Fundamentals of Materials Modelling for Metals Processing Technologies: Theories and Applications

Title Page
Copyright
Preface
Introduction
Contents
Chapter 1: Metal Forming and Materials Modelling
1.1 Introduction to Metal Forming Processes
	1.1.1 Compressive forming
	1.1.2 Sheet metal forming
	1.1.3 Advantages of forming
1.2 Modification of Microstructure through Forming
	1.2.1 Grain size
	1.2.2 Elimination of defects
	1.2.3 Hardening
	1.2.4 Failure of materials in forming
1.3 Methods of Materials Modelling
	1.3.1 Constitutive equations
	1.3.2 Modelling of mechanical and physical properties of materials
	1.3.3 Unified constitutive equations and state variables
Chapter 2: Mechanics of Metal Deformation
2.1 Crystallised Materials and Plastic Deformation
	2.1.1 Crystallised materials
	2.1.2 Plastic deformation in single crystals
2.2 Dominant Deformation Mechanisms
	2.2.1 Plastic deformation in cold forming
	2.2.2 Viscoplastic deformation in warm and hot metal forming
2.3 Stress and Strain Definitions
	2.3.1 Stresses
	2.3.2 Displacements, strains and strain rates
	2.3.3 Finite deformation and other strain definitions
	2.3.4 Stress and strain relationships
	2.3.5 Elastic strain energy
2.4 Yield Criteria
	2.4.1 von-Mises yield criterion
	2.4.2 Tresca
	2.4.3 Graphical illustration of von-Mises and Tresca yield surfaces
	2.4.4 Other yield criteria
2.5 Stress States for Different Metal Forming Conditions
	2.5.1 Simple deformation conditions
	2.5.2 Stress states in forming processes
Chapter 3: Unified Constitutive Modelling Techniques
3.1 Viscoplastic Potential and Basic Constitutive Laws
	3.1.1 Basic definitions for elastic-plastic problems
	3.1.2 Calculation of plastic strains
	3.1.3 Viscoplastic potentials
3.2 Hardening in Plastic Deformation
	3.2.1 Isotropic hardening
	3.2.2 Kinematic hardening
3.3 State Variables and Unified Constitutive Equations
	3.3.1 Unified constitutive equations
	3.3.2 Solution of the unified constitutive equations
	3.3.3 Determination of constants within the equations
	3.3.4 Multiaxial constitutive equations
Chapter 4: Plasticity in Cold Metal Forming
4.1 Application Domains
4.2 Incremental Methods and Hardening Laws
	4.2.1 Uniaxial behaviour
	4.2.2 Plastic flow rules based on von-Mises yield criterion
4.3 Other Plastic Flow Rules
	4.3.1 Hill’s anisotropic yield criterion and flow rule
	4.3.2 Isotropic flow rule with Tresca criterion
4.4 Kinematic Hardening Law
Chapter 5: Viscoplasticity and Microstructural Evolution in Warm/Hot Metal Forming
5.1 Application Domains
5.2 Viscoplastic Deformation of Metals
	5.2.1 High temperature creep
	5.2.2 Stress relaxation
	5.2.3 Basic features of viscoplasticity
5.3 Superplasticity and Deformation Mechanisms
	5.3.1 The process and features
	5.3.2 Strain rate hardening, sensitivity and ductility
	5.3.3 Materials modelling for SPF
5.4 Modelling of Viscoplasticity and Hardening
	5.4.1 Dissipation potential and normality law
	5.4.2 Viscoplastic flow of materials
	5.4.3 Isotropic hardening equations
5.5 Dislocation Hardening, Recovery and Recrystallisation
	5.5.1 Evolution of dislocation density
	5.5.2 Recrystallisation
	5.5.3 Modelling of grain evolution
	5.5.4 Effect of recrystallisation and grain size on dislocation density
	5.5.5 Effect of grain size on viscoplastic flow of materials
5.6 Examples of Unified Viscoplastic Constitutive Equations
	5.6.1 Unified constitutive equations for superplasticity
	5.6.2 Unified viscoplastic constitutive equations for hot rolling of steels
Chapter 6: Continuum Damage Mechanics in Metal Forming
6.1 Concept of Damage Mechanics
	6.1.1 Definition of damage and damage variables
	6.1.2 Specific damage definition methods
6.2 Damage Mechanisms, Variables and Models
	6.2.1 Kachanov creep damage equation
	6.2.2 Damage due to multiplication of mobile dislocations in high temperature creep
	6.2.3 Damage due to creep-constrained cavity nucleation and growth
	6.2.4 Damage due to continuum cavity growth
	6.2.5 Damage and deformation mechanisms in metal forming
6.3 Modelling of Stress State on Damage Evolution
	6.3.1 Stress-state damage models for high temperature creep
	6.3.2 Stress-state damage models for hot forming
	6.3.3 2D stress-state model for hot stamping
6.4 Modelling of Damage in Cold Metal Forming
	6.4.1 Rice and Tracey model
	6.4.2 Strain energy model
	6.4.3 Gurson’s model
6.5 Modelling of Damage in Warm/Hot Metal Forming
	6.5.1 Damage modelling for superplastic forming
	6.5.2 Grain size and strain rate effects in hot forming
6.6 Damage Healing in Hot Compressive Forming
Chapter 7: Numerical Methods for Materials Modelling
7.1 The Numerical Framework in Materials Modelling
	7.1.1 Methods of solving ODE-type constitutive equations
	7.1.2 Determination of unified constitutive equations from experimental data
7.2 Numerical Integration
	7.2.1 Explicit Euler method
	7.2.2 Midpoint method
	7.2.3 Runge–Kutta method
	7.2.4 Implicit Euler method
7.3 Error Analysis and Step-size Control Methods
	7.3.1 Error and step-size control
	7.3.2 Unit problems in unified constitutive equations
	7.3.3 Unitless error assessment method
7.4 A Case Study for Implicit Numerical Integration
	7.4.1 Implicit integration method
	7.4.2 Normalised error estimation and step-size control
	7.4.3 Jacobian matrix and computational efficiency
	7.4.4 Comments on solving ODE-type unified constitutive equations
7.5 Formulation of Objective Functions for Optimisation
	7.5.1 Specific features of objective functions for materials modelling
	7.5.2 Shortest distance method with correction (OF-I)
	7.5.3 Universal multi-objective function (OF-II)
	7.5.4 True error definition multi-objective function (OF-III)
	7.5.5 Assessment of the features of the objective function
7.6 Optimisation Methods for Determining Constitutive Equations from Experimental Data
	7.6.1 Concept of optimisation
	7.6.2 Gradient-based optimisation method
	7.6.3 Evolutionary programming (EP)-based method
7.7 Examples for the Determination of Constitutive Equations
	7.7.1 System development for materials modelling
	7.7.2 Determination of constitutive equations
	7.7.3 Discussion
Chapter 8: Materials and Process Modelling in Metal Forming Applications
8.1 The Framework for Advanced Metal Forming Process Modelling
8.2 Modelling for Superplastic Forming
	8.2.1 Unified SPF constitutive equations
	8.2.2 FE model and numerical procedures
	8.2.3 Grain size effect on forming of the Ti-6Al-4V rectangular box
	8.2.4 Forming of Al-Zn-Mg box at 515 °C.
8.3 Creep Age Forming (CAF) of Large Aluminium Panels
	8.3.1 CAF process and deformation mechanisms
	8.3.2 Age hardening of aluminium alloys
	8.3.3 Unified creep ageing constitutive equations
	8.3.4 Numerical procedures for CAF process simulations
	8.3.5 CAF process modelling results
8.4 HFQ of Aluminium Panel Components
	8.4.1 Introduction to the HFQ process
	8.4.2 Forming limit in hot stamping
	8.4.3 Unified constitutive equations for HFQ aluminium
	8.4.4 An examination of HFQ characteristics
8.5 Hot Rolling of Steel
	8.5.1 Unified viscoplastic constitutive equations
	8.5.2 FE model and simulation procedures
	8.5.3 Prediction results
8.6 Modelling of Two-phase Titanium Alloys During Forging
	8.6.1 Hot forming of Ti-6Al-4V gas turbine blades
	8.6.2 Deformation and softening mechanisms
	8.6.3 Unified viscoplastic constitutive equations
	8.6.4 Determined unified viscoplastic constitutive equations
Chapter 9: Crystal Plasticity for Micro-forming Process Modelling
9.1 Crystal Plasticity and Micro-forming
	9.1.1 Micro components and size effects
	9.1.2 Crystal plasticity
9.2 Crystal Plasticity Constitutive Equations
	9.2.1 Crystal kinetics
	9.2.2 Crystal viscoplasticity constitutive equations
9.3 Generation of Grain Structures
	9.3.1 Grain distribution and generation algorithms
	9.3.2 Grain generation with physical material parameters
	9.3.3 Creation of 2D-VGRAIN system
9.4 Creation of Cohesive Zones and 3D Grain Structures
	9.4.1 Cohesive zones
	9.4.2 3D grain structures
9.5 VGRAIN System Development
	9.5.1 Overall system
	9.5.2 Grain structure generation
9.6 Case Studies for Micro-forming Process Modelling
	9.6.1 Necking in plain strain tension
	9.6.2 Extrusion of micro-pins
	9.6.3 Hydroforming of micro-tubes
	9.6.4 Compression of micro-pillars
Appendix A: Examples of Determined Unified Viscoplastic Constitutive Equations
References
Index