Experimental Investigation and Numerical Modeling of Non-monotonic Creep Behavior of UHPWPE Used in
Orthopedic Implants
1
1
Colin Yeakle, +1Fazeel Khan, and 2Said Gomaa
Department of Mechanical and Manufacturing Engineering, Miami University, Oxford, OH
2
DePuy, a Johnson & Johnson Company, Warsaw, IN
ABSTRACT INTRODUCTION:
The reliable modeling of creep in orthopedic polymeric components such
as tibial inserts is critical for validating their in-vitro and in-vivo performance
and long term stability. While current specialized creep or constitutive
models [1,2] can be used fairly reliably in modeling creep, deformation
characteristic lying beyond the scope of these models have been identified. It
is typically assumed that under tensile creep conditions, strain will increase
over time, exhibiting primary, secondary, or tertiary behavior. Conversely,
during a more realistic compressive creep condition for a tibial UHMWPE
insert, the magnitude of the strain would be expected to increase (larger
negative value) over time as well. However, prior loading histories have been
found to have a singular effect on the nature of the creep behavior to the
extent that strain can decrease even under tensile stress conditions, and even
exhibit a rate reversal behavior in which the rate of change of strain changes
sign during a test interval. This behavior poses new challenges for numerical
modeling, and the modifications to the viscoplasticity theory based on
overstress (VBO) model have yielded promising results at capturing the
aforementioned creep deformation characteristics. Experimental data and
simulation results are presented in this abstract.
MATERIALS AND METHODS:
An Instron 5867 servo-mechanical test frame running the BlueHill2
software and equipped with Instron axial and transverse extensometers was
used for the compressive tests. Solid cylindrical samples of uniform crosssection were tested between compression platens. Tensile tests were
conducted on a MTS servo hydraulic test frame operated through the FlexTest
40 SE digital controller. MTS axial and transverse extensometers were used
on the solid cylindrical samples.
The materials included in this study were supplied by DePuy and included
moderately irradiated and annealed UHMWPE commercially known as XLK,
and anti-oxidant UHMWPE commercially known as AOX which is irradiated
but not annealed.
Loading to the target stress values was performed in strain rate control. To
assess the effect of prior rate, loading was performed at two different strain
rates:   1  104 s-1 and   1  103 s-1 . The full prior loading history
consisted of loading a sample to 6% strain in tension or compression, and then
(partially) unloading the sample to the target stress value, which was selected
so as to represent high, medium, and low stress values relative to the
maximum value from which the sample was unloaded. In the following
discussion, a rate reversal is defined as the occurrence of a change in the
algebraic sign of the strain rate during creep.
RESULTS and DISCUSSION:
Samples were loaded in compression to a maximum strain of -6%, and then
unloaded to the target test value. The value of the stress corresponding to this
strain for each of the aforementioned rates was approximately -20 and -25
MPa for the slow and fast strain rates, respectively. In creep tests performed
on the loading and unloading segment of the stress-strain at
  20 MPa (high), the magnitude of the strain was, as expected observed to
increase over time, with a transition to secondary creep after approximately 1
hour. At a (low) stress value of   5 MPa , a contrast in the behavior of the
material in shown in Figure 1, in which a test on the loading segment of the
stress-strain curve yields an expected increase in the strain magnitude, but the
test on the unloading segment produces a decrease in the strain magnitude.
The previously alluded to rate reversal behavior is recorded at -12 MPa (an
arbitrary value to represent the intermediate stress range) is illustrated in
Figure 2 in which an initial increase in strain followed by a decrease is in
evidence. The magnitude of the initial increase in strain compared to the
subsequent decrease, and the time for this reversal to occur is governed by the
magnitude of the test point. This behavior is only quantitatively affected by
the prior loading rate, but a faster prior rate has always been observed to
produce a higher magnitude of accumulated creep strain.
The viscoplasticity theory based on overstress (VBO) is a state variable based
model that has been successfully applied to the numerical modeling of
polymers [3, 4]. The basic formulation of the model is based on the standard
linear solid, and recent modifications have entailed a series coupling of two
arrangements to produce two overstress terms. This has enabled the model to
simulate non-monotonic changes in the strain rate due to opposite signs of the
overstress. The incorporation of this model into FEA schemes for simulating
polymer deformation behavior is expected to produce results with greater
fidelity with the natural behavior of the UHMWPE used in orthopedic
implants.
SIGNIFICANCE:
Existing material models, unlike the modified VBO formulation, are
unable to accurately capture negative creep and creep rate reversal in
polymers. VBO, therefore, has the potential of greatly enhancing the accuracy
of numerical simulations used to predict polymer deformation behavior.
Figure 1: Square symbols show increase in strain during creep on the loading
segment, while the diamond symbols illustrate that a decrease in strain during
creep is observed in creep at the same stress level (5 MPa) but on the
unloading segment of the stress-strain curve..
Figure 2: Illustration of rate reversal in creep at -12 MPa with two prior
loading rates.
REFERENCES:
[1] Bergstrom, J et al., Biomaterials, 2003, 24, 1365-80.
[2] Matsoukas, G. et al., J. Biomech. Eng., 2009, 131, 041011-22.
[3] Dusunceli, N. and Colak, O., Int. J. Plast., 2008, 24, 1224-42.
[4] Khan, F. and Yeakle, C., Int. J. Plast., 2010
Poster No. 1041 • ORS 2012 Annual Meeting