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.     

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.     

Modelling of damage development and failure in notched-bar multiaxial creep tests

Finite‐element predictions of creep rupture in notched specimens are presented in this work. A damage model linked to the creep strain rate and stress triaxiality has been used to predict creep life under multiaxial stress conditions and the predictions have been compared with experimental data for a C–Mn steel. Finite‐element analyses have been conducted using primary–secondary (PS) and primary–secondary–tertiary (PST) creep laws. As expected a PST analysis gives a shorter predicted rupture life than a PS analysis. An additional term was included in the model to allow for an increase in hydrostatic strain due to creep damage. The incorporation of this term improved the agreement between the experimental data and the finite‐element predictions. A further enhancement to the model was to model the initiation and growth of a sharp crack in the vicinity of the notch, through the use of a nodal release technique linked to the damage evolution. It was found that the predictions obtained using the nodal release technique were very similar to those from the PST creep model incorporating the hydrostatic damage term. The effect of mesh size has also been examined and the finite‐element predictions were seen to be quite mesh sensitive with a finer mesh generally giving a shorter predicted life.     

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.     

Creep fatigue of a directionally solidified Ni‐base superalloy – smooth and cylindrically notched specimens

Turbine blade life modelling is complicated by the presence of notches, dwells, high temperatures, thermal cycles and temperature gradients. Furthermore, directionally solidified (DS) Ni‐base superalloys are highly anisotropic. This work seeks to characterize the response of the DS Ni‐base superalloy CM247LC subjected to isothermal low cycle fatigue at either 750 or 950 °C. This study considers the effects of strain rate, dwells at the maximum temperature, and stress concentrations. Experiments were conducted under uniaxial loading on smooth and cylindrically notched round‐bar specimens in both longitudinal and transverse orientations. The location of the creep‐fatigue crack is at the maximum Hill's effective stress in the notched specimens. In addition, the notch behaviour is discussed in light of finite element analysis using an anisotropic elastic‐crystal viscoplastic material model.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

Prediction on fatigue life of U‐notched PMMA plate

In this paper, fatigue life prediction of U‐notched polymethyl methacrylate (PMMA) plate is numerically investigated based on the combination of fatigue damage mechanism and fatigue crack propagation mechanism. First, strength and stiffness degeneration criterions during the fatigue process are established on the basis of nonlinear progressive damage evolution, and the fatigue crack initiation life is estimated. Second, fatigue crack propagation phase is analysed through virtual crack closure technique. The fatigue crack propagation life before totally fracture is also predicted. Finally, finite element models of PMMA plate weakened by lateral symmetric U‐notch are built up using ABAQUS, and the total fatigue life of notched plate is calculated by combining the crack initiation life with the crack propagation life. These results will play an important role for evaluating the fatigue life of U‐notched PMMA plate.     

Notch effect on creep damage for Hastelloy C276-BNi2 brazing joint

The brazed structures have geometrical discontinuities like fillets working as notches. These notches have great effect on creep crack initiation and propagation. This paper studies the notch effect on creep damage for Hastelloy C276-BNi2 brazed joint, and the effects of notch type, notch radius and notch angle on creep damage have been investigated. The results show that the creep damage initiates in the filler metal. Different notch types bring different stress states, and generate different stress triaxialities and equivalent creep strains (CEEQs), leading to different creep damages. The maximum creep damage is generated in the notch tip for V-type notch, while the maximum creep damage is located at 0.4 mm away from the notch tip for C-type notch. For U-type notch, the location of the maximum creep damage moves from the notch tip to the inside gradually as the notch radius increases. With the increase of notch radius and notch angle, the failure time of creep damage increases for U-type and V-type notches, while it decreases for C-type notch. The creep failure is prone to happen to V-type notch because it belongs to sharp notch.     

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.     

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.     

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.     

Induced out‐of‐plane mode at the tip of blunt lateral notches and holes under in‐plane shear loading

As it is well known the Poisson's effect in a cracked plate subjected to anti‐symmetric plane loading leads to the generation of a coupled out‐of‐plane singular mode. Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by sharp V‐notches and might play a role in failure initiation phenomena of notched plates subjected to Mode II loading, especially in the presence of a large notch opening angle. Dealing with blunt notches with a large notch radius, and not just with sharp notches, the presence or not of an out‐of‐plane mode does not appear to have been systematically investigated in the past. The main aim of this work is to confirm the existence of the stress field associated with the out‐of‐plane mode (Mode O) and to describe its main features in the presence of a notch radius significantly different from zero. The analyses include U‐notches, as well as circular and elliptic holes. The strain energy density in a 3D control volume is utilized to identify the most critical zone (with respect to failure initiation) through the plate thickness at the notch tip.     

Finite element analysis of notched bar skeletal point stresses and dimension changes due to creep

In this investigation, finite element calculations have been performed to obtain the creep stress distributions generated in circumferentially notched bar test‐pieces. They have also been made to determine the relation between axial extension and notch throat diameter changes. It has been found that an approximate skeletal point can be identified where the stress state is insensitive to the power law stress dependence of creep. Consistent trends in skeletal point stress ratios to those given in an existing Code of Practice for notch bar creep testing have been obtained. Nevertheless updated values, particularly for sharp notches, are proposed and these have now been inserted into a new version of the Code of Practice. In contrast, the link between extension and notch throat diameter changes has been found to depend on the creep stress index as well as the notch geometry. It is anticipated that the analysis can be used to establish the multi‐axial creep stress deformation and rupture behaviour of materials.     

Fracture investigation of U‐notch made of tungsten–copper functionally graded materials by means of strain energy density

The averaged strain energy density over a well‐defined control volume was employed to assess the fracture of U‐notched specimens made of tungsten–copper functionally graded materials under prevalent mode II loading. The boundary of control volume was evaluated by using a numerical method. Power law function was employed to describe the mechanical properties (elasticity modulus, Poisson's ratio, fracture toughness and ultimate tensile stress) through the specimen width. The effect of notch tip radius and notch depth on notch stress intensity factors and mode mixity parameter χ were assessed. In addition, a comparison based on fracture load between functionally graded and homogeneous W–Cu was made. Furthermore, in this research, it was shown that the mean value of the strain energy density over the control volume can be accurately determined using coarse meshes for functionally graded materials.     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.     

Ratcheting‐fatigue behaviour of bainite 2.25Cr1MoV steel with tensile and compressed hold loading at 455°C

The ratcheting behaviour of a bainite 2.25Cr1MoV steel was studied with various hold periods at 455°C. Particular attention was paid to the effect of stress hold on whole‐life ratcheting deformation, fatigue life, and failure mechanism. Results indicate that longer peak hold periods stimulate a faster accumulation of ratcheting strain by contribution of creep strain, while double hold at peak and valley stress has an even stronger influence. Creep strains produced in peak and valley hold periods are noticeable and result in higher cyclic strain amplitudes. Dimples and acquired defects are found in failed specimen by microstructure observation, and their number and size increase under creep‐fatigue loading. Enlarged cyclic strain amplitude and material deterioration caused by creep lead to fatigue life reduction under creep‐fatigue loading. A life prediction model suitable for asymmetric cycling is proposed based on the linear damage summation rule.     

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.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

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.     

The role of first non‐singular stress terms in mixed mode brittle fracture of V‐notched components: an experimental study

This paper investigates the effects of the first non‐singular stress terms on the fracture assessment of sharp V‐notches under mixed mode loading. First, numerical studies have been performed on a fracture test configuration called single V‐notched ring (SVR) specimen. Then, the notch stress intensity factors as well as the coefficients of the first non‐singular stress terms, which are vital parameters in brittle fracture of V‐notched components, were calculated via a finite element over‐deterministic algorithm for a wide range of loading and geometry conditions. The obtained results demonstrate that the SVR specimen is able to provide a complete range of mode mixities from pure mode I to pure mode II loading conditions. The numerical results, next, have been converted to dimensionless parameters and are illustrated in several graphs. Indeed, these graphs can be easily employed by the engineers for rapid calculation of the corresponding notch stress intensity factors and the coefficients of the first non‐singular stress terms in the SVR specimen. The obtained fracture parameters are then submitted to the maximum tangential stress criterion to assess the effects of the first non‐singular terms on fracture behaviour of the specimen. Finally, an experimental study has been performed on the SVR specimen made of Nayriz Marble rock for two notch angles with a complete range of mode mixities. The obtained experimental data confirm the significant role of the first non‐singular stress terms. In fact, these results show that considering only the singular stress terms may induce an average error of 38% in the predicted fracture loads, which can be decreased to about 12% just by adding the contribution of the first non‐singular terms to the maximum tangential stress criterion.