Superplastic Flow

The present book aims at the following: - To outline briefly the techniques of mechanics of solids, particularly as it applies to strain rate sensitive materials, - to assess the present level of investigations on the mechanical behaviour of superplastics, - to formulate the main issues and challenges in mechanics of superplasticity, - to analyse the mathematical models/constitutive equations for superplastic flow from the viewpoint of mechanics, - to review the models of superplastic metal working processes, - to indicate with examples possible new results that can be obtained using the methods of mechanics of solids. It is intended for a variety of readers who may be interested in the phenomenon of superplasticity for different reasons: materials scientists and physicists working in educational institutions and R&D units, those who wish to work on the applications of superplasticity, engineers in industry, students at senior undergraduate and postgraduate levels and those who wish to understand the phenomenology and mechanics of superplasticity without involvement in actual research. A reader who has exposure to standard differential and integral calculus and elementary tensor calculus at a level taught to senior undergraduate students at a technical university should have no difficulty in following the treatments. The analytical procedures are explained in an Appendix with simple examples.

Texte du rabat

Superplasticity is the ability of polycrystalline materials under certain conditions to exhibit extreme tensile elongation in a nearly homogeneous/isotropic manner. Historically, this phenomenon was discovered and systematically studied by metallurgists and physicists. They, along with practising engineers, used materials in the superplastic state for materials forming applications. Metallurgists concluded that they had the necessary information on superplasticity and so theoretical studies focussed mostly on understanding the physical and metallurgi­ cal properties of superplastic materials. Practical applications, in contrast, were led by empirical approaches, rules of thumb and creative design. It has become clear that mathematical models of superplastic deformation as well as analyses for metal working processes that exploit the superplastic state are not adequate. A systematic approach based on the methods of mechanics of solids is likely to prove useful in improving the situation. The present book aims at the following. 1. Outline briefly the techniques of mechanics of solids, particularly as it applies to strain rate sensitive materials. 2. Assess the present level of investigations on the mechanical behaviour of superplastics. 3. Formulate the main issues and challenges in mechanics ofsuperplasticity. 4. Analyse the mathematical models/constitutive equations for superplastic flow from the viewpoint of mechanics. 5. Review the models of superplastic metal working processes. 6. Indicate with examples new results that may be obtained using the methods of mechanics of solids.

Contenu

1 Phenomenology of Superplastic Flow.- 1.1 Historical.- 1.2 Mechanical Behaviour of Superplastics.- 1.2.1 Mechanical Tests.- 1.2.2 Typical Experimental Results.- 1.2.3 Conditions for Superplastic Flow.- 1.3 Strain Rate Sensitivity of Superplastic Flow.- 1.3.1 Strain Rate Sensitivity Index, m.- 1.3.2 'Universal' Superplastic Curve.- 1.3.3 Stability of Uniaxial Superplastic Flow.- 1.4 Superplasticity from the Point of View of Mechanics.- 1.4.1 On the Definition of Superplasticity.- 1.4.2 On Experimental Studies Concerning Superplasticity.- 1.4.3 On the Presentation of Results Obtained.- 1.4.4 On Some Parameters of Superplastic Flow.- 1.4.4.1 Range of Optimal Flow.- 1.4.4.2 Mechanical Threshold.- 1.4.4.3 Activation Energies.- 1.4.4.4 Structure and Mechanical Response.- 1.4.5 On Stability of Superplastic Flow.- 2 Mechanics of Solids.- 2.1 The Subject.- 2.2. Basic Concepts.- 2.2.1 Concept of a Continuum.- 2.2.2 Stress, Strain and Strain Rate States.- 2.3 General Laws and Boundary Value Problems.- 2.4 Mathematical Models of Materials.- 2.4.1 Typical Models for Describing Mechanical Behaviour.- 2.4.2 Mechanical Models/Analogues.- 2.4.3 Theories of Plasticity.- 2.4.4 Theories of Creep.- 2.4.4.1 Phenomenology of Creep.- 2.4.4.2 Internal Variable Approach.- 2.5 Experiments in Mechanics.- 2.5.1 Mechanical Tests on Materials.- 2.5.2 Influence of Testing Machine.- 3 Constitutive Equations for Superplastics.- 3.1 Basic Requirements of Constitutive Equations.- 3.2 Phenomenological Constitutive Equations.- 3.2.1 Standard Power Law.- 3.2.2 Polynomial Models.- 3.2.3. Mechanical Modelling.- 3.2.3.1 Generalised Maxwell Body.- 3.2.3.2 Generalised Bingham Body.- 3.2.3.3 Mechanical Threshold: Analyses of Karim and Murty.- 3.2.3.4 Smirnov's Mechanical Analogue.- 3.2.3.5 Models of Murty-Banerjee and Zehr-Backofen.- 3.2.3.6 Combinations of Non-Linear Viscous Elements.- 3.2.4 Smirnov's Model.- 3.2.5 Anelasticity.- 3.2.6 Kinks on the Load Relaxation Curves.- 3.2.7 Mechanistic Model.- 3.2.8 Activation Energies.- 3.3 Physical Constitutive Equations.- 3.3.1 Classical Models.- 3.3.2 Modern Theories.- 3.3.2.1 Model of Ghosh.- 3.3.2.2 Model of Hamilton.- 3.3.2.3 The Model of Pschenichniuk-Astanin-Kaibyshev.- 3.3.2.4 The Model of Perevezentsev et al.- 3.4 Construction of Constitutive Equations.- 3.4.1 Common Scheme.- 3.4.2 Model of Padmanabhan and Schlipf.- 3.5. Constitutive Equations in Tensor Form.- 3.5.1 Non-Uniaxial Stress-Strain States.- 3.5.2 Some Tensor Constitutive Equations.- 3.6 Material Constants from Technological Tests.- 3.6.1 Inverse Problems.- 3.6.2 Constant Pressure Forming of a Rectangular Membrane.- 3.6.3 Constant Pressure Forming of a Circular Membrane.- 3.6.4 Model of Padmanabhan and Schlipf.- 4 Boundary Value Problems in Theory of Superplastic Metalworking.- 4.1 General Formulation of the Boundary Value Problem for Metalworking Processes.- 4.1.1 Basic Concepts and Principal Equations.- 4.1.2 Initial and Boundary Conditions.- 4.1.3 Damage Accumulation.- 4.2 Model Boundary Value Problems in Mechanics of Superplasticity.- 4.2.1 Couette Flow of Superplastics.- 4.2.1.1 Newtonian Viscous Liquid.- 4.2.1.2 Shvedov-Bingham Plastic.- 4.2.1.3 Non-Linear Viscous Material.- 4.2.2 Combined Loading of a Cylindrical Rod by Axial Force and Torque.- 4.2.3 Free Bulging of Spherical and Cylindrical Shells.- 4.2.3.1 Free Forming of a Sphere.- 4.2.3.2 Free Forming of an Infinite Cylindrical Shell.- 4.3 Numerical Solving of Boundary Value Problems in Superplasticity.- 4.3.1 Features of Boundary Value Problems in Mechanics of Superplasticity.- 4.3.2 Finite Element Modelling of Superplastic Metalworking Processes.- 4.3.3 Numerical Models of Superplastic Sheet Forming Processes.- 4.3.3.1 Principal Equations of Membrane Theory.- 4.3.3.2 Numerical Solutions of the Principal Equations of Membrane Theory.- 5 Mathematical Modelling of Superplastic Metalworking Processes.- 5.1 Modelling of Superplastic Bulk Forming Processes.- 5.1.1 General Comments.- 5.1.2 Compression of a Disc using Platens.- 5.1.3 Forging of a Disc by Rotating Dies.- 5.1.3.1 Formulation of the Simplified Boundary Value Problem.- 5.1.3.2 Solving the Simplified Boundary Value Problem.- 5.1.3.3 Analysis of the Solution Obtained.- 5.1.4 Extrusion.- 5.1.5 Die-less Drawing.- 5.1.6 Roll Forming Processes.- 5.1.7 Clutching.- 5.2 Modelling of Sheet Metal Processes.- 5.2.1 Simplifications in Modelling SPF and SPF/DB Processes.- 5.2.2 Main Challenges in Modelling SPF and SPF/DB Processes.- 5.2.3 SPF of Hemispherical Domes.- 5.2.3.1 Finite Strain Behaviour.- 5.2.3.2 Jovane's Model.- 5.2.3.3 Geometric /Kinematic Models.- 5.2.3.4 Model of Cornfield-Johnson and its Modifications.- 5.2.3.5 Holt's Model and its Modifications.- 5.2.4 Free Forming of Spherical Vessels.- 5.2.4.1 Description of the Process.- 5.2.4.2 Mathematical Model.- 5.2.4.3 Wrinkling in Superplastic Forming.- 5.2.5 SPF of a Long Rectangular Membrane.- 5.2.5.1 T…