin is used as a structural material, the effect of impact loading must be taken into consideration in design. In the present study, the dynamic fracture toughness of epoxy resin filled with SiO₂ particles has been evaluated both by the absorbed energy method and by the impact load obtained from the instrumented Charpy type impact test. Therefore, the absorbed energy has been analysed to evaluate the real fracture toughness. Moreover, the influence of inertial loading on the impact load must be also considered; therefore, the dynamic fracture toughness has been evaluated by the formula taking the inertial loading effect into consideration. Thus both fracture toughness values evaluated from absorbed energy and from impact load have been compared; as a result, a good agreement has been ascertained.It is common to perform impact test on specimens with blunt notches since they are easy to be prepared. However, variation of fracture toughness with notch root radius in the brittle material cannot be ignored. Therefore, the influence of notch root radius on the fracture toughness has been examined. As a result, it has been ascertained that the variation of fracture toughness with notch root radius follows the formula presented by Williams.     

On the study of the creep damage development in circumferential notch specimens

Numerical calculations with K–R damage law have been performed to study the creep damage development in circular notch specimens under constant loading. The emphasis was placed on the roles of notch radius, material constant- and applied stress. The results show that the distributions of stresses under creep conditions are different from those of previous studies. Creep damage development and life are different for different notch specimens, and the distributions of the maximum creep damage in the minimum cross-section vary with the notch radius. The creep damage is remarkably affected by the applied stress, material parameter- and notch radius. Higher stress and tri-axial stress state parameter- can cause the creep damage to develop faster.