THERMO-MECHANICAL ANALYSIS OF TURNING OF THREE

DIFFERENT ALUMINIUM ALLOYS USING FEM

Mavallapalli Saraschandra, Prudvi Krishna Maladi, Gurrala Bhargav Avinash, Prof.K.Padmanabhan

msaraschandra@gmail.com, prudvijnv9@gmail.com, avirbhav.3@gmail.com ,padmanabhan.k@vit.ac.in

Abstract:

Toughness, high strength, less Weight is the area of interest that every automotive and aerospace

industries are working on – AA 2024, 6061, 7075 being the most used materials with the desired

properties mentioned above. In this paper the chip formation, stress, strain rates, heat

generation due to the turning conditions, residual stresses and the failure of the materials have

been conducted by Finite Element Method (FEM) using the simulation software Abaqus.

Keywords: Lagrangian, ALE, Eurelian, Abaqus, FEM

1. Introduction

Machining is the process done for the

removal of the excess material from the

casted or formed components to meet the

required specifications. During machining,

the temperature at the tool-chip interface in

particular, will be very high due to the heat

generation. A temperature rise, heat partition

and transferred heat at the contact between

tool and chip are the key parameters for

accurate prediction of tool wear, tool life

and surface integrity. The heat generation

mainly depends on the machinability of

work material, the thermo-physical

properties of the cutting material which are

essential factors for predicting the

Temperature distribution and heat

dissipation at the tool–work material

Interface. The physical phenomena

occurring at this interface depends on the

local conditions of stress (contact pressure

and frictional stress), sliding velocity,

cutting temperature and local properties of

the tool–work material. The complexity of

thermo mechanical Phenomena occurring

during the chip formation process make

difficult the estimation of the heat exchange

at the cutting zone.

There is a lot of effort put into the field of

automotive and aerospace industries in the

last three decades for the high strength to

weight ratio materials. Aluminium alloys are

the materials that show widespread

properties. They are offering a number of

different mechanical and thermal properties.

In addition, they are relatively easy to shape

metals, especially in material removal

processes, such as machining aluminum

alloys as a class is considered as the family

of materials offering the highest levels of

machinability. Still research is going on for

the optimized working parameters for the

dry machining of aluminium alloys.

Different theories had been proposed for the

aluminium alloys machining. Eulerian

approach, Lagrangian approach and

Arbitrary Lagrangian Eulerian approach is

the most widely used and promising

approach in the Finite Element Method

based simulation which is a non

linear/explicit method with help of Abaqus

software for machining of the aluminium

alloys to plot the heat generation during the

machining is the main interest of this paper

Is a couple field thermo-mechanical

analysis, in FEA, is done using the simple

linear equation [A] {u} = {B}.

In such analysis time does not play any role.

On the other hand a dynamic analysis (or

transient or modal analysis also) follows a

more complex governing equation which is

like:

[M] {𝑢}̈ +[C] {𝑢}̈ + [K] {u} = {F}

Implicit solution is one that is based on the

calculation of previous timestep. This is

called Euler Time Integration Scheme. The

solution is stationary; in other case there are

large time steps in the current model

(problem). This is also called an

unconditionally stable scheme. Calculation

of inverse stiffness matrix is the

disadvantage as {u} vector is directly

solved. And calculation of an inverse is a

computationally intensive step. This is

especially so when non linearities are

present, as the Stiffness matrix itself will

become a function of u.

In an explicit analysis, instead of solving for

{u}, {u"} is calculated and we just have to

invert the mass matrix [M]. In case lower

order elements are used, which an explicit

analysis always prefers, the mass matrix is

also a lumped matrix, or a diagonal matrix,

whose inversion is a single step process of

just making the diagonal elements

reciprocal. Hence this is very easily done.

But disadvantage is that the Euler Time

integration scheme is not used in this, and

hence it is not unconditionally stable. So we

need to use very small time steps.

�̇� (I+ 1/2) = �̇� (i- 1/2) + ∆𝑡(𝑖+1) + ∆𝑡𝑖

2 �̈�(𝑖)

𝑢(𝑖+1) = 𝑢𝑖 + ∆𝑡(𝑖+1) �̇� (i+ 1/2 )

2. Literature survey

O. Pantale, J.-L. Bacaria, O. Dalverny, R.

Rakotomalala, S. Caperaa Gave a wide-cut

information of how to model the orthogonal

machining in which the chipping of the

work is purely based on the inherent nature

of the work a mathematical model stresses

on the above and the entire description of

what machinability is complete procedure

for the simulation of the cutting operation

Starting from the identification of the

constitutive and damage laws of the

material, a numerical model is built, for

which it must be emphasized that the

formation of the chip involves the intrinsic

behavior of the material, then bringing a

comprehensive model of what is called

‘‘machinability’’.

J. Zouhar, M. Piska have done the mesh

taking the lagrangian method and Johnson-

cook model for the chip propagation and

also modeled the cutting tool geometry and

also the few factors that influence the tool

and work as well during the machining

process a primary study and calculations

based on FEM for the orthogonal machining

of the ASIS1045 steel has been done.

Cutting tool used for the simulation was

modeled with different rake/edge geometry.

FE mesh used the Lagrangian formulation

with Johnson-Cook plasticity model and

Johnson Cook damage law for the chip

separation criteria. Cutting force, stress,

temperature and chip formation were

calculated also. The computer simulation

confirmed previous experimental works and

will be worked out for conventional turning

operations and milling consequently.

Tarek Mabrouki, Franc- ois Girardin,

Muhammad Asad, Jean-Franc- ois Rigal

worked about the AA 2024 how the finite

element method model is considered and

uniting the damage and plastic-elastic

fracture. A numerical model confirming the

increase in the partition of the chip with the

increase in the machining parameters and

how would be the chip shape in the overall

machining process and when the

fragmentation of the chip takes place has

been given an awful mode.

Dmitry Viktorovitch Evdokimov, Dmitry

Gennadievitch Fedorov and Dmitry

Leonidovich Skuratov Computation of

temperature measures in the tool and work

with the changing parameters using ANSYS

and restrained stresses within the work using

ABAQUS.

Claudia H. Nascimento & Alessandro R.

Rodrigues & Reginaldo T. Coelho explained

about With the FEM simulation it has

become easier to note down the different

process parameters that change during the

non-linear analysis at the tool-chip interface.

Nitin Sawarkar, Ghanshyam Boob Has

explicated how the machining parameters

and aesthetics and be optimized and reduce

the stresses within the work can be

optimized and the time consumption with a

better mathematical computation using FEM

using ABAQUS Jianhui Shang, Steve

Hatkevich, Larry Wikerson Regarding the

AA-6061 how the meshing is to be given at

the deformation part and the non-deforming

position of the work piece is given. The

Johnson-cook model parameters have been

taken to know interpret the damage and the

fracture of the material.

Kasper Cramon Jorgensen, Vivian Swan

Using a mathematical model following

lagrangian method in ABAQUS with the

Johnson-cook parameters and refined

meshing are useful in the hinder large plastic

contortions and anticipate the failure

mechanisms.

3. Model preparation

Lagrangian method

The lagrangian method is that the Finite

Element mesh and work piece contort united

and perhaps contortions are large. It is

widely used as it does very fast

computations and no transportation of the

work with mesh is to be deliberated. The

material constraints need not be preset.

Eurelian method The material moves by

the given mesh. It is necessary to calculate

the work parameters at the required

locations. Gravid deformations are formed

and the time step for solution will be high

and the chip formation is to feed prior to the

simulation. It is often used in hydrodynamic

problems.

Arbitrary lagrangian Eulerian method

Arbitrary lagrangian Eulerian method is a

synergy of both Eulerian (used for mocking

up the surrounding area of the tip of the

tool) lagrangian (used for the designing the

free flow of the material at its limits). It is

exclusively used in shell elements for

explicit dynamics.

Smooth particle hydrodynamics method

It is a pure lagrangian method with no

meshing and grid. It is easy to compute large

deformations because of lack of mesh and

calculation of interactions between separated

material particles.

Element Modeling:

In Abaqus There is Different types of

methods of meshing and different meshing

elements are there.

For Meshing a Solid model hexahedral brick

elements and tetrahedral brick elements are

there in the software. From that hexahedral

brick is used to mesh the both work piece

and tool.

In the Metal cutting operation Work, chip,

tool are the major parts in these work is

meshed with the element type of explicit

couple field element, tool will be meshed

with the standard couple field element and

remaining work piece is meshed with

standard 3d-stress element.

Material Properties:

The work piece undergoes deformation at

every element the tool passes by, according

to the tool preset movements following the

given explicit algorithm.

Johnson-cook turns out to be the best

method for the simulation of machining, to

study problems on fast deformations (large

strain rates i.e.; criteria of equivalent strain).

The equation that Johnson-cook strain rate

for the machining is

𝜎𝑦 = [𝐴 + 𝐵(𝜀̅𝑝𝑛)] [1+c 𝑙𝑛�̇̅�𝑝

�̇�0 ] [1-

(𝑇−𝑇𝑟𝑜𝑜𝑚

𝑇𝑚𝑒𝑙𝑡−𝑇𝑟𝑜𝑜𝑚) 𝑚 ]

𝜎𝑦 = Equivalent plastic strain rate

[𝜀 ̅𝑝 ] = Equivalent plastic strain

n = Strain hardening index

𝜀̅̇𝑝 = equivalent plastic strain rate

𝜀̇0 = Initial dimensionless plastic strain rate

Tmelt = Melt temperature

Troom = work piece transition temperature

A, B, C are constants.

Here AA2024, AA6061, AA7075 are

Materials assigned to the work piece.

SS-4340 is the material assigned to tool.

Properties of the different of al-alloys as

represented in the below tables:

Table-1 Material Properties of Al Alloys [6]

Density

(Kg/m3)

Young’s

Modulus

Gpa

Poisson’s

ratio

Specific

heat

(J/Kg.C)

Thermal

conductivity

(W/m.C)

Coefficient of

Expansion

10-6/c

AA-2024 2700 73 0.34 881 164 14

AA-6061 2780 70 0.33 942 154 35

AA-7075 2810 71 0.32 858 120 22

Table-2 Johnson-cook Constants of Al-Alloys

A(MPa) B(MPa) n m Tmelt(oc)

AA-2024 352 440 0.42 1 520

AA-6061 324 114 0.42 1.34 655

AA7075 527 575 0.72 1.61 621

Table-3 Johnson-cook Damage Parameters of Al-Alloys

D1 D2 D3 D4 D5

AA-2024 -0.13 1.5 -0.13 0 0

AA-6061 -0.77 1.45 -0.47 0 0

AA-7075 -0.112 .442 -0.5723 0.016 1.099

Procedure:

For the finite element analysis of metal

cutting using Abaqus dynamic, temp,

explicit process is used. In this analysis

Contact pair is defined between the chip and

the tool by Node to surface definition with

friction followed by coulomb’s law, heat

generation, and thermal conductance. After

defining the contact pair time step of 0.001s

is defined .Boundary conditions are applied

on bottom of work piece as encastre, tool as

fixed one in final step tool have motion with

a distance of length of work piece.

Model with boundary conditions

Meshed Model

Fixing the tool initial and

velocity in final step

4. Results and Discussions:

AA 2024:

Von-mises plots:

At 2.5e-4s At 5e-4s At 7.5e-4s

Temperature Plots:

At 2.5e-4s At 5e-4s At 7.5e-4s

the above plots are explaining about the von-mises plots and temperature distribution of the tool

and chip interface at 0.25ms,0.5ms,0.75ms.In this plots Maximum von-mises stress is on the chip

tool interface 432MPa and Maximum temperature of 6870C on cutting tool.

The above picture has shown that the surface finish ,waviness after machining and chip

morphology after cutting.

AA6061:

Von-mises:

At 2.5e-4s At 5e-4s At 7.5e-4s

Temperature:

At 2.5e-4s At 5e-4s At 7.5e-4s

the above plots are explaining about the von-mises plots and temperature distribution of the tool

and chip interface at 0.25ms,0.5ms,0.75ms.In this plots Maximum von-mises stress is on the chip

tool interface 421MPa and Maximum temperature of 8810C on cutting tool. Below two pictures

have shown that the surface finish ,waviness after machining and chip morphology after cutting.a

small variation in surface texture and in chip also.

AA7075:

At 2.5e-4s At 5e-4s At 7.5e-4s

At 2.5e-4s At 5e-4s At 7.5e-4s

the above plots are explaining about the von-mises plots and temperature distribution of the tool

and chip interface at 0.25ms,0.5ms,0.75ms.In this plots Maximum von-mises stress is on the chip

tool interface 463MPa and Maximum temperature of 1243s0C on cutting tool. Below two

pictures have shown that the surface finish ,waviness after machining and chip morphology after

cutting.a small variation in surface texture and in chip also. At the same time in aa7075

discontinous chip formation have observed.

Conclusions:

The main aim of this contribution concerns

the comprhension of physical phenemonen

accompyning chipformation,maximum

stresses,maximum temperatures according to

different aluminium alloys. The main aim of

tis work for introducing fem methodology

which explains an original approach

concerns of coupled thermal-explicit

dynamic analysis.

5.References:

[1]. “Finite Element Method in Machining

Processes” by Angelos.P. Markopoulus ,A

series of Manufacturing series and surface

Engineering in Springer edited by J. Paulo

Davim Page no.29-52

[2]. “Manufacturing Processes-1, Cutting”

by Fritz klocke, RWTH edition published by

Springer Publications page no.197-206.

[3]. “Metal cutting mechanics and Finite

Element Modeling” by Viktor P. Astakhov

and José C. Outeiro ,published By Springer

,Machining fundamentals and Recent

Advances Edited by Paulo Davim Page no.

13-23

[4]. “FEM simulation on Metal cutting using

a new approach to model chip formation” by

Viktor P. Astakhov, Xinran Xiao published

in IJAMFO Page no.16-20.

[5]. “ Simulation Of Orthogonal cutting

Process Using ALE approach” by Jafar

Takabi,Hamed Sadeghinia,M.r. Razphar

published in 3rd International Conference on

Applied and theoretical

mechanics,spain,December-14-16,2007

Page no.151-155.

[6]. www.asm.matweb.com

[7]. “Machining Process Simulation” by

Claudia H. Nascimento & Alessandro R.

Rodrigues & Reginaldo T. Coelho

[8]. “Finite Element based Simulation of

Orthogonal Cutting Process to Determine

Residual Stress Induce” by Nitin Sawarkar,

Ghanshyam Boob published in International

Journal of Computer Applications.

[9]. “Thermal Stress Research of

Processing and Formation of Residual Stress

When End Milling of a Work piece” by

Dmitry Viktorovitch Evdokimov, Dmitry

Gennadievitch Fedorov and Dmitry

Leonidovich Skuratov.

[10]. “Numerical and experimental study of

dry cutting for an aeronautic aluminium

alloy (A2024-T351)” by Tarek Mabrouki,

Franc- ois Girardin, Muhammad Asad, Jean-

Franc- ois Rigal.