Publications
200 results found
Zheng Z, Waheed S, Balint D, et al., 2018, Slip transfer across phase boundaries in dual phase titanium alloys and the effect on strain rate sensitivity, International Journal of Plasticity, Vol: 104, Pages: 23-38, ISSN: 0749-6419
Dislocation transmission through α/β phase boundaries in titanium alloys is studied using integrated crystal plasticity (CP) and discrete dislocation plasticity (DDP) modelling techniques, combined with experimental micro-pillar compression test results. Direct dislocation transmission together with the nucleation of new dislocations ahead of a pile-up at an α/β interface, termed indirect slip transfer, are both assessed and their role in controlling microstructure-dependent strain rate sensitivity considered. A critical shear stress criterion for direct slip transfer across an α/β interface in Ti-6242 has been established by capturing the local slip penetration through the phase boundary using CP and DDP comparisons with experimental two phase micro-pillar compression. The competition between direct and indirect slip transfer has been investigated using a single Frank-Read source DDP model. Direct slip transfer is found to occur only under specific conditions which have been quantified. The strain rate sensitivity of dual phase titanium alloys is demonstrated to depend on average pile-up size which is significantly influenced by α/β morphology.
Chen B, Jiang J, Dunne FPE, 2018, Is stored energy density the primary meso-scale mechanistic driver for fatigue crack nucleation?, International Journal of Plasticity, Vol: 101, Pages: 213-229, ISSN: 0749-6419
Fatigue crack nucleation in a powder metallurgy produced nickel alloy containing a non-metallic inclusion has been investigated through integrated small-scale bend testing, quantitative characterisation (HR-DIC and HR-EBSD) and computational crystal plasticity which replicated the polycrystal morphology, texture and loading. Multiple crack nucleations occurred at the nickel matrix-inclusion interface and both nucleation and growth were found to be crystallographic with highest slip system activation driving crack direction. Local slip accumulation was found to be a necessary condition for crack nucleation, and that in addition, local stress and density of geometrically necessary dislocations are involved. Fatemi-Socie and dissipated energy were also assessed against the experimental data, showing generally good, but not complete agreement. However, the local stored energy density (of a Griffith-Stroh kind) identified all the crack nucleation sites as those giving the highest magnitudes of stored energy.
Zheng Z, Balint D, Dunne F, 2017, Mechanistic basis of temperature-dependent dwell fatigue in titanium alloys, Journal of the Mechanics and Physics of Solids, Vol: 107, Pages: 185-203, ISSN: 0022-5096
The temperature-dependent dwell sensitivity of Ti-6242 and Ti-6246 alloys has been assessed over a temperature range from −50∘C to 390 °C using discrete dislocation plasticity which incorporates both thermal activation of dislocation escape from obstacles and slip transfer across grain boundaries. The worst-case load shedding in Ti-6242 alloy is found to be at or close to 120 °C under dwell fatigue loading, which diminishes and vanishes at temperatures lower than −50∘C or higher than 230 °C. Load shedding behaviour is predicted to occur in alloy Ti-6246 also but over a range of higher temperatures which are outside those relevant to in-service conditions. The key controlling dislocation mechanism with respect to load shedding in titanium alloys, and its temperature sensitivity, is shown to be the time constant associated with the thermal activation of dislocation escape from obstacles, with respect to the stress dwell time. The mechanistic basis of load shedding and dwell sensitivity in dwell fatigue loading is presented and discussed in the context of experimental observations.
Chen B, Jiang J, Dunne F, 2017, Microstructurally-sensitive fatigue crack nucleation in Ni-based single and oligo crystals, Journal of the Mechanics and Physics of Solids, Vol: 106, Pages: 15-33, ISSN: 1873-4782
An integrated experimental, characterisation and computational crystal plasticity study of cyclic plastic beam loading has been carried out for nickel single crystal (CMSX4) and oligocrystal (MAR002) alloys in order to assess quantitatively the mechanistic drivers for fatigue crack nucleation.The experimentally validated modelling provides knowledge of key microstructural quantities (accumulated slip, stress and GND density) at experimentally observed fatigue crack nucleation sites and it is shown that while each of these quantities is potentially important in crack nucleation, none of them in its own right is sufficient to be predictive. However, the local (elastic) stored energy density, measured over a length scale determined by the density of SSDs and GNDs, has been shown to predict crack nucleation sites in the single and oligocrystals tests. In addition, once primary nucleated cracks develop and are represented in the crystal model using XFEM, the stored energy correctly identifies where secondary fatigue cracks are observed to nucleate in experiments. This (Griffith-Stroh type) quantity also correctly differentiates and explains intergranular and transgranular fatigue crack nucleation.
Cuddihy MA, Stapleton A, Williams SJ, et al., 2017, On cold dwell facet fatigue in titanium alloy aero-engine components, International Journal of Fatigue, Vol: 97, Pages: 177-189, ISSN: 0142-1123
This paper investigates the mechanisms of facet nucleation through combining aero-engine manufacturer disc component test data with microstructure-sensitive crystal plasticity finite element (CPFE) models. Full-scale component testing has been carried out in a manner representative of in-service conditions. Elastic FE analyses of discs under these conditions and fully accounting for thermal and residual processing strains have also been carried out. Disc facet nucleation sites have been identified and the local stress states evaluated in order to establish crystal plasticity oligocrystal sub-models. The oligocrystal RVE models provide knowledge of hard-soft grain stresses under dwell loading, and the consequent load shedding in order to provide stresses required for the facet nucleation.The disc component facet observations together with the crystal plasticity sub-model oligocrystal approach provide persuasive evidence that a hard-soft grain combination is required for facet formation, that the remote stress state influences the resolved shear stress on the soft grain initiating slip (with tensile uniaxial stress state more damaging than a tension-tension biaxial stress state), and that the load shedding which results is essential in pushing up the hard-grain basal stress to nucleate facets.
Jiang J, Dunne F, Britton T, 2017, Toward predictive understanding of fatigue crack nucleation in Ni-based Superalloys, JOM, Vol: 69, Pages: 863-871, ISSN: 1047-4838
Predicting when and where materials fail is a holy grail for structural materials engineering. Development of a predictive capability in this domain will optimize the employment of existing materials, as well as rapidly enhance the uptake of new materials, especially in high-risk, high-value applications, such as aeroengines. In this article, we review and outline recent efforts within our research groups that focus on utilizing full-field measurement and calculation of micromechanical deformation in Ni-based superalloys. In paticular, we employ high spatial resolution digital image correlation (HR-DIC) to measure surface strains and a high-angular resolution electron backscatter diffraction technique (HR-EBSD) to measure elastic distortion, and we combine these with crystal plasticity finite element (CPFE) modeling. We target our studies within a system of samples that includes single, oligo, and polycrystals where the boundary conditions, microstructure, and loading configuration are precisely controlled. Coupling of experiment and simulation in this manner enables enhanced understanding of crystal plasticity, as demonstrated with case studies in deformation compatibility; spatial distributions of slip evolution; deformation patterning around microstructural defects; and ultimately development of predictive capability that probes the location of microstructurally sensitive fatigue cracks. We believe that these studies present a careful calibration and validation of our experimental and simulation-based approaches and pave the way toward new understanding of crack formation in engineering alloys.
Ashton P, Jun TS, Britton TB, et al., 2017, The effect of the beta phase on the micromechanical response of dual-phase titanium alloys, International Journal of Fatigue, Vol: 100, Pages: 377-387, ISSN: 1879-3452
This paper investigates the role of beta phase on the micro-mechanical behaviour of dual-phase titanium alloys, with particular emphasis on the phenomenon of cold dwell fatigue, which occurs in such alloys under room temperature conditions. A strain gradient crystal plasticity model is developed and calibrated against micro-pillar compression test data for a dual-phase alpha-beta specimen. The effects of key microstructural variables, such as relative beta lath orientation, on the micromechanical response of idealised alpha-beta colony microstructures are shown to be consistent with previously-published test data. A polycrystal study on the effects of the calibrated alpha-beta crystal plasticity model on the local micromechanical variables controlling cold dwell fatigue is presented. The presence of the alpha-beta phase is predicted to increase dwell fatigue resistance compared to a pure alpha phase microstructure.
Zhang Z, Dunne FPE, 2017, Microstructural heterogeneity in rate-dependent plasticity of multiphase titanium alloys, Journal of the Mechanics and Physics of Solids, Vol: 103, Pages: 199-220, ISSN: 1873-4782
Polycrystalline rate-dependent plasticity is found to originate from heterogeneous slip system/phase rate response. Micro-mechanism under low stress and low temperature (T < 0.3Tm) has been shown to be different from conventional rate sensitivity expectations. Hence the constitutive framework developed is dependent on the crystallographic orientation, properly capturing micro-scale anisotropic rate behaviour.The intrinsic rate anisotropy of the HCP α prism and basal and BCC β phase slip systems in Ti-6242, recently determined from micro-pillar and crystal plasticity modelling, have been utilised to investigate the structural strain rate sensitivities of colonies, polycrystals, bimodal and basket weave microstructures.The rate sensitivity of colony structures is dominated by the HCP α phase behaviour, at least for alloys containing up to ∼20% volume fraction β phase, and is largely independent of β-lath orientation. The apparent anisotropy of a1, a2 and a3 basal resolved shear stresses in Ti-6242 colonies is shown to originate from the local crystal stress states established as opposed to the α−β interfaces.Texture and α−β morphology are shown to affect rate dependence and to corroborate that the basal rate sensitivity is stronger than that for prism slip in Ti-6242. Morphological effects are shown to affect rate dependence but not strongly, but the number of HCP α phase variants in basketweave structures is found to have a significant effect with higher numbers of variants leading to lower strain rate sensitivities. This is potentially important in designing alloys to resist cold dwell fatigue.
Zheng Z, Balint D, Dunne F, 2017, Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue, Acta Materialia, Vol: 127, Pages: 43-53, ISSN: 1359-6454
This paper addresses the role of grain boundary slip transfer and thermally-activated discretedislocation plasticity in the redistribution of grain boundary stresses during cold dwell fatigue intitanium alloys. Atomistic simulations have been utilised to calculate the grain boundary energies fortitanium with respect to the misorientation angles. The grain boundary energies are utilised within athermally-activated discrete dislocation plasticity model incorporating slip transfer controlled byenergetic and grain boundary geometrical criteria. The model predicts the grain size effect on the flowstrength in Ti alloys. Cold dwell fatigue behaviour in Ti-6242 alloy is investigated and it is shown thatsignificant stress redistribution from soft to hard grains occurs during the stress dwell, which isobserved both for grain boundaries for which slip transfer is permitted and inhibited. However, thegrain boundary slip penetration is shown to lead to significantly higher hard-grain basal stresses nearthe grain boundary after dwell, thus exacerbating the load shedding stress compared to animpenetrable grain boundary. The key property controlling the dwell fatigue response is argued toremain the time constant associated with the thermal activation process for dislocation escape, but theslip penetrability is also important and exacerbates the load shedding. The inclusion of a macrozonedoes not significantly change the conclusions but does potentially lead to the possibility of a largerinitial facet.
Collins DM, Erinosho T, Dunne FPE, et al., 2016, A synchrotron X-ray diffraction study of non-proportional strain-path effects., Acta Materialia, Vol: 124, Pages: 290-304, ISSN: 1359-6454
Common alloys used in sheet form can display a significant ductility benefit when they are subjected to certain multiaxial strain paths. This effect has been studied here for a polycrystalline ferritic steel using a combination of Nakajima bulge testing, X-ray diffraction during biaxial testing of cruciform samples and crystal plasticity finite element (CPFE) modelling. Greatest gains in strain to failure were found when subjecting sheets to uniaxial loading followed by balanced biaxial deformation, resulting in a total deformation close to plane-strain. A combined strain of approximately double that of proportional loading was achieved. The evolution of macrostrain, microstrain and texture during non-proportional loading were evaluated by in-situ high energy synchrotron diffraction. The results have demonstrated that the inhomogeneous strain accumulation from non-proportional deformation is strongly dependent on texture and the applied strain-ratio of the first deformation pass. Experimental diffraction evidence is supported by results produced by a novel method of CPFE-derived diffraction simulation. Using constitutive laws selected on the basis of good agreement with measured lattice strain development, the CPFE model demonstrated the capability to replicate ductility gains measured experimentally.
Zheng Z, Balint D, Dunne F, 2016, Dwell fatigue in two Ti alloys: an integrated crystal plasticity and discrete dislocation study, Journal of the Mechanics and Physics of Solids, Vol: 96, Pages: 411-427, ISSN: 0022-5096
It is a well known and important problem in the aircraft engine industry that alloy Ti-6242 shows a significant reduction in fatigue life, termed dwell debit, if a stress dwell is included in the fatigue cycle, whereas Ti-6246 does not; the mechanistic explanation for the differing dwell debit of these alloys has remained elusive for decades. In this work, crystal plasticity modelling has been utilised to extract the thermal activation energies for pinned dislocation escape for both Ti alloys based on independent experimental data. This then allows the markedly different cold creep responses of the two alloys to be captured accurately and demonstrates why the observed near-identical rate sensitivity under non-dwell loading is entirely consistent with the dwell behaviour. The activation energies determined are then utilised within a recently developed thermally-activated discrete dislocation plasticity model to predict the strain rate sensitivities of the two alloys associated with nano-indentation into basal and prism planes. It is shown that Ti-6242 experiences a strong crystallographic orientation-dependent rate sensitivity while Ti-6246 does not which is shown to agree with recently published independent measurements; the dependence of rate sensitivity on indentation slip plane is also well captured. The thermally-activated discrete dislocation plasticity model shows that the incorporation of a stress dwell in fatigue loading leads to remarkable stress redistribution from soft to hard grains in the classical cold dwell fatigue rogue grain combination in alloy Ti-6242, but that no such load shedding occurs in alloy Ti-6246. The key property controlling the behaviour is the time constant of the thermal activation process relative to that of the loading. This work provides the first mechanistic basis to explain why alloy Ti-6242 shows a dwell debit but Ti-6246 does not.
Dunne FPE, Guan Y, Britton TB, et al., 2016, Crystal Plasticity Modelling and HR-DIC Measurement of Slip Activation and Strain Localisation in Single and Oligo-crystal Ni Alloys under Fatigue, International Journal of Plasticity, Vol: 88, Pages: 70-88, ISSN: 0749-6419
Single crystal (CMSX4) and oligocrystal (MAR002) nickel have been studied using three-point beambending under conditions of cyclic loading. SEM images have enabled identification of slip activation,and high resolution digital image correlation has been utilized to quantify the developing strain fieldsand the strain localization in both single and oligocrystals in fatigue. The single and oligocrystalmicrostructures have been replicated within crystal plasticity finite element models and the fatigueloading analysed such that grain-by-grain comparisons of slip may be carried out. Single and multipleslip activation, slip localisation and microstructure-sensitive stress evolution have been examined.Single crystal bend fatigue gives rise to non-symmetric slip fields and localisation depending oncrystallographic orientation. Modelling correctly captures slip activation and the developing nonsymmetricslip fields. Oligocrystal slip is markedly heterogeneous, with grain misorientations drivingstrong variations, also reasonably captured by the model. Microstructure behaviour is found to varyspatially and include elastic-plastic hysteresis which is stable, and which undergoes mean stressrelaxation so that plastic shakedown occurs. Remarkable variations occur between locations eitherside of grain boundaries, providing appropriate opportunities for fatigue crack nucleation.
Zhang Z, Jun T, Britton TB, et al., 2016, Determination of Ti-6242 α and β slip properties using micro-pillar test and computational crystal plasticity, Journal of the Mechanics and Physics of Solids, Vol: 95, Pages: 393-410, ISSN: 0022-5096
The properties and behaviour of an α−β colony Ti-6242 alloy have been investigated at 20 °C utilising coupled micro-pillar stress relaxation tests and computational crystal plasticity. The β-phase slip strength and intrinsic slip system strain rate sensitivity have been determined, and the β-phase shown to have stronger rate sensitivity than that for the α phase. Close agreement of experimental observations and crystal plasticity predictions of micro-pillar elastic-plastic response, stress relaxation, slip activation in both α and β-phases, and strain localisation within the α−β pillars with differing test strain rate, β morphology, and crystal orientations is achieved, supporting the validity of the properties extracted. The β-lath thickness is found to affect slip transfer across the α−β−α colony, but not to significantly change the nature of the slip localisation when compared to pure α-phase pillars with the same crystallographic orientation. These results are considered in relation to rate-dependent deformation, such as dwell fatigue, in complex multiphase titanium alloys.
Jiang J, Yang J, Zhang T, et al., 2016, Microstructurally sensitive crack nucleation around inclusions in powder metallurgy nickel based superalloys, Acta Materialia, Vol: 117, Pages: 333-344, ISSN: 1359-6454
Nickel based superalloys are used in high strength, high value applications, such as gas turbine discs in aeroengines. In these applications the integrity of the disc is critical and therefore understanding crack initiation mechanisms is of high importance. With an increasing trend towards powder metallurgy routes for discs, sometimes unwanted non-metallic inclusions are introduced during manufacture. These inclusions vary in size from ~ 10 μm to 200 μm which is comparable to the grain size of the Nickel based superalloys. Cracks often initiate near these inclusions and the precise size, shape, location and path of these cracks are microstructurally sensitive. In this study, we focus on crack initiation at the microstructural length scale using a controlled three-point bend test, with the inclusion deliberately located within the tensile fibre of the beam. Electron backscatter diffraction (EBSD) is combined with high spatial resolution digital image correlation (HR-DIC) to explore full field plastic strain distributions, together with finite element modelling, to understand the micro-crack nucleation mechanisms. This full field information and controlled sample geometry enable us to systematically test crack nucleation criteria. We find that a combined stored energy and dislocation density provide promising results. These findings potentially facilitate more reliable and accurate lifing prediction tools to be developed and applied to engineering components.
Zheng Z, Balint D, Dunne F, 2016, Discrete dislocation and crystal plasticity analyses of load shedding in polycrystalline titanium alloys, International Journal of Plasticity, Vol: 87, Pages: 15-31, ISSN: 0749-6419
The focus of this paper is the mechanistic basis of the load shedding phenomenon that occurs under the dwell fatigue loading scenario. A systematic study was carried out using a discrete dislocation plasticity (DDP) model to investigate the effect of crystallographic orientations, localised dislocation behaviour and grain combinations on the phenomenon. Rate sensitivity in the model arises from a thermal activation process at low strain rates, which is accounted for by associating a stress- and temperature-dependent release time with obstacles; the activation energy was determined by calibrating an equivalent crystal plasticity model to experimental data. First, the application of Stroh's dislocation pile-up model of crack nucleation to facet fracture was quantitatively assessed using the DDP model. Then a polycrystalline model with grains generated using a controlled Poisson Voronoi tessellation was used to investigate the soft-hard-soft rogue grain combination commonly associated with load shedding. Dislocation density and peak stress at the soft/hard grain boundary increased significantly during the stress dwell period, effects that were enhanced by dislocations escaping from pile-ups at obstacles. The residual stress after dwell fatigue loading was also found to be much higher compared to standard fatigue loading. Taylor (uniform strain) and Sachs (uniform stress) type assumptions in a soft-hard grain combination have been assessed with a simple bicrystal DDP model. Basal slip nucleation in the hard grain was found to be initiated by high stresses generated by strong pile ups in the soft grain, and both basal and pyramidal slip nucleation was observed in the hard grain when the grain boundary orientation aligned with that of an active slip system in the soft grain. The findings of this study give new insight into the mechanisms of load shedding and faceting associated with cold dwell fatigue in Ti alloys used in aircraft engines.
Peng Z, Tian G, Jiang J, et al., 2016, Mechanistic behaviour and modelling of creep in powder metallurgy FGH96 nickel superalloy, Materials Science and Engineering A, Vol: 676, Pages: 441-449, ISSN: 0921-5093
The creep properties of a nickel-based superalloy at 700 °C and 690 MPa resulting from differing aging heat treatments have been investigated. The heat treatments gave rise to significantly different tertiary γ′ precipitate distributions which in turn influence the propensity for precipitate shearing. The creep life was found to decrease with an increase of volume fraction of tertiary γ′. It is shown that the γ′ precipitates undergo shearing by matrix dislocations resulting in residual stacking faults which have been identified from TEM studies.A physically-based crystal slip model for creep deformation in FGH96 has been developed. A critical γ′ precipitate size is found to exist above which precipitate shearing occurs by strongly-coupled dislocations pairs. The critical size for FGH96 superalloy is less than 15 nm, which is smaller than most of the γ′ precipitates in the aged treated samples. A bimodal precipitate hardening model has been presented from which the slip strength resulting from differing heat treatments may be determined. Creep strain rate is found to decrease with increasing slip strength. The crystal slip model successfully captures the effect of heat treatment (in terms of γ′ precipitate distributions) on resulting creep behaviour in alloy FGH96.
Zhang Z, Jun T-S, Britton TB, et al., 2016, Intrinsic anisotropy of strain rate sensitivity in single crystal alpha titanium, Acta Materialia, Vol: 118, Pages: 317-330, ISSN: 1359-6454
The room temperature intrinsic strain rate sensitivities (SRS) of basal and prismatic slip systems have been determined for the α (HCP) phase of a titanium alloy (Ti-6242), through coupled crystal plasticity modelling and micro-pillar compression experiments. Load-displacement data from displacement hold tests, in both experiment and simulation, have enabled determination of the rate-dependent slip rule within the crystal plasticity model. Slip system SRS has been obtained, via micro-pillars orientated for single basal and prismatic slip. Crystal plasticity modelling explicitly captures micro-pillar geometry, crystal orientation, as well as the stiffnesses of components of the experimental testing frame and sample mounting. Consideration of the stiffness of the adhesive and load frame is shown to be essential for extraction of the intrinsic rate-dependent material response, rather than the structural response, even in single phase micro-pillar compression experiments. We find that the intrinsic SRS of basal slip is stronger than that for prismatic slip. This finding has significant implications in understanding the anisotropic rate-dependent response of hexagonal materials applied extensively under extreme loading conditions.
Wan VVC, Cuddihy MA, Jiang J, et al., 2016, An HR-EBSD and computational crystal plasticity investigation of microstructural stress distributions and fatigue hotspots in polycrystalline copper, Acta Materialia, Vol: 115, Pages: 45-57, ISSN: 1873-2453
High resolution EBSD studies on a deformed copper polycrystal have been carried out to quantify the microstructural residual stress distributions, and those of stress state including triaxiality of importance in defect nucleation studies. Crystal plasticity analysis of a representative, similarly textured, model polycrystal has been carried out showing that the experimental distributions of microstructural residual stress components, effective stress, hydrostatic stress and stress triaxiality are well captured.The crystal model enables point-wise microstructural Schmid factors to be calculated both globally (ie with respect to the macroscopic remote loading) and locally from full knowledge of the grain-level stress state. Significant differences are demonstrated such that global Schmid analysis tends to overestimate slip activity and the frequency of high Schmid factors, indicating that the local microstructural heterogeneity is significant and caution is necessary in interpreting polycrystal behaviour using global Schmid factors.A stored energy criterion for fatigue crack nucleation indicates that preferential sites for fatigue crack nucleation are local to grain boundaries (as opposed to triple junctions), and that hard-soft grain interfaces where high GND densities develop are preferable.
Wan VVC, MacLachlan DW, Dunne FPE, 2016, Integrated experiment and modelling of microstructurally-sensitive crack growth, International Journal of Fatigue, Vol: 91, Pages: 110-123, ISSN: 1879-3452
An assessment is presented of modelling methodologies which explicitly address microstructurally-sensitive crack growth paths in bcc polycrystal ferritic steel. A number of microstructurally differing polycrystal samples are subjected to fatigue and crack nucleation and growth, demonstrating transgranular and intergranular crack paths in characterised microstructures. Microstructurally representative extended finite element crystal modelling, coupled cohesive zone modelling, coupled explicit grain boundary modelling, and plasticity are utilised to assess predicted crack paths against the experimental observations. The incorporation of strong and weak boundary zones when coupled with X-FEM was found to provide quantitative prediction of the transition from transgranular to intergranular cracking and to capture accurately the observed crack paths. Crack tip plasticity was found to have limited effect on microstructurally-sensitive crack path.
Zhang T, Jiang J, Britton B, et al., 2016, Crack nucleation using combined crystal plasticity modelling, high-resolution digital image correlation and high-resolution electron backscatter diffraction in a superalloy containing non-metallic inclusions under fatigue, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 472, ISSN: 1471-2946
A crystal plasticity finite-element model, which explicitly and directly represents the complex microstructures of a non-metallic agglomerate inclusion within polycrystal nickel alloy, has been developed to study the mechanistic basis of fatigue crack nucleation. The methodology is to use the crystal plasticity model in conjunction with direct measurement at the microscale using high (angular) resolution-electron backscatter diffraction (HR-EBSD) and high (spatial) resolution-digital image correlation (HR-DIC) strain measurement techniques. Experimentally, this sample has been subjected to heat treatment leading to the establishment of residual (elastic) strains local to the agglomerate and subsequently loaded under conditions of low cyclic fatigue. The full thermal and mechanical loading history was reproduced within the model. HR-EBSD and HR-DIC elastic and total strain measurements demonstrate qualitative and quantitative agreement with crystal plasticity results. Crack nucleation by interfacial decohesion at the nickel matrix/agglomerate inclusion boundaries is observed experimentally, and systematic modelling studies enable the mechanistic basis of the nucleation to be established. A number of fatigue crack nucleation indicators are also assessed against the experimental results. Decohesion was found to be driven by interface tensile normal stress alone, and the interfacial strength was determined to be in the range of 1270–1480 MPa.
Wan VVC, Jiang J, MacLachlan DW, et al., 2016, Microstructure-sensitive fatigue crack nucleation in a polycrystalline Ni superalloy, International Journal of Fatigue, Vol: 90, Pages: 181-190, ISSN: 1879-3452
Large-grained polycrystalline Ni alloy RS5 has been tested in fatigue. Morphology and texture have been characterised using EBSD and utilised to construct representative 3D finite element crystal plasticity models. A stored energy criterion has been used to predict scatter in fatigue crack nucleation life and the results compared with experimental findings. Good quantitative prediction of experimental fatigue lives is obtained. The observed progressive increase in scatter with decreasing strain range is captured. The stored energies for fatigue crack nucleation determined for Ni alloy RS5 and ferritic steel and were found to be 13,300 J/m2 and 580 J/m2 respectively, showing very good consistency with the corresponding Griffith fracture energies of 48,700 J/m2 for Ni alloy and 1900 J/m2 for ferritic steel.Local microstructural variations are shown to influence corresponding grain-level stress–strain response. At the microstructural level, purely elastic, reversed plastic and ratcheting behaviour are all observed. In addition, plastic and elastic shakedown are also found to occur which depend upon features of the microstructure and the nature of the applied loading. These phenomena all influence fatigue crack nucleation.
Erinosho TO, Collins DM, Wilkinson AJ, et al., 2016, Assessment of X-ray diffraction and crystal plasticity lattice strain evolutions under biaxial loading, International Journal of Plasticity, Vol: 83, Pages: 1-18, ISSN: 1879-2154
A methodology to simulate X-ray diffraction lattice strains using crystal plasticity, replicating in-situ synchrotron experimental measurements during the deformation of a low-carbon steel, has been developed. Uniquely, the model calculated lattice strains for full Debye–Scherrer diffraction rings, providing the in-plane lattice strain distributions determined from crystal plasticity. Thus, a direct method of comparison between experimental and crystal plasticity results becomes possible. The model considered two forms of hardening whilst subjecting the material to two dissimilar proportional strain-paths; uniaxial and balanced biaxial deformation. Both deformation paths showed influence on resulting lattice strain distributions which were also found to depend upon texture. Biaxial straining led to a stronger dependence on the material's hardening behaviour and this was attributed to the higher rate of work hardening seen under biaxial compared to uniaxial straining. However, biaxial deformation showed quite isotropic lattice strains distribution, irrespective of initial texture or hardening. Quantitatively, good agreement between the computed and experimentally determined lattice strain distributions was obtained for each strain path. This success demonstrates the possibility of calibrating crystal plasticity model parameters using such methodologies, or simply to provide insight into the governing mechanisms in polycrystal deformation.
Jun T, Zhang Z, Sernicola G, et al., 2016, Local strain rate sensitivity of single α phase within a dual-phase Ti alloy, Acta Materialia, Vol: 107, Pages: 298-309, ISSN: 1359-6454
We have performed in-situ micropillar compression to investigate the local strain rate sensitivity of single α phase in dual-phase Ti alloy, Ti-6Al-2Sn-4Zr-2Mo (wt%). Electron backscatter diffraction (EBSD) was used to identify two grains, anticipated to primarily activate ⟨a⟩ slip on the basal and prismatic plane respectively. Comparative micropillars were fabricated within single α laths and load-hold tests were conducted with variable strain rates (on the order of 10-2 to 10-4s-1). Local strain rate sensitivity exponent (i.e. m value) is determined using two types of methods, constant strain rate method (CSRM) and conventional stress relaxation method (SRM), showing similar rate sensitivity trends but one order higher magnitude in SRM. We thus propose a new approach to analyse the SRM data, resulting in satisfactory agreement with the CSRM. Significant slip system dependent rate sensitivity is observed such that the prism slip has a strikingly higher m value than the basal. Fundamental mechanisms differing the rate sensitivity are discussed with regards to dislocation plasticity, where more resistance to move dislocations and hence higher hardening gradients are found in the basal slip. The impact of this finding for dwell fatigue deformation modes and the effectiveness of the present methodology for screening new alloy designs are discussed.
Zheng Z, Balint D, Dunne F, 2016, Rate sensitivity in discrete dislocation plasticity in hexagonal close-packed crystals, Acta Materialia, Vol: 107, Pages: 17-26, ISSN: 1873-2453
The origin of the rate-sensitive behaviour of plasticity over strain rate regimes from 10−5 to 105 s−1 has been assessed with reference to three key mechanisms: dislocation nucleation, time of flight (dislocation mobility) and thermally activated escape of pinned dislocations. A new mechanistic formalism for incorporating thermally activated dislocation escape into discrete dislocation plasticity modelling techniques is presented. It is shown that nucleation and dislocation mobility explain rate-sensitive behaviour for strain rates in the range 102 to 105 s−1, but cannot do so for significantly lower strain rates, for which thermally-activated dislocation escape becomes the predominant rate-controlling mechanism. At low strain rates, and for a model Ti alloy considered at 20 °C, the strong experimentally observed rate-sensitive behaviour manifested as stress relaxation and creep is shown to be captured well by the new thermal activation discrete dislocation plasticity model, which otherwise simply cannot be captured by nucleation or mobility arguments. Increasing activation energy leads to a higher energy barrier and as a consequence, a higher dislocation escape time. Conversely, increasing obstacle spacing tends to diminish the thermal activation time.
Jiang J, Zhang T, Dunne F, et al., 2016, Deformation compatibility in a single crystalline Ni superalloy, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 472, Pages: 1-24, ISSN: 1364-5021
Deformation in materials is often complex and requires rigorous understanding to predict engineering component lifetime. Experimental understanding of deformation requires utilization of advanced characterization techniques, such as high spatial resolution digital image correlation (HR-DIC) and high angular resolution electron backscatter diffraction (HR-EBSD), combined with clear interpretation of their results to understand how a material has deformed. In this study, we use HR-DIC and HR-EBSD to explore the mechanical behaviour of a single-crystal nickel alloy and to highlight opportunities to understand the complete deformations state in materials. Coupling of HR-DIC and HR-EBSD enables us to precisely focus on the extent which we can access the deformation gradient, F, in its entirety and uncouple contributions from elastic deformation gradients, slip and rigid body rotations. Our results show a clear demonstration of the capabilities of these techniques, found within our experimental toolbox, to underpin fundamental mechanistic studies of deformation in polycrystalline materials and the role of microstructure.
Zhang Z, Eakins DE, Dunne FPE, 2015, On the Formation of Adiabatic Shear Bands in Textured HCP Polycrystals, International Journal of Plasticity, Vol: 79, Pages: 196-216, ISSN: 0749-6419
Adiabatic shear band (ASB) formation in textured HCP polycrystals has been investigatedunder regimes of high rate compression and shear loading using dynamic thermomechanicallycoupled, dislocation-based crystal plasticity modelling. The balance betweenrate of plastic dissipation leading to internal heat generation versus rate of thermal diffusionat a crystallographic length scale has been shown to be pivotal for the formation or otherwiseof ASBs. Micro-texture has been found to have a key role in both advancing and inhibitingshear band growth, and its control offers the possibility of new alloys with higher impactstrength over strain rate range 2 1 10 to 5 110 s-1. Texture has been found to lead to widevariations in applied macroscopic strain at which ASB formation occurs, such that strain levelin isolation is inappropriate as a universal indicator of ASB onset.High-rate shear loading is found to lead to lower onset strains for ASBs compared to highrate compression, but the dependence of both on texture leads to considerable variation instrain level for ASB formation. A preliminary map demarcating ASB onset has beenestablished over regimes of applied strain and texture for dynamic shear and compression.
Erinosho TO, Dunne FPE, 2015, Lattice strains at cracks in single crystal titanium: elastic distortion and GND contributions, International Journal of Solids and Structures, Vol: 80, Pages: 237-245, ISSN: 1879-2146
There is evidence from diffraction experiments that significant peak broadening is measured local to crack tips and this has been attributed to the development of geometrically necessary dislocations (GNDs) which are retained upon unloading. This is reasonable due to the stress singularity found locally at the crack which is expected to activate slip on favourably oriented slip systems, potentially resulting in plastic strain gradients and geometrically necessary dislocation development. Hence, a systematic study is presented here to ascertain the contributions of both elastic distortional strain and GND density to lattice deformation local to the crack at loaded and subsequently unloaded states.The results show that whilst elastic strains dominate lattice distortion in comparison to GNDs at the loaded state i.e. at the peak load applied, these strains are largely recovered upon unloading and the contribution from GND development subsequently dominates the broadening seen. Two initial crystallographic configurations were considered. In the example in which the crystal c-axis was oriented parallel to the loading direction, the <c+a> pyramidal systems contributed most to slip with <a> basal slip system contributing to a lesser extent. However, in the example where the c-axis was oriented perpendicular to the loading direction, the <c+a> pyramidal and <a> prismatic systems were the more significant contributors to slip and the <a> basal contributing to a lesser extent. However, basal, prismatic and c+a pyramidal slip systems were found to be active in both examples and this was attributed to significant lattice rotation driven by locally high stresses which enabled otherwise badly oriented slip systems to become favourable for slip. Finally, increases in GND density were seen upon unloading for c-axis orientation parallel with loading. This was attributed to the influence of <c+a> pyramidal slip on reverse plasticity leading to diffu
Lan B, Lowe M, DUNNE F, 2015, A spherical harmonic approach for the determination of HCP texture from ultrasound: a solution to the inverse problem, Journal of the Mechanics and Physics of Solids, Vol: 83, Pages: 179-198, ISSN: 0022-5096
A new spherical convolution approach has been presented which couples HCP single crystal wave speed (the kernel function) with polycrystal c-axis pole distribution function to give the resultant polycrystal wave speed response. The three functions have been expressed as spherical harmonic expansions thus enabling application of the de-convolution technique to enable any one of the three to be determined from knowledge of the other two. Hence, the forward problem of determination of polycrystal wave speed from knowledge of single crystal wave speed response and the polycrystal pole distribution has been solved for a broad range of experimentally representative HCP polycrystal textures. The technique provides near-perfect representation of the sensitivity of wave speed to polycrystal texture as well as quantitative prediction of polycrystal wave speed. More importantly, a solution to the inverse problem is presented in which texture, as a c-axis distribution function, is determined from knowledge of the kernel function and the polycrystal wave speed response. It has also been explained why it has been widely reported in the literature that only texture coefficients up to 4th degree may be obtained from ultrasonic measurements. Finally, the de-convolution approach presented provides the potential for the measurement of polycrystal texture from ultrasonic wave speed measurements.
Jun T, Sernicola G, Dunne FPE, et al., 2015, Local deformation mechanisms of two-phase Ti alloy, Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing, Vol: 649, Pages: 39-47, ISSN: 0921-5093
This paper describes a study of local deformation mechanisms in two-phase Ti alloy, Ti–6Al–2Sn–4Zr–2Mo, by performing in-situ micropillar compression tests. A colony microstructure was examined and select grains identified for examination were chosen with EBSD measurements. These grains were chosen to isolate individual slip systems within each test. Micropillars of tri-crystal (α–β–α) structure were fabricated from four determined regions, and compression tests were performed using a displacement-controlled nanoindenter set inside a SEM, with a constant displacement rate. The results show that the α/β morphology significantly affects the local deformation behaviour. For these colony structures, Schmid's law in general enables anticipation of local slip activity, but the presence and morphology of the β phase can significantly alter the apparent yielding point and work hardening response. The role of interfaces within these tri-crystal pillars is discussed.
Zhang Z, Cuddihy MA, Dunne FPE, 2015, On rate-dependent polycrystal deformation: the temperature sensitivity of cold dwell fatigue, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol: 471, ISSN: 0080-4630
A temperature and rate-dependent crystal plasticity framework has been utilized to examine the temperature sensitivity of stress relaxation, creep and load shedding in model Ti-6Al polycrystal behaviour under dwell fatigue conditions. A temperature close to 120oC is found to lead to the strongest stress redistribution and load shedding, resulting from the coupling between crystallographic slip rate and slip system dislocation hardening. For temperatures in excess of about 230oC, grain-level load shedding from soft to hard grains diminishes because of the more rapid stress relaxation, leading ultimately to the diminution of the load shedding and hence, it is argued, the elimination of the dwell debit.Under conditions of cyclic stress dwell, at temperatures between 20 and 230oC for which load shedding occurs, the rate-dependent accumulation of local slip by ratcheting is shown to lead to the progressive cycle-by-cycle redistribution of stress from soft to hard grains. This phenomenon is termed cyclic load shedding since it also depends on the material’s creep response, but develops over and above the well-known dwell load shedding, thus providing an additional rationale for the incubation of facet nucleation.
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