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Effect of zinc on strength and fatigue resistance of amalgam
Dent Mater 11:24-33, January, 1995
Effect of zinc on strength and fatigue resistance of amalgam John H. Watkins’, Hiroshi Nakajima’, Koji Hanaoka”, Leanna Zhaol, Tsugio Iwamoto2, Toru Okabe’
‘Department of Biomaterials Science, Baylor College of‘Dentistr.v, Dallas, Texas, lJSA 2Department of’Operative Dentistry, Kanagawa Dental College, Kanagaula, JAPAN
ABSTRACT Objectives. This study was conducted to determine the effect of zinc in amalgam on the static mechanical properties and resistance to fatiguecrack propagation of amalgams. Methods. Fatigue, creep, compressive and flexure tests were performed on high-Cu Dispersalloy (Johnson and Johnson Dental Products Co., East Windsor, NJ, USA) and low-Cu Velvalloy (S.S. White Dental Products Int., Philadelphia, PA, USA) in both Zn-containing and Zn-free formulations. Linear Elastic Fracture Mechanics principles were used to characterize the fatigue behavior (crack lengths were monitored). Results. The incorporation of Zn into these amalgams significantly improved their fatigue and creep resistance, while the effect of Zn on the static compressive and flexure strengths was not consistent. Zn significantly increased (p < 0.05) the resistance to fatigue crack propagation during Stage It crack growth for both amalgams, and increased the variations in crack velocity for a given stress intensity difference. without visibly altering the path or nature of the fatigue cracks. Possible influences on fatigue behavior were the mixed microstructure (particles and matrix), the nature of the crack tip, and creep. Significance. The superior resistance to tensile fatigue crack propagation of amalgams containing small amounts of Zn (-1 wt%) in vitro compared with amalgams with no Zn correlated with the superior resistance to marginal breakdown in viva of Zn-containing amalgams. The range of stress intensities over which stable cracks could propagate was small, while the large variations observed in fatigue crack growth rates for individual materials invalidate predicting a unique fatigue life from the empirical equations obtained.
INTRODUCTION The presence of Zn in amalgam is considered to have an important influence on the physical, mechanical and electrochemical properties of amalgams (Johnson and Ptienbarger, 1980). In clinical studies, Zn-containing amalgam restorations have revealed superior resistance to marginal breakdown compared to Zn-free amalgam restorations (Wilson and Ryge, 1963; Watson et al., 1973; Mahler et al., 1980; Berry et al.,
24 Watkins et a/./Effect of zinc on amalgam
1986; Osborne and Berry, 1992). However. there are no studies which have been able to link property changes induced by Zn in amalgams to the resistance to marginal breakdown. Many aspects of marginal breakdown remain unclear. particularly, the nature of the stresses which act on restorations in the oral cavity. Using a mechanical model of a restored tooth, Granath and Hiltcher (1970) predicted that tensile stresses would develop across the margin as a result of compressive loading of the edge of the tooth. By means of finite element modeling, Derand (1977) suggested that compressive stresses which develop at the margin could cause creep. With another finite element model, Goel et al. ( 1992 1 predicted tensile stresses in many locations in a restored tooth loaded in compression. Asaoka ( 1994) suggested creep as the controlling factor in marginal breakdown from another finite element simulation. Thus, the mechanical properties of amalgams which are likely to control the process of marginal breakdown cannot be reliably predicted from knowledge of‘ the stresses acting on amalgams. Through attempts to establish the controlling factoris j responsible for marginal breakdown, the microstructure, the mechanical properties and electrochemical properties of amalgams have been investigated. With regard to the microstructure, the distribution of Zn in amalgam has been studied by Jensen et al. (1976) who showed that Zn dissolved in the y: phase without altering the basic microstructure. Thus it appears that the observed changes in the physical properties are a result of fine scale microstructural changes. Investigatingthis in the transmission electron microscope, Boswell ( 1979 I discovered that the removal of Zn from the formulation of a high-copper amalgam seemed to introduce faulting in the microstructure. Since Mahleret aL.( 1975) found a good correlation between the creep value and the occurrence of marginal breakdown in low-copper amalgam restorations, creep resistance has been the mechanical property which has shown the most promise for predicting the resistance of low-copper amalgams to
marginal breakdown. However, creep resistance is not a reliable indicator, as Gale and Osborne (1980) and Gale et al. (1982) were unsuccessful at making this correlation for high-copper amalgams. Additional factors must, therefore, be significant in the process of marginal breakdown of high69.6 17.7 11.8 0.67 M copper amalgam restorations. Dispersalloy Zn-Free 72.0' 17.0+ 11.0' 0.0' L Other mechanical properties such as the flexure and compressive strengths have not shown 2.75 0.93 M 15 45.3to.7 070287 a good correlation to marginal breakdown; this has led to investigations of the other more complex properties, such as the fatigue resistance (Wilkinson and Haack, 1958; Mahler and Van Eysden, 1969; Sutow et al., 1985; Zardiackas and Bayne, 1985; McCabe and Carrick, Co., East Windsor, NJ, USA). These amalgams were supplied 1987). These studies have concentrated on the compressive by each manufacturer in a Zn-containing and a Zn-free fatigue testing of amalgam but have not shown a conclusive link between marginal fracture and fatigue resistance. In such formulation; both formulations were tested (Table 1). Each amalgam alloy was triturated using an amalgamator experiments, the stress distributions generated within the wari Mix III, L. D. Caulk, Milford, DE, USA). T&nation cylindrical specimens are not simple, as evidenced by the conditions were chosen for each pair of amalgams to obtain a myriad of radial cracks found in some failed specimens (Sutow et al., 1985). Furthermore, in this type of experiment, it is similar residual Hg percentage (Table 1); these Hg levels were chosen to be similar to clinical restorations. The residual Hg difhcult to record the progression of the fatigue cracks. was calculated for all specimens used in each test from weight The tensile fatigue behavior of amalgams was investigated measurements of the condensed Hg. by Miyakuni (1981) who conducted three-point bending Creep and Compressive Strength Tests. Cylindrical fatigue tests on edge-notched beam-shaped specimens of specimens, 4 mm in diameter and 8 mm high, were prepared amalgam. This study was able to correlate increased fatigue resistance with copper content. In Miyakuni’s experiments, a according to the procedures outlined in ANSI/ADA notch was put under cyclic tensile loading under plane strain Specification No. 1 for dental amalgam alloys. The creep value conditions, i.e., the crack tip advanced under tri-axial tensile of each 7 d aged amalgam was determined by the method given in this same specification. The compressive strength of stress. 7 d aged amalgam specimens was tested using a universal Since the effect of tensile stresses across the tooth amalgam interface has been suggested as a factor in the testing machine (Instron 1125, Canton, MA, USA) with a process of marginal breakdown, fatigue experiments which crosshead speed of 0.25 mm/mm at room temperature. Three isolated the tensile stresses from compressive stresses might to five specimens of each amalgam were tested for both creep and compressive strength measurements. be more appropriate for establishing the importance of the fatigue resistance of amalgams to marginal breakdown. Thus, Transverse Rupture Strength Tests. Beam-shaped specithe present investigation uses Miyakuni’s method to find the mens of each amalgam were made since cylindrical specimens fatigue resistance of various amalgams. were inappropriate for transverse rupture strength and Linear Elastic Fracture Mechanics (LEFM) is used fatigue testing. After trituration, each amalgam was condensed extensively in materials science to characterize crack using a hydraulic condensing machine into a specially built initiation and propagation behavior in materials (Suresh, stainless steel mold 25 mm long, 3.4 mm wide and 2.4 mm 1991a). Crack growth rates are recorded against varying stress deep under a pressure of 14 MPa for 60 s. The specimens were intensity difference of the fatigue cycle @IQ (ASTM, 1991). then aged at 37 2 I% in air for 1 d and then trimmed and polished into a 2.0 mm x 3.0 mm x 25 mm size using#600 Sic LEFM permits the fatigue behavior of materials to be characabrasive paper under water. Each specimen was again aged terized with results that are independent of the specimen plaat37klCinair. nar geometry: a limitation of “strength!number-of-cycles-toThe transverse rupture strength of each 7 d aged specimen fracture” (S/N) fatigue data. Therefore, in these experiments, the instantaneous crack length was measured over a range of was determined by conducting a three-point bend test to failAK values, and the data analyzed by LEFM. ure at room temperature. Using the universal testing The objective of this study was to examine the effect of Zn machine at 0.25 mm/mm., the load was applied to the center of the 2 mm x 25 mm face of the specimen with support pins in amalgam on the static mechanical properties and fatigue 3 mm in diameter spaced at 16 mm. resistance of amalgams and to find a possible link between tensile fatigue resistance of amalgams and marginal The creep values and compressive and transverse rupture strengths were compared for the four amalgams using the breakdown. one-way ANOVA test and Scheffe’s test (SPSS for Windows, MATERIALS AND METHODS SPSS Inc., Chicago, IL, USA) at p = 0.05. Materials. Two amalgams were used in this study: a low-copper Fatigue Tests. Wee 7 d aged beam-shaped specimens lathe-cut amalgam (Velvalloy, S. S. White Dental Products (2 mm x 3 mm x 25 mm) of each amalgam were prepared Int., Philadelphia, PA, USA) and a high-copper admixed using the same procedure as described above for the transamalgam (Dispersalloy, Johnson & Johnson Dental Products verse rupture strength tests, with some additional machining
Dental Materials/January
1995
25
~~Tfj 3.0 mm
0.5 mm diam. holes Slot (0.3 mm x 1 34 mm)
Fig. 7. The geometry of the edge-notched beam specimens used in the fatigue tests. The cyclic load is applied directly above the notch while the support pins are below the beam and spaced 16 mm apart. The holes are used for the crack length monitoring circuits: refer to Fig. 2b.
(b)
Fig. 2. The fatigue testing apparatus: (a) the loading mechanism which applies a cyclic load to the specimen in three-point bending; and (b) crack length monitoring and load measurement circuits [inset of (a)]: (A) specimen; (B) pins 16 mm apart; (C) load cell; (D-J) load train driven by (K-L) motor-crank mechanism; (M) cycle counter; (N) polycarbonate box and constant heat source (0) maintains the specimen at 37 + 1%; (P) micro-switch terminates the test at specimen fracture; (Q) strain-gauge bridge for load cell; (R) constant current power supply; (S-T) voltmeter and data logger. 1). A”Tr’ -shaped notch 1.34 * 0.03 mm deep and 0.3 mm wide was cut perpendicular to the 2 mm x 25 mm face in the center of the beam using a diamond disk; no additional sharpening of the notch was undertaken so that study of the crack initiation process could be observed. In order to monitor the crack propagation by means of the electric potential crack monitoring technique (ASM Committee on Fatigue Crack Propagation, 19851, 0.5 mm pin holes were drilled inta both ends of the specimen and also both sides adjacent to the notch. Electrical wires from the monitoring equipment were glued (Fig.
26
Watkins et a/./Effect of zinc on amalgam
into these pin holes with conducting silver paint. All specimens were subjected to a 2 Hz tension/tension loading cycle in a three-point bending fatigue machine to put the notch under cyclic tensile stress (Fig. 2 ). The design of the fatigue test equipment was the same as that used by Miyakuni (1981). A load ratio, P,,,JF’,llllh, of 0.3 and a maximum load of 9.4 N forVelvalloy and 11.0 N for Dispersalloy were used. The cyclic frequency was chosen to simulate the approximate chewing frequency of humans, an important consideration in view of the strain rate sensitivity of amalgams (Espevik. 1977 I. Regarding the maximum load levels selected, the main requirement during these tests was to obtain steady fatigue crack propagation over a measurable crack length before tiacture. A balance was found between minimizing the load to avoid sudden fracture within a few cycles and maximizing the load to obtain the lowest measurable crack growth rates. i.c.. finding the approximate “endurance limit” or stress intensity threshold. All tests were conducted in air at 37 r 1°C. Tests were stopped either at 10”cycles (5.8 d) or at fracture. With each amalgam, three specimens were tested. Me~surcvwz t of’ Instantaneous Crack Lxgth. During testing, the advance of the crack was recorded by the ASM electric potential crack monitoring technique (Fig. 2b) rASM Committee on Fatigue Crack Propagation, 1985). This technique applies a constant direct current through the specimen via the electrodes attached to the ends of the: specimen (Et) and measures the potential difference across the fatigue crack via the electrodes adjacent to the crack (S!. Using the constant current reference circuit as the fatigue crack grows. the remaining cross-sectional area of the specimen decreases and the potential difference increases (from Ohm’s law 1. During these tests. the reference circuit was maintained at 0.9 A, and the specimen was isolated from the rest ofthe fatigue test equipment by insulating the load bearing pins t H) (Fig. 2 J, The crack length in t,he specimens was determined by comparing the potential increase to the reference potential using a calibration curve prepared prior to the experiment (Fig. 3 1. The relationship between the average crack length and the measured potential difference across the notch was determined as follows. Single edge-notched specimens of amalgam. identical t,o those used in the main experiments, werr subjected to fatigue loading. As the fatigue crack propagatid. when the potential difference reached a certain fraction of the initial potential, the test was terminated. Five specimens were tested which spanned the range of potential difrerences encountered in the main tests. Each specimen was subsequently fractured using the procedure described for the transverse r-upturc tests, but using a crosshead speed of 25 mm/min to promote “fast-fYacture” failure. The fi-acturcd surfaces were examined in the SEM and photographed at low magnification (48x) from a direction normal LOthe surface. The fatigue-fractured surface was characterized by its rough and undulating appearance compared to the smooth and flat fast-fractured surface. The fatigue crack length was measured in five evenly spaced locations across the width of the specimen, then averaged. An empirical relationship, Eq. I (Fig. 3), relating the measured crack length. a. to thr measured potential difference across the notch,V, was obtained by curve-fitting the data (Table-Curve, Handel Scientific, San Rafael, CA, USA, to the quadratic regression model described in the study by Miyakuni i 1981 J:
0.7
j
g 0.6 0” E I
I
go.5
-
m . C 3 Y m
t
supports
b
0.4 i 1.2 1.3 1.1 1.0 Normalized Potential across Crack, V / V, Fig, 3. The calibration curve used to estimate the instantaneous crack length, a, of a specimen under fatigue loading from the electric potential difference,V, measured across the fatigue crack. Each experimental data point was determined by partly fatiguing beam specimens (Fig. l), measuring the potential difference across the notch, than rapidly fracturing the specimen and averaging measurements of crack length (n.5) evenly spaced across the width of the crack. The data point in the bottom left corner of the graph corresponds to the reference potential difference, V,, and zero crack length (notch only).
+L’.h”
v (Ulz
+4.374
v (11
-2.228
where V is the initial potential across the notch (0.200 mv), h is the depth of the notch (-1.34 mm), and W is the width of the specimen (3.00 mm). The correlation of this relationship to the data was strong (9 = 0.982). Analysis of Fatigue Data by Fracture Mechanics. The principles of Linear Elastic Fracture Mechanics (LEFM) were used to characterize the fatigue behavior of the four amalgams. For LEFM to be valid for a given material and loading condition, the criterion of “small scale yielding” must be satisfied. Small scale yielding implies that all of the plastic deformation in the specimen is restricted to a narrow region ahead of the crack tip (Fig. 41, whereas the remainder of the specimen only experiences elastic deformation. In view of the well documented viscoelastic behavior of amalgams, i.e., creep (Hera, 1983; Okabe et al., 1985), stress relaxation (Papadogianniset al., 19871, etc., the conformity of amalgams to small-scale yielding was of some concern to the authors. However, the cycle frequency used was considerably faster than the visco-plastic response time of these amalgams, e.g., 0.5 s for one load cycle compared to the order of a minute for significant creep to occur. Furthermore, large-scale yielding is not expected because amalgams typically display low ductility under rapid loading conditions (Espevik, 1977). Thus, the assumption of LEFM appears to be justified. The crack length us. number of cycles (a us. N) data for each test was converted to the crack propagation rate us. the stress intensity dif%erence of the fatigue cycle (da/dN us. AK) data, where AK = K, - I(min.The stress intensities at the upper and lower limits of the fatigue cycle, &, K,i,, were calculated using the standard expression for an edge-notched beam in three-point bending (ASTM, 19831. Since it is impossible to
Fig. 4. The situation at the crack tip: under the far-field stress,a, a plastic zone will develop at the crack tip, the size of which depends on the crack and specimen geometries and the material parameters through Eqn (4). For plane strain, Eqn. (3) must be satisfied.
resolve cycle by cycle crack growth rates in this type of fatigue study,the standard methods used to analyze fatigue data (ASM Committee on Fatigue Crack Propagation, 1985) calculate average growth rates over many cycles (typically thousands). In this study, da/dN values were calculated for individual tests using the “Incremental Polynomial Method” (k = 51, a cubicpolynomial, least-squares-fit method. Crack growth behavior typically falls into three stages: I, crack initiation; II, stable growth; and III, rapid final growth (Suresh, 1991a). Paris and Erdogan (1963) proposed an empirical crack growth rate law for Stage II cracks:
$=C.(*Kp where C and m are empirical constants, obtained by curve-fitting the data (see next section). Calculations were made to ensure that the current experiments conformed to the plane strain condition, i.e., the minimum allowable beam depth, 2
trnin
>
2.5
L1
(3)
KIC
-
ay
where values of the fracture toughness, K,, were estimated from the literature (Espevik, 1980; Cruikshanks-Boyd and Lock, 1983) and the yield strength, o, , was measured in the present compressive strength tests. Therefore, the plane strain fracture toughness, Kit, of each specimen under fatigue conditions was estimated as the stress intensity at fracture. Continuing the assumptions of LEFM, the radius of the plastic zone at the crack tip, rp (Fig. 4), can be estimated from Irwin’s equation &win, 1960): (4)
which assumes monotonic tensile loading in plane strain. This equation is also valid for fatigue loading if the load is always tensile (Suresh, 1991b), hence was used in this study to
Dental Materials/January
1995
27
! Dispersalloy Dispersalloy Velvalloy
Zn-free
0.29 f 0.04 ’
422k 10
0.50 + 0.06 ~
344+16
1.85 + 0.20
325 f
77k17
j 7
61*8 103+
7
scanning electron microscope (JSM-35CF, JEOL, Peabody MA, USA). Both the fatigued region of the fracture surfaces and the final catastrophic fracture region (“fast fractured”) were inspected, as the characteristics in these regions were expected to be Merent. The aims of these observations were to link fracture mechanics data with microstructural features and to compare the material behavior under fatigue and sudden j( fracture conditions, Phase identifications were made based 1 on previous microstructural studies on amalgams (Mitchell 1 et al.. 1987). Since the Y, grain structure was largel>l undeformed in the fast fracture surfaces, the size range ofthe y, grains was estimated for each amalgam.
RESULTS estimate the largest plastic zone size at the maximum stress intensity of the fatigue cycles, K,,_ , as the crack propagated. Statistical Analysis of Fatigue Data. Simple linear regression methods were used to both fit the data from each test material to the equation for Stage II crack growth, Eq. 2, and to compare materials for significant differences. Since the crack velocities obtained in this study were average values, obtained by a least-squares-fit method of arbitrary order, not absolute values, these regression analyses were only used to compare materials in a semi-quantitative manner, particularly the rp values. First the fatigue crack propagation data were transformed to log(AK) us. log(daidN). Next, simple linear regression equations, i.e.,
were fitted to each data set, i.e., the combined data from each material, where the slope and intercept of the regression are equivalent to the exponent, m, and log of the constant, C, in Eq. 2. Correlation coefficients, % , and 95%) confidence bands were calculated for each regression line. Before analysis, the data for Stages I and III crack growth were removed by selecting approximate linear ranges of AK for each set of data. Regarding the number of specimens, the ASTM standard for fatigue testing of metals (ASTM, 19911 recommends that two tests are usually sufficient to characterize the fatigue behavior of a metal. They state that variations in crack velocity of up to + 50% are possible for each AK value and that larger variations may occur below crack velocities of lo-” mm/cycle. Three tests for each material were performed in the current experiments. In order to determine which of the amalgams had faster crack propagation than the others, statistical methods were used to compare pairs of simple linear regression equations (Zar, 1984). First, the two slopes were tested for significant differences (t-test using pooled statistics, p = 0.05). Ifthe slopes were not found to differ, then a common slope was computed for both regression equations, and then the intercepts were tested using a similar method (p = 0.05). If the intercepts were not significantly different, then both regression equations described the same population; otherwise, there were two populations, the one with the greater intercept having significantly faster crack propagation than the other Fractographic Obseruation. The surfaces of the amalgam specimens fractured in fatigue tests were observed using a 28 Watkins et a/./Effect of zinc on amalgam
Creep. ADA creep values of each amalgam are shown in Table 2. Low-copper amalgam Velvalloy, whether Zn-free or Zn-containing, revealed significantly higher (p < 0.05~ creep values than high-copper amalgam Dispersalloy. Creep values of Zn-containing Velvalloy were significantly lower (p < 0.05 ) than those of the Zn-free amalgam, while no significant difference (p < 0.05) was found between Dispersalloy with or without Zn. Static Strengths. The results from the compression and transverse rupture strength tests are shown in Table 2. The addition of Zn to Velvalloy significantly reduced (p < 0.05) the compressive strength, while the addition ofZn to Dispersalloy significantly increased (p < 0.05) the compressive strength. No sign&ant difference (p < 0.05 ) was found between Zn-free amalgams Velvalloy and Dispersalloy, but of the Zn-containing amalgams, Dispersalloy had significantly higher compressive strengths (p < 0.05) than Velvalloy The addition of Zn to Velvalloy significantly reduced (p < 0.05) the transverse rupture strength, while the addition of Zn to Dispersalloy did not significantly influence (p < 0.05 I the transverse rupture strength. No significant difference (p < 0.05) was found between Zn-containing amalgams Velvalloy and Dispersalloy, but of the Zn-free amalgams. Dispersalloy had significantly lower transverse rupture strengths (p < 0.05) than Velvalloy Fatigue Resistance. The change in crack velocity da/dN, with stress intensity difference, aK, for all tests is shown in Fig. 5a: higher crack velocity for the same stress intensity difference implies lower resistance to fatigue loading. Since cracks did not propagate to a measurable length (-5 urn J during 10”cycles in two of the Zn-containing Dispersalloy tests, the maximum load level was increased to 13.0 N for the last test (from 11.0 N); only data from this third test appears in Fig. 5. Low-copper amalgam Velvalloy appeared to exhibit crack initiation behavior, i.e., Stage I crack growth, whereas high-copper amalgam Dispersalloy did not. Note that the average crack velocities below lo-’ mm/cycle were not included, as the changes in crack length over many cycles were below the resolution of the test equipment. To simplify explanation of the statistical analyses, the logarithmically transformed crack propagation data (excluding crack initiation data) and the regression lines are shown in Fig. 5b; a summary of the regression analyses is given in Table 3. For Velvalloy with or without Zn, all data points in the interval 0.95
le-7
b 0.8
.
. 1.0
Stress Intensity
1.2 Difference,
(4
. I
1.4
I
1.6 1.8 AK (MPa.m”.5)
1
I
/
0.0
0.1
0.2 to9 (AK)
(W
Fig. 5. Change in the average fatigue crack growth rate, da/dN, with the increasing stress intensity difference of the fatigue cycle, AK, for &free and &-containing Velvalloy and Dispersalloy. Higher crack velocity for the same AK implies lower resistance to fatigue loading: (a) Raw data showing crack initiation in Velvalloy (AK < 0.95);(b) selected log(AK) and log (da/dN) data used for curve fitting and statistical analyses (Table 3) showing regression lines, Eq. 5, i.e., goodness of fit to the Paris crack growth law, Eq. 2:0, Velvalloy (Zn-free); IJ, Velvalloy (Zn-containing); T, Dispersalloy (Zn-free); h, Dispersalloy (Zn-containing); (-) statistically significant regression lines; (--) individual regression lines; and () 95% confidence bands for regression lines.
tercept, log (C,), of the Zn-containing amalgam regression was significantly lower (p < 0.05) than the Znfree amalgam regression. That is, for both Velvalloy and Dispersalloy, the Zn-containing amalgam had significantly lower crack velocities than the Zn-fi-ee amalgam over the range of validity of the test: i.e., 0.95 < AK < 1.35 MPa.m”.5 for Velvalloy, and Dispersalloy 7.29 -7.63 0.56 7.11 -7.60 2.54x10-' 1.05- 1.65 1.05 < AK < 1.65 MPa.mO.” for Dispersalloy Zn-free 7.07 -7.01 0.78 7.11 -7.01 9.60x1@* 1.05-1.65 Dispersalloy. In fact, values of constant C, in Eq. 2 (Table 3) show Velvalloy 2.14 -5.63 0.32 2.43 -5.64 2.28~10.~ 0.95- 1.35 that Zn effectively reduced the Velvalloy Zn-free 3.20 -5.29 0.64 2.43 -5.26 5.47x10-6 0.95- 1.35 average crack growth rates by a factor of three in Dispersalloy and a factor of two in Velvalloy over the above AK ranges. Added significance to the Zn-containing versus Zn-free Dispersalloy comparison is provided by the two fatigue tests in which the Zn-containing correlation coefficients and constants m, and log(C) from Eq. 5 for each of the four individual regression equations are Dispers-alloy did not propagate measurable cracks under the same AK level which caused cracks in the Zn-free amalgam to given in Table 3: the Zn-free Dispersalloy data had the best mm/cycle. correlation (P = 0.78) to the Stage II crack growth law, propagate at > 10m7 Comparing next the Zn-containing Velvalloy with the Eq. 2, while the Zn-containing Velvalloy data had the worst Zn-free Dispersalloy regressions, Dispersalloy had a sign& correlation (1= 0.32). The Zn-containing amalgams had poorer cantly greater slope (p < 0.05). Since the intersection of these correlation to Eq. 2 than the corresponding Zn-free two regression lines was at a AK value greater than those of amalgams, i.e., greater scatter in the data. The maximum the fatigue data, it was concluded that Velvalloy had signifivariation in crack velocity was around + 150% (Zn-containing cantly higher (p < 0.05) crack velocities than Dispersalloy, Velvalloy) which is three times greater than for usual irrespective of the Zn-content, for 1.05 < AK < 1.35 MPa.m”,5. structural materials [this comparison is made assuming simi, crack lar order of the cubic least-squares-fit (see Methods section) of Therefore, over the range 1.05
Dispersalloy
0.03
1.33”
2.36
Dispersalloy Zn-free
0.03
1.33
2.27 k 0.04
0.54 - 1.70
Velvalloy
0.06
1.48”
1.93*0.11
0.63 - 2.19
Velvallov Zn-free
0.06
I .4a”
1.95 + 0.07
0.63 - 2.25
-
0.75 - 1.85
than in Dispersalloy, ranging from approximately l-2 pm. The fatigue-l?acturedVelvalloy surfaces Wig. 6d) showed some regions with evidence of ductile transgranular fracture similar to Dispersalloy, but once again, with more rounded features. The overall shape of the fatigue crack front just before finai fracture was generally not a smooth line in any of the specimens examined. Typically, the crack front appeared to be formed by a series of elliptical cracks which had propagated perpendicularly to the direction of the applied stress.
DISCUSSION
testing, Eq. 3, and the Kc values at fracture during fatigue cycling are shown in Table 4. All tests conformed to the plane strain condition. The K,? values from these fatigue tests are consistently higher than measured in standard fracture toughness tests in previous studies. No statistical difference was found between the Zn-containing and Zn-free Velvalloy amalgams (p < 0.02), while Dispersalloy could not be tested because only one Zn-containing Dispersalloy specimen fractured in these tests. Plastic Zone Size in Fatigue. Table 4 gives estimates of the size range of the plastic zone at the crack tip, rp, during the fatigue tests from Eq. 4. This equation predicts that rp will increase as the crack grows due to increased stress intensity, Km,, under constant maximum load. The larger values of rp in Velvalloy compared to Dispersalloy are a consequence of the lower value of yield strength measured in that material. Fractographic Observation. At low magnification, e.g., 48x, the fatigue-fractured regions of the fracture surfaces could be distinguished from the “fast-l?actured” regions because of their rough and undulating appearance compared to the smooth and flat fast-fractured surface. At higher magnifications, e.g., 1000x, further differences could be distinguished, although the trends in Dispersalloy were more pronounced than in Velvalloy At this magnification, no differences could be discriminated between the Zn and Zn-free versions of either amalgam. Typical fast&a&red and fatigue-fractured surfaces ofboth amalgams are shown in Fig. 6. The fast-fractured surface of Dispersalloy (Fig. 6a) showed mostly features characteristic of brittle intergranular fracture, i.e., sharply defined y1 grain boundaries with little deformation of the y, grains. The ‘yl grain size ranged from approximately l-3 urn. In addition, the fatigue-fractured surfaces of Dispersalloy (Fig. 6b) showed some regions with features characteristic of ductile transgranular fracture, i.e., some areas with crater features and other relatively large areas (compared to the y, grain size) with poorly distinguishable grain boundaries. The small light gray specks in Fig. 6b are 7’rods. In contrast, the fracture features of Velvalloy were not as well defined, both from fatigue and fast fracture. Fig. 6c shows a typicalVelvalloy fast-fracture surface which has mostly intergranular fracture, but with more rounded grain boundaries than found in Dispersalloy The y1grain size was smaller
30 Watkins et a/./Effect of zmc on amalgam
Creep. These results are consistent with earlier studies (Jendresen and Ryge, 1960; Johnson and Paffenbarger, 1980) which reported that the creep values for Zn-containing amalgams decreased with increasing Zn-content of the alloys. Static Strengths. The spread in the transverse rupture strength data for all amalgams made differences in the behavior of Zn-containing US.Zn-free amalgams diflicult to determine. Nevertheless, the compressive strength data showed significant differences that do not conform to the findings of Johnson and Paffenbarger C1980) who reported an increase in the compressive strength as the Zn-content of the alloys increased. They explained that the increase in compressive strength seemed to be due to the increase in cohesive forces between grain boundaries in the matrix phase (normally fracture in amalgam occurs at the grain boundaries 1. However, the amalgams tested in their study did not contain copper. Effects of‘Microstructure on Fatigue Behavior: In both Velvalloy and Dispersalloy, the addition of Zn significantly increased the resistance to fatigue crack propagation during Stage II crack growth, and increased the variations in crack velocity for a given AK value without visibly altering the path or nature of the fatigue cracks, Many metallic materials exhibit Stage II crack growth which closely and repeatably follows Eq. 2. The deviations from unique Stage II crack growth of these amalgams are most likely due to inhomogeneous microstructures, i.e., some regions have more resistance to crack propagation than others. The fi-a&graphic results indicate that the distribution of‘ Zn in these amalgams is much finer than the yi grain size. This supports previous microstructural observations (Jensen et al., 1976; Boswell. 1979) which reported no separate Zn-rich phase; instead they reported that Zn was incorporated. This suggests that Zn increases the fatigue resistance of amalgams by substitutional solid solution hardening, although evidently without a significant effect on the strength. However, the larger variations in crack velocities of the Zn-containing amalgams suggest that adding Zn increases the heterogeneity of the microstructure. Interestingly, Boswell(1979) observed by transmission electron microscopy that, in general, the y1grains in the matrix of Zn-free Dispersalloy contained micro-twins, whereas manyy, grams in the Zn-containing Dispersalloy were not faulted. This heterogeneous faulting effect was attributed to the addition of Zn, and could explain the increased variation in the fatigue crack velocities for Zn-containing amalgams. Nevertheless, the coarsest and most apparent heterogeneity in the microstructures of these amalgams is the presence of the unreacted Ag-Sn-Cu particles. Crack acceleration and deceleration have been observed for spherical inclusions in
Fig. 6. Typical fractographs of Dispersalloy (a,b) and Velvalloy (cd). The rapidly fractured surfaces (a$) have mostly undeformed polyhedral T, grain structures with sharply defined grain boundaries indicating brittle intergranular fracture @IF); in addition to BIF areas, fatigue-fractured surfaces (b,d) had some regions with crater features, labeled A, and other regions that are larger in area than the T, grain size, with poorly delineated grain boundaries, B, indicating partly ductile transgranular fracture. Velvalloy has similar but less distinct features than Dispersalloy. Approximate T, grain sizes were estimated from fast-fracture regions: 1-3 urn for Dispersalloy and l-2 urn for Velvalloy.
steel (Clark, 1979): with increasing inclusion diameter, the magnitude of the deviations from exponential growth, Eq. 2, increased. In view of the large numbers of hard inclusions in the y1 matrix of these amalgams in the form of unreacted particle cores, it is not surprising that the crack growth behavior is not ideally exponential. Furthermore, the non-linear shape of the crack front just before final fracture suggests that crack propagation through the matrix is controlled by crack pinning events, e.g., the AgSn-Cu particles may pin the advancing crack front. In Velvalloy, decreased resistance to fatigue loading compared to Dispersalloy is expected due to the presence of the yZphase and absence of the r\’ rods in the y1matrix. The yZ phase generally responds poorly to static loading compared to all other phases found in amalgams, and is not likely to behave any better under cyclic loading. Moreover, then’ phase is generally attributed to increasing the resistance to deformation of the matrix in high-copper amalgams.
“Short crack” phenomena may also explain some of the variations in crack velocity recorded in these tests. Suresh (1991b) suggests that short crack phenomena can be associated with the size of the plastic zone at the crack tip, rP, (Fig. 4) approaching the dimension of a microstructural feature, e.g., the matrix grain size, which can cause the deformation around the crack tip to be elastic rather than plastic. This effect can retard the crack growth rate under increasing stress intensity. In these tests, rP was estimated to be between 0.5 and 2.3 pm, which is close to the range of the y1grain size (l-3 pm). These phenomena require further investigation on amalgams before any conclusions can be made. Effects of Creep on the Fatigue Behavior. The observed differences between the fractured surfaces of Velvalloy and Dispersalloy, excluding the expected microstructural differences, are evidence of the greater susceptibility of Velvalloy to creep. Because of creep, more deformation of the y1 grain structure is expected in Velvalloy fracture surfaces DentalMaterials/January
7995
31
than in Dispersalloy both during fatigue and fast fracture, as confirmed by the observed rounded features. During these fatigue tests, suitable conditions for the occurrence of creep were present since, by definition, the plastic zone around the crack tip is continually cycled to the yield stress, and the test duration was long (>l d). Therefore, there will be high enough stresses generated in the specimens to cause creep both inside and outside the plastic zone. However, creep outside the plastic zone at the crack tip was evidently not widespread, as no permanent deformation of the whole beam was detected. Therefore, Linear Elastic Fracture Mechanics assumptions were valid in these fatigue tests. Creep is likely to accelerate the fatigue crack propagation during these tests because lower resistance to fatigue is usually observed in metals that creep; creep damage to the crystal structure is additive to the fatigue damage. The relevance of creep on the fatigue behavior has been suggested in other studies (Mahler and Van Eysden, 1969; Sutow et cd., 1985; Williams and Cahoon, 1989). The apparent correlation between the static and dynamic creep process (% = 0.937) reported in Mahler and Van Eysden’s study (1969) could be because creep dominated the fatigue process. In that study, the mean stress of the fatigue cycle was equal to the applied creep stress. l+acture Toughness in Fatigue. The values of fracture toughness for these specimens are consistently higher than previously reported for standard fracture toughness tests on amalgams (Cruickshanks-Boyd and Lock, 1983; Lloyd and Adamson, 1985). One possible explanation for this behavior is that more energy is absorbed during fracture from an extended fatigue crack than from a short fatigue pre-crack because of differences in the nature of the crack tip, i.e., either the crack tip becomes blunt under cyclic loading, or the crack branches. Another possible explanation is that the highest stress in the fatigue cycle occurs at the lowest strain rate, i.e., when the load reaches its maximum level, the strain rate is zero (from sinusoidal motion). For some amalgams, K,, reduces with increasing strain rate (Cruickshanks-Boyd and Lock, 1983). Since the crack will propagate under zero strain rate in these fatigue tests, they should yield the maximum fracture toughness of these amalgams. Fractographic Observation. The present fractographic results are contrary to those of Sutow et al. (1985) who reported intergranular cracks in their compressive fatigue experiments. However, this may be explained in terms of the differences in the fatigue conditions, i.e., compression/tension loading vs. the tension/tension loading used in the present study; and crack initiation from many existing flaws vs. initiation from one sharp notch. Clinical Significance. The ranking of plane strain fatigue resistance of the amalgams tested has some interesting correlation with their resistance to marginal breakdown. The effect of incorporating Zn in high-copper amalgams Dispersalloy and Tytin was to reduce the incidence of marginal breakdown (Berry et al., 19861, while the present studies show that Zn reduces the fatigue crack propagation rates in Dispersalloy Moreover, high-copper Dispersalloy had more resistance to both marginal breakdown (Osborne et al., 1978) and fatigue crack propagation (present work) than low-copper Velvalloy. Fatigue testing of other amalgams under similar conditions is necessary before the resistance to
32
Watkins et a/./Effect of z/nc on amalgam
in vitro fatigue crack propagation can be considered as a predictor of the in viva resistance to marginal breakdown. For all of these amalgams, the range of AK over which stable cracks could propagate was small in comparison to structural materials like steels, etc., which is a consequence of the low fracture toughness of amalgams. This means that there is a small likelihood of encountering stress levels where fatigue will dominate the breakdown of these materials, i.e., preexisting flaws in the material are most likely either not to propagate cracks, or to rapidly propagate them by fast fracture. Another way of stating this is that fatigue will dominate the breakdown of these amalgams only when the applied cyclic stress levels fall into a narrow range for a given pre-existing flaw size. The large variations observed in fatigue crack propagation rates for individual materials invalidate predicting a unique fatigue life from the given regression equations. More tests for each material are necessary before adequate statistics can be developed to predict a distribution of probable lifetimes. ~.g., shortest, longest, expected.
ACKNOWLEDGMENTS This study was supported by NIHYNIDR grant DE 06539.
Address Hiroshi
correspondence
and repnnt
wquesth to:
Nakajima
Department
of Riomatwials
Scicnw
Baylor College of Dentistry F’.O. Box 660677 Dallas. TX 752664677
ITSA
REFERENCES Asaoka K ( 1994). Effects of creep value and occlusal force on marginal adaption of amalgam filling. J Dent Res 73 (9):1539-1545. ASM Committee on Fatigue Crack Propagation (1985,. Fatigue crack propagation. In: Newby JR ct al., editors. Metals Handbook. Vol. 8. MechanicalTesting. Metals Park, OH: American Society for Metals, 376-402. ASTM f 1983 ). E399-83: Standard test method for plane-strain fracture toughness of metallic materials. In: Annual Book of ASTM Standards. Vol. 03.02. 540-541. ASTM C1991). E647-91: Standard test method measurement of fatigue crack growth rates. In: Annual Book of ASTM Standards. Vol. 03.02.674-701. Berry TG, Osborne JW, Hatch RA ( 1986% A clinical study of’ zinc-containing high-copper amalgams. Gen Den 341463-465. Boswell PG ( 1979). Transmission electron metallography of. non-y, silver dental amalgam. Scripta Ikfetallurgicrr 13:383-388. Clark Jr WG, (1979). Effect of spherical discontinuities on fatigue crack growth rate performance. In: Smith CW, editor. Fracture Mechanics. ASTM STP 677. Metals Park, OH: American Society for Testing and Materials, 303-319. Cruickshanks-Boyd DW, Lock WR (19833. Fracture toughness of dental amalgams. Btimaterials 4:234-242. de Freitas JF ( 1979). A survey of the elemental composition of alloy for dental amalgam. Aust Dent J 24:17-25.
Derand T (1977). Marginal failure of amalgam Class II restorations. JDent Res 56:481-485. Espevik S (1977). Stress/strain behavior of dental amalgams. Acta Odontol Stand 36:103-111. Espevik S (1980). Properties of amalgams made from lathe-cut high-copper amalgam alloys. Acta Odontol Stand 38: 145-150. Gale EN, Osborne JW (1980). Clinical performance of amalgam as predicted by physical property tests. J Dent Res 59:61-62. Gale EN, Osborne Jw, Winchell PG (1982). Fracture at the margins of amalgam as predicted by creep, zinc content, and gamma-2 content. JDent Res 61:678-680. Goel VK, Khera SC, Gurasami S, Chen RCS (1992). Effect of cavity depth on stresses in a restored tooth. JProsthet Dent 67(2):174-183. Granath LE, Hiltcher R (1970). Strength of edge of Class II cavity restorations in relation to buccolingual shape of cavity. Odontal Revy 21:189-197. Hero H (1983). On creep mechanisms in amalgam. J Dent Res 62:44-50. Irwin GR ( 1960). Plastic zone near a crack and fracture toughness. In: Proceedings of the 7th Sagamore Ordnance Materials Conf., Vol. IV. (1960) New York: Syracuse University, 63-70. Jendresen MD, Ryge G (1960). Effects of particle thickness of zinc and non-zinc alloys. Dent Prog 1:25-29. Jensen SJ, Andersen P, Olsen KB, UtoR L (1976). On the solubility of zinc in the y1 phase of the silver-mercury system. Scar& JDent Res 841338-341. Johnson LB, Ptienbarger GC (1980). The role of zinc in dental amalgams. JDent Res 59:1412-1419. Lloyd CH, Adamson M (1985). The fracture toughness (Kc) of amalgams. J Oral Rehab 12:59-68. Mahler DB, Van Eysden J (1969). Dynamic creep of dental amalgam. J Dent Res 48:501-508. Mahler DB, Marantz RL, Engle JH (1980). A predictive model for the clinical marginal fracture of amalgams. J Dent Res 59:1420-1427. Mahler DB, Van Eysden J, Terkla LG ( 1975). Relationship of creep to marginal fracture of amalgams. IADR Prog & Abstr, No. 553. McCabe JF, Carrick TE (1987). Dynamic creep of dental amalgam as a function of stress and number of applied stress cycles. J Dent Res 66:1346-1349. Mitchell RJ, Ogura H, Nakamura K, Hanawa T, Marker VA, Okabe T (1987). Characterization of fractured surfaces of dental amalgam. In: International Symposium on Testing
and Failure Analysis, Nov. 9-13, 1987, Los Angeles, CA. ASM International. Miyakuni S (1981). Study on the fatigue test of dental amalgam by the potential drop method. Kanagawashigaku 16:157-171. Okabe T, Butts MB, Galloway S, Twiggs SW, Mitchell RJ (1985). Change in creep rate and microstructure in an aged, low copper amalgam. J Biomed Mater Res 19:727746. Osborne JW, Berry TG (1992). Zinc-containing high-copper amalgams: A 3-year clinical evaluation. Am J Dent 5: 43-45. Osborne JW, Gale EN, Chew CL, Rhodes BF, Phillips RW (1978). Clinical performance and physical properties of twelve amalgam alloys. J Dent Res 57:983-988. Papadogiannis Y, Boyer DB, Lakes RS (1987). Creep of amalgams at low stresses. J Dent Res 66:1569-1575. Paris PC, Erdogan F (1963). A critical analysis of crack propagation laws. J Basic Eng, 7Yan.sASME 85:528-534. I&ark RJ, Young WC (1986). Formulas for Stress and Strain. 5th ed. Singapore: McGraw-Hill, 89-208. Suresh S (1991a). Fatigue crack growth in ductile solids. In: Davis EA, Ward IM, editors. Fatigue of Materials. Cambridge Solid State Science Series. Cambridge: Cambridge University Press, 190-221. Suresh S (1991b). Principles of fracture mechanics and their implications for fatigue. In: Davis EA, Ward IM, editors. Fatigue of Materials. Cambridge Solid State Science Series. Cambridge: Cambridge University Press, 141-189. Sutow EJ, Jones DW, Hall GC, Milne EL (1985). The response of dental amalgam to dynamic loading. J Dent Res 64~62-66. Watson PA, Phillips RW, Swartz ML, Gilmore HW (1973). A comparison of zinc-containing and zinc-free amalgam restorations. J Pros&t Dent 29:536-541. Wilkinson EG, Haack DC (1958). A study of the fatigue characteristics of silver amalgam. JDent Res 37:136-143. Williams PT, Cahoon JR (1989). Amalgam marginal breakdown caused by creep fatigue rupture. J Dent Res 68(7):1188-1193. Wilson CJ, Ryge G (1963). Clinical study of dental amalgam. JAm Dent Assoc 66:763-771. Zar JH (1984). Comparing simple Linearregression equations. In: Biostatistical Analysis. 2nd ed. Englewood ClifXs,New Jersey: Prentice-Hall Inc., 292-305. Zardiackas LD, Bayne SC (1985). Fatigue characterization of nine dental amalgams. Biomaterials 6:49-54.
DentalMaterials/January 1995 33
Effect of zinc on strength and fatigue resistance of amalgam John H. Watkins’, Hiroshi Nakajima’, Koji Hanaoka”, Leanna Zhaol, Tsugio Iwamoto2, Toru Okabe’
‘Department of Biomaterials Science, Baylor College of‘Dentistr.v, Dallas, Texas, lJSA 2Department of’Operative Dentistry, Kanagawa Dental College, Kanagaula, JAPAN
ABSTRACT Objectives. This study was conducted to determine the effect of zinc in amalgam on the static mechanical properties and resistance to fatiguecrack propagation of amalgams. Methods. Fatigue, creep, compressive and flexure tests were performed on high-Cu Dispersalloy (Johnson and Johnson Dental Products Co., East Windsor, NJ, USA) and low-Cu Velvalloy (S.S. White Dental Products Int., Philadelphia, PA, USA) in both Zn-containing and Zn-free formulations. Linear Elastic Fracture Mechanics principles were used to characterize the fatigue behavior (crack lengths were monitored). Results. The incorporation of Zn into these amalgams significantly improved their fatigue and creep resistance, while the effect of Zn on the static compressive and flexure strengths was not consistent. Zn significantly increased (p < 0.05) the resistance to fatigue crack propagation during Stage It crack growth for both amalgams, and increased the variations in crack velocity for a given stress intensity difference. without visibly altering the path or nature of the fatigue cracks. Possible influences on fatigue behavior were the mixed microstructure (particles and matrix), the nature of the crack tip, and creep. Significance. The superior resistance to tensile fatigue crack propagation of amalgams containing small amounts of Zn (-1 wt%) in vitro compared with amalgams with no Zn correlated with the superior resistance to marginal breakdown in viva of Zn-containing amalgams. The range of stress intensities over which stable cracks could propagate was small, while the large variations observed in fatigue crack growth rates for individual materials invalidate predicting a unique fatigue life from the empirical equations obtained.
INTRODUCTION The presence of Zn in amalgam is considered to have an important influence on the physical, mechanical and electrochemical properties of amalgams (Johnson and Ptienbarger, 1980). In clinical studies, Zn-containing amalgam restorations have revealed superior resistance to marginal breakdown compared to Zn-free amalgam restorations (Wilson and Ryge, 1963; Watson et al., 1973; Mahler et al., 1980; Berry et al.,
24 Watkins et a/./Effect of zinc on amalgam
1986; Osborne and Berry, 1992). However. there are no studies which have been able to link property changes induced by Zn in amalgams to the resistance to marginal breakdown. Many aspects of marginal breakdown remain unclear. particularly, the nature of the stresses which act on restorations in the oral cavity. Using a mechanical model of a restored tooth, Granath and Hiltcher (1970) predicted that tensile stresses would develop across the margin as a result of compressive loading of the edge of the tooth. By means of finite element modeling, Derand (1977) suggested that compressive stresses which develop at the margin could cause creep. With another finite element model, Goel et al. ( 1992 1 predicted tensile stresses in many locations in a restored tooth loaded in compression. Asaoka ( 1994) suggested creep as the controlling factor in marginal breakdown from another finite element simulation. Thus, the mechanical properties of amalgams which are likely to control the process of marginal breakdown cannot be reliably predicted from knowledge of‘ the stresses acting on amalgams. Through attempts to establish the controlling factoris j responsible for marginal breakdown, the microstructure, the mechanical properties and electrochemical properties of amalgams have been investigated. With regard to the microstructure, the distribution of Zn in amalgam has been studied by Jensen et al. (1976) who showed that Zn dissolved in the y: phase without altering the basic microstructure. Thus it appears that the observed changes in the physical properties are a result of fine scale microstructural changes. Investigatingthis in the transmission electron microscope, Boswell ( 1979 I discovered that the removal of Zn from the formulation of a high-copper amalgam seemed to introduce faulting in the microstructure. Since Mahleret aL.( 1975) found a good correlation between the creep value and the occurrence of marginal breakdown in low-copper amalgam restorations, creep resistance has been the mechanical property which has shown the most promise for predicting the resistance of low-copper amalgams to
marginal breakdown. However, creep resistance is not a reliable indicator, as Gale and Osborne (1980) and Gale et al. (1982) were unsuccessful at making this correlation for high-copper amalgams. Additional factors must, therefore, be significant in the process of marginal breakdown of high69.6 17.7 11.8 0.67 M copper amalgam restorations. Dispersalloy Zn-Free 72.0' 17.0+ 11.0' 0.0' L Other mechanical properties such as the flexure and compressive strengths have not shown 2.75 0.93 M 15 45.3to.7 070287 a good correlation to marginal breakdown; this has led to investigations of the other more complex properties, such as the fatigue resistance (Wilkinson and Haack, 1958; Mahler and Van Eysden, 1969; Sutow et al., 1985; Zardiackas and Bayne, 1985; McCabe and Carrick, Co., East Windsor, NJ, USA). These amalgams were supplied 1987). These studies have concentrated on the compressive by each manufacturer in a Zn-containing and a Zn-free fatigue testing of amalgam but have not shown a conclusive link between marginal fracture and fatigue resistance. In such formulation; both formulations were tested (Table 1). Each amalgam alloy was triturated using an amalgamator experiments, the stress distributions generated within the wari Mix III, L. D. Caulk, Milford, DE, USA). T&nation cylindrical specimens are not simple, as evidenced by the conditions were chosen for each pair of amalgams to obtain a myriad of radial cracks found in some failed specimens (Sutow et al., 1985). Furthermore, in this type of experiment, it is similar residual Hg percentage (Table 1); these Hg levels were chosen to be similar to clinical restorations. The residual Hg difhcult to record the progression of the fatigue cracks. was calculated for all specimens used in each test from weight The tensile fatigue behavior of amalgams was investigated measurements of the condensed Hg. by Miyakuni (1981) who conducted three-point bending Creep and Compressive Strength Tests. Cylindrical fatigue tests on edge-notched beam-shaped specimens of specimens, 4 mm in diameter and 8 mm high, were prepared amalgam. This study was able to correlate increased fatigue resistance with copper content. In Miyakuni’s experiments, a according to the procedures outlined in ANSI/ADA notch was put under cyclic tensile loading under plane strain Specification No. 1 for dental amalgam alloys. The creep value conditions, i.e., the crack tip advanced under tri-axial tensile of each 7 d aged amalgam was determined by the method given in this same specification. The compressive strength of stress. 7 d aged amalgam specimens was tested using a universal Since the effect of tensile stresses across the tooth amalgam interface has been suggested as a factor in the testing machine (Instron 1125, Canton, MA, USA) with a process of marginal breakdown, fatigue experiments which crosshead speed of 0.25 mm/mm at room temperature. Three isolated the tensile stresses from compressive stresses might to five specimens of each amalgam were tested for both creep and compressive strength measurements. be more appropriate for establishing the importance of the fatigue resistance of amalgams to marginal breakdown. Thus, Transverse Rupture Strength Tests. Beam-shaped specithe present investigation uses Miyakuni’s method to find the mens of each amalgam were made since cylindrical specimens fatigue resistance of various amalgams. were inappropriate for transverse rupture strength and Linear Elastic Fracture Mechanics (LEFM) is used fatigue testing. After trituration, each amalgam was condensed extensively in materials science to characterize crack using a hydraulic condensing machine into a specially built initiation and propagation behavior in materials (Suresh, stainless steel mold 25 mm long, 3.4 mm wide and 2.4 mm 1991a). Crack growth rates are recorded against varying stress deep under a pressure of 14 MPa for 60 s. The specimens were intensity difference of the fatigue cycle @IQ (ASTM, 1991). then aged at 37 2 I% in air for 1 d and then trimmed and polished into a 2.0 mm x 3.0 mm x 25 mm size using#600 Sic LEFM permits the fatigue behavior of materials to be characabrasive paper under water. Each specimen was again aged terized with results that are independent of the specimen plaat37klCinair. nar geometry: a limitation of “strength!number-of-cycles-toThe transverse rupture strength of each 7 d aged specimen fracture” (S/N) fatigue data. Therefore, in these experiments, the instantaneous crack length was measured over a range of was determined by conducting a three-point bend test to failAK values, and the data analyzed by LEFM. ure at room temperature. Using the universal testing The objective of this study was to examine the effect of Zn machine at 0.25 mm/mm., the load was applied to the center of the 2 mm x 25 mm face of the specimen with support pins in amalgam on the static mechanical properties and fatigue 3 mm in diameter spaced at 16 mm. resistance of amalgams and to find a possible link between tensile fatigue resistance of amalgams and marginal The creep values and compressive and transverse rupture strengths were compared for the four amalgams using the breakdown. one-way ANOVA test and Scheffe’s test (SPSS for Windows, MATERIALS AND METHODS SPSS Inc., Chicago, IL, USA) at p = 0.05. Materials. Two amalgams were used in this study: a low-copper Fatigue Tests. Wee 7 d aged beam-shaped specimens lathe-cut amalgam (Velvalloy, S. S. White Dental Products (2 mm x 3 mm x 25 mm) of each amalgam were prepared Int., Philadelphia, PA, USA) and a high-copper admixed using the same procedure as described above for the transamalgam (Dispersalloy, Johnson & Johnson Dental Products verse rupture strength tests, with some additional machining
Dental Materials/January
1995
25
~~Tfj 3.0 mm
0.5 mm diam. holes Slot (0.3 mm x 1 34 mm)
Fig. 7. The geometry of the edge-notched beam specimens used in the fatigue tests. The cyclic load is applied directly above the notch while the support pins are below the beam and spaced 16 mm apart. The holes are used for the crack length monitoring circuits: refer to Fig. 2b.
(b)
Fig. 2. The fatigue testing apparatus: (a) the loading mechanism which applies a cyclic load to the specimen in three-point bending; and (b) crack length monitoring and load measurement circuits [inset of (a)]: (A) specimen; (B) pins 16 mm apart; (C) load cell; (D-J) load train driven by (K-L) motor-crank mechanism; (M) cycle counter; (N) polycarbonate box and constant heat source (0) maintains the specimen at 37 + 1%; (P) micro-switch terminates the test at specimen fracture; (Q) strain-gauge bridge for load cell; (R) constant current power supply; (S-T) voltmeter and data logger. 1). A”Tr’ -shaped notch 1.34 * 0.03 mm deep and 0.3 mm wide was cut perpendicular to the 2 mm x 25 mm face in the center of the beam using a diamond disk; no additional sharpening of the notch was undertaken so that study of the crack initiation process could be observed. In order to monitor the crack propagation by means of the electric potential crack monitoring technique (ASM Committee on Fatigue Crack Propagation, 19851, 0.5 mm pin holes were drilled inta both ends of the specimen and also both sides adjacent to the notch. Electrical wires from the monitoring equipment were glued (Fig.
26
Watkins et a/./Effect of zinc on amalgam
into these pin holes with conducting silver paint. All specimens were subjected to a 2 Hz tension/tension loading cycle in a three-point bending fatigue machine to put the notch under cyclic tensile stress (Fig. 2 ). The design of the fatigue test equipment was the same as that used by Miyakuni (1981). A load ratio, P,,,JF’,llllh, of 0.3 and a maximum load of 9.4 N forVelvalloy and 11.0 N for Dispersalloy were used. The cyclic frequency was chosen to simulate the approximate chewing frequency of humans, an important consideration in view of the strain rate sensitivity of amalgams (Espevik. 1977 I. Regarding the maximum load levels selected, the main requirement during these tests was to obtain steady fatigue crack propagation over a measurable crack length before tiacture. A balance was found between minimizing the load to avoid sudden fracture within a few cycles and maximizing the load to obtain the lowest measurable crack growth rates. i.c.. finding the approximate “endurance limit” or stress intensity threshold. All tests were conducted in air at 37 r 1°C. Tests were stopped either at 10”cycles (5.8 d) or at fracture. With each amalgam, three specimens were tested. Me~surcvwz t of’ Instantaneous Crack Lxgth. During testing, the advance of the crack was recorded by the ASM electric potential crack monitoring technique (Fig. 2b) rASM Committee on Fatigue Crack Propagation, 1985). This technique applies a constant direct current through the specimen via the electrodes attached to the ends of the: specimen (Et) and measures the potential difference across the fatigue crack via the electrodes adjacent to the crack (S!. Using the constant current reference circuit as the fatigue crack grows. the remaining cross-sectional area of the specimen decreases and the potential difference increases (from Ohm’s law 1. During these tests. the reference circuit was maintained at 0.9 A, and the specimen was isolated from the rest ofthe fatigue test equipment by insulating the load bearing pins t H) (Fig. 2 J, The crack length in t,he specimens was determined by comparing the potential increase to the reference potential using a calibration curve prepared prior to the experiment (Fig. 3 1. The relationship between the average crack length and the measured potential difference across the notch was determined as follows. Single edge-notched specimens of amalgam. identical t,o those used in the main experiments, werr subjected to fatigue loading. As the fatigue crack propagatid. when the potential difference reached a certain fraction of the initial potential, the test was terminated. Five specimens were tested which spanned the range of potential difrerences encountered in the main tests. Each specimen was subsequently fractured using the procedure described for the transverse r-upturc tests, but using a crosshead speed of 25 mm/min to promote “fast-fYacture” failure. The fi-acturcd surfaces were examined in the SEM and photographed at low magnification (48x) from a direction normal LOthe surface. The fatigue-fractured surface was characterized by its rough and undulating appearance compared to the smooth and flat fast-fractured surface. The fatigue crack length was measured in five evenly spaced locations across the width of the specimen, then averaged. An empirical relationship, Eq. I (Fig. 3), relating the measured crack length. a. to thr measured potential difference across the notch,V, was obtained by curve-fitting the data (Table-Curve, Handel Scientific, San Rafael, CA, USA, to the quadratic regression model described in the study by Miyakuni i 1981 J:
0.7
j
g 0.6 0” E I
I
go.5
-
m . C 3 Y m
t
supports
b
0.4 i 1.2 1.3 1.1 1.0 Normalized Potential across Crack, V / V, Fig, 3. The calibration curve used to estimate the instantaneous crack length, a, of a specimen under fatigue loading from the electric potential difference,V, measured across the fatigue crack. Each experimental data point was determined by partly fatiguing beam specimens (Fig. l), measuring the potential difference across the notch, than rapidly fracturing the specimen and averaging measurements of crack length (n.5) evenly spaced across the width of the crack. The data point in the bottom left corner of the graph corresponds to the reference potential difference, V,, and zero crack length (notch only).
+L’.h”
v (Ulz
+4.374
v (11
-2.228
where V is the initial potential across the notch (0.200 mv), h is the depth of the notch (-1.34 mm), and W is the width of the specimen (3.00 mm). The correlation of this relationship to the data was strong (9 = 0.982). Analysis of Fatigue Data by Fracture Mechanics. The principles of Linear Elastic Fracture Mechanics (LEFM) were used to characterize the fatigue behavior of the four amalgams. For LEFM to be valid for a given material and loading condition, the criterion of “small scale yielding” must be satisfied. Small scale yielding implies that all of the plastic deformation in the specimen is restricted to a narrow region ahead of the crack tip (Fig. 41, whereas the remainder of the specimen only experiences elastic deformation. In view of the well documented viscoelastic behavior of amalgams, i.e., creep (Hera, 1983; Okabe et al., 1985), stress relaxation (Papadogianniset al., 19871, etc., the conformity of amalgams to small-scale yielding was of some concern to the authors. However, the cycle frequency used was considerably faster than the visco-plastic response time of these amalgams, e.g., 0.5 s for one load cycle compared to the order of a minute for significant creep to occur. Furthermore, large-scale yielding is not expected because amalgams typically display low ductility under rapid loading conditions (Espevik, 1977). Thus, the assumption of LEFM appears to be justified. The crack length us. number of cycles (a us. N) data for each test was converted to the crack propagation rate us. the stress intensity dif%erence of the fatigue cycle (da/dN us. AK) data, where AK = K, - I(min.The stress intensities at the upper and lower limits of the fatigue cycle, &, K,i,, were calculated using the standard expression for an edge-notched beam in three-point bending (ASTM, 19831. Since it is impossible to
Fig. 4. The situation at the crack tip: under the far-field stress,a, a plastic zone will develop at the crack tip, the size of which depends on the crack and specimen geometries and the material parameters through Eqn (4). For plane strain, Eqn. (3) must be satisfied.
resolve cycle by cycle crack growth rates in this type of fatigue study,the standard methods used to analyze fatigue data (ASM Committee on Fatigue Crack Propagation, 1985) calculate average growth rates over many cycles (typically thousands). In this study, da/dN values were calculated for individual tests using the “Incremental Polynomial Method” (k = 51, a cubicpolynomial, least-squares-fit method. Crack growth behavior typically falls into three stages: I, crack initiation; II, stable growth; and III, rapid final growth (Suresh, 1991a). Paris and Erdogan (1963) proposed an empirical crack growth rate law for Stage II cracks:
$=C.(*Kp where C and m are empirical constants, obtained by curve-fitting the data (see next section). Calculations were made to ensure that the current experiments conformed to the plane strain condition, i.e., the minimum allowable beam depth, 2
trnin
>
2.5
L1
(3)
KIC
-
ay
where values of the fracture toughness, K,, were estimated from the literature (Espevik, 1980; Cruikshanks-Boyd and Lock, 1983) and the yield strength, o, , was measured in the present compressive strength tests. Therefore, the plane strain fracture toughness, Kit, of each specimen under fatigue conditions was estimated as the stress intensity at fracture. Continuing the assumptions of LEFM, the radius of the plastic zone at the crack tip, rp (Fig. 4), can be estimated from Irwin’s equation &win, 1960): (4)
which assumes monotonic tensile loading in plane strain. This equation is also valid for fatigue loading if the load is always tensile (Suresh, 1991b), hence was used in this study to
Dental Materials/January
1995
27
! Dispersalloy Dispersalloy Velvalloy
Zn-free
0.29 f 0.04 ’
422k 10
0.50 + 0.06 ~
344+16
1.85 + 0.20
325 f
77k17
j 7
61*8 103+
7
scanning electron microscope (JSM-35CF, JEOL, Peabody MA, USA). Both the fatigued region of the fracture surfaces and the final catastrophic fracture region (“fast fractured”) were inspected, as the characteristics in these regions were expected to be Merent. The aims of these observations were to link fracture mechanics data with microstructural features and to compare the material behavior under fatigue and sudden j( fracture conditions, Phase identifications were made based 1 on previous microstructural studies on amalgams (Mitchell 1 et al.. 1987). Since the Y, grain structure was largel>l undeformed in the fast fracture surfaces, the size range ofthe y, grains was estimated for each amalgam.
RESULTS estimate the largest plastic zone size at the maximum stress intensity of the fatigue cycles, K,,_ , as the crack propagated. Statistical Analysis of Fatigue Data. Simple linear regression methods were used to both fit the data from each test material to the equation for Stage II crack growth, Eq. 2, and to compare materials for significant differences. Since the crack velocities obtained in this study were average values, obtained by a least-squares-fit method of arbitrary order, not absolute values, these regression analyses were only used to compare materials in a semi-quantitative manner, particularly the rp values. First the fatigue crack propagation data were transformed to log(AK) us. log(daidN). Next, simple linear regression equations, i.e.,
were fitted to each data set, i.e., the combined data from each material, where the slope and intercept of the regression are equivalent to the exponent, m, and log of the constant, C, in Eq. 2. Correlation coefficients, % , and 95%) confidence bands were calculated for each regression line. Before analysis, the data for Stages I and III crack growth were removed by selecting approximate linear ranges of AK for each set of data. Regarding the number of specimens, the ASTM standard for fatigue testing of metals (ASTM, 19911 recommends that two tests are usually sufficient to characterize the fatigue behavior of a metal. They state that variations in crack velocity of up to + 50% are possible for each AK value and that larger variations may occur below crack velocities of lo-” mm/cycle. Three tests for each material were performed in the current experiments. In order to determine which of the amalgams had faster crack propagation than the others, statistical methods were used to compare pairs of simple linear regression equations (Zar, 1984). First, the two slopes were tested for significant differences (t-test using pooled statistics, p = 0.05). Ifthe slopes were not found to differ, then a common slope was computed for both regression equations, and then the intercepts were tested using a similar method (p = 0.05). If the intercepts were not significantly different, then both regression equations described the same population; otherwise, there were two populations, the one with the greater intercept having significantly faster crack propagation than the other Fractographic Obseruation. The surfaces of the amalgam specimens fractured in fatigue tests were observed using a 28 Watkins et a/./Effect of zinc on amalgam
Creep. ADA creep values of each amalgam are shown in Table 2. Low-copper amalgam Velvalloy, whether Zn-free or Zn-containing, revealed significantly higher (p < 0.05~ creep values than high-copper amalgam Dispersalloy. Creep values of Zn-containing Velvalloy were significantly lower (p < 0.05 ) than those of the Zn-free amalgam, while no significant difference (p < 0.05) was found between Dispersalloy with or without Zn. Static Strengths. The results from the compression and transverse rupture strength tests are shown in Table 2. The addition of Zn to Velvalloy significantly reduced (p < 0.05) the compressive strength, while the addition ofZn to Dispersalloy significantly increased (p < 0.05) the compressive strength. No sign&ant difference (p < 0.05 ) was found between Zn-free amalgams Velvalloy and Dispersalloy, but of the Zn-containing amalgams, Dispersalloy had significantly higher compressive strengths (p < 0.05) than Velvalloy The addition of Zn to Velvalloy significantly reduced (p < 0.05) the transverse rupture strength, while the addition of Zn to Dispersalloy did not significantly influence (p < 0.05 I the transverse rupture strength. No significant difference (p < 0.05) was found between Zn-containing amalgams Velvalloy and Dispersalloy, but of the Zn-free amalgams. Dispersalloy had significantly lower transverse rupture strengths (p < 0.05) than Velvalloy Fatigue Resistance. The change in crack velocity da/dN, with stress intensity difference, aK, for all tests is shown in Fig. 5a: higher crack velocity for the same stress intensity difference implies lower resistance to fatigue loading. Since cracks did not propagate to a measurable length (-5 urn J during 10”cycles in two of the Zn-containing Dispersalloy tests, the maximum load level was increased to 13.0 N for the last test (from 11.0 N); only data from this third test appears in Fig. 5. Low-copper amalgam Velvalloy appeared to exhibit crack initiation behavior, i.e., Stage I crack growth, whereas high-copper amalgam Dispersalloy did not. Note that the average crack velocities below lo-’ mm/cycle were not included, as the changes in crack length over many cycles were below the resolution of the test equipment. To simplify explanation of the statistical analyses, the logarithmically transformed crack propagation data (excluding crack initiation data) and the regression lines are shown in Fig. 5b; a summary of the regression analyses is given in Table 3. For Velvalloy with or without Zn, all data points in the interval 0.95
le-7
b 0.8
.
. 1.0
Stress Intensity
1.2 Difference,
(4
. I
1.4
I
1.6 1.8 AK (MPa.m”.5)
1
I
/
0.0
0.1
0.2 to9 (AK)
(W
Fig. 5. Change in the average fatigue crack growth rate, da/dN, with the increasing stress intensity difference of the fatigue cycle, AK, for &free and &-containing Velvalloy and Dispersalloy. Higher crack velocity for the same AK implies lower resistance to fatigue loading: (a) Raw data showing crack initiation in Velvalloy (AK < 0.95);(b) selected log(AK) and log (da/dN) data used for curve fitting and statistical analyses (Table 3) showing regression lines, Eq. 5, i.e., goodness of fit to the Paris crack growth law, Eq. 2:0, Velvalloy (Zn-free); IJ, Velvalloy (Zn-containing); T, Dispersalloy (Zn-free); h, Dispersalloy (Zn-containing); (-) statistically significant regression lines; (--) individual regression lines; and () 95% confidence bands for regression lines.
tercept, log (C,), of the Zn-containing amalgam regression was significantly lower (p < 0.05) than the Znfree amalgam regression. That is, for both Velvalloy and Dispersalloy, the Zn-containing amalgam had significantly lower crack velocities than the Zn-fi-ee amalgam over the range of validity of the test: i.e., 0.95 < AK < 1.35 MPa.m”.5 for Velvalloy, and Dispersalloy 7.29 -7.63 0.56 7.11 -7.60 2.54x10-' 1.05- 1.65 1.05 < AK < 1.65 MPa.mO.” for Dispersalloy Zn-free 7.07 -7.01 0.78 7.11 -7.01 9.60x1@* 1.05-1.65 Dispersalloy. In fact, values of constant C, in Eq. 2 (Table 3) show Velvalloy 2.14 -5.63 0.32 2.43 -5.64 2.28~10.~ 0.95- 1.35 that Zn effectively reduced the Velvalloy Zn-free 3.20 -5.29 0.64 2.43 -5.26 5.47x10-6 0.95- 1.35 average crack growth rates by a factor of three in Dispersalloy and a factor of two in Velvalloy over the above AK ranges. Added significance to the Zn-containing versus Zn-free Dispersalloy comparison is provided by the two fatigue tests in which the Zn-containing correlation coefficients and constants m, and log(C) from Eq. 5 for each of the four individual regression equations are Dispers-alloy did not propagate measurable cracks under the same AK level which caused cracks in the Zn-free amalgam to given in Table 3: the Zn-free Dispersalloy data had the best mm/cycle. correlation (P = 0.78) to the Stage II crack growth law, propagate at > 10m7 Comparing next the Zn-containing Velvalloy with the Eq. 2, while the Zn-containing Velvalloy data had the worst Zn-free Dispersalloy regressions, Dispersalloy had a sign& correlation (1= 0.32). The Zn-containing amalgams had poorer cantly greater slope (p < 0.05). Since the intersection of these correlation to Eq. 2 than the corresponding Zn-free two regression lines was at a AK value greater than those of amalgams, i.e., greater scatter in the data. The maximum the fatigue data, it was concluded that Velvalloy had signifivariation in crack velocity was around + 150% (Zn-containing cantly higher (p < 0.05) crack velocities than Dispersalloy, Velvalloy) which is three times greater than for usual irrespective of the Zn-content, for 1.05 < AK < 1.35 MPa.m”,5. structural materials [this comparison is made assuming simi, crack lar order of the cubic least-squares-fit (see Methods section) of Therefore, over the range 1.05
Dispersalloy
0.03
1.33”
2.36
Dispersalloy Zn-free
0.03
1.33
2.27 k 0.04
0.54 - 1.70
Velvalloy
0.06
1.48”
1.93*0.11
0.63 - 2.19
Velvallov Zn-free
0.06
I .4a”
1.95 + 0.07
0.63 - 2.25
-
0.75 - 1.85
than in Dispersalloy, ranging from approximately l-2 pm. The fatigue-l?acturedVelvalloy surfaces Wig. 6d) showed some regions with evidence of ductile transgranular fracture similar to Dispersalloy, but once again, with more rounded features. The overall shape of the fatigue crack front just before finai fracture was generally not a smooth line in any of the specimens examined. Typically, the crack front appeared to be formed by a series of elliptical cracks which had propagated perpendicularly to the direction of the applied stress.
DISCUSSION
testing, Eq. 3, and the Kc values at fracture during fatigue cycling are shown in Table 4. All tests conformed to the plane strain condition. The K,? values from these fatigue tests are consistently higher than measured in standard fracture toughness tests in previous studies. No statistical difference was found between the Zn-containing and Zn-free Velvalloy amalgams (p < 0.02), while Dispersalloy could not be tested because only one Zn-containing Dispersalloy specimen fractured in these tests. Plastic Zone Size in Fatigue. Table 4 gives estimates of the size range of the plastic zone at the crack tip, rp, during the fatigue tests from Eq. 4. This equation predicts that rp will increase as the crack grows due to increased stress intensity, Km,, under constant maximum load. The larger values of rp in Velvalloy compared to Dispersalloy are a consequence of the lower value of yield strength measured in that material. Fractographic Observation. At low magnification, e.g., 48x, the fatigue-fractured regions of the fracture surfaces could be distinguished from the “fast-l?actured” regions because of their rough and undulating appearance compared to the smooth and flat fast-fractured surface. At higher magnifications, e.g., 1000x, further differences could be distinguished, although the trends in Dispersalloy were more pronounced than in Velvalloy At this magnification, no differences could be discriminated between the Zn and Zn-free versions of either amalgam. Typical fast&a&red and fatigue-fractured surfaces ofboth amalgams are shown in Fig. 6. The fast-fractured surface of Dispersalloy (Fig. 6a) showed mostly features characteristic of brittle intergranular fracture, i.e., sharply defined y1 grain boundaries with little deformation of the y, grains. The ‘yl grain size ranged from approximately l-3 urn. In addition, the fatigue-fractured surfaces of Dispersalloy (Fig. 6b) showed some regions with features characteristic of ductile transgranular fracture, i.e., some areas with crater features and other relatively large areas (compared to the y, grain size) with poorly distinguishable grain boundaries. The small light gray specks in Fig. 6b are 7’rods. In contrast, the fracture features of Velvalloy were not as well defined, both from fatigue and fast fracture. Fig. 6c shows a typicalVelvalloy fast-fracture surface which has mostly intergranular fracture, but with more rounded grain boundaries than found in Dispersalloy The y1grain size was smaller
30 Watkins et a/./Effect of zmc on amalgam
Creep. These results are consistent with earlier studies (Jendresen and Ryge, 1960; Johnson and Paffenbarger, 1980) which reported that the creep values for Zn-containing amalgams decreased with increasing Zn-content of the alloys. Static Strengths. The spread in the transverse rupture strength data for all amalgams made differences in the behavior of Zn-containing US.Zn-free amalgams diflicult to determine. Nevertheless, the compressive strength data showed significant differences that do not conform to the findings of Johnson and Paffenbarger C1980) who reported an increase in the compressive strength as the Zn-content of the alloys increased. They explained that the increase in compressive strength seemed to be due to the increase in cohesive forces between grain boundaries in the matrix phase (normally fracture in amalgam occurs at the grain boundaries 1. However, the amalgams tested in their study did not contain copper. Effects of‘Microstructure on Fatigue Behavior: In both Velvalloy and Dispersalloy, the addition of Zn significantly increased the resistance to fatigue crack propagation during Stage II crack growth, and increased the variations in crack velocity for a given AK value without visibly altering the path or nature of the fatigue cracks, Many metallic materials exhibit Stage II crack growth which closely and repeatably follows Eq. 2. The deviations from unique Stage II crack growth of these amalgams are most likely due to inhomogeneous microstructures, i.e., some regions have more resistance to crack propagation than others. The fi-a&graphic results indicate that the distribution of‘ Zn in these amalgams is much finer than the yi grain size. This supports previous microstructural observations (Jensen et al., 1976; Boswell. 1979) which reported no separate Zn-rich phase; instead they reported that Zn was incorporated. This suggests that Zn increases the fatigue resistance of amalgams by substitutional solid solution hardening, although evidently without a significant effect on the strength. However, the larger variations in crack velocities of the Zn-containing amalgams suggest that adding Zn increases the heterogeneity of the microstructure. Interestingly, Boswell(1979) observed by transmission electron microscopy that, in general, the y1grains in the matrix of Zn-free Dispersalloy contained micro-twins, whereas manyy, grams in the Zn-containing Dispersalloy were not faulted. This heterogeneous faulting effect was attributed to the addition of Zn, and could explain the increased variation in the fatigue crack velocities for Zn-containing amalgams. Nevertheless, the coarsest and most apparent heterogeneity in the microstructures of these amalgams is the presence of the unreacted Ag-Sn-Cu particles. Crack acceleration and deceleration have been observed for spherical inclusions in
Fig. 6. Typical fractographs of Dispersalloy (a,b) and Velvalloy (cd). The rapidly fractured surfaces (a$) have mostly undeformed polyhedral T, grain structures with sharply defined grain boundaries indicating brittle intergranular fracture @IF); in addition to BIF areas, fatigue-fractured surfaces (b,d) had some regions with crater features, labeled A, and other regions that are larger in area than the T, grain size, with poorly delineated grain boundaries, B, indicating partly ductile transgranular fracture. Velvalloy has similar but less distinct features than Dispersalloy. Approximate T, grain sizes were estimated from fast-fracture regions: 1-3 urn for Dispersalloy and l-2 urn for Velvalloy.
steel (Clark, 1979): with increasing inclusion diameter, the magnitude of the deviations from exponential growth, Eq. 2, increased. In view of the large numbers of hard inclusions in the y1 matrix of these amalgams in the form of unreacted particle cores, it is not surprising that the crack growth behavior is not ideally exponential. Furthermore, the non-linear shape of the crack front just before final fracture suggests that crack propagation through the matrix is controlled by crack pinning events, e.g., the AgSn-Cu particles may pin the advancing crack front. In Velvalloy, decreased resistance to fatigue loading compared to Dispersalloy is expected due to the presence of the yZphase and absence of the r\’ rods in the y1matrix. The yZ phase generally responds poorly to static loading compared to all other phases found in amalgams, and is not likely to behave any better under cyclic loading. Moreover, then’ phase is generally attributed to increasing the resistance to deformation of the matrix in high-copper amalgams.
“Short crack” phenomena may also explain some of the variations in crack velocity recorded in these tests. Suresh (1991b) suggests that short crack phenomena can be associated with the size of the plastic zone at the crack tip, rP, (Fig. 4) approaching the dimension of a microstructural feature, e.g., the matrix grain size, which can cause the deformation around the crack tip to be elastic rather than plastic. This effect can retard the crack growth rate under increasing stress intensity. In these tests, rP was estimated to be between 0.5 and 2.3 pm, which is close to the range of the y1grain size (l-3 pm). These phenomena require further investigation on amalgams before any conclusions can be made. Effects of Creep on the Fatigue Behavior. The observed differences between the fractured surfaces of Velvalloy and Dispersalloy, excluding the expected microstructural differences, are evidence of the greater susceptibility of Velvalloy to creep. Because of creep, more deformation of the y1 grain structure is expected in Velvalloy fracture surfaces DentalMaterials/January
7995
31
than in Dispersalloy both during fatigue and fast fracture, as confirmed by the observed rounded features. During these fatigue tests, suitable conditions for the occurrence of creep were present since, by definition, the plastic zone around the crack tip is continually cycled to the yield stress, and the test duration was long (>l d). Therefore, there will be high enough stresses generated in the specimens to cause creep both inside and outside the plastic zone. However, creep outside the plastic zone at the crack tip was evidently not widespread, as no permanent deformation of the whole beam was detected. Therefore, Linear Elastic Fracture Mechanics assumptions were valid in these fatigue tests. Creep is likely to accelerate the fatigue crack propagation during these tests because lower resistance to fatigue is usually observed in metals that creep; creep damage to the crystal structure is additive to the fatigue damage. The relevance of creep on the fatigue behavior has been suggested in other studies (Mahler and Van Eysden, 1969; Sutow et cd., 1985; Williams and Cahoon, 1989). The apparent correlation between the static and dynamic creep process (% = 0.937) reported in Mahler and Van Eysden’s study (1969) could be because creep dominated the fatigue process. In that study, the mean stress of the fatigue cycle was equal to the applied creep stress. l+acture Toughness in Fatigue. The values of fracture toughness for these specimens are consistently higher than previously reported for standard fracture toughness tests on amalgams (Cruickshanks-Boyd and Lock, 1983; Lloyd and Adamson, 1985). One possible explanation for this behavior is that more energy is absorbed during fracture from an extended fatigue crack than from a short fatigue pre-crack because of differences in the nature of the crack tip, i.e., either the crack tip becomes blunt under cyclic loading, or the crack branches. Another possible explanation is that the highest stress in the fatigue cycle occurs at the lowest strain rate, i.e., when the load reaches its maximum level, the strain rate is zero (from sinusoidal motion). For some amalgams, K,, reduces with increasing strain rate (Cruickshanks-Boyd and Lock, 1983). Since the crack will propagate under zero strain rate in these fatigue tests, they should yield the maximum fracture toughness of these amalgams. Fractographic Observation. The present fractographic results are contrary to those of Sutow et al. (1985) who reported intergranular cracks in their compressive fatigue experiments. However, this may be explained in terms of the differences in the fatigue conditions, i.e., compression/tension loading vs. the tension/tension loading used in the present study; and crack initiation from many existing flaws vs. initiation from one sharp notch. Clinical Significance. The ranking of plane strain fatigue resistance of the amalgams tested has some interesting correlation with their resistance to marginal breakdown. The effect of incorporating Zn in high-copper amalgams Dispersalloy and Tytin was to reduce the incidence of marginal breakdown (Berry et al., 19861, while the present studies show that Zn reduces the fatigue crack propagation rates in Dispersalloy Moreover, high-copper Dispersalloy had more resistance to both marginal breakdown (Osborne et al., 1978) and fatigue crack propagation (present work) than low-copper Velvalloy. Fatigue testing of other amalgams under similar conditions is necessary before the resistance to
32
Watkins et a/./Effect of z/nc on amalgam
in vitro fatigue crack propagation can be considered as a predictor of the in viva resistance to marginal breakdown. For all of these amalgams, the range of AK over which stable cracks could propagate was small in comparison to structural materials like steels, etc., which is a consequence of the low fracture toughness of amalgams. This means that there is a small likelihood of encountering stress levels where fatigue will dominate the breakdown of these materials, i.e., preexisting flaws in the material are most likely either not to propagate cracks, or to rapidly propagate them by fast fracture. Another way of stating this is that fatigue will dominate the breakdown of these amalgams only when the applied cyclic stress levels fall into a narrow range for a given pre-existing flaw size. The large variations observed in fatigue crack propagation rates for individual materials invalidate predicting a unique fatigue life from the given regression equations. More tests for each material are necessary before adequate statistics can be developed to predict a distribution of probable lifetimes. ~.g., shortest, longest, expected.
ACKNOWLEDGMENTS This study was supported by NIHYNIDR grant DE 06539.
Address Hiroshi
correspondence
and repnnt
wquesth to:
Nakajima
Department
of Riomatwials
Scicnw
Baylor College of Dentistry F’.O. Box 660677 Dallas. TX 752664677
ITSA
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and Failure Analysis, Nov. 9-13, 1987, Los Angeles, CA. ASM International. Miyakuni S (1981). Study on the fatigue test of dental amalgam by the potential drop method. Kanagawashigaku 16:157-171. Okabe T, Butts MB, Galloway S, Twiggs SW, Mitchell RJ (1985). Change in creep rate and microstructure in an aged, low copper amalgam. J Biomed Mater Res 19:727746. Osborne JW, Berry TG (1992). Zinc-containing high-copper amalgams: A 3-year clinical evaluation. Am J Dent 5: 43-45. Osborne JW, Gale EN, Chew CL, Rhodes BF, Phillips RW (1978). Clinical performance and physical properties of twelve amalgam alloys. J Dent Res 57:983-988. Papadogiannis Y, Boyer DB, Lakes RS (1987). Creep of amalgams at low stresses. J Dent Res 66:1569-1575. Paris PC, Erdogan F (1963). A critical analysis of crack propagation laws. J Basic Eng, 7Yan.sASME 85:528-534. I&ark RJ, Young WC (1986). Formulas for Stress and Strain. 5th ed. Singapore: McGraw-Hill, 89-208. Suresh S (1991a). Fatigue crack growth in ductile solids. In: Davis EA, Ward IM, editors. Fatigue of Materials. Cambridge Solid State Science Series. Cambridge: Cambridge University Press, 190-221. Suresh S (1991b). Principles of fracture mechanics and their implications for fatigue. In: Davis EA, Ward IM, editors. Fatigue of Materials. Cambridge Solid State Science Series. Cambridge: Cambridge University Press, 141-189. Sutow EJ, Jones DW, Hall GC, Milne EL (1985). The response of dental amalgam to dynamic loading. J Dent Res 64~62-66. Watson PA, Phillips RW, Swartz ML, Gilmore HW (1973). A comparison of zinc-containing and zinc-free amalgam restorations. J Pros&t Dent 29:536-541. Wilkinson EG, Haack DC (1958). A study of the fatigue characteristics of silver amalgam. JDent Res 37:136-143. Williams PT, Cahoon JR (1989). Amalgam marginal breakdown caused by creep fatigue rupture. J Dent Res 68(7):1188-1193. Wilson CJ, Ryge G (1963). Clinical study of dental amalgam. JAm Dent Assoc 66:763-771. Zar JH (1984). Comparing simple Linearregression equations. In: Biostatistical Analysis. 2nd ed. Englewood ClifXs,New Jersey: Prentice-Hall Inc., 292-305. Zardiackas LD, Bayne SC (1985). Fatigue characterization of nine dental amalgams. Biomaterials 6:49-54.
DentalMaterials/January 1995 33