Finite element analysis and experimental research on notched strengthening effect of P92 steel

Abstract

The notched strengthening effect during creep of P92 steel has been studied by finite element analysis and experimental research. It was found that there was a transforming tendency from ductile to brittle at the root of the notch and the extent of the transforming intensified with the increment of the nominal stress. It was the transforming tendency that increased the value of creep life enhancement factor. With the help of finite element software, Kachanov–Rabotnov creep damage constitutive model was embedded into the interface program and the notched specimens creep was simulated. The result has shown the Kachanov–Rabotnov model can be used to simulate the notched strengthening effect of P92 steel accurately when the material constant α?=?0·73.     

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.     

Research on elastic-plastic creep damage of notched P92 steel specimens

Creep tests were performed on P92 steel specimens with notches of three different sizes at 650 °C. The results showed that the specimens switched from exhibiting ductility to showing brittleness at their center and at the notch root under multiaxial stress, but to varying degrees. This transformation was accompanied by a decrease in the reduction in area as well as in the number of dimples in the sample cross-section. The multiaxiality had a marked impact on the precipitation of the secondary phase, with its value determining the extent of precipitation of the secondary phase at the center and the root of the notch during creep. Using finite element analysis, an elastic-plastic creep damage model is embedded into the interface program and the creep behavior of the notched specimens was simulated. The results showed that plastic deformation at the notch root can accelerate specimen damage.     

Effects of creep ductility and notch constraint on creep fracture behavior in notched bar specimens

The creep rupture life of U-type notched specimens and smooth specimens has been calculated based on the ductility exhaustion damage model using stress-dependent creep ductility. Effects of creep ductility and notch constraint on creep fracture behaviour in notched bar specimens have been investigated. The results show that the U-type notch exhibits notch strengthening effect under a wide range of stress level and notch constraint condition (notch acuity) for creep ductile materials. The lower equivalent stress in notched specimens plays main role for reducing creep damage and increasing rupture life. The rupture life of notched specimens of creep brittle materials (with lower creep ductility) decreases with the increase in stress level and notch constraint. With increasing creep ductility and decreasing notch constraint, the degree of the notch strengthening effect increases. In creep life designs and assessments of high-temperature components containing notches, the material creep ductility, notch constraint and stress levels need to be fully considered.     

Investigating creep rupture and damage behaviour in notched P92 steel specimen using a microscale modelling approach

Idealized random grains separated by pseudo grain boundaries were generated by using Voronoi tessellation to simulate the polycrystalline microstructure. Combined with finite element analyses, this approach made it possible to addressing crack initiation and progressive failure due to crack growth in notched bar geometries of P92 steel at high temperature. The calculations provided good predictions for creep rupture lives of notched specimen with different notch radii and external stress. Simultaneously, irregular crack growth shape, intergranular crack mode, and wedge cracks at triple grain interaction were captured in the model. The crack initiation positions were found to be influenced by notch radius and applied stress causing high stress triaxiality at the subgrain level. Furthermore, the preferential crack growth directions were changed as the notch varied from sharp to blunt.     

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.     

Numerical prediction of notch bluntness effect on fracture resistance of SM490A carbon steel

The present work investigates the notch radius effect on fracture resistance using the finite element (FE) damage analysis based on the multiaxial fracture strain model. The damage model was determined from experimental data of notched bar tensile and fracture toughness test data using a sharp‐cracked compact tension specimen. Then, the FE damage analysis was applied to simulate fracture resistance tests of SM490A carbon steel specimens with different notch radii. Comparison of simulated results with experimental data showed good agreement. Further simulation was then performed to see effects of the specimen size, thickness, and side groove on J‐R curves for different notch radii. It was found that effects of the specimen size and thickness became more pronounced for the larger notch radius. Furthermore, it was found that without side groove, tearing modulus for notched specimens was similar to that for cracked specimens, regardless of the notch radius.     

Fully plastic analyses for notched bars and plates using finite element limit analysis

In the present work, fully plastic analyses for notched bars and (plane strain) plates in tension are performed, via finite element (FE) limit analysis based on non-hardening plasticity, from which plastic limit loads and stress fields are determined. Relevant geometric parameters are systematically varied to cover all possible ranges of the notch depth and radius. For the limit loads, it is found that the FE solutions for the notched plate agree well with the existing solution. For the notched bar, however, the FE solutions are found to be significantly different from known solutions, and accordingly the new approximation is given. Regarding fully plastic stress fields, it is found that, for the notched plate, the maximum hydrostatic (mean normal) stress overall occurs in the center of the specimen, which strongly depends on the relative notch depth and the notch radius-to-depth ratio. On the other hand, for the notched bar, the maximum hydrostatic stress can occur in between the center of the specimen and the notch tip. The maximum hydrostatic stress for a given notch depth can occur not for the cracked case, but for the notched case with a certain radius. This is true for both bars and plates. For a given notch radius, on the other hand, the maximum hydrostatic stress increases monotonically with the decreasing notch radius.     

Research on representative stress and fracture ductility of P92 steel under multiaxial creep

Creep experiments on both plain and notched specimens were conducted at 650 °C over a stress range of 120–185 MPa. The notch strengthening effect was found to exhibit in notched specimens. By using stress components at the skeletal point, several expressions of representative stress were compared to validate their effectiveness in predicting creep rupture lives of P92 steel under multiaxial stress states. The results showed that Hayhurst representative stress was more suitable for life predictions of P92 steel. In the mean time, the relationship between the fracture ductility and multiaxiality was presented to investigate the influence of the multiaxial stress states on creep rupture behavior of P92 steel. A more reasonable prediction model was proposed, and the validity of the model was verified by experimental data.     

Research on hardness variation for P92 notched specimen creep experiment

In order to study the hardness variation of P92 steel during creep in multiaxial stress state, creep experiments of specimens with various notches were conducted under different stresses at 650°C. The hardness and microstructure changes were investigated after creep experiments. The factors related to the hardness of P92 steel notched specimens were discussed. The Kachanov-Robotnov constitutive model for the creep of P92 steel was used to calculate the stress state and damage of P92 steel notched specimens during creep. The results showed that the hardness of P92 steel notched specimens decreased with the decrease of stress level and the increase of multiaxiality. The relationship among hardness, secondary phase precipitates, multiaxiality and damage were discussed.     

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.     

Influence of temperature on multiaxial creep behaviour of 304HCu austenitic stainless steel

Effect of temperature on multiaxial creep behaviour of 304HCu austenitic stainless steel has been investigated. The multiaxiality was introduced by incorporating notches in smooth specimens. Creep rupture life increased with notch acuity ratio having a saturation/decline tendency. Notch strengthening increased with temperature, stress and notch sharpness. Multiaxial ductility decreased rapidly with notch sharpness and tended towards saturation. Fracture mode was found to change from transgranular ductile to intergranular creep depending on the stress, temperature and notch sharpness. Finite element analysis of notched specimens along with orientation imaging microscopic study was carried out to assess the deformation and damage at different normalised stress ratio. A temperature independent unique master plot for multiaxial rupture life as a function of stress has been established.     

The fracture behaviour of notched specimens of polymethylmethacrylate

The fracture behaviour of notched specimens of polymethylmethacrylate has been examined for a wide range of geometries in Charpy impact tests, and in tensile and slow bend fracture tests. It was found that the failure of the very sharply notched specimens was consistent with linear elastic fracture mechanics and defined a constant fracture toughness K _IC for a constant notch tip radius, whereas the blunt notched specimens failed at a constant critical stress at the root of the notch.     

Fracture of U-notched specimens under mixed mode: Experimental results and numerical predictions

The first part of the paper gives an account of 153 fracture tests on blunted notched specimens (with notches of root radius ranging from 0.3 to 4.0 mm), loaded under mixed mode (ranging from almost pure mode I to mode II, and beyond). Maximum loads and initial crack angles were measured as a function of notch root radius and loading mixity. Such results can help in evaluating numerical models of the fracture of notched components. The second part of the paper deals with the suitability of the cohesive crack concept for predicting fracture loads under mixed mode. Use of local mode I was considered for numerical computations. Comparison of experimental results with numerical predictions was significantly accurate. Diagrams of fracture loci for notched components loaded under mixed mode are discussed.     

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.     

Isochronous creep rupture loci on deviatoric plane and its application to P92 steel creep behaviour under multiaxial stress state

The transformation relationship of the coordinate variables between principal stress space and deviatoric stress plane has been deduced and the isochronous creep rupture loci of disparate criteria have been described on deviatoric stress plane so as to analyze the creep behaviour under multiaxial stress state. The creep experiments of P92 steel smooth and notched specimens subjected to various stresses at 650 °C have been conducted. A modified constitutive model for the creep of P92 steel has been proposed and used to simulate the creep of P92 steel notched specimens with FEA software. The FEA results were consistent with the experimental data and the fracture morphology observation. It was found that the Hayhurst criterion had the best correlation with the experimental results of P92 steel under multiaxial stress state than other criteria through the comparison of the isochronous creep rupture loci on deviatoric plane.     

Effects of ferrite grain size, notch acuity and notch length on brittle fracture stress of notched specimens of low carbon steel

The effects of ferrite grain size, notch acuity and notch length on brittle fracture stress and fracture toughness of notched specimens were experimentally studied at −196°C for a low-carbon steel.

For the case of smaller notch root radius, fracture stress and fracture toughness are not so much conspicuously affected by ferrite grain size. The effect of ferrite grain size will increase with increase of notch root radius. Fracture stress and fracture toughness will decrease with increase of d^−1/2 (d = grain size diameter) a smaller range of d^−1/2, and increase nearly linearly with increase of d^−1/2 in larger range of d^−1/2, and, thus have minimum at some value of d^−1/2.     

Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500 °C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.     

Notched fatigue behavior including load sequence effects under axial and torsional loadings

Notch effects on axial and torsion fatigue behaviors of low carbon steel were investigated. Fully-reversed tests were conducted on thin-walled tubular specimens with or without a transverse circular hole. A shear failure mechanism was observed for both smooth and notched specimens and under both axial and torsion loadings. The notch effect was more pronounced under axial loading, in spite of higher stress concentration factor in torsion. The commonly used nominal S–N approach with fatigue notch factor in conjunction with von Mises effective stress resulted in overly conservative life predictions of both smooth and notched torsion fatigue lives. Neuber’s rule yielded notch root stress and strain amplitudes close to the FEA results for both axial and torsion loadings. The local strain approach based on effective strain obtained from Neuber’s rule or FEA resulted in poor correlation of the fatigue life data of smooth and notched specimens. The Fatemi–Socie critical plane parameter represented the observed failure mechanism and resulted in very good correlations of smooth and notched specimens fatigue data under both axial and torsion loadings. In block loading tests with equal number of alternating axial and torsion cycles at the same stress level, beneficial effect of axial loading was observed. Possible potential reasons for this unexpected behavior are discussed.