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Short –Term Creep Strain Prediction of Thermoplastic Material Using
Finite Element Analysis from Experimental Data
N. Sukesh1,a
, C. Subramanian2,b
, K. Annamalai1,c
, C. D. Naiju1,d
1
SMBS, VIT University, Vellore, 632014, India.
2
Shinas College of Technology, Oman
a
royal_suki@yahoo.com,b
janisubu@gmail.com,c
kannamalai_in@yahoo.com,d
naijucd@gmail.com
Keywords: Finite element tool, Parametric analysis, Creep strain, Empirical model
Abstract. A method for prediction of polypropylene creep behavior with the aid of finite element
tool is discussed in this paper. Parametric analysis is carried out on polypropylene material to
calculate creep strain using Ansys Parametric Design Language (APDL) at various stress and
temperature levels. The procedure takes account of nonlinear stress-strain characteristics at various
temperatures obtained from monotonic tensile experimental data. The Garofalo creep material
model which takes account of both isotropic hardening plasticity and creep behavior is used to
predict the creep strain for one hour and compared with experimental results. Parametric analysis on
polypropylene material revealed the dependence of temperature and stress on creep strain.
Empirical model was developed for predicting the creep behavior of polypropylene for various
temperatures and stress levels with the help of obtained finite element results. Developed model
was found to be sufficient for predicting the creep strain for long duration.
Introduction
The utilization of injection molded thermoplastic materials is being increased because of near net
shaped capability, good dimensional accuracy, and mass production ability [1]. Main motivation of
utilizing thermoplastic materials in automobile industries is to reduce weight and thereby fuel
consumption. Common problem associated with the unreinforced thermoplastics is creep under
moderate to severe stress at elevated temperature. Creep resistance of thermoplastic composites is
significantly improved by increase in fiber loadings [2]. Later the effect of temperature on the creep
characteristics of polycarbonate is investigated and a relationship is developed based on Arrhenius
theory to develop creep master curves [3]. Pegoretti and Ricco [4] studied the propagation of crack
under creep for varying temperature conditions for polypropylene composites and observed that
speed with which the crack progresses was dependent on the test temperature. Krishnaswamy [5]
performed extensive creep rupture testing on high density polyethylene pipes at various hoop stress
levels and temperatures and observed the dependency of density and crystallinity towards failure.
Houshyar [6] reported the improvement in creep properties with the addition of long polypropylene
fibers in propylene-co-ethylene (PPE) matrix and visualized the improvement in interfacial
properties.
Trans-crystallization of the polypropylene matrix was observed in the PPE samples due to the
thin layer of matrix on the reinforcement, which was attributed to good impregnation and wetting of
the fibers. Greco [7] investigated the flexural creep behavior for compression molded glass fiber
reinforced polypropylene at various applied stress level. Findley and Khosla [8] conducted creep
tests for unreinforced thermoplastics; polyethylene, polyvinyl chloride and polystyrene.
Approximation was carried out for the linear viscoelastic region by power law and compared the
2012 2nd International Conference on Smart Materials and Nanotechnology in Engineering
Lecture Notes in Inform ation Technology, Vol.20
978-1-61275-019-4/ 10/ $25.00 © 2012 IERI SMNE2012
280

creep performance by estimating the power law coefficient and power law exponent. Power law
model was modified by Hadid [9] by incorporating the time and stress dependence during creep
loading of polyamide specimens and estimated four parameters for describing the deformation
occurring in the material. Hadid [10] used stress–time superposition principle to predict long-term
material creep behavior of injection molded fiber glass reinforced polyamide. Experiments were
performed at various strain rates and later predicted for creep performance at various stresses. Banik
[11] reported the improvement in creep resistance due to unidirectional reinforcement for
polypropylene-polypropylene composites. Four parameter models were used to fit the experimental
data and good agreement was visualized. Nylon 6/6 had the least creep compliance than
polypropylene and high-density polyethylene.
Even though lot of works have been carried out in the past to predict the creep strain of
thermoplastic material, the use of finite element tool have not been explored in the past to depict the
creep strain. Hence in this work an attempt is made to emulate the creep behavior of polypropylene
material at various stress and temperature levels and with the obtained results empirical model was
developed for predicting the creep strain for twenty four hours to reduce the computational time
involved in finite element analysis.
Methodology
The geometry of the polypropylene specimen used for the creep analysis pertaining to ASTM-D
638 standard is shown in Fig.1. The numerical creep investigation was performed by using finite
element software, Ansys10®. Ansys Parametric Design Language was used for modeling the
geometry. The tensile specimen was modeled using PLANE183, which is a higher order 2-D, 8-
node element. PLANE183 has quadratic displacement behavior and is well suited to modeling
irregular meshes. The element supports plasticity, large deflection and large strain capabilities. A
typical finite element mesh of the tensile specimen is shown in Fig. 2. One end of the specimen is
completely fixed to emulate the stationary grip of the tensile testing machine and the other end is
applied with a pressure load.
Fig. 1 Tensile Test Specimen Fig. 2 Meshed Model
Modeling products realistically and accurately often requires use of nonlinear capabilities. Hence
in this problem the nonlinear material characteristics of thermoplastic polypropylene are given as
input using the TB command. TB is the command which activates a data table for nonlinear
material properties. In the present investigation, experimental monotonic stress-strain curve of
Zhou and Mallick [12] was extracted and analyzed using data capturing software Windig 2.5, where
the tensile data were captured for temperatures ranging from 21.5°C to 75° C. The tensile stress-
strain curve conducted at a strain rate of 0.5m/s for various temperatures is shown in Fig. 3.
Material properties are given as input using MPTEMP command. Garofalo creep model is used
for predicting the creep strain at various stress and temperature level. The generalized Garofalo
creep model is represented as
sinh
Where,
= change in equivalent creep strain with respect to time
through = Garofalo creep model constants = 2.1125e-6 = 1.566
= 0.1736 = 1000 = Equivalent stress T = Temperature (Absolute)
Load
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Fig. 3 Stress-Strain Curve of polypropyle Fig. 4 Creep Strain Vs Time for various loads (Dropik, 2008)
(Zhou and Mallick , 2002)
In the present investigation, experimental creep strain with respect to time of Dropik [13] was
extracted and analyzed using data capturing software Windig 2.5 to calculate the constants. The
experimental creep strain with respect to time is shown in Fig. 4.
Results and Discussion
Thermoplastic materials are viscoelastic materials which respond to induced stress by two
mechanisms: viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied
mechanical energy as frictional heat and results in permanent material deformation. Elastic
deformation stores the applied mechanical energy as completely recoverable material deformation.
The extent to which one or the other of these mechanisms dominates the overall response of the
material is determined by the temperature and by the duration and magnitude of the stress or strain.
The predicted creep strain versus time using finite element analysis at different stress ranging from
7.5 MPa to 17.5 MPa is shown in Fig. 5.
Fig. 5 Creep Strain Vs Time for Various Stress Fig. 6 Creep Strain Vs Time for Various Temperature
Levels using Finite Element Analysis
For most amorphous polymers there exists a linear viscoelastic region and a transition from
linear to non-linear viscoelasticity. The graph gives a vivid picture that PP exhibits a strong non-
linear behavior with the stress dependence and time dependence. The linearity of this material
seems to exist only at small stresses. This could be due to the structural features of semi crystalline
polymers. At a lower stress level the thermoplastic material showed slightly less creep. At higher
stress level significant creep was observed. The predicted data for the creep strain versus time at
different temperature ranging from 25° C to 40° C is shown in Fig. 6. As expected, variation of the
test temperature shows a notable effect on the creep behavior of the polypropylene material with
enhanced creep tendency as the temperature is increased. This effect can be recognized as the effect
282

of temperature on the mobility of the macromolecular chains. With the increase in temperature,
mobility of the macromolecules increases which leads to higher deformation of the thermoplastic
material.
Empirical Model for Creep Strain
In order to reduce the time required for predicting the creep strain for long term duration using
finite element analysis an attempt have been carried out to fit an empirical relation on the obtained
finite element results. In creep strain Vs time for various stress levels plot, best fit is achieved with
the power law function. Power law function defines a relation between creep strain and time with
constant coefficients. The power law function is given as;
. (1)
Where,
ε = Time dependent creep strain a = Power law coefficient t = time, seconds
n = Power law exponent
Power law model is simple in approach and predicts non-linear creep behavior of polypropylene.
It is observed that the two parameters of the power law function ‘a’ and ‘n’ depend on stress levels.
Table 1 shows the dependency of power law coefficients on various stress values. It is inferred from
table that ‘a’ and ‘n’ show a strong dependence of stress level.
Table 1 Power Law Parameters for Polypropylene
Pressure [N/mm2
]
Power law
coefficient, a
Power law
exponent, n
Correlation
index, R²
7.50 3.00E-06
0.9701 0.9968
10.0 5.00E-06
0.9857 0.9974
12.5 1.00E-05
0.9899 0.9965
15.0 3.00E-05
1.0004 0.9944
17.5 3.00E-05
1.0004 0.9944
Fig.7 Variation of Power Law Exponent for Fig. 8 Variation of Power Law Coefficient for
Various Stress Values Various Stress Values
The dependencies of power law coefficient and power law exponent with various stress values
are plotted. Fig.7 shows dependency of power law exponent on various stress values. Fig. 8 shows
the dependency of power law coefficient on various stress values.
The best fitting curve proposed between n and σ takes the form:
n = b e c σ
. (2)
Similarly the best fitting curve proposed between a and σ takes the form:
a = d σ f
. (3)
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Where b, c, d, f are curve fitting parameters.
Equations (2) and (3) are used in (1) and substituting values of curve fitting parameters Creep Strain
can be written as,
.9 . .
. (4)
In order to validate the finite element results, experimental data from LUO Wen-bo [14] was
extracted using Windig 2.5 and plotted. Fig. 9 shows the experimental and finite element results.
Strain rate is determined by partially differentiating equation (4) with respect to time as:
.9 . E .
∆
.
(5)
Where, Δ is the error resulting from the first order incremental approximation.
Dropik have also observed a similar variation between the experimental and finite element
results and indicated that Ansys solutions for lower stresses range closer to the experimental results.
The variation is because of the first order approximation error, and stress term is not dealt with the
partial differentiation. It is also to be noted that it shows less error for lower stress ranges, but error
increases with increase in stress level for a higher range of stress levels. Fig.10 shows variation of
Von Mises Creep Strain calculated from Empirical relation and Ansys parametric design language
for a stress level of 10N/mm2
.
Fig. 9 Variation of Von Mises Creep Strain Fig.10 Variation of Power Law Exponent for
with Respect to 24hours of Time Various Temperature values
Table 2 Dependency of Power Law Coefficients on Various Stress Values
Temperature [°C]
Power law
coefficient, a
Power law
exponent, n
Correlation
index, R²
40 1E-06
0.9958 0.9755
35 1E-06
0.9875 0.9737
30 1E-06
0.9802 0.9761
25 1E-06
0.9727 0.9784
Fig.11 Variation of Power Law Exponent for Fig.12 Comparison of Ansys and Theoretical Values for
Various Temperature Values Creep Strain at 35°C
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Similar approach is made considering temperature effect on creep of polypropylene. Table 2
shows the dependency of power law coefficients on various stress values. Variation of power law
exponent for various temperature levels is plotted in Fig.11. The comparison of creep strain rate
values calculated by Ansys and calculated by empirical relation is plotted in Fig.12 for 35°C
temperature level.
The empirical relation is found to be,
. .
.
Conclusions
Short term creep behavior of thermoplastic polypropylene was predicted in this paper using finite
element tool. Nonlinear characteristics of polypropylene were included in the program by
incorporating the stress strain data from the experimental values. Creep strain was calculated with
respect to time using the Garofalo model for various stress and temperature level worked within the
elastic range. Creep strain was found to be increased with respect to temperature and stress level
and found to be sensitive with respect to the tested parameters. In order to reduce the computation
time an empirical model is developed for relating the creep behavior of polypropylene with respect
to temperature and stress. Empirical relation was found to be agreeing with experimental results and
thus computational time can be reduced.
References
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[12] Yuanxin Zhou., P. K. Mallick., Effects of Temperature and Strain Rate on the Tensile Behavior
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