J. BIOMED. MATER. RES.
VOL. 10, PP. 805-828 (1976)
Fracture Characteristics of Acrylic Bone Cements. I. Fracture Toughness THOMAS A. FREITAG* and STEPHEN L. CANNON,** Materials Department, Xchool of Engineering and Applied Science, University of California, Los Angeles, California
Summary The vital first phase of the overall materials study to protract the life of the total joint replacements is the identification of the fracture toughness and fatigue properties of bone cements. Information gained from fatigue testing, performed in a manner which simulates in vivo conditions, and fracture toughness, which is a measure of the propensity of a crack to propagate, is the first step towards the prediction of the life of the total joint replacement. This study is concerned with the fracture toughness of Zimmer and Simplex-P cold-curing bone cements. Following cement fabrication conditions which closely approximate clinical procedures, fracture toughness testing was conducted on cement specimens which were immersed in bovine serum a t 37°C in order t o simulate in vivo conditions. I n addition, a similar study was completed on specimens, tested in air a t ambient temperature for purposes of comparison. Results of this procedure, when analyzed by a Student’s t-test a t the 95% confidence level with eight degrees of freedom, indicate that both Zimmer and Simplex-P exhibit a higher fracture toughness in the simulated physiological environment. I n order t o determine whether the addition of barium sulfate to these cements compromises the fracture toughness, the above described testing rationale was repeated, indicating the existence of a complicated relationship between the different testing environments and barium sulfate. The importance of these results lies in the fact that an increased fracture toughness indicates that a cement will inherently exhibit a greater degree of resistance to the propagation of cracks, which could contribute to the ultimate failure of the total joint replacement.
BACKGROUND With the advent of monomer-polymer dough-molding techniques in 1938, poly(methy1 methacrylate) materials enjoyed widespread *Present address: Ralph Parsons Co., Inc., Pasadena, California 91124. **To whom all correspondence should be addressed. 805 @ 1976 by John Wiley & Sons, Inc.
806
FREITAG AND CANNON
use in the fabrication of dentures. Consequently, the development of technology relating to suitable polymerization systems and their manipulation made possible the utilization of these polymeric materials in many other in vivo and ex vivo prosthetic devices.' Favorable dental and medical experiences with a number of these devices in varying applications probably indicated the implementation of acrylics as a fixation medium for certain orthopedic implants, especially the femoral component of the total hip replacement.2-1° Although this latter idea of a total hip prosthesis was not recent (indeed, it had been proposed as early as 189011), the clinical efficacy of these procedures prior to the appearance of acrylic cements was not encouraging. The basic problem was one of preventing slippage between the femoral stem of the prosthesis and the medullary canal, the exception being with younger patients using a Moore-type prosthesis.12 Since the majority of all implant candidates are over 60 years old, the typical femur encountered has a thin cortex and spacious medullary canal. It has been with these cases that a truly significant improvement in prognosis has been manifested. One primary reason for this success is that the cement modifies the prosthesis-biologic interface; i.e., a continuous bridging is afforded which is important technically in that the distribution of stresses transmitted between prosthesis and bone is made more uniform and continuous. Prior to this procedure, stress concentrations on the order of 3500 psi had been estimated to exist under certain circumstance~.~ Such a situation was undesirable from the standpoints of possible aggravation of bone resorption and permanent deformation of bone (a viscoelastic material) which both lead to the foreshortening of prosthesis utility. The metallic femoral component, acrylic cement, and bone have been modeled by McNeice13 as a composite structure (Fig. 1). When no slippage occurs between the interfaces of the components of this structure, a uniform transferral of stress between metal prosthesis and bone exists. However, if relative motion occurs between the components of the composite structure, the stress distribution changes radically, and the tensile stresses in the cement can increase from about 1000 psi to as much as 3000 psi.13 This may be problematical in that it is possible that high tensile stresses can initiate cracks in the acrylic component which cause loosening of the metal prosthesis and, ultimately, failure of the metallic stem.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
807
Fig. 1. Composite structure modeled by McNeice and Am~tutz.1~
Clinical studies preformed by the Division of Orthopedics at the UCLA School of Medicine have indicated that cement cracking is intimately involved in the loosening and subsequent failure of metal pros these^.'^ As cracks initiate and propagate through the acrylic, the metal prosthesis loosens, thereby promoting further crack growth in the acrylic as well as high stresses in the metallic stem. It has been postulated that prostheses failures in vivo are due to these high stresses which cause crack initiation which, in turn, leads to the eventual failure of the stem. It is possible that the likelihood of stem failure can be accentuated by cyclic loading or fatigue. The cyclic nature of loading on the prosthetic hip joint, e.g., walking, could promote increased crack growth in the acrylic resulting in an increase in the rate of loosening of the metal prosthesis. The previous discussion indicates the importance of the role of the acrylic cement in the composite structure. Clearly, if the life of
808
FIZEITAG AND CANNON
the prosthetic joint is to be maximized, the mechanical properties of the acrylic cement must be characterized. Therefore, this twopart investigation is concerned with the characterization of the fracture toughness and the fatigue behavior of acrylic bone cements: results and conclusions of the fracture toughness studies will comprise this paper, while the fatigue results will appear in a sequel.
THEORETICAL The independent variables selected in this investigation were the fabrication pressure, additive content, and testing environment. Fabrication pressure was chosen as a n independent variable because preliminary investigations showed that fabrication pressure has an effect on mechanical properties as well as on porosity of the coldcuring acrylics. Additive content was chosen as a variable because
Fig. 2. Mode I-type loading.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
809
one of the cements is available commercially with differing contents of BaS04and the possibility that the addition of BaS04may unduly compromise the fracture characteristics of the cement. Two testing environments were selected because of the desirability of testing in a simulated physiological environment, viz., bovine serum a t 37"C, in addition to the convenience of testing in air a t ambient temperature as a control. The dependent variable in this study is fracture toughness. Fracture toughness, or the critical stress-intensity factor as it is sometimes called, is usually denoted by Kr,. The I refers t o the type of loading (cf. Fig. 2), and the c denotes a critical value. Thus, when the stress-intensity factor K I equals the fracture toughness KI,, a crack will grow until the material fails. The importance of studying this dependent variable lies in the fact that knowledge of the fracture toughness will give a n indication of the propensity of the bone cement to resist crack growth and thereby obviate all the aforementioned problems attendant t o cement cracking. The determination of fracture toughness values for acrylic bone cements involves an assumption that is commonly made for metals, but must be carefully considered for polymeric materials. It is assumed that deformation in these polymers follows Hooke's law. As can be seen in Figure 3,14 poly(methy1 methacrylate) (PMMA) exhibits a linear stress-strain relationship over a wide range of
10
20
30
ELONGATION, PERCENT
Fig. 3. Stress-strain relationships for different temperatures (from Alfrey").
FREITAG AND CANNON
810
strain. This is important in that PMMA is a primary ingredient in both Simplex-P and Zimmer acrylic bone cements, and the temperature and range of stress levels in this study are well within the linear region of Figure 3, as will be verified later. Additionally, a number of other workers15-1s have assumed with reasonable success t h a t PMMA behaves in a linear elastic fashion. For a linear elastic solid, Griffith’s worklg was one of the first which predicted a failure stress due t o the presence of a flaw. It was noted that the increase of potential energy due t o the surface tension of the crack (later called surface energy) must be balanced by the decrease in the potential of the strain energy and the applied forces.z0 Griffith found that eq. ( 1 ) is satisfactory for plane strain in a linear elastic material.Z0
where u is the far-field stress at failure with the presence of a flaw of size 2a, E is Young’s modulus, Y is Poisson’s ratio, and y is the surface energy associated with the crack faces. Setting GI = 27 (2) and recallingz1 KI = dEGI(1-3 (3) then substituting into eq. (1) leads t o eq. (4). Kr
(4)
= afia
Equation (4) is the expression for the stress-intensity factor in a n infinite plate with a crack of length 2a (plane strain conditions). A more general form of eq. (4)is K I = Y2/Z (5) where Y is a geometric correction factor that includes the stress term. If a crack is introduced into a standard Charpy bar (cf. Fig. 4) and the Charpy bar subjected to three-point bend loading, then according t o Brown and Srawley,22
Y
=
=Bw2 (1.93
-
3.07
- 25.11
(-:>”
+ 25.8 (t)4) (6)
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
-
.800
8 .00+
L
" l . 0 0 1 R
I
I
811
"TIT+ w!!
2.165-----(
k . 3 ; d
where B is the thickness, zu is the width, and M is the moment at the crack. By testing Charpy bars to failure in three-point bending, the condition ( K I = Kr,) can be determined for the material being tested.
MATERIAL ACQUISITION AND PREPARATION Two types of cold-curing acrylic bone cement and some acrylic sheet were obtained for the research program. Zimmer bone cement consists of 90 wt yo PMMA and 10 wt yo BaS04. Simplex-P bone cement consists of 15 wt Yo PMMA, 75 wt % of the methacrylatestyrene copolymer, and 10 wt yoBaS04. I n addition, the Simplex-P and Zimmer cements were obtained without the BaSOr, which is added to impart radiopacity t o the cement. The acrylic sheet, Plexiglas I1 UVA, was manufactured by Rohm and Haas and used for a control in the experimentation. A number of parameters must be controlled during the mixing and subsequent implantation of acrylic cements. Figure 5 depicts the temperature history of a polymerizing acrylic rna~s.2~Briefly, liquid PMMA monomer is added and mixed with powdered PMMA polymer, the ratio being 1 m1/2 g on a weight basis. After a time, the polymerizing material becomes dough-like in that it may be kneaded or worked by hand for 8-10 min after initial mixing, a t which point the material "sets up'' into a rigid, brittle mass. As indicated by Figure 5, the polymerization reaction is exothermic, and the setting time is arbitrarily designated as the time corresponding t o the point a t which the temperature of the dough is midway between the mixing (ambient) temperature and the maximum
FREITAG AND CANNON
812
I (TmW
I&
a
+
AMBIENT)
a ? i w n
5k
WORKING TIME BEGIN MIX
TIME
Fig. 5. Schematic graph showing exothermic temperature changes occurring in acrylic cements during the polymerization process (from Meyer e t al.23).
temperature achieved. The working time is obviously the interval between dough and set time. After dough time, the cement was inserted into a mold (Fig. 6) and pressure was applied for 15 min. The rationale for the application of pressure was that the porosity caused by mixing and evaporation of monomer could be controlled to some extent by applying fabrication pressures of 5, 25, and 50 psi on the acrylic cement while it was polymerizing in the mold. Aftter 15 min, samples were removed from the mold and machined into Charpy bars (cf. Fig. 4).
EXPERIMENTAL The experimental procedure was conceived according to a factorial experimental design (Table I), which allows the determination of TABLE I Factorial Experimental Design Layout Factors
Levels
Environment
2
Fabrication Pressure
3
BaS04 Concentration
2
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
813
Fig. 6. Charpy bar mold.
effects due to specific factors and facilitates an orderly presentation of data.24 Fracture toughness was measured by means of Charpy bars (cf. Fig. 4), tested in an Instron testing machine in three-point bending a t a crosshead rate of 0.2 in./min. Due to the difficulty of producing an even crack front by either fatigue precracking or precracking with a razor blade, a cutter was utilized and the machined notch had a root radius of 0.0015 in. To verify that a root radius of 0.0015 in. was small enough to give a valid value of fracture toughness,* Charpy bars were machined from Plexiglas I1 UVA to serve as a control. Fracture toughness Kr, values were calculated via eqs. ( 5 ) and (6) and then compared with values of Kre calculated from literature data25(Table 11). Since this comparison indicated close agreement between experimental data versus K r , values calculated from literature data the proposed rationale ‘for obtaining fracture toughness values was deemed acceptable. Fracture toughness specimens were tested in two environments: bovine serum *No ASTM specification exists for fracture toughness testing of polymeric materials.
FIZEITAG AN11 CANNON
814
TABLE I1 Comparison of Control and Literature ValuesZ6 of Fracture Toughness . ~ i t e r a t u r epsi
-
I r w i n and Kies Berry
Jm. 1319.0 889.9
Vanden Boogaert
1143.0
Benbow and Roesler
1392.9
Benbow
1289.6
Berry
744.5
Broutman and McGary
689.3
Gurney
1989.8
AVERAGE
1182.3
Control psi
- J;T;I
Plexiglas I1 UVA AVERAGE
1150
(purchased from Miles Labs.) atJ37 f 2°C and air at ambient (22OC) temperature.
RESULTS Some fracture toughness results are shown in Figures 7 and 8 and in the Appendix, while others, analyzed by means of a Student’s t-test, are displayed in Tables 111-XV. The t values entered therein are a result of a Student’s t-test comparison of the fracture toughness values calculated from samples tested under the listed conditions in the tables. For example, in Table 111, testing environment (in this case, air a t ambient temperature) and additive content (10.0 wt yo B a s 0 3 are held constant, and the fracture toughness values for the two brands of cement, viz., Simplex-P and Zimmer, are compared. Table VII shows the t values resulting from the comparison of fracture toughness results at different additive concentrations of BaS04 in Simplex-P cement. The environment, air a t ambient temperature, was held constant for tests at each additive concentration. The starred entries in the tables indicate significant differences at different confidence levels: one star denotes a significant difference at the 90% confidence level, two stars denote a significant difference a t the 95% confidence level, three stars a significant difference at the
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
815
98% confidence level, and four stars indicate a significant difference a t the 99% confidence level (cf. Table XVI). The confidence level of the significant differences was determined by comparing the calculated entries in Tables 111-XV to a tabular t value. For eight degrees of freedom, the tabular t values of interest to this study are listed in Table XVI.26
12
N
b
-
10
IIi;, / a -
-
zu6
I
4
I
12
?2
10
-
J
a -
I
.-
a 0
2-
6
-
4 '
'
I
816
FREITAG AND CANNON
TABLE 111 Student’s &Tests Comparing K I , Data from Simplex-P and Zimmer Bone Cements with 10.0% BaSOl Tested in Air a t Ambient Temperature Zimmer Cement F a b r i c a t i o n Pressure
5 psi KIc
0)
941
25 p s i 1016
50 p s i
960
C , L
c
a
0E) v m I
5 psi
799
:.
25 p s i
959
E ;
50 psi
942
J L
n
A
2.65** -
c
w e -a 4o .r
1.55 0.58
m
Note: Underlined t values denote a higher fract,ure toughness a t a confidence level of a t least 90% for Zimmer cement. See Table XVI for definitions of confidence levels.
can be seen from a comparison of Figures 7 and 8, the fracture toughness of Zimmer cement a t 5 psi fabrication pressure is higher than the fracture toughness of Simplex-P cement under the same conditions. Table 111 shows that there is a significant difference a t the 95y0 confidence level between the two cements when fabricated a t 5 psi. A comparison of Figures 7 and 8 also shows that as the fabrication pressure increases the difference between the two cements decreases. Table I11 shows that there are no significant differences between the two cements for fabrication pressures of 25 psi or 50 psi. The superior fracture toughness of Zimmer cement over Simplex-P cement a t 5 psi fabrication pressure could be a result of Zimmer, a homopolymer, being able t o achieve a greater degree of ordering under a smaller amount of fabrication pressure than Simplex-P, which is a randomly polymerized copolymer. The more stereoregular nature of Zimmer as compared t o Simplex-P would permit the greater degree of ordering, thus accounting for the difference in fracture toughness. Evidently, the difference in fracture toughness disappears because a n increase in fabrication pressure will have little additional effect on the ordering of Zimmer cement.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
817
TABLE I V Student’s &Tests Comparing K I , Data for Simplex-P and Zimmer Bone Cements with 10.0% BaS04 Tested in Bovine Serum a t 37°C Ziner
Cement
F a b r i c a t i o n Pressure
KPc
+ It e 3
$
V
n
-
n
. E r
5 psi
1019
25 p s i
1045
50 p s i
1265
L L
5 psi
25 p s i
50 p s i
1150
1294
1215
4.22** -
s
5
m
8.1 O****
v
. L r
2
.68
LL
b
Note: See footnote of Table 111. Also, see Table XVI for definitions of confidence levels.
Similar effects are noted when the fracture toughness testing is done in bovine serum a t 37°C (cf. Table IV). Table I V shows that Zimmer cement has superior fracture toughness a t fabrication pressures of 5 psi and 25 psi, the former a t the 98% confidence level and the latter a t the 99% confidence level. Again, the fabrication pressure effect is not noticeable a t 50 psi. (Fracture toughness values are listed in the Appendix.) Conversely, if the BaS04 is not present in either cement, Zimmer has a higher fracture toughness that Simplex-P for all fabrication pressures for tests in each environment (cf. Tables V and VI). Also, the absence of BaS04 increases the fracture toughness of Zimmer cement when compared to SimplexP cement. t Values for the comparison of fracture toughness of Simplex-P cement are listed in Table VII, while t values for the same comparisons for Zimmer cement are listed in Table VIII. The presence of BaS04 apparently reduces the fracture toughness. Table VII indicates that Simplex-P with 0.0 wt yo BaS04 has a higher fracture toughness at the 5 psi fabrication pressure with a confidence level
818
FREITAG ANT) CANNON
TABLE V Student's &Tests Comparing K I ,Data from Simplex-P and Zimmer Bone Cements with 0.0% BaS04 Tested in Air a t Ambient Temperature
KIc
w +
J
1126
1087
1147
3
c v l
w v I
O aE
v 5
-A
2o
.$
'G
w
n
5 psi
948
25 p s i
959
50 p s i
926
****
4.46
E
m
u
v ) n m LL
****
4.34
9.58****
Note: See footnote of Table 111. Also, see Table XVI for definitions of confidence levels.
TABLE VI Student's &Tests Comparing K I , Data from Simplex-P and Zimmer Bone Cements with 0.0% BaS04 Tested in Bovine Serum a t 37°C Zinuner Cement F a b r i c a t i o n Pressure 5 psi
KIc
1200
25 p s i
50 p s i
1235
1167
W C C ,ZLi
wvl
"5:2
5 psi
957
25 p s i
943
50 p s i
1037
6.12
****
a c x1 'r 0
5%
6.38
****
n u E. Lr
mz .r
3.50
****
LL
Note: See footnote to Table 111. Also, see Table XVI for definitions of confidence levels.
FILACTURE CHARACTERISTICS OF BONE CEMENTS. I
819
TABLE VII Student’s &Tests Comparing K I , Data from Simplex-P Bone Cement with 0.0% and 10.0% concentrations of BaS04 Tested in Air a t Ambient Temperature Simplex-P
Cement 10.0% BaSOq
Fabrication Pressure
d v) 0
m
=
w
9 %
o
w
+Ca JL
f ’.-=
v
5 psi
o
b
n
25 psi
m
A 2 a J L
~n
nlu
.in
50 D s i
ELL
Note: The underlined t value denotes a higher fracture toughness a t a confidence level of a t least 90% for Simplex-P with 0.0% BaS04. See Table XVI for definitions of confidence levels. TABLE VIII Student’s &Tests Comparing K I , Data from Zimmer Bone Cement with 0.0% and 10.0% Concentrations of BaS04 Tested in Air At Ambient Temperature
am wr m
w
KI c
a
w In
94 1
1016
960
?o En 5 psi
1126
‘t n
25 p s i
1087
ELL
50 psi
1147
g
i% v L c
N
v
4.80
**** 2.08
*
I
5.56
****
82 0
FREITAG AND CANNON
of 95%, but there is no significant difference at the other fabrication pressures. Comparatively (cf. Table VIII), Zimmer cement has superior fracture toughness for all fabrication pressures when it contains no BaS04. These reductions could occur because of insufficient polymer bonding to the BaS04 powder, or the BaS04 might inhibit ordering. A more pronounced effect of BaS04 on Zimmer cement, as compared to Simplex-P cement, can be seen by a comparison of Tables I11 and V and by recalling the results of Tables VII and VIII. The increase of fracture toughness due to the removal of BaS04 from Zimmer cement (cf. Table VIII), and the comparatively small change in fracture toughness due to the removal of BaS04 from Simplex-P cement suggest that the BaS04 may interfere with the order of the polymer, i.e., since Simplex-P orders less, the addition of BaS04 affects it less, while for Zimmer, BaS04 interferes more noticeably with the ordering at all fabrication pressures. A comparison of Tables I11 and V shows that for 10.0 wt yo BaS04, the fracture toughness of Zimmer cement is superior only at the 5 psi level (cf. Table 111), but for the 0.0 wt yo BaS04 the fracture toughness of Zimmer cement is superior to Simplex-P cement at all fabrication pressures (cf. Table V). Clearly, 10.0 wt Yo BaS04 has a more detrimental effect on the cement that has the greater tendency to order. BaS04 shows evidence of interacting with testing environment, which can be seen by comparing Table VII and I X and by comparing Tables VIII and X. For Simplex-P cement, Table VII shows a significant difference at 5 psi fabrication pressure for tests conducted in air at ambient temperature, and Table IX shows significant differences at 25 psi and 50 psi fabrication pressures for tests conducted in bovine serum at 37°C. For Zimmer cement, Table VIII shows significant differences at all fabrication pressures for tests in air at ambient temperature, whereas, Table X shows a significant difference only at 5 psi fabrication pressure for tests in bovine serum a t 37°C. These comparisons show the significant differencethat exists between different BaS04concentrations depends on the environment in which the cements were tested. Holding the other independent variables constant, the two testing environments can have different effects on the two bone cements.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
821
TABLE I X Student’s &Tests Comparing K I , Da.ta from Simplex-P Bone Cement with 0.0% and 10.0% Concentrations of BaS04 Tested in Bovine Serum a t 37°C Simplex-P Cement 10.0% BaS04 Fabrication Pressure 5 psi -t 0 Ln
KIc
m
H a LJ O . s m m
5 psi
o
957
I I
25 psi
1019
I
1.27
I
50 psi
1045
1265
W a J
E J lLL a
5 oc
v
25 psi
.r
! a m
&
2
3.33***
50 psi
a J L
n n m ELL wl
.r
Note: Underlined t values denote a higher fracture toughness at a confidence level of a t least 90% for Simplex-P with 10.0% BaS04. See Table XVI for definitions of confidence levels. TABLE X Student’s &Tests Comparing Krc Data from Zimmer Bone Cement with 0.0% and 10.0% Concentrations of BaSOl Tested in Bovine Serum a t 37°C Zimmer Cement 10.0% BaSOq Fabrication Pressure 5 psi
25 psi
5 0 psi
Note: See footnote of Table VIII. Also, see Table XVI for definitions of confidence levels.
FREITAG AND CANNON
822
Table X I Student’s &Tests Comparing Krc Data from Simplex-P Bone Cement with 10.0% BaS04 Tested in Air a t Ambient Temperature and in Bovine Serum a t 37°C Simplex-P
Tested
i n Bovine Serum a t 37°C
Fabrication Pressure
5 psi
25 p s i
50 p s i
5 psi 25 p s i 50 p s i
Note: Underlined t values denote a higher fracture toughness a t a confidence level a t of a t least 90% for tests run in bovine serum a t 37°C. See Table XVI for definitions of confidence levels.
Table XI shows that the fracture toughness of Simplex-P cement is greater when tested in bovine serum at 37°C than when the same material is tested in air at ambient temperature. In comparison, results from tests in the two environments show little difference for Simplex-P containing 0.0 w t yo BaS04, except at the 50 psi fabrication level (cf. Table XII). In contrast, Table XI11 indicates that Zimmer cement, containing 10.0 wt yo BaSOr and tested in bovine serum a t 3 7 T , has a higher fracture toughness than the same cement when tested in air at ambient temperature. If the BaS04 is not present in Zimmer cement, the higher fracture toughness values were found from tests in bovine serum for fabrication pressures of 5 psi and 25 psi, while there is no significant difference between fracture toughness values obtanied from tests in the two environments at 50 psi fabrication pressure. However, in general, bovine serum at 37°C was found to increase the fracture toughness for all concentrations of BaS04, as well as for each brand of cement. The suggestion is made that the bovine serum at the crack tip could act as a plasticiz-
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
823
Table XI1 Student's t-Tests Comparing K I . Data from Simplex-P Bone Cement with 0.0% BaSOn Tested in Air a t Ambient Temperature and in Bovine Serum at 37°C Simplex-P
Tested i n Bovine Serum a t 37°C F a b r i c a t i o n Pressure
r
L .r
4
C
L
.r
v) x
KIc
957
943
1037
U v )
w
w
C m1 a L
0 I - =
5 psi
948
25 p s i
959
50 p s i
926
0.20
.r
4J
7x 2 W
0.45
.r
L
- n a E
.r
m L
4.55****
v)
TALBE XI11 Student's t-Tests Comparing K I . Data from Zimmer Bone Cement with 10.0% BaSO. Tested in Air at Ambient Temperature and in Bovine Serum a t 37°C Zimner
Tested i n Bovine Serum a t 37°C F a b r i c a t i o n Pressure
5 psi L 4
.-
KI c
w L
1150
25 p s i 1294
50 p s i 1215
c vv))
'r
F ,$'
5 psi
941
25 p s i
1016
50 p s i
960
6.39****
c, v )0 0 c I-
m
.r N
7.66**** 5.62****
LL
Note: See footnote of Table XI. Also, see Table XVI for definitions of confidence levels.
FREITAG AND CANNON
824
ing agent, thereby increasing fracture toughness, or the bovine serum could simply act as a protective agent in that i t acts to sequester the specimens from air, a more aggressive environment. I n addition t o the previously discussed comparisons, the fracture toughness results in air at ambient temperature and for each cement a t each concentration of BaS04were compared t o fracture toughness results obtained from tests on the control, Plexiglas I1 UVA (cf. Table XV and Figs. 7 and 8). As can be seen from Table XV, the significant differences were at the 99% confidence level for all comparisons except the comparison between Plexiglas I1 UVA and Zimmer cement without BaS04, where there was no significant difference a t the 5 and 50 psi fabrication pressures. This is puzzling because it would be expected that no significant difference should exist at 25 psi either, but such was not the case.
CONCLUSIONS 1) Specimens tested in bovine serum a t 37°C exhibited increased fracture toughness over those tested in air a t ambient temperature. TABLE XIV Student’s &Tests Comparing Kz, Data from Zimmer Bone Cement with 0.0% BaS04 Tested in Air a t Ambient Temperature arid in Bovine Serum a t 37°C Zimmer Tested i n Bovine Serum a t 37°C F a b r i c a t i o n Pressure
KIc
1200
5 psi
1126
Z.T8*
25 p s i
1087
50 p s i
1147
L . 4r
1235
1167
(u L
. T r YYI I
f
~
a J L + Y I E
2
3.42****
m U
f$ .r
0.55
u
N
Note: See footnote of Table XI. Also, see Table XVI for definitions of confidence levels.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
825
TABLE XV Student’s t-Tests Comparing Kr. Data from Plexiglas I1 UVA with Zimmer Containing 10.0% BaS04, Zimmer Containing 0.0% BaS04, Simplex-P Containing 10.0% BaS04,and Simplex-P Containing 0.0% BaS04,in Air a t Ambient Temperature F a b r i c a t i o n Pressures 5 psi
50 p s i
25 p s i
Zimmer
10.0% BaS04
5.819***
=****
3.540****
Zimner
0.0% BaS04
0.673
2.062*
0.067
Simplex-P
10.0% BaS04
6.898****
5.853****
6.950****
Simplex-P
0.0 BaS04
5.393****
6.094****
9.360***
Note: Underlined t values denote a higher fracture toughness a t a confidence level of at least 90% for Plexiglas I1 UVA. See Table XVI for definitions of confidence levels.
TABLE XVI Tabular t Values for Eight Degrees of Freedom for 90-99% Confidence Levels Confidence L i m i t
Designation i n Tables 111 xv
-
t.lO,
8
90%
*
t.05,
8
95%
**
t.02, 8
98%
***
t.O1,
99%
****
8
FREITAG AND CANNON
826
2) BaS04 reacts with the bovine serum environment when i t is present in both Zimmer and Simplex-P acrylic bone cements; i.e., fracture toughness of the specimens increases. 3) When fabricated a t 5 psi, Zimmer acrylic bone cement shows superior fracture toughness for all additive concentrations and environments when compared t o Simplex-P acrylic bone cement. It is hypothesized that Zimmer’s superior properties are due either t o polymer chain ordering or t o the possibility that the methacrylatestyrene copolymer in Simplex-P exhibits a n inherently lower K I , value.
APPENDIX Fracture Toughness Values*
Fabrication Pressure (psi)
+
Cement wt yoBaSOl
KI Test Environment Bovine Air Serum -
~-
5 25 50 5 25 50 5 25 50 5 25 50
Simplex-P, 10.Oyo BaS04 Simplex-P, 10.0% BaS04 Simplex-P, 10.Oyo BaS04 Simplex-P, 0.0% BaS04 Simplex-P, 0. OY0BaS04 Simplex-P, 0.0% BaS04 Zimmer, 10.O~oBaS04 Zimmer, 10.0% BaS04 Zimmer, 10.Oyo BaS04 Zimmer, 0.0% BaS04 Zimmer, 0.0% BaS04 Zimmer, 0.0% BaS04 Plexiglas I1 UVA
799 959 942 948 959 926 941 1016 960 1126 1087 1147 1150
-
1019 1045 1265 957 943 1037 1150 1294 1215 1200 1235 1167
Fracture Toughness Calculation A fracture toughness calculation for a Zimmer specimen containing 0.0% BaS04 and fabricated a t 5 psi is presented below. The following quantities were measured from the Charpy bar specimen : *The values represent the average of five replicates.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
827
Thickness: B = .395 in. Width: W = .394 in. Crack length: a = . l o 0 in. a/W = .254in. The following quantity was measured by noting the load necessary t o break a specimen in three-point bending. Prrgture
=
50 1b
From the Introduction:
Kr, = Y d i Y
=
E[1.93 BW2
- 3.07 - 25.11
(+y
+ 25.8 (G)~]
To calculate M , the moment at the notch:
M
Krc =
=
.800
P / 2 = .400 P
6(.400) 50 [1.93 - 3.07 (.254)
( .395) ( .394)2
+ 14.53 (.254)2
1
- 25.11 (.2M)3 + 25.8 (.254)4 dm KIc = 1106psi -
dz
This study was conducted under the auspices of the National Institutes'of Health, contract number NIH I A AM-16120. The authors wish to thank Dr. Harlan C. Amstutz and his UCLA research team for their interest and assistance, Howmedica Inc., for the donation of Simplex-P cement, and Messrs. Heinz Blessing and David Anuda, and Zimmer USA Inc., for the donation of Zimmer cement.
828
FREITAG AND CANNON
References 1. D. C. Smith, J. Biomed. Muter. Res. S y m p . No. 1, 189 (1971). 2. S. Kiaer, in Proc. Cinquieme Congres International de Chirugie Orthopedique, Stockholm, 1961, Bruxelles Imprimerie Lielens, 1953. 3. E. J. Habonsh, Bull. Hosp. J . Dis., 14, 242 (1953). 4. E. Henrickson, K. Jansen, and W. Krough-Poulsen, Acta Orthop. Scand., 22. 141 (1952). 5. W. T. Spence, J . Neurosurg., 11, 219 (1954). 6. L. L. Wiltse, R. H. Hale, and J. C. Stenehjern, J. Bone Joint Surg., 39A, 961 (1957). 7. J. Charnley, J . Bone Joint Surg., 42B. 28 (1960). 8. J. Charnley, J . Bone Joint Surg., 46B. 518 (1964). 9. N. R. Crozzoli, Minerva Ortop., 16, 399 (1965). 10. N. R. Crozzoli, Minerva Ortop., 16,395 (1965). 11. J. T. Scales, J . Bone Joint Surg., 50B, 698 (1968). 12. F. M. Follacci and J. Charnley, Clin. Orthop. Rel. Res., 62, 156 (1969). 13. G. M. McNeice and H. C. Amstutz, Proceedings of the 6th International Congress of Biomechanics, University of Jyvaskyla, June 1975. 14. T. Alfrey, Jr., Mechanical Behavior of High Polymers, Interscience, New York, 1948, p. 516. 15. I. Constable, L. E. Culver, and J. G. Williams, Int. J . Fract. Mech., 6, 279 (1970). 16. B. Mukherjee and L). J. Burns, Eng. Fract. Mech., 4, 675 (1972). 17. J. Constable, J. G. Williams, and D. J. Burns, J. Mech. Eng. Sci., 12, 20 (1970). 18. S. Arad, J. C. Radon, and L. E. Culver, paper presented a t the International Congress on Fracture, Munich, Germany, 1973. 19. A. A. Griffith, Phil. Trans. Roy. Soc. (London),A221, 163 (1921). 20. A. A. Griffith, in Proceedings of the International Congress for Applied Mechanics, Delft, 1924, pp. 55-63. 21. D. Broek, Elementary Engineering Fracture Mechanics, Noorhoff International Publishing Company, Leyden, 1974, p. 17. 22. W. F. Brown and J. E. Srawley, ASTM STP No. 410, p. 13. 23. P. R. Meyer, Jr., e t al., J. Bone Joint Surg., 55A, 149 (1973). 24. C. R. Hicks, Fundamental Concepts in the L)esign of Experiments, Holt, Rinehart and Winston, New York, 1964. 25. J. P. Berry, in Fracture, H. Liebowitz, Ed., Academic Press, New York, 1972. 26. W. Volk, Applied Statistics for Engineers, McGraw-Hill, New York, 1958, pp. 98-135.
Received November 3, 1975 Revised December 30, 1975
VOL. 10, PP. 805-828 (1976)
Fracture Characteristics of Acrylic Bone Cements. I. Fracture Toughness THOMAS A. FREITAG* and STEPHEN L. CANNON,** Materials Department, Xchool of Engineering and Applied Science, University of California, Los Angeles, California
Summary The vital first phase of the overall materials study to protract the life of the total joint replacements is the identification of the fracture toughness and fatigue properties of bone cements. Information gained from fatigue testing, performed in a manner which simulates in vivo conditions, and fracture toughness, which is a measure of the propensity of a crack to propagate, is the first step towards the prediction of the life of the total joint replacement. This study is concerned with the fracture toughness of Zimmer and Simplex-P cold-curing bone cements. Following cement fabrication conditions which closely approximate clinical procedures, fracture toughness testing was conducted on cement specimens which were immersed in bovine serum a t 37°C in order t o simulate in vivo conditions. I n addition, a similar study was completed on specimens, tested in air a t ambient temperature for purposes of comparison. Results of this procedure, when analyzed by a Student’s t-test a t the 95% confidence level with eight degrees of freedom, indicate that both Zimmer and Simplex-P exhibit a higher fracture toughness in the simulated physiological environment. I n order t o determine whether the addition of barium sulfate to these cements compromises the fracture toughness, the above described testing rationale was repeated, indicating the existence of a complicated relationship between the different testing environments and barium sulfate. The importance of these results lies in the fact that an increased fracture toughness indicates that a cement will inherently exhibit a greater degree of resistance to the propagation of cracks, which could contribute to the ultimate failure of the total joint replacement.
BACKGROUND With the advent of monomer-polymer dough-molding techniques in 1938, poly(methy1 methacrylate) materials enjoyed widespread *Present address: Ralph Parsons Co., Inc., Pasadena, California 91124. **To whom all correspondence should be addressed. 805 @ 1976 by John Wiley & Sons, Inc.
806
FREITAG AND CANNON
use in the fabrication of dentures. Consequently, the development of technology relating to suitable polymerization systems and their manipulation made possible the utilization of these polymeric materials in many other in vivo and ex vivo prosthetic devices.' Favorable dental and medical experiences with a number of these devices in varying applications probably indicated the implementation of acrylics as a fixation medium for certain orthopedic implants, especially the femoral component of the total hip replacement.2-1° Although this latter idea of a total hip prosthesis was not recent (indeed, it had been proposed as early as 189011), the clinical efficacy of these procedures prior to the appearance of acrylic cements was not encouraging. The basic problem was one of preventing slippage between the femoral stem of the prosthesis and the medullary canal, the exception being with younger patients using a Moore-type prosthesis.12 Since the majority of all implant candidates are over 60 years old, the typical femur encountered has a thin cortex and spacious medullary canal. It has been with these cases that a truly significant improvement in prognosis has been manifested. One primary reason for this success is that the cement modifies the prosthesis-biologic interface; i.e., a continuous bridging is afforded which is important technically in that the distribution of stresses transmitted between prosthesis and bone is made more uniform and continuous. Prior to this procedure, stress concentrations on the order of 3500 psi had been estimated to exist under certain circumstance~.~ Such a situation was undesirable from the standpoints of possible aggravation of bone resorption and permanent deformation of bone (a viscoelastic material) which both lead to the foreshortening of prosthesis utility. The metallic femoral component, acrylic cement, and bone have been modeled by McNeice13 as a composite structure (Fig. 1). When no slippage occurs between the interfaces of the components of this structure, a uniform transferral of stress between metal prosthesis and bone exists. However, if relative motion occurs between the components of the composite structure, the stress distribution changes radically, and the tensile stresses in the cement can increase from about 1000 psi to as much as 3000 psi.13 This may be problematical in that it is possible that high tensile stresses can initiate cracks in the acrylic component which cause loosening of the metal prosthesis and, ultimately, failure of the metallic stem.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
807
Fig. 1. Composite structure modeled by McNeice and Am~tutz.1~
Clinical studies preformed by the Division of Orthopedics at the UCLA School of Medicine have indicated that cement cracking is intimately involved in the loosening and subsequent failure of metal pros these^.'^ As cracks initiate and propagate through the acrylic, the metal prosthesis loosens, thereby promoting further crack growth in the acrylic as well as high stresses in the metallic stem. It has been postulated that prostheses failures in vivo are due to these high stresses which cause crack initiation which, in turn, leads to the eventual failure of the stem. It is possible that the likelihood of stem failure can be accentuated by cyclic loading or fatigue. The cyclic nature of loading on the prosthetic hip joint, e.g., walking, could promote increased crack growth in the acrylic resulting in an increase in the rate of loosening of the metal prosthesis. The previous discussion indicates the importance of the role of the acrylic cement in the composite structure. Clearly, if the life of
808
FIZEITAG AND CANNON
the prosthetic joint is to be maximized, the mechanical properties of the acrylic cement must be characterized. Therefore, this twopart investigation is concerned with the characterization of the fracture toughness and the fatigue behavior of acrylic bone cements: results and conclusions of the fracture toughness studies will comprise this paper, while the fatigue results will appear in a sequel.
THEORETICAL The independent variables selected in this investigation were the fabrication pressure, additive content, and testing environment. Fabrication pressure was chosen as a n independent variable because preliminary investigations showed that fabrication pressure has an effect on mechanical properties as well as on porosity of the coldcuring acrylics. Additive content was chosen as a variable because
Fig. 2. Mode I-type loading.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
809
one of the cements is available commercially with differing contents of BaS04and the possibility that the addition of BaS04may unduly compromise the fracture characteristics of the cement. Two testing environments were selected because of the desirability of testing in a simulated physiological environment, viz., bovine serum a t 37"C, in addition to the convenience of testing in air a t ambient temperature as a control. The dependent variable in this study is fracture toughness. Fracture toughness, or the critical stress-intensity factor as it is sometimes called, is usually denoted by Kr,. The I refers t o the type of loading (cf. Fig. 2), and the c denotes a critical value. Thus, when the stress-intensity factor K I equals the fracture toughness KI,, a crack will grow until the material fails. The importance of studying this dependent variable lies in the fact that knowledge of the fracture toughness will give a n indication of the propensity of the bone cement to resist crack growth and thereby obviate all the aforementioned problems attendant t o cement cracking. The determination of fracture toughness values for acrylic bone cements involves an assumption that is commonly made for metals, but must be carefully considered for polymeric materials. It is assumed that deformation in these polymers follows Hooke's law. As can be seen in Figure 3,14 poly(methy1 methacrylate) (PMMA) exhibits a linear stress-strain relationship over a wide range of
10
20
30
ELONGATION, PERCENT
Fig. 3. Stress-strain relationships for different temperatures (from Alfrey").
FREITAG AND CANNON
810
strain. This is important in that PMMA is a primary ingredient in both Simplex-P and Zimmer acrylic bone cements, and the temperature and range of stress levels in this study are well within the linear region of Figure 3, as will be verified later. Additionally, a number of other workers15-1s have assumed with reasonable success t h a t PMMA behaves in a linear elastic fashion. For a linear elastic solid, Griffith’s worklg was one of the first which predicted a failure stress due t o the presence of a flaw. It was noted that the increase of potential energy due t o the surface tension of the crack (later called surface energy) must be balanced by the decrease in the potential of the strain energy and the applied forces.z0 Griffith found that eq. ( 1 ) is satisfactory for plane strain in a linear elastic material.Z0
where u is the far-field stress at failure with the presence of a flaw of size 2a, E is Young’s modulus, Y is Poisson’s ratio, and y is the surface energy associated with the crack faces. Setting GI = 27 (2) and recallingz1 KI = dEGI(1-3 (3) then substituting into eq. (1) leads t o eq. (4). Kr
(4)
= afia
Equation (4) is the expression for the stress-intensity factor in a n infinite plate with a crack of length 2a (plane strain conditions). A more general form of eq. (4)is K I = Y2/Z (5) where Y is a geometric correction factor that includes the stress term. If a crack is introduced into a standard Charpy bar (cf. Fig. 4) and the Charpy bar subjected to three-point bend loading, then according t o Brown and Srawley,22
Y
=
=Bw2 (1.93
-
3.07
- 25.11
(-:>”
+ 25.8 (t)4) (6)
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
-
.800
8 .00+
L
" l . 0 0 1 R
I
I
811
"TIT+ w!!
2.165-----(
k . 3 ; d
where B is the thickness, zu is the width, and M is the moment at the crack. By testing Charpy bars to failure in three-point bending, the condition ( K I = Kr,) can be determined for the material being tested.
MATERIAL ACQUISITION AND PREPARATION Two types of cold-curing acrylic bone cement and some acrylic sheet were obtained for the research program. Zimmer bone cement consists of 90 wt yo PMMA and 10 wt yo BaS04. Simplex-P bone cement consists of 15 wt Yo PMMA, 75 wt % of the methacrylatestyrene copolymer, and 10 wt yoBaS04. I n addition, the Simplex-P and Zimmer cements were obtained without the BaSOr, which is added to impart radiopacity t o the cement. The acrylic sheet, Plexiglas I1 UVA, was manufactured by Rohm and Haas and used for a control in the experimentation. A number of parameters must be controlled during the mixing and subsequent implantation of acrylic cements. Figure 5 depicts the temperature history of a polymerizing acrylic rna~s.2~Briefly, liquid PMMA monomer is added and mixed with powdered PMMA polymer, the ratio being 1 m1/2 g on a weight basis. After a time, the polymerizing material becomes dough-like in that it may be kneaded or worked by hand for 8-10 min after initial mixing, a t which point the material "sets up'' into a rigid, brittle mass. As indicated by Figure 5, the polymerization reaction is exothermic, and the setting time is arbitrarily designated as the time corresponding t o the point a t which the temperature of the dough is midway between the mixing (ambient) temperature and the maximum
FREITAG AND CANNON
812
I (TmW
I&
a
+
AMBIENT)
a ? i w n
5k
WORKING TIME BEGIN MIX
TIME
Fig. 5. Schematic graph showing exothermic temperature changes occurring in acrylic cements during the polymerization process (from Meyer e t al.23).
temperature achieved. The working time is obviously the interval between dough and set time. After dough time, the cement was inserted into a mold (Fig. 6) and pressure was applied for 15 min. The rationale for the application of pressure was that the porosity caused by mixing and evaporation of monomer could be controlled to some extent by applying fabrication pressures of 5, 25, and 50 psi on the acrylic cement while it was polymerizing in the mold. Aftter 15 min, samples were removed from the mold and machined into Charpy bars (cf. Fig. 4).
EXPERIMENTAL The experimental procedure was conceived according to a factorial experimental design (Table I), which allows the determination of TABLE I Factorial Experimental Design Layout Factors
Levels
Environment
2
Fabrication Pressure
3
BaS04 Concentration
2
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
813
Fig. 6. Charpy bar mold.
effects due to specific factors and facilitates an orderly presentation of data.24 Fracture toughness was measured by means of Charpy bars (cf. Fig. 4), tested in an Instron testing machine in three-point bending a t a crosshead rate of 0.2 in./min. Due to the difficulty of producing an even crack front by either fatigue precracking or precracking with a razor blade, a cutter was utilized and the machined notch had a root radius of 0.0015 in. To verify that a root radius of 0.0015 in. was small enough to give a valid value of fracture toughness,* Charpy bars were machined from Plexiglas I1 UVA to serve as a control. Fracture toughness Kr, values were calculated via eqs. ( 5 ) and (6) and then compared with values of Kre calculated from literature data25(Table 11). Since this comparison indicated close agreement between experimental data versus K r , values calculated from literature data the proposed rationale ‘for obtaining fracture toughness values was deemed acceptable. Fracture toughness specimens were tested in two environments: bovine serum *No ASTM specification exists for fracture toughness testing of polymeric materials.
FIZEITAG AN11 CANNON
814
TABLE I1 Comparison of Control and Literature ValuesZ6 of Fracture Toughness . ~ i t e r a t u r epsi
-
I r w i n and Kies Berry
Jm. 1319.0 889.9
Vanden Boogaert
1143.0
Benbow and Roesler
1392.9
Benbow
1289.6
Berry
744.5
Broutman and McGary
689.3
Gurney
1989.8
AVERAGE
1182.3
Control psi
- J;T;I
Plexiglas I1 UVA AVERAGE
1150
(purchased from Miles Labs.) atJ37 f 2°C and air at ambient (22OC) temperature.
RESULTS Some fracture toughness results are shown in Figures 7 and 8 and in the Appendix, while others, analyzed by means of a Student’s t-test, are displayed in Tables 111-XV. The t values entered therein are a result of a Student’s t-test comparison of the fracture toughness values calculated from samples tested under the listed conditions in the tables. For example, in Table 111, testing environment (in this case, air a t ambient temperature) and additive content (10.0 wt yo B a s 0 3 are held constant, and the fracture toughness values for the two brands of cement, viz., Simplex-P and Zimmer, are compared. Table VII shows the t values resulting from the comparison of fracture toughness results at different additive concentrations of BaS04 in Simplex-P cement. The environment, air a t ambient temperature, was held constant for tests at each additive concentration. The starred entries in the tables indicate significant differences at different confidence levels: one star denotes a significant difference at the 90% confidence level, two stars denote a significant difference a t the 95% confidence level, three stars a significant difference at the
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
815
98% confidence level, and four stars indicate a significant difference a t the 99% confidence level (cf. Table XVI). The confidence level of the significant differences was determined by comparing the calculated entries in Tables 111-XV to a tabular t value. For eight degrees of freedom, the tabular t values of interest to this study are listed in Table XVI.26
12
N
b
-
10
IIi;, / a -
-
zu6
I
4
I
12
?2
10
-
J
a -
I
.-
a 0
2-
6
-
4 '
'
I
816
FREITAG AND CANNON
TABLE 111 Student’s &Tests Comparing K I , Data from Simplex-P and Zimmer Bone Cements with 10.0% BaSOl Tested in Air a t Ambient Temperature Zimmer Cement F a b r i c a t i o n Pressure
5 psi KIc
0)
941
25 p s i 1016
50 p s i
960
C , L
c
a
0E) v m I
5 psi
799
:.
25 p s i
959
E ;
50 psi
942
J L
n
A
2.65** -
c
w e -a 4o .r
1.55 0.58
m
Note: Underlined t values denote a higher fract,ure toughness a t a confidence level of a t least 90% for Zimmer cement. See Table XVI for definitions of confidence levels.
can be seen from a comparison of Figures 7 and 8, the fracture toughness of Zimmer cement a t 5 psi fabrication pressure is higher than the fracture toughness of Simplex-P cement under the same conditions. Table 111 shows that there is a significant difference a t the 95y0 confidence level between the two cements when fabricated a t 5 psi. A comparison of Figures 7 and 8 also shows that as the fabrication pressure increases the difference between the two cements decreases. Table I11 shows that there are no significant differences between the two cements for fabrication pressures of 25 psi or 50 psi. The superior fracture toughness of Zimmer cement over Simplex-P cement a t 5 psi fabrication pressure could be a result of Zimmer, a homopolymer, being able t o achieve a greater degree of ordering under a smaller amount of fabrication pressure than Simplex-P, which is a randomly polymerized copolymer. The more stereoregular nature of Zimmer as compared t o Simplex-P would permit the greater degree of ordering, thus accounting for the difference in fracture toughness. Evidently, the difference in fracture toughness disappears because a n increase in fabrication pressure will have little additional effect on the ordering of Zimmer cement.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
817
TABLE I V Student’s &Tests Comparing K I , Data for Simplex-P and Zimmer Bone Cements with 10.0% BaS04 Tested in Bovine Serum a t 37°C Ziner
Cement
F a b r i c a t i o n Pressure
KPc
+ It e 3
$
V
n
-
n
. E r
5 psi
1019
25 p s i
1045
50 p s i
1265
L L
5 psi
25 p s i
50 p s i
1150
1294
1215
4.22** -
s
5
m
8.1 O****
v
. L r
2
.68
LL
b
Note: See footnote of Table 111. Also, see Table XVI for definitions of confidence levels.
Similar effects are noted when the fracture toughness testing is done in bovine serum a t 37°C (cf. Table IV). Table I V shows that Zimmer cement has superior fracture toughness a t fabrication pressures of 5 psi and 25 psi, the former a t the 98% confidence level and the latter a t the 99% confidence level. Again, the fabrication pressure effect is not noticeable a t 50 psi. (Fracture toughness values are listed in the Appendix.) Conversely, if the BaS04 is not present in either cement, Zimmer has a higher fracture toughness that Simplex-P for all fabrication pressures for tests in each environment (cf. Tables V and VI). Also, the absence of BaS04 increases the fracture toughness of Zimmer cement when compared to SimplexP cement. t Values for the comparison of fracture toughness of Simplex-P cement are listed in Table VII, while t values for the same comparisons for Zimmer cement are listed in Table VIII. The presence of BaS04 apparently reduces the fracture toughness. Table VII indicates that Simplex-P with 0.0 wt yo BaS04 has a higher fracture toughness at the 5 psi fabrication pressure with a confidence level
818
FREITAG ANT) CANNON
TABLE V Student's &Tests Comparing K I ,Data from Simplex-P and Zimmer Bone Cements with 0.0% BaS04 Tested in Air a t Ambient Temperature
KIc
w +
J
1126
1087
1147
3
c v l
w v I
O aE
v 5
-A
2o
.$
'G
w
n
5 psi
948
25 p s i
959
50 p s i
926
****
4.46
E
m
u
v ) n m LL
****
4.34
9.58****
Note: See footnote of Table 111. Also, see Table XVI for definitions of confidence levels.
TABLE VI Student's &Tests Comparing K I , Data from Simplex-P and Zimmer Bone Cements with 0.0% BaS04 Tested in Bovine Serum a t 37°C Zinuner Cement F a b r i c a t i o n Pressure 5 psi
KIc
1200
25 p s i
50 p s i
1235
1167
W C C ,ZLi
wvl
"5:2
5 psi
957
25 p s i
943
50 p s i
1037
6.12
****
a c x1 'r 0
5%
6.38
****
n u E. Lr
mz .r
3.50
****
LL
Note: See footnote to Table 111. Also, see Table XVI for definitions of confidence levels.
FILACTURE CHARACTERISTICS OF BONE CEMENTS. I
819
TABLE VII Student’s &Tests Comparing K I , Data from Simplex-P Bone Cement with 0.0% and 10.0% concentrations of BaS04 Tested in Air a t Ambient Temperature Simplex-P
Cement 10.0% BaSOq
Fabrication Pressure
d v) 0
m
=
w
9 %
o
w
+Ca JL
f ’.-=
v
5 psi
o
b
n
25 psi
m
A 2 a J L
~n
nlu
.in
50 D s i
ELL
Note: The underlined t value denotes a higher fracture toughness a t a confidence level of a t least 90% for Simplex-P with 0.0% BaS04. See Table XVI for definitions of confidence levels. TABLE VIII Student’s &Tests Comparing K I , Data from Zimmer Bone Cement with 0.0% and 10.0% Concentrations of BaS04 Tested in Air At Ambient Temperature
am wr m
w
KI c
a
w In
94 1
1016
960
?o En 5 psi
1126
‘t n
25 p s i
1087
ELL
50 psi
1147
g
i% v L c
N
v
4.80
**** 2.08
*
I
5.56
****
82 0
FREITAG AND CANNON
of 95%, but there is no significant difference at the other fabrication pressures. Comparatively (cf. Table VIII), Zimmer cement has superior fracture toughness for all fabrication pressures when it contains no BaS04. These reductions could occur because of insufficient polymer bonding to the BaS04 powder, or the BaS04 might inhibit ordering. A more pronounced effect of BaS04 on Zimmer cement, as compared to Simplex-P cement, can be seen by a comparison of Tables I11 and V and by recalling the results of Tables VII and VIII. The increase of fracture toughness due to the removal of BaS04 from Zimmer cement (cf. Table VIII), and the comparatively small change in fracture toughness due to the removal of BaS04 from Simplex-P cement suggest that the BaS04 may interfere with the order of the polymer, i.e., since Simplex-P orders less, the addition of BaS04 affects it less, while for Zimmer, BaS04 interferes more noticeably with the ordering at all fabrication pressures. A comparison of Tables I11 and V shows that for 10.0 wt yo BaS04, the fracture toughness of Zimmer cement is superior only at the 5 psi level (cf. Table 111), but for the 0.0 wt yo BaS04 the fracture toughness of Zimmer cement is superior to Simplex-P cement at all fabrication pressures (cf. Table V). Clearly, 10.0 wt Yo BaS04 has a more detrimental effect on the cement that has the greater tendency to order. BaS04 shows evidence of interacting with testing environment, which can be seen by comparing Table VII and I X and by comparing Tables VIII and X. For Simplex-P cement, Table VII shows a significant difference at 5 psi fabrication pressure for tests conducted in air at ambient temperature, and Table IX shows significant differences at 25 psi and 50 psi fabrication pressures for tests conducted in bovine serum at 37°C. For Zimmer cement, Table VIII shows significant differences at all fabrication pressures for tests in air at ambient temperature, whereas, Table X shows a significant difference only at 5 psi fabrication pressure for tests in bovine serum a t 37°C. These comparisons show the significant differencethat exists between different BaS04concentrations depends on the environment in which the cements were tested. Holding the other independent variables constant, the two testing environments can have different effects on the two bone cements.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
821
TABLE I X Student’s &Tests Comparing K I , Da.ta from Simplex-P Bone Cement with 0.0% and 10.0% Concentrations of BaS04 Tested in Bovine Serum a t 37°C Simplex-P Cement 10.0% BaS04 Fabrication Pressure 5 psi -t 0 Ln
KIc
m
H a LJ O . s m m
5 psi
o
957
I I
25 psi
1019
I
1.27
I
50 psi
1045
1265
W a J
E J lLL a
5 oc
v
25 psi
.r
! a m
&
2
3.33***
50 psi
a J L
n n m ELL wl
.r
Note: Underlined t values denote a higher fracture toughness at a confidence level of a t least 90% for Simplex-P with 10.0% BaS04. See Table XVI for definitions of confidence levels. TABLE X Student’s &Tests Comparing Krc Data from Zimmer Bone Cement with 0.0% and 10.0% Concentrations of BaSOl Tested in Bovine Serum a t 37°C Zimmer Cement 10.0% BaSOq Fabrication Pressure 5 psi
25 psi
5 0 psi
Note: See footnote of Table VIII. Also, see Table XVI for definitions of confidence levels.
FREITAG AND CANNON
822
Table X I Student’s &Tests Comparing Krc Data from Simplex-P Bone Cement with 10.0% BaS04 Tested in Air a t Ambient Temperature and in Bovine Serum a t 37°C Simplex-P
Tested
i n Bovine Serum a t 37°C
Fabrication Pressure
5 psi
25 p s i
50 p s i
5 psi 25 p s i 50 p s i
Note: Underlined t values denote a higher fracture toughness a t a confidence level a t of a t least 90% for tests run in bovine serum a t 37°C. See Table XVI for definitions of confidence levels.
Table XI shows that the fracture toughness of Simplex-P cement is greater when tested in bovine serum at 37°C than when the same material is tested in air at ambient temperature. In comparison, results from tests in the two environments show little difference for Simplex-P containing 0.0 w t yo BaS04, except at the 50 psi fabrication level (cf. Table XII). In contrast, Table XI11 indicates that Zimmer cement, containing 10.0 wt yo BaSOr and tested in bovine serum a t 3 7 T , has a higher fracture toughness than the same cement when tested in air at ambient temperature. If the BaS04 is not present in Zimmer cement, the higher fracture toughness values were found from tests in bovine serum for fabrication pressures of 5 psi and 25 psi, while there is no significant difference between fracture toughness values obtanied from tests in the two environments at 50 psi fabrication pressure. However, in general, bovine serum at 37°C was found to increase the fracture toughness for all concentrations of BaS04, as well as for each brand of cement. The suggestion is made that the bovine serum at the crack tip could act as a plasticiz-
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
823
Table XI1 Student's t-Tests Comparing K I . Data from Simplex-P Bone Cement with 0.0% BaSOn Tested in Air a t Ambient Temperature and in Bovine Serum at 37°C Simplex-P
Tested i n Bovine Serum a t 37°C F a b r i c a t i o n Pressure
r
L .r
4
C
L
.r
v) x
KIc
957
943
1037
U v )
w
w
C m1 a L
0 I - =
5 psi
948
25 p s i
959
50 p s i
926
0.20
.r
4J
7x 2 W
0.45
.r
L
- n a E
.r
m L
4.55****
v)
TALBE XI11 Student's t-Tests Comparing K I . Data from Zimmer Bone Cement with 10.0% BaSO. Tested in Air at Ambient Temperature and in Bovine Serum a t 37°C Zimner
Tested i n Bovine Serum a t 37°C F a b r i c a t i o n Pressure
5 psi L 4
.-
KI c
w L
1150
25 p s i 1294
50 p s i 1215
c vv))
'r
F ,$'
5 psi
941
25 p s i
1016
50 p s i
960
6.39****
c, v )0 0 c I-
m
.r N
7.66**** 5.62****
LL
Note: See footnote of Table XI. Also, see Table XVI for definitions of confidence levels.
FREITAG AND CANNON
824
ing agent, thereby increasing fracture toughness, or the bovine serum could simply act as a protective agent in that i t acts to sequester the specimens from air, a more aggressive environment. I n addition t o the previously discussed comparisons, the fracture toughness results in air at ambient temperature and for each cement a t each concentration of BaS04were compared t o fracture toughness results obtained from tests on the control, Plexiglas I1 UVA (cf. Table XV and Figs. 7 and 8). As can be seen from Table XV, the significant differences were at the 99% confidence level for all comparisons except the comparison between Plexiglas I1 UVA and Zimmer cement without BaS04, where there was no significant difference a t the 5 and 50 psi fabrication pressures. This is puzzling because it would be expected that no significant difference should exist at 25 psi either, but such was not the case.
CONCLUSIONS 1) Specimens tested in bovine serum a t 37°C exhibited increased fracture toughness over those tested in air a t ambient temperature. TABLE XIV Student’s &Tests Comparing Kz, Data from Zimmer Bone Cement with 0.0% BaS04 Tested in Air a t Ambient Temperature arid in Bovine Serum a t 37°C Zimmer Tested i n Bovine Serum a t 37°C F a b r i c a t i o n Pressure
KIc
1200
5 psi
1126
Z.T8*
25 p s i
1087
50 p s i
1147
L . 4r
1235
1167
(u L
. T r YYI I
f
~
a J L + Y I E
2
3.42****
m U
f$ .r
0.55
u
N
Note: See footnote of Table XI. Also, see Table XVI for definitions of confidence levels.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
825
TABLE XV Student’s t-Tests Comparing Kr. Data from Plexiglas I1 UVA with Zimmer Containing 10.0% BaS04, Zimmer Containing 0.0% BaS04, Simplex-P Containing 10.0% BaS04,and Simplex-P Containing 0.0% BaS04,in Air a t Ambient Temperature F a b r i c a t i o n Pressures 5 psi
50 p s i
25 p s i
Zimmer
10.0% BaS04
5.819***
=****
3.540****
Zimner
0.0% BaS04
0.673
2.062*
0.067
Simplex-P
10.0% BaS04
6.898****
5.853****
6.950****
Simplex-P
0.0 BaS04
5.393****
6.094****
9.360***
Note: Underlined t values denote a higher fracture toughness a t a confidence level of at least 90% for Plexiglas I1 UVA. See Table XVI for definitions of confidence levels.
TABLE XVI Tabular t Values for Eight Degrees of Freedom for 90-99% Confidence Levels Confidence L i m i t
Designation i n Tables 111 xv
-
t.lO,
8
90%
*
t.05,
8
95%
**
t.02, 8
98%
***
t.O1,
99%
****
8
FREITAG AND CANNON
826
2) BaS04 reacts with the bovine serum environment when i t is present in both Zimmer and Simplex-P acrylic bone cements; i.e., fracture toughness of the specimens increases. 3) When fabricated a t 5 psi, Zimmer acrylic bone cement shows superior fracture toughness for all additive concentrations and environments when compared t o Simplex-P acrylic bone cement. It is hypothesized that Zimmer’s superior properties are due either t o polymer chain ordering or t o the possibility that the methacrylatestyrene copolymer in Simplex-P exhibits a n inherently lower K I , value.
APPENDIX Fracture Toughness Values*
Fabrication Pressure (psi)
+
Cement wt yoBaSOl
KI Test Environment Bovine Air Serum -
~-
5 25 50 5 25 50 5 25 50 5 25 50
Simplex-P, 10.Oyo BaS04 Simplex-P, 10.0% BaS04 Simplex-P, 10.Oyo BaS04 Simplex-P, 0.0% BaS04 Simplex-P, 0. OY0BaS04 Simplex-P, 0.0% BaS04 Zimmer, 10.O~oBaS04 Zimmer, 10.0% BaS04 Zimmer, 10.Oyo BaS04 Zimmer, 0.0% BaS04 Zimmer, 0.0% BaS04 Zimmer, 0.0% BaS04 Plexiglas I1 UVA
799 959 942 948 959 926 941 1016 960 1126 1087 1147 1150
-
1019 1045 1265 957 943 1037 1150 1294 1215 1200 1235 1167
Fracture Toughness Calculation A fracture toughness calculation for a Zimmer specimen containing 0.0% BaS04 and fabricated a t 5 psi is presented below. The following quantities were measured from the Charpy bar specimen : *The values represent the average of five replicates.
FRACTURE CHARACTERISTICS OF BONE CEMENTS. I
827
Thickness: B = .395 in. Width: W = .394 in. Crack length: a = . l o 0 in. a/W = .254in. The following quantity was measured by noting the load necessary t o break a specimen in three-point bending. Prrgture
=
50 1b
From the Introduction:
Kr, = Y d i Y
=
E[1.93 BW2
- 3.07 - 25.11
(+y
+ 25.8 (G)~]
To calculate M , the moment at the notch:
M
Krc =
=
.800
P / 2 = .400 P
6(.400) 50 [1.93 - 3.07 (.254)
( .395) ( .394)2
+ 14.53 (.254)2
1
- 25.11 (.2M)3 + 25.8 (.254)4 dm KIc = 1106psi -
dz
This study was conducted under the auspices of the National Institutes'of Health, contract number NIH I A AM-16120. The authors wish to thank Dr. Harlan C. Amstutz and his UCLA research team for their interest and assistance, Howmedica Inc., for the donation of Simplex-P cement, and Messrs. Heinz Blessing and David Anuda, and Zimmer USA Inc., for the donation of Zimmer cement.
828
FREITAG AND CANNON
References 1. D. C. Smith, J. Biomed. Muter. Res. S y m p . No. 1, 189 (1971). 2. S. Kiaer, in Proc. Cinquieme Congres International de Chirugie Orthopedique, Stockholm, 1961, Bruxelles Imprimerie Lielens, 1953. 3. E. J. Habonsh, Bull. Hosp. J . Dis., 14, 242 (1953). 4. E. Henrickson, K. Jansen, and W. Krough-Poulsen, Acta Orthop. Scand., 22. 141 (1952). 5. W. T. Spence, J . Neurosurg., 11, 219 (1954). 6. L. L. Wiltse, R. H. Hale, and J. C. Stenehjern, J. Bone Joint Surg., 39A, 961 (1957). 7. J. Charnley, J . Bone Joint Surg., 42B. 28 (1960). 8. J. Charnley, J . Bone Joint Surg., 46B. 518 (1964). 9. N. R. Crozzoli, Minerva Ortop., 16, 399 (1965). 10. N. R. Crozzoli, Minerva Ortop., 16,395 (1965). 11. J. T. Scales, J . Bone Joint Surg., 50B, 698 (1968). 12. F. M. Follacci and J. Charnley, Clin. Orthop. Rel. Res., 62, 156 (1969). 13. G. M. McNeice and H. C. Amstutz, Proceedings of the 6th International Congress of Biomechanics, University of Jyvaskyla, June 1975. 14. T. Alfrey, Jr., Mechanical Behavior of High Polymers, Interscience, New York, 1948, p. 516. 15. I. Constable, L. E. Culver, and J. G. Williams, Int. J . Fract. Mech., 6, 279 (1970). 16. B. Mukherjee and L). J. Burns, Eng. Fract. Mech., 4, 675 (1972). 17. J. Constable, J. G. Williams, and D. J. Burns, J. Mech. Eng. Sci., 12, 20 (1970). 18. S. Arad, J. C. Radon, and L. E. Culver, paper presented a t the International Congress on Fracture, Munich, Germany, 1973. 19. A. A. Griffith, Phil. Trans. Roy. Soc. (London),A221, 163 (1921). 20. A. A. Griffith, in Proceedings of the International Congress for Applied Mechanics, Delft, 1924, pp. 55-63. 21. D. Broek, Elementary Engineering Fracture Mechanics, Noorhoff International Publishing Company, Leyden, 1974, p. 17. 22. W. F. Brown and J. E. Srawley, ASTM STP No. 410, p. 13. 23. P. R. Meyer, Jr., e t al., J. Bone Joint Surg., 55A, 149 (1973). 24. C. R. Hicks, Fundamental Concepts in the L)esign of Experiments, Holt, Rinehart and Winston, New York, 1964. 25. J. P. Berry, in Fracture, H. Liebowitz, Ed., Academic Press, New York, 1972. 26. W. Volk, Applied Statistics for Engineers, McGraw-Hill, New York, 1958, pp. 98-135.
Received November 3, 1975 Revised December 30, 1975
