Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Journal of Materials Science
Published in: Journal of Materials Science 6/2020

01-10-2019 | Metals & corrosion

Formation of stress- and thermal-induced martensitic nanostructures in a single crystal with phase-dependent elastic properties

Authors: Mahdi Javanbakht, Mojtaba Adaei

Published in: Journal of Materials Science | Issue 6/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In the present paper, the effect of phase-dependent elastic properties on martensitic phase transformations (PTs) in a single crystal is investigated using the phase field approach. The simplest phase dependence of elastic properties is defined by different Young’s moduli for austenite (A) and martensite (M), and its effect is investigated for thermal- and stress-induced propagation of an A–M interface. The phase dependence of elastic properties is then included using the quadratic elastic energy with two constants different for A and martensitic variants. The coupled system of phase field and elasticity equations is solved using the nonlinear finite element method, and various examples of PTs are studied. A planar A–M interface propagation is studied under different thermal and mechanical loadings. It is revealed that the effect of phase-dependent elastic properties is more pronounced when thermal strain is included due to the interplay of elastic, transformational and thermal strains. The thermal-induced growth of a martensitic nucleus and the effect of periodic boundary conditions on the nucleus growth are investigated for both phase-independent (PI) and phase-dependent (PD) elastic properties with thermal strain and without it. Martensitic PTs with two variants are studied under different loadings using a one-fourth model and symmetric boundary conditions to reduce the effect of stress concentrations. Martensitic PTs with two variants are also studied in the presence of two circular holes for both the PI and PD elastic properties. This pronounces the significant effect of heterogeneous stress concentration and the size on the PTs. The effect of phase-dependent elastic properties is also studied on twinning in a martensitic grain embedded inside an austenitic matrix under overcooling. The obtained results reveal a significant effect of phase-dependent elastic properties on different types of martensitic PTs and remarkably change the interpretation of structural transformations at the nanoscale.
previous article Gold nanodahlias: potential nanophotosensitizer in photothermal anticancer therapy
next article Enhancement of electrical conductivity in aluminum single crystals by boron treatment in solid state

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Jacobs AE, Curnoe SH, Desai RC (2003) Simulations of cubic-tetragonal ferroelastics. Phys Rev B 68:224104
2.
Jin YM, Artemev A, Khachaturyan AG (2001) Three-dimensional phase field model of proper martensitic transformation. Acta Mater 49:2309–2320
3.
Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113–140
4.
Levitas VI, Lee DW, Preston DL (2010) Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations. Int J Plasticity 26:395–422
5.
Levitas VI, Javanbakht M (2011) Phase-field approach to martensitic phase transformations: effect of martensite–martensite interface energy. Int J Mater Res 102:652–665
6.
Seol DJ, Hu SY, Li YL, Chen LQ, Oh KH (2003) Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate. Met Mater Int 9:221–226
7.
Rasmussen KO, Lookman T, Saxena A, Bishop AR, Albers RC, Shenoy SR (2001) Three-dimensional elastic compatibility and varieties of twins in martensites. Phys Rev Lett 87:055704
8.
Denoual C, Caucci AM, Soulard L, Pellegrini YP (2010) Phase-field reaction-pathway kinetics of martensitic transformations in a model Fe3Ni alloy. Phys Rev Lett 105:035703
9.
Clayton JD, Knap J (2011) A phase field model of deformation twinning: nonlinear theory and numerical simulations. Phys D 240:841–858
10.
Levitas VI, Roy AM, Preston DL (2013) Multiple twinning and variant-variant transformations in martensite: phase-field approach. Phys Rev B 88:054113
11.
Wang YU, Jin YM, Khachaturyan AG (2003) Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films. Acta Mater 51:4209–4223
12.
Hu SY, Li YL, Zheng YX, Chen LQ (2004) Effect of solutes on dislocation motion: a phase-field simulation. Int J Plast 20:403–425
13.
Rodney D, LeBouar Y, Finel A (2003) Phase field methods and dislocations. Acta Mater 51:17–30
14.
Wang YU, Li J (2010) Phase field modeling of defects and deformation. Acta Mater 58:1212–1235
15.
Levitas VI, Javanbakht M (2012) Advanced phase field approach to dislocation evolution. Phys Rev B 86:140101
16.
Slutsker J, Thornton K, Roytburd AL, Warren JA, McFadden GB (2006) Phase field modeling of solidification under stress. Phys Rev B 74:014103
17.
18.
Levitas VI, Jafarzadeh H, Farrahi GH, Javanbakht M (2018) Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses. Int J Plast 111:1–35
19.
20.
Msekh MA, Silani M, Jamshidian M, Areias PM, Zhuang X, Zhuang X, Zi G (2016) Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model. Compos Part B Eng 93:97–114
21.
Levitas VI, Warren JA (2016) Phase field approach with anisotropic interface energy and interface stresses: large strain formulation. J Mech Phys Solids 91:94–125
22.
Mamivand M, Asle Zaeem M, Hel Kadiri (2013) A review on phase field modeling of martensitic phase transformation. Comp Mater Sci 77:304–311
23.
Finel A, Bouar YL, Gaubert A, Salman U (2010) Phase field methods: microstructures, mechanical properties and complexity. C R Phys 11:245–256
24.
Artemev A, Jin Y, Khachaturyan AG (2001) Three-dimensional phase field model of proper martensitic transformation. Acta Mater 49(7):1165–1177
25.
Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite-martensite. Phys Rev B 66:134206
26.
Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis. Phys Rev B 66:134207
27.
Levitas VI, Preston DL, Lee DW (2003) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. III. Alternative potentials, critical nuclei, kink solutions, and dislocation theory. Phys Rev B 68:134201
28.
Hu SY, Henager CH, Chen LQ (2010) Simulations of stress-induced twinning and de-twinning: a phase field model. Acta Mater 58:6554–6564
29.
Levitas VI, Lee DW (2007) Athermal resistance to interface motion in the phase-field theory of microstructure evolution. Phys Rev Lett 99:245701
30.
Zhang W, Jin YM, Khachaturyan AG (2007) Phase field microelasticity modeling of heterogeneous nucleation and growth in martensitic alloys. Acta Mater 49:565–574
31.
Levitas VI, Javanbakht M (2010) Surface tension and energy in multivariant martensitic transformations: phase-field theory, simulations, and model of coherent interface. Phys Rev Lett 105:165701
32.
Levitas VI, Javanbakht M (2011) Surface-induced phase transformations: multiple scale and mechanics effects and morphological transitions. Phys Rev Lett 107:175701
33.
Levitas VI, Levin VA, Zingerman KM, Freiman EI (2009) Displacive phase transitions at large strains: phase-field theory and simulations. Phys Rev Lett 103:025702
34.
Levitas VI (2013) Phase-field theory for martensitic phase transformations at large strains. Int J Plast 49:85–118
35.
Javanbakht M, Barati E (2016) Martensitic phase transformations in shape memory alloy: phase field modeling with surface tension effect. Comp Mater Sci 115:137–144
36.
Mirzakhani S, Javanbakht M (2018) Phase field-elasticity analysis of austenite–martensite phase transformation at the nanoscale: finite element modeling. Comput Mater Sci 154:41–52
37.
De Suvranu (2017) A phase-field model for shock-induced α-γ phase transition of RDX. Int J Plast 88:140–158
38.
Schoof E, Schneider D, Streichhan N, Mittnacht T, Selzer M, Nestler B (2018) Multiphase-field modeling of martensitic phase transformation in a dual-phase microstructure. Int J Solids Struct 134:181–194
39.
Segawa M, Yamanaka A, Nomoto S (2017) Multi-phase-field simulation of cyclic phase transformation in Fe-C-Mn and Fe-C-Mn-Si alloys. Comp Mater Sci 136:67–75
40.
Levitas VI (2014) Phase field approach to martensitic phase transformations with large strains and interface stresses. J Mech Phys Solids 70:154–189
41.
Levin VA, Levitas VI, Zingerman KM, Freiman EI (2013) Phase-field simulation of stress-induced martensitic phase transformations at large strains. Int J Solids Struct 50:2914–2928
42.
Yamanaka A, Takaki T, Tomita Y (2010) Elastoplastic phase-field simulation of martensitic transformation with plastic deformation in polycrystal. Int J Mech Sci 55:245–250
43.
Kundin J, Raabe D, Emmerich H (2011) A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite. J Mech Phys Solids 59:2082–2102
44.
Mamivand M, Zaeem MA, Kadiri HE, Chen LQ (2013) Phase field modeling of the tetragonal-to-monoclinic phase transformation in zirconia. Acta Mater 61:5223–5235
45.
Mamivand M, Zaeem MA, Kadiri HE (2014) Shape memory effect and pseudoelasticity behavior in tetragonal zirconia polycrystals: a phase field study. Int J Plast 60:71–86
46.
Mamivand M, Zaeem MA, Kadiri HE (2014) Phase field modeling of stress-induced tetragonal-to-monoclinic transformation in zirconia and its effect on transformation toughening. Acta Mater 64:208–219
47.
Levitas VI (2013) Thermodynamically consistent phase field approach to phase transformations with interface stresses. Acta Mater 61:4305–4319
48.
Yeddu HK, Borgenstam A, Agren J (2013) Stress-assisted martensitic transformations in steels: a 3-D phase-field study. Acta Mater 61:2595–2606
49.
Malik A, Amberg G, Borgenstam A, Agren J (2013) Effect of external loading on the martensitic transformation–A phase field study. Acta Mater 61:7868–7880
50.
Heo TW, Chen LQ (2014) Phase-field modeling of displacive phase transformations in elastically anisotropic and inhomogeneous polycrystals. Acta Mater 76:68–81
51.
Momeni K, Levitas VI (2015) A phase-field approach to solid–solid phase transformations via intermediate interfacial phases under stress tensor. Int J Solids Struct 71:39–56
52.
Yeddu HK, Lookman T (2015) Phase-field modeling of the beta to omega phase transformation in Zr–Nb alloys. Mater Sci Eng A 634:46–54
53.
Tuma K, Stupkiewicz S, Petryk H (2016) Size effects in martensitic microstructures: finite-strain phase field model versus sharp-interface approach. J Mech Phys Solids 95:284–307
54.
Cui S, Wan J, Zuo X, Chen N, Rong Y (2016) Interface stress evolution of martensitic transformation in MnCu alloys: a phase-field study. Mater Design 109:88–97
55.
Denoual C, Vattré A (2016) A phase field approach with a reaction pathways-based potential to model reconstructive martensitic transformations with a large number of variants. J Mech Phys Solids 90:91–107
56.
Toloui M, Militzer M (2018) Phase field modeling of the simultaneous formation of bainite and ferrite in TRIP steel. Acta Mater 144:786–800
57.
Levitas VI, Javanbakht M (2014) Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms. Nanoscale 6(1):162–166
58.
Levitas VI, Javanbakht M (2015) Interaction between phase transformations and dislocations at the nanoscale. Part 1. General phase field approach. J Mech Phys Solids 82:287–319
59.
Levitas VI, Javanbakht M (2015) Interaction between phase transformations and dislocations at the nanoscale. Part 2: phase field simulation examples. J Mech Phys Solids 82:164–185
60.
Javanbakht M, Levitas VI (2016) Phase field simulations of plastic strain-induced phase transformations under high pressure and large shear. Phys Rev B 94:214104
61.
62.
Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis. Phys Rev B 66:134207
63.
Clapp PC, Besquart CS, Shao Y, Zhao Y, Rifkin JA (1994) Transformation toughening explored via molecular dynamics and Monte Carlo simulations. Modell Simul Mater Sci Eng 2:551–557
64.
Wang Y, Liu ZK, Chen LQ (2004) Thermodynamic properties of Al, Ni, NiAl, and Ni3Al from first-principles calculations. Acta Mater 52:2665–2671
65.
Wang C, Xu J, Hu X, Chen D, Sun H, Yu B (2011) Elastic and thermodynamic characteristics of NiAl and Ni3Al from first-principles calculations. Int J Mod Phys B 25:3623–3631
Metadata
Title
Formation of stress- and thermal-induced martensitic nanostructures in a single crystal with phase-dependent elastic properties
Authors
Mahdi Javanbakht
Mojtaba Adaei
Publication date
01-10-2019
Publisher
Springer US
Published in
Journal of Materials Science / Issue 6/2020
Print ISSN: 0022-2461
Electronic ISSN: 1573-4803
DOI
https://doi.org/10.1007/s10853-019-04067-6

Other articles of this Issue 6/2020

Journal of Materials Science 6/2020 Go to the issue

Composites & nanocomposites

Compressive strength and thermal insulation properties of the 3D woven spacer composites with connected spacer yarn structure

Energy materials

MnO2@NiO nanosheets@nanowires hierarchical structures with enhanced supercapacitive properties

Chemical routes to materials

Selective removal of CO from hydrocarbon-rich industrial off-gases over CeO2-supported metal oxides

Chemical routes to materials

Electrowetting behaviour of thermostable liquid over wide temperature range

Chemical routes to materials

Facile fabrication of mechanically stable non-iridescent structural color coatings

Polymers & biopolymers

A model for roughness statistics of heterogeneous fibrous materials

Premium Partners

    Image Credits