Law of mixture in an austenite-ferrite dual phase material

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Introduction

In steelmaking, a number of processes are employed in order to achieve the desired final product. The mechanical properties are modified through control of the microstructure which can be done by a combination or one of the following:
– Modifying the alloy composition which in turn will modify the equilibrium and non equilibrium second phases present in a material, including their volume fractions, shapes and sizes and distribution.
– Heat treatment can also be used to modify the mechanical properties through altering the defect structure, grain size, and also the other aspects already mentioned under alloy composition.

Stacking Fault

Stacking faults are one of the most important planar defects found in metallic materials that give rise to the major difference in deformation behaviour of austenite and ferrite phases. A stacking fault is easier to consider in face centred cubic (fcc) structure as a disturbance in the ABC stacking sequence of the close packed {111} layers. The energy difference arising between a perfect ABC stacking sequence and an imperfect or disturbed stacking sequence is termed the stacking fault energy (SFE). The interaction between stacking fault energy and dislocations forms the fundamental basis of plastic deformation and hence other processes important to rolling. Plastic deformation in austenitic steels can occur through different mechanisms and the most important deciding factor in the operating mechanism is the stacking fault energy (SFE). The SFE of austenitic steels has been reported to vary typically in the range of 14 – 28 mJ/m2 [45], [46], [47], though this can vary due to alloying, as will be shown shortly.

Edge and Screw Dislocations

For an edge dislocation, climb of only one slip plane is possible per vacancy (or a set of vacancies) at a time due to the Burgers vector being perpendicular to the dislocation. On the other hand, in a screw dislocation, the Burgers vector and the dislocation are parallel, thus making any valid slip plane containing the dislocation a possible alternative slip plane. The orientation of the Burgers vector and the slip plane of the dislocation, therefore, fundamentally distinguish the way the dislocation can move. Whereas the screw dislocation can move by slip or glide in any valid direction perpendicular to the line itself, an edge dislocation can only glide in its single slip plane [59], [60]. However, through climb an edge dislocation is also able to move in a direction perpendicular to its slip plane.

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Cross slip of dislocations

Apart from climb, dislocations can cross slip to another valid slip plane in the same direction to avoid other dislocations in their slip plane or obstacles such as precipitates, especially at intermediate temperatures [62]. Cross slip is prominent in metals with high SFE, for the reason that will be elaborated shortly and only screw dislocations can cross slip as their Burgers vector lie parallel to the dislocation line. Though cross slip is thermally activated, it does not however require the diffusion of vacancies [3].

Chapter 1
1.1 Background of duplex stainless steels
1.2 The hot rolling process of steels
1.3 Problem Statement
1.4 Objectives
Chapter 2
2.1 Introduction
2.2 Plastic deformation in the two-phase region
2.2.1 Stacking Fault
2.2.2 Edge and Screw Dislocations
2.2.4 Cross slip of dislocations
2.2.5 Law of mixture in an austenite-ferrite dual phase material
Chapter 3
3. Plastic Flow Stress and Related Mechanisms
3.1 Recrystallization and Softening
3.1.1 Classical nucleation theory
3.1.2 Strain induced boundary migration
3.1.3 Subgrain rotation and coalescence model
3.2 Dynamic Recrystallization
3.2.1 Dynamic recrystallization in single phase austenite
3.2.2 Dynamic recrystallization in single phase ferrite
3.2.3 Dynamic recrystallization in the two phase (austenite + ferrite) region
3.3 Dynamic induced ferrite transformation
3.4 Critical strain for DT and DRX in austenite
Chapter 4
4.1 Constitutive Equations
4.2 The Zener-Hollomon Parameter (Z)
4.3 Determining the material constants
4.4 Mean flow stress (MFS)
4.5 The Hot Working Window
Chapter 5
5.1 Experimental Procedure
5.2 Hot Compression Tests
5.2.1 Single-hit uniaxial compression test
5.2.2 Multi-pass uniaxial compression test
5.3 Microstructural Analysis
5.4 Phase prediction
Chapter 6
6.1 Experimental Results
6.2 Flow stress analysis
6.2.1 Single hit Bahr Dilatometer tests
6.2.2 Multipass deformation tests
6.3.1 Phase fraction measurement
6.3.2 Volume fraction changes during inter-pass time
6.4 EBSD Analysis
6.4.1 Effect of temperature at low strain rate (0.1s-1)
6.4.2 Effect of temperature at high strain rate (15 s-1)
6.4.3 Effect of strain
6.4.4 Effect of inter-pass time
6.5 Modelling the saturation stress flow behaviour
6.5.1 Hyperbolic sinh equation
Chapter 7
7.1 Discussion
7.1.1 Region I: Strain Hardening Modelling
7.1.2 Region II: Flow softening
7.1.3 Coupling the E-M model to the Avrami model
7.1.4 Implications of findings on in-plant Steckel Mill
Chapter 8
8.1 Conclusions
8.2 Recommendations for future work
References