Download The influence of texture on phase transformation in metastable austenitic stainless steel PDF

TitleThe influence of texture on phase transformation in metastable austenitic stainless steel
LanguageEnglish
File Size4.0 MB
Total Pages132
Table of Contents
                            Samenvatting
Summary
Introduction
	About this thesis
	Outline
Crystalline texture
	Description of crystal orientations
	Measurement of Textures
	The Orientation Distribution Function
	Discretization of the ODF
	Summary
Martensitic transformations
	Martensitic transformations
		The Ms temperature
	Crystallography of martensitic transformations
	Stress-induced transformation
		Stepwise transformation
	Material behavior
		Determination of the critical driving force
		TRansformation Induced Plasticity (TRIP)
		Temperature & transformation during deformation
	Transformation & austenitic texture
		Driving Force in Generalized Spherical Harmonics
	Summary
Influence of texture on transformation
	Material
	Experiments
		Steel 1 (Untextured)
		Steel 2 (Textured)
	Austenitic textures
		Steel 1 (Untextured)
		Steel 2 (Textured)
	Texture Based Stress Induced Transformation model
	Discussion
		Texture evolution
		Driving Force Distribution
		TBSIT Model
	Summary
Influence of texture evolution on transformation
	Extended macro-mechanical transformation model
		General Overview
		Discretization
		Homogenization
		Stress-induced transformation
		Transformation
		Crystal Rotations
	Simulations
		Individual Grain Behavior
		Simulated Texture Evolution
		Full Model Calculations
		Influence of step size
	Experiments
		Texture evolution due to Transformation only
		Texture evolution due to Deformation only
		Texture evolution due to Transformation and Deformation
	Discussion
		Austenitic texture
		Transformation behavior
		Material behavior
	Summary
Transformation & Non-Monotonic Deformation
	Experimental Setup
	Experimental Results
		Proportional Experiments
		Strain reversal experiments
		Non-Proportional Experiments
	Strain Reversal Simulations
		TBSIT
		Advanced Model
	Discussion
	Summary
Conclusions & Recommendations
Appendix Crystallography of martensitic transformations
	Multiplicity of solution
Bibliography
                        
Document Text Contents
Page 1

The influence of texture on phase transformation

in metastable austenitic stainless steel

P. Hilkhuijsen

Page 2

This research was carried out under project number M63.1.09324
in the framework of the Research Program of the Materials innovation
institute (M2i) in the Netherlands (www.m2i.nl).

The influence of texture on phase transformation in metastable
austenitic stainless steel

P. Hilkhuijsen
PhD thesis, University of Twente, Enschede, The Netherlands
August 2013

ISBN 978-90-365-0125-5
Keywords: Transformation, Austenite, Martensite, Texture, Strain Path
1st and only printing August 2013

Printed by Ipskamp Drukkers B.V., Enschede, Nederland

Page 66

54

2. Process Parameters

a) The prescribed global stress state (e.g. uniaxial stress, plane stress,
shear stress, etc.).

Figure 5.1 shows a flow diagram of the model. After an initiation step, a
simulation procedure starts where during each simulation cycle a strain incre-
ment is calculated and applied. Each step in the simulation cycle is discussed
below.

In the initiation step of the model, the material is represented by a finite
number of grains. Each of these grains has an orientation, expressed by Euler
angles [φ1 Φ φ2] with respect to an external coordinate system, see Figure 2.3,
such that together, they represent the austenitic texture provided by the ODF.
The discretization scheme used in this work is discussed in Section 5.1.2. It
is assumed that all grains undergo the same strain (Voigt-Taylor constraint).
Therefore, the locations of the grains with respect to each other are not relevant.
Since the strains in all grains are equal, there is no direct interaction between
grains when transformation occurs in a grain. Instead the global average stress
is used for an interaction mechanism, as will be discussed later.

The strain increment dε is divided in two parts: a prescribed part dε0 and
an unknown part dε1. Strain dε0 is the strain imposed by the type of simulation
(e.g. uniaxial, plane, shear) and is applied to the grains in the first step in the
simulation cycle.

The average stress over all grains during a simulation must agree with the
type of simulation performed and is prescribed at the beginning of the simu-
lation. The unknown part of the strain increment, dε1, follows from this pre-
scribed stress state. This is calculated in step two of the simulation cycle. Now,
the total strain increment dε is known.

In step three of the cycle it is determined whether a grain can transform
from the austenite to the martensite phase given the strain increment dε. This
is based on the criterion for transformation provided by the stress-induced trans-
formation theory, which was discussed in Section 3.3. The criterion for transfor-
mation, provided by this theory, is based on the stress in the austenite phase of
the grain. To calculate this stress, the strain increment in the austenite phase
must be calculated first. At the start of the simulation, all grains are austenitic.
Therefore, the strain in the austenite is equal to the strain increment dε, deter-
mined in step one. At later stages, when part of a grain has transformed into the
martensite phase, the strain in the grain is distributed over both phases. The
martensite has different mechanical properties from the austenite phase, and

Page 67

55

y

n

U U> critmax

2. Calculate

dε1

3. Calculation

U

4. Transform

Grain

1. Apply

dε0

0. Initiation

5. Crystal

Rotations

T
ra

n
s
fo

rm
a
ti
o
n

S
u
b
-C

y
c
le

S
im

u
la

ti
o
n
C

y
c
le

Next

Cycle

y

n

Figure 5.1: Flow diagram of the model.

Page 131

119

[63] J. Eshelby, “The elastic field outside an ellipsoidal inclusion,” Proceedings
of the Royal Society of London, vol. 252, no. 1271, pp. 561–569, 1959.

[64] E. S. Perdahcioglu and H. J. M. Geijselaers, “Constitutive modeling of two
phase materials using the mean field method for homogenization,” Inter-
national Journal of Material Forming, vol. 4, no. 2, pp. 93–102, 2011.

[65] G. Lielens, P. Pirotte, A. Couniot, F. Dupret, and R. Keunings, “Predic-
tion of thermo-mechanical properties for compression moulded composites,”
Composites Part A: Applied Science and Manufacturing, vol. 29, no. 1-2,
pp. 63–70, 1998.

[66] J. Bishop and T. Hill, “A theory of the plastic distortion of a polycrys-
talline aggregate under combined stresses,” Philosophical Magazine Series
7, vol. 42, no. 327, pp. 414–427, 1951.

[67] P. van Houtte, S. Li, M. Seefeldt, and L. Delannay, “Deformation texture
prediction: from the taylor model to the advanced lamel model,” Interna-
tional Journal of Plasticity, vol. 21, pp. 589–624, 2005.

[68] R. Lebensohn and C. Tomé, “A self-consistent anisotropic approach for the
simulation of plastic deformation and texture development of polycrystals:
application to zirconium alloys,” Acta metallurgica et materialia, vol. 41,
no. 9, pp. 2611–2624, 1993.

[69] M. Crumbach, G. Pomana, P. Wagner, and G. Gottstein, “A taylor type
deformation texture model considering grain interaction and material prop-
erties. part i - fundamentals,” Recrystallization and grain growth, vol. 2,
pp. 1053–1060, 2001.

[70] H.-J. Bunge, “Some applications of the taylor theory of polycrystal plas-
ticity,” Kristall und Technik, vol. 5, pp. 145–175, 1970.

[71] D. Peirce, R. J. Asaro, and A. Needleman, “An analysis of nonuniform and
localized deformation in ductile single crystals,” Acta Metallurgica, vol. 30,
no. 6, pp. 1087–1119, 1982.

[72] E. S. Perdahcioglu, Constitutive Modeling of Metastable Austenitic Stain-
less Steel. PhD thesis, University of Twente, 2008.

[73] J. Post, K. Datta, and J. Beyer, “A macroscopic constitutive model for a
metastable austenitic stainless steel,” Materials Science and Engineering
A, vol. 485, no. 1-2, pp. 290–298, 2008.

Page 132

120

[74] H. Pijlman, Sheet material characterisation by multi-axial experiments.
PhD thesis, University of Twente, 2001.

[75] T. Hoc, G. Dirras, and C. Rey, “Mesostructure of the localization in pre-
strained mild steel,” Materials Science and Engineering: A, vol. 319-321,
pp. 304–307, 2001.

[76] J. Fernandes and J. Schmitt, “Dislocation microstructures in steel during
deep drawing,” Philosophical Magazine A, vol. 48, no. 6, pp. 841–870, 1983.

[77] E. Rauch and J.-H. Schmitt, “Dislocation substructures in mild steel de-
formed in simple shear,” Materials Science and Engineering A, vol. 113,
pp. 441–448, 1989.

[78] E. Rauch and S. Thuillier, “Rheological behaviour of mild steel under mono-
tonic loading conditions and cross loading,” Materials Science and Engi-
neering A, vol. 164, no. 1-2, pp. 255–259, 1993.

[79] A. Turner, “Cyclic deformation behavior of type 304 stainless steel at el-
evated temperature,” Metallurgical and materials transactions A, vol. 10,
no. 2, pp. 225–234, 1979.

[80] T. Hasegawa, T. Yakou, and S. Karashima, “Deformation behaviour and
dislocation structures upon stress reversal in polycrystalline aluminium,”
Materials Science and Engineering, vol. 20, pp. 267–276, 1975.

[81] E. C. Bain, “Nature of martensite,” Trans. AIME, vol. 70, p. 25, 1924.

Similer Documents