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Polycrystal homogenization accounting for channeling. Methodology and first results

Polycrystal homogenization accounting for channeling. Methodology and first results. Diogo GONCALVES , Maxime SAUZAY with the contribution of: Bertrand SICAUD and Jerôme HAZAN. 1 st Plenary meeting, 13-14 February, 2019. SUMMARY 1- Background/Objectives

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Polycrystal homogenization accounting for channeling. Methodology and first results

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  1. Polycrystal homogenization accounting for channeling.Methodology and first results Diogo GONCALVES , Maxime SAUZAY with the contribution of: Bertrand SICAUD and JerômeHAZAN 1st Plenary meeting, 13-14 February, 2019

  2. SUMMARY 1- Background/Objectives 2- New localization rule (three scales) 3- First results 4- Conclusions and interactions with other sub-tasks GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  3. Background • FCC metals/alloys and -Fe at room temperature • Plastic slip occurs in thin bands which usually cross all the single crystal or grain of size • The matrix between slip bands behaves almost elastically ; • Two main characteristic lengths: • - slip band thickness, (periodicity) • - slip band interspacing, d • Activation of low number of active slips systems even under strong plastic deformations • - Polycrystal of 316L SS traction, 𝐸 = 17 %, ~70% of the analyzed grains in single slip Surfaces micrographs: 10% deformed brass [2], 17% deformed 316L SS [1], 4.46% deformed copper [3] and 4.23% deformed 𝜶-Fe [3]. Tensile tests at room temperature [1]Hazan, 2019. PhD dissertation, UPMC. [2]Fourie and, Wilsdorf , 1959. ActaMetallurgica 7, 339–349 [3] Kahloun et al., 2016. International Journal of Plasticity 84, 277–298. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  4. Background • FCC metals/alloys and 𝜶-Fe at room temperature • Plastic slip occurs in thin bands which usually cross all the single crystal or grain of size • The matrix between slip bands behaves almost elastically ; • Two main characteristic lengths: • - slip band thickness, e (periodicity) • - slip band interspacing, d • Activation of low number of active slips systems even under strong plastic deformations • - Polycrystal of 316L SS traction, 𝐸 = 17 %, ~70% of the analyzed grains in single slip Similar behavior is observed in irradiatedmetals/alloys (BCC iron [1], F-M steels [2,3]) Channeling Deformation F82H, 15.2dpa at 236°C, 1305appm, tested at 250°C [2] [1] Eldrup et al., (2002) Journal of Nuclear Materials, 307-311, 912-917. [2] Wang et al., (2016). Journal of Nuclear Materials 468, 246–254. [3] Maloy et al., (2002). www.researchgate.net GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  5. Background The deformation of irradiated metallic polycrystals results in: • strong increase in the yield stress [1]  qualitatively predicted by combined MD – DD simulations [2,3]; • almost no strain-hardening in single and in polycrystals  qualitatively predicted by DD simulations (channelling)[1,2]; • Low number of active slips systems • Clear bands if neglecting coplanar slip • Irradiated stainless steels • 5 dpa and • Only one or two slip channel family is observed in each grain [4]. Effect of irradiation on the flow curve at T = 300 °C[1] [1] Chaouadi, R., 2008. Journal of NuclearMaterials 372, 379–390 [2] Li et al., 2011. Computational Materials Science 50, 2496–2501 [3] Arsenlis et al., 2012. ActaMaterialia 60, 3748–3757 [4] Jiao et al., 2018.. Journal of Nuclear Materials 501, 312–318. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  6. Background Irradiatedmetals/alloys • Ironpolycrystal [2] • 304L SS polycrystal [1] ~ perfect plasticity ~ perfect plasticity Tensile curves, Irradiated 304L SS (left) and Iron (right) [1] Hureet al., (2018). Contribution of Materials Investigations and Operating Experience to Light Water NPPs’ Safety, Performance and Reliability. [2] Eldrup et al., (2002).. Journal of Nuclear Materials 307–311, 912–917. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  7. Background “Standard” homogenization models • Polycrystalline homogenization • Mean field approaches (Eshelby’s solution) • Full field approaches (FE and FFT calculations) • Predictions of standard homogenization model  Intergranular hardening in the “ideal” elastic-plastic framework with is much to high in comparison to the experimental curves of irradated polycrytals Mean field approaches schematization Overall tensile responses of the different self-consistent approaches and the FE computations in the case quasi-ideal elastic-plasticity (no hardening and no strain rate effect) [1]. [1] Gonçalves et al, submitted, 2018. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  8. Background “Standard” homogenization models • Polycrystalline homogenization • Mean field approaches (Eshelby’s solution) • Full field approaches (FE and FFT calculations) • The number of slip systems activated by grain increases very quickly with the remote strain because of the local multiaxial stress tensor. • Predictions of standard homogenization model  More than three slip systems activated as [1]. Mean field approaches schematization Number of active slip systems by grain for two different self-consistent models. A slip system, i, is assumed to be active when . [1] Gonçalves et al, submitted, 2018. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  9. Background Why should we incorporate channels in the model ? • Plastic slip negligible between channels  lower internal stresses expected due the lower multiaxiality at the grain scale • Activation of a low number of channels (slip systems) • Low hardening behavior, characteristic of irradiated materials • A better agreement with experimental tensile curves and observations is expect Objectives • Propose and apply a dedicated mean-field homogenization model accounting for slip localization inside F-M blocks; • Comparing the results with experimental data  irradiated BCC metals/alloys (and some FCC ones, because the much more numerous data available) • Validating this modelling by comparing mean-field and full-field homogenization predictions GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  10. Mean field homogenization accounting for channeling • Hypotheses: • 1)  Each channel/slip bad is embedded in an elastic matrix • The channels/slip bands are characterized by a length (grain size, ) and a thickness, ,which can be measured experimentally; Elastic matrix Mean grain size, Channel thickness, Inter-channelspacing, Schematic view of a penny-shaped ellipsoid  Schematically view of plastic slip bands embedded in an elastic matrix. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  11. Mean field homogenization accounting for channeling • Hypotheses: • 1)  Each channel/slip band is embedded in an elastic matrix • The channels/slip bands are characterized by a length (grain size, ∅) and a thickness, 𝑒, which can be measured experimentally; • Solution of the Eshelby problem for one activated slip system which plane is parallel to the channel one: • Average channel (ch) stresses depending on the remote shear stress, , the elastic shear modulus, , the channel/ slip band plastic slip, • The ratio leading to muchlowerinternal stresses insidethe polycrystal and thenlowerstrainhardening. ) Shear stress computed accounting for the activated channel GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  12. Mean field homogenization accounting for channeling • Hypotheses: • 1)  Each channel/slip band is embedded in an elastic matrix • The channels/slip bands are characterized by a length (grain size, ∅) and a thickness, 𝑒, which can be measured experimentally; • Solution of the Eshelby problem for one activated slip system which plane is parallel to the channel one: • 2)  Each channel/slip band obeys plasticity laws based on the equations resulting from DDD - [Kubin et al., 2008] FCC crystals [1] 100 randomly oriented crystals 12 slip systems  {111}<110> Total dislocation density  2 families of mobile dislocation (edge and screw) and 1 family of edge-dipoles BCC crystals [2,3] 100 randomly oriented crystals corresponding to blocks 24 slip systems  2 families: {110}<111> and {112} <111> Total dislocation density  2 families of mobile dislocations: edge and screw dislocations Low-angle boundaries (LAB)*  24 families of symmetric tilt boundaries and 6 families of twist boundaries (neglected as a first approach because the misorientations are vey low) [1] Gonçalves et al, submitted, 2018 [2] Giroux et al., 2010. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 527, 3984–3993. [3] Giordana et al., 2012. Materials Science and Engineering: A 550, 103–111. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  13. Mean field homogenization accounting for channeling • Hypotheses: • 1)  Each channel/slip band is embedded in an elastic matrix • The channels/slip bands are characterized by a length (grain size, ∅) and a thickness, 𝑒, which can be measured experimentally; • Solution of the Eshelby problem for one activated slip system which plane is parallel to the channel one: • 2)  Each channel/slip band obeys plasticity laws based on the equations resulting from DDD - [Kubin et al., 2008] • 3) The channels/slip bands inside each grain are able to accommodate all of the plastic deformation of the grain • fraction of channels into the grain: • plastic strain tensor of channels: • plastic strain tensor of grains: [1] Ménard (2005). PhD Dissertation, Université Bordeaux I, Bordeaux. [2] Kahloun et al. (2016) International Journal of Plasticity 84, 277–298. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  14. Mean field homogenization accounting for channeling • Hypotheses: • 1)  Each channel/slip band is embedded in an elastic matrix • The channels/slip bands are characterized by a length (grain size, ∅) and a thickness, 𝑒, which can be measured experimentally; • Solution of the Eshelby problem for one activated slip system which plane is parallel to the channel one: • 2)  Each channel/slip band obeys plasticity laws based on the equations resulting from DDD - [Kubin et al., 2008] • 3) The channels inside each grain are able to accommodate all of the plastic deformation of the grain: • 4) The channels are considered as sufficiently long and close one from another (𝑑≪𝜙), resulting in a 'quasi-homogeneous' stresses state in each grain (validation by crystal FE computations under progress). Schematically view of stress state inside the crystal. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  15. Mean field homogenization accounting for channeling • Hypotheses: • 1)  Each channel/slip band is embedded in an elastic matrix • The channels/slip bands are characterized by a length (grain size, ∅) and a thickness, 𝑒, which can be measured experimentally; • Solution of the Eshelby problem for one activated slip system which plane is parallel to the channel one: • 2)  Each channel/slip band obeys plasticity laws based on the equations resulting from DDD - [Kubin et al., 2008] • 3) The channels inside each grain are able to accommodate all of the plastic deformation of the grain: • 4) The channels are considered as sufficiently long and close one from another (𝑑≪𝜙), resulting in a 'quasi-homogeneous' stresses state in each grain (validation by crystal FE computations under progress). • 5) In the case of uniform stresses on the channels/bands, the stress in the grain is then calculated by GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  16. Channel/slip bands parameters FCC metals/alloys BCC metals/alloys [1] Neuhauser et al. (1975).Acta Metallurgica 23, 441–453. [2] Ménard (2005). PhD Dissertation, Université Bordeaux I, Bordeaux. [3] Sicaud (2017), Private communication. [4] Kahloun et al. (2016) International Journal of Plasticity 84, 277–298. [5] Kramer et al. (2005) Acta Materialia 53, 4655–4664. [6] Byun, private communication [7] Sharp, J. (1967). Philosophical Magazine 16, 77-. [8] Yao et al. (2004). J. Nucl. Mater. 329, 1127–1132. [9] Hashimoto et al. (2006). Journal of NuclearMaterials, 351, 295–302. [10] Kahloun et al. (2016). International Journal of Plasticity 84, 277–298. [11] Wang et al. (2016). Materials Characterization 118, 225–234.

  17. Results FCC alloys (not irradiated) • Constant inter-band spacing, 𝑑 Tensile curves, 316L SS (left) and Cu30%Zn (right) • Low SFE polycrystals: • Low thickness, e, values similar to irradiated materials • intragranular hardening • dislocation density evolution laws • quasi-linearhardening Number of active slip systems per grain for different mean grain sizes for 316L SS. A slip system, , is assumed to be active when GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  18. Results Irradiatedmetals/alloys • Hypothese: • 1)  The number of channels increases with the plastic deformation [1] Implementation of a model considering a critical value of plastic strain, reached in the channels Experimental observations [1,2] Lower internal stresses [1] Hashimoto et al. (2006). Journal of Nuclear Materials, 351, 295–302. [2] Ménard(2005). PhD Dissertation, Université Bordeaux I, Bordeaux. [3] Kahloun et al. (2016) International Journal of Plasticity 84, 277–298. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  19. Irradiatedmetals/alloys • Hypotheses: • 1)  The number of channels in the crystal increases with plastic deformation [1,2] • When the active slip channel reaches a critical value of plastic strain, , a new channel appears in the crystal to accommodate the plastic strain • 2) The corresponding evolution of the inter-band • distance is expressed by: Better agreement with irradiated materials Tensile curves, EP. Model with increasing of the channels number inside the grains [1] Ménard (2005). PhD Dissertation, Université Bordeaux I, Bordeaux. [2] Kahloun et al. (2016) International Journal of Plasticity 84, 277–298. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  20. Conclusions|Perspectives • 1)  Implementation of a scale transition model based on channeling deformations, based on experimental observation • Simulation using experimental measurements carried out on different irradiated materials: • BCC-Iron, F-M steels(under progress) • Definition of inputs parameters according experimental observations (under discussion) • Channels thickness • PAG size, packet size, block size (F-M steels) • Initial critical stress, depending on the irradiation dose • 2)  Development of plastic crystalline laws for BCC crystals, based on DDD calculations • Take into account the effect of irradiation defects • 3) For future works: validation of this model in comparison to FE Computation curves (under progress by B. Sicaud) • Effect of lattice rotation due plastic deformation FE Computation mesh: squared grain, in a homogeneous matrix, containing a fixed number of slip bands (developped by B. Sicaud) GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  21. M4F project generalities • 1)  Task 5.1.1 – Mean-field homogenization accounting for channeling • D5.1 (CEA, TRC and METU) – Month 36  ~07/2020 • 2) Event and publications: • Conferences (Oral presentations) • Matériaux2018 (Strasbourg, France) – Diogo GONCALVES – “Homogénéisation du comportement polycristallin : Considérer la plasticité à l’échelle des grains ou des bandes de glissement ? "  • TMS 2019 (San Antonio, Texas, USA) – Bertrand SICAUD – "Accounting for slip band at the grain scale in polycrystalhomogenizationapplied to FCC metals and alloys" • IIB 2019 (Paris, France) – Diogo GONCALVES – "Polycrystalline homogenization accounting for grain size effects through slip bands” • 3) Future works will be discussed in a meeting this afternoon: MaximeSauzay (CEA), Diogo Gonçalves (CEA), Dome Tanguy (CNRS), Chen Jia-Chao (PSI) , Mercedez Hémandez-Mayoral (Ciemat) GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  22. This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 755039 GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  23. Background “Standard” homogenization models • Polycrystalline homogenization • Mean field approaches (Eshelby’s solution) • Full field approaches (FE and FFT calculations) • The number of slip systems activated by grain increases very quickly with the remote strain because of the local multiaxial stress tensor. • These approaches ignore the intra-granular scale location, and therefore some of the influence of SFE. In many standard homogenization schemes, the grain size is accounted for in the mean-free path evaluation (Saada’s model). Standard polycrystal models are not able to reproduce the strong effect of SFE on the Hall-Petch coefficient [1]. Evolution of the Hall-Petch coefficient with stacking fault energy. Comparison of the results of the Kröner and Kröner-Secant mean-field models and experimental measurements [1]. [1] Gonçalves et al, submitted, 2018. GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  24. Results FCC metals/alloys Number of active slip systems per grain for different mean grain sizes for 316L SS. A slip system, , is assumed to be active when Number of active slip systems per grain for different FCC metals and alloys. A slip system, , is assumed to be active when GONCALVES / M4F 1st Plenary Meeting, 14th Feb 2019

  25. Prédictions Results FCC metals/alloys Evolution of the Hall-Petch coefficient () with the normalized stacking fault energy. Comparison of the results of the BG model with those of Kröner and Kröner-Secant mean-field models and experimental measurements [1]. [1] Gonçalves et al, submitted, 2018. MATÉRIAUX2018 | 19 nov 2018

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