• This is the author's version of a work that was accepted for publication in the journal, International Journal of Plasticity. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.A definitive version was subsequently pub-
AbstractDiscrete dislocation dynamics (DDD) has been used to model the deformation of nickelbased single crystal superalloys with a high volume fraction of precipitates at high temperature. A representative volume cell (RVC), comprising of both the precipitate and the matrix phase, was employed in the simulation where a periodic boundary condition was applied. The dislocation Frank-Read sources were randomly assigned with an initial density on the 12 octahedral slip systems in the matrix channel. Precipitate shearing by superdislocations was modelled using a back force model, and the coherency stress was considered by applying an initial internal stress field. Strain-controlled loading was applied to the RVC in the [001] direction. In addition to dislocation structure and density evolution, global stress-strain responses were also modelled considering the influence of precipitate shearing, precipitate morphology, internal microstructure scale (channel width and precipitate size) and coherency stress. A three-stage stress-strain response observed in the experiments was modelled when precipitate shearing by superdislocations was considered.The polarized dislocation structure deposited on the precipitate/matrix interface was found to be the dominant strain hardening mechanism. Internal microstructure size, precipitate shape and arrangement can significantly affect the deformation of the single crystal superalloy by changing the constraint effect and dislocation mobility. The coherency stress field has a negligible influence on the stress-strain response, at least for cuboidal precipitates considered in the simulation. Preliminary work was also carried out to simulate the cyclic deformation in a single crystal Ni-based superalloy using the DDD model, although no cyclic hardening or softening was captured due to the lack of precipitate shearing and dislocation cross slip in this alloy.
Citation: ZHAO, L. and TONG, J., 2008. A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature. Journal of the Mechanics and Physics of Solids, 56 (12), Additional Information:• This is the author's version of a work that was accepted for publication in the Journal of the Mechanics and Physics of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subse-
AbstractViscoplastic crack tip deformation behaviour in a nickel-based superalloy at elevated temperature has been studied for both stationary and growing cracks in a compact tension (CT) specimen using the finite element method. The material behaviour was described by a unified viscoplastic constitutive model with non-linear kinematic and isotropic hardening rules, and implemented in the finite element software ABAQUS via a userdefined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack growth plane.Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip. Finite element simulation of crack growth was carried out under a constant ∆K-controlled loading condition, again ratchetting was observed ahead of the crack tip, similar to that for stationary cracks.A crack growth criterion based on strain-accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilised in the prediction of crack growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results.
Cure residual stress and its effect on damage in unidirectional fibre-reinforced polymer-matrix composites under transverse loading were studied using a micromechanical unit cell model and the finite element method. The overall residual stress introduced from curing was determined by considering two contributions: volume shrinkage of matrix resin from the crosslink polymerization during isothermal curing and thermal contraction of both resin and fibre as a result of cooling from the curing temperature to room temperature. To examine the effect of residual stress on failure, a model based on the Maximum Principal Stress criterion and stiffness degradation technique was used for damage analysis of the unit cell subjected to mechanical loading after curing. Predicted damage initiation and evolution are clearly influenced by the inclusion of residual stress. Residual stress is always detrimental for transverse compressive loading and pure shear loading. For transverse tensile loading, residual stress is detrimental for relatively low resin strength and beneficial for relatively high resin strength. Failure envelopes were obtained for both biaxial normal loading and combined shear and normal loading and the results show that residual stress results in a shifting and contraction of the failure envelopes.
Citation: KARABELA, A. ... et al., 2011
AbstractOxidation damage, combined with fatigue, is a concern for nickel-based superalloys utilised as disc rotors in high pressure compressor and turbine of aero-engines. A study has been carried out for a nickel-based alloy RR1000, which includes cyclic experiments at selected temperatures (700°C~800°C) and microscopy examination using Focused Ion Beam (FIB). The results suggest that the major mechanism of oxidation damage consists of the formation of surface oxide scales and internal micro-voids and oxide particles beneath the oxide scales, which become more severe with the increase of temperature. Applying a cyclic stress does not change the nature of oxidation damage but tends to enhance the extent of oxidation damage for temperatures at 750°C and 800°C. The influence of cyclic stress on oxidation damage appears to be insignificant at 700°C, indicating a combined effect of cyclic stress and temperature. Further energy dispersive x-ray (EDX) analyses show the enrichment of Cr and Ti, together with lower Ni and Co levels, in the surface oxide scales, suggesting the formation of brittle Cr 2 O 3 , TiO 2 , NiO and Co 3 O 4 oxides on the specimen surface.Penetration of oxygen into the material and associated internal oxidation, which leads to further 2 material embrittlement and associated failure, are evidenced from both secondary ion imaging and EDX analyses.
A B S T R A C T The evolution of the stress-strain fields near a stationary crack tip under cyclic loading at selected R-ratios has been studied in a detailed elastic-plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R-ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic-plastic finite element simulations of advancing fatigue cracks were carried out under plane-stress, plane-strain and generalized plane-strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane-strain and generalized plane-strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane-stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack-closure measurement, and indeed on the role of plasticity-induced crack closure in the reduction of the applied stress intensity factor range.
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