STUDY OF VISCOELASTIC PROPERTIES OF THIN INTERFACE LAYERS BY ULTRASONIC WAVES

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STUDY OF VISCOELASTIC PROPERTIES OF THIN

INTERFACE LAYERS BY ULTRASONIC WAVES

S. Rokhlin

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C10, suppl4ment au n012, Tome 46, dkcembre 1985 page C10-809

STUDY OF VISCOELASTIC PROPERTIES OF THIN INTERFACE LAYERS BY ULTRASONIC WAVES

S

.

I. ROKHLIN'

Department of Materials Engineering, Ben-Gurion University of

the Negev, PO Box 653, Beer-Sheva, 84105. Israel

Abstract: An ultrasonic method for evaluation of interface properties is outlined. The m sbased on utilization of ultrasonic interface waves for bonded semispaces and of Lamb waves for bonded layers. The interface wave induces only shear stresses on the interface, which makes it possible to estimate the effective complex shear modulus of the interface. The technique is applied for evaluation of viscoelastic properties of thin polymer adhesive films between solids.

I

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INTRODUCTION

Ultrasonic interface waves have great potential for interface study due to their ability t o penetrate into the material and to propagate along an interface. Usually the interface can be modeled by a thin layer with properties different from those of the base material. The case of propagation of interface waves in a system of two solid half spaces separated by a viscoelastic layer was recently studied both theoretically and experimentally by Rokhlin et. al.[l].

Although t h e interface wave technique was originally developed for studying adhesively bonded interfacest2-61 i t seems that the technique can be used for study of bicrystal interfaces. In this paper we describe the results of studying by interface waves the polymerization of thin interface adhesive layers.

I1

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INTERFACE WAVE METHOD

One can estimate the viscoelastic properties of the interface layer by measuring the velocity and attenuation of t h e interface wave el]

.

We showed that the complex shear moddus of an interface layer fiO is related by a simple expression t o the interface wave velocity Vi.

2 where a= Vt/Vi is the normalized wave number for the interface wave; a l = a -By;

2 2 2 % 2

a =2WW; W=a

+p

;@=(a -1) ; y=(a2-y?l$lK;4=(~2-4a

f l

A,. is the characteristic function f & the Rayleigh wave, V and V are the Hhear and longitudinal wave velocities in the substratep is the density of the inttrface kilm material, p and p s r e the density and the shear modulu$ respectively, of the substrate, f is the frequency and h = 2 r f h l V t is the nondimensional film thickness, 2h is t h e thickness of the film.

Equation (1) is valid a t h

<<

i:,where

A:

is the length of shear wave in the material of the

'On Sabbatical leave at the Ohio State University, Department of Welding Engineering, Columbus, OH 43210, U.S.A.

~10-810 JOURNAL DE PHYSIQUE

interface film. When this condition is not satisfied, shear modulus determined from Equation (1) can be refined on t h e basis of t h e more e x a c t equations[1]. To determine t h e complex shear modulus p

,

one should substitute into Eq-(1) t h e complex wave number a

,

which is calculated on t h e bas& of measured velocity and loss factor of interface waves. Numerical analysis shows t h a t sensitivity of this method is high in the range of film thickness which a r e small as compared with t h e length of i n t e r f a c e waves.

I t is possible t o sign o u t t h e principal f e a t u r e s of the method, which indicate t h a t t h e use of t h e interface waves for t h e evaluation of thin interface layers is promising: I) t h e interface wave produces shear stresses a t the interface; 2) t h e interface wave propagates along t h e interface and hence is sensitive to small changes in t h e properties of t h e bond; 3) t h e interface wave c a n b e used for evaluation of very thin layers, when 2h/%<<0.01, where 2h is the thickness of t h e interface layer and

A

is t h e length of the shear wave in t h e substrate; 4) a s shown below, interface waves can b e Jsed for evaluation of multilayered interface films.

As an example, reconstruction of the complex shear modulus of adhesive from experimental d a t a is shown in Fig. 1. The d a t a were taken in the course of bonding t w o steel substrates with epoxy resin. The thickness of adhesive film is 1 2 p

TIME (rnin)

Fig. 1 The normalized complex shear modulus fl

//J.

calculated from smoothed measured values of t h e interface wave velocity a n 8 t h e transmission losses. The dashed horizontal line represents direct measurements of t h e normalized film shear modulus12 a f t e r f p polymerization. The steel shear modulus was taken as p= 0.809.10 dyn/cm

.

I t is reasonable t o consider a multilayered model of a bond line. According t o this model, t h e shear modulus of t h e layer calculated on t h e basis of t h e measured velocity and attenuation of interface waves is the effective shear modulus peff. I t characterizes the effective elastic properties of t h e multilayered adhesive system. The qualitative description of t h e properties of t h e interface wave can be given on t h e basis of the matrix method. We obtained a series expansion of t h e e x a c t solution with respect t o t h e thickness of interface films. The approximation for the multilayered system makes i t possible t o write the characteristic equatior: for the velocity of t h e interface wave in the form of equation (1) in which p o and po a r e replaced by peff and peff and

2h is t h e thickness of the adhesive layer. hw, P , p

,

a r e t h e thicknesses, density and shear m$dulus of t h e thin boundary layer between inter fa& layer and substrates.

experimentally measured velocity will be smaller than the actual modulus of the film. For example, in t h e case of absence of shear bonding between t h e interface layer and a t least one of the substrates (slip contact) the velocity of the interface wave will be d o s e t o the Rayleigh wave velocity and the calculated p. will be equal t o zero. It is thus seen t h a t t h e interface wave velocity will characterize the 6 k d between the interface layer and the substrates, i.e., t h e interfacial (adhesion) strength. This means t h a t the ratiopeff/CLcan be used a s a criterion of t h e bond strength. If the effective shear modulusp f f is measured for a given bond, and the shear

modulus of the interface is measured on a refgrence specimen, then Equation (2) can be used for estimating the properties of the boundary layers between the interface layer and t h e substrates.

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EVALUATION OF THE CURING O F STRUCTURAL ADHESIVES BY ULTRASONIC INTERFACE WAVES

The curing of structural adhesives is performed in nonisothermal conditions. The standard cure c cle consists of rising temgerature a t a constant rate for 40 min. from room temperatue

₈

t o 120 C (for FM-73) and t o 180 C (for FM

-

300 K). Temperature changes modify the elastic moduli of t h e adhesive film and substrates (adherends). To measure the adhesive properties under nonisothemal conditions, it is necessary t o eliminate the effect of temperature variations in the substrates and transducers. For this purpose a differential measuring arrangement, in the form of an acoustic bridge, was suggested and analyzed 133

.

A computerized ultrasonic system was developed to measure the phase difference of t h e ultrasonic signals from t h e two arms of the bridge [7]

.

I

6

-

6

1.0-

3

I;

as-

S

s

,-

3

j;

8

TIME (min) Fig. 2 Comparison of the ultrasonic

data with the variation of the relative bond strength in the course of the cure.

20 60 LOO 140 180 220 260 300

TIME (minl

Fig. 3 Data for FM-73 adhesive a t different temperatures

Some examples of an application of the method for study of t h e curing of structural adhesives are given below. The changes of t h e time delay of t h e interface wave during curing of t h e FM- 73 structural adhesive a r e shown in Fig. 2 by black circles. The shear strength data obtained in different stages of curing process are also shown in this figure. It is seen t h a t a rise in t h e velocity of the interface wave (rise in the shear modulus of the adhesive) corresponds precisely to t h e time interval of t h e bond-strength growth. Fig. 3 shows results of t h e measurements a t different temperatures of the curing. In Fig. 4 these results a r e summarized in the form of an Arrhenius plot from which t h e activation energy of the curing reaction for t h e FM-73 adhesive was found t o be equal t o 9.3 Kcal/mole. The data for FM-300K structural adhesive a r e shown in Fig. 5. The cure temperatures for this adhesive are higher than for FM-73. The working frequency for all these examples was 0.5 MHz.

C10-812 JOURNAL DE PHYSIQUE

The techique discussed above is applicable to evaluation of thick bonded adherends. It was further developed for evaluation of thin sheet bonding using Lamb waves. An example of time delay and amplitude changes of an ultrasonic signals during adhesive curing is shown in Fig. 7. In this experiment two aluminum plates, each 1.5mm thick, were bonded with 8%of Epon 815 Resin. The measurement frequency was I MHz. The signal changes in Fig.7 correspond

to

the transformation of the So mode to t h e A1 mode during adhesive curing.

TEMPERATURE "C

"

-1 0 l l ' I . ' . I

2.5 2.6 2.7 2.8 2.9 3.0

INVERSE TEMPERATURE (

$

O K x 1 0 3

Fig. 4 An Arrhenius plot of the cure data.

A G I N G ( D A Y S )

Fig. 6 The change in time delay as a function of the aging time.

TIME (min.)

Fig. 5 Data for FM-300K adhesive a t different temperatures.

Fig. 7 The time delay for Lamb wave signal during adhesive curing. 0 8

I

,-

I

C 0 4 - i

-

I- 4 0 2 - I

,

O REFERENCES

Rokhlin, S.I., Hefets, M., and Rosen, M., J. Appl. Phys.,

51

(1980) 3579. Rokhlin, S.I., 3. Composite Mater., 17 (1983) 15.

Rokhlin, S.I., J. Acoust. Soc. Am., 77(1983) 1619.

Rokhlin, S.I., Hefets, M. and Rosen-., J. Appl. Phys., 52 (1981) 2847. Rokhlin, S.I. and Rosen M., Thin Solid Films,

89

(1982) lT3.

Rokhlin, S.I. in ItAdhesive Joints: Their Formation Characteristics and Testing," K.L. Mittal, ed., Plenum Press, N.Y. (1 984).

Rokhlin, S.I. This Volume.