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Russian Journal of Biomechanics
RESIDUAL STRESS MEASUREMENTS OF ULTRA-HIGH MOLECULAR WEIGHT POLYETHYLENE FOR ARTIFICIAL JOINTS
M. Ohta*, S. Tsutsumi*, S.-H. Hyon*, Y.-B. Kang*, H. Tanabe**, Y. Miyoshi**
* Institute for Frontier Medical Sciences, Kyoto University, 53 Kawahara-cho, Shogoin, Sakyo-ku, Kyoto 606-8507, Japan, E-mail: ohta@frontier.kyoto-u.ac.jp
** School of Engineering, The University of Shiga Prefecture, 2500, Hassaka-cho, Hikone, Shiga, 522-8533, Japan
Abstract. One of the clinical problems in the artificial joints is wear of ultra-high molecular weight polyethylene (UHMWPE). Our new method to improve the wear resistance of UHMWPE was to irradiate it by y-ray slightly and compress during the molten state, and this novel method resulted in very good wear properties for artificial joints. However, a question was arisen whether the compressed UHMWPE might have residual stresses, because of having molecular orientation. The residual stresses may cause deformation in machining and storage. Three kinds of samples were prepared for measurement of residual stresses using the wide-angle X-ray diffraction method. One was the original uncompressed sample (Sample C: control). The second one (Sample A) was a crystallized sample under molecular orientation at the molten state and the third was a compressed sample (Sample B) beiow the melting point. Very low residual stresses were confirmed in Samples A and C, while higher tensile stresses were observed in Sample B. Shrinkage with increasing temperature of the samples was also measured for detection of residual stresses. When the deformation happens at low temperature, it can be noted that the residual stresses exist in the amorphous phase. Slight expansion was observed in Sample C. Sample A did not shrink appreciably until 80°C, while Sample B began to shrink at significantly lower temperatures. It was concluded that residual stresses in Sample A, which was the crystallized sample under molecular orientation at the molten state, were similar to the conventional sample (Sample C). And it was confirmed that the Sample A was a novel material for artificial joints from both view points of low residual stresses and high wear resistance compared with the conventional materials, Samples B and B'.
Key words: residual stress measurements, ultra-high molecular weight polyethylene, artificial joints, experiment
Wear particles of ultra-high molecular weight polyethylene (UHMWPE) generated during functioning of joint replacements have been associate with metallosis, osteolysis and prosthetic loosening, and these factors often necessitate revision surgery [1-8]. Many attempts to improve the wear performance of UHMWPE have been reported concerning the raw material and the component designs [9-16].
Our previous studies [17-21] reported that wear resistance was improved using a slightly cross-linked UHMWPE that was compressed uni-axially during the molten state and then crystallized. It was found that the wear resistance of the compressed sample was enhanced from the results of reciprocating wear tests. Wide angle X-ray studies revealed that
Introduction
the compressed samples had a very special spatial orientation in the crystalline phase. The crystalline plane (200) was preferentially orientated parallel to the compressed surface, which means that the c-axis of the orthorhombic crystal form was located almost perfectly parallel to that surface.
When a crystalline sample is deformed elastically in such a manner that the strain is uniform over relatively large distances, the lattice plane spacing in the crystal form changes from a stress-free value to some new value corresponding to the magnitude of the applied stresses [22]. The uniform macrostrain causes a shift in the diffraction lines to new 20 positions. From this shift the strain can be calculated and, knowing the strain, the stress present can be determined. In general, the effect of residual stresses is the same as the effect of stress with a mechanical load, therefore, a compressed residual stress causes increasing fatigue strength, while a tensile one causes decreasing fatigue strength.
The purpose of this paper is to clarify the existence of residual stresses in UHMWPE materials.
Experiment
Preparation of Samples
Two different molding methods were prepared. The starting material for these methods was a commercial UHMWPE (Sample C) from Mitsui Chemical Co. Japan, with a
viscosity average molecular weight of 5.5 • 106. Figure 1 shows relationships among samples.
First, the compression method of a slightly cross-linked UHMWPE during the molten state was performed. Blocks of original UHMWPE were irradiated by 60Co y-rays under reduced pressure at room temperature. Sample C-0.8 means a sample, Sample C, which was then irradiated at a dose of 0.8 Mrad. To investigate effects of y-rays, Sample C was compressed and the sample was named as Sample D.
Sample A was irradiated at a dose of 0.5 Mrad, and was compressed at 200°C, which was higher than the melting point (about 140°C). The compression speed was about 1 cm/min, and the total compression load was about 4,200 kgf. Then the samples were cooled to
Fig. 1. Scheme of used samples. 31
room temperature over a period of 2 hours. The cooling time from 140°C to 80°C demanded by the Japanese Industrial Standard (JIS) was about 1 hour. In this procedure, the sample thickness was reduced in accordance with increases in the compression.
The compression ratio (CR) was defined by the ratio of the final thickness to the original thickness of the sample.
The following process relates to Sample B. Blocks of original UHMWPE were heated at 120°C, which was below the melting point, for more than 3 hours. After the heating, the UHMWPE was compressed at the same speed as Sample A. The load was more than 10,000 kgf.
To clarify the effect of annealing in Sample C, a sample was left at 110°C for 22 hours and was named Sample Ca.
Principles of sin2ij/ Method
Figure 2 shows a schematic diagram of the sin \j/ method. When X-rays are introduced along the SO line at an angle of v|/o to the sample surface, the diffraction occur at the lattice plane that is perpendicular NO line. The SO line crosses the NO line at an angle of r) and the X-ray is reflected along the OD line. The strain ew, perpendicular to the lattice plane is expressed by the following formula using principal stresses oi and 02 that are parallel to the surface,
2 2 (a, cos (p + a2sm <p) . 2 fai+a^)
V|/=(1 + V)X -E -~XSm ¥~VX £ ( )
where <p = 90+ ^S and v is Poisson's ratio of the sample; a<? is defined as the stress located on
2 2 the OP'line (a^ = O] cos (p + a2sin 9).
Therefore, equation (1) is rewritten as the following equation,
,, s acp .2 (a, +a2)
= (l + v)x~-xsm y-vx- £ '
when the distance of the lattice plane is defined as 80, stresses leave the space at A8, and using the diffraction angle 9,
e = AS _ AO
Sn tan6
and
Note that
a,„=--ä-_LJ 520
K l2(l + v)xtanGJ' M
529
a • 2
asm v|)
then a9 = K xM, where K is termed the stress constant, so called X-ray stress constant. If 29-sin2i|/ line is reduced, i.e. the slope (M) is negative, the a<p has a positive value and there are tensile stresses in the sample. However, when the line is increased, the cfy has a negative value and the sample has compressed stresses.
Measurement of X-ray Diffraction
The measurements of residual stresses in the crystalline phase were performed by a Residual Stress Analyzer (VI. 1.5, Rigaku Co., Japan) with Cr-Ka X-rays (X = 2.2897Gx xlO~i0m) generated at 40 kV and 40 mA. The scanning step was 0.10 degree and the step time was 1.0 second. Ten points of sin \\i from 0.0 to 0.5 every 0.05 were selected.
Measurement of Deformation
The deformation measurement was carried out with increasing temperature from -
150 C to 130 C at 2°C/min to detect the existence of residual stresses both in the amorphous
and crystalline phases. The surface perpendicular to the compressed axis was cut to a
rectangular parallelepiped and the length was measured by a viscoelastic analyzer (Rheogel-
E4000, UBM Co. Ltd). Shrinkage was calculated using the following formula,
. , Sample length - The original length
Shrinkage =-----—--. . ----—
1 he original length
where the original length was defined as the length at 0°C.
Determination of X-ray Stress Constant
The X-ray stress constant (K) of each sample was determined using the findings of dynamic modulus [22]. The storage moduli of Samples A, B, B', C, Ca, C-0.8, and D at room temperature 27°C were 1.21, 1.15, 0.86, 0.99, 1.06, 0.99, 0.99 GPa, respectively. The Poisson's ratio of 0.45 was applied to all samples. From these factors, stress constants of various samples were calculated as shown in Table 1.
Results and discussion
Figure 3 shows the intensity chart of X-ray diffraction as a function of 29. It was observed that there were several peaks from 120° to 150° and the 135° peak and the 140° peak were selected as single measurable peaks, respectively.
Figure 4 shows the 29—sin2\|/ line of Sample C. The slope (M) of the line was -0.12±0.10, the stress was calculated as 0.29±0.25 MPa, where the confidence limit 68.3% was used as the error tolerance.
The slope (M) of the line of Sample A was -0.20±0.13 in Figure 5. The stress was 0.59±0.39 MPa.
Table 1. Stress constants (K), slopes (M) and residual stresses (ct(i,) measured for various samples.
Sample Stress constant (K) (Mpa) Slope (M) Residual stresses (<r„)(MPa)
Sample A -3.02 -0.20±0.10 0.59±0.39
Sample B -2.87 -0.49±0.22 1.39±0.64
Sample B' -2.14 -0.48±0.33 1.03±0.70
Sample C -2.47 -0.12±0.10 0.29±0.25
Sample Ca -2.64 0.08±0,03 -0.20±0.07
Sample C-0.8 -2.47 0.14±0.09 -0.76±0.06
Sample D -2.16 -0.06±0.04 0.13±0.08
4.5
2.0
120 125 130 135 140 145 150
29
Fig. 3. Intensity of X-ray diffraction as a function of 20 from 120° to 150°.
sir>2¥ sin2 y
Fig. 4. 26-sinV line of Sample C. Fig. 5. 20-sin2\|/ line of Sample A.
135.7
135.4
CD CM
135.1
134.8
135.7
135.4
135.1
0.1 0.2 0.3 0.4 0.5 sin2 \|/
Fig. 6. 29-sin2\|/ line of Sample B.
134.8
0 0.1
0.3 0.4 0.5
sin2 \\)
Fig. 7. 29-sinV line of Sample B'.
135.7
135.4
CD CM
135.1
134.8
0 0.1 0.2 0.3 0.4 0.5 sin2
Fig. 8. 28—sin2vj/ line of Sample C-0.8.
135.7
135.4
CD CM
135.1
134.8
135.7
135.4
CD CM
0.1 0.2 0.3 0.4 0.5 Sin2 Vj/
Fig. 9. 20—sin2v^ line of Sample D.
135.1
134.8
0.1 0.2 0.3 0.4 0.5 sin2 V|/
Fig. 10. 29-sinV line of Sample Ca.
Figures 6 and 7 show the 28-sin v|/ lines of Sample B and B', respectively. The slopes (M) were -0.49±0.22 and -0.48±0.33, respectively. The stresses were 1.4±Q.64 MPa and 1.0±0.70 MPa, respectively. It was found that these stresses were clearly higher than those of Sample A and Sample C. Moreover, if the first 5 points of Sample B' were selected, the slope (M) was -2.8 and the stress value was 6.1 MPa. It was revealed that the existence of residual stress in Sample B' was about 10.3-fold higher than that in Sample A, while, the Young's modulus of Sample A was 1.4-fold higher than that of Sample B. Therefore, it was confirmed that the residual stresses of Samples A and C were significantly low, compared with Samples B and B'.
In order to examine the effects of y-ray irradiation, compression and crystallization, and the residual stresses of Samples C-0.8, D, and Ca were measured. Figure 8 shows the 26-
0.1 0.05 0
<D gp
% -0.05
M
00
-0.1 -0.15 -0.2
0 20 40 60 80 100 120 140
Temperature (°C) Fig. 11. Shrinkage as a function of temperature.
Treatment Temperature
Lower < Tm < Higher
Fig. 12. Analysis of treatment temperature effects.
sin2\|/ line of Sample C-0.8 and the slope (M) was 0.14±0.09. The stress value was -0.76±0.06 MPa. Figures 9 and 10 show those of Samples D and Ca. The slopes (M) were -0.06±0.04 and 0.08±0.03, respectively. It was found that the residual stresses of these samples were similar and nearly zero, suggesting that both methods of y-ray irradiation and compression without y-ray irradiation had no influence on residual stresses. In addition, the crystallization introduced no effects.
Figure 11 shows shrinkage values of samples as a function of temperature. Sample B shrunk at 80°C and moreover, Sample B' shrunk below 60°C, while Samples C and A did not shrink below 130°C. These findings show that all these molecular orientated samples including Sample A have a shrinkage behavior as a function of temperature, due to the existence of the orientation in the crystalline phases. It was confirmed that the differences in shrinkage behavior between Samples B and A depend on the differences in circumstances in the amorphous phase. The amorphous phases in Samples B and B' were stressed, while this phase in Sample A was relaxed.
In Figure 12, we considered the reason why the differences of relationship between the manufacturing processes and the molecular orientation of Samples B and A occurred. Samples B and B' was manufactured by compression with crystalline phase, while Sample A was compressed without crystalline phase. From these process differences, the orientations of Samples B and B' happened furiously not only in the crystalline phase, but also in the amorphous phase. Moreover, residual stresses existed in both phases. However the orientation of Sample A was observed only in the crystalline phase because the crystallization happened naturally from the melting process. Therefore it was confirmed that Sample A was untroubled with residual stresses, and was a novel material that was free from deformation and wear problems of artificial joint bearings.
Conclusions
From the above findings of the present study, the following conclusions could be
drawn.
• • • 9
• Residual stresses were measured by shrinkage and X-ray diffraction sin vj/ methods. The
9 o
sin \\f method was performed at 20 of 135 .
• Several samples were prepared. One was a compression of a slightly cross-linked UHMWPE sample at the molten state (Sample A), and the others (Samples B and B') were compression of original UHMWPE samples (Sample C) below the melting point.
• High residual stresses were not observed in Sample A and Sample C.
• There were relatively higher residual stresses in Sample B and Sample B', which were in the tensile state.
• The shrinkages of Samples B and B' started at 80 C and 60 C, respectively, while Sample A did not shrink over 130 C. Therefore, the amorphous phases in Samples B and B' showed also tensile residual stresses.
• Sample A was a novel material that was free from deformation and wear problems of artificial joint bearings.
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ИЗМЕРЕНИЕ ОСТАТОЧНЫХ НАПРЯЖЕНИЙ В СВЕРХВЫСОКОМОЛЕКУЛЯРНОМ ПОЛИЭТИЛЕНЕ ДЛЯ ИСКУССТВЕННЫХ СУСТАВОВ
М. Ота, С. Цуцуми, С.-Х. Хион, Я.-Б. Канг, X. Танабе, Я. Миоши (Киото, Япония)
Искусственные суставы из сверхвысокомолекулярного полиэтилена широко применяются в клинической практике. Важной проблемой здесь является уменьшение износа на поверхности сустава, что связано с увеличением долговечности суставов. Авторы данной работы ранее предложили способ обработки полиэтилена, приводящий к увеличению сопротивления износу. Метод состоит в облучении у -лучами и сжатии в расплавленном состоянии. В связи с этим возникает вопрос о наличии при такой обработке остаточных напряжений в материале, которые могут привести к снижению прочностных свойств изделий. В данной работе проведено экспериментальное исследование остаточных напряжений в полиэтилене, полученном новым методом, а также для сравнения в необработанном материале и в материале, подвергнутом деформации в кристаллическом состоянии. Остаточные напряжения определялись методом деформации рентгеновских лучей, а также из измерения усадки при изменении температуры. Показано, что материал, полученный по методике авторов, имеет наиболее высокое усталостное сопротивление и малые остаточные напряжения в сравнении с исследованными материалами. Библ. 22.
Ключевые слова: сверхвысокомолекулярный полиэтилен, искусственный сустав, остаточные напряжения, эксперимент, сопротивление износу
Received 12 June 2001
