Joining by plating: Optimization of occluded angle

Surface Technology, 10 (1980) 133 - 145

133

© Elsevier Sequoia S.A., Lausanne - - P r i n t e d in the Netherlands

JOINING BY PLATING: OPTIMIZATION OF OCCLUDED ANGLE

J. W. DINI, H. R. JOHNSON and Y. R. KAN

Sandia Laboratories, Livermore, Calif. 94550 (U.S.A.) (Received July 16, 1979)

Summary An empirical method for predicting the minimum angle necessary for maximum joint strength in materials joined by plating was developed by way of a proposed power law failure function whose coefficients are taken from ring shear and conical head tensile data for plating/substrate combinations and whose exponent is determined from one set of plated joint data. Experimental results are presented for A1-Ni-A1 (7075-T6) and AM363-NiAM363 joints, and the failure function is used to predict joint strengths for A1-Ni-A1 (2024-T6), UTi-Ni-UTi and Be-Ni-Be.

1. Introduction

Electroplating is sometimes used to join metals that cannot be joined by conventional techniques [ 1, 2]. The process typically involves machining a taper on the parts to be joined, mating them, buiding up the tapered region with a thick electrodeposit and machining to final dimensions. Figure 1 is a scheme of the joining process. Complete details of the technique including applications and property data have already been reported [1, 2]. The influence of the taper angle on the mechanical performance of the joint has not been rigorously addressed. Rather, those wanting to use the process have been guided by design criteria, intuition and experience. The purpose of this work was to provide a method for analyzing the influence of the degree of taper on joint strength in order to predict the minimum angle necessary for optimum adhesion without needing to fabricate and test a large number of joints. In Section 2 we present the results of shear and tension tests for nickel plating, which is the most commonly used electrodeposit for joining applications. The bond strengths obtained provide the primary input to the calculations. In Section 3 a failure function for plated joints is proposed. It gives the joint strength as a function of occluded angle in the form of a power law whose exponent N must be determined (at least within the scope of the present analysis) from a fit to one set of plated joint data. Experiments on nickel-plated joints are described in Section 4. A determination of N is

134

I

II

AI

!

Assemble Machine taper

Ni plate

Machine

Cu strike on AI

Fig. 1. Steps in the joining-by-plating process. made from aluminum data and the value is used to predict joint strengths for other parent materials (Section 5). The results of the theoretical calculations are compared with data on AM363 stainless steel joints. Conclusions are given in Section 6. 2. Ring shear and tension test data for nickel plating Quantitative shear and tensile strengths of plating/substrate combinations are more easily obtained than plated joint strength data. The techniques for obtaining these bond strength data are basically as follows. For the ring shear test a cylindrical rod is coated with separate rings of electrodeposit of predetermined width. The rod is forced through a hole in a hardened steel die, the hole diameter being greater than that of the rod b u t less than that of the rod and the coating (Fig. 2). The bond strength (interface shear strength) Ss (in mega-newtons per square metre or pounds-force per square inch)is determined by the formula S s = W / T r d t where d is the diameter of the rod, t the width of the deposit and W the force required to cause failure in the specimen. For the tension test, samples are prepared by thickly plating a fiat substrate on both sides with electrodeposit. Conical head specimens are machined from the composite and then tested using standard tension testing procedures. Figure 3 shows specimen dimensions and a cut-away view of a

135

SPECIMEN UNDER TEST (CUT AWAY VIEW)

SO STRATE\

P TEO OEPOS,T--,

12712"6olA.~

':

25.4 +o.,~'

-

' :::::::::::-~

12.7

-

~ ~

12.4 D I A . 12.6

15.9 D I A . 16.i

19.0

Fig. 2. Ring shear test specimen. specimen under test. The normal tensile strength Sn is given by the formula Sn = W/(rrd2/4). Details of both these tests are included in ref. 3 along with data and references for substrate/coating combinations tested by these techniques. Table 1 includes ring shear and conical head tensile test data for a number of substrates of interest for possible joining by nickel plating. Values for 7075-T6 aluminum and AM363 stainless steel are included. A comparison of the shear-to-tensile ratios for these two materials shows a wide variation -from 0.44 for aluminum to 0.94 for AM363. These data were used to c o m p u t e theoretical joint strengths as discussed in Section 3.

3. Phenomenological joint strength function The object of this analysis was to determine the m i n i m u m occluded angle ~ for o p t i m u m joint strength using the interface shear strength Ss and

136

i:i:!~ii:i:i:i;:iiiii!ii! :ti!i:ii"~i:i~i

SPECIMEN UNDER TEST (CUT AWAY VIEW

PLATED D E P O S I T -

- P L A T E D DEPOSIT

£

SUBSTRATE

1 5.3

l

J I--

J I

STOCK (12.2 MIN,)

( A L L DIMENSIONS ARE IN rnm)

Fig. 3. Conical head test specimen.

tensile strength Sn obtained experimentally from the ring shear and tension tests respectively. However, as will be seen, because of our lack of knowledge of h o w Ss and Sn interact to comprise the joint strength, it is also necessary to have some representative joint data for one parent material. The m e t h o d TABLE 1 Bond strengths for various materials plated with nickel a

Material

Beryllium U-0.8Ti Aluminum (7075-T6) Aluminum (2024-T6) Stainless steel (AM363)

Conical head tensile strength

Ring shear strength

(MN m - 2 )

(lbf i n - 2)

(MN m - 2 )

(lbf in - 2 )

317 507 572 445 490

46 73 83 64 71

252 247 250 221 455

36 35 36 32 60

000 500 000 500 000

Shear-to-tensi strength ratio

500 800 200 000 000

0.79 0.49 0.44 0.50 0.94

aSee ref. 3 for details of these tests. Plating was done in a nickel sulfamate solution.

137

is first to establish a failure criterion for the bonding interface. This is used to find the joint strength as a function of Ss, Sn, a and a parameter N which contains information on the coupling between Ss and Sn. A fit of the failure function to one set of joint data then determines the value of N for that plating material, and thus amin can be predicted for other parent materials with the same plating material. When a joint is loaded axially the bonded interface is under combined shear and tensile stresses. Figure 4 shows a sketch of a typical plated joint, with an occluded angle a, subjected to a nominal axial load o applied at both ends. The detailed elastic stress field in the joint is very complex and is a strong function of a and of the parent and plated material properties. At the failure load, however, the stress state at the bonding interface is uniform because of the plasticity effect. The tensile stress On and shear stress r in the interface can be calculated for the equilibrium condition by the formulae On = 1 a ( 1 + c o s ~) (1)

T=~O sin The proposed interface failure function is based on ideas developed by Mises and by Tresca [4]. The form suggested by their work is f($n, T)-----(~-n]

"1"( ~ S

--1

(2)

where Sn is the normal tensile strength obtained from the conical head tension test, Ss the shear strength obtained from the ring shear test and N a dimensionless constant (which needs to be determined from joint strength data). The experimentally determined Sn = W / ( ~ d 2 / 4 ) and S s = W/rrdt do n o t take stress concentration into account. This is justifiable, however, since any stress concentration at the bonding interface must be smoothed by local plasticity at the failure load so that the shear and tensile stresses are in fact uniform. The failure function f(On, r) will never be greater than zero, and the failure criterion is f(On, r) = 0. F o r N = 2 and S s / S n = 1/x/~, f(On, r) becomes Mises' maximum distortion energy yield criterion for an isotropic material, whereas for N = 2 and S s / S n = 1/2 it is Tresca's maximum shear stress yield

on

o

•

,4~

o n

o.

Fig. 4. A typical plated joint w i t h o c c l u d e d angle a~ under tensile and shear stresses r e s p e c t i v e l y .

an axial load o. r and a n are the

138

criterion. Both Mises' and Tresca's criteria take account of the fact t h a t the first stress invariant (the hydrostatic component) has no effect on the yielding of the isotropic material. In plated joints, however, the ratio of shear to tensile strength varies from 0.44 for AI-Ni-A1 to 0.94 for AM363Ni-AM363; in addition, the hydrostatic stress c o m p o n e n t does affect the failure at the interface. Therefore, even though the proposed failure function has the same form as the yield criteria of Mises and Tresca it c a n n o t be assumed that N = 2 will be suitable. The value of N will depend on the degree of interaction between the shear and tensile stresses. Figure 5 shows the failure function f(an, r) for some specific values of N. N = oo corresponds to no interaction between the shear and tensile stresses so t h a t the presence of shear stress will n o t reduce the tensile strength of the interface and vice versa. When N = 2 (the Mises or Tresca ellipse) there is mild interaction; when N = 1 there is very strong interaction. Because of the interaction the shear stress c o m p o n e n t considerably reduces the tensile strength of the interface. By substituting an and r of eqn. (1) into the failure function, the joint strength a can be expressed in terms of the occluded angle ~, the interface tensile strength Sn, the shear strength Ss and N by the equation = l( +1 1 - ~~ cos ~

)N(Isino~)Nf--IlN+ ~

(3)

a S, Ss The effect of power N on the joint strength a at various occluded angles is plotted in Fig. 6 for given interface tensile a n d shear strengths. The joint strength has a value of S, at e = 0 for all values of N when Sn < Sp, the strength of the parent material. For low N, a first decreases with increasing ~, reflecting the interaction between the shear and tensile stress components. The horizontal line a = Sp at larger values of e represents the tensile strength of the weakest material. Since joints can never be stronger than the tensile strength of the parent material, for large occluded angles the joint will fail in

N=~

N=2N=I

g

N=~

so

Ss

I t I I D Sn

(l n

L

I

90 °

180 ~

Occluded angle ~'

Fig. 5. Plots o f t h e failure f u n c t i o n f ( a n , T) = 0 in t h e On-7" p l a n e for various values o f t h e e x p o n e n t N. Fig. 6. T h e j o i n t s t r e n g t h o as a f u n c t i o n o f o c c l u d e d angle ~ ( e q n . (3)) for various values o f N. T h e h o r i z o n t a l line o = Sp r e p r e s e n t s t h e s t r e n g t h o f t h e p a r e n t m a t e r i a l .

139

the parent material instead of at the interface if the angle ~ for ~ = Sp is the m i n i m u m occluded angle necessary to achieve the m a x i m u m joint strength. The value of N for joints with a given plating is determined from a fit of a to a representative set of joint strength data, as shown in Fig. 6.

4. Plated joint data The widest variation in the ratio of shear to tensile strength in Table 1 is for aluminum and stainless steel. It was therefore decided to determine N from a fit to aluminum/nickel joint strength data and, on the basis of t h a t N value, to test the predicted values of joint strength against stainless steel data. Our confidence in the phenomenological theory for use with other parent materials would depend on the closeness of fit. We joined aluminum rods (7075-T6) and also AM363 stainless steel rods with nickel plating. On both sets of rods we used tapers ranging from 4 ° to 55 ° (Fig. 7). All rods had an inner diameter of 3.2 mm (0.125 in) and a wall thickness of 1.59 m m (0.0625 in). For the joining process an aluminum cylinder slightly less than 3.2 m m (0.125 in) in diameter was inserted through the inner diameter of the specimens to provide support and to keep t h e m aligned during nickel plating. The zinc immersion m e t h o d (zincating) was used to prepare the alumin u m for plating. This provides an adherent base onto which other metals can

A =

4 ~

15 ° 30 ° 45 ° 55 °

\ A

.

•

-

-

7.9

mm

Fig. 7. Specifications for tapered joints.

~

.

.

.

12.7

ran,

140

be deposited. To prepare stainless steel for plating, a Wood's nickel strike was used [5]. In this m e t h o d the oxide film is removed and replaced with a thin film of nickel which serves as a base for subsequent plating. After plating, the cylinders were removed and the outer diameters of the joined parts were machined to final dimensions. Figure 8 shows some rods after joining. The rods were tested to failure by using an Instron machine and specially designed jaws. The data for aluminum rods joined by nickel plating are presented in Fig. 9. They show t h a t m a x i m u m strength joints were obtained whenever the occluded angle was 120 ° or more. For angles less than 120 ° , joint strengths progressively decreased as the occluded angle decreased. For occluded angles of 120 ° or more, failure always occurred in the aluminum. When the occluded angle was less than 120 ° , failure occurred at the interface between the aluminum and the plating. The data for the AM363 stainless steel rods joined by nickel plating are presented in Fig. 10. Maximum strength joints were obtained when the occluded angle was 90 ° or more.

5. Comparison of theory and experiment Figure 11 shows the measured A1-Ni-A1 (7075-T6) joint data, represented by circles, and the failure function with N = 1, 1.2, 2 and oo. The best fit is f o u n d for N = 1.2 (full curve). Corresponding data for A M 3 6 3 - N i AM363 are shown in Fig. 12 along with the predicted curve for N = 1.2

Fig. 8. E x a m p l e s o f r o d s j o i n e d b y plating. S h o w n are t u b e s p e c i m e n s w i t h a 4 ° t a p e r ( t o p ) , a 15 ° t a p e r ( m i d d l e ) and a 30 ° t a p e r ( b o t t o m ) .

141 I

'

I

I

I

I

I

I

I

I

100,000

80,000

)

.-=-_

500

60,000

400

z

E

3oo }

40,000

200

E

20,000 100

I 80

i

70

,

I

90

,

I

I , J , l 110 120 130 Occluded angle (degrees)

,

100

I 140

,

,

I 150

~

J 160

,

170

Fig. 9. Joint strength data (o) as a function of occluded angle for A1-Ni-A1 (7075-T6). The curve is a guide for the eye only.

'

]

'

]

I

'

I

550

8 0 0 0 0 --

0

0

'0.

'500

70000 450 ~

E Z

60000 400

50000

-

i -350

-

70

90

110 Occluded

130

150

170

angle (degrees)

Fig. 10. Joint strength data (o) as a function of occluded angle for AM363-Ni-AM363. The curve is a guide for the eye only.

(full curve) and, for c o m p a r i s o n , curves for N = 1.0 and N -- 2.0. T h e N = 1.2 fit is fairly g o o d a l t h o u g h the N = 1.0 fit is n o t unreasonable. Using N = 1.2 for t h e A 1 - N i - A 1 ( 7 0 7 5 - T 6 ) joint, the predicted o p t i m u m angle (the m i n i m u m angle for m a x i m u m j o i n t strength, at o = Sp) is 1 2 3 ° and t h e m e a s u r e d angle is a b o u t 1 2 0 ° . T h e predicted o p t i m u m angle for the A M 3 6 3 - N i - A M 3 6 3 j o i n t is 8 3 ° and the m e a s u r e d angle is a b o u t 9 0 °. T h e

142 100,000

I

I

1

/

I

I

I

I

f

600 80,000

- x-~

- -'-'---2

~

~

N=2

O=Sp

"~ -r g " /

.. ~

O

60,000

500

-- 400

Sn = 83,000 psi (573 M N / m 2) Ss = 36,200 psi (250 M N / m 2)

N=I

40,000

c~ z

-- 300

O M e a s u r e d data - - 200

20,000 Ni

r

100

T

I

I

I

I

I

I

I

I

20

40

60

80

100

120

140

160

180

Occluded angle ~ (degree)

F i g . 1 1 . F i t o f t h e j o i n t s t r e n g t h f u n c t i o n a s a f u n c t i o n o f o c c l u d e d a n g l e t o t h e A1 N i - A 1 (7075-T6) data. The N = 1.2 fit (full curve) isthe best. Other fits (N = 1.0, 2.0, ~) are s h o w n as b r o k e n l i n e s .

100,000 ~

,

I

'

I

'

I

'

I

'

I

'

1

]

i

[

i

600 80,000 ~ -

I..~N

= 2 & o =

~z

60,000 --

"~"~'~--.~

N = 1

O

400

~.--- -~''//

Sn = 71,000 psi (490 M N / m 2) Ss = 66,000 psi (455 M N / m 2) O M e a s u r e d data

40,000

300

i

l 20

i

I 40

i

I 60

,

M963 I 80

A ,

[

E

200

(Y

o --tA

500

Sp

,

1 O0

691--- o I

120

,

I 140

,00 ,

I 160

i

0 180

Occluded angle c~ (degree)

Fig. 12. Comparison AM363-Ni-AM363. N= 2.0.

of the joint strength function for N = 1.2 (full curve) with data for Also shown are theoretical curves (broken lines) for N = 1.0 and

weakest predicted joints for both aluminum alloy and stainless steel occur at ~ 70 °. The reduction in strength is a b o u t 159 MN m -2 (from 524 MN m -2 to 3 6 4 MN m -2) for the A1-Ni-A1 (7075-T6) joint and about 48 MN m -2 (from 503 MN m -2 to 4 5 5 MN m -2) for the A M 3 6 3 - N i - A M 3 6 3 joint. The large reduction in strength for the aluminum alloy joint is caused by its low

143 ratio of interface shear strength to tensile strength (250 MN m -2 to 572 MN

m-2). Using the shear and tensile strength data listed in Table 1, the joint strengths predicted for A1-Ni-A1 (2024-T6), B e - N i - B e and U T i - N i - U T i joints are plotted in Figs. 13 - 15. The predicted optimum angles are listed in Table 2 together with optimum angles for 7075-T6 aluminum alloy and AM363 stainless steel joints. The very small predicted optimum angle (a = 90 °) for B e - N i - B e is due to its high ratio of shear strength to tensile strength (~0.79).

6. Conclusions A failure criterion has been proposed for predicting the strength as a function of occluded angle for plated joints subjected to an axial load. It is in the form of a power law whose coefficients are extracted from shear and tensile test data and whose exponent N must at present be determined from a fit to a representative set of plated joint data. For nickel, data on A1-Ni-A1 (7075-T6) showed N to be about 1.2, which was found to be consistent with A M 3 6 3 - N i - A M 3 6 3 data. The value of N = 1.2 appears to represent a strong interaction between the shear and tensile stresses at the nickel-parent material interface. We conclude that the proposed failure function can be used with confidence as a guide in fabricating nickel-plated joints with other materials. 100,000

I

r

I

I

T

r

600 80,000 -

~

60,000 -

500 ~mln

= 122 °

-- 400 E

N = 1.2

E

-- 300 40,000 - Sn = 64,500 psi (445 M N / m 2) Ss = 32,000 psi (221 M N / m 2)

-- 200

20,000 --

40

I

I

I

I

I

I

60

80

100

120

140

160

Occluded

angle

~

100

180

(degree)

Fig. 13. Predicted joint strength as a function o f occluded angle for A I - N i - A I (2024-T6).

144 100,000

F

q

I

I

]

]

600 80,000

/

,

~m in ~ 123°

/

500

~•

60,000

4OO ~

N = 1 . 2 ~

3oo

E 40,000 Sn = 73,500 psi (507 MN/m 2) Ss = 35,800 psi (247 MN/m 2)

200

20,000 100

0 40

I 60

I 80

I 100

I 120

I 140

I 160

180

Occluded angle ~ (degree)

Fig. 1 4 . P r e d i c t e d j o i n t s t r e n g t h as a f u n c t i o n o f o c c l u d e d angle for U T i - N i - U T i .

100,000

I

I

I

]

I

I

600 80,000

Sn = 46,000 psi (317 MN/m 2) Ss = 36,500 psi 252 MN/m 2 500

60,000

400 E

~ --~min = 90°

v

J

N=1,2

300

40,000

200 c~

20,000 100

40

I

I

I

I

k

I

60

80

100

120

140

160

Occluded angle ~ (degree)

Fig. 1 5 . P r e d i c t e d j o i n t s t r e n g t h as a f u n c t i o n o f o c c l u d e d angle for B e - N i - B e .

180

145 TABLE 2 P r e d i c t e d a n d m e a s u r e d o p t i m u m o c c l u d e d angles

Material

Predic ted optimum angle

Measured o p t i m u m angle

Aluminum (7075-T6) Stainless steel ( A M 3 6 3 ) Aluminum (2024-T6) U-0.8Ti Beryllium

123 ° 83 ° 122 ° 123 ° 90 °

120 ° 90 ° -

Predictions for the joint strengths as a function of occluded angle are given for A1-Ni-A1 (2024-T6), U T i - N i - U T i and B e - N i - B e . It would be of interest to test the failure function for other plating materials to see whether the general form is universal and, if so, to investigate .the variation of N with plating material.

Acknowledgment This work was supported by the U.S. Department of Energy under Contract At~29-1)-789. References 1 J . W . Dini a n d H. R. J o h n s o n , Met. Eng. Q., 14 (1) ( 1 9 7 4 ) 6. 2 J. W. Dini a n d H. R. J o h n s o n , E l e c t r o c h e m i c a l j o i n i n g : process, a p p l i c a t i o n s , a n d p r o p e r t y d a t a , SME Teeh. Paper AD75-855, Society o f M a n u f a c t u r i n g Engineers, D e a r b o r n , M i c h i g a n , U.S.A., 1 9 7 5 . 3 J. W. Dini a n d H. R. J o h n s o n , A d h e s i o n t e s t i n g o f d e p o s i t - s u b s t r a t e c o m b i n a t i o n s , A m . Soc. Test. Mater., Spec. Tech. Publ. 640, 1 9 7 8 , p. 305. 4 R. Hill, The Mathematical Theory o f Plasticity, O x f o r d U n i v e r s i t y Press, O x f o r d , 1 9 6 7 , p p . 15 - 23. 5 D. W o o d , Met. Ind. (N.Y.), 36 ( 1 9 3 8 ) 3 3 0 .