RHEOLOGY BULLETIN Publication oi the Society oi Rheology

Volume 35 No. 3 September, 1966

ANNUAL WINTER MEETING TRAVEL TO ATLANTIC CITY THE SOCIETY OF RHEOLOGY The best air service to Atlantic City is via Philadelphia, serviced by 11 leading airlines: Allegheny, American, Delta, MIRAMAR HOTEL - MOTEL Eastern, Lufthansa, National, Northeast, Northwest, Pan SANTA BARBARA, CALIFORNIA American, TWA and United. Limousine service delivers FEBRUARY 6-8, 1967 conventioners directly to Atlantic City hotels and motels in 65-75 minutes. The service operates several times daily A ccomm odations and is increased as demand requires to meet the needs of For reservations and preregistration send request before convention attenders. Make reservations through airline January 1, 1967 to M. C. Shen, North American Aviation ticket agents or travel agencies, with the Salem Transpor- Science Center, 1049 Camino Dos Rios, Thousand Oaks, tation Company or the Yellow Limousine Company at the California with name, address, affiliation, dates of arrival and International Airport - Philadelphia. Limited direct air departure, and accommodations desired. Single rooms are service to Atlantic City is offered by Allegheny Airlines available at $10, $12 or $16 a day. There are also twin- from Boston, New York City, Pittsburgh and Washington, bedded rooms costing $8 a person. Give the name of person D. C. Personalized air service is offered by Southern Jersey to share twin room if possible. Airways operating from Bader Field, just five minutes from Call for Papers most hotels.

Deadline for abstracts of papers for the Winter Meeting Train service to the convention site is by connection with is December 1, 1966. Please confine abstracts to 400 words the Pennsylvania-Reading Seashore Lines at 30th Street or and send to Chairman of Program Committee: North Broad Street Stations of the Pennsylvania Railroad J. L. White, (Chairman), U. S. Rubber Company, Research in Philadelphia. Laboratory, Wayne, New Jersey. Bus schedules prevail for those coming from short dis- A. Eisenberg, Department of Chemistry, University of tances. Forty daily buses operate from the Port Authority California, Los Angeles, California. Bus Terminal in New York City. Two companies - Public D. J. Plazek, Mellon Institute, 4400 Fifth Avenue, Pitts- Service and Lincoln - offer non-stop service from New York burgh, Pennsylvania 15213. to Atlantic City in hours, via the Garden State Parkway. N. W. Tschoegl, Division of Engineering and Applied From Philadelphia, Public Service operates non-stop service Mechanics, California Institute of Technology, Pasadena, to Atlantic City in 75 minutes. California. Motorists traveling from the west may utilize continuous turnpike and expressway systems. THE BINGHAM MEDAL, 1966 Dr. Prince E. Rouse of the Los Alamos Scientific Laboratory ANNOUNCEMENTS has been selected as the 1966 recipient of the Bingham Medal, 1. The Ultrasonics Symposium sponsored by the Group on in recognition of work carried out while he was associated Sonics and Ultrasonics of the IEEE will be held on with The Franklin Institute. His theoretical formulation October 12-15, 1966 at the Statler Hilton Hotel, Cleveland, of the problem of the dynamics of polymer chains, published Ohio. Among the principal topics to be featured are: in 1953, provided a physically realistic mode! whose rheo- Industrial Ultrasonics, Phonon Interactions, Medical logical behavior could be expressed in a simple and useful Ultrasonics, Microwave Devices and Techniques, Ma- fashion. His concurrent experimental studies, in collabor- terials and Continuum Mechanics and Military Sonics ation with K. Sittel and E. D. Bailey, provided the first and Ultrasonics. of many confirmations of the essential validity of this model. 2. A joint symposium on the Rheology and Texture of Most of our present descriptions of the rheological properties Foodstuffs will be held at the School of Pharmacy, of amorphous polymers and polymer solutions have been University of London, Brunswick Square, London W.C.I derived directly from this pioneering work of Rouse. on the 5th and 6th January, 1967. The Award will be presented at the banquet during our 3. Deformation and Flow in High Polymer Systems was annual meeting to be held at the Traymore Hotel in Atlantic the theme of the British Society of Rheology Conference City, October 31 to November 2. John D. Ferry of the at Loughborough University of Technology on September University of Wisconsin will introduce Dr. Rouse. 14, 15, and 16, 1966.

1 Finally, certain comparisons are made between other exist- ing theories of nonlinear constitutive equations and the RHEOLOGY BULLETIN writer's theory.

Raymond R. Myers, Editor 'R. A. Schapery, "Application of Thermodynamics to Thermomechanical, Fracture, and Birefringent Phenomena Department of Chemistry in Viscoelastic Media," J. Appl. Phys., 3-5, 1964, 0pp. Kent State University 1451-1465. 2R. A. Schapery, "A Theory of Nonlinear Thermovisco- Kent, Ohio, 44240 elasticity Based on Irreversible Thermodynamics," Proe. 5th U. S. Nat. Cong. Appl. Mech, June 1966, pp. 511-530. 3R. A. Schapery, "An Engineering Theory of Nonlinear PROGRAM Viscoelasticity with Applications," Int. J. Solids and Structures, 2, July, 1966. 37th ANNUAL MEETING 10:15 a.m. Break SOCIETY OF RHEOLOGY A-3 Traymore Hotel, Atlantic City, N.J. 10:30 a.m. "Nonlinear Viscoelastic Response from the Vieiv- October .'51 - November '2, 1966 point of Kinetic Theory," J. C. HALPIN, Air Force Materials Laboratory, Wright-Patterson AFB, Ohio.

MONDAY, OCTOBER 31, 1966 Modern continuum mechanics has successfully contrib- uted to the theory of nonlinear viscoelastic phenomena SESSION A - Monday Morning through the studies of the restrictions imposed on the permissible forms of constitutive equations by general Chairman: N. W. TSCHOEGL, California Institute of Tech- invariance principles, and by the more special invariance nology, Pasadena, California requirements which pertain to the structural symmetries of the material. Although invariance considerations im- A-l pose serious restrictions on the form an adequate theory 8:45 a.m. INVITED LECTURE: "The Rheology of Metals", must take; the theory still remains undefined and quite E. W. HART, General Electric Company, Schenectady, arbitrary in nature. In effect the invariance principle New York. defines the criterion by which one may judge whether a proposed constitutive relationship is permissible or not Theories of Bulk Viscoelastic Behavior. but it does not define the specific structure of the con- stitutive relationships. The solution of the problem is A-2 then undefined unless additional information is obtained 9:45 a.m. "Physical Aspects of Simplified Constitutive Equa- from the molecular theories and nonequilibrium thermo- tions Derived from Irreversible Thermodynamics," R. A. dynamics and statistical mechanics. SCHAPERY, Purdue University, Lafayette, Indiana. Relatively simple constitutive equations for nonlinear Recently this author has presented an approximate viscoelastic media, with and without transient temper- treatment of the problem utilizing the Kinetic Theories ature, have been developed by the writer in a series of of the elastic and viscoelastic response of rubber like three papers.1-2'»' Specifically, single-integral expressions solids. The result of this effort was the formulation of a for multiaxial behavior were derived by combining irre- single integral constitutive relationship in which the non- versible thermodynamic principles with assumptions based linearity is introduced through the measure of strain; a on actual nonlinear response of unfilled and filled polymers. nonlinear function of the strain or strain tensor. Extensive These equations readily yield, as a special case, nonlinear experimental data obtained independently by this author relaxation moduli wherein strain and time-dependence and T. L. Smith for simple uniaxial tension have been appear as separate factors; this form has been observed presented which substantiates the essential characteristics by many investigators for wide ranges of strain, time of the deformation function. An additional test of the and temperature, and is the basis for Halpin's molecular theory is the execution of multiple step creep and recovery theory of nonlinear viscoelasticity. experiments. Experimentation indicates that the single integral approach can predict the response to a variable This paper deals with physical aspects of these equations excitation history. In fact it is possible to predict the in greater detail. Predicted and experimental mechanical increasing and decreasing sides of a stress-strain cycle and behavior is compared using several common uniaxial and as a consequence one obtains a prediction of the energy biaxial loading histories; good agreement is shown for a stored and energy dissipated for the cycle. The theory wide variety of polymeric materials. Physical significance predicts a proportional relationship of the energy stored of the nonlinear material property functions is brought or dissipated upon the square of the nonlinear deformation out in this comparison, and it is shown how these functions function at the point of maximum extension for the cycle. can be evaluated graphically by using uniaxial and biaxial Experimentation also supports this point. Consequences test data. A sufficient number of tests required to com- of this form of linearization, which reduces a nonlinear pletely characterize an incompressible material is discussed. problem to linear mechanics, shall be discussed.

2 A-4 B l-l

11:00 a.m. "The Exponential Extension-Ratio History," 2:00 p.m. "On the Molecular Theories of Polymer Solutions," B. BERNSTEIN, Illinois Institute of Technology, Chicago, R. E. DEWAMES, W. F. HALL, and M. C. SHEN, North Illinois, and W. GOLDBERG, Purdue University, Lafayette, American Aviation Science Center, Thousand Oaks, Indiana. California.

According to the elastic fluid theory of Bernstein, Kearsley On the Molecular Theories of Polymer Solutions. R. E. and Zapas, a knowledge of the responses to single step DeWames, W. F. Ilall and M. C. Shen, North American relaxation provides sufficient information to be able to Aviation Science Center, Thousand Oaks, California. This determine the mechanical properties of an incompressible paper reports on a review of the basic molecular theories elastomer. It is further shown that in simple extension of polymer viscoelasticity and the proper extension of the time derivative of the true stress,

was not good at the higher extensions. Reasons for this PFEIFFER, JR., L. A. HOLMES, and J. D. FERRY, University will be discussed. of Wisconsin, Madison, Wisconsin.

Calf thymus deoxyribonucleic acid was degraded by high- A-o shear stirring to molecular weights (M) in the range from 11:30 a.m. "A Fluctuation-Dissipation Theorem Approach 1.0 to 3.2 x 10® and purified by chromatography on methy- to Mechanical Relaxation in Solid Polymers," Y. II. PAO, lated bovine serum albumin. Dynamic viscoelastic prop- erties of the fragmented products, in aqueous glycerol Bell Telephone Laboratories, Murray Hill, New Jersey, solutions in the concentration range (c) from 0.003 to A general expression has been obtained for the complex 0.01 g./ml., were investigated with the apparatus of Birn" dynamic modulus of solid polymers. The approach used boim and Ferry. At values of the product cM higher than is that of the fluctuation-dissipation theorem or equiva- 4 x 103, the frequency dependence of the components of lent^ that of Kubo Theory. In this present formulation the complex shear modulus, G' and G", displayed a plateau any of the macroscopic viscoelastic functions can be re- region in which G' < G" - wv^s, similar to that observed lated to a statistical mechanical time dependent correlation in concentrated solutions of coiling polymers where it is function. Subject to some simplifying assumptions, it is attributed to an entanglement network (to is radian fre- shown that detailed knowledge of the specific heat of the quency, Vj volume fraction of solvent, and rjs solvent solid suffices to yield information on the frequency and viscosity). The width of this plateau region on the loga- temperature dependences of loss peaks of the solid. This rithmic frequency scale is given by A = 3.8 (log cM - 3.56). type of formulation also facilitates comparison of mechan- (The same relation applies to earlier measurements on ical and dielectric relaxation spectra. poIy-X-benzyl-L-glutamate in the helical configuration). At lower values of cM, the frequency dependence super- fically resembles that predicted by the theory of Zimm for flexible coiled macromolecules. However, fitting to MONDAY AFTERNOON the theory gives highly discrepant values for molecular SESSION Bl weights, while fitting the low-frequency end of the dis- Chairman: H. MARKOVITZ persion to the theory of Kirkwood and Auer for rigid Mellon Institute, Pittsburgh, Pennsylvania. rods gives reasonable agreement for both molecular weight Polymer Solutions and rotary diffusion coefficient. It is concluded that the

3 helical fragments appear as rigid rods in their behavior viseoelastic rheological models, and to evaluate the ability at very low frequencies, but at hipher frequencies reveal of the models to describe the material functions of the substantial flexural flexibility. The behavior of rod-like fluids. In particular the Spriggs 4-constant model, the macromolecules is compared with that of flexible coils, WJFLMB model, and the OWFS model were tested. especially with respect to the manifestations of network- Although generally satisfactory, all three models give an like structures. incorrect slope for the normal stresses in the "power-law region."

Bl-8 Falling spheres were used to measure the zero shear- 3:00 p.m. "Normal Stresses in the Simple Shear Flow of rate viscosity 7/0; the Weissenberg Rheogoniometer was used to measure non-Newtonian viscosity, a normal stress Concentrated Polymer Solutions", M. C. WILLIAMS, Uni- T T difference u — n, and the complex viscosity; the Ferranti- versity of California, Berkeley, California. Shirley viscometer was used to make additional measure- ments of the non-Newtonian viscosity; and the Birnboim A molecular theory previously advanced for the de- apparatus (at Professor J. D. Ferry's laboratory) was scription of stress in sheared polymer solutions is reviewed. employed for measuring the complex viscosity. The general expression for the stress tensor "" derived by Fixman is evaluated in an approximate fashion for the case of concentrated solutions by means of an explicit consideration of interpolymer forces. This involves the PART II introduction of an arbitrary but reasonable polymer seg- Rheological Properties of Three Solutions. Part U. Re- ment distribution function v (R) which leads to an inter- molecular potential dependent on shear rate v. The pair laxation and Groivth of Shear and Normal Stresses," J. D.

correlation function g(r) used to compute macroscopic IIUPPLER*, I. F. MACDONALD, T. W. SPRIGGS, L. A. properties is perturbed in terms of Kirkwood's friction HOLMES, and 11. B. BIRD, University of Wisconsin, Madison, coefficient Three rheological functions, 7rl2, (TT,, - 7r22), Wisconsin. and (TTII - T33), are obtained as functions of v and are dis- played graphically. A unique feature is that the related The same three solutions used in Part I were used for

normal stress difference (tt22 - 7r33) is shown to have the measuring the stress relaxation after cessation of steady

same sign as (xu - ttm) at low shear, a result in agreement flow and the stress growth at the inception of steady flow with all experimental data but not predicted by other (including the "overshoot" phenomenon). Both shear theories. and normal stress behavior were observed. In addition "interrupted flow" (a turret-shaped function for the ve- A comparison of these functions with two sets of cone- locity-gradient) was studied. and-plate data (8.0% polyvinyl alcohol in water, and 6.86% polyisobutylene in cetane) shows that shear and The data were used to evaluate the three rheological normal stress measurements can be simultaneously de- models mentioned in Part I. These models all make the scribed at low shear. Values of a time-constant are obtained same predictions for stress relaxation, but differ markedly by the curve-fitting procedure, and are found to be quan- in their predictions for stress growth. The Spriggs 4- titatively reasonable. constant model predicts oscillatory behavior, the OWFS model predicts no stress overshoot, and the WJFLMB predicts stress overshoot. The experimental data for the three solutions tested seem to be described best by the 3:30 p.m. Break WJFLMB model.

* Present address: ESSO Production Research Laboratory Bl-4 Houston, Texas 3:45 p.m. "Rheological Properties of Three Solutions, Part I.

Non-Newtonian Viscosity, Normal Stresses-, and Complex

Viscosity," J. D. HUPPLER, L. A. HOLMES, and E. ASHARE, Bl-5

University of Wisconsin, Madison, Wisconsin. 4:15 p.m. "Relaxation Studies on Polymer Solutions," W. PHILIPPOFF, Esso Research and Engineering Company, The shear-dependent viscosity v, the shear-dependent Linden, New Jersey. normal stress difference -T22i and the frequency de- pendent complex viscosity have been measured for three The emergence of the concept of "recoverable shear s" solutions: in the flow of solutions of polymers, or more generally

1. 2% Polyisobutylene in Primol 355 viscoelastic liquids, necessitates a more detailed examin- ation of its measurement in recoil and mechanism. 2. 1.5% Dow ET597 in 50-50 glycerine-water

3. Aluminum Soap 7% in decalin (Al-laurante) The influence of the constants of the instrument used on the measured physical properties of the investigated The shear-dependent research data extend over about 6 material especially the time-dependent stress-relaxation decades, the normal stress data over about 3 Y decades, 2 and recoil are studied. This gives the limits of the time and the frequency dependent data over about decades! resolution in practical cases. Especially for the Weissenberg The data used to find the constants in several nonlinear rheogoniometer the relaxation measurement in shear gives a vastly different result that the one in normal stress due to It was further found that three relaxation functions the properties of the instrument. The dependence of the which are independent of the deformation and are propor- recoil on time at different shear stresses for a 3% solution tional to the same function of time are sufficient to describe 6 of a polyisobutylene M = 15 x 10 in decalin is studied. the state of deformation. The investigation, as is very often the case, is possible only in the strongly non-Newtonian range. Apparently The form of the constitutive relation of this material the drop in viscosity from its limiting value j/0 is the main is in the usual notation

influence in determining the "valid" range of recoil measure- t ÔC r1 ÔC» Gj (t-r) kk ments. The recoil-time curve is not exponential. Ô T d r j G2(t-r)—±dr

Stress relaxation measurement made by stopping the r1 Z"1 ac -1 ÔCil ) -1 + J G (t-r) {c («)-^u -l-}d p(«)C instrument after steady flow using birefringence on the 3 jl +Cu T+ ij same solution are performed, showing that the extinction Under conditions of uniaxial stress the above equation angle x remains constant during relaxation, the decay takes the explicit form being faster than in the recoil experiment. The constancy of x suggests that normal stresses and shear stresses decay -.03 ti (5.7 x2+100 . Uo) at the same rate. The decay is roughly exponential with = * (-30 ) x2 - ± time. The viscosity in the calculation of the relaxation

time is the lower one under shear conditions, not the where ti is the axial stress per unit deformed area and t "initial viscosity" at low rates of shear. denotes time in minutes.

This paper represents one phase of research performed Bl-6 by the Jet Propulsion Laboratory, California Institute 4:45 p.m. "Stress Relaxation Upon Cessation of Steady Flow of Technology, sponsored by the National Aeronautics of Polymer Melts and Solutions," R. A. STRATTON, Mobil and Space Administration, Contract NAS7-100. Chemical Company, Metuchen, New Jersey. **Professor, University of Iowa, Ames, Iowa; Visiting The accurate measurement of small normal stresses is Professor, Polymer Research Section, Jet Propulsion extremely difficult, while the measurement of shear stress Laboratory, California Institute of Technology, Summer relaxation following cessation of steady flow is relatively 1966. simpler and easier. It is shown that from the latter experi- References ment the steady state shear compliance Je and hence the recoverable shear strain and the first normal stress differ- 1. Green, A. E. and Rivlin, R. S., Arch. Rat. Mech. ence P - P22 can be calculated. Measurements of P - P 1} n 22 Anal. 1, 1 (1957). and shear stress relaxation were made with the Weissenberg Rheogoniometer. Results were obtained for dilute solu- 2. Coleman, B. D. and Noll. W., Rev. Mod. Phys. 33, tions of high molecular weight polystyrene and polyiso- 239 (1961). butylene, silicones, and undiluted monodisperse polystyrene. Very good agreement is obtained between the measured 3. Valanis, K. C., Presented at 36th Annual Meeting of the Society of Rheology, October 1965. values of Pu - P22 and those calculated from stress relax- ation. Some data calculated from flow birefringence and "recoil" measurements are also compared. It was found B2-2 that the method works well into the non-Newtonian region if the apparent rather than the zero rate of shear 2:30 p.m. "Deformation and Rupture of an Unfilled Styrene- viscosity is used in the equations. Butadiene Vulcanízate in Biaxial and Uniaxial Tension,"

T. L. SMITH, J. A. RINDE, and J. E. FREDERICK, Stanford

Research Institute, Menlo Park, California. MONDAY AFTERNOON SESSION B2 Stress-strain and rupture data in biaxial and uniaxial tension were obtained on an unfilled styrene-butadiene Chairman: A. N. GENT, University of Akron, Akron, Ohio. vulcanízate at extension rates between 0.02 and 20 inches Filled and Unfilled Elastomers per minute at 25, 35, 50, 70, and 90°C. Thin - wall cyl- indrical specimens were stretched in the axial direction B2-1 while gas pressure inside a specimen was regulated to 2:00 p.m. "Large Multiaxial Deformation Behavior of a maintain constant its original outside diameter and thus Filled Silicone Rubber," K. C. VALANIS, University of to obtain a pure shear deformation on the outside surface. Iowa, Ames, Iowa, and R. F. LANDEL, Jet Propulsion From the tests, the stress cr, and the extension ratio Xi in the axial direction were obtained along with the cir- Laboratory, Pasadena, California. cumferential stress <72. Uniaxial tests were made 011 rings Under conditions of uniaxial and biaxial stress relaxation cut from the gage section of a cylindrical specimen. it has been found that the mechanical response of a filled

silicone rubber can be adequately described by the current All cylindrical specimens broke cleanly and perpendicular mathematical theory vof large viscoelastic deformation to the stretch direction. By applying time-temperature (Refs. 1, 2, 3). superposition to rupture data from both biaxial and uni- axial tests, composite plots were obtained which show the 3:30 p.m. Break

marked dependence of o^b,

The stress-strain data were slightly time-dependent at This paper is concerned with a study on the dynamic each temperature. One-minute biaxial data at all temper- mechanical behavior of rubberlike material filled with atures gave single curves on plots of log 3«n/F (1) and log spherical particles of finely divided aluminum of prescribed volume concentrations, in a frequency range of 100 to 3

Aviation Science Center, Thousand Oaks, California, and A theory that considers composite rubber system as JULIUS L. JACKSON*, Howard University, Washington, D.C- made up of an elastic substance (aluminum) randomly disposed in a matrix of a viscoelastic substance (rubberlike The Elliott-Lippmann anisotropy factor, which is useful material) has been developed. The theory predicts the in calculating the internal enerpy contribution to stress, dynamic behavior of the material in terms of static creep is derived in terms of current statistical theory of rubber properties of constituent materials for uniaxial and volu- elasticity. The final equation is identical to that of Khans- metric compression loading and volume concentration of anovich and Flory. The new derivation, however, offers the filler in the rubber matrix. Comparison of the theoret- greater insight into the physical basis of the equation for ically predicted values with the experimental results has the anisotropy factor and will facilitate subsequent dis- been found to be reasonably good. Finally, the paper cussion of the experimental results on the thermoelastic discusses the influence of temperature and filler concen- behavior of natural rubber. Stress-temperature measure- trations on the dynamic mechanical behavior. ments were carried out up to the elongation ratio, a, of

2.0. An automatic stress-relaxometer was constructed for This investigation is a part of the research project spon- this purpose which can be completely enclosed in a con- sored by the Army Research Office, Durham, N. C., trolled environment. Experiments were so conducted as under project No. 20010501B700. to minimize possible chemical effects and non-equilibrium conditions. Relative internal energy contribution to stress, B2-5 fe/f, is calculated as a function of a in terms of statistical and thermodynamic theories. Both of these yield similar 4:15 p.m. "Dynamic Shear Behavior of a Polyurethane results. It is shown that in the region of low strains Propellant," N. W. TSCHOEGL, * California Institute of

(1.0 <« <1.5), fa/f decreases rapidly with increasing a, but Technology, Pasadena, California, and T. L. SMITH,

appears to remain constant at 1.5 <«<2.0. This obser- Stanford Research Institute, Menlo Park, California. vation is not in agreement with the prediction of the current statistical theory of rubber elasticity, which stip- The dynamic moduli of a polyurethane propellant were ulates that the energy effects are intramolecular and determined at 11 temperatures between -40 and 60°C independent of deformation. Implications of these findings and at as many as 14 frequencies between 0.064 and 24.5 are discussed. It is suggested that perhaps at low strains cps at each temperature. Tests were made on convention- the intermolecular interactions are large in comparison ally bonded specimens 1.25 inches in diameter and 0.50 with intramolecular energies, but become relatively insig- inch thick. The data were corrected to a shear strain nificant at higher elongation ratios. The temperature amplitude of 0.01. Both the G' and G" data at the different coefficient of unperturbed chain dimensions is also cal- temperatures could be precisely superposed to give com- culated from thermoelastic data. It only constant in the posite curves which show the dynamic moduli at frequencies region 1.5

6 the WLF equation. Over the frequency and temperature General Session ranges covered, the storage modulus increased from about C2 1.4 X 107 dynes/cm2 (205psi) to 1.4 X 109 dynes/cm2 9:45 a.m. "Distribution of Relaxation Times and Annealing (20,500 psi), the latter value being less than the expected glassy modulus by a factor of 8 to 10. The mechanical of B.S.C. Glass," P. B. MACEDO and A. NAPOLITANO, loss tangent had a shallow maximum at log ua'f = - 1.2; National Bureau of Standards, Washington, D. C. above log oia-p = 6.0, it decreased rapidly with increasing The relation between time-temperature dependence of frequency. In the range - 2 < log coa'p < 6, the loss strain (annealing) and frequency dependence of moduli tangent varied only ± 12% above the mean value in is considered. Spinner and Napolitano have compared this frequency range. two glasses of identical composition and index of refrac- tion (density) one in equilibrium, and the second in a non- ""Present address: California Institute of Technology, equilibrium state by their behavior upon further annealing. Pasadena, California. It is shown that the time dependence of the strain in these experiments is linear and permits the calculation of the distribution of relaxation times. Topological and mechan- ical models for the distribution are investigated. A topo- B2-6 logical model is found which not only explains the temper- 4:45 p.m. "The Influence of Vacuole Formation on the ature dependence of viscosity, but also the resistivity Response and Failure of Solid Propellants," R. J. FARHIS, experiments of Ritland. In doing so Tool's fictive temper- Aerojet-General Corporation, Sacramento, California. ature is extended to two parameters, which can explain both equilibrium and non-equilibrium glasses. The temp- The mechanical response and failure of solid propellants erature dependence of the viscosity is due to «a true acti- are shown to be related to the formation and growth of vation energy rather than a free volume or configuration vacuoles which cause strain dilatation in these materials. entropy effect. The stress (thermal) strain experiment A simple statistical interpretation of the dilatation-strain gives a distribution many decades narrower than the behavior has been used to assess both the cumulative stress (pressure) strain work previously done in the re- and instantaneous frequencies of vacuole formation with laxation region by Kurkjian. Since no pressure was applied strain. This provides a method for describing analytically no "delayed elastic relaxation" takes place in the thermal the initiation and extent of microscopic failures which experiment. Thus, there is the added advantage of only govern the non-linear stress-strain response and ultimate measuring the structural distribution of relaxation times. failure of this type of material. Stress-strain and dilata- tion-strain data taken under various conditions of super- This analysis is applied to a borosilicate crown glass, imposed pressure shows that the strong effect of super and it is found that T2/r, « 8 (Gaussian b = .6). This imposed hydrostatic pressure on propellant behavior is narrow distribution indicates that the flow in this material s 6 the result of suppressed vacuole formation. is monomeric rather than polymeric (10 < ra/ri ^ 10 ). The monomeric nature of silicate glasses has been post- ulated by Bockris et. al from zero frequency compres- sibility measurements at high temperatures, but was questioned when Westman proved that phosphate glasses MONDAY EVENING are polymeric. The present work together with Macedo and Litovitz distribution of relaxation times in B2O3 in- 9:00 p.m. Film Showing dicates that the iceberg picture of Bockris is correct for the borates and silicates. The ratio of the average volume "Rheological Behavior of Fluids," H. MARKOVITZ, Mellon to average shear relaxation time is found to be « 2, in Institute, Pittsburgh, Pennsylvania. good agreement with other associated liquids.

"Secondary Flow," E. S. TAYLOR, Massachusetts Insti- tute of Technology, Cambridge, Massachusetts. 10:15 a.m. Break "Deformation of Continuous Media," J. LUMLEY, Penn- sylvania State University, University Park, Pennsylvania. C3

10:30 a.m. "Viicoelastic Properties of Polydimethylsiloxanes,"

TUESDAY, NOVEMBER 1 J. M. O'REILLY and W. M. PREST, Jr., General Electric Research and Development Center, Schenectady, New SESSION C - Tuesday Morning York.

Chairman: L. NIELSEN, Monsanto Company, St. Louis, The dynamic viscosity 17' (oj) and dynamic modulus Missouri. G'(w) of polydimethylsiloxanes with viscosity average 4 molecular weights, Mv, between 5 x 10 and 1 x 10® have been measured at frequencies between 0.1 and 30 cps at Invited Lecture temperatures from 25-200°C. These measurements, ro- 8:45 a.m. " The Rheology of Inorganic Glasses," M. GOLDSTEIN, tational viscosity and normal stresses were made using Yeshiva University, New York, New York. cone-plate geometry on a Rheogoniomet.er. The zero shear

7 3 4 viscosity, ijo, is proportional to Mv ' indicating that the measurements have been made below the glass temper- molecular weight of all these samples is above the en- ature where isothermal volume contraction can be ob- tanglement molecular weight of this polymer. A scale served with the concomitant shift of the retardation factor m = 1.6 can be used to superimpose ^'(mto) and spectrum to longer times. y(i) and m is independent of molecular weight and temp- The molecular weight dependence of the steady state erature. Normal stresses are proportional to 715 at low compliance is being determined and that of the viscosity shear rates and parallel the behavior of G' (to). Continuum is being established beyond the range previously measured. theories predict that P -Pn{y)/^i2 = G' (u>)/w2 and we u To date three unexpected observations have been made: find PII-P (7)/2 ^ G' (to) when to = 7. There is a definite 22 1) the steady state compliance appears to have a temper- relation between PU-P (7) and G' (to) which is inde- L2 ature dependence that is greater than expected and in pendent of molecular weight and temperature. the opposite sense than the rubberlike entropie response found in crosslinked systems; 2) the "entanglement plateau" Dynamic viscosity and rigidity can be examined in is not clearly established unless the molecular weight is light of molecular theories which predict that relaxation about 5 x 105 or higher; 3) the behavior in the region of times are directly proportional to rj and molecular weight 0 glassy response appears to show a slight molecular weight and inversely proportional to temperature. Relaxation dependence. times determined from 77' (to) and G' (to) for silicones are dependent only on viscosity and not on molecular weight. The effect of temperature on the relaxation time, other than through the viscosity is small, rj' (to) and G' (to) for TUESDAY AFTERNOON different molecular weights and temperature can be super- imposed onto a master curve if the reduced frequency SESSION D is taken as r) to. The master curve has the general char- 0 Chairman: J. C. BRODNYAN, Rohm and Haas Company, acteristics predicted by molecular theories such as Rouse's. Springhouse, Pennsylvania.

General Session

C4 2:00 p.m. "General Solutions in the Hydrostatic Theory of

11:00 a.m. "Secondary Transitions of Poly {Methyl Metha- Liquid Crystals," J. L. ERICKSEN, Johns Hopkins Uni- crylate) and Their Activation Energies as Determined by versity, Baltimore, Maryland.

Shear and Tensile Creep Compliance Measurement*,'' A primary function of a hydrostatic theory of liquid E. V. THOMPSON, American Cyanamid Company, Stamford, crystals is to predict orientation patterns which occur in Connecticut. these fluids. Certain patterns are universal, being possible for arbitrary forms of the stored energy function. Our The activation energy of the so-called 0 process of purpose is to characterize these. It turns out that there poly (methyl methacrylate) has been determined by nu- are three types of such patterns, one of which is frequently merous methods including shear creep and stress relaxation observed. measurements and is found to be about 18-20 kcal /mole. However, insufficient creep data exists to clearly define other secondary transitions in this polymer. Since a pos- D2 sible 7 process has been detected by high frequency ex- periments at about -30 °C and numerous workers have 2:30 p.m. "Linear Free Energy Effects in the Poly {vinyl found a transition in the 25-70°C range using various Chloride)-ester System from Creep Compliance, Melt and dilatometric techniques, it is of interest to extend the Solution Viscosity Techniques,'" R. J. HAMMOND and E. M. temperature range of the creep measurements in an effort SMOLEY, Armstrong Cork Company, Lancaster, Penn- to locate these other transitions. sylvania.

Current literature indicates that considerable effort is being made to relate the rheological behavior of various materials to molecular mechanisms of flow. Implicit in 11:30 a.m. "The Temperature and Molecular Weight De- the viscoelastic spectra of various substances is the mole- pendence of the Viscoelastic Behavior of Polystyrene," D. J. cular configuration and motion that gives shape to the PLAZEK and V. M. O'ROURKE, Mellon Institute, Pitts- stress relaxation or creep compliance curves. In dilute burgh, Pennsylvania. solutions or concentrated melts at higher temperatures flow curves give indications of molecular arrangements The viscoelastic creep and creep recovery behavior of present causing deviation from some previously defined anionieally polymerized polystyrene is being investigated rheological standard. Research on high polymers has as a function of molecular weight. A torsional apparatus generally taken the course of investigations into pure one which employs a magnetic bearing and induced torques component or two component solvent-polymer systems. on the moving element, the rotor, is the principal tool Experimental evidence obtained can thus be used for purely being used. The recoverable compliance is being measured phenomonological, molecular or general processing appli- from glassy levels at relative short times out to steady cation depending on the objectives of the program. In state levels at relative long times where possible. Some research on poly (vinyl chloride) melts, complications arise due to the presence of necessary impurities (thermal in T, finally leveling off at a value of approximately 300 stabilizers and secondary plasticizers). While it is possible shear units and remaining constant with additional in- to describe the flow properties of these melts and solutions creases in shear stress. This behavior is similar to that by suitable empirical equations, it is difficult to predict observed with polyethylene in the region where melt beyond any gross qualitative aspect what general chemical fracture occurs. In these experiments, however, the tran- or physical property will result from small changes in the sition takes place in a rotational instrument under con- basic formulation. It is, therefore, quite impossible to tinuous shear in which no "entrance effects" can be post- explore the rheological beha vior of poly (vinyl chloride) ulated as causing melt fracture. without understanding and evaluating the magnitude of the effect of these added substances. Our primary con- During the progress of this investigation it was as- siderations here are directed at understanding the nature certained that the rotational viscometer could be used of the interaction of ester-type plasticizers with polyvinyl to determine elasticity in aluminum soap solutions under chloride) and its nodel, 1,3-dichloropropane compliance, dynamic conditions. Quantitative evaluation of the re- dilute solution and melt viscosity characteristics. The sults produced data which correlated with dynamic test method employed represents a departure from conventional data obtained by a variety of techniques. The authors thought in that the rheological behavior has been success- believe that this is a unique and novel method for measuring fully correlated to both Hammett and Taft substituent the dynamic rheological properties of viscoelastic materials. constants as implied in Eyring's concept of absolute re- action rates. While changes in interaction free energies and enthalpies evolve simply and naturally from this technique, the significant conclusion obtained from these 3:30 p.m. Break data is that the generally accepted "hydrogen-bonding" interaction hypothesis of poly (vinyl chloride) with esters is clearly absent. D4 3:45 p.m. 'Elastomer Processing and Application of Rheo-

logical Fundamentals," J. L. WHITE and N. TOKITA, U. S.

Rubber Company Research Center, Wayne, New Jersey. D3 A rational analysis of elastomer processing in a rubber 3:00 p.m. "Rheology of Aluminum Dilaurate in Toluene," mechanical goods plant is described. The various phases F. H. GASKINS, U. S. Army Edgewood Arsenal, Maryland, of processing are divided into unit operations. The theory of non-linear isotropic visoelasticity is then applied to J. C. BRODNYAN, Rohm and Haas Company, Springhouse, these unit operations and characteristic dimensionless Pennsylvania, and W. PHILIPPOFF, Esso Research and proups derived. From the above analysis the most im- Engineering Company, Linden, New Jersey. portant rheological properties to be specified are the re- laxation modulus, laminar shear viscosity and a tearing The stress-optical properties of aluminum dilaurate- energy. The significance of the maximum relaxation time toluene solutions were investigated over a wide range in is discussed. shear rates, D. Flow curves of 1,2 and 3 weight-percent of the aluminum soap dispersed in toluene displayed the The limitations and asymptotic nature of the Rivlin- type of behavior previously reported by Weber and Ericksen and second order fluid theories are described in Bauer('): i.e., Newtonian behavior at low shear rates, this development. The reason for the Coleman-Duffin- 2 l pronounced shear thinning at D greater than 10- sec - Mizel paradox are noted. and dependence of apparent shear stress, f, on length- to-radius ratio, L/R, of the capillary tubes used at high The paper is concluded by a study of the behavior shear rates. of raw rubber on a two roll mill. The differences in be- havior between natural rubber, emulsion butadiene-styrene Flow birefringence behavior was similar. For example, copolymer and the newer Ziegler and butyl lithium stereo at low shear rates the degree of birefringence, AT;, increased elastomers are discussed. in proportion to D and the extinction angle, x> was nearly 45°. Above a critical shear rate, AJJ increased overpro- portionally, finally leveling out at a high value. Simul- TUESDAY EVENING taneously, x decreased equally rapidly to about 1 Despite Society of Rheology Business Meeting these dramatic changes in dependence of r, Atj and x on D,

the stress optical coefficient remained constant over the Banquet and Presentation of Bingham Medal entire range of variables.

Elastic recoverable shear strains, or simply "recoverable WEDNESDAY, NOVEMBER 2 shears", s, were calculated from the variance of r with L/R. These were found to be in good agreement with SESSION E data obtained from normal stress measurements in a Chairman: R. F. LANDEL, Jet Propulsion Laboratory, Weissenberg Rheogoniometer. At low shear stress s in- Pasadena, California. creased linearly with x• Above a critical shear stress the

recoverable shear increased rapidly with small increases Invited Lecture El The oscillating deformation and orientation of liquid 8:45 a.m. "Rheological Problems in the Earth Sciences," drops of low viscosity agreed with a theory derived from B. KAMB, California Institute of Technology, Pasadena, that for steady flow. When the drop viscosity was increased, California. however, the deformation lagged the velocity-gradient due to dissipation of energy in dilatational flow inside the Flow Behavior drop.

Rigid spheres drifted radially to equilibrium positions

E2 determined by Womersley's dimensionless parameter a and the relative size b/R of the particle to the tube radius, 9:45 a.m. "Deformational Behavior of Viscoelastic Materials the migration velocity being a function of a, b/R and in Processes Defined by Small Time Constants," A. B. the radial position. In pulsatile flow, the migration velocity METZNER and M. JOHNSON, University of Delaware, near the wall increased and the equilibrium position shifted Newark, Delaware. inwards at low values of a.

It may be shown analytically that in the asymptotic Cylindrical particles exhibited not only radial migration limit of very rapidly changing deformation rates materials but also a drift in orbit constant with the long axis of a ordinarily considered to be fluids may take on the char- rod and the faces of a disc becoming oriented in the planes acteristics of elastic solids. For example the stresses be- passing through the tube axis as found in steady flow at come dependent upon total deformation, not on deformation high Reynolds numbers. The migration velocity depended rate. These conclusions follow simply from either the on the orientation of the cylinder axis in addition to the Oldroyd or the Green-Rivlin approximations to material parameters for spheres. behavior. Fluid drops also migrated radially in oscillatory flow. The essential part of the presentation of this paper When the drop viscosity was very low, the drop migrated consists of a short motion picture filmed at 1,000 - 5,000 to the tube axis, but when it was high, the drop migrated frames per second, in which the response of a low viscosity more or less like a rigid sphere. fluid suddenly deformed by impacting a blunt object upon it is observed. One notes a large (6" - 12" in radius) conical With concentrated suspensions, the velocity profile, the sheet of fluid is formed, moves outward rapidly and then amplitude and phase of the oscillating pressure-gradient returns to nearly its initial configuration. The duration and the power dissipated per unit length of the tube were of this elastic recoil experiment is approximately 10 milli- influenced by radial migration of particles. The velocity seconds. Some considerations on the use of this experi- profile of concentrated suspensions became blunted as the mental technique for obtaining material parameters quanti- particle-free layer developed near the wall. The power tatively, which may then be used to characterize the dissipated for oscillatory motions of rigid sphere suspensions material behavior in other high Deborah number experi- generally decreased with time after passing through a ments, arc included. maximum value. The power dissipated in fluid drop suspensions decreased as a definite drop-free zone developed near the wall.

10:15 a.m. Break The relevance of some of these phenomena, which will be illustrated by a cine film, to several problems in sus- E3 pension rheology will be discussed.

10:30 a.m. "Oscillatory Flow of Suspensions Through Tubes," Projection facilities required: 16 mm. cine film (silent) M. TAKANO and S. G. MASON, McGill University, and 35 mm. slides Pulp and Paper Research Institute of Canada, Montreal, Canada. E4

The translation, rotation and radial migration of neu- 11:00 a.m. "Quantitative Relationship Between Steady-State trally buoyant rigid spheres, rods and discs, as well as Flow Curve and Molecular Weight Distribution of Poly- the deformation and radial migration of fluid drops sus- ethylene," N. NAKAJIMA, Allied Chemical Corporation, pended in Newtonian liquids undergoing oscillatory and Morris Township, New Jersey. pulsatile flows through circular tubes were studied.

Mechanical response of matter arises from various me- The axial displacements of small spheres, rods and discs chanical elements which compose the matter. One of the m oscillatory flow were generally in agreement with the most important features of the element is its size. At theory of Womersley for homogeneous fluids, and in the lower temperature and/or the higher frequency, the pulsatile flow could be predicted by superposition of the responding elements are smaller. On the other hand, the oscillatory and the steady flows. The rotations of the response of the larger elements can be observed at the cylindrical particles were in accord with the theory based higher temperature and/or the lower frequency. If an on slow steady flow when the fluctuating velocity-gradient appropriate condition is chosen, then, the responding ele- was used. When the particles were very close to the wall, ments can be made to coincide with the dimension of however, both translatjonal and rotational slip were ob- polymer chain. In other words, a quantitative, though served as in steady flow. relative, information on the molecular weight distribution

— 10 — can be obtained from the mechanical measurement. For trated solutions of polyisobutenes. This new relationship thermoplastic materials, such condition can be obtained may be suitable for expressing the non-Newtonian flow in the melt, steady-state flow behavior, where the shear of other linear amorphous polymers. A general approach rate is analogous to the frequency. Examples of such of this type is of value for predicting and tailoring the studies were shown with linear polyethylene (') and poly- flow properties of polymers. propylene (2). A logical extension of the study is to dis- cover the quantitative relation between the flow curve and the fractionation data. Such a relationship was derived, using four commercial samples and two synthetic blends WEDNESDAY AFTERNOON of polyethylene. These six resins represent a wide variety of the commercial material. The molecular weight dis- SESSION Fl tribution thus calculated from the flow curve is in good Chairman: R. S. PORTER, University of Massachusetts, agreement with the fractionation data (3) within the Amherst, Massachusetts. accuracy of the latter measurement. Therefore, it is pos- sible to calculate the molecular weight distribution from the flow curve: The applicability of the method, however, Flow Behavior is limited to the single peaked, smooth but not necessarily symmetric distribution. The present study provides some Fl-1 insight into the molecular mode of the response. It is 2:00 p.m. "Steady Flow and Dynamic Oscillatory Experi- dependent not only on the chain length but also on the ments on Polymer Melts," L. L. BLEYLER, JR., and T. W. medium, where the chain is placed. This is quite analogous to the environmental effect in the spectroscopic measure- HUSEBY, Bell Telephone Laboratories, Murray Hill, New

ment. In the case of the mechanical measurement, how- Jersey. ever, the interaction with the environment is much more significant. Classically, this was interpreted as an en- We present here a correlation scheme for the behavior tanglement of chains. At the high shear rate, where the of bulk polymer melts in steady flow and dynamic os- polymeric chain as a whole can no longer respond as a cillatory experiments. The correlation is not limited to mechanical unit, only the segmental motion is permitted. low shear rates, but is theoretically valid for all frequencies Namely, the polymer exhibits a rubbery response. This and shear rates. Basis for the scheme derives from Pao's behavior was also traditionally interpreted as the chain theory for viscoelastic liquids. The result, s = (2cot<5)co = K, entanglement. where s is recoverable shear strain and cot 8 = .,,. [ ^ (j (co) (1) NAKAJIMA, N. and P. S. L. WONG, Trans. Soc. Rheol., (reciprocal of the loss factor), is easily derived and pro- 9:1 3 (1965). vides the key to the correlation. The remaining results are

(2) NAKAJIMA, N. and P. S. L. WONG, J. Appl. Polymer r?(K) = {>?'(co)[l + 2 cot2 5)}co = K Sci., 9, 3141 (1965). G(K) = {G'(co)[l + I tan2 5]}co = K (3) NAKAJIMA, N„ J. Polymer Sci., Part A-2, 5, 101 (1966).

2 t12(K) = {G"(w)[l + 2 cot 5]} w = K

2 E5 P,i(K)-P22(K) = { 2G' (co) [ 1 + 2 cot 5]} CO = K where the quantities have their usual meaning. Thus the 11:30a.m. "A Relationship between Molecular Weight Dis- steady flow shear viscosity is expected to equal or exceed tribution and Non-Newtonian Floiv for Polyisobutenes," the dynamic viscosity at all ferquencies and shear rates. R. S. PORTER, M. J. R. CANTOW, and J. F. JOHNSON, Similarly, the correlation predicts that G exceeds or equals Chevron Research Corporation, Richmond, California. G' over the entire frequency ranee. At low shear rates, T12 should correlate with G" and the first normal stress In recent years it has been demonstrated widely that difference is given by 2G'. relationships do exist between molecular weight distri- bution and the non-Newtonian flow of linear amorphous Experimental results are shown and compared to pre- polymers. Variations in distribution cause marked de- dicted behavior. Steady flow experiments were performed viations from general reduced variable curves for non- in a capillary rheometer and dynamic results were ob- Newtonian flow.. This conclusion means that reduced tained using a Maxwell Orthogonal Rheometer. variables must involve more than a single molecular weight average. This complexity has been evaluated in this study by equating shear relaxation spectra for polymer solutions Fl-2 to their respective molecular weight distributions. Mole- 2:30 p.m. "Velocity Profiles of a Non-Newtonian Fluid in cular weight distributions have been generated by column Helical Flow," D. R. REA and W. 11. SCHOWALTER, Princeton fractionation, measured by gel permeation chromatography, and expressed in terms of their standard deviations. The University, Princeton, New Jersey. distributions, expressed in the common form of Mw/Mn, Flow behavior of a 3 percent solution of polyisobutylene ranged from 3.07 to 1.01. The procedure has been success- (Vistanex L-100) dissolved in Decalin was studied in helical fully applied to non-Newtonian flow curves for concen- flow at 25° C. Helical flow was generated by simultaneously

— 11 — imposing an axial pressure gradient and a rotational torque Fl-5 on the fluid as it passed through a H inch gap between 4:15 p.m. "Taylor Instability in Elastic Fluids" C. DIJGAN concentric cylinders which were 18 inches long. The inner and outer cylinders had nominal diameters of 3 and 4 and M. M. DENN, University of Delaware, Newark, inches, respectively. A flow visualization technique was Delaware. developed which permitted quantitative measurement of An experimental defermination of the hydrodynamic velocity profiles in the helical flow field. Light was scattered stability of elastic fluids in laminar flow between rotating to a camera-microscope assembly from minute tracer par- concentric cylinders was carried out. As predicted by ticles (approximately 5-micron bubbles) located in the test analyses for second order fluids, the critical Taylor Number fluid. From the resulting photographs both direction and for the onset of instability was below that of a Newtonian magnitude of the velocity vector could be determined as fluid of the same apparent viscosity. The quantitative a function of position in the flow field. agreement between theory and experiment was sufficiently

Results indicate that the correspondence between helical good to suggest the use of stability measurements as a flow and Poiseuille flow which is predicted for simple fluids means of estimating normal stresses in elastic fluids, par- in viscometric flows is in fact observed to a close approxi- ticularly dilute solutions of interest in drag reduction mation. One concludes that the spatial variation in di- studies. rection of flow which exists in helical flow does not have an important effect on the flow of the polyisobutylene solution under conditions studied in these experiments, a SESSION F2 result consistent with the theory of simple fluids. Chairman: J. L. WHITE, U. S. Rubber Tire Company, Detroit Michigan. Velocity profile measurements at two axial positions in the helical flow field indicated that a fully developed General Session velocity profile was readily established. F2-1 A supplementary result is the perfection for non-New- 2:00 p.m. "Fatigue Under Complicated Load Histories. Law tonian flows of a versatile optical technique that permits measurement of velocity profiles without disturbance of of Cumulative Damage" D. C. PREVORSEK and M. L. the flow field. BROOKS, Central Research Laboratory, Allied Chemical Corporation, Morristown. New Jersey.

Fl-3 The applicability of Miner's law of cumulative damage 3:00 p.m. "Parallel Plane Rotational ViscometerI. M. to predict lifetimes in experiments involving complex load

KRIEGER and M. WOODS, Case Institute of Technology, histories is examined. Lifetimes estimated by 2 '. = l (tb)i Cleveland, Ohio. are compared with those calculated by the expression for the time to rupture derived by Prevorsek and Lyons The distribution of shear rate and shear stress is analyzed assuming that the time to rupture can be approximated for the steady shear motion of a non-Newtonian fluid by the time to form an unstable crack. For experiments between rotating parallel planes. A relationship similar in which the loading conditions became increasingly severe to that obtained by Weissenberg for the capillary visco- with time, lifetimes predicted by Miner's law are longer meter is obtained, permitting the true viscosity to be than those calculated from the rate of crack propagation, calculated from the apparent viscosity. Confirming ex- the opposite being found for experiments in which the perimental data are presented. loading conditions become decreasingly severe with time. Experimental data on hand are in agreement with these 3:30 p.m. Break findings. Effects of changes in the structural parameters P, ^ and AF* and of variations in the experimental con- Fl-4 ditions on the accuracy of the lifetime estimates are dis- 3:45 p.m. "Behavior of Suspended Matter in Rapidly Accel- cussed. erating Viscoelastic Fluids - The Uebler Effect," A. B. METZNER, University of Delaware, Newark, Delaware. F2-2

The observation that large bubbles entrained in accel- 2:30 p.m. "Failure of 0.95 Density Polyethylene Under erating viscoelastic fluids may suddenly stop and remain Constant Load in Agressive Stress-Cracking Environments," stationary for long periods of time, though imbedded in G. E. FULMER, W. R. GRACE and Company, Clarksville, a region of high fluid velocities, is noted and described. An analysis of this phenomenon, termed the Uebler effect, Maryland. shows that it may be expected to occur with all particulate The creep failure of polyethylene in Igepal CO 630 was matter provided that the continuum field fluid is acceler- measured as functions of temperature and molecular ating sufficiently rapidly to generate high stresses as a weight. Boltzman kinetics are found applicable to creep result of fluid stretching, and provided these stresses curves if failure mechanism changes are accomodated. change sufficiently rapidly in the direction of the velocity Reduced variable treatment of the data gives a master vector in the flow field. creep failure curve with the same shift factors used for the failure envelope. To describe the failure, both a master chosen film geometries were determined for five non- creep curve and a failure envelope are required. A re- Newtonian fluids. duced multivariant force variable which depends on the failure mechanisms is necessary. Three distinct failure Potential applications of the above analysis may be in mechanisms were observed; ductible, elastic, and brittle. the study of bearings, mechanical isolators, valveless pumps Eyring kinetic theory can be useful in the analysis of and other mechanical devices and biomechanical phen- the failure data. omena.

3:30 p.m. Break

F2-3 F2-4 3:00 p.m. "The Dynamic Response of Periodically Deformed 3:45 p.m. "Responses of Model Materials to Impact" I. J. Non-Newtonian Fluid Films," C. WACHMANN, D. E. GRUNTFEST, General Electric Company, Space Technology DOUGHERTY, and C. H. T. PAN, Mechanical Technology Center, King of Prussia, Pennsylvania. Incorporated, Latham, New York. As part of a continuing exploration of the mechanical Analysis has shown that a squeeze film of a non-New- behavior of materials which have temperature dependent tonian fluid possessing a shear dependent viscosity would properties, the effect of a hammer blow on a small sample show a time average superambient or subambient pressure of model viscoelastic material is considered. In this situ- when subjected to a transverse skew periodic deformation. ation, the duration of the experiment is long compared The magnitude of this effect depended on the fluid con- with the time required for stress equilibrium to develop sistency and the degree of deviation from the Newtonian and short in comparison with the thermal relaxation time regime and on the skewness of the deformation. Elastic of the sample. The analysis shows how a material which properties did not contribute to this net pressure effect responds in an almost perfectly elastic manner to a light and determined only the rapidity with which the transients blow can respond in a viscous manner to a heavy blow. would disappear. It also suggests that a homogeneous continuum with prop- erties that would make it acceptable as a structural ma- The squeeze film analyzed was formed between two terial must be brittle. This result may contribute to the semi-infinite flat parallel plates moving 180° out of phase understanding of the important relationship between with respect to each other. One complete cycle of film microstructure and ductility. deformation consisted therefore of a compression stroke and a return stroke. The hammer experiment involves relatively high strain

A pseudoplastic fluid showed a net subambient pressure rates which vary continuously during the deformation. when the compression stroke was less than one half period, In earlier work, the constant deformation rate case was and a net superambient pressure when more than one studied. The latter situation is difficult to produce in half period. A dilatant fluid showed the reverse effects. the laboratory in the range of rates of interst here and is No net super- or subambient pressures were indicated if likely to arise in practice. the deformation was symmetric. Newtonian fluids showed none of these effects. F2-5 The implications of the super- or subambient pressure 4:15 p.m. "Linear Viscoelasticity and Flow in Lipstick,'" responses are that a net load support or a net suction R. A. WALL and G. F. DASHER, Clairol Research Labor- can be achieved when a non-Newtonian fluid film is de- atories, Stamford, Connecticut. formed in a skew periodic fashion.

An apparatus is described for measuring the shear creep Analysis proceded as a solution of the equations of compliance and recovery of lipsticks in the shear strain conservation of mass and of conservation of linear mo- region of up to 0.06. Shear stresses applied to the lipsticks mentum subject to the appropriate boundary conditions. are of the order of 103 d.ynes/cm2. Creep and recovery The visco-elastic fluid was represented by a Maxwell cycles studied are identical in length and range up to about model with a "power-law" viscosity and a single relaxation s time X. 3 x 10 sec. Some representative commercial lipsticks are studied and it is found that, as would be expected, The mathematics was made more tractable by order- there are easily measured differences in the compliance of-magnitude simplifications which, however, imposed behavior. The object of the study is to obtain basic rhe- some restrictions on squeeze film deformations and flow ological parameters for correlation with product perform- rates. The instantaneous plate loading W(t) could be ance characteristics as described by consumer test panels. represented by the integral-differential equation The creep and recovery cycles for stresses below the limit of linear stress - instantaneous strain relationship W(t) + I W(t) = I F(t) may be described by the behavior of a series Maxwell- Voigt model combination. The time course of the experi- The forcing function F(t) had integral form and contained mental creep and recovery curves are described by the the values of squeeze film geometry, fluid consistency and theoretical relationships using a single set of four model flow behavior index. By Fourier analysis the time average parameters for all stresses below the above mentioned plate loading was determined. Actual values of W for limit.

— 13 — The viscosity corresponding to the dashpot in the Max- creep experiment. The outcome of this analysis is the well element (derived from the small strain creep com- conclusion that for the lipsticks studied, the shear stress pliance data) is compared with the apparent viscosity at opposing irrecoverable deformation (print-out) over seven large strains (measured at higher shear rates in a plate orders of magnitude of shear rate and going from very and cone rheometer). It is found that in the plate and small to very large strains, is roughly (within a factor of 3) cone rheometer the apparent viscosity is about seven constant. The somewhat lower shear stress observed in orders of magnitude lower than the Maxwell dashpot the plate and cone measurement could very easily be due viscosity, however, the shear rate in the plate and cone to high shear rate work softening produced in the oper- system is seVen orders of magnitude higher than in the ation of placing the sample in the instrument.

CHARTER FLIGHT TO JAPAN 1968 The Fifth International Congress on Rheology is scheduled interest would furnish the information requested below prior for October 7-11, 1968 in Kyoto, Japan. The Society is to November 15, 1966. As the sponsoring organization will exploring possibilities for one or more charter flights to Japan not necessarily be the Society of Rheology, please bring to coincide with this Congress. Because tentative arrange- this announcement to the attention of your associates and ments with an airline should be made about 18 months in friends who may not be members of the Society. advance, it will be helpful if those who have a potential

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Please mail above to Thor L. Smith, Stanford Research Institute, Menlo Park, California, 94025.

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