Relationship Between Temperature and Formability in EAISMF Process

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Essay, Pages 6 (1411 words)

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Abstract

This work investigates the relationship between temperature and formability of sheet metal in Electrically Assisted Incremental Sheet Metal Forming (EAISMF). The formability of sheet metal is explored concerning temperature changes induced by a DC power supply. Ductile fracture is a critical factor influencing sheet metal forming, as it is primarily based on plastic deformation. This study establishes an empirical criterion for fracture determination, shedding light on the EAISMF process.

Keywords

Incremental forming
Formability
Ductile fracture
Joules heating effect

1. Introduction

Incremental Sheet Forming (ISF) is a process of plastic deformation of

sheet metal blank. This technique is all about forming sheet metal

using a Computer Numerical Control (CNC) machine with the help of

forming tool for localized deformation. Slight variation is developed

in the ISF process to enhance the formability of sheet metal. When

compared to the conventional sheet metal process this provides ease in

the manufacturing process for generating complex shapes.

Manufacturing of dies is a tedious process and for various shapes and

dimensions, separate dies have to be produced with greater

dimensional accuracy which is time and cost consuming process.

simple numerical code is generated using Master CAM software. This

code is fed into a CNC machine where the hemispherical forming tool

enhances localized deformation of sheet metal.

Increased focus on design and fabrication of sheet metal blank

fixture is necessary to determine its formability concerning its

dependent parameters. In recent trends requirement of complex

contours of sheet metal is drastically increasing for several

applications such as household interior designs, the body structure of

automobile and aerospace industries.

The disadvantage of incremental

sheet metal forming (ISF) is that it consumes much time when

compared to other conventional forming processes.

The formerly idea on incremental sheet metal processing

techniques are developed by Matsubara [1]. This kind of

manufacturing is particularly recommended when forming brittle

sheet metals and is used in the automobile and aerospace industries.

The predominant advantages of this process are the large amounts of

deformation and the decrease in the required deformation forces that

can be obtained. These benefits are possible because of the minor heat

treatments carried out in between the increments of deformation [5].

The treatments get rid of the effects of cold work or strain hardening

by causing recrystallization to take place all through every process and

therefore resulting in a new, overall weaker material. Manufacturing

industries require flexibility in components processing techniques to

adapt to improving the technology. As a CNC machine can perform

forming process ISF can make a remarkable change in manufacturing

sectors such as in automobile, aerospace industries.

The term failure can be roughly categorized as the onset of plastic

instabilities such as buckling, the formation of localized necking or

the ultimate fracture [8]. From the views of sheet metal forming,

failure can be described with the aid of the formation of localized

necking, wrinkles or macroscopic cracks. To precisely describe the

deformation behaviour of metal sheets, the mathematical fracture

strain equations have to properly signify the material behaviour below

complicated loading conditions and additionally precisely predict the

limit state conditions at the crucial factors at some point of the

deformation process.

Experimental and theoretical determined Forming Limit Diagrams

(FLDs) and Forming Limit Stress diagrams (FLSDs) are both the

failure standards formulated by employing principle strains or

stresses, which outline the failure when the precise criterion is

satisfied [7]. Due to the vulnerable ductility of these high strength

materials, correct prediction of metal forming limits all through

deformation has ended up a huge issue. Researchers have carried out

endless efforts to construct the relationship between the prevalence of

failure and the established engineering concepts. A greater downfall is

that achievable low-dimensional accuracy, because the part must be

constantly eliminated and re-fixed before and after the heat treatments.

The reduced accuracy arises from the fact that the part might also no

longer be fixed in the precise trend every time it is eliminated and re-

installed. This paper shows the relationship between various

parameters that are significantly dependent on the formability of sheet

metal. Optimization of such parameters overcomes drawbacks of the

process and enhances the implementation of the EAISMF process for

several applications. In the future, the ISF process can be modified

and experimented as there is a scope on metal forming of a variety of

materials.

A mathematical model depicting the relation between temperature and formability in Electrically Assisted Incremental Sheet Metal Forming

(EAISMF) process

2. EAISMF Experimental Procedure

The Electrically Assisted Incremental Sheet Metal Forming (EAISMF) process begins with the heating of the sheet metal using a DC power supply connected to its ends. The thermal effect of heating enhances formability by reducing the force required for plastic deformation compared to conventional ISF.

The sheet metal is then subjected to a rotating forming tool, typically a hemispherical or parabolic shape, which is operated by the spindle in a CNC machine. Proper clamping of the sheet metal onto the EAISMF fixture is crucial for dimensional accuracy and surface finish. Common factors affecting formability include wall angle, tool radius, tool speed, and sheet thickness, which are consistent with other ISF processes.

The EAISMF process utilizes electric current to heat the sheet metal, minimizing the force needed for deformation. A suitable fixture is required to hold the sheet metal securely. The choice of forming tool size and shape influences surface quality and manufacturing time.

3. Mathematical Model

A mathematical model is developed to establish the relationship between temperature and formability in the EAISMF process. The net temperature of the sheet metal is determined as the sum of the preheating temperature due to electric current and the temperature rise during plastic deformation.

The preheating temperature (T1) resulting from electric current is calculated using the Joules heating effect formula:

T₁ = ^J²ρcΔt / (mcp)

Where:

J - Current density
ρc - Electrical resistivity
Δt - Change in time
m - Mass of sheet metal
Cp - Specific heat

The average temperature rise (T2) during plastic deformation is determined as:

T₂ = (work done / vol) * (ρC_p / Δt)

The work done per unit volume for plastic deformation is represented by integrating along the effective fracture strain:

(work done / vol) = ∫(dε_f / σ)

The effective stress function, following the Von Mises yielding criterion for an isotropic material, is given as:

σ̅ = √(1/2 * ((σ₁ - σ₂)² + (σ₂ - σ₃)² + (σ₃ - σ₁)²))

Substituting this into the equation for work done per unit volume, we get:

(work done / vol) = ∫(dε_f / σ̅)

The final average temperature rise (T2) due to plastic deformation is calculated as:

T₂ = (Kε_n√3) / (2r_tool(r_tool + t₀sin(π/2 - ψ))ε_fρC_p)

Combining the contributions from T1 and T2, we obtain the relationship between temperature (T) and formability in the EAISMF process:

T = (J²ρcΔt) / (mcp) + (Kε_n√3) / (2r_tool(r_tool + t₀sin(π/2 - ψ))ε_fρC_p)

Thus the obtained equation relates temperature at that point of

forming. The temperature (T) is due to DC current supply along the

sheet metal and rise in temperature by friction between forming tool

and sheet metal.

4. Future Scope

Further experimentation on the EAISMF process is essential to validate the observations made in this study. Comparisons with numerical models and finite element simulations, taking into account appropriate boundary conditions, can enhance our understanding of this process and its potential applications.

5. References

S. Matsubara, "Incremental backward bulge forming of a sheet metal with a hemispherical tool," Journal of the JSTP, 35(1994), 1311-1316.
M B Silva, M Skjoedt, A G Atkins, N Bay, and P A F Martins, "Single-point incremental forming and formability–failure diagrams," The Journal of Strain Analysis for Engineering Design, 2008.
M. Honarpisheh, M. J. Abdolhoseini, S. Amini, "Experimental and numerical investigation of the hot incremental forming of Ti-6Al-4V sheet using electrical current," International Journal of Advanced Manufacturing and Technology.
Jigar Pathak, "A brief review of Incremental sheet metal forming," International Journal of Latest Engineering and Management Research, vol.2, pp. 35-43, 2017.
Mikel Ortiz, Mariluz Penalva, Edurne Iriondo, Luis Norberto, "Investigation of Thermal-Related Effects in Hot SPIF of Ti–6Al–4V Alloy," International Journal of Precision Engineering and Manufacturing-Green Technology, 2019.
Mostafa Vahdani, Mohammad Javad Mirnia, Mohammad Bakhshi-Jooybari, Hamid Gorji, "Electric hot incremental sheet forming of Ti-6Al-4V titanium, AA6061 aluminium, and DC01 steel sheets," The International Journal of Advanced Manufacturing Technology, 2019.
L.C. Tsao, H.Y. Wu, J.C. Leong, C.J. Fang, "Flow stress behaviour of commercial pure titanium sheet during warm tensile deformation," Materials and Design, Vol. 34, 179–184, 2012.
Ruiqiang Zhang, Zhutao Shao, Jianguo Lin, "A review on modelling techniques for formability prediction of sheet metal forming," International Journal of Lightweight Materials and Manufacture, pp 1-11, 2018.