139 research outputs found
Multiscale analysis of thermomechanical stresses in double wall transpiration cooling systems for gas turbine blades
No full textDouble wall transpiration cooling (DWTC) is a new technology that allows the gas turbine inlet temperatures to be increased beyond current levels to promote higher engine efficiency. DWTC systems consist of outer hot and inner cooler walls, connected by pedestals, which contain film cooling and impingement holes, respectively. In order to employ these new systems, an evaluation of the stresses that drive fatigue and ratchetting at critical stress raisers is essential. We present a modelling framework which combines Computational Fluid Dynamics (CFD)-heat transfer solutions for the temperature field in DWTC systems, with theoretical and Finite Element (FE) elastic solutions for the thermal (T) stress and centrifugal (CF) stress fields. We demonstrate that uniaxial tensile CF loading causes much higher stress concentration factors (SCF) at cooling holes and wall-connecting pedestals than the thermally induced biaxial stresses. A theoretical framework is developed, supported by FE studies, that captures the dependence of the SCF on important geometric parameters, such as wall thicknesses, pedestal height and hole size, spacing and inclination angle, which provides important information for the optimisation of these systems. A key observation of relevance to both conventional and non-conventional turbine blade designs, is that the superposition of tensile CF stresses to compressive T stresses is beneficial for the performance at the critical film hole features; for double wall blades, however, the superposition degrades the performance at impingement holes and pedestals, as in these locations the T stresses are also tensile. These stresses can be balanced by using an optimal wall thickness ratio. Our elastic solutions can be readily used in analyses for predicting structural ratchet boundaries based on shakedown theory and the local cyclic strain range that drives thermomechanical fatigue in DWTC systems
On the evaluation of the Bauschinger effect in an austenitic stainless steel—The role of multi-scale residual stresses
No full textIn this work, a physically based self-consistent model is developed and employed to examine the microscopic lattice response of pre-strained Type 316H polycrystalline austenitic stainless steel subjected to uniaxial tensile and compressive loading. The model is also used to explain the Bauschinger effect observed at the macroscopic length-scale. Formulated in a crystal based plasticity framework, the model incorporates detailed strengthening effects associated with different microstructural elements such as forest dislocation junctions, solute atoms and precipitates on individual crystallographic slip planes of each individual grain within the polycrystal. The elastoplastic response of the bulk polycrystal is obtained by homogenizing the response of all the constituent grains using a self-consistent approach. Micro-plasticity mechanisms and how these influence the Bauschinger effect are illustrated in terms of the role of residual stresses at different length-scales. Overall, predictions are in good agreement with experimental data of the Bauschinger effect and the corresponding meso-scale lattice response of the material, with the latter measured by neutron diffraction. The results demonstrate that transient softening of the material is related to residual stresses at different length scales. In addition, the (Type III) residual stress at the micro-scale slip system level extends the strain range over which the tensile and compressive reloading curves of the pre-strained material merge
An improved method to model dislocation self-climb
No full textDislocations can provide short circuit diffusion paths for atoms resulting in a dislocation climb motion referred to as self-climb. A variational principle is presented for the analysis of problems in which fast dislocation core diffusion is the dominant mechanism for material redistribution. The linear element based self-climb model, developed in our previous work [1] Liu, Cocks and Tarleton (2020 J. Mech. Phys. Solids 135 103783), is significantly accelerated here, by employing a new finite element discretisation method. The speed-up in computation enables us to use the self-climb model as an effective numerical technique to simulate emergent dislocation behaviour involving both self-climb and glide. The formation of prismatic loops from the break-up of different types of edge dislocation dipoles are investigated based on this new method. We demonstrate that edge dipoles sequentially pinch-off prismatic loops, rather than spontaneously breaking-up into a string of loops, to rapidly decrease the total dislocation energy.</div
A phase field model for the growth and characteristic thickness of deformation-induced twins
No full textDeformation-induced twinning is an important mechanism in metals with a limited number of slip deformation modes. The mechanisms for twin nucleation and growth are not completely understood, and modelling these processes is challenging because of the different length and time scales involved. Twins grow at the speed of sound up to a length of several millimetres and thickness of only a few microns. We present a phase field model for twinning, coupled with a dislocation-density based model for slip, implemented within the crystal plasticity finite element method. Softening of the critical resolved shear stress for twinning is used to reproduce the shear localisation that is typical of twin bands. Two interaction terms are introduced. The first one is a non-local term that models the interaction between residual dislocations at the twin interface and mobile dislocations in untwinned regions. The second is a local term that models the hardening of the twin system due to the presence of dislocations. By introducing these interaction terms, it is possible to reproduce a discrete pattern of twin bands after deformation. These interaction terms and interaction strength parameters determine the nucleation and spatial position of twins, twin thickness and number density of twins as a function of strain. The model is validated by comparing the simulated twin phase field with the dynamic formation of twins in tension, as measured by electron backscatter diffraction experiments on α-uranium. This model sheds light on the mechanism that determines twin growth and twin thickness. Specifically, twins stop thickening after a critical density of residual dislocations at the twin interface is reached. The interaction coefficients are interpreted in terms of the stacking fault energy in order to apply the model to different metals
A theoretical and computational investigation of mixed mode creep crack growth along an interface
No full textIn this paper, we propose a theoretical framework for studying mixed mode (I and II) creep crack growth under steady state creep conditions. In particular, we focus on the problem of creep crack growth along an interface, whose fracture properties are weaker than the bulk material, located either side of the interface. The theoretical framework of creep crack growth under mode I, previously proposed by the authors, is extended. The bulk behaviour is described by a power-law creep, and damage zone models that account for mode mixity are proposed to model the fracture process ahead of a crack tip. The damage model is described by a traction-separation rate law that is defined in terms of effective traction and separation rate which couple the different fracture modes. Different models are introduced, namely, a simple critical displacement model, empirical Kachanov type damage models and a micromechanical based model. Using the path independence of the C∗-integral and dimensional analysis, analytical models are developed for mixed mode steady-state crack growth in a double cantilever beam specimen (DCB) subjected to combined bending moments and tangential forces. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models and a scaling function (Ck) is determined in terms of a dimensionless quantity ϕ0 (which is the ratio of geometric and material length scales), mode mixity χ and the deformation and damage coupling parameters. We demonstrate that the form of the Ck-function does not change with mode mixity; however, its value depends on the mode mixity, the deformation and damage coupling parameters and the detailed form of the damage zone. Finally, we demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments for mode I and II loading conditions
A theoretical and computational investigation of mixed mode creep crack growth along an interface
No full textIn this paper, we propose a theoretical framework for studying mixed mode (I and II) creep crack growth under steady state creep conditions. In particular, we focus on the problem of creep crack growth along an interface, whose fracture properties are weaker than the bulk material, located either side of the interface. The theoretical framework of creep crack growth under mode I, previously proposed by the authors, is extended. The bulk behaviour is described by a power-law creep, and damage zone models that account for mode mixity are proposed to model the fracture process ahead of a crack tip. The damage model is described by a traction-separation rate law that is defined in terms of effective traction and separation rate which couple the different fracture modes. Different models are introduced, namely, a simple critical displacement model, empirical Kachanov type damage models and a micromechanical based model. Using the path independence of the C ∗ -integral and dimensional analysis, analytical models are developed for mixed mode steady-state crack growth in a double cantilever beam specimen (DCB) subjected to combined bending moments and tangential forces. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models and a scaling function ( C k ) is determined in terms of a dimensionless quantity ϕ 0 (which is the ratio of geometric and material length scales), mode mixity χ and the deformation and damage coupling parameters. We demonstrate that the form of the C k -function does not change with mode mixity; however, its value depends on the mode mixity, the deformation and damage coupling parameters and the detailed form of the damage zone. Finally, we demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments for mode I and II loading conditions.</p
Simulating hydrogen in fcc materials with discrete dislocation plasticity
No full textWe have performed discrete dislocation plasticity simulations of hydrogen charged microcantilever bend tests on an fcc material at realistic hydrogen concentrations. This was achieved by accounting for the near-core solute-solute interactions which was found to reduce the dislocation nucleation time and stress. Dislocation pile-ups were observed at the neutral mid plane of the cantilever, and hydrogen was found to increase the number of dislocations in the pile-ups. Meanwhile, hydrogen was observed to decrease the flow stress due to the reduced dislocation core force. This was in contrast to the first-order hydrogen elastic shielding mechanism which was found to be negligible at realistic concentrations. Local stress elevation was observed in the presence of hydrogen in simulations which included an obstacle close to the free surface of the microcantilever, indicating how hydrogen might induce premature stress controlled failure
Formation of prismatic dislocation loops during unloading in nanoindentation
No full textThe formation of prismatic dislocation loops during nanoindentation of bcc iron is simulated with discrete dislocation plasticity. Interestingly, it is not the loading phase, but the unloading phase of the test which is found to be crucial for prismatic loop formation when indenting a (001) crystal surface. In this case, prismatic loops do not form during loading, but develop as the indenter is removed, in contrast to (111) indentation where prismatic loops are nucleated almost immediately upon loading
Creep-plasticity-fatigue calculations in the design of porous double layers for new transpiration cooling systems
No full textNew porous double layer (PDL) transpiration cooling technologies can allow gas turbine entry temperatures to be increased beyond current limits towards higher engine efficiency. However, PDL systems require inclined film holes with stress concentration factors in excess of 3.8. Combination of thermoelastic Finite Element (FE) analysis with Neuber type local strain approaches gives similar cyclic strain range predictions with cyclic plasticity-creep FE analysis. Fatigue crack initiation at film holes occurs with a low number of cycles due to excessive plasticity. Our study establishes links between elastic-inelastic analyses and between material phenomena-PDL geometry and indicates pathways of improving life
A modelling framework for coupled hydrogen diffusion and mechanical behaviour of engineering components
No full textIn this paper, we propose a finite element formulation for solving coupled mechanical/diffusion problems. In particular, we study hydrogen diffusion in metals and its impact on their mechanical behaviour (i.e. hydrogen embrittlement). The formulation can be used to model hydrogen diffusion through a material and its accumulation within different microstructural features of the material (dislocations, precipitates, interfaces, etc.). Further, the effect of hydrogen on the plastic response and cohesive strength of different interfaces can be incorporated. The formulation adopts a standard Galerkin method in the discretisation of both the diffusion and mechanical equilibrium equations. Thus, a displacement-based finite element formulation with chemical potential as an additional degree of freedom, rather than the concentration, is employed. Consequently, the diffusion equation can be expressed fundamentally in terms of the gradient in chemical potential, which reduces the continuity requirements on the shape functions to zero degree, C0, i.e. linear functions, compared to the C1 continuity condition required when concentration is adopted. Additionally, a consistent interface element formulation can be achieved due to the continuity of the chemical potential across the interface—concentration can be discontinuous at an interface which can lead to numerical problems. As a result, the coding of the FE equations is more straightforward. The details of the physical problem, the finite element formulation and constitutive models are initially discussed. Numerical results for various example problems are then presented, in which the efficiency and accuracy of the proposed formulation are explored and a comparison with the concentration-based formulations is presented
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