# gradient dependent deformation of two phase single crystals

### Constitutive modelling of anisotropic creep deformation in

2. Lack of test data. 3. Limited knowledge of deformation mechanisms and therefore the phenomena that need to be included in a successful model.The development of constitutive models to describe deformation of two phase superalloy single crystal generally falls into one of three categories. Gurtin M.E. A finite-deformation gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations. International Journal of Plasticity 24 702–725 (2008) CrossRef zbMATH Google Scholar

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Gurtin M.E. A finite-deformation gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations. International Journal of Plasticity 24 702–725 (2008) CrossRef zbMATH Google Scholar 2. Lack of test data. 3. Limited knowledge of deformation mechanisms and therefore the phenomena that need to be included in a successful model.The development of constitutive models to describe deformation of two phase superalloy single crystal generally falls into one of three categories.

Get Price### Simulation of Torsion of Thin FCC Single Crystal Wires by

The size effects observed in the torsion of thin FCC single crystal wires is modelled by the employment of mechanism-based strain gradient crystal plasticity (MSG-CP). In the formulation the total slip resistance in each active slip system is assumed to be due to a mixed population of forest obstacles arising from both statistically stored and geometrically necessary dislocations. Modelling plastic deformation in a single-crystal nickel-based superalloy using the precipitate phase that ranges between 40 and 70 . and gradient-dependent deformation (Meissonnier et al

Get Price### Modelling plastic deformation in a single-crystal nickel

Nov 15 2016 · The crystal plasticity was applied to study creep (Zhao et al. 2006) fatigue (Kiyak et al. 2008) thermal-mechanical fatigue (Shenoy et al. 2005) indentation (Zambaldi et al. 2007) and gradient-dependent deformation (Meissonnier et al. 2001) of single crystal nickel superalloys. In this work a gradient-and rate-dependent crystallographic formulation is proposed to investigate the macroscopic behaviour of two-phase single crystals. The slip-system-based constitutive formulation relies on strain-gradient concepts to account

Get Price### Evolution of Layered Structures in a Gradient-Dependent

Gradient-Dependent Viscoplastic Material C. Faciu A. Molinari To cite this version phase transitions in shape memory single crystals. 1. INTRODUCTION Phase transitions in continuum bodies are a subject of intense studies in mechanics mathematics localization of deformation 3 4 phase transitions 2 16-181 and other physical Mar 13 2007 · Elastically anisotropic physically based length-scale- and rate-dependent crystal plasticity finite element investigations of a model hcp polycrystal are presented and a systematic study was carried out on the effects of combinations of crystallographic orientations on local grain-level stresses and accumulated slip in cycles containing cold dwell.

Get Price### Mechanistic Modelling of Deformation and Void Growth

A rate dependent crystallographic formulation is introduced to describe the in-elastic deformation behaviour of the latest generation of single crystal superalloys. The evolution of the current dislocation and obstacle network is described through appropriate slip resistance and internal or back stress variables for each slip system. Many two-phase alloys work-harden much faster than do pure single crystals. This is because the two phases are not equally easy to deform. Based on gradient-dependent plasticity where an

Get Price### Deformation process in single crystalstec-science

Introduction ð110 Þ for the two modes are related by a rotation angle of twin¼70.53 (Figure 1c). For convenience we define new coordinate axes (x 0 y z0) along ½001 ½110 and ½110 directions respectively. 2.2. Phase-field formulation of deformation twinning Within a single crystal or a given grain in a polycrystal of a fcc solid it requires 12Get Price### Temperature dependence of elastic and plastic deformation

Single-phase solid-solution refractory high-entropy alloys (HEAs) show remarkable mechanical properties such as their high yield strength and substantial softening resistance at elevated temperatures. Hence the in-depth study of the deformation behavior for body-centered cubic (BCC) refractory HEAs is a critical issue to explore the uncovered/unique deformation mechanisms. Gurtin M.E. A finite-deformation gradient theory of single-crystal plasticity with free energy dependent on the accumulation of geometrically necessary dislocations. Int. J. Plast. 26 1073–1096 (2010). doi 10.1016/j.ijplas.2010.02.002 CrossRef zbMATH Google Scholar

Get Price### (PDF) Strain gradient effects on microscopic strain field

A ®nite deformation rate-dependent strain gradient crystal plasticity formulation 3.1. Kinematics and the principle of virtual work Consider a material point in a strain gradient solid which is displaced from its position X in the undeformed con®guration by a displacement u to position x in the current con®guration. Gradient-Dependent Deformation of Two-phase Single Crystals a gradient- and rate-dependent crystallographic formulation is proposed to investigate the macroscopic behaviour of two-phase single

Get Price### Development of a model for simulation of micro-twin and

Microstructures induced by a stress gradient in a nickel-based superalloy. Anisotropic creep behavior of a nickel-based super-alloy compared with single phase nickel solid solution and γ′ phase single crystals. Gradient-dependent deformation of two-phase single crystals. Oct 22 2020 · Room temperature deformation of single crystals of Ti 5 Si 3 with the hexagonal D8 8 structure investigated by micropillar compression tests

Get Price### Equivalent plastic strain gradient enhancement of single

Apr 19 2012 · A geometrically linear single crystal model extended by an energetic hardening term based on the gradient of the equivalent plastic strain γ eq has been introduced. The direct finite-element implementation of the theory is computationally expensive due to the need of piecewise differentiable shape functions for the plastic slip parameters λ α . The creep deformation behavior of superalloy single crystal is strongly temperature stress orientation and alloy dependent. For a single-crystal superalloy there are 3 different modes of creep deformation under regimes of different temperature and stress Rafting Tertiary and Primary.

Get Price### Gradient crystal plasticity modelling of anelastic effects

Mar 11 2014 · It is now a well known phenomenon that thin films are susceptible to size effects which can be captured adequately by gradient plasticity theories. Besides the scale dependency metal thin films also exhibit time dependent behavior anelasticity (deformation recovery over time following elastic spring back upon load removal) and creep (permanent deformation developed over time at constant Nov 01 2000 · Gradient-dependent deformation of two-phase single crystals 1. Introduction. A major factor contributing to the formation of microcracks or damage in single crystals strengthened 2. Characteristic length scales in two-phase single crystals. The microstructure of single crystals

Get Price### Crystal plasticity finite‐element modelling of cyclic

Apr 13 2020 · The constitutive framework was based on the large‐deformation rate‐dependent CP theory. 9 20 The total deformation gradient F is decomposed into two multiplicative components which are the elastic part (F e) whereas the plastic deformation in the single crystals is only caused by the shear flow along crystalline slip systems. The Abstract In this work a gradient- and rate-dependent crystallographic formulation is proposed to investigate the macroscopic behaviour of two-phase single crystals.

Get Price### A phenomenological creep model for nickel-base single

May 08 2018 · For the purpose of good reproduction and prediction of creep deformation of nickel-base single crystal superalloys at intermediate temperatures a phenomenological creep model is developed which accounts for the typical γ/γ microstructure and the individual thermally activated elementary deformation processes in different phases.The internal stresses from γ/γ lattice ð110 Þ for the two modes are related by a rotation angle of twin¼70.53 (Figure 1c). For convenience we define new coordinate axes (x 0 y z0) along ½001 ½110 and ½110 directions respectively. 2.2. Phase-field formulation of deformation twinning Within a single crystal or a given grain in a polycrystal of a fcc solid it requires 12

Get Price### Temperature dependence of elastic and plastic deformation

Single-phase solid-solution refractory high-entropy alloys (HEAs) show remarkable mechanical properties such as their high yield strength and substantial softening resistance at elevated temperatures. Hence the in-depth study of the deformation behavior for body-centered cubic (BCC) refractory HEAs is a critical issue to explore the uncovered/unique deformation mechanisms. An FFT based strain gradient crystal plasticity study of grain boundaries "Gradient-dependent deformation of two-phase single crystals" J. Mech. Phy. Solids 48 (2000). 2 P. Eisenlohr M. Diehl R.A. Lebensohn and F. Roters "A spectral method solution to crystal

Get Price### Strain gradient plasticity in gradient structured metals

Many two-phase alloys work-harden much faster than do pure single crystals. This is because the two phases are not equally easy to deform. Based on gradient-dependent plasticity where an Dec 28 2009 · Experimental and crystal plasticity studies of deformation and crack nucleation in a titanium alloy Show all authors Wilkinson A. J. Anisotropy in the plastic flow properties of single crystal alpha titanium determined from micro cantilever beams O Dowd N. P. Gradient-dependent deformation of two-phase single crystals J. Mechanics

Get Price### Modelling plastic deformation in a single-crystal nickel

Nov 15 2016 · The crystal plasticity was applied to study creep (Zhao et al. 2006) fatigue (Kiyak et al. 2008) thermal-mechanical fatigue (Shenoy et al. 2005) indentation (Zambaldi et al. 2007) and gradient-dependent deformation (Meissonnier et al. 2001) of single crystal nickel superalloys. Oct 12 2018 · Because of the aforementioned unique GSFE the γ-TiAl crystals deform differently from the FCC crystals. According to previous experimental studies 5 11 13 plastic deformation of bulk single

Get Price### A single-crystal model for the high-strain rate

A continuum model for the high-rate thermo-mechanical deformation of single-crystal cyclotrimethylene trinitramine (RDX) is developed. The model includes the effects of anisotropy large deformations nonlinear thermo-elasticity phase transformations and plastic slip. A multiplicative decomposition of the deformation gradient is used. An FFT based strain gradient crystal plasticity study of grain boundaries "Gradient-dependent deformation of two-phase single crystals" J. Mech. Phy. Solids 48 (2000). 2 P. Eisenlohr M. Diehl R.A. Lebensohn and F. Roters "A spectral method solution to crystal

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