257
Ind. Eng. Chem. Prod. Res. Dev. 1885, 24, 257-263
Literature Cited
.;
Hansmnn, H.; Mode, G. AdMslon 1982, 819, 10. Heymanni K. In Haftung ais Bas's fur Stoffverbunde und Verbundwerkstoffe"; WM, 1983. Kaeibie, D. H.: Uy, K. C. J . Adhes. 1970, 2, 50. Kinioch, A. J. J . Met. Scl. 1980, 50, 2141. M a @ ,P.; Peibker. P. "Handbuch Feuetverzinken"; VEB Leipzig. 1970.
Mittai, K. L. "Adhesion Measurements of Thin Films, Thick Films, and Bulk Coatings": ASTM STP No. 840, Philadelphia, 1978. Skiarczyk, C. Ph.D. Dlssertion, University of Saarbrucken, 1983. Strlevens, F. A.; Rawllngs, R. D. J . O//Chem. Assoc. 1980, 63, 412.
Received for reuiew April 9, 1984 Accepted February 4, 1985
Material Characterization of Structural Adhesives in the Lap Shear Mode. 2. Temperature-Dependent Delayed Failure Erol Sancaktar" and Steven C. Schenck Depadment of Mechanical and Indushlal Englneerlng, Clarkson College of Technology, Potsdam, New York 13676
Creep behavior of structural adhesives is an important design consideration, especially if high levels of stress and temperature are present. This paper focuses attention on the temperaturedependent creep rupture behavior of structural adheshres in the bonded form. Two dlfferent mathematical relations are proposed for this purpose. First, applicability of Zhurkov's creep rupture equation to structural adhesives in the bonded form is assessed with the use of slngle-lap creep data: second, an empirical extension of Crochet's delayed failure equation is proposed to account for the effects of high temperature. In order to assess the applicability of the proposed relations, data on the room and elevated temperature creep rupture behavior of three different structural adhesive: :in the bonded form) are presented.
Introduction In the absence of catastrophic crack propagations, the failure of lap joints may occur in one of the following modes: (1)rupture of the adhesive layer when the ultimate stress is reached; (2) creep rupture of the adhesive when a high level of constant load is used; (3) failure of the adherends. Failure in the third mode will be unlikely when metal adherends such as steel or titanium are used. It is necessary, however, to consider the first two modes of failure for the design of adhesively bonded joints. Adhesive rupture in the constant strain rate mode was discussed in the fiist paper by Sancaktar et al. (1984). This paper will present a discussion of adhesive rupture in the creep mode. Analytical Considerations Mechanical properties of polymeric materials are affected by creep, particularly at elevated temperatures. Creep is time and temperature dependent inelastic deformation and is usually measured in a test environment of constant stress and constant temperature. Designers are usually interested in two aspects of creep: (1)creep at low stress levels over a long period of time, where creep strains are described as a function of time for constant stress and temperature values; (2) creep at high stress levels resulting in delayed failures. 1. Creep at Low Stress Levels. There are a number of empirical and theoretical methods to express creep strains as functions of time. A complete empirical method for predicting creep curves has been described by Larke and Parker (1971). They use mathematical equations for primary, secondary, and tertiary tensile creep regions to utilize the existing creep data for prediction of other creep curves. Their method also enables estimation of strain and time values when the primary creep merges into the secondary stage and the secondary creep merges into the tertiary stage. Theoretical equations describing creep strains as functions of time and stress are based on linear or nonlinear
o 196-4321 1851 I224-025780 1.501o 0
viscoelastic constitutive equations. A. Linear Constitutive Equations. (i) The Kelvin model which has the constitutive equation (to apply to pure shear)
? + (Gr)/cl=
r/cl
(1)
where G and p refer to the shear elastic modulus and viscosity coefficient, respectively, provides the creep equation Y =
(TO/G)U - exp[-(Gt)/pIl
(2)
where ro is the level of constant shear stress. Equation 2 represents delayed elasticity in creep as the creep strain y approaches the values rO/Gat infinite time. (ii) The Maxwell model which has the constitutive equation
i. = (+/G) + ( r / d
(3)
provides the creep equation Y =
+ (N/G)I
(TO/CL)[~
(4)
The Maxwell model is usually suitable for characterization of uncross-linked polymers since their deformation process may occur in the form of flow under long-time or slow rate loading. (iii) The modified Bingham model (Brinson, 1974) which has the constitutive equations
~ = T / G ( 7 5 0)
(5)
and
9 = (+/GI
+
(T
-
e)/p
(e c c
where 8 and r& are elastic limit and ultimate shear stresses, respectively, will provide the creep equation = (TO + to/^) > e) (6)
wcl
This model was recently used by the authors to describe 1985 American Chemical Society
258
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 2, 1985
the constant strain rate shear stress-strain behavior of two different cross-linked (epoxy) thermosetting adhesives in the bonded form (Schenck and Sancaktar, 1983). (iv) The Chase-Goldsmith model (1974) which has the constitutive equations -y
= 7/Go
(7
5
(7)
7J
a11 ? = (+/Go)
(7
- T,)/P
(7
> T9)
where T, = Go@+ GIT)/(Go+ Gl), p = G,,p/(Go+ Gl), will provide the creep equation -j
= (fl/G,)[exp(-C,t/d - 11 f ( r o / G J [ l - exp(-G,t/dl + (70/GO) exp(-Glt/d (8)
where G, = (GoGl)/(Go+ Gl). The Chase-Goldsmith model was applied by Sancaktar and Padgilwar (1982) to describe the creep behavior of LARC-3 thermoplastic adhesive in the bonded lap shear mode. B. Nonlinear Constitutive Equation. The nonlinear power-law response in creep is represented by (9) Y = TOPO + &[t ex~(970)I”l where Do is the instantaneous compliance and D1,n, and 9 are material parameters which characterize the nonlinear time- and stress-dependent behavior. Equation 9 is described on the basis of Schapery’s (1969) nonlinear constitutive equation. It was recently applied by Cenci and Sancaktar (1984) in creep characterization of bulk thermoplastic resins. The well-established time-temperature superposition principle (TTSP) can be used in conjunction with the aforementioned creep relations (eq 2, 4, 6, 8, and 9) to extend the creep data obtained at higher temperatures to values at longer times in the same strain range. As long as no structural changes occur in the material at high temperatures, TTSP can be used for amorphous and semicrystalline thermoplastics and thermosets for extrapolation purposes. As suggested by Darlington and Turner (1978), the application of the TTSP can even be extended into the nonlinear viscoelastic region. In order to apply this principle, one should first construct a “master curve”, where the complete compliance-time behavior is plotted at a constant temperature. For the “master-curve” a reference temperature Tois chosen. The relation for the compliance observed at any time t and temperature Toin terms of the experimentally observed compliance values at different temperatures T is given by Ahlonis et al. (1972) as
D ( To,t) = (P( ‘I?T / P( To)To)D( T ,t
( 10)
where D ( t ) = y ( t ) / r and ~ ( 7 ‘ is ) the temperature-dependent density. The term uT that appears in eq 10 is a time shift factor which can be obtained with the application of the famous WLF equation. 2. Creep at High Stress Levels. A. Crochet’s Delayed Failure Equation. Naghdi and Murch (1963) defined a yield surface as a function of stress (au)plastic strain ( E ; ) , work-hardening due to path history (K,j) and time history of loading-deformation (x,) so that (11) f = f(a,, €8, XIj’ KIj) = 0 The general yield condition given by eq 11was later simplified by Naghdi and Murch (1963) and Crochet (1966) with the use of a Mises yield criterion to the form f =
1 -sIjsIj - k 2 = 0; 2
[k = ~(x,K)]
(12)
On the basis of the theory of elastic perfectly plastic solids, Crochet (1966) neglected the work-hardening term and assumed k to be a function of x only. He described Iz as a monotonically decreasing function of x and asserted that k ( x ) has a lower bound for large values of x. This behavior was graphically shown by Crochet (1966) in his paper. The functional behavior of k described above was later interpreted mathematically by Brinson (1974) in the form
Y ( t )= A ’ + B’exp(-C’x) (13) where Y(t)is the time-dependent maximum stress and A’, B’, and C’are material parameters. The specific functional form of x was described by Crochet (1966) as where the superscripts v and E refer to the viscoelastic and elastic strains, respectively. Equation 13 was later interpreted by Sancaktar and Padgilwar (1982) to apply to the pure (lap) shear condition with T
=A
+ B exp(-Cx,)
(15)
= YP2 - - 8 2
(16)
where xs
and y12refers to the familiar “engineering” shear strain. Apparently, an expression for xe can be obtained by subtracting the elastic shear strain Y~ = T / G from the proposed creep equation (such as the eq 2,4, 6,8, and 9) to subsequently obtain xs. This can be done since delayed failure occurs only in those elements loaded up into the viscoelastic region. Following the procedure described above, the use of the Maxwell model creep relation (eq 4) to evaluate xs (eq 16) first and subsequent substitution in eq 15 results in 7
=A
+ B exp[-C~t/p]
(17)
Following the same procedure with the modified Bingham model we get T = A + B exp[-C(~- f l ) t / p ] (18) Similar application with the Kelvin model results in 7 = A + B exp[C exp(-Gtlp)] (19) Note that the asymptotic value for eq 17 and 18 is the material constant A whereas it is A B for eq 19. Apparently eq 19 describes a much faster approach in time of the rupture stresses to their asymptotic values. The application of the Chase-Goldsmith model and the nonlinear model results in more complex forms of the delayed failure relation (eq 15). The asymptotic values A of eq 17 and 18 and A B of eq 19 are important design parameters, as they represent the maximum safe stress values below which creep failures are not expected to occur. One can express A and/or ( A + B ) values as a function of the applied temperature to represent experimental data in an empirical fashion. The application of Crochet’s equation to high-temperature creep data is justified by the applicability of the timetemperature superposition principle to the creep equations (1,2, 4, 6, 8, and 9). B. Zhurkov’s Temperature-Dependent Creep Rupture Equation. Zhurkov’s creep rupture equation is based on the theory of chemical reaction rates which employs an exponential relation between time and applied stress. The theory of rate processes assumes that the rate at which the number of unbroken (polymeric) molecular bonds N diminishes is proportional to the number of unbroken bonds, i.e.,
+
+
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 2, 1985
dN/dt = - f N
259
(20)
The rate factor f is assumed to be proportional to the probability of bond breakage due to thermal fluctuation and tensile force with the equation
t = (l/tO) exp{-[Uo - F(u)l/KTl
(21)
where K is Boltzmann's constant, T i s the absolute temperature, Vois the activation energy (interatomic bond energy for polymers), tois a constant on the order of the s, and F ( u ) is a molecular oscillation period of function of the applied stress. The form of F(u) can be arbitrarily chosen as Xu where the material constant X is alluded to the free energy density functional of the stress history for viscoelastic solids. On this basis Zhurkov (1965) determined that the time-to-rupture t , of fibers or strips subjected to uniaxial stress u was given by
t , = t oexp{(Uo- Xa)/KTJ
(22)
Since eq 22 permits failure at vanishing stress, it was modified by Slonimskii et al. (1977) to the form
t , = to exp[(Vo/R7?
- (YO]
(23)
where Uois a constant activation energy per mole (associated as an energy-barrier term), R is the universal gas constant, and a is a constant. It should be noted that a theoretical relation similar in form to eq 22 was reported by Bueche in 1958.
Experimental Procedures In order to assess the applicability of the proposed relations, data on the room and elevated temperature creep rupture behavior of three different structural adhesives (in the bonded lap shear mode) will be presented. The model adhesives were: (1) FM 73, (2) FM 300, and (3) Thermoplastic Polyimidesulfone. These adhesives were used to bond two 2.54 cm wide, 0.127 cm thick titanium alloy strips which were exact copies of each other. The resulting single-lap specimens were in accordance with ASTM D1002 specifications. The overlap length was 1.27 cm and the adhesive thicknesses varied from -0.127 mm to -0.229 mm. All test specimens were prepared at NASA Langley Research Center. The preparation of Thermoplastic Polyimidesulfone adhesive and the processing of the test specimens have been described in detail by St. Clair and Yamaki (1982). Thermoplastic Polyimidesulfone is a high-temperature adhesive with thermoplastic properties and solvent resistance. It is a novel adhesive developed at NASA Langley Research Center. The adhesive FM 300 is a modified epoxy adhesive film supplied with a "tricot-knit" carrier cloth which offers a good mixture of structural and handling properties. Its product information brochure reports a service range of -55 to 150 "C with excellent moisture and corrosion resistance. The adhesive FM 73 is a modified epoxy adhesive film with a polyester knit fabric which offers optimum physical properties. Its product information brochure reports a service range of -55 to 120 "C with high resistance to moisture. Both FM 73 and FM 300 adhesives are manufactured by the American Cyanamid Co. The bonding procedures for these adhesives are described in detail in American Cyanamid Co. product information brochures. The shear stress in the lap joints was assumed to be uniform and was calculated by dividing the load applied to the adherends by the overlap area. The shear strains were defined as bondline deformation divided by the average bondline thickness. For this reason precision measurements of bondline thicknesses and bondline lengths were done with the aid of a microscope under a magnifi-
Figure 1. Creep rupture data and comparison with Zhurkov's equation for FM 73 adhesive.
cation of 40X. A high-precision,air-cooled clip-on gage was used for shear strain measurements. Two notches were milled 2.51 cm apart on the overlap side of the single lap specimens so that the clip-on gages could be attached in them. The notches were 0.254 cm deep and 0.0254 cm wide. Stress concentrations due to the notches in the adherends were estimated to be negligible. Any adherend deformation that occurred within the measuring range of the clip-on gage was calculated and subtracted from the experimental data to obtain the adhesive strains. Groups of 24 to 28 single-lap specimens with the model adhesives were provided by the NASA Langley Research Center. The mechanical testing of these single-lap specimens was performed either on a Tinius-Olsen Universal testing machine or on a Model 1331 Instron Servohydraulic testing machine depending on their availability. Room and high-temperature creep tests were performed with an initial crosshead rate of 0.76 cm/min. Each adhesive was tested in creep at least at 4 different stress levels above the elastic limit shear stress (found from both room and high-temperature constant strain rate tests) and at three or four different temperature levels. The FM 73 adhesive creep tests were performed at temperature levels of 21,54, and 82 "C. The FM 300 adhesive creep tests were performed at temperature levels of 21, 82, 121, and 148 "C. The Thermoplastic Polyimidesulfone adhesive creep tests were performed at temperature levels of 21, 121,177, and 232 "C. The maximum test temperature for each adhesive was determined on the basis of product information available in the literature. The high-temperature creep tests were performed with the aid of an environmental chamber which was attached to the testing machine. Results and Discussion Experimental results previously obtained (Sancaktar et al., 1984) revealed that the constant strain rate shear stress-strain behavior of both FM 73 and FM 300 adhesives could be represented with the use of modified Bingham model. Room temperature creep tests on FM 73 adhesive showed significant viscoelastic-plastic effects in the tertiary region when high levels of creep stress were applied. Higher magnitudes of creep strains were reached at elevated temperatures. The sudden plastic flow to failure (the tertiary region) observed at room temperature was not evident at elevated temperatures. Creep rupture data for FM 73 are shown in Figures 1 and 2. Figure 1 illustrates the comparison of Zhurkov's (modified) equation (eq 23) with the experimental data. As may be observed, data and theory show good agreement at elevated temperatures. The room temperature data, however, do not
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 2, 1985
260
Table I. Material Constants Obtained on the Basis of Crochet's Equation" for FM 73 Creep Rupture Data (See Figure 2) K , (psi-min)-' C, (psi-min)-' T, O F 0, psi A , psi B, psi (MPa-min)-' ("C) (MPa) (MPa-min)-' (MPa) (MPa) 3097 826 2999 276 X lo4 31 X lo4 70 (5.7) (20.7) (1.9 x 104) (0.2 x 104) (21) (21.4) 1750 960 1727 120 x 10" 16 X 10" 130 (6.6) (11.9) (0.8 X 10") (0.1 x 104) (54) (12.1) 982 768 975 653 X lo4 93 x 10" 180 (4.5 x 104) (0.6 X 10") (82) (6.71 (5.3) (6.8) "Crochet's theory based on Maxwell model: ~ ( t=)A
+ B exp[-K(r(t) - >)t).
0 0 0 EXPERIUENTAL
4.0
I
DATA
-
--
Ro
modified Bingham model: ~ ( t=) A
ENVIROYMERIAL T E M P E W I L R E ("C)
;5
0,
1
INSTANT RUPTURE DATA PROM CONSTANT STRAIN RATE TESTS
? L
3.2
+ B exp[-C(~(t))t].Crochet's theory based on
5;
7;
26
i""
24
CROCHET'S THEORY BASED ON MODIFIED BINGHAH MODEL CROCHET'S THEORY BASED ON KAXWFLL MODEL 22
\ 70°F !210C)
i
I
I
1
I
1
12
10
I
I
Lni
14r
--Jr
0
Figure 2. Creep rupture data and comparison with Crochet's equation for FM 73 adhesive. The asymptotic values are well defined experimentally by no failure at long times.
EXPERIMENTAL DATA
- BEST FITTING CURVE
T 'E l m l n
0
50
150
100
200
2 50
ENVIRONHENTAL TEWPERATURE ('F)
show agreement with theory. The constants U, and a used to fit Zhurkov's equation to the creep rupture data are also shown in Figure 1. Comparison of the FM 73 creep rupture data with Crochet's equation (eq 15) is shown in Figure 2. It can be seen that the behavior is a decaying exponential one with respect to time. The plots reach an asymptotic stress level, below which creep failures are not expected to occur. The highest points in Figure 2 (shown as solid black symbols) represent ultimate shear stress values obtained from the highest rate shear stress-strain curves. Figure 2 reveals that the delayed failure behavior of FM 73 can be predicted accurately by employing either the Maxwell or modified Bingham models. The solid and broken lines in Figure 2 represent Crochet's relations (eq 17 and 18) based on the Maxwell and modified Bingham models, respectively. The elastic limit stresses (e) in eq 18 are determined from the constant strain rate stress-strain data by extrapolation. Figure 3 shows the variation of the maximum-or safe-level of creep stress values (below which creep failures are not expected to occur) with environmental temperature. The maximum creep stress values represent the asymptotic stress levels (Le,, material constants A in Table I) obtained with the application of Crochet's equation. Apparently, the relation between the asymptotic shear stress level and temperature is a linear one for the range of data shown. Room and elevated temperature creep testing of FM 300 adhesive revealed the presence of tertiary creep regions.
Figure 3. Variation of maximum (safe) creep stress with environmental temperature for FM 73 adhesive. 5HEXR
:FEAR
CTRL3S
lMPE
STRESS l k s
Figure 4. Creep rupture data and comparison with Zhurkov's equation for FM 300 adhesive.
As expected, higher levels of creep strain were reached at elevated temperatures. Figure 4 shows the comparison of experimental creep rupture data with Zhurkov's relation (eq 23). Data and theory show poor agreement. Comparison of the creep rupture data with Crochet's equation based on the Maxwell and modified Bingham models (eq
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 2, 1985 261 Table 11. Material Constants Obtained on the Basis of Crochet’s Equation“ for FM 300 Creep Rupture Data (See Figure 5) K , (psi-min)-’ C, (psi-mi&’ T,O F 0, psi A, psi E , psi (MPa-min)-’ (“C) (MPa) (MPa-min)-’ (MPa) (MPa) 2974 3675 725 239.1 X 10” 83.9 X 10” 70 (165 X 10”) (0.58 X 10”) (21) (5.0) (20.5) (25.3) 1600 2441 137.8 X 10” 2800 23.9 X 10” 180 (19.3) (11.0) (16.8) (0.95 X 10“) (0.17 X 10”) (82) 2075 1577 2005 549.4 x 10” 111.9 x 104 250 (14.3) (10.9) (13.8) (3.79 x 10”) (0.77 X 10”) (121) 1350 1579 1343 795.6 X 10” 165.8 X 10” 300 (5.48 X 10”) (1.14 X 10”) (149) (9.3) (9.3) (10.9) ~~
“Crochet’s theory based on Maxwell model: r ( t ) = A
+ B exp[-K(r(t) - e)t].
+ E exp[-C(r(t))t]. Crochet‘s theory based on modified Bingham model: r ( t ) = A ENVIRONIESTAL TEMPERATURE
0 A 0 0 EXPERIMENTAL A
(‘C)
DATA
INSTANT RUPTURE DATA FROM CONSTANT STRAIN RATE TESTS
-CROCHET’S THEORY BASED ON HODIFIE BINGHAY YODEL --CROCHET’S MODEL
THEORY B A S E D O N W W E L L
16
i 0 EXPERIMENTAL LO
120
80
160
200
DATA
-BEST FITTING CURVE
:.O 240
TIME ( n l n )
Figure 5. Creep rupture data and comparison with Crochet’s equation for FM 300 adhesive. The asymptotic values are well defined experimentally by no failure at long times.
17 and 18) is shown in Figure 5. The appropriate constants used in fitting Crochet’s equations to the creep rupture data are shown in Table 11. Examination of Figure 5 reveals that the use of the modified Bingham model results in a slightly better fit. The authors believe that Crochet’s equation provides a better fit to the experimental creep rupture data in comparison to Zhurkov’s equation. Figure 6 shows variation of the maximum-or safe-level of creep stress values (i.e., material constants A in Table 11) with environmental temperature. Apparently, the relation between the asymptotic stress level and temperature is a nonlinear one, for the range shown. Experimental results revealed that Thermoplastic Polyimidesulfone exhibits weak rate dependence. Because of this reason a nonlinear elastic power function relation of the form 7
= Pr”
(24)
(where P and m are material constants) was fitted to the constant strain rate stress-strain data. Room temperature creep data on Thermoplastic Polyimidesulfone revealed lower secondary creep rates in comparison to the other thermosetting adhesives studied. The presence of tertiary creep regions were evident in both room and elevated
50
150 200 ENVIRONMENTAL TEMPERATURE (‘F)
100
250
300
Figure 6. Variation of maximum (safe) creep stress with environmental temperature for FM 300 adhesive.
temperature creep data. The creep behavior of Polyimidesulfone was affected considerably by the interfacial (adhesive-adherend and adhesive-fiber) fracture processes, especially at elevated temperatures. Visual examination of post-failure surfaces revealed that the extent of interfacial separation increased with increasing environmental temperature. This was attributed to inadequate surface treatment of the carrier cloth and adherends. Consequently, the interfacial bonds deteriorated quickly at elevated temperatures. Such interfacial separations resulted in failures without appreciable adhesive deformation. Hence, lower levels of creep strains were observed at comparable stress levels when the test temperature was increased. Comparison of Zhurkov’s equation (23) with the experimental data showed poor agreement. The authors attribute this partially to the interfacial fracture processes described above. The discrepancy between the data and theory was greater at the room temperature and 232 “C conditions. Figure 7 shows comparison of creep rupture data with Crochet’s equation based on the Maxwell model (eq 17). Since the constant strain rate stress-strain behavior of the
262
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 2, 1985
rj
10
1
I
100
200
150
I
I
'01
3n0
1
3
.
-
I
.
11
T
Figure 7. Creep rupture data and comparison with Crochet's equation for thermoplastic Polyimidesulfone adhesive. The asymptotic values are well defined experimentally by no failure at long times. Table 111. Material Constants Obtained on the Basis of Crochet's Equationn for Thermoplastic Polyimidesulfone (See Figure 7) C, (psi-min)-' A , psi B , psi (MPa-min)-' (MPa) (MPa) 46.7 X lo4 1054 3267 (0.32 X lo4) (22.5) (7.3) 27.4 X lo* 685 2765 (0.19 x 104) (19.1) (4.7) 157.7 X 10" 1069 2270 (1.09 x 10-6) (15.7) (7.4) 2052 109.4 X lo4 370 (14.1) (0.75 X lo4) (2.6) OCrochet's theory based on Maxwell model: ~ ( t=) A
+ B exp-
[-C(T(t))t].
Polyimidesulfone adhesive was determined to be approximately nonlinear elastic (i.e,, a viscoelastic model could not be fitted to the experimental data) and since the creep behavior could not be characterized with any viscoelastic model, the simplest model which would yield the best fitting form of Crochet's equation was utilized. On this basis, Crochet's equation provided a better fit to the experimental data in comparison to Zhurkov's equation. The appropriate constants used in fitting Crochet's equation (based on the Maxwell model) to the creep rupture data are shown in Table 111. Figure 8 shows variation of the maximum-or safelevel of creep stress values (below which creep failures are not expected to occur) with environmental temperature. The maximum creep stress values represent the asymptotic shear stress levels (Le., material constants A in Table 111) obtained with the application of Crochet's equation. A sharp decrease in the level of maximum creep stress is observed for temperatures above 177 "C.
I
1V11\14
71\IPFRATlRL
*Q@ i
,or,
Fl
Figure 8. Variation of maximum (safe) creep stress with environmental temperature for Thermoplastic Polyimidesulfone adhesive.
Conclusions Based on the single-lap shear experimental data from the three adhesives studied, we can conclude that Crochet's equation provides a better description of the temperature-dependent creep rupture data in comparison to Zhurkov's equation. Zhurkov's equation, in general, provided poor fit for the room-temperature creep rupture data. Furthermore, when interfacial separations were present (a common occurrence in adhesively bonded joints), the fit was poor at all temperatures. The use of Crochet's equation provides much more latitude in fitting creep rupture data because of the availability of many different viscoelastic models including the nonlinear ones. Even when the application of a viscoelastic model to the constant strain rate or creep stress-strain data of an adhesive is not possible (or not known), Crochet's equation can still be applied in an empirical fashion to represent the temperature-dependent creep rupture data. Such an application was demonstrated in this paper with the use of data from Thermoplastic Polyimidesulfone adhesive. Acknowledgment This work was supported by NASA Langley Research Center under NASA Grant NAG-1-284. Dr. William S. Johnson was the NASA technical monitor, and his assistance in the conduct of this work is gratefully acknowledged. The authors also wish to express appreciation to Dr. Terry L. St. Clair of NASA Langley for his guidance and assistance throughout the implementation of this project. Registry No. F M 73, 60181-90-0; FM 300, 71210-48-5.
Literature Cited Amerlcan CyanamM Co. FM 73 Adhesive Fllm Product Information Brochure; Havre de Grace, MD 21078. American CyanamM Co. FM 300 Adhesive Film Product Informatlon Brochure: Havre de Grace, MD 21078
203
Ind. Eng. Chem. Prod. Res. Dev. 1985, 2 4 , 263-269 Ahlonis, J. J.; MacKnlght, W. J.; Shen, M. “Introduction to Polymer Viscoelasticlty”; Wlley-Interscience: New York, 1972. Brlnson, H. F. ”Deformation and Fracture of High Polymers”. Kausch, H. H.; Hassell, J. A.; Jaffee, R. I..Ed.; Plenum: New York, 1974. Bueche, F. J . Appl. f h y s . 1958, 29, 1231. Cencl, N. A,; Sancaktar, E. “Qeometrical and Material Nonllnearkles In Single Lap Joints Bonded wlth Thermoplastic Adhesives”, Clarkson College of Technology, Report No. 095, Potsdam, NY, 1984. Chase, K. W.; GoMsmlth, W. Exp. Mech. 1974, 74(1), 10. Crochet, M. J. J . Appl. Mech. 1966, 33, 327. Darlington, M. W.; Turner, S. ”Creep of Engineering Materials”; Mechanical Engineering Publications Ltd.: London, 1978. Larke, E. C.; Parker, R. J. “Advances in Creep Design”; Wlley: New York, 1971. Naghdl, P. M.; Murch. S. A. J . Appl. Mech. 1963, 30, 321. Sancaktar. E.; Padgilwar, S.J . Mech. Des. 1982, 704(3), 643.
Sancaktar, E.; Schenck, S. C.; Padgllwar, S. Ind. Eng. Chem. Prod. Res. Dew. 1984. 23. 426. Schapery, R. A. folym. Eng. S d . 1989, 9(4), 295. Schenck, S.C.; Sancaktar, E. “MaterialCharacterization of Structural Adhesives In the Lap Shear Mode”, NASA Contractor Report 172237, National Technical Information Service, Springfield, VA, 1983. Slonimskll, 0. L.; Askadskii, A. A,; Kazantseva, V. V. folym. Mech. 1977, 5 , 647. St. Clair, T. L.; Yamaki, D. A. “A Thermoplastic Polyimidesulfone”, NASA Technical Memorandum 84574, National Technical Information Service, Springfield, VA, 1982. Zhurkov, S. N. I n t . J . Fracture Me&. 1985, 7 , 311.
Received for review January 25, 1984 Accepted December 17,1984
Behavior of Elastomeric Lip Seals Subjected to Shaft Radial Vibrations Including Inertial Effects Edrearlo Pratl Istituto di Meccanica Applicata alle Macchine, Universlty of Bologna, 40 736 Bologna, Italy
This paper deals wlth a theoretical as well as an experimental study of the dynamic behavior of elastomeric lip seals for rotating shafts when Interference as well as static and dynamic eccentricities are present. A mathematical model which simulates the viscoelastic and inertial characteristics of the web-lip-spring system is presented. The parameters of the model are experimentally evaluated. The model makes it possible to determine lip-shaft contact conditions analytically as a function of the shaft angular velocity and justifies contact phenomena not previously reported. In loss of contact conditions the dynamic lip profile is theoretically determined and experimentally verified and the area of the gap surface is theoretically evaluated. A nomograph for a quick and easy determination of lip-shaft contact conditions is presented, taking into account the seal parameters and operating conditions.
Introduction Elastomeric lip seals for rotating shafts usually consist of a body (with a metal reinforcement), a flexible conical web, and a sealing lip loaded by a coil spring (see Figure 1). The sealing effect is due to the contact force arising from the interference between lip and shaft. In practical applications, a misalignment between the axis of the lip wedge and the axis of the rotating shaft may arise from manufacturing inaccuracies of the seal or from positioning errors of the seal housing or of the shaft axis. This misalignment is defined as “static eccentricity” (constant in value and in direction with respect to time) and is represented by the distance AB = e, of Figure 2. The flexural deflection of the shaft and the radial clearances of the bearing cause a misalignment between the geometrical axis of the shaft and its rotation axis. This misalignment is designated as “dynamic eccentricity” and = ed of Figure 2. A is represented by the distance nonuniform contact pressure distribution between lip and shaft, which depends on e,, produces increased wear and poor sealing performance of the seal. During shaft rotation, ed causes a radial oscillatory motion of the lip which may lose contact with the shaft. This produces a gap through which the sealed fluid (i.e., oil) leaks. In order to prevent the previously outlined malfunctionings, the seal manufacturers’ catalogs state the recommended initial interference as a function of shaft diameter and the maximum sum of static and dynamic eccentricities according to angular velocity and/or shaft diameter. However, these recommendations are often too 0196-4321/85/1224-0263$01.50/0
general and insufficient since they neglect the variations in the mechanical seal response depending on the elastomer used and the lip geometry. Since normal service conditions comprise the presence of e, and ed, a more extensive knowledge of the radial lip behavior is important for both manufacturers and users. Particular aspects of this problem have been previously examined by Ishiwata and Hirano (1964), Voigt (1975), Voigt and Troppens (1975a, b) and more recently by Schuck and Muller (1981), Kanaya et al. (1984), Muller and Ott (1984). However, the results presented so far do not permit a general evaluation of the problem since they are difficult to interpret in applications different from those examined by the above authors. In this paper, the experimental and theoretical investigations on the lip-shaft contact conditions that have produced a general prediction method of the seal behavior when interference as well as static and dynamic eccentricities are present is reported. For the first time, the influence of the inertial effects due to the seal oscillating mass is included. Such inertial effects explain the mechanism of contact and loss of contact conditions of great practical significanceand which are not found in literature. The characterizing parameters of the dynamic behavior of the web-lip-spring system are experimentally evaluated. They are introduced in a mathematical model of the seal which makes it possible to determine: (i) the angular velocities beyond which loss of contact between lip and shaft occurs as a function of 6, e,, and ed; (ii) the part of the lip which loses contact with the shaft; (iii) the lip 0 1985 American Chemical Society
