banerjee2015

Author’s Accepted Manuscript
Determination of Johnson cook material and failure
model constants and numerical modelling of
Charpy impact test of armour steel
A. Banerjee, S. Dhar, S. Acharyya, D. Datta, N.
Nayak
PII: S0921-5093(15)30022-8
DOI: http://dx.doi.org/10.1016/j.msea.2015.05.073
Reference: MSA32401
To appear in: Materials Science & Engineering A
Received date: 13 December 2014
Revised date: 15 May 2015
Accepted date: 23 May 2015
Cite this article as: A. Banerjee, S. Dhar, S. Acharyya, D. Datta and N. Nayak,
Determination of Johnson cook material and failure model constants and
numerical modelling of Charpy impact test of armour steel, Materials Science &
Engineering A, http://dx.doi.org/10.1016/j.msea.2015.05.073
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Determination of Johnson Cook material and failure model constants and
numerical modelling of Charpy impact test of armour steel
A. Banerjeec
*
, S. Dhara, S. Acharyyaa, D. Dattab, N. Nayakd
aJadavpur University, Kolkata, India
bIndian Institute of Engineering Science and Technology, Shibpur, India
cPXE Chandipur, DRDO, Min of Defence, Govt. of India, presently under PhD programme of
Jadavpur University, Kolkata
dPXE Chandipur, DRDO, Min of Defence, Govt. of India
ABSTRACT
The behavior of typical armour steel material under large strains, high strain rates and elevated
temperatures needs to be investigated to analyse and reliably predict its response to various types
of dynamic loading like impact. An empirical constitutive relation developed by Johnson and
Cook (J – C) is widely used to capture strain rate sensitivity of the metals. A failure model
proposed by Johnson and Cook is used to model the damage evolution and predict failure in
many engineering materials. In this work, model constants of J – C constitutive relation and
damage parameters of J – C failure model for a typical armour steel material have been
determined experimentally from four types of uniaxial tensile test. Some modifications in the J –
C damage model have been suggested and Finite Element simulation of three different tensile
tests on armour steel specimens under a relatively high strain rate (10-1 s-1), high triaxiality and
elevated temperature respectively has been done in ABAQUS platform using the modified J – C
failure model as user material sub – routine. The simulation results are validated by the
experimental data. Thereafter, a moderately high strain rate event viz. Charpy impact test on
armour steel specimen has been simulated using J – C material and failure models with the same
* Corresponding author, E-mail address: [e-mail]

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material parameters. Reasonable agreement between the simulation and experimental results has
been achieved.
Keywords: Johnson – Cook material and failure models, Charpy test, armour steel, Finite Element
analysis, numerical simulation
1. INTRODUCTION
Dynamic loads are encountered in a wide spectrum of phenomena viz. automotive applications,
high speed machinery and defence applications like high speed projectile impact on armour. The
behavior of materials under dynamic loading conditions differs significantly from quasi static
loading due to the effects of inertia, stress reflection and rate sensitivity of material [1]. Finite
Element (FE) formulation based on dynamic equilibrium equation is used in explicit model to
take care of inertia. In order to capture the effect of rate sensitivity, appropriate modeling of the
behavior of the material under high strain rates is an essential prerequisite. However, due to the
complexity of the problem, various material models have been proposed by several researchers
on a case to case basis rather than development of a universal model catering for a large variety
of materials under different loading conditions.
Johnson – Cook material model [2] is a popular constitutive relation for metals, widely used in
simulation of impact and penetration related problems [3-7]. The popularity is more due to the
simple form of the equation and the relative ease of determination of the model constants. A few
tensile tests under various loading conditions are generally sufficient to determine the five
constants.
Impact testing techniques were established in order to ascertain the fracture characteristics of
materials and thereby prevent sudden or brittle failure of engineering materials when subjected to
dynamic loads. One of the most prominent impact tests is the Charpy impact test that gives
information regarding the behavior of material under impact load [8, 9, 10]. Charpy test is a low-

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cost and reliable technique that measures the energy consumed in breaking a notched specimen
simply supported at both ends when hammered by a swinging pendulum. The presence of notch
simulates the pre-existing cracks found in large structures that increase the probability of brittle
fracture [11].
Armour steel is a low-alloy medium carbon steel suitably heat treated to produce a tempered
martensite microstructure that gives an excellent combination of strength and ductility. Steel
armour is used as the protective cover of Battle Tanks and armoured vehicles that are subjected
to ballistic impact by fast moving military projectiles. A high degree of hardness and toughness
is an essential requirement for armour material. The response of the armour steel material to the
high loads occurring over small intervals of time needs to be understood to analyse the ballistic
impact phenomena and make reliable predictions.
Zejian Xu et al [12] have experimentally investigated the plastic behavior of 603 armour steel at
strain rates ranging from 10-3 s-1 to 4500 s-1 and temperatures from 288 K to 873 K. Compression
tests were conducted on an MTS hydraulic testing machine for 10-3 s-1 ≤ ≤ 1 s-1 and on SHPB
for the higher strain rates. Elevated temperatures were attained with electro – thermal cells.
Thermal softening was found to play a leading role in its competition with the effects of strain
rate and work hardening. The five material constants of Johnson – Cook and six of KHL material
models determined from the experimental results have been used to model a dynamic
phenomenon viz. strain rate jump test. The predicted data were found to be satisfactorily close to
the experimental results, with the KHL model exhibiting superior applicability for the material.
Whittington et al [13] investigated the mechanical response and damage evolution of Rolled
Homogenous Armour (RHA) steel, processed to Mil-A-12560H specification, through low and
high strain rate tension, compression and torsion tests at 20oC and 300oC . Fractography was
performed to quantify the number density of nucleated voids and size distribution of voids. An

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Internal State Variable (ISV) plasticity / damage model was used to capture the varying effects of
temperature, strain rate and stress state for the RHA steel. Reasonable accuracy of the model has
been demonstrated.
However, a detailed experimental work for the determination of J – C material and J – C failure
model constants for armour steel material, in general, is not readily available in the open
literature. In this work, the behavior of a low alloy, medium carbon steel material typically used
in fabrication of armoured vehicles has been studied through extensive experimentation under
various loading conditions. Material constants for J – C material and failure models have been
determined from an analysis of the experimental data. A modified damage growth law has also
been proposed. The model constants have been validated through numerical modeling of tensile
tests on armour steel specimens conducted under a relatively high strain rate (10-1 s-1), high
triaxiality level and elevated temperature (500oC) followed by comparison of the simulation
results with experimental data. Thereafter, an attempt has been made to simulate a moderately
high strain rate phenomenon like Charpy impact test on the same material using J – C material
and failure models and the experimentally determined material constants in a commercial FE
code, ABAQUS - Explicit. The predicted behavior has then been compared with experimental
data.
2. MATERIAL AND FAILURE MODELS
2.1 Johnson – Cook constitutive relation
In the framework of von Mises incompressible plasticity, the yield function is given as
Φ =
3
2ij ij
SS
- σc = 0 (1)
Here, Sij stands for deviatoric stress tensor and σc is the current yield stress.