Material Forming Processes
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Preface xi
Chapter 1. Forming Processes 1
1.1. Introduction& 1
1.2. Different processes 1
1.2.1. Smelting 2
1.2.2. Machining 3
1.2.3. Powder metallurgy 5
1.3. Hot and cold forming 6
1.3.1. Influence of the static parameters 9
1.3.2. Hydroforming 12
1.3.3. The limitations of the process 13
1.3.4. Deep drawing 14
1.4. Experimental characterization 14
1.5. Forming criteria 16
1.5.1. Influence of the structure of sheet metal 18
1.5.2. Physical strain mechanisms 20
1.5.3. Different criteria 21
Chapter 2. Contact and Large Deformation Mechanics 23
2.1. Introduction 23
2.2. Large transformation kinematics 23
2.2.1. Kinematics of the problem in spatial coordinates 24
2.3. Transformation gradient 25
2.4. Strain measurements 26
2.4.1. Polar decomposition of F 26
2.4.2. Strain rate tensor 27
2.4.3. Canonical decomposition of F 28
2.4.4. Kinematics of the problem in convective coordinates 28
2.4.5. Transformation tensor 29
2.4.6. Strain rate measures 32
2.4.7. Strain tensor 35
2.5. Constitutive relations 36
2.5.1. Large elastoplastic transformations 38
2.5.2. Kinematic decomposition of the transformation 41
2.6. Incremental behavioral problem 42
2.6.1. Stress incrementation 42
2.6.2. Strain incrementation 44
2.6.3. Solution of the behavior problem 46
2.7. Definition of the P.V.W. in major transformations 49
2.7.1. Equilibrium equations 49
2.7.2. Definition of the P.V.W 50
2.7.3. Incremental formulation 51
2.8. Contact kinematics 52
2.8.1. Definition of the problem and notations 52
2.8.2. Contact formulation 53
2.8.3. Formulation of the friction problem 53
2.8.4. Friction laws 54
2.8.5. Coulomb's law 54
2.8.6. Tresca's law 55
Chapter 3. Stamping 57
3.1. Introduction 57
3.2. Forming limit curve 59
3.3. Stamping modeling: incremental problem 60
3.3.1. Modeling of sheet metal 61
3.3.2. Spatial discretization: finite elements method 62
3.3.3. Choice of sheet metal and finite element approximation 63
3.4. Modeling tools 64
3.4.1. Tool surface meshing into simple geometry elements 64
3.4.2. Analytical representation of tools 65
3.4.3. Bezier patches 65
3.5. Stamping numerical processing 72
3.5.1. Problem statement 73
3.5.2. The augmented Lagrangian method 75
3.6. Numerical simulations 79
3.6.1. Sollac test 81
Chapter 4. Hydroforming 83
4.1. Introduction 83
4.2. Hydroforming 85
4.2.1. Tube hydroforming 85
4.2.2. Sheet metal hydroforming 86
4.3. Plastic instabilities in hydroforming 87
4.3.1. Tube buckling 88
4.3.2. Wrinkling 90
4.3.3. Necking 91
4.3.4. Springback 92
4.4. Forming limit curve 92
4.5. Material characterization for hydroforming 94
4.5.1. Tensile testing 95
4.5.2. Bulge testing 95
4.6. Analytical modeling of a inflation test 97
4.6.1. Hill48 criterion in planar stresses 97
4.7. Numerical simulation 100
4.8. Mechanical characteristic of tube behavior 101
Chapter 5. Additive Manufacturing 105
5.1. Introduction 105
5.2. RP and stratoconception 107
5.3. Additive manufacturing definitions 109
5.4. Principle 113
5.4.1. Principle of powder bed laser sintering/melting 114
5.4.2. Principle of laser sintering/melting by projecting powder 116
5.5. Additive manufacturing in the IT-based development process 117
5.5.1. Concept "from the object to the object" 117
5.5.2. Key element of the IT development process 118
Chapter 6. Optimization and Reliability in Forming 121
6.1. Introduction 121
6.2. Different approaches to optimization processes 122
6.2.1. Limitations of the deterministic approaches 124
6.3. Characterization of forming processes by objective functions 125
6.4. Deterministic and probabilistic optimization of a T-shaped tube 126
6.4.1. Problem description 126
6.4.2. Choice of the objective function and definition of the stresses 127
6.4.3. Choice of the uncertain parameters 128
6.4.4. Choice of the objective function and the stresses 130
6.4.5. Deterministic formulation of the optimization problem 132
6.4.6. Probabilistic formulation of the optimization problem 133
6.4.7. Optima sensitivity to uncertainties 140
6.5. Deterministic and optimization-based reliability of a tube with two expansion regions 142
6.5.1. Problem description 142
6.5.2. Deterministic and reliabilist formulation of the optimization problem 147
6.6. Optimization-based reliability of circular sheet metal hydroforming 150
6.6.1. Problem description 150
6.6.2. Construction of the objective function and of the stresses 151
6.6.3. Effects diagram 151
6.6.4. Deterministic solution of the optimization problem 155
6.6.5. Reliabilist solution of the optimization problem 157
6.6.6. Effect of uncertainties on the optimal variables 159
6.7. Deterministic and robust optimization of a square plate 160
6.7.1. Robust resolution of the optimization problem 166
6.8. Optimization of thin sheet metal 168
Chapter 7. Application of Metamodels to Hydroforming 171
7.1. Introduction 171
7.2. Sources of uncertainty in forming 172
7.3. Failure criteria 173
7.3.1. Failure criteria for necking 174
7.3.2. Failure criteria for wrinkling 174
7.4. Evaluation strategy of the probability of failure 175
7.4.1. Finite element model and choice of uncertainty parameters 176
7.4.2. Identification of failure modes and definition of boundary states 180
7.4.3. Identification of elements and critical areas 181
7.5. Critical strains probabilistic characterization 185
7.5.1. Choice of numerical experimental design 186
7.5.2. Construction of metamodels 186
7.5.3. Validation and statistical analysis of metamodels 187
7.5.4. Fitting of distributions 187
7.6. Necking and wrinkling probabilistic study 193
7.7. Effects of the correlations on the probability of failure 196
7.7.1. Spatial estimation of the probability of failures 197
Chapter 8. Parameters Identification in Metal Forming 199
8.1. Introduction 199
8.2. Identification methods 199
8.2.1. Validation test 200
8.3. Welded tube hydroforming 203
8.3.1. Thin sheet metal hydroforming 205
Appendices 213
Appendix 1. Optimization in Mechanics 215
Appendix 2. Reliability in Mechanics 223
Appendix 3. Metamodels 233
Bibliography 243
Index 253
1
Forming Processes
1.1. Introduction
The field of metal forming comprises a wide range of semifinished and finished products. Each requirement of the acquisition criteria is defined, justifying the use of various forming processes. A number of recurring characteristics can be observed in the desired shapes. The latter should respond with the best dimensional precision possible and the most suitable surface condition for its usage. The final product must meet material health conditions for usage properties with the least possible continuity defects. There is, therefore, an interest in what the most appropriate macro- and microstructures are.
1.2. Different processes
Metallic materials offer a rich range of independent or combined forming methods. Among the large families, the following processes are identified:
- - smelting;
- - machining;
- - powder metallurgy;
- - hot or cold plastic strain forming.
Each of these processes present characteristics of optimal quality, variable depending on the material being used, on the dimensions and on the desired accuracy, on the metallurgical quality, on the final cost and on the quantity. The choice is oriented according to specific criteria:
- - the abilities of the material in relation to the different processes (particular attention should be given to the difference between a foundry alloy and alloys deemed "wrought") regarding the form and the dimension of the product;
- - the defined metallurgical health (limitation of defects such as cracks, porosities and chemical segregations);
- - the usage properties of the product in the mechanical field;
- - the desired surface condition (in terms of cleanliness, roughness, of residual stresses, etc.).
1.2.1. Smelting
The metal or the alloy is melted inside a crucible and then it is poured into a specific mold inside which it will solidify when cooled down. Complex forms can be obtained often linked with a minimum of induced thickness. Large variations of the latter involve consequences on the development of the final properties. Casting workpieces are produced from simple and often fairly cheap traditional techniques. This results in obtaining monobloc parts whose quality and mechanical properties are lower than those of wrought products (products having undergone hot hammering in order to obtain the desired properties often in a compulsory direction). There are numerous and very varied molding techniques depending on shape, quantities and on the quality requirements:
- - The mold is made up of sand and inside it a cavity can be found that will represent the resulting piece. The first operation consists of building a pattern generating the shape of the desired casting by integrating the machining allowances and the useful drafts. The pattern represents the mold cavity left in the sand when the mold is closed. The mold is opened to extract the pattern therefrom and closed to the molten metal. When solidification is achieved after slow cooling, the mold is broken in order to retrieve the final product. One casting is thus obtained per mold.
- - The mold is in metal and thus is reusable. The cooling proves to be much faster than the sand casting process. The pattern is obtained by machining the mass and with respect to the hollow parts, they can be achieved with eventually destructible cores.
- - Die-casting integrates a metal mold but the filling of the pattern is ensured by means of a piston that pushes the liquid at high speed in a short period of time (a few 1/10 of a second). A slight overpressure can be maintained in the mold, which has the effect of properly feeding the pattern, while avoiding the design of a hot-top to perform this function. The mechanization of the process is total. On the other hand, the tools undergo very significant repeated efforts, which reduces their life expectancy (20,000-50,000 parts depending on the nature of the cast alloy).
- - Centrifugal casting concerns all so-called revolution parts. The fundamental difference lies at the level of the introduction of liquid material, which is carried out along an axis around which the mold revolves. The centrifugal force promotes uniform filling. The structural composition is finer and full.
Figure 1.1. Gravity die casting accompanied by the obtained casting
1.2.2. Machining
Machining is a material removal operation making use of a cutting tool. This process allows for highly accurate complex forms and a controlled surface finishing. Different processes are identified and classified into two large categories. The first involves chip formation, which mainly includes turning, milling, grinding and drilling. The second does not involve chip formation and designates flow-turning, electrical discharge machining, shearing and waterjet cutting. From a structural point of view, machining only alters a superficial layer of the material, which therefore causes a hardening of the surface. As a result, we can observe the creation of a residual sublayer stress field, causing significant heating in the superficial layer. Ease of machining is linked to the physical contact of the tool-workpiece pair during machining. It depends not only on the mechanical behavior of the material (resistance, consolidation and malleability of the machined material) but also on its thermal behavior. A low resistance is recommended, which means a sufficient malleability, however this facilitates chip breaking. It can also be noted that a good thermal conductivity most often facilitates the machining. As a result of adding cold or hot particles, the cutting conditions can be improved (controlled inclusions of low melting point lead or even sulfides, etc.). These latter facilitate the fragmentation of the chip:
- - Chip formation: Machining takes place following optimized cutting conditions, which consider the geometry of the cutting tool, the cutting fluid and the dimension of the non-deformed chip. It is formed following primary shearing of the metal when making contact with the cutting edge of the tool and following a secondary shear when in contact with the external edge of the tool. This effort zone undergoes superficial strain hardening and heating. In addition, the chip is subjected to the same efforts coupled to the tool on its external edge. Futhermore, the cutting speed Vc plays a paramount role and is thus expressed:
with Vc expressed in m/min, rotational speed in rpm and tool diameter for milling.
- - The machined surface: It is defined by a heated and hard-tempered underlying superficial area. The microstructure can therefore be modified (constituents or phase change) or even undergo local strain hardening by cold working. Often, there remains a significant local residual stress field. Moreover, microcracks can be observed.
- - The chip: When the material is fragile, it quickly becomes fragmented into lemels (for example some smeltings). In the event that it is ductile and slightly consolidates. However, when this consolidation occurs as a result of the hardening phenomenon, it easily fragments. On the other hand, a few obstacles to chip formation may surge notably due to heating and pressure. A galling phenomenon can be observed between tool and chip forming a build-up edge. It is defined by lemel stuck to the tool. Thus, the maximal temperature is variable according to the cutting speed and the hardness of the tool. The stress and strain field induced by the cutting enforces an increase in the temperature of the metal.
As a result to the cutting conditions, the tool is subjected to the following observations:
- - adhesive wear;
- - abrasive wear;
- - damage due to atomic diffusion or to oxidation;
- - damage due to thermal fatigue;
- - irreversible deformation (creeping).
1.2.3. Powder metallurgy
This process consists of obtaining a final piece adapted to special needs by means of compression and sintering. From the agglomeration of very fine powders, a compacted object is produced with a form very close to that desired. Then, we control the cohesion of the powder with a thermal sintering process. Different applications can be identified, used in specific categories of workpieces:
- - in cases where the production of controlled fine-porosity metal products with complicated forms is sought after;
- - in pieces composed of refractory metals presenting a good resistance to heat;
- - in alloys that cannot be obtained by smelting, notably tungsten or some magnetic materials such as soft magnetic metal ferrite composites. As an example, we can therefore cite cermets composed of "coarse" ceramics particles distributed in a metal matrix. In the field of cutting tools, we come accross cobalt matrix-based indexable lathe tools;
- - in friction materials of which brake pads or clutch discs are made of;
- - in electrical contact materials of which we can cite as an example silver-or copper-based contacts.
This technique is often used when some materials are hardly fusible or seldom deformable by plastic deformation. We then obtain products with improved microstructure, finer and more homogeneous than that observed by smelting as some nickel-based superalloys. It is also popular as an alternative with...
