Numerical Analysis of Warm Drawability of Magnesium Alloy

Contents

Title page

Certification

Dedication

Acknowledgements

Abstract

Contents

List of figures

List of table

Nomenclature

Abbreviations

1.0 Introduction
1.1 Background
1.2 Deep Drawing of Sheet Metal
1.2.1 Presses
1.2.2 Deep Drawing Process Set-Up
1.3 Tribology in Metal Forming
1.3.1 Lubrication Regimes
1.3.2 Navier–Stokes Equations
1.3.3 The General Reynolds Equation
1.3.4 The Bauschinger Effect
1.4 Finite Element Analysis
1.4.1 Types of Finite Element Methods
1.5 Research Objectives

2.0 Literature Review
2.1 Studies Related to Lubrication in Metal Forming
2.2 Studies Related to Process Parameters in Deep Drawing
2.3 Workability of Magnesium Alloy in Deep Drawing

3.0 Methodology
3.1 Procedures for Analysis and Evaluation
3.2 Experimental Tooling Design
3.2.1 Press Specifications
3.2.2 Tool Design Considerations
3.2.2.1 Minimum blank diameter, D₁
3.2.2.2 Number of Draws
3.2.2.3 Limiting Draw Ratio, LDR
3.2.2.4 Length of punch, h₂
3.2.2.5 Maximum required pressure, P
3.2.2.6 Volume of work piece before and after forming, V
3.2.2.7 Other necessary parameters
3.2.3 Design considerations for jigs and fixtures
3.2.4 Materials Selection
3.2.5 Effect of Lubrication on Sliding Friction

4.0 Results and Discussion
4.1 Design Calculations/Values
4.1.1 Blank thickness, S
4.1.2 Punch nose or the die corner radius
4.1.3 The minimum height of the cup, h₁
4.1.4 The cup diameter, d
4.1.5 Minimum blank diameter, D₁
4.1.6 Limiting Draw Ratio, LDR
4.1.7 Length of punch, h
4.1.8 Maximum required pressure, P
4.1.9 Other necessary parameters
4.1.10 Dimensions of die accessories
4.2 Design Drawings
4.3 Finite Element Simulation
4.3.1 Experimental setup for FEA
4.3.2 Simulation Results
4.3.2.1 Analysis Based on Temperature Variation
4.3.2.2 Variation of the Blank Holder Force with the Drawing Speed
4.3.2.3 Variation of the Punch Nose Radius with the Blank Holder Force
4.3.2.4 Variation of the Punch Nose Radius with the Drawing Speed
4.4 Discussion

5.0 Conclusion and Recommendations
5.1 Conclusion
5.2 Recommendation

REFERENCES

CERTIFICATION

This is to certify that the thesis entitled,“Numerical Analysis of Warm Drawability of Magnesium Alloy” submitted byAYOWOLE, Olubusuyi A. (Mat. No.: 119044045), in partial fulfillment of the requirements for the award of Master of Science in Mechanical Engineering (Design and Production Option) in the Department of Mechanical Engineering University of Lagos during the 2012/2013 session

It is an authentic work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in this thesis has not been submitted to any other university/institute for award of any Degree or Diploma.

DEDICATION

This M.Sc thesis is solely dedicated to the Almighty God, the giver of life and knowledge.

ACKNOWLEDGEMENT

Firstly, I give glory, honour and praise to the Almighty God for His grace and mercy. Without His help, my dream of bagging an M.Sc degree would not have been realizable. With a grateful heart, I wish to appreciate the efforts of my highly esteemed supervisor, Dr. J.S Ajiboye. Thanks so much for your fatherly gestures in the process of carrying out this research work. Also, I specially thank all lecturers and management staff members of the department of mechanical engineering, University of Lagos, especially the HOD, Dr. E.O.B Ogedengbe.

I want to thank my parents, Mr. Isaac Aremu Ayowole and Mrs Julianah Ore Ayowole, for the legacy of quality education given to me and my siblings. I am proud to have you as my parents. Special thanks to my elder brother, Bukola Ayowole and my younger siblings (Fisayo, Bukunmi, Damilola and Tolu) for their support during the course of my post graduate studies. I sincerely express my profound gratitude to my cousins, Clement Obitayo and Toyin Olufemi for their kind gestures in times of need.

I also appreciate the support of the following institutions: Covenant University, University of Ibadan and Nigeria Machine Tools (Osogbo). They were all very helpful in providing logistical support in the course of this research work.

Special thanks to the following people for their moral and financial support: Professor Obinna L. Chukwu (Dean, School of Postgraduate Studies, UNILAG), Pastor (Mrs.) Yemisi Etomi, Engr. Kehinde Oshikoya, Mr. Oluwafemi Alaba, Mr. Paul Onoviran, Dr. S. Ayo Dada, Pastor Amos Adewumi and Engr. Rotimi Ismail.

Without the availability of my good friends, I would not have made it this far. Special thanks to my friends in the M.Sc class: Oluyemi Bankole, Kelechi Felix, Oyinbo Sunday, Adeleye Rotimi, Olusegun Feranmi. I appreciate your availability when I needed you most.

Finally, I wish to appreciate all members of HIGRO Ensemble and everyone or organization who has contributed directly or indirectly to the successful completion of my M.Sc programme.

Thanks and God bless you all.

ABSTRACT

Despite being the lightest structural metal, magnesium alloys have been required to be processed at elevated temperatures because of their poor workability at low temperatures due to their hexagonal closed-packed (HCP) crystal structure. In this research work, a Finite Element Simulation of the non-isothermal warm deep drawing of a cylindrical cup, formed from a 1.45mm thick disc of Mg Alloy AZ31, was carried out with the commercial FE software ANSYS. A deep drawing die set designed and drafted with the aid of AUTODESK INVENTOR was subsequently constructed and a deep drawing process was carried to test run the practicability of the die set. From the simulation results, the deep drawing of AZ31 took place more effectively under warm working conditions compared to when carried out at room temperature. Under a non-isothermal warm working condition (ranging between 423K and 523K), the blank holder force, drawing speed and the punch hole radius were varied with one another to investigate their effects on the warm drawability of the alloy, with the results indicating that the drawing speed and the punch radius affect the warm drawability of the material more than the blank holder force. Judging from the results obtained from simulation as compared to observations made from the test run experiment, it was noted that the material fails due to tearing, when the punch radius is too small, and that wrinkling takes place when the punch radius is too large. It was therefore concluded that, to obtain a desirable quality of job in the warm deep drawing of AZ31, a numerical/experimental optimization procedure is much helpful in the determination of the best value for the punch radius.

LIST OF FIGURES

Fig. 1.1: Schematic of the deep drawing process

Fig. 1.2: schematic of stages in the deep drawing process

Fig. 1.3 (a b): Experimental (left) and Industrial (right) Hydraulic presses

Fig. 1.4: A tribo-system according to czichos

Fig. 1.5: Stribeck Curve

Fig. 1.6a: FEM mesh created by an analyst prior to finding a solution to a magnetic problem using FEM software

Fig. 1.6b: FEM solution to the problem of 1.6a, involving a cylindrically shaped magnetic shield.

Fig 4.1: Labeled components of the tool

Fig. 4.2: A 3D model of the tooling setup

Fig. 4.3: Longitudinal section through the tooling setup

Fig. 4.4: Schematic of the tooling setup showing top parts

Fig. 4.5: Schematic of the tooling setup showing bottom parts

Fig. 4.6: Longitudinal section through the die components assembly

Fig. 4.7: A 3D model of the die components assembly showing top parts

Fig. 4.8: A 3D model of the die components assembly showing bottom parts

Fig. 4.9: A solid model of the FE experimental setup

Fig. 4.10: A meshed model of the FE experimental setup

Fig. 4.11 (a b): Simulation interface for AZ31 deep drawing at room temperature.

Fig 4.12 (a b): Simulation interface for AZ31 deep drawing under warm working

Fig. 4.13: Stress-Strain relationship for AZ31 deep drawing with varied working temperature.

Fig 4.14 (a b): Simulation interface for AZ31 deep drawing with BHF 0kN at 0.2m/s

Fig. 4.15 (a b): Simulation interface for AZ31 deep drawing with BHF 0kN at 0.4m/s.

Fig 4.16 (a b): Simulation interface for AZ31 deep drawing with BHF 0kN at 0.6m/s

Fig. 4.17: Stress-Strain relationship for AZ31 deep drawing at BHF 0kN with varied drawing speed

Fig. 4.18 (a b): Simulation interface for AZ31 deep drawing with BHF 8.26kN at 0.2m/s.

Fig 4.19 (a b): Simulation interface for AZ31 deep drawing with BHF 8.26kN at 0.4m/s.

Fig 4.20 (a b): Simulation interface for AZ31 deep drawing with BHF 8.26kN at 0.6m/s

Fig. 4.21: Stress-Strain relationship for AZ31 deep drawing at BHF 8.26kN with varied drawing speed

Fig. 4.22 (a b): Simulation interface for AZ31 deep drawing with BHF 10.03kN at 0.2m/s

Fig. 4.23 (a b): Simulation interface for AZ31 deep drawing with BHF 10.03kN at 0.4m/s

Fig. 4.24 (a b): Simulation interface for AZ31 deep drawing with BHF 10.03kN at 0.6m/s

Fig. 4.25: Stress-Strain relationship for AZ31 deep drawing at BHF 10.03kN with varied drawing speed

Fig. 4.26 (a b): Simulation interface for AZ31 deep drawing with BHF 11.8kN at 0.2m/s.

Fig 4.27 (a b): Simulation interface for AZ31 deep drawing with BHF 11.8kN at 0.4m/s.

Fig 4.28 (a b): Simulation interface for AZ31 deep drawing with BHF 11.8kN at 0.6m/s

Fig. 4.29: Stress-Strain relationship for AZ31 deep drawing at BHF 11.8kN with varied drawing speed

Fig. 4.30 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 0kN

Fig. 4.31 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 8.26kN

Fig. 4.32 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 10.03kN

Fig. 4.33 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 11.8kN

Fig. 4.34: Stress-Strain relationship for AZ31 deep drawing with punch radius 4mm and varied BHF

Fig. 4.35 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 0kN

Fig. 4.36 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 8.26kN

Fig. 4.37 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 10.03kN

Fig. 4.38 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 11.8kN

Fig. 4.39: Stress-Strain relationship for AZ31 deep drawing with punch radius 4.5mm and varied BHF

Fig. 4.40 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 0kN

Fig. 4.41 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 8.26kN

Fig. 4.42 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 10.03kN

Fig. 4.43 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 11.8kN

Fig. 4.44: Stress-Strain relationship for AZ31 deep drawing with punch radius 5mm and varied BHF

Fig. 4.45 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at 0.2m/s

Fig 4.46 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at 0.4m/s

Fig 4.47 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at 0.6m/s

Fig. 4.48: Stress-Strain relationship for AZ31 deep drawing with punch radius 4mm and varied speed

Fig. 4.49 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at 0.2m/s

Fig. 4.50 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at 0.4m/s

Fig. 4.51 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at 0.6m/s

Fig. 4.52: Stress-Strain relationship for AZ31 deep drawing with punch radius 4.5mm and varied speed

Fig. 4.53 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at 0.2m/s

Fig 4.54 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at 0.4m/s

Fig 4.55 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at 0.6m/s

Fig. 4.56: Stress-Strain relationship for AZ31 deep drawing with punch radius 5mm and varied speed

LIST OF TABLE

Table 3.1: Materials used for tool components and work piece

Table 4.1: Dimensions of die components

Table 4.2: Process Parameters for Finite Element Model

Table 4.3: Values of Yield Stress from Varying the Drawing Speed with the BHF Table 4.4: Values of Yield Stress from Varying the Punch Nose Radius with the BHF

Table 4.5: Values of Yield Stress from Varying the Punch Nose Radius with Drawing Speed

NOMENCLATURE

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ABBREVIATIONS

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CHAPTER 1

1.0 INTRODUCTION

1.1 Background

Magnesium (Mg) has an atomic number of 12. It is the lightest among the metals for structural application. It has a density of 1.74 g/cm3. It also has considerably low melting temperature of 649oC, slightly lower than that of aluminum. Mg alloys are much more workable at elevated temperatures than at room temperature. The advantages of Mg, among others are: tougher than plastic, better damping capacity as compared to cast iron and aluminum, electromagnetic interference (EMI) shielding than that of plastic, heat dissipation much higher than that of plastics, absorb vibration energy effectively and recyclability. Mechanical properties of Mg alloys vary depending on composition and weight percentages of constituting elements in the alloying system. (R. H. Mohd et al 2009)[1].

Despite being the lightest structural metal, magnesium alloys have exhibited poor workability at low temperatures due to their hexagonal closed-packed (HCP) crystal structure, consequently required them to be processed at elevated temperature. Their highly affinity to oxygen lead them to an easy oxidation. Moreover, they have poor corrosion resistance, poor creep resistance as well as fatigue failure but these can be improved by various techniques of surface treatments and alloying additions.

The mechanical properties of a magnesium alloy at room temperature are dependent on whether the alloy is a cast or wrought alloy as described below:

- Magnesium cast alloys: the proof stress for an Mg cast alloy is typically between 75 and 200 MPa. Its tensile strength ranges between 135 and 285 MPa and it elongation between 2% and 10%. Typical density is 1.8 g/cm3 and Young's modulus is 42 GPa. Most common cast alloys of magnesium are: AZ63, AZ81, AZ91, AM50, AM60, ZK51, ZK61, ZE41, ZC63, HK31, HZ32, QE22, QH21, WE54, WE43 and Elektron 21.
- Magnesium wrought alloys: the proof stress for an alloy in this category is typically between 160 and 240 MPa, the tensile strength is between 180 and 440 MPa and elongation is between 7 and 40%. The most common Mg wrought alloys are: AZ31, AZ61, AZ80, Elektron 675, ZK60, M1A, HK31, HM21, ZE41 and ZC71. Wrought magnesium alloys have a special feature. Their compressive proof strength is smaller than tensile proof strength. After forming, wrought magnesium alloys have a stringy texture in the deformation direction, which increases the tensile proof strength. In compression the proof strength is smaller because of twinning, which happens more easily in compression than in tension in magnesium alloys because of the hexagonal lattice structure.

Named alloys of Mg include Elektron, Magnox and Magnuminium. Also, Aluminium alloys with magnesium include Birmabright and Magnalium.

In the past, the demand for magnesium alloy as a structural material was not high because of its less availability commercially as well as limited manufacturing methods. However, the use of magnesium alloys in sheet forming processes is still limited because of their low formability at room temperature and the lack of understanding of the forming process of magnesium alloys at elevated temperatures. Since its alloy is a HCP metal and has poor formability, the formed products of magnesium alloy is still limited. (M. Sivanandini et al 2012)[2]

Magnesium alloy sheet was used in manufacturing military aircraft during and after the Second World War. They are used today in the automotive industry, mainly in sand and die castings; the development of lightǦweight vehicle is in great demand for enhancement of fuel efficiency and dynamic performance. The vehicle weight can be reduced effectively by using lightweight materials such as magnesium alloys. The low density of magnesium makes it approximately 35% lighter than aluminum and approximately 78% lighter than steel. Hence, successful implementation of magnesium in transportation industries would bring significant weight-saving benefits. Due to its lightweight and high specific strength, magnesium alloy has been considered as a promising alternative for high-strength steel and aluminum in some applications and has been widely used for structural components in the aerospace, electronics, and automobile industry to replace some existing materials. (B. L. Mordike and T. Ebert, 2001)[3]

It has been established that AZ31 Mg alloy is a general purpose alloy with moderate strength. It can achieved good deep drawability at temperature as low as 1750C by applying MoS2 lubricant. (Iwanaga et. al., 2004)[4]. Xia et. al. (2005)[5] also noted thatAZ31 Mg alloy can be processed smoothly as low as 1000C owing to the ultra fine grain size of 0.2-0.5μm.

1.2 Deep Drawing of Sheet Metal

Sheet metal forming (SMF) is one of the most widely used manufacturing processes for the fabrication of a wide range of products in many industries. The reason behind sheet metal forming gaining a lot of attention in modern technology is due to the ease with which metal may be formed into useful shapes by plastic deformation processes in which the volume and mass of the metal are conserved and metal is displaced from one location to another. (G. Ramesh et al 2013)[6].

Deep drawing is one of the extensively used sheet metal forming processes in the industries to have mass production of cup shaped components in a very short time. In deep drawing, a flat blank of sheet metal is shaped by the action of a punch forcing the metal into a die cavity. Sheet metal forming is one of the most common manufacturing processes to plastically deform a material into a desired shape. Products of deep drawing include hundreds of automotive components, beverage cans, consumer appliances, submarine hulls, and aircraft frames. Based on the geometry, the volume and the material, sheet metal forming can be divided into various categories such as stamping, deep drawing, stretch forming, rubber forming, and super plastic forming. Among these, Stamping and deep drawing are the most common operations. Deep drawing products in modern industries usually have a complicated shape, so these have to undergo several successive operations to obtain a final desired shape. Trimming of the flange is one of those operations and that is used to remove the ears i.e. to have uniform shape of the flange on all the sides of the final product. These are formed due to uneven metal flow in different directions, which is primarily due to the presence of the planar anisotropy in the sheet.

1.2.1 Presses

Presses are machine tools used to change the shape of a work piece by the application of pressure. Presses can be classified based on the following:

1.) Their mechanism: hydraulic, mechanical, pneumatic
2.) Their function: forging presses, stamping presses, press brakes, punch press, etc.
3.) Their structure: knuckle - joint press, screw press
4.) Their controllability: conventional or servo-presses

A hydraulic press, which is mainly used for deep drawing operations, is a device using a hydraulic cylinder to generate a compressive force. It uses the hydraulic equivalent of a mechanical lever.

1.2.2 Deep Drawing Process Set-Up

This involves the positioning of the blank in the deep drawing tooling. The tooling comprises of a die, punch, blank holder, and jigs and fixtures. All the components of this deep drawing tooling are appropriately located on a press, which is the machinery required for the operation. The components of the deep drawing tooling are described below.

1.) Fixtures are used as a locating and holding device for the component of a specific operation. It however does not guide the cutting tool.
2.) A jig is a device in which a component is held and located for a specific operation in such a way that it will guide one or more cutting tools to the same zone of machining.
3.) The die is the main tool, typically attached to the lower portion of the die set. The die contains a recess that provides space for the shaping or shearing of sheet metal.
4.) The punch is the tool typically attached to the upper portion of the die set that shapes or penetrates the sheet metal.
5.) The blank holder holds down the outer rim of the metal sheet as it is drawn into the die cavity.

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Fig. 1.1: Schematic of the deep drawing process

Editorial note: Figure 1.2 was removed due to copyright issues.

Fig. 1.2: schematic of stages in the deep drawing process

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Fig. 1.3 (a b): Experimental (left) and Industrial (right) Hydraulic presses

1.3 Tribology in Metal Forming

In Rowe (1969)[7] the term 'tribology' is defined as the science and technology of interacting surfaces in relative motion and of the practices related thereto.

According to Czichos (1978)[8], tribology is best studied by looking at the system of parameters influencing the frictional behaviour of bodies in contact with each other. This means that not only the contact itself is of importance but also that the environment of the contact plays a role.

A general tribo-system is shown in figure 1.4 below.

Editorial note: Figure 1.4 was removed due to copyright issues.

Fig. 1.4: A tribo-system according to czichos

The tribological behaviour of this system is governed by the operational parameters. Together, these properties and parameters form the operational condition of the system. In a general system, the operational condition is governed by the following operational parameters: load, velocity and temperature. Next to these parameters, macro- and micro-geometry, thermal properties, mechanical properties and, in the case of a lubricant, rheological properties play an important role. Taken together, the operational condition governs the frictional behaviour of the SMF contact and determines in which lubrication regime the contact operates. For this reason, it is important to know the range of values of the operational parameters and the element properties for the case of SMF contacts (Haar, 1996)[9].

1.3.1 Lubrication Regimes

Applying lubricants in SMF processes have a number of effects (Haar, 1996)[9]:

1.) Lowering the total force needed for the operation, usually the friction force for lubricated contacts is much lower than for 'dry' contacts.
2.) Prevention of wear, of the sheet and the tools, caused by adhesion and adhesion related problems.
3.) Assurance that the products will meet the quality requirements. It is possible to control the sheet material flow into the die by means of friction and lubrication.

Earlier researches have shown that lubricated contacts did not have a constant coefficient of friction. The friction force in a lubricated tribo-system is described as a function of one or more of the operational parameters. Depending on the value of the parameter(s) used. a tribo-system can operate in the following lubrication regimes (Haar, 1996) [9]:

- Elasto-Hydrodynamic Lubrication ((E)HL) regime: there is no physical contact between the interacting surfaces of the contact, the load is carried completely by the lubricant film between the surfaces. The coefficient of friction, μ, therefore has a rather low value, of the order of 0.01. For fully separated surfaces it is possible to use fluid dynamics theory, e.g. the Navier-Stokes equations (eqn. 1.1 below) or the Reynolds equation (eqn. 1.3 below), for calculating pressures and film thicknesses.
- Boundary Lubrication (BL) regime: there is physical contact between the interacting surfaces. The load is carried entirely by the surface roughness peaks which are in physical contact with each other. Friction is determined by the layers adhered to the surfaces. The coefficient of friction is in the range of 0.1 μ 0.3.
- Mixed Lubrication (ML) regime: this is the regime in-between the BL regime and the (E)HL- regime, the load on the contact is partly carried by the lubricant and partly by the interacting surface roughness peaks. The friction coefficient will therefore have an intermediate value i.e., 0.01 μ 0.1. For this lubrication regime few models are available.

The Stribeck curve (fig. 1.5 below) is often used to illustrate the lubrication regimes in a typical tribo-system.

Editorial note: Figure 1.5 was removed due to copyright issues.

Fig. 1.5: Stribeck Curve

1.3.2 Navier–Stokes Equations

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This is a statement of the conservation of momentum in a fluid and it is an application of Newton's second law to a continuum; in fact this equation is applicable to any non-relativistic continuum and is known as the Cauchy momentum equation.

This equation is often written using the material derivative D v/ Dt, making it more apparent that this is a statement of Newton's second law:

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The left side of the equation describes acceleration, and may be composed of time-dependent or convective effects (also the effects of non-inertial coordinates if present). The right side of the equation is in effect a summation of body forces (such as gravity) and divergence of stress (pressure and shear stress).

1.3.3 The General Reynolds Equation

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The equation can either be used with consistent units or nondimensionalized.

The Reynolds Equation assumes:

- The fluid is Newtonian.
- Fluid viscous forces dominate over fluid inertia forces. This is the principal of the Reynolds number.
- Fluid body forces are negligible.
- The variation of pressure across the fluid film is negligibly small (i.e. )
- The fluid film thickness is much less than the width and length and thus curvature effects are negligible. (i.e. and ).

For some simple bearing geometries and boundary conditions, the Reynolds equation can be solved analytically. Often however, the equation must be solved numerically. Frequently this involves discretizing the geometric domain, and then applying a finite technique – often finite difference method (FDM), finite volume method (FVM), or finite element method (FEM).

1.3.4 The Bauschinger Effect

The Bauschinger effect refers to a property of materials where the material's stress/strain characteristics change as a result of the microscopic stress distribution of the material. For example, an increase in tensile yield strength occurs at the expense of compressive yield strength.

While more tensile cold working increases the tensile yield strength, the local initial compressive yield strength after tensile cold working is actually reduced. The greater the tensile cold working, the lower the compressive yield strength.

The Bauschinger effect is normally associated with conditions where the yield strength of a metal decreases when the direction of strain is changed. It is a general phenomenon found in most polycrystalline metals. The basic mechanism for the Bauschinger effect is related to the dislocation structure in the cold worked metal. As deformation occurs, the dislocations will accumulate at barriers and produce dislocation pile-ups and tangles. Based on the cold work structure, two types of mechanisms are generally used to explain the Bauschinger effect.

1.4 Finite Element Analysis

The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for differential equations. It uses variational methods to minimize an error function and produce a stable solution.

FEM is best understood from its practical application, known as finite element analysis (FEA). FEA as applied in engineering is a computational tool for performing engineering analysis. It includes the use of mesh generation techniques for dividing a complex problem into small elements, as well as the use of software program coded with FEM algorithm. In applying FEA, the complex problem is usually a physical system with the underlying physics such as the Euler- Bernoulli beam equation, the heat equation, or the Navier-Stokes equations expressed in either Partial differential equation (PDE) or integral equations, while the divided small elements of the complex problem represent different areas in the physical system.

FEA is a good choice for analyzing problems over complicated domains like cars and oil pipelines, when the domain changes (e.g during a solid state reaction with a moving boundary), when the desired precision varies over the entire domain, or when the solution lacks smoothness. For instance, in a frontal crash simulation it is possible to increase prediction accuracy in mportant areas like the front of the car and reduce it in its rear, therefore reducing cost of the simulation.

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Fig. 1.6a: FEM mesh created by an analyst prior to finding a solution to a magnetic problem using FEM software.

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Fig. 1.6b: FEM solution to the problem of 1.6a, involving a cylindrically shaped magnetic shield.

1.4.1 Types of Finite Element Methods

The Applied Element Method, Generalized finite element method, Mixed finite element method, Extended finite element method, Smoothed finite element method, Fiber Beam Method, Spectral methods, Meshfree methods, Discontinuous Galerkin methods, Finite element limit analysis, Stretched grid method.

Other types include:

1.) hp-FEM, which combines adaptively, elements with variable size h and polynomial degree p in order to achieve exceptionally fast, exponential convergence rates, and
2.) hpk-FEM, which adaptively combines elements with variable size h, polynomial degree of the local approximations p and global differentiability of the local approximations (k-1) in order to achieve best convergence rates.

1.5 Research Objectives

- To investigate the effect of process variables on the deformation behaviour of Magnesium Alloy AZ31 at warm working conditions.
- To design and fabricate a deep drawing die set used for the deep drawing of a cylindrical cup from a metal disc.
- To carry out a Finite Element Simulation of the non-isothermal warm deep drawing of a cylindrical cup from a metal disc, in comparison to analogical experimental results, with the commercial FE software ANSYS using AZ31 Mg Alloy as material case study.

CHAPTER 2

2.0 LITERATURE REVIEW

Putting the topic of this study into consideration, a number of previous works have been reviewed. This is meant to enhance the understanding of the extent to which research activities have affected specific investigation in the direction of the numerical analysis of the warm deep drawability of Mg alloy sheet. Reviews carried out have been grouped into three categories namely:

1. Studies related to lubrication in metal forming
2. Studies related to process parameters in deep drawing
3. Workability of magnesium alloy in deep drawing

2.1 Studies Related to Lubrication in Metal Forming

Haar (1996)[9] investigated the influence of local contact conditions and deformation as regards friction in sheet metal forming, with considerable emphases on the deep drawing process. He presented different material models including the von Mises model and the Nadai model. It was mentioned that other material models were also developed mainly as variations on earlier models by von Mises and Nadai. These models, though complicated, have been proven to provide acceptable results most of the time. Haar also derived a theoretical model for determining the coefficient of friction on the basis of existing contact models and elasto-hydrodynamic lubrication (EHL) models. With this model it is possible to obtain realistic generalized Stribeck curves which could be used as a model for describing the local coefficient of friction in FEM simulations of SMF processes. However, the success of the model is said to depend strongly on certain assumptions. To establish reliability, Haar further developed a model based on experiments. For the sheet/tool contacts operating in the boundary lubrication (BL) regime and high in the mixed lubrication regime, this experimental-based model is said to be necessary to verify the theoretical model. An empirical friction model, based on curve-fitting of the generalized Stribeck curve was developed. With such a model, as shown in eqn. 2.1 below, there is a possibility of determining the local coefficient of friction during SMF simulations. L is lubrication number.

Abbildung in dieser Leseprobe nicht enthalten

Yuanjie (2008)[10] explored the possibility of using Laser texturing on the tool and its relevance to micro-lubrication in bulk forming. High interface friction was noticed as a primary cause for adhesive pickup in cold working of alloys. This study investigated reduction of interface friction through laser texturing of die surfaces, with the hypothesis that textures entrap lubricants hence improving boundary lubrication. Coarse and fine microgrooves were created using pulsed laser on hardened H-13 dies, and tests with axis symmetric aluminum alloy rings and plane strain rectangle coupons carried out with different lubricants. Both ring test and plain stain stamping test were proven to have several limitations including low interface pressures and low surface expansions. However, their advantages including ease of experimentation, ease of texturing, ease of measurement and reasonable sensitivity to frictional changes. Yuanjie concluded that the lubrication regimes change at different reductions during metal forming, and thus provides knowledge on how to support surface lubrication after regime changes. This study can be applied to friction control on sheet metal forming processes, through the partial control of metal flow to improve product quality and reduce scrap rate.

Arentoft, Bay, Tang and Jensen (2009)[11] developed a new lubricant carrier for metal forming, using severe cold forging processes as case study, for solving lubrication problems in order to avoid hazardous environmental impact. The study was targeted at providing an environmental friendly and more effective alternative to the conventional lubricant carrier mechanism, where a coating of zinc phosphate is done to create pockets suitable for entrapment of lubricant. The lubricant carrier, which is electrochemically deposited, is a coating of two insoluble metals (Tin and Zinc). The film coating is subsequently etched with diluted hydrochloric acid, whereby the Zn is removed, leaving a porous Sn layer. The diluted acid is considered environmentally harmless. The system was tested in conventional ring compression tests and double cup extrusion test. Its performance to impede galling was furthermore tested by severe stressing in single cup extrusion. When lubricating with a low viscosity mineral oil, which can penetrate into the porous coating, promising results were demonstrated with regards to significantly lower friction as well as increased resistance towards galling compared to non-coated surfaces. When the coating was applied to a common cold forging steel and lubricated with soap, the friction and resistance to galling was at the same level or even better than the conventional phosphate coating. An advantage of the new coating is said to be the expected improved environmental impact compared to the phosphating process.

Using alloyed gray cast iron at test material, Vadiraj, Kamaraj and Sreenivasan (2011)[12] compared the friction and wear performance of four solid lubricants namely: Molybdenum disulfide (MoS2), graphite, boric acid and Titanium dioxide (TiO2) . These lubricants were applied on the dry surface and the effect of sliding speed on their friction and wear performance was investigated in depth. Vadiraj et al intended to simulate the worst possible dry condition frequently experienced by sliding parts of industrial machineries under oil starved conditions. MoS2 and graphite were reported to show 30 to 50% reduction in mass loss compared to other lubricants at sliding speeds between 1.0 to 2.5m/s. Friction coefficient was observed to reduce with increase in sliding speeds for all the conditions. Friction coefficient of dry as well as lubricant coated samples also varied from 0.2 to 0.55 with MoS2 showing the lowest value (0.2). Boric acid and TiO2 coated samples showed high friction coefficients at higher sliding speeds; this suspected to be due to poor lubricity and adherence. As reported, this could also be due to sliding resistance offered by lubricant coated samples with predominant asperities interaction. MoS2 and graphite coated samples also generated lowest frictional temperature compared to other conditions.

Syahrullail, Zubil, Azwadi and Ridzuan (2011)[13] evaluated the viability of palm oil when used as a lubricant in cold work. Forward plane strain extrusion process was used to carry out the study. Syahrullail et al compared the performances of palm oil with additive-free paraffinic mineral oil. They investigated the velocity and the effective strain distribution in the deformation area of a workpiece extruded with Refined Bleached and Deodourized (RBD) palm stearin by cold work forward plane strain extrusion experiments and visioplasticity analysis. The experimental and analytical results of RBD palm stearin were compared to additive-free paraffinic mineral oils VG95 and VG460. It was found that RBD palm stearin can reduce the extrusion load compared to additive-free paraffinic mineral oil. RBD palm stearin, as also established, can produce a surface product with a low surface roughness value. They also found that the reduction of frictional constraint (reduction of load) affected the velocity and the effective strain distribution in the deformation area of the workpiece.

Ngaile, Cochran and Stark (2006)[14] developed a new metal forming lubricant based on polymeric materials. The lubricant was developed through emulsion copolymerization. Copolymers with the common composition of stearyl methacrylate and 2-hydroxyethyl methacrylate acid phosphate were made with three secondary polymers: methyl methacrylate, butyl acrylate, and 2-hydroxyethyl methacrylate. The performance of the developed lubricant was evaluated using the ring compression and twist compression tests. They compared the performance of the polymeric lubricant against a zinc-phosphate-coating-based lubricant, and three other commercial lubricants. The polymeric lubricant was observed to exhibit at least equal performance in all tests conducted at room temperature. Ngaile et al established that the preliminary test results indicated an effectiveness of the developed lubricant for non-severe deformation processes.

Hubert, Dubar, Christiansen, Bay and Dubois (2012)[15] examined liquid lubrication mechanisms in sheet metal forming at mesoscopic scale The study involved numerical as well as experimental analyses of the lubrication mechanisms, applying a numerical strategy to quantify the final shape of the lubricant pockets, and a testing to calibrate the numerical model.

2.2 Studies Related to Process Parameters in Deep Drawing

Altan, Groseclose, Billur, Subramonian and Mao (2012)[16] examined some advances and challenges in sheet metal forming technology. They understudied the practical determination of material properties and lubricants for optimum forming conditions as well as Finite Element simulations related to the study. Bulge and dome tests were carried out to determine flow stress, cup draw tests to evaluate lubricants, effects of punched hole quality on fracture limits in flanging, FE simulation of hot stamping to obtain tailored properties, spring back in bending, and application of servo drive presses to improve formability in forming of AHSS and Al alloys.

Bhatt (2013)[17] determined the effects of various parameters on forming limit diagram (FLD) using finite element (FE) analysis. In his research, Bhatt studied the effect of strain hardening exponent (n), punch velocity sheet thickness on FLD using FE based HYPERFORM software. A deep drawn cup was chosen for analysis. The results of the finite element analysis demonstrated that formability increases with increasing n-value and sheet thickness. However, more iteration were said to be required to determine the variation of punch velocity with formability.

Hol, Cid Alfaro, De Rooij and Meinders (2010)[18] proposed a numerical procedure, of modeling for sheet metal forming, which couples the different friction mechanisms. They presented a general overview of the numerical procedure and the translation from micro to macro modeling was outlined. The numerical procedure was used to calculate the coefficient of friction during large scale FE simulations. The numerical procedure included two flattening mechanisms to describe the real area of contact, a friction model including ploughing and adhesion effects to calculate the coefficient of friction and statistical parameters to make the translation from micro- to macro modeling. Hol et al applied the numerical procedure to a full scale sheet metal forming simulation which reportedly showed the applicability of the developed algorithm. It was observed that the results of the simulations showed that relatively low values of the coefficient of friction are found in case of normal loading only, the first flattening mechanism. If a second flattening mechanism is applied, flattening due to stretching, much more promising results were predicted to be obtainaible.

Hauer, Vierzigmann, Willner and Engel (2011)[19] developed a halfspace model for the numerical simulation of friction in metal forming. They described the halfspace as an infinite space which is limited in one direction by a surface. In the developed halfspace model, the contact of the halfspace surface with a rigid and perfectly flat plane was analysed. The halfspace approach has a significant advantage because only the surface has to be discretised, as compared to the Finite Element Analysis where the whole bulk has to be discretised. Consequently, the numerical effort and thus the calculation time in the halfspace model were observed to be much lower than in FE- modelling. Hauer et al integrated the retarding effect of hydrostatic pressure in closed lubricant pockets on asperity flattening into the developed halfspace model. They further compared the results of the calculation of the real contact area of rough surfaces to experimental data from ultrasonic inspection. Friction coefficients calculated with the halfspace model were also compared to results of strip drawing tests. The good agreement between the strip drawing tests and the numerical simulations was used to establish that the presented halfspace model is an adequate technique to simulate the contact of rough surfaces.

Jurkovic, Jurkovic and Buljan (2006)[20] carried out an experiment to define a mathematical model that can be used to determine the influence of lubricant and degree of deformation on friction coefficient. They modelled the coefficient of friction by means of a second order polynomial with interactions for two input parameters - lubricant and degree of deformation. Jurkovic et al developed software - MODSIM (Modelling and SIMulation). MODSIM has an ability to form adequate mathematical model using input values of process parameters and experimentally obtained output values. With the MODSIM software, they tested the mathematical model by varying the input values of the process thereby facilitating optimization of the process. The developed software (MODSIM) allows for the 2D simulation of the friction coefficient model for the various values of parameters. However, they established a link between MODSIM and MATLAB for the purpose of 3D simulation. The obtained results and mathematical model were said to indicate that the coefficient of friction is dependent on the strain and type of the lubricant used. The study carried out by Jurkovic et al, as reorted, showed that the experimental methods and modelling can be successfully used for defining the tribological state of processes in the metal forming processes.

Ramesh, Chandra and Reddy (2013)[6] carried out analysis for optimization of blank holding force (BHF) developed for cup drawing operation by using explicit finite element package LS DYNA.

In their study, Ramesh et al carried out a die design for a cup of 30mm diameter and deep with 1 mm thickness. They calculated blank holding force was from the empirical formula. By an iterative procedure the optimum blank holding force was obtained. Attempt was made to determine the force in the drawing operation and failure of the cup. Hence, it was pointed out that the higher the BHF, the higher the frictional forces between the blank and blank holder, the higher the loads required for drawing operation and the higher the strains developed in the cup walls between the die and punch, thereby reducing thickness of the section. , Ramesh et al found out the optimum blank holding force by checking the condition of non-formation of wrinkles at different coefficient of friction at (0.045, 0.06, 0.1, 0.13, and 0.15) and at different die radius (2, 3, 4, 5 and 6mm) and the values of blank holding force was taken where no wrinkles was formed for different coefficient of friction and for different die radius. It was established that there will be an optimum die radius where max plastic strain and max von-Mises are minimum. The graphs were plotted and the results were studied.

Wurster, Liewald, Blaich and Mihm (2011)[21] developed a procedure for an automated virtual optimization of variable blank holder force distributions for deep-drawing processes using LS- Dyna and optiSLang. This procedure made it possible to identify optimized blank holder force distribution in space and time without manual investigation of optimization results during finite element analysis prior to manufacturing of deep drawing die. They carried out the optimization of variable in space by using adaptive response surface method. For automated optimization of blank holder force distributions variable in time, they utilized the tolerance margin method for further optimization runs. The method was tested successfully for a conical cup and afterwards it has been implemented in deep-drawing of fender shaped geometry. The results, as reported, showed a defect-free part without sidewall wrinkling and reduced maximum thinning by 19% compared to initial simulation. Afterwards, tolerance margin method was used for significant segments’ optimization of blank holder force distribution variable in time. This method provided the possibility to reduce thinning by 3% again. At the same time, the defect-free part did not show any sidewall wrinkling. The developed automated procedure for optimization is proven to have an increased time-efficiency and elimination of diversity in interpretation of simulation results.

Gharib, Wifi, Younan and Nassef (2006)[22] developed an optimization system intended for use in the determination of the optimum (BHF) scheme that minimizes punch force, without running into wrinkling and/or tearing, which are the two process limits. The optimized linear BHF scheme was reported to result in an improved cup forming when compared to that produced by the constant BHF scheme. They optimized the BHF scheme for different cases of drawing ratios and die coefficients of friction in order to analyze the nature of the optimum linear BHF scheme. It was found that the slope of the linear BHF scheme increases with the increase in the drawing ratio in a linear manner. Also, the intercept of the function was observed to show a nearly linear variation with the drawing ratio. Gharib et al deduced a general equation for the optimum blank holder force at any drawing ratio for a typical deep-drawn cup.

2.3 Workability of Magnesium Alloy in Deep Drawing

Mohd Ruzi, Norhamidi, Abu, Khairur, Nor, Sufizar A, Mohd Halim and Murtadhahadi (2009)[1] reviewed the processing of magnesium alloys in air at elevated temperatures. Their investigation, with respect to the said alloys, included mechanical properties, the effect of temperature on workability as well as thermal and corrosive aspects. They presented some of wrought magnesium alloys of AZ, ZK and WE systems in order to find out the issues relating to their workability on various deformation conditions. It was realized that the principle of processing wrought Mg alloys is temperature. The workability at elevated temperature, strain rate and grain size on mechanical properties were investigated and they were dependent variables. Mohd Ruzi et al summarized the literatures published in the academic journals and the workability deformation temperature for wrought Mg alloys were justified. As discovered, the requirements for wrought Mg alloy to become superplastic includes a fine grain size, typically below 10μm, low strain rate as well as maintaining of fine grain structure at high temperatures. They also pointed out that: One, corrosion resistance can be improved by various surface modification techniques. Two, creep failure can be reduced and/or eliminated by using highly creep resistance Mg alloys. Three, fatigue strength can be improved by an appropriate addition of manganese contents. The finding of the study by Mohd Ruzi et al is very useful for the selection of wrought Mg alloy and their feasible for potential near-net-shape manufacturing technology.

Ghaffari Tari and Worswick (2012)[23] investigated the of different process parameters such as punch speed and punch and die temperature in deep drawing experiments of aZ31 magnesium alloy. They also studied the effect of temperature gradient on formability of the said alloy. In their experiments, they considered two different heat treatments of AZ31, namely O-temper and partially annealed material (H24). The minimum forming temperature possible for the current rig were studied for both heat treatments. Three separate controllers for the heating system were used to have an independent control over the temperature at each of the experiment components (punch, die, blank holder), with an additional heating system embedded in the punch to investigate a wider range of temperature gradient from close to isothermal conditions associated with large difference between punch and die temperature. It was observed that forming at lower punch speeds resulted in a more uniform distribution of strain. Also, at higher punch speeds more micro cracks were formed at the punch radius region. Ghaffari Tari and Worswick made some findings about the effect of temperature gradient at die and blank holder temperature of 245˚C. A low gradient was discovered to lead to fracture during the early stages of deformation while a near isothermal temperature gradient condition led to tearing during the final stages of forming. At near to isothermal conditions necking around the punch radius was also observed.

In support of experimental studies, Hai, Itoh, Sakai, Kamado and Y. Kojima (2008)[24] simulated the behavior of a cylindrical deep drawing of magnesium alloy sheets at elevated temperatures using a non-isothermal finite element based on DEFORM 3D commercial software. Certain deductions were made from the study. One, the LDRs of AZ31 and AZ52 was observed to increase with increase in forming temperature and the maximum values obtained at 498 K though the LDRs predicted by simulation were said to be slightly lower compare to the experiment results. Two, the punch force predicted by FE simulation reportedly overestimated the experimental results, either due to high blank holder force and/or high shear stress caused by interface friction coefficient. Three, the thinning distribution observed in simulation agreed with experimental result. Hai et al finally ascertained that the thermo-viscoplasticity DEFORM3D FEM code could successfully capture the deformation behavior and specific characteristics of the warm sheet forming process.

Palaniswamy, Ngaile and Altan (2004)[25] conducted a study focused on non-isothermal finite element (FE) simulation of a round cup and a rectangular pan from Mg alloy AZ31B sheet at elevated temperatures using commercial FE codes DEFORM 2D and 3D, respectively. They compared the results of the simulation with experimental results, and both were seen to predict increase in limiting draw ratio (LDR) with increase in temperature. For simulation, maximum LDR was obtained at the forming temperature of 200 ◦C. Simulations by Palaniswamy et al were conducted for the experimental cases published by Droder (1999)[26] and Doege et al (2001)[27]. The forming load predicted by simulation for round cup and rectangular pan, as noticed, overestimated the experimental results. However, the trend predicted by simulation matched well with experiment. Higher punch force in the simulation was suspected to result from high frictional shear stress at interface. The maximum thinning and tearing was observed at the cup wall in simulation and experiment, contrary to the observations in conventional stamping where the thinning occurs in the punch corner radius. This was speculatively attributed to the fact that the cup walls in warm forming were at high temperature compared to punch corners, thus, the yield strength of material in cup wall was low compared to punch corner radius. LDR predicted by simulations by Palaniswamy et al for round cup for different forming temperatures were observed to be lower compared to the experimental results. As in the study carried out by Hai et al, thermo-elastic–visco-plastic FEM code used in this study was said to successfully capture the deformation modes and the specific characteristics of the warm sheet forming process.

Li, Zhao, Ma and Gao (2012)[28] investigated the flow stress characteristics of AZ31B magnesium alloy sheet at elevated temperatures. They obtained the true stress-strain curves of AZ31B the alloy sheet using uniaxial tensile tests at temperatures ranging from 50oCto 300oC and initial strain rates ranging from 0.001/s to 0.1/s. The effects of temperature and strain rate on the flow stress were analyzed. The results as presented by Li et al showed that the flow stress decreases and the elongation at fracture increases with increasing temperature and decreasing strain rate, and the formability is improved obviously. They developed two mathematical models to determine the flow stress at hot deformation condition. The first model is based on the Fields- Backofen equation, and the second model based on a natural exponential form whose exponent is a quadratic function. By comparison of the calculated results with experimental data, it was proved that the flow stresses calculated by the Fields–Backofen model only give a good fit to the measured ones at the work-hardening stage, but it cannot describe the softening behavior after the peak stress. Whereas, the exponential model, as described, does not only accurately reflect work hardening before the peak stress, but approaches more closely at the dynamic softening stage of the flow stress than that of the Fields–Backofen model.

Sivanandini, Dhami and Pabla (2012)[2] researched into the formability of magnesium alloys with efforts to optimize process parameters by analyzing the causes of defects in order to improve the Limit Drawing Ratio of magnesium alloy work pieces. They studied the combined effect of strain rate and temperature on material formability. Formability test results showed that a new magnesium sheet alloy, yttrium-containing ZW41, was significantly more formable than traditional magnesium alloys AZ31 and ZK10. The improvement was linked to a more random texture in the new alloy, which diminished the tendency for gross, catastrophic shear instability. Sivanandini et al reported that the formability of Magnesium alloys increased at elevated temperatures depending on the thickness and the forming process adopted.

Watari, Paisarn, Koga, Haga, Davey and Rasgado (2004)[29] investigated plastic formability of cast magnesium alloy that were hot rolled after roll strip. The study was meant to ascertain the feasibility of semi-solid strip casting process of AZ31B magnesium alloy. Hot rolling and heat treatment conditions were changed to examine which conditions were appropriate for producing AZ31B wrought magnesium alloys after strip casting process. Watari et al performed microscopic observation of the crystals of the manufactured wrought magnesium alloys. The grain size of the manufactured wrought magnesium alloys sheets was less than 10 micrometers. It was found that a limiting drawing ratio of 2.7 was possible in a warm deep drawing test of the cast magnesium alloy sheets after being hot rolled. They found that appropriate roll speeds are from 5 to 25 meters per minutes at 625 °C, and from 5 to 10 meters per minutes at 630°C. In the hot rolling process, a temperature of 400°C was said to be necessary to avoid cracks occurring in cast magnesium alloys. It was also found that appropriate annealing condition was 350°C for two hours in the hot rolling Ngoc-Trung, Oh Suk, Chung, Myoung-Gyu, Ji-hoon and Heon (2014)[30] studied the mechanical behavior of AZ31B Mg alloy sheets under monotonic and cyclic loadings at different temperatures, ranging from room temperature to 250 °C. They recorded behaviors showing significant twinning during initial in-plane compression and untwining in subsequent tension at and slightly above room temperature. Strong yielding asymmetry and nonlinear hardening behavior were noticed. Ngoc-Trung et al observed considerable Bauschinger effects, transient behavior, and variable permanent softening responses near room temperature, but these were said to show reduction and virtual disappearance as the temperature increased. A critical temperature was identified to account for the transition between the twinning-dominant and slip-dominant deformation mechanisms. Different stress–strain responses were found out to be inherent to the activation of twinning at lower temperatures and non-basal slip systems at elevated temperatures. According to them, below the transition point, stress–strain curves of cyclic loading tests exhibited concave-up shapes for compression or compression following tension. This unusual shape was said to disappear when the temperature was above the transition point and shrinkage of the elastic range and variation in Young’s modulus due to plastic strain deformation during stress reversals were also observed. The texture-induced anisotropy of both the elastic and plastic behaviors was characterized experimentally. They proposed a hardening model, which successfully reproduced the cyclic stress–strain curves, including yield asymmetry, a Bauschinger effect, transient and permanent softening, and the unusual concave-up shape.

Takuda, Morishita, Kinoshita and Shirakawa (2005)[31] measured and analyzed the flow curves of the AZ31 magnesium alloy sheet at elevated temperatures. They measured the flow stress of magnesium alloy AZ31 sheet at various temperatures, strains and strain rates, and the relationships between them were analyzed. Takuda et al proposed a formula for the flow stress in a simple form with the work-hardening exponent, n, the strain rate sensitivity exponent, m, and the parameter, K, and the temperature.

Palumbo, Sorgente, Tricarico, Zhang and Zheng (2006)[32] investigated the deep drawing process of Mg alloy sheet in Warm conditions; they propagated that through the temperature the number of independent slip systems of the Mg alloys can be enlarged. A FE model and an equipment for warm deep drawing tests were created, to provide for experimental-numerical method, which they adopted; the most efficient heating positioning and the most suitable way of performing the warm deep drawing process was evaluated using data coming from the numerical model and temperature and punch load acquisition coming from experimental activity. They obtained a Limit Drawing Ratio (LDR) equal to 2.6 for AZ31 Mg alloy (cross rolled, thickness 0.6mm) at a temperature of 170oC using heater embedded in the female die; Drawing Ratio was equal to 3.1 for the same Mg alloy (thickness 0.6mm) obtained setting the temperature of the blank holder at 250oC (throughout heaters embedded in it) and cooling the central part using a water cooled punch. Three heating techniques were investigated. One, punch cooled and kept far from the blank during the heating phase, CP. Two, punch not cooled and kept far from the blank during the heating phase, P. Three, punch cooled and kept in contact with the blank during the whole heating phase, CPC. They discovered that no variation in the microstructure occurred in the specimen if the temperature is kept lower during all the process (the CPC heating technique instead of the CP one). In addition a stronger influence of the temperature of the material in the flange region was highlighted on the Punch Load; in particular when comparing the maximum deep drawing force concerning the CP and the CPC heating conditions, considering the very similar temperature levels in the blank centre region, a large difference was recognised, which they suspected to be due to temperature difference realised in the Blank Holder.

Ghale and Wankhade (2013)[33] studied the influence of temperature of blank, on the deep drawing process using Altair HyperForm and RADIOSS simulation tool. They predicted the optimum value of temperature to get maximum Limiting Draw Ratio (LDR) assuming isothermal condition; though in actual there is heat loss from the blank. They recommendd that the results be validated with the experiment to check accuracy.

Watari, Koga, Davey, Alonso Rasgado and Haga (2003)[34] performed an experimental investigation into the warm deep drawability of magnesium alloy sheets that were hot-rolled after a semi-solid roll strip casting process. They used magnesium alloy AZ31B in the experiment to ascertain the effectiveness of semisolid roll strip casting. The temperature of the molten magnesium, and the roll speeds of the upper and lower rolls were varied to find an appropriate manufacturing condition. Warm rolling and heat treatment conditions were changed to examine which condition would be appropriate for producing wrought magnesium alloys with good formability. They also performed microscopic observation of the crystals of the finished products. Watari et al found that a limiting drawing ratio of 2.4 was possible in a deep drawing process of the cast magnesium alloy sheets that were hot-rolled after a semi-solid roll strip casting process, using a relatively low drawing speed of 2.5 mm/s. They also found that the grain size of the cast products is 30 micrometers before hot rolling and that after hot rolling, the grain size of the cast magnesium alloy sheets can be reduced to 10 micrometers.

CHAPTER 3

3.0 METHODOLOGY

3.1 Procedures for Analysis and Evaluation

Carried out in this study is a series of analysis to optimize process parameters using compared results from simulations, done with a FEM commercial software ANSYS, and experiments.

Some process parameters are specifically considered from empirical models. These process parameters are:

(i) Punch nose radius
(ii) Die corner radius
(iii) Clearance
(iv) Blank holder force
(v) Drawing temperature

Furthermore, values obtained from the optimized process parameters are incorporated into the design of the deep drawing die, punch, jigs and fixtures. The die and its accessories are then fabricated. A simple deep drawing test running of the die is done with aluminum alloy 1200 sheet to authenticate the suitability of the die in carrying out an eventual experiment on the warm deep drawability of the magnesium alloy AZ31-O.

3.2 Experimental Tooling Design

The experimental setup includes the positioning of the deep drawing die and its accessories on a hydraulic press. The part of the experimental setup categorized as die accessories includes the punch as well as certain jigs and fixtures.

3.2.1 Press Specifications

In this design, the physical features of the hydraulic press intended to be used for the deep drawing experiment are taken into cognizance. These include:

(i) Bed size
(ii) Outer ram diameter
(iii) Inner ram diameter
(iv) Load capacity

3.2.2 Tool Design Considerations

The design considerations for deep drawing die and punch (Pandey and Singh, 2001)[35] includes the minimum blank diameter, number of draws, limiting draw ratio, length of punch, maximum required pressure and other necessary parameters as follows:

3.2.2.1 Minimum blank diameter, D1

Abbildung in dieser Leseprobe nicht enthalten

rp is the punch nose or the die corner radius (taken as 4 times blank thickness, S)
h1 is the minimum height of the cup
d is the cup diameter

3.2.2.2 Number of Draws

The number of draws is greatly dependent on the percentage reduction (eqn 3.2 below) for a particular draw.

Abbildung in dieser Leseprobe nicht enthalten

1st draw (recommended % Reduction): 45-48%
2nd draw (recommended % Reduction): 30%
3rd draw (recommended % Reduction): 20%

As the ratio T/D decreases, wrinkle tendency increases.

3.2.2.3 Limiting Draw Ratio, LDR

Abbildung in dieser Leseprobe nicht enthalten

D2 is the target maximum blank diameter

3.2.2.4 Length of punch, h2

Abbildung in dieser Leseprobe nicht enthalten

3.2.2.5 Maximum required pressure, P

Abbildung in dieser Leseprobe nicht enthalten

Us is the ultimate tensile strength of the work piece.

Also,

Abbildung in dieser Leseprobe nicht enthalten

3.2.2.6 Volume of work piece before and after forming, V

Abbildung in dieser Leseprobe nicht enthalten

Where the sheet thickness, S and the shell thickness, t is related by:

Abbildung in dieser Leseprobe nicht enthalten

3.2.2.7 Other necessary parameters

F_N: blank holder force

Blank holder force is 0.7 to 1 % of the total of the yield and ultimate tensile strength of the work piece

F_p: punch force or drawing force
U: clearance between die and punch
d_v: punch vent diameter

3.2.3 Design considerations for jigs and fixtures

Part analysis to aid the design of other die accessories (i.e. jigs and fixtures) is carried out as follows:

1. Die shoe

l_m: body outer diameter

d_m: body hole diameter

h_m: Body height

l_n: base outer diameter

d_n: base hole diameter hn: Base height

2. Punch Sleeve

d_f: external diameter

d_g: internal diameter

h_d: hole depth

h_f: sleeve height

3. Blank holder

d_h: external diameter

d_i: internal diameter

h_b: blank holder height

4. Blank holder sleeve

d_q: external diameter

d_r: internal diameter = di

h_b: sleeve height

3.2.4 Materials Selection

The various parts of the experimental tooling are made of appropriate materials. These materials are shown in table 3.1 below

Table 3.1: Materials used for tool components and work piece

Abbildung in dieser Leseprobe nicht enthalten

3.2.5 Effect of Lubrication on Sliding Friction

The sliding friction coefficient (www.skf.com)[36] for full-film and mixed lubrication conditions can be estimated using

Abbildung in dieser Leseprobe nicht enthalten

where

φbl = weighting factor for the sliding friction coefficient equation

Abbildung in dieser Leseprobe nicht enthalten

μ_sl = sliding friction coefficient

e = base of natural logarithm ≈ 2,718

n = Rotational speed [r/min]

ν = kinematic viscosity at operating temperature of the oil or the base oil viscosity of the grease [mm2/s]

d_m = bearing mean diameter [mm] = 0,5 (d + D)

μ_bl = coefficient depending on the additive package in the lubricant, generally ≈ 0,15

μ_EHL = sliding friction coefficient in full-film conditions

Value for μEHL is 0.02 for cylindrical roller bearings.

CHAPTER 4

4.0 RESULTS AND DISCUSSION

4.1 Design Calculations/Values

With the use of existing empirical models, the appropriate parameters needed to determine the geometry of the experimental die set are worked out in this section.

4.1.1 Blank thickness, S

S = 1.45mm

4.1.2 Punch nose or the die corner radius (recommended as 3 times blank thickness, S), rp

r_p = 3S = 1.45 x 3 = 4.35mm ≈ 4.5mm

4.1.3 The minimum height of the cup, h1

h₁ = 45mm

4.1.4 The cup diameter, d

d = 30mm

4.1.5 Minimum blank diameter, D1

Recall equation 3.1;

Abbildung in dieser Leseprobe nicht enthalten

4.1.6 Limiting Draw Ratio, LDR

From eqn. 3.3;

Abbildung in dieser Leseprobe nicht enthalten

D₂ is the target maximum blank diameter

Target LDR = 3.5

Abbildung in dieser Leseprobe nicht enthalten

4.1.7 Length of punch, h2

From eqn. 3.4;

Abbildung in dieser Leseprobe nicht enthalten

Where d = 60mm is the punch diameter

Abbildung in dieser Leseprobe nicht enthalten

4.1.8 Maximum required pressure, P

From eqn. 3.5;

Abbildung in dieser Leseprobe nicht enthalten

4.1.9 Other necessary parameters

Blank holder force, FN

Note: Blankholder force is 0.7 to 1 % of the total of the yield and ultimate tensile strength of the workpiece.

Abbildung in dieser Leseprobe nicht enthalten

Punch force or drawing force, FP is taken as equal to P

Clearance between die and punch, U = 2.0 X sheet thickness (S)

4.1.10 Dimensions of die accessories

1. Die shoe

Body outer diameter, lm = 100mm

Body hole diameter, dm =76mm

Body height, hm = 45mm

Base outer diameter, ln = 145mm

Base hole diameter, dn = 40mm

Base height, hn = 12mm

2. Punch sleeve

External diameter, df = 45mm

Internal diameter, dg = 33.6mm

Hole depth, hd = 43.6mm

Sleeve height, hf = 60mm

3. Blank holder

External diameter, dh = 76mm

Internal diameter, di = 45mm

Blank holder height, hb = 25mm

4. Blank holder sleeve

External diameter, dq = mm

Internal diameter, dr = 45mm

Sleeve height, hh = 30mm

4.2 Design Drawings

This work includes the design and construction of a deep drawing die set for the forming of a hollow circular cup. The drafting of the deep drawing die set was carried out using the CAD software; AUTODESK INVENTOR. A detailed and comprehensive engineering drawing of the die set components are shown in this section.

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Fig. 4.1: Labeled components of the tool

Table 4.1: Dimensions of die components

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Fig. 4.2: A 3D model of the tooling setup

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Fig. 4.3: Longitudinal section through the tooling setup

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Fig. 4.4: Schematic of the tooling setup showing top parts

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Fig. 4.5: Schematic of the tooling setup showing bottom parts

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Fig. 4.6: Longitudinal section through the die components assembly

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Fig. 4.7: A 3D model of the die components assembly showing top parts

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Fig. 4.8: A 3D model of the die components assembly showing bottom parts

4.3 Finite Element Simulation

The use of magnesium alloys is limited because of their low formability. The formability of these materials can be increased by forming at higher temperature. And with the help of simulation tools, a huge amount of capital can be saved by doing different trials rather than the actual experiment. In this study, a simulation procedure is carried out using the finite element commercial package ANSYS. The process parameters used for simulation are shown in table 4.1 below.

Table 4.2: Process Parameters for Finite Element Model

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4.3.1 Experimental setup for FEAIn this work, the Finite Element Method is used to carry out an extensive study. The finite element experimental setup is as shown in fig. 4.9 below.

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Fig. 4.9: A solid model of the FE experimental setup.

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Fig. 4.10: A meshed model of the FE experimental setup.

4.3.2 Simulation Results

Different process parameters are varied in this research work, in order to carry out a thorough investigation into the behaviour of the magnesium alloy sheet during warm deep drawing.

Comparative studies are carried out as follows:

(1.) Deep drawing at both room temperature and warm non-isothermal condition, keeping other process parameters constant.
(2.) Variation of the blank holder force with the drawing speed, keeping other process parameters constant.
(3.) Variation of the punch nose radius with the blank holder force, keeping other process parameters constant.
(4.) Variation of the punch nose radius with the drawing speed, keeping other process parameters constant.

4.3.2.1 Analysis Based on Temperature Variation

A comparative analysis is carried out in this section for a comprehensive investigation. This is aimed at studying how a variation of forming temperatures affects the formability of AZ31 magnesium alloy during the deep drawing process. With the same set of parameters, a simulation procedure was carried out for the deep drawing of the work piece at room temperature as well as under warm working conditions.

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Fig. 4.11 (a b): Simulation interface for AZ31 deep drawing at room temperature.

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Fig. 4.12 (a b): Simulation interface for AZ31 deep drawing under warm working.

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Fig. 4.13: Stress-Strain relationship for AZ31 deep drawing with varied working temperature.

4.3.2.2 Variation of the Blank Holder Force with the Drawing Speed

In this section, four different values of the BHF are varied against three different values of the drawing speed. The simulated results are shown for the different cases and a comparative graph is shown at the end of different stages in the section. Values for the BHF in kN are 0, 8.26, 10.03 and 11.8 while values for the drawing speed in m/s are 0.2, 0.4 and 0.6.

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Fig. 4.14 (a b): Simulation interface for AZ31 deep drawing with BHF 0kN at 0.2m/s.

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Fig. 4.15 (a b): Simulation interface for AZ31 deep drawing with BHF 0kN at 0.4m/s.

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Fig. 4.16 (a b): Simulation interface for AZ31 deep drawing with BHF 0kN at 0.6m/s.

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Fig. 4.17: Stress-Strain relationship for AZ31 deep drawing at BHF 0kN with varied drawing speed.

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Fig. 4.18 (a b): Simulation interface for AZ31 deep drawing with BHF 8.26kN at 0.2m/s.

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Fig. 4.19 (a b): Simulation interface for AZ31 deep drawing with BHF 8.26kN at 0.4m/s.

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Fig. 4.20 (a b): Simulation interface for AZ31 deep drawing with BHF 8.26kN at 0.6m/s.

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Fig. 4.21: Stress-Strain relationship for AZ31 deep drawing at BHF 8.26kN with varied drawing speed.

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Fig. 4.22 (a b): Simulation interface for AZ31 deep drawing with BHF 10.03kN at 0.2m/s.

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Fig. 4.23 (a b): Simulation interface for AZ31 deep drawing with BHF 10.03kN at 0.4m/s.

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Fig. 4.24 (a b): Simulation interface for AZ31 deep drawing with BHF 10.03kN at 0.6m/s.

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Fig. 4.25: Stress-Strain relationship for AZ31 deep drawing at BHF 10.03kN with varied drawing speed.

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Fig. 4.26 (a b): Simulation interface for AZ31 deep drawing with BHF 11.8kN at 0.2m/s.

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Fig. 4.27 (a b): Simulation interface for AZ31 deep drawing with BHF 11.8kN at 0.4m/s.

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Fig. 4.28 (a b): Simulation interface for AZ31 deep drawing with BHF 11.8kN at 0.6m/s.

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Fig. 4.29: Stress-Strain relationship for AZ31 deep drawing at BHF 11.8kN with varied drawing speed.

4.3.2.3 Variation of the Punch Nose Radius with the Blank Holder Force

In this section, three different values for the nose radius are varied against four different values of the BHF. The simulated results are shown for the different cases and a comparative graph is shown at the end of different stages in the section. Values for the nose radius in mm are 4, 4.5 and 5, while values for the BHF in kN are 0, 8.26, 10.03 and 11.8.

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Fig. 4.30 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 0kN

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Fig. 4.31 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 8.26kN

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Fig. 4.32 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 10.03kN

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Fig. 4.33 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at BHF 11.8kN

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Fig. 4.34: Stress-Strain relationship for AZ31 deep drawing with punch radius 4mm and varied BHF.

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Fig. 4.35 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 0kN

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Fig. 4.36 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 8.26kN

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Fig. 4.37 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 10.03kN

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Fig. 4.38 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at BHF 11.8kN

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Fig. 4.39: Stress-Strain relationship for AZ31 deep drawing with punch radius 4.5mm and varied BHF.

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Fig. 4.40 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 0kN

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Fig. 4.41 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 8.26kN

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Fig. 4.42 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 10.03kN

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Fig. 4.43 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at BHF 11.8kN

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Fig. 4.44: Stress-Strain relationship for AZ31 deep drawing with punch radius 5mm and varied BHF.

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4.3.2.4 Variation of the Punch Nose Radius with the Drawing Speed

In this section, three different values for the nose radius are varied against three different values of the drawing speed. The simulated results are shown for the different cases and a comparative graph is shown at the end of different stages in the section. Values for the nose radius in mm are 4, 4.5 and 5, while values for the drawing speed in m/s are 0.2, 0.4 and 0.6.

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Fig. 4.45 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at 0.2m/s

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Fig. 4.46 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at 0.4m/s

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Fig. 4.47 (a b): Simulation interface for AZ31 deep drawing with punch radius 4mm at 0.6m/s

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Fig. 4.48: Stress-Strain relationship for AZ31 deep drawing with punch radius 4mm and varied speed.

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Fig. 4.49 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at

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Fig. 4.50 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at 0.4m/s

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Fig. 4.51 (a b): Simulation interface for AZ31 deep drawing with punch radius 4.5mm at 0.6m/s

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Fig. 4.52: Stress-Strain relationship for AZ31 deep drawing with punch radius 4.5mm and varied speed.

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Fig. 4.53 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at 0.2m/s

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Fig. 4.54 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at 0.4m/s

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Fig. 4.55 (a b): Simulation interface for AZ31 deep drawing with punch radius 5mm at 0.6m/s

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Fig. 4.56: Stress-Strain relationship for AZ31 deep drawing with punch radius 5mm and varied speed.

4.4 Discussion

A series of FE simulations has been carried out to identify the extent to which each test parameter affects the warm deep drawing of the alloy AZ31. The test parameters varied in the simulation include the working temperature range, blank holder force, drawing speed and the punch hole radius.

As shown in fig. 4.57 below, a set of deep drawing die was constructed based on the design details in chapters 3 and 4 above. To establish the authenticity of the numerical simulation carried out in this research work, the functionality of the deep drawing die was established with a test run experiment using aluminum 1200 alloy disc plate, shown in fig. 4.58 below, as the work piece. A sample from the deep drawing of the material is shown in fig. 4.59 below.

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Fig. 4.57: A set of deep drawing die

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Fig. 4.58: Aluminum 1200 alloy sheet disc

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Fig. 4.59: A sample from the deep drawn aluminum alloy

Fig. 4.13 shows the stress-strain curves for the simulation carried out by varying the working temperature between room temperature and warm working non-isothermal conditions. The maximum equivalent stress around the yield point is 27.16MPa at room temperature and 49.5MPa under warm working conditions. It can be deduced that the warm working of AZ31 produces a better output than its cold working. This therefore confirms earlier inferences; that magnesium alloys are more suitably workable under warm working conditions, as compared to cold working.

Fig. 4.17 shows the stress-strain curves for the simulation carried out by varying three different values of drawing speed in a process when the blank holder is not used (i.e. BHF is 0kN ). At speeds of 0.2m/s, 0.4m/s and 0.6m/s, the maximum equivalent stress values around the yield point are 18.06MPa, 20.68MPa and 20.12MPa respectively. As compared to the 49.5MPa that characterized the controlled the deep drawing carried out under warm working conditions, the results indicate an earlier failure of the material. The relatively early failure of the material could be attributed to the uncontrolled placement of the short-diameter blank on the die opening, during the deep drawing process. Fig. 4.21 shows the stress-strain curves for the simulation carried out by varying the three different values of drawing speed against a blank holder force of 8.26kN. The yield stresses are 26.43MPa, 27.43MPa and 26.52MPa respectively. In fig. 4.25, the three different values of drawing speed were varied against BHF of 10.03kN and the equivalent yield stress values are 35.97MPa, 33.67MPa and 39.02MPa respectively. Also, in fig. 4.29, the three different values of drawing speed were varied against BHF of 11.8kN and the equivalent yield stress values are 39.3MPa, 39.4MPa and 46.33MPa respectively. The trend in the yield stress values shows that the BHF of 8.26kN was not sufficient enough to yield the relatively better outputs obtained from using a BHF of 10.03kN or 11.8kN. The most preferred process, with the highest yield stress of 46.33MPa, in this series occurred by drawing at 0.6m/s using a BHF of 11.8kN. The corresponding yield stress values, obtained by varying the drawing speed and BHF values under consideration, are given in table 4.3 below.

Table 4.3: Values of Yield Stress from Varying the Drawing Speed with the BHF

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Similar curves to the stress-strain relationships in figs. 4.17, 4.21, 4.25 and 4.29 were plotted in figs. 4.34, 4.39 and 4.44 based on the result of the simulation carried out by respectively varying three different values of the punch radius (i.e. 4mm, 4.5mm and 5mm) against BHF values of 0kN, 8.26kN, 10.03kN and 11.8kN. The corresponding yield stress values, obtained by varying the punch nose radius with the BHF values under consideration, are given in table 4.4 below. The most preferred process, with the highest yield stress of 36.7MPa, in this series occurred by drawing with a punch radius of 4.5mm and a BHF of 10.03kN.

Table 4.4: Values of Yield Stress from Varying the Punch Nose Radius with the BHF

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Furthermore, figs. 4.48, 4.52 and 4.56 present the curves plotted from the results of the simulation carried out by varying three different values of the punch radius with drawing speed values of 0.2m/s, 0.4m/s and 0.6m/s. The corresponding yield stress values, obtained by varying the punch nose radius with the drawing speed values under consideration, are given in table 4.5 below. The most preferred process, with the highest yield stress of 53.38MPa, in this series occurred by drawing with a punch radius of 5mm and a drawing speed of 0.6m/s.

Table 4.5: Values of Yield Stress from Varying the Punch Nose Radius with Drawing Speed

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CHAPTER 5

5.0 Conclusion and Recommendations

5.1 Conclusion

This research work focuses on the extent to which important parameters affect the warm deep drawing of the magnesium alloy AZ31. A deep drawing die set has been designed and constructed. The design of the die set, which has been carried out with the aid of AUTODESK INVENTOR drafting application, has been uploaded for a numerical simulation of the intended process. The simulation of the warm deep drawing process for AZ31 has been carried out using the commercial FE software ANSYS. The effects of process variables on the warm deep drawing, of the alloy under consideration, have been investigated.

The effects of the working temperature range was studied by varying the working conditions while keeping other parameters constant. It has been observed that the deep drawing of AZ31 takes place more effectively under warm working conditions compared to when carried out at room temperature. The blank holder force, drawing speed and the punch hole radius have also been varied with one another to determine their effects on the warm deep drawing of the alloy under consideration. It has been observed that the drawing speed and the punch radius affect the forming of the material, more than the blank holder force, under a non-isothermal warm working condition with the working temperature ranging between 423K and 523K. By comparing the results obtained from simulation to the results of the test run experiment, it has been observed that if the punch radius is too small the material fails due to tearing, and that wrinkling takes place when the punch radius is too large. It has therefore been inferred that, to balance the process parameters in the warm deep drawing of AZ31, an optimization procedure helps in the determination of the best value for the punch radius.

5.2 Recommendation

To further authenticate the deformation behavior, of the alloy AZ31, as established through the numerical simulation procedure in this present work, a full scale experimental verification of the study is recommended. The experimental verification would be mostly reliable if carried out in a standard laboratory environment.

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