Net Section Stress Research Articles

Surface crack propagation in plate specimens of 1Cr-1Mo-1/4V turbine rotor steel under creep-fatigue condition.

It is important to know the crack propagation behavior under creep-fatigue condition in order to insure the security of high temperature components. In this study, crack propagation tests were conducted using two sizes of plate specimens of a 1Cr-1Mo-1/4V forged steel with a through or surface crack at 550°C. Regardless of the specimen size and crack shape, the crack propagation rate was correlated well with creep J-integral range, whereas it was not with elastic stress intensity factor nor net section stress. A numerical simulation method was successfully developed for the surface crack propagation on the basis of the relationship between crack propagation rate and creep J-integral range.

A new method for measuring dynamic fracture toughness of rock

In the presence of extensive non-linearity followed by notch-induced plasticity, without subcritical crack growth, the stress at which crack spreading occurs from a hole is predicted using the unnotched strength and parameters computed from the load-displacement record, namely the applied energy, the initial slope of the load-displacement record and the non-linearity index. Thus the applied energy coupled with the non-linearity index and slope of the initial portion of the load-displacement record can be successfully used for design purposes when holes are present in structural members. The fracture parameters are also expressed in non-dimensional form using the net section stress and this is found to be a linear function of notch parameter, which is defined as the ratio of notch diameter to specimen width, w. This makes its application to design purposes simple, once the load-displacement record is established. Experimental investigations agree quite well with the theoretical predictions.

摩擦圧接継手の耐破壊性能について Ｓ４５Ｃの摩擦圧接継手の場合

In order to determine the requisite value of toughness for friction welded joints on the basis of fracture mechanics, Charpy impact test and fracture toughness test were carried out at various temperatures on the friction welded butt joints composed of carbon steel JIS. S45C and the base metal.The experimental results indicated that the Charpy absorbed energy of the friction welded joints was almost equal to that of the base metal in the temperature range below room temperature, while the absorbed energy of the joints was about a half of those for the base metal above room temperature. The fracture toughness of the friction welded joints increased with an increase in temperature, but the toughness was slightly lower than those of the base metal over the whole temperature range. Particularly, in the temperature range above 185K, the value of the net section stress σnet for fracture of the joint was higher than the 0.2% proof stress of the base metal.When the transition temperature for the Charpy absorbed energy was compared with that for the fracture toughness, the former was much higher than the latter. This suggests that the fracture toughness for the joints is high enough, even when the Charpy absorbed energy is low. Furthermore, the usable critical stress for the friction joints with circumferential or penny-shaped cracks was estimated for various kinds of specimen size and temperature based on the experimental results of fracture toughness.

Investigations on the influence of internal nitridation on creep crack growth in alloy 800 H

For two batches of Alloy 800 H with Al contents of 0.02 and 0.34 pct, creep crack growth was investigated at 1000 °C in air and in an Ar-5 pct H2 atmosphere. TheK concept, the net-section stress concept, and theC* concept of creep fracture mechanics were applied when plotting the experimental results. TheC* concept proved to give the best correlation between load parameter and crack growth rate. A good agreement was observed between the experimental results and the model calculations for crack extension by constrained diffusive cavity growth. Strong internal nitridation, which occurred in the air tests and which had been shown to increase the creep strength in creep rupture tests, did not show any significant influence on the creep crack growth rate in comparison with tests in an Ar-5 pct H2 atmosphere, in which no internal nitridation was observed. Also, the differences in the Al contents of the two batches did not play a role. This behavior is explained by the fact that neither the nitride particles nor the particle matrix interface is a particularly weak site in the material. It also becomes obvious that theC* concept can be rather insensitive to precipitation strengthening effects, if these only affect the parameterB in Norton's creep law.

Failure of cracked engineering structures: Fracture mechanics or flow stress controlled

The paper demonstrates that, as the material toughness increases, failure of a cracked engineering structure progressively changes from being fracture mechanics controlled to being primarily flow stress controlled. This means that provided the toughness is sufficient, failure, even though it occurs by the onset of fracture at a crack tip followed by stable (and then unstable) crack propagation, can be predicted via classic limit-load theories using an appropriate value for the net-section stress across the uncracked section. Although the appropriate net-section stress is not unique for a given material, but depends on the geometrical configuration under consideration, nevertheless for practical purposes uniqueness may be assumed when making failure predictions. The net-section stress methodology is appropriate if the imposed deformations are load-controlled, but is conservative when these deformations are displacement-controlled; in this case failure of a structure is critically dependent on its elastic flexibility.

Use of Neuber's rule to estimate the fatigue life of notched specimens of ASME SA 106-B steel piping in 288°C air

Fatigue strain-life tests were conducted on notched specimens of ASME SA 106-B piping steel at PWR operating temperatures (288°C (550°F)), under completely reversed loading. Fatigue limits at 10 7 cycles were estimated for smooth specimens to be 185 MPa (26·8 ksi) at 24°C and 232 MPa (33·7 ksi) at 288°C. The higher fatigue strength observed at the PWR temperature is postulated to be caused by dynamic strain aging processes. However, a reduction in fatigue strength in the low cycle fatigue regime was observed in 288°C air environment tests, which may indicate that the current ASME Section III design curve for carbon steels is nonconservative in its positioning. Notch strain histories were estimated for the notched specimen tests using various interpretations of Neuber's rule. It was concluded that the use of the fatigue notch concentration factor (K f) in the Neuber relation in conjunction with the uniaxial cyclic stress-strain curve provided the best correlation of notched specimen fatigue data with results obtained from smooth sp̀ecimen tests. The notched specimen strain-life results derived from the application of Neuber's rule alone proved to be conservative when compared with smooth specimen test results to such an extent that Neuber-generated notch stresses and strain amplitudes cannot accurately be compared with the mean data curves derived from the ASME Section III fatigue curves for carbon steels which are based on net section stress measurements.

Evaluation of JAERI's ductile pipe fracture test results on stainless steel and carbon steel piping

At JAERI a ductile pipe fracture test program has been conducted as part of a piping integrity and safety research program on LWRs. In the program the ductile pipe fracture behavior of piping under 4-point bending load without internal pressure has been investigated using 3-, 6-, 12-inch diameter stainless steel and 6-inch diameter carbon steel pipes with a through-wall or a part-through circumferential crack in the inner surface of the test pipes. In this paper are described the evaluation of the pipe test data with respect to the validity of net-section stress approach and the flaw acceptance criteria of ASME code Sec.XI, IWB 3640. Pipe fracture data are also used to evaluate the critical conditions at the onset of an unstable ductile pipe fracture under displacement controlled bending load, and a procedure is presented to evaluate the stability of the piping system against unstable ductile fracture using empirical expressions of pipe fracture data.

Influence of material properties and geometry on the limit load behaviour of flawed structures

On the basis of previous results, 1 two effects are discussed which may raise the actual plastic limit load of a structure above a lower bound limit load estimated according to plasticity theory. A database has been used that includes more than 1200 fracture mechanics experiments performed by many industrial companies and research institutions. A wide variety of specimen shapes, as well as pressure vessel and piping components, which were made of ferritic and austenitic steels common to nuclear power plant applications, have been evaluated. Firstly, finite element calculations as well as simple plastic limit load evaluations show that the strain hardening capacity of the material does not in general raise the flawed structure's ultimate load such as to reach a net section stress equal to the mean of yield and ultimate tensile strength. Secondly, many of the tests reveal that the anticipated gain due to increasing triaxiality of stress state with bigger structures (stress hardening), which has sound theoretical backing, is actually zero. Hence, upon applying the method of plastic limit loads to assess the integrity of flawed structures, the analyst is well advised to consider only the yield strength and the state of plane stress.

Effect of temperature on crack growth in type 304 stainless steel

Investigations have been carried out to study crack growth behaviour in type 304 stainless steel under constant-load creep conditions in the temperature range 550–650°C. At 550 and 600°C the load point deflection rate bears a unique relation to the creep crack growth rate, independent of the load. However, the results at 650°C show that the relation is load dependent. The parameters, stress intensity factor and net section stress, do not describe the crack growth rate well and there is wide scatter. The energy rate line integral C ∗ appears to be applicable at 550 and 600°C but not at 650°C where it gives a systematic segregation of data. On the basis of a phenomenological approach a new parameter is derived which appears to correlate well with the creep crack growth at all the three temperatures investigated. This approach also provides an index which can differentiate between creep brittle and creep ductile materials.

Failure prediction of low-carbon steel pressure vessel and cylinder models

The failure loads predicted by failure assessment methods (namely the net-section stress criterion; the EPRI engineering approach for elastic-plastic analysis; the CEGB failure assessment route; the modified R6 curve by Milne for strain hardening; and the failure assessment curve based on J estimation by Ainsworth) have been compared with burst test results on externally, axially sharp notched pressure vessel and open-ended cylinder models made from typical low-carbon steel St45 seamless tube which has a transverse true stress-strain curve of straight-line and parabola type and a high value of ultimate strength to yield. It was concluded from the comparison that whilst the net-section stress criterion and the CEGB route did not give conservative predictions, Milne's modified curve did give a conservative and good prediction; Ainsworth's curve gave a fairly conservative prediction; and EPRI solutions also could conditionally give a good prediction but the conditions are still somewhat uncertain. It is suggested that Milne's modified R6 curve is used in failure assessment of low-carbon steel pressure vessels.

J-Integral and Crack Opening Displacement as Crack Initiation Criteria in Rubber

Abstract 1. Evaluation of ∫σdδ where σ is the net section stress and δ is the deformed crack tip diameter requires only one specimen to characterize the initiation of crack growth in unfilled and carbon-black-filled NR. 2. ∫σdδ is equal to one half of the J-integral for crack growth initiation, which is identical to the Thomas tearing energy for a blunt notch. 3. The critical J-integral for crack initiation increases linearly with carbon black content. 4. The critical crack tip radius for crack initiation is independent of carbon black content, and the required crack tip region stress increases linearly with carbon black content.

The effect of a superimposed compressive load on the failure of a stainless steel pipe containing a through-wall circumferential crack: Part I: Bending deformation is load-controlled

A net-section stress failure criterion is currently used to determine the critical size of circumferential crack for austenitic stainless steel as used in nuclear reactor piping systems. The acceptable crack size for prescribed applied loadings is determined by assuming that failure occurs when the stress across the net-section (that is the pipe cross-section area reduced by the crack area) attains a critical value, the stress at the cracked section being calculated on the basis of the undeformed pipe configuration. However, an axial compressive load can give an increased bending moment if the stress calculation is based on the deformed pipe configuration. This paper therefore examines the effect of an axial compressive load, superimposed upon a bending load, on the failure of piping due to the presence of a through-wall circumferential crack. The results show that the failure assessment should be based on the deformed configuration even when the axial load is only a small fraction of the pipe's Euler critical load, or otherwise the net-section stress approach can give non-conservative failure predictions.

Macroscopic creep crack growth in type 316 stainless steel.: III. Application of linear and nonlinear elastic fracture mechanics

Creep crack propagation rates have been measured in Type 316 steel at 625°C and correlated in terms of linear and nonlinear elastic fracture mechanics parameters. Two differing specimen geometries from each of two different casts of steel have been used and it appears that crack growth predictions based on a net section stress correlation are preferred to those based on stress intensity factor or the creep energy rate line integral C∗. More importantly an effect of geometrical constraint has been observed, with crack propagation rates decreasing with increasing specimen constraint.

Leak before break evaluation of a plate with a surface crack subjected to tension

The thick-shell line spring method combined with the complentary energy method has been applied to the analysis of load-displacement curves and crack opening angle (COA) for work-hardening plates with a surface crack. The growth of the surface crack has been simulated based upon the COA-criterion, and the condition of the leak before break (LBB) has been discussed for a surface-cracked plate subjected to tension. It has been found that the LBB condition highly depends on the original shape of the surface crack. Short and deep surface cracks satisfy the LBB condition, while flat and shallow cracks do not. Further, the results have been compared with the net section stress criterion.

Effect of triaxial stress-state on creep fracture in Inconel alloy X-750

Smooth specimens and circumferentially notched bars with a “Bridgman” notch geometry were tested uniaxially at 700° C in air in the stress range of 340 to 700 MPa. The results indicated that the material was notch strengthened on the basis of net section stress,σa. However, when the fracture lifetimes were plotted as a function of the Bridgman effective stress,σe, all the data points fell approximately on one line. Cavity nucleation sites changed systematically from notch throat at the highest stress to notch root at the low stress. The notch rupture ductility in the notched specimens were found to have a lower value than in the smooth ones at all stresses.

Unstable crack growth in a component subject to constant applied loads. II: Effect of crack size and component width

When a crack grows slowly, by, for example, a stress corrosion mechanism, in a component that is subject to constant applied loads, it is possible that there will be a transition from slow growth to unstable non-environmentally-assisted (plastic) growth. Part I of this investigation 1 examined the plane strain deformation of a non-work-hardening solid containing two symmetrically situated deep cracks, and with tension of the small remaining ligament. The main conclusion was that the transition from stress corrosion crack growth to plastic crack growth, accompanied by instability, should not occur under constant load conditions until the general yield state is almost attained, even though a material's resistance to plastic crack growth might be only moderate. The present paper extends the earlier study by analysing the more general model of a solid of finite width containing two symmetrically situated cracks of equal depth. Irrespective of the crack size and solid width, it is shown that unstable plastic crack growth should not occur until the general yield state is almost attained, even if the plastic crack growth resistance is only moderate. The scope of the conclusion reached in Part I is therefore broadened, and the results therefore provide further support for the view that the occurrence of unstable plastic fracture under load control conditions approximately correlates with the attainment of a critical net-section stress across the remaining ligament. The results consequently provide additional underpinning for the currently used empirical net-section stress approach for predicting failure under load control conditions.

Use of the net-section stress approach for predicting the failure of thin tubes

The failure of stainless steel piping containing circumferential cracks has been predicted on the basis that crack extension occurs when the net-section stress exceeds some critical value. This paper addresses the question as to whether the net-section stress approach can be applied to the failure of thin tubes, for example Inconel steam generator tubes. The results of a theoretical analysis suggest that the approach should be applicable when it is used to predict the development of a part-through and part-circumference crack into a through-wall crack.

An approximate elastoplastic analysis of the effect of plane strain at the surface of a notch

An approximate elastoplastic analysis of a notch in plane strain is developed using an extended Neuber approach. The multiaxial stress/strain state at the notch surface is dependent upon a parameter which is readily obtained from the numerical solution of a transcendental equation for each level of the net section stress. Excellent agreement with the results of a finite element analysis of a double-edge-notched specimen was obtained.

The incorporation of displacement-controlled loadings within the net-section stress failure criterion

A net-section stress failure criterion can be used to evaluate the critical flaw size for a material having a high fracture resistance. A simple analysis shows that the stress arising from displacement-controlled loadings should be taken into account fully if the applied tearing modulus exceeds a critical value.

Fatigue life prediction of filled polypropylene based on creep rupture

AbstractTo predict the fatigue performance of talc‐filled polypropylene in engineering applications, a simple relationship using constant stress data to predict the cycles‐to‐failure (Nf) was developed: where k and n are constants from creep rupture tests, v is the cyclic frequency (≤1 Hz to avoid self‐heating), f(n) is a function that accounts for the wave form, and a is the peak cyclic stress with a zero minimum stress. For stress concentrations produced by central holes, σ is taken as the average net section stress and the effect of the stress concentration is ignored. Extensive tests were used to verify this expression for cyclic frequencies of 1.0 and 0.1 Hz, sinusoidal and triangular waveforms, stress concentrations produced by small and large holes, and 20 and 40 percent talc filler content.