In this paper, the high-temperature constitutive behaviour of an additively manufactured ductile nickel-based superalloy is investigated and modelled, with application to thermomechanical fatigue, low-cycle fatigue and creep conditions at temperatures up to 800°C. Thermomechanical fatigue tests have been performed on smooth specimens in both in-phase and out-of-phase conditions at a temperature range of 100−800°C, and creep tests at 625°C, 700°C, 750°C and 800°C. Additionally, low-cycle fatigue tests at different strain ranges and load ratios have been performed at 700°C, and tensile tests have been performed at 600°C, 700°C and 800°C. A clear anisotropic mechanical response is obtained in the experiments, where the anisotropic effects are larger at high stress levels in creep loadings. To capture this behaviour, a rate-dependent strain based on a double-Norton model has been adopted in the model, by which the creep and mid-life response of the thermomechanical fatigue tests can be simulated with good accuracy.

This is the second volume of the concurring series of Reports in Applied Mechanics, which is based on the outcome of the advanced project course TMPM10 in Applied Mechanics at Linköping University during the autumn of 2023. The course lay-up is based on several industrial or in-house research related projects within the field of Solid Mechanics concerning fatigue, topology optimisation, structural dimensioning, contacts etc, and Fluid Mechanics concerning fluid dynamics, flow, aerodynamics, heat transfer etc. The students tackle industry or forefront research relevant projects in close collaboration with industry from near and neighbouring regions or the university and work in project groups to solve the given tasks within the time limit of the course. Close collaboration with the industry is necessary to define planning, update and feedback for further evaluation at the industry. This year there were a total of six projects performed during the course of 2023, four within Solid Mechanics and two in Fluid Mechanics. Some projects were performed in tight collaboration with industry partners, and had a close application to real industrial problems. The other were related to in-house research projects, pushing the research front forward. This has been a good opportunity for the students to show-off all their gained knowledge and apply it in the best possible way to make innovative solutions in the respective projects. Something they all managed to do with success!

The crack initiation life of a ductile additively manufactured nickel-based superalloy is studied and modeled for low-cycle fatigue and thermomechanical fatigue conditions up to 600 degrees C. Isothermal experiments were performed on smooth specimens at temperatures up to 600 degrees C with different applied strain ranges. Additionally, thermomechanical fatigue experiments at 100-450 degrees C and 100-600 degrees C were performed on smooth specimens under in-phase and out-of-phase conditions. A life prediction model accounting for the anisotropy was developed, where the temperature cycle is accounted with a Delta T$$ \Delta T $$-functionality, generating good agreements with the experiments. The model was also validated on notched specimens undergoing thermomechanical fatigue conditions at 100-500 degrees C using simplified notch correction methods.

In warm pre-stressing (WPS), the fracture resistance of cracked steel components is raised when subjected to certain temperature-load histories. WPS’s beneficial effects enhance safety margins and potentially prolong fatigue life. However, understanding and predicting the WPS effects is crucial for employing such benefits. This study utilised pre-cracked compact tension specimens made from steam turbine steel for WPS and baseline fracture toughness testing. Two typical WPS cycles were investigated (L-C-F and L-U-C-F), and an increase in fracture resistance was observed for both cycles. The WPS tests were simulated using finite element analysis to understand its effects and predict the increase in fracture resistance. A local approach was followed based on accumulative plastic strain magnitude ahead of the crack tip. Since cleavage fracture is triggered by active plasticity, the WPS fracture is assumed when accumulated plasticity exceeds the residual plastic zone formed at the crack tip due to the initial pre-load.

Using the stress intensity factor to describe the stress field around a crack has become widely adopted due to its simplicity. The stress intensity factor depends on the applied nominal stress, the crack length, and a geometrical factor. Geometrical factors can be obtained from handbook solutions or, for complicated cases, through finite element simulations. Carefully defining the geometrical factor with realistic boundary conditions is vital to obtain accurate values for the stress intensity factor. For fatigue life predictions, even a small error in the stress intensity factor may get amplified as the total fatigue life is computed through integration over thousands of crack growth increments. A commonly used specimen geometry for fatigue crack growth testing is the single-edge cracked specimen. For such a specimen, the crack on one side of the geometry introduces bending, which, to some degree, is constrained by the grips that hold the specimen in the testing rig. The effect of bending on the geometrical factor, and consequently on the stress intensity factor, is generally overlooked due to the assumption that the test rig grips are infinitely stiff. Not considering the bending effects could lead to an inaccurate evaluation of the stress intensity factor, especially for long crack lengths. This work investigated the effect of bending on the stress intensity factor for a single-edge cracked specimen. Different grip dimensions were studied to understand the degree of bending and its impact on the stress intensity factor. The work resulted in recommendations for accurately evaluating the stress intensity factor for single-edge cracked specimens.

Exploring crack growth behaviour is needed to establish accurate fatigue life predictions. Cracked specimens were tested under strain-controlled out-of-phase thermomechanical fatigue conditions. The tests included dwell times and three different minimum temperatures. Higher minimum temperature gave faster crack growth rates while the additions of dwell times showed no effects. Crack closure was observed in all the tests where the addition of dwell times and change in minimum temperature displayed little to no effect on crack closure stresses. Finite element models with a sharp stationary crack and material parameters switching provided acceptable predictions for the maximum, minimum, and crack closure stresses.

Crack closure effects are known to have a large impact on crack growth behaviour. In this work, tests were performed on Inconel 792 specimens under TMF loading conditions at 100–850 °C with extended hold times at tensile stress. The effective stress-intensity range was estimated experimentally using a compliance-based method leading to the conclusion that crack closure appears to have a primary impact on the crack growth behaviour for this material under the conditions studied. The crack closure behaviour for the tests was successfully modelled using numerical simulations, including creep.

Understanding of crack growth behaviour is necessary to predict accurate fatigue lives. Out-of-phase thermomechanical fatigue crack propagation tests were performed on FB2 steel used in high-temperature steam turbine sections. Testing results showed crack closure where the compressive part of the fatigue cycle affected crack growth rate. Crack closing stress was observed to be different, and had more influence on the growth rate, than crack opening stress. Crack growth rate was largely controlled by the minimum temperature of the cycle, which agreed with an isothermal crack propagation test. Finite element models with stationary sharp cracks captured the crack closure behaviour.

Additive manufacturing (AM) offers new possibilities in gas turbine technology by allowing for more complex geometries. However, the fatigue performance, including crack initiation and crack propagation of AM gas turbine material, is not fully known. In addition, AM materials shows anisotropic properties due to the columnar grain growth in the building direction during the AM process, which needs to be accounted for. Also, an AM component often solidifies with a cellular dendritic structure during the manufacturing process. In the present study, the bulk material of an AM adopted nickel-based superalloy based on Hastelloy X was subjected to low-cycle fatigue (LCF) loading at room temperature. The LCF tests were conducted in strain control on additively manufactured smooth bars,with two different build orientations (with an angle of 0° and 90° relative to the building platform). The LCF results showed that the major part of the fatigue life is spent in the crack initiation phase, namely 78% to 99% of the total fatigue life. Based on the experiments, a model to predict the crack initiation life was developed that takes the anisotropic material behaviour into account. The last part of the fatigue life, the crack propagation phase, was studied on a microstructural level, where initial fractography of the ruptured LCF specimens revealed that the dendritic structure was visible on the fracture surface. It was noted that the dendritic structure could easily be mistaken for regular striations although they represent a different fracture mechanism. The fracture surfaces were therefore cross sectioned and possible correlations between fracture surface characteristics and underlying microstructure were studied using electron backscatter diffraction and electron channelling contrast imaging. The outcome showed that the dendritic structure had some effect on the LCF crack propagation behaviour by interdendritic tearing, which was discussed.

Materials made for modern steam power plants are required to withstand high temperatures and flexible operational schedule. Mainly to achieve high efficiency and longer components life. Nevertheless, materials under such conditions experience crack initiations and propagations. Thus, life prediction must be made using accurate fatigue models to allow flexible operation. In this study, fully reversed isothermal low cycle fatigue tests were performed on a turbine rotor steel called FB2. The tests were done under strain control with different total strain ranges and temperatures (20 °C to 625 °C). Some tests included dwell time to calibrate the short-time creep behaviour of the material. Different fatigue life models were evaluated based on total life approach. The stress-based fatigue life model was found unusable at 600 °C, while the strain-based models in terms of total strain or inelastic strain amplitudes displayed inconsistent behaviour at 500 °C. To construct better life prediction, the inelastic strain amplitudes were separated into plastic and creep components by modelling the deformation behaviour of the material, including creep. Based on strain range partitioning approach, the fatigue life depends on different damage mechanisms at different strain ranges at 500 °C. This allows for the formulation of life curves based on either plasticity-dominated damage or creep-dominated damage. At 600 °C, creep dominated while at 500 °C creep only dominates for higher strain ranges. The deformation mechanisms at different temperatures and total strain ranges were characterised by scanning electron microscopy and by quantifying the amount of low angle grain boundaries. The quantification of low angle grain boundaries was done by electron backscatter diffraction. Microscopy revealed that specimens subjected to 600 °C showed signs of creep damage in the form of voids close to the fracture surface. In addition, the amount of low angle grain boundaries seems to decrease with the increase in temperature even though the inelastic strain amplitude was increased. The study indicates that a significant amount of the inelastic strain comes from creep strain as opposed of being all plastic strain, which need to be taken into consideration when constructing a life prediction model.