International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 07 Issue: 05 | May 2020 www.irjet.net p-ISSN: 2395-0072
© 2020, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1476
Evaluation of Johnson-Cook Material Model Parameters of AA6063-T6
Devesh Rajput
1
, Ankit Singh
2
, Arpit
3
, Sanjay Kumar
4
1,2,3
Student, Mechanical Engineering Department, Delhi Technological University, Delhi, India
4
Assistant Professor, Mechanical Engineering Department, Delhi Technological University, Delhi, India
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Abstract - The present work deals with the stimulus of
strain rate on the behaviour of commercial aluminium alloy
6063-Temper 6. It is a medium strength alloy commonly
referred to as architectural alloy and expected to have a low
strain rate sensitivity. Consistent and judicious
characterization of the material behaviour under the coupled
effects of strain, strain rate, and temperature on the material
flow stress is remarkably crucial to design as well as optimize
the process parameters for industrial practice. Tensile tests
were performed at room temperature at strain rates starting
from 10
-4
to 10
-1
s
-1
. The alloy exhibited a low but positive
strain rate dependence of material strength at the
investigated strain rates. The stress-strain relations obtained
through these tests were employed for calibrating Johnson-
Cook (J-C) material model. An empirical constitutive relation
stated by Johnson and Cook (J–C) is extensively used to capture
the strain rate sensitivity of the metals. In this work, model
constants of J–C constitutive relation have been determined
experimentally from the uni-axial tensile test.
Key Words: Johnson-Cook, Material model, AA6063-T6,
Strain rate, flow stress, ASTM – E8M.
1. INTRODUCTION
Aluminium alloys have developed as a strong candidate
material for defence, aeronautical and automotive
applications due to their low density, tremendous strength,
and high corrosion resistance. But their mechanical
behaviour has to be thoroughly understood to utilize their
potential for such demanding applications. This requires a
more profound understanding of the material properties,
which is very complex due to the relationship between large
plastic deformations, high strain rates, thermal softening as a
result of adiabatic heating of materials, material
deterioration, and fracture. The theory in continuum
mechanics referred to as viscoplasticity [5] explains the rate-
dependent inelastic response of solids. Rate-dependence in
this setting means that the deformation of the material
depends on the rate at which loads are employed.
Numerical techniques have surfaced as an efficient and cost-
effective tool for investigating material behaviour. The
reliability of numerical results depends massively on the
exactness of material models used to interpret the dynamic
behaviour of materials under consideration. The Johnson-
Cook material model [1] is one of the most manageable
models with five parameters, which can describe the
material response at high temperatures, high strains, and
high strain-rates and is often used in simulations. In addition
to the material model, a failure model introduced by Johnson
and Cook is used to model the damage progression and
foretell failure in many engineering materials.
2. LITERATURE SURVEY
Johnson and Cook (1983) suggested a simple model to
describe the plastic behaviour of metals under dynamic
loading. The model defines the equivalent flow stress as a
function of strain, strain rate, and temperature.
*
*
( )(1 ln )(1 )
n m
eq
eq eq
A B C T
(1)
where A is Yield stress, B is Hardening modulus, C is Strain
rate coefficient, n is Hardening exponent and m is thermal
softening parameter. These are to be determined
experimentally.
eq
is equivalent plastic strain,
*
eq
is the ratio
of equivalent plastic strain rate to a reference plastic strain
rate. T
*
is the homologous temperature and is defined as
* r
m r
T T
T
T T
(2)
where T is the current temperature of the material, Tm is
the melting temperature of material and Tr is room
temperature. The first, second and third set of brackets in
equation (1) picture the effect of isotropic strain hardening,
strain rate hardening and thermal softening sequentially in
an uncoupled manner.
Dislocation dynamics based material models like Zerilli-
Armstrong model (1987) and Mechanical Threshold Stress
model (Follansbee and Cocks 1988) have been introduced to
judge linked nature of strain rate and thermal sensitivity but
they have not been able to overtake Johnson-Cook (J-C)
model due to complexity in the calibration of constants.
3. JOHNSON-COOK MATERIAL MODEL
A review study of material parameters of Johnson-Cook
constitutive and failure model (Johnson and Cook 1983,
1985) for some regularly used aluminium alloys
acknowledges that various researchers have obtained
different parameters for the same alloy. Therefore, it is very
important for researchers working in crucial areas to be self-
governing in the calibration of dynamic material models.
3.1 Method for calibration of J-C material model
The fundamental concept in the quantification of J-C material
model is to isolate the effect of strain hardening, strain rate
hardening and thermal softening on the plastic behaviour of