Effect of stress distribution on the strength of joints in ultrasonically-welded plastics

Effect of stress distribution on the strength of joints in ultrasonicallywelded plastics Y. Yamaguchi and S. Amano

Experiments have been carried out which verify the theoretical equations for the stress distribution in a bar-specimen o f plastic material subject to axial ultrasonic waves. It was also shown that the temperature rise in the bar is directly proportional to the amount o f stress and that maximum tensile strength o f a welded j o i n t in the plastic is obtained with maximum temperature rise or maximum stress. Key words: plastics; welded joints; ultrasonic welding; tensile strength.

Ultrasonic welding of plastics is now widely used and has been extensively reported.l-s However, although previous work, eg by Mori 6'7 and others, has dealt with the correlation between the stress produced in plastics by ultrasonic vibration and the temperature rise in the material, there has so far been no experimental work reported on the correlation between the stress and the welding effect. This present investigation was intended to demonstrate experimentally how the stress distribution in plastics rods, butt welded by an ultrasonic longutidinal wave applied along their common axis, contributes to heat generation, and thus temperature rise, in the material; and how these factors affect the welded joint. Polymethylmethacrylate (PMMA), polyoxymethylene (POM), and polycarbonate (PC) were used.

Theoretical basis When a rod of length L and diameter d is directly attached to the tool horn of an ultrasonic transducer, with the direction of vibration as shown in Fig. 1, and resonated, the principal stress produced at a distance x measured from the free end AA is represented by the equationS'9:

otx ) = p c v g -I sin ~ " x

C

(1)

where p is the density of the vibrating body, v is the vibration velocity of the sample component, c is the propagation velocity of the longitudinal wave along the sample, and w is the angular frequency. With the distance from the horn, - x , as abscissa and the stress, o(x). as ordinate, for PMMA(p = 1.18g/cm 3. E = 350 kgf/mm 2) and an angular frequency of 2 x 104/s, the plot for Otx) as shown in Fig. 2 is obtained: this gives otx ) as expressed by Equation (1). In addition, the amplitude a can be determined from the measured value of the reciprocating displacement t (since a = t/2): the temperature rise &Tat each point after the vibration for 30 s was

measured with a radiation pyrometer.* These values as functions of L: (= --x) are collectively shown in Fig. 2. The curves clearly show that both the stress O(x) and the temperature rise AT take maximum values at points q) and @where the amplitude a is zero.

Experiments Free-end resonance experiments were carried out to examine the experin]ental validity of the theoretical Equation ( l ). To investigate the welding effect, pressure welding experiments were carried out in which positive pressure was applied to the end surface of the sample and measurements of t. a, A T . o (etc) were made. The stress at each point x was calculated using Equation (I) and the displacement t measured using a travelling microscope.

Test pieces Three materials, EMMA,POM and PC, were used: Table l gives details of their physical and mechanical properties, including resonant wave length Xr as determined by Equation (2);

Xr=jl (F} 1/2

(2)

where f is the frequency (Hz), and g is the acceleration due to gravity. The diameters d and lengths L of the sample rods were as shown in the right column of Table 1, for resonance and pressurized tests separately.

Resonance tests The following results were obtained when the rod was not divided into the parts M1 and M2 (Fig. 1), the far end (AA) • Infrared radiation pyrometer, type Thermospott 6T11, with a measurement range of 0-300°C, manufactured by San-E; Company Ltd, Japan.

0143-7496/82/030181-05 $03.00 © 1982 Butterworth & Co (Publishers) Ltd

INT.J.ADHESION AND ADHESIVES JULY 1982

181

4

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)

?

.3 ~

30 !

,

~

"

~,

0

/

;

/

v

S,~rfoce

;\F-t

<

20

Fig. 1 Schematic of the arrangements for ultrasonic welding of plastics

-z

was left unrestricted, d and L were as specified in Table 1, and an ultrasonic vibration of 20 kHz was applied to the rod to attain resonance. The reciprocating displacement t, amplitude a, and temperature rise AT after 30 s vibration were determined as functions of location L2 along the axis. Fig. 3 shows the measured longitudinal reciprocating displacement at each point as a function of the distance L2 from the horn, for the three materials. The measured wave lengths are approximately equal to the length L of the rods, and, though somewhat longer than the theoretical values, decrease in the order; eMMA, POM, PC, ie the same order as that of the theoretical wave lengths X, given in Table I. The amplitude a (= t/2) observed for each material reduces with increasing distance from the horn; this is best displayed with Pc, then POM, with PMMA showing only slight damping. The resonance characteristics of PMMA have been shown in Fig. 2 as the representative of the three plastics. As another example, the stress O(x) and temperature rise AT for POM measured in resonance tests are given in Fig. 4 as a function of L2. Analogous to Fig. 2. O(x) and AT take maximum values near the points 1 and 2 where t = 0 or a = 0, indicating that the points are wave nodes.

",

,'

U o

I.(\

_

1.'

,:

,

/'7: .,,. ;. ~ ;!/:o:.

~ ,'x

/:

'

~,,

/ t,'tt

iO

, /

", / \ ~'~

.,

:,

,7 :

',!-' '?:C :

50

~"s'QncP *r.Dr'r

ht~rr

~.,

.

r~r~-I

. 4

(1) Apparent tensile welding strength: ajo (2) Actual tensile welding strength:

oj -

P,r~x

(3)

Ao Pma~

(4)

Aw

-;

Fig. 2 Relationships between t, a, Olx ) , AT and L 2 for PMMA circular bar

~.

POM

PMMA

PC

b,<

=

,. 'i>-,,/%.

,

.

,oL "",

: # .

/

,

¢

/

i

/i

'

/

..... ~ . ~

Plastic rods M~ and M2 of the same material, as shown in Fig. 1, were contacted end-to-end at aa, at a distance L2 cm from the horn, and vibrated by an ultrasonic wave, whilst under compression by force P. After a specified period of vibration, the following values of welding characteristics were determined by longitudinal tension tests on the welded interface aa:

20

40

69

.............

80

tOO

D~stonce from horn end. L 2 (rnm)

Fig. 3

Relationships between t and L 2 for P M M A , PC and POM

(3) Welding efficiency'

17j = -)1°

(5)

- where Ao is the original cross-sectional area of the rods, Aw is the actual welded area measured after breaking, and Prmx is the tensile force needed to break the welded part. Experiments were carried out on rods of the three materials, with d , L . and L2 as specified in Table 1: a pressure p (= P/Ao) of 4.4 or 6.6 kgf/cm 2 was applied•

Properties end dimensions of test ipecimens

Materials

PMMA POM PC

p (g/cm 3)

1.18 1.42 1.20

E (kgf/mm 2)

350 366 211 ~" 2 4 6

Xr* (ram)

83.9 69.7 67.4

,_/Eft ,,2 "x,= ttp!

182

"

'~

}"

Pressure welding experiments

Table 1.

I

//,

J

OL

V,

/

I N T . J . A D H E S I O N A N D A D H E S I V E S J U L Y 1982

Free end test

Applied pressure test

d (mm)

L (ram)

d (mm)

L (mm)

L 2 (mm)

20 20 20

120 80 73

15.4 15.8 15.4

110 80 73

10 ~" 100 10 ~" 70 10 ~ 60

[ 30~ "SOi-

o

\. ': : 3oi-.~

_

't- . r',k.----~ A"X~, \'<\

<., --*-,

.,"-v"

• ,¢

h" *,i'

;

", ,';

'/;

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20

".

",,

40 Lz(mm}

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60

80

Reiationshiosbetweent, a , O ( x ) , A T a n d L 2 f o r P O M

Fig. 4

: '

oo

-,o

//

°li, o}

Fig. 5 is the plot of pip, oj, and Qj against L2 of I',',tMA ultrasonically welded under 4.4 kgf/cm 2 compressive pressure. All the characteristics take the highest values when the welded interface is such that L: is either nearest to point 1 or 2. where a = 0 and O(x) is maximum. Fig. 6 is the same plot of pip. oj. and r7i against L : of the same material. PMMA. butt welded under a pressure of 6.6 kgf/cm 2. It can be seen that the wave length is reduced to half that which occurred in the free-end tests. The total length contains two wave lengths and four peaks of the curve of reciprocating displacement t. Consequently, the plot of temperature rise has four peaks, and stress is estimated to follow the O(x) curve. The stress takes maximum values at four points 1 . 2 . 3 , and 4; that is, twice as much as that which appeared in the free-end tests. It thus appears that pip, oj, and r~j take maximum values at each point where the stress is largest and the temperature is highest. When POM is ultrasonically welded under 6.6 kgf/cm 2 pressure, the amplitude a, estimated stress o, temperature rise AT. oj. and r/j are as plotted in Fig. 7 as functions of L2. As well as the case shown in Fig. 6. the wave length is one-half that shown in Fig. 4, and the stress takes maximum values at four points 1,2, 3, and 4, where AT. oj and r~j also take the highest values.

..............

?:•

x

o

•,

I

•

t2

Discussion

.0

0

20

40

60 L z ~rnml

80

Comparing the cases in which the far end surface is either free or compressed, the wave length of the latter is one-half that of the former. In both cases, in the region where O(x) = 0 in free vibration (between points 1 and 2), the stress takes a minimum value and the welding characteristics are poor. In the latter case, the additional regions whose o is made zero by pressurization (between point 1 and 2. or 3 and 4) have welding characteristics reduced to some extent. Fig. 8 represents the correlation between the amplitude a and the temperature rise AT of PMMA: it can be seen that AT decreases as a increases. The correlation between the temperature rise and the tensile strength of the welded specimen. (oi) at various values of L2 observed in pressure

"

I OC

Fig. 5 Relationships between a, afx ~. o i, Ojo, ~j and L 2 for P M M A with an applied pressure of 4.4 kgf/cn~ 2 "

7 i ;¢'

.:.-. '

I

'.,

~ i00

\ r~

°

C

50

I O0 L 2 {mm

Fig. 6 Relationships b e t w e e n t, a, z~T, oj, pip , r/j and L 2 f o r P M M A w i t h an applied pressure of 6.6 k g f / c m 2

INTJ.ADHESION AND ADHESIVES JULY 1982

183

r. . . . . . . ...4

IOOi

f-x "nl

~,

j,

/,. /\' \/ \

c,.

• /,

.f'IL , / " t A\

,, .i\

i

•

<3

,x

.--

~

"'

i

1

E

_ij2 ~ T:'

5O

I

I"

:

0

,%

~.~ ' ~ ~.. •

~'-

I

!0 40 60 nO L 2 (ram) F~g. 7 Relationships between a, o, AT, oj, ?2j and L 2 for POM with an applied pressure of 6.2 kgf/cm 2 0

..........

20

70 . . . . . .

welding experiments are collectively shown for each material in Fig. 9. In general, oi increases with AT, and, on a comparative basis, o i decreases in the order PC, POM, PMMA.

g

6o,

Conclusions

In the process of butt welding of plastics by ultrasonic vibration, the main stress produced at the welding interface perpendicular to the direction of the vibration achieves a maximum value when the interface is located at points having zero amplitude, ie at the nodes. At these points the highest temperature rise occurs. At resonance, with a free end surface, the stress O(x) at the point x inside the far end is represented by the equation

50-

~C

x/ //x

40.,-

~I~//~A/~A~/ ! x

:

x

P0M

k

<3 30" /x//o~-

O(x) = p c v g -1 sin -~ x

..... P M M A

c

which has been experimentally verified.

.i iI ! i

/ ......................... ~ 0 t 2

\

• •

\

\

If the end surface is compressed by a longitudinal pressure of about 6 kgf/cm 2 during ultrasonic vibration, the distribution of the amplitude is altered, so that the distribution of the stress is also changed, giving a wave length one-half that of the free.end vibration value and doubling the number of maximum-stress points. In the vicinity of each maximumstress point, the temperature rise AT is a maximum and good welding characteristics are obtained: at the point where O(x) = 0 in free vibration, the temperature rise is lowest and welding characteristics are considerably reduced, even with pressurized welding.

\

\ \

\.

Zl-

\

i

\ \

,F

_X* •\

i

\• \

184

5

Fig. 9 Relationships between A T and oj for PMMA, POM and PC, respectively

\

3

Fig. 8

I 4

~1 ( kgf/mmZ)

°\

e\

T

5

f0

20

A T (°C) Relationships between a and AT for PMMA

References 30

INT.J.ADHESION A N D A D H E S I V E S JULY 1982

1

I~H~klr, U. 'Uttrasghallsghweitzen yon Kinststoffen' Kunststoffe 57 No 10 (1967) pp 755-760

Saito, K., Kamon, T., Miwa, Y. and Saeki, K. 'Ultrasonic bonding of plastics, Part 1 ' J Adhesion Soc Japan 7 (1971 ) pp81-87:ibid,'Part 2,'8 (1972) pp8-14 ibid,'Part 3,'8 (1972) pp 311-314: ibid, 'Part 4 . ' 8 11972) pP 315-321

7

Mori, E., Kaneko, S. and Okawa, J. 'Ultrasomc welding of plastics', J Acoustical Soc Japan 28 (1972) pp 136-137

8

Hongo, K. and Tsuyuki, Y. Engineering Vibration (Mor~kita Publishing Co, 1974) p 5 and p99

3

Saito, K., Kamon, T., Miwa, Y. and Saeki, K. 'Studies on ultrasonic bonding, Part 5' J Adhesion Soc Japan 10 (1974) pp 95-104

9

Takahashi, S. et al. 'Fatigue test of magnetostrictive and electrostrictwe materials' 28 (1972) pp 241-251

4

Yamaguchi, Y. et al. 'Study on the ultrasonic welding of plastics' J Japan Soc Plastic Tech 14 (1968) pp619-630 and p 691-697

5

Yamaguchi, Y. et al. 'Ultrasonic welding of plastics', Research Reports of K oga k u in University No 26 (1969) pp 52-64

6

Mori, E. et al. 'Ultrasonic welding of plastics', Proc Ultrasonics International (1973) pp 16-18

2

Authors The authors are both at Kogakuin Universit.v. 1-24-2 NishishiNuku, Shinjuki-ku, Tokyo 160, Japan. Inquiries should be directed to Professor Yamaguchi.

INT.&ADHESION

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