Process Modelling of Metal Forming and Thermomechanical Treatment

It is the objective of the series IIMaterials Research and Engineeringll to publish information on technical facts and pro­ cesses together with specific scientific models and theories. Fundamental considerations assist in the recognition of the origin of properties and the roots of processes. By providing a higher level of understanding, such considerations form the basis for further improving the quality of both traditional and future engineering materials, as well as the efficiency of industrial operations. In a more general sense, theory helps to integrate facts into a framework which ties relations between physical equilibria and mechanisms on the one hand, product development and econo­ mical competition on the other. Aspects of environmental compati­ bili ty, conservation of resources and of socio-cul tural inter­ action form the final horizon - a subject treated in the first ll volume of this series, IIMaterials in World Perspective . The four authors of the present book endeavor to present a comprehensive picture of process modelling in the important field of metal forming and thermomechanical treatment. The reader will be introduced to the rapidly-growing new field of application of computer-aided numerical methods to the quanti­ tative simulation of complex technical processes. Extensive use is made of the state of scientific knowledge related to materials behavior under mechanical stress and thermal treat­ ment.

1 Preface.- 2 Mathematical Modelling.- 2.1 Introduction.- 2.2 Infinitesimal Theory of Plasticity.- 2.2.1 Yield Criteria.- 2.2.2 Work Hardening.- 2.2.3 Plastic Deformation.- 2.3 Problem Solution.- 2.3.1 System Approach.- 2.3.2 Detailed Mechanics Approach.- 2.4 Elementary Analysis or “Slab Method”.- 2.4.1 The General Case.- 2.4.2 The Plane Strain Situation.- 2.4.2.1 Frictionless Strip Drawing.- 2.4.2.2 Lateral Flow between Parallel Dies.- 2.4.2.3 Plane Strain Lateral Flow between Inclined Dies.- 2.4.2.4 Flow into a Rib.- 2.4.3 The Axisymmetric Situation.- 2.4.3.1 Stress Distribution for the Flat Axisymmetric Case.- 2.4.3.2 Stress Distribution for Converging Outward Flow.- 2.5 Upper-Bound Method.- 2.6 Finite Element Analysis.- 2.6.1 Introduction and Historical Perspective.- 2.6.2 Finite Element Background.- 2.6.3 Stress-Strain Formulations.- 2.6.3.1 Elastic-Plastic Formulations.- 2.6.3.2 Rigid-Plastic Formulations.- 2.6.4 Thermal Formulations.- 2.6.5 Finite Element Equations.- 2.6.5.1 Velocity Equations.- 2.6.5.2 Temperature Equations.- 2.6.5.3 Time Dimension.- 2.6.6 Forming Specifics.- 2.6.7 Summary and Future Developments.- References Chapter 2.- 3 Physical Modelling.- 3.1 Similarity Theory.- 3.1.1 Basic Principles.- 3.1.2 Similarity Laws in Metal Forming.- 3.2 Application and Basic Techniques.- 3.3 Material Flow in Forging ― Examples.- 3.4 Simulation of Material Deformation in Turbine Blade Forging.- 3.5 Conclusions.- References Chapter 3.- 4 Modelling of Forging.- 4.1 Introduction.- 4.2 System Modelling in Hot Die Upsetting.- 4.2.1 Heat Transfer Analysis.- 4.2.2 Non-Dimensional Analysis.- 4.2.3 Hot-Die Upsetting System Modelling.- 4.2.3.1 Temperature Calculation.- 4.2.3.2 Stress and Strain Calculation.- 4.2.3.3 Determination of the Shearing Zone in Closed Die Forging.- 4.2.3.4 Stresses.- 4.2.3.5 Flash Width Calculation.- 4.2.3.6 Force Calculations.- 4.2.3.7 Description of the Computer Program.- 4.2.3.8 Experimental Verification of the System Modelling.- 4.2.4 Optimization of Process Parameters.- 4.2.4.1 Geometrical Parameters.- 4.2.4.2 Maximum Allowable Die Stress.- 4.2.4.3 Influence of Thermal Barrier Thickness.- 4.2.4.4 Optimum Conditions for Forging NIM 80 A Billets.- 4.2.4.5 Isolines of Maximum Deformation.- 4.2.4.6 Evaluation of Optimum Variable Ram Speed.- 4.2.5 Coupled FEM Analysis of Forging.- 4.2.5.1 Introduction.- 4.2.5.2 Principle of Induction Heating.- 4.2.5.3 Influence of an Inhomogeneous Temperature Distribution on the Forging Process.- 4.2.5.4 Process Model and Boundary Conditions.- 4.2.5.5 Calculations, Experiments and Results.- 4.2.5.6 Local Strain and Temperature Distribution.- 4.2.5.7 Future Applications of Coupled FEM Process Models.- 4.3 Plane Strain Modelling of Closed Die Forging.- 4.3.1 Elementary Analysis Approach.- 4.3.2 CAD/CAM and Process Modelling of Closed Die Forging.- 4.3.2.1 The DIEDESIGN Software.- 4.3.2.2 Geometrical Input Data Description.- 4.3.2.3 Process Modelling of the Forging Process.- 4.3.2.4 Forging Loads Minimization and Flash Positioning.- 4.3.2.5 Preform and Flash Definition.- 4.3.2.6 Center of Loading.- 4.3.3 Application of CAD/CAM to Forge a Blade in a Nickel-Base Alloy.- 4.3.4 FEM Plane Strain Analysis of Blade Forging.- 4.3.4.1 Deformations.- 4.3.4.2 Effective Strains and Strain Rates.- 4.3.4.3 Stresses.- 4.3.4.4 Friction.- 4.4 Plan Strain Modelling of Thin Rib Forging.- 4.4.1 Elementary Analysis Approach.- 4.4.1.1 Forging Stress Distribution.- 4.4.1.2 Plate-Rib Forging Model.- 4.4.1.3 Rib Forging Model.- 4.4.1.4 Rib Forging Model with the Effect of the Radius.- 4.4.1.5 Experiments and Results.- 4.4.1.6 Conclusions.- 4.4.2 FEM Plane Strain Analysis of Thin Rib Forging.- 4.4.2.1 The FEM Model for the Rib Forging.- 4.4.2.2 Metal Deformation.- 4.4.2.3 Strain Distribution.- 4.4.2.4 Forging Pressure.- 4.4.3 Stress and Strain Analysis of Forging Dies.- 4.4.3.1 The Finite Element Model.- 4.4.3.2 Deformations at the Nodal Points.- 4.4.3.3 Stress Distribution.- 4.5 Finite Element Analysis of a Complex Axisymmetric Shape.- 4.5.1 Deformations.- 4.5.2 Strains.- 4.5.3 Die Stress.- References Chapter 4.- 5 Modelling of Rolling.- 5.1 Introduction.- 5.2 Measurements of Lateral Spread.- 5.3 Computer-Aided Roll Pass Design.- 5.3.1 Input of the Geometry of the Profile.- 5.3.2 Modifications to the Profile.- 5.3.3 Calculation and Modification of the Neutral Line.- 5.3.4 Determination of the Starting Profile (Preform).- 5.3.5 Roll Forming Parameters Calculations.- 5.3.6 Roll Pass Schedule and Roll Geometry.- 5.4 Results.- 5.5 CAD/CAM in Steel Profile Production.- 5.5.1 CAD of Shape Rolls.- 5.5.2 CAM of Shape Rolls at the CAD Workstation.- References Chapter 5.- 6 Modelling of Drawing.- 6.1 Introduction.- 6.2 Upper-Bound Analysis of Round-To-Square Drawing.- 6.2.1 The Upper-Bound Solution.- 6.2.2 The Geometrical Model.- 6.2.3 The Velocity Fields.- 6.2.4 Reduction of Area.- 6.2.5 Flow Lines.- 6.2.6 Optimization of the Theoretical Flow Field.- 6.2.7 Analysis of Process Parameters.- 6.2.8 Conclusions.- 6.3 Finite Element Analysis of Bar Drawing.- 6.3.1 The Finite Element Approach.- 6.3.2 Finite Element Formulation.- 6.3.3 Optimization.- 6.3.4 Finite Element Model.- 6.3.5 Restraints, Die Boundaries and Initial Conditions.- 6.3.6 Finite Element Results.- 6.3.7 Conclusions.- References Chapter 6.- 7 Modelling of Thermomechanical Treatment.- 7.1 Introduction.- 7.2 Determination of Heat Transfer Coefficients in Quenching.- 7.2.1 Approach to the Determination of the Heat Transfer Coefficient.- 7.2.2 Experimental Setup.- 7.2.3 Results.- 7.3 Quenching of Steel Plate through Water Flushing.- 7.3.1 Introduction.- 7.3.2 Analysis of the Heat Transfer.- 7.3.3 Influence of Scale Formation on the Heat Transfer.- 7.3.4 Experimental Technique.- 7.3.5 Material Properties.- 7.3.6 Experimental Results.- 7.4 Modelling of Quenching of Complex Parts.- 7.4.1 Introduction.- 7.4.2 Quenching of an Aluminum Impeller.- 7.4.3 Simulation.- 7.4.3.1 Temperature Calculations.- 7.4.3.2 Residual Stress and Distortion Calculations.- 7.4.4 Comparison with Experiments.- 7.4.5 Conclusions.- 7.5 Modelling of Heat Treatment of Large Forgings.- References Chapter 7.- 8 Outlook.