torsional stiffness and fatigue study of surface-mounted compliant leaded systems

7
IEEE TRANSACTIONS ON COMPONENTS,HYBRIDS, AND MANUFACTURINGTECHNOLOGY, VOL. 16, NO. 6, SEWEMBER 1993 577 Torsional Stiffness and Fatigue Study of Surface-Mounted Compliant Leaded Systems Peter A. Engel and Timothy M. Miller Abstraet-Circuit cards with surface-soldered compliant leaded modules are often subjected to torque tests to ensure their struc- tural integrity.The present work exploresthe stiffness and fatigue behavior of such structures. A torsional load tester was devised, exerting cyclic mechanical torque at a desired fixed amplitude and frequency. 'histing loads up into the nonlinear load range were applied. Lead forces were computed by structural analysis methods, and these were compared with finite element results. The Engel-Ling coupled plate theory [l] was found to correspond well to finite element results. Fatigue failures occurred in the solder for J-leads and in the leads for gullwings. Fatigue curves resembled the Coffin-Manson law. NOMENCLATURE a c1, c2 D Dc Dm D, f' E F h Kz L m N N P T WP W &j 4 S W E v (Square) module size. Ritz coefficients. Plate rigidity. Card rigidity. Module rigidity. Fm/P. Modulus of elasticity. Lead force. Plate thickness. Lead stiffness. (Square) card size. Number of modules in cluster. Half the number of leads along a module side. Number of load cycles. TIL. Lead spacing. Card torque. Card deflection. Card comer deflection. Module deflection. Kronecker delta. Strain. Angle of twist. Poisson's ratio. DID,. Manuscript received December 22, 1992; revised February 8, 1993. This paper was presented at the 1992 Electronic Components and Technology Conference, San Diego, CA, May 1%20, 1992. P. A. Engel is with the Department of Mechanical and Industrial Engineer- ing, State University of New York at Binghamton, Binghamton, NY 13902. T. M. Miller is with Dresser-Rand Corporation, Painted Post, NY 14870. IEEE Log Number 9211649. Fig. 1. Circuit board with module attached in center. 11. INTRODUCTION RINTED circuit cards (or boards) are often subjected to P twisting by product assurance agencies, so as to verify the structural integrity or ruggedness of a product. Torsional deformations also occur during various stages of product life, such as in handling, vibration, and shock. Considering the multitude of geometric and material parameters describing the circuit board, the module(s), and the leads attaching the latter to the board (Fig. l), there is great need in formulating engineering stress and strain response in the interest of product reliability. The present paper explores the relationships that arise between torsional load and deformation (i.e., stiffness), and the fatigue life of leads that is a function of the twist amplitude applied to the circuit card. We shall study a square card to which a central square module is attached (Fig.2). Thermal cycling and the ensuing fatigue of leadless and leaded circuit board systems was dealt with by Engelmaier and others (see, for example, [2]-[4]). Barker et al. [5] considered mixed thermal and vibrational cycling. Engel et al. [6] did analytical and experimental stiffness studies and fatigue tests on various circuit board systems subjected to bending. 0148-6411/93303.00 0 1993 IEEE

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Page 1: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

IEEE TRANSACTIONS ON COMPONENTS, HYBRIDS, AND MANUFACTURING TECHNOLOGY, VOL. 16, NO. 6, SEWEMBER 1993 577

Torsional Stiffness and Fatigue Study of Surface-Mounted Compliant Leaded Systems

Peter A. Engel and Timothy M. Miller

Abstraet-Circuit cards with surface-soldered compliant leaded modules are often subjected to torque tests to ensure their struc- tural integrity. The present work explores the stiffness and fatigue behavior of such structures. A torsional load tester was devised, exerting cyclic mechanical torque at a desired fixed amplitude and frequency. 'histing loads up into the nonlinear load range were applied. Lead forces were computed by structural analysis methods, and these were compared with finite element results. The Engel-Ling coupled plate theory [l] was found to correspond well to finite element results. Fatigue failures occurred in the solder for J-leads and in the leads for gullwings. Fatigue curves resembled the Coffin-Manson law.

NOMENCLATURE

a c1, c2 D Dc D m D, f' E F h Kz L m N N P

T

W P W & j

4

S

W

E

v

(Square) module size. Ritz coefficients. Plate rigidity. Card rigidity. Module rigidity.

Fm/P . Modulus of elasticity. Lead force. Plate thickness. Lead stiffness. (Square) card size. Number of modules in cluster. Half the number of leads along a module side. Number of load cycles. TIL. Lead spacing. Card torque. Card deflection. Card comer deflection. Module deflection. Kronecker delta. Strain. Angle of twist. Poisson's ratio.

DID,.

Manuscript received December 22, 1992; revised February 8, 1993. This paper was presented at the 1992 Electronic Components and Technology Conference, San Diego, CA, May 1%20, 1992.

P. A. Engel is with the Department of Mechanical and Industrial Engineer- ing, State University of New York at Binghamton, Binghamton, NY 13902.

T. M. Miller is with Dresser-Rand Corporation, Painted Post, NY 14870. IEEE Log Number 9211649.

Fig. 1. Circuit board with module attached in center.

11. INTRODUCTION RINTED circuit cards (or boards) are often subjected to P twisting by product assurance agencies, so as to verify

the structural integrity or ruggedness of a product. Torsional deformations also occur during various stages of product life, such as in handling, vibration, and shock. Considering the multitude of geometric and material parameters describing the circuit board, the module(s), and the leads attaching the latter to the board (Fig. l), there is great need in formulating engineering stress and strain response in the interest of product reliability.

The present paper explores the relationships that arise between torsional load and deformation (i.e., stiffness), and the fatigue life of leads that is a function of the twist amplitude applied to the circuit card. We shall study a square card to which a central square module is attached (Fig.2).

Thermal cycling and the ensuing fatigue of leadless and leaded circuit board systems was dealt with by Engelmaier and others (see, for example, [2]-[4]). Barker et al. [5] considered mixed thermal and vibrational cycling. Engel et al. [6] did analytical and experimental stiffness studies and fatigue tests on various circuit board systems subjected to bending.

0148-6411/93303.00 0 1993 IEEE

Page 2: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

578 IEEE TRANSACTIONS ON COMPONENTS, HYBRIDS, AND MANUFACTURING TECHNOLOGY. VOL. 16, NO. 6, SEPTEMBER 1993

Fig. 2. Schematic of module/kad card system in torsion.

Engel and Vogelmann [7] gave an approximate engineering analysis of torsionally loaded circuit board assemblies, where the corner lead force clearly dominated; this approximation was valid mostly for plastic modules and stiff leaded sys- tems with relatively sparse lead spacings. Engel and Ling [ 11 formulated a general analytical method for torsionally loaded, square coupled plate systems. Lau [8] used finite element analysis to describe the stiffness of gullwing and J-type leads. Kotlowitz [9] derived and tabulated formulas for the fixed-free spring constants of various leads. Engel et al. [6] used experimental-analytical methods and found the actual lead support conditions corresponded to a module-fixed, card-hinged combination. Generalization from the torsional treatment of a single square module to that of module clusters is treated in [7] and [lo].

111. TESTING METHODS

A. Apparatus The torsion testing apparatus consisted of data gathering

equipment and the test equipment. The data gathering was accomplished by an IBM PC for recording the loads and the displacements, and a video camera with a recorder for filming the fatigue tests.

The actual test equipment is an MTS load tester, with two specially designed torsional fixtures and the circuit card spec- imens. The torsional fixtures, Fig. 3, were made of aluminum and fabricated in several sections, so as to accommodate various sizes and shapes of card segments. Each fixture had a cylinder that was threaded down the center so that it could be mounted to the MTS machine. Attached to each cylinder was a 12.5-cm (5-in) square plate used to support two posts in diagonally opposite corners of the plate. Another optional plate could be attached to the main plate. The optional plate had holes drilled diagonally across; these allowed the posts to be moved closer, permitting the use of different size circuit cards. Each post contained a screw that had a stainless steel ball bearing mounted to the top. Resting the circuit card on the ball bearings, a point load application was simulated; this condition was used in the stiffness tests. Another application of the screws would be tightening them down on the card, for applying reversible loading in the fatigue tests.

Fig. 3 . Load fixture.

The stiffness testing of a card or card/module assembly was performed in such a way as to compare with finite element models. The card was placed on top of the ball bearing loaders of the bottom fixture; each corner of the circuit card had a predrilled hole located 6.25 mm (114 in) from each edge of the card. The holes were not large enough to allow the ball bearings to pass through; their role was to stabilize the card during testing. The top fixture had the same loading devices and would apply the load to two opposing corners of the card. The applied load measurements by the MTS machine needed to be divided by 2 because the force was distributed among two loading points. The measured displacement (6) was the displacement of the two loading points, assuming the other two holding points are fixed. Therefore, if quarter symmetry is assumed, the displacement needs to be divided by 2 assuming all four points move, thus the equivalent load needs to be divided by 4 for half the displacement (1/26) at one comer of the card.

Gullwing leads of Copper 42 alloy material protruded from ceramic modules of 25 mm (1 in) square size. The J-leaded modules were plastic filled (PLCC). The cards were 1.524 mm (0.060 in) thick and made of epoxy glass (FR-4); their square size varied between 89 and 125 mm (3.5 and 5 in). The elastic and geometric parameters of the card, module, and lead specimens are described in Table I.

B. Fatigue Testing

The fatigue study was implemented in a low-cycle, displacement-controlled mode in which the circuit card was subjected to a fully reversed load at the constant frequency of 1/30 Hz. Failure was defined as a partial or total separation of the lead from the cardimodule structure. To determine the time at which failure occurred, test runs were filmed with the camera focused on two sides of the module and the attached leads. The camera was attached to a VCR and a monitor; its magnification was set at 64 x . A monitor was used to allow for periodic evaluations of the testing while the latter was performed. After completion of the test, signaled by a drastic

Page 3: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

ENGEL AND MILLER TORSIONAL STIFFNESS AND FATIGUE STUDY OF LEADED SYSTEMS 519

TABLE I SIZE AND PHYSICAL PARAMETERS OF CIRCUIT

CARD, CERAMIC MODULE AND GULLWING LEAos

Circuit card Size 3.5 x 3.5 in (89 x 89 mm) Thickness 0.060 in (1.524 mm) Modulus of elasticity 3.20 Mlb/in2 (22.06 GPa) Poisson's ratio 0.3

1.0 x 1.0 in (25 x 25 mm) Thickness 0.10 in (2.54 mm) Modulus of elasticity 40.0 Mlb/in2 (275.79 GPa) Poisson's ratio 0.34 No. of leads 144 Lead spacing 0.0265 in (0.673 mm)

Stiffness (fixed-free) 45.33 Ibf/in (7.94 N/mm) Stiffness (fixed-fixed) 575.60 Ibf/in (100.80 N/mm) Modulus of elasticity 17.5 Mlb/in2 (120.66 GPa) Poisson's ratio 0.326

Ceramic module Size

Leads Cross-section 6.5 x 12.0 mils (0.16 x 0.3 mm)

Fig. 4. Gullwing lead failure.

Fig. 5. Head failure.

load drop, the film could be viewed; this allowed for an easier and more accurate cycle count than visual inspection.

The gullwing leads were found to fail as a result of flexural fatigue (Fig. 4) at the module interface. J-leads tended to fail at the solder joint, Fig. 5. In either type of attachment, the comer leads failed predominantly.

Iv. STIFFNESS OF CIRCUIT CARDS AND ASSEMBLIES

Torsional stiffness tests of a circuit card typically show a gradual uptum of the T versus 4 diagram, signaling the onset of large deflections when membrane forces become significant at w > h/3 [ll]. The square card comer deflection w p caused by a torque T = PL (Fig. 6) was modeled by finite element

Fig. 6. Torque of a plain circuit card.

I

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

.................................................. _ ......................... ,J ................................. .............................................

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

Fig. 7. Torque of a module assembly.

(ANSYS) methods using shell elements. The board, leads, and module were considered to have a linearly elastic stress-strain behavior. Both a linear elastic and a geometrically nonlinear membrane analysis were made, and the latter showed the upturn feature. The corresponding experimental upturn was somewhat milder. The elastic problem has an exact solution, namely,

PL2 8(1 - v ) D

w p =

and this also showed close agreement with the other curves of Fig. 6.

When a square module is attached in the center, as in Fig. 2, an increase in torsional stiffness is demonstrated by Fig. 7. The linear finite element analysis and experimental results closely straddle the Engel-Ling linearly elastic analytical prediction [ 11. Geometrically nonlinear finite element analysis substantially overestimates the stiffness increase.

Lead forces are vastly more difficult to measure than tor- sional assembly stiffness. For this reason, credence is given to analytical methods of lead force calculation if the stress analysis accurately predicts the stiffness, Since the Engel-Ling method agreed quite well with both measurements and finite

Page 4: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

-

580 IEEE TRANSACTIONS ON COMPONENTS, HYBRIDS, AND MANUFA(*TURING TECHNOLOGY, VOL. 16, NO. 6, SEPTEMBER 1993

EFFECT OF LEAD STIFFNESS ON FORCE DISTRIBUTION

Force IJbf)

ai a2 a3 a4 #s #s 07 as .omma(Y;~wiulsem~am LEAD X (From Center to Corner)

10 111 APPLIED DEFLECTION

Fig. 8. Lead force distribution

element models of stiffness, it was accepted for lead force prediction as well.

V. LEAD FORCE CALCULATION

Surface mounted modules subjected to flexing (flexure and twisting) develop large axial ( z directional) lead forces F ; this component constitutes the brunt of the lead force; all other lead force components may be practically neglected [I], [6]. Of course the K, lead stiffness must be evaluated considering eccentric bending action, rather than longitudinal rodlike action [7], [9]. K, has proven to have crucial influence on the maximum lead forces [6], [7], and not only regarding their magnitude but their distribution as well. Both finite element analysis and the Engel-Ling theory show that at small K , values the lead force distribution is linear, growing from zero at the center to a maximum at the module corner. Increasing K, , the distribution tends to start through a shallow negative region toward a more pronounced positive peak at the corner, Fig. 8. It follows through physical and analytical grounds [ 11 that stiff modules and closely spaced flexible lead springs will tend to yield linear distributions, while flexible modules such as a PLCC with sparsely spaced stiff leads, will yield strongly peaking corner lead forces.

Note that the use of (1) neglects the presence of the central module, which should add an increment AkT to the torsional stiffness k ~ o = 4( 1 - v ) D of the card. This additional stiffness can be calculated by the Engel-Ling theory as

Dr E 2w(v,; 1: 1) P

A l c ~ = C-UJ(vr: .rc. U T ; 1.1). (2) z = 1

The notation is given in the Appendix. The treatment of module clusters of m modules as a simple extension of the case of a single central module is based on the increase of the torsional stiffness by a commensurate number, m terms computed by (2); this is explained in [7] and [lo]. Suppose the twist 4 is kept as a constant load. Once the torsional

GULLWING FATIGUE DATA DISPLACEMENT CONTROLLED FATIGUE ANALYSIS

WO. DIWLACEYENT fm) h h d 9.2s - 0.128

8 -

2.7s - 2.6 - 0.096 -

2.2s - 0.089

0.079

1.7s - 0.M9

1,s - o.os9 1.26 - 0.049

- 2 - -

- - -

1 - + - 0.099

0 . 7 S - " ' ~ " " ' 0.08

NUMBER OF CYCLES (NI 0 SO 100 160 200 2SO 300 360 400 460 600

Fig. 9. Gullwing experimental fatigue data.

stiffness k~ = k ~ o + mAkT has been obtained, the lead force distribution will then be computed due to the increased torque T = k ~ 4 . This lead force distribution will be approximately the same for all modules of the same size, no matter where the module is located along the card.

For the module/lead/card system of Fig. 7, the numerical values of k~ and k ~ o were 34 590 and 26 000 N . mm (306 and 230 in + lbf), respectively, justifying the increase of slope of the P versus wp curve from Fig. 6 to that of Fig. 7. The relationship used is kl- = P L 2 / ( 2 w p ) .

VI. FATIGUE STUDY

A. Gullwing Module Assembly

Using a constant displacement controlled analysis and a constant frequency of loading at room temperature, a wp-Nf plot is obtained by varying the amplitude of the applied displacement. The applied displacement is a fully reversed cyclic loading on the circuit card that varies from 1.0 mm (0.0394 in) to 2.5 mm (0,098 in). This creates a logarithmic distribution of the number of cycles from 451 to 37.5, as shown in Fig. 9. Each point on the curve represents a test specimen. Using a method such as the Engel-Ling method, the wp-Nf plot can be converted to an F-Nf or c-Nf plot. Equation (3) is a curve fit equation from the experimental data:

This allows an accurate prediction of the fatigue life of a component when the circuit card is subjected to an applied displacement or force. As determined from the experimental data, when a square 8.9-cm (3.5-in) circuit card is subjected to a twisting load which produces a deflection as small as half the thickness of the circuit card, the leads will have a short fatigue life.

Page 5: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

ENGEL AND MILLER: TORSIONAL STIFFNESS AND FATIGUE STUDY OF LEADED SYSTEMS 581

J-LEAD FATIGUE DATA DISPLACEMENT CONTROLLED FATlGUE ANMYSlS

0.177

0.167

Fig. 10. J-lead experimental fatigue data.

B. J-Lead Module Assembly The testing of the J-lead module/lead/card assemblies fol-

lows the same guidelines as the testing of the gullwing leaded modules. The fatigue life of these modules ranged from 512 to 14.75 cycles for a displacement range of 3.25 mm (0.128 in) to 5.5 mm (0.217 in), respectively (Fig. 10). These data could also be converted to an F-Nf plot or e-Nf, as previously described.

VII. RESULTS AND DISCUSSION

Three major mechanical effects in simple compliant leaded systems were investigated herein: torsional stiffness, lead force distribution, and fatigue. For a quantitative understanding of these effects, the correspondence of numerical and experi- mental data with a reliable analysis method needed to be established.

Based on the assumption of linear axial spring action by equally spaced leads, the Engel-Ling linear elastic theory was found to correspond accurately to finite element (ANSYS) results in the small displacement range. The correspondence was so satisfactory that the finite element calculations were discontinued after running several types of parameters, ranging from softer modules (plastic leaded chip carriers, PLCC) to ceramic ones that were used in the present experimental work. Other parameters that were varied were the lead stiffness and spacing, and the size of the card and module. The analytical theory yields n simultaneous equations in n unknown lead forces along the side of the square module; n z a/2s.

For the relatively moderate lead stiffness and dense spacing used with the ceramic modules, the lead force distribution proved to be close to linear, with the maximum lead force F,, arising in the comer lead. For PLCC modules [7], the comer force was found to rise sharply over the rest of the lead forces.

Calculating F,, from P, the external force creating the torque T = P L , one would first establish the ratio f = F,,/P from the theory (appendix); T would either be given,

or a specified twist q5 or card comer deflection w p would yield it through T = kT . q5 and q5 = 2wp/L. The torsional stiffness I ~ T , increased by the module over that of the bare card, must be measured or calculated [see (2)].

misting an L = 8.9 cm card with a 25-mm ceramic module on it, a deflection w p = 0.1 mm would be caused by a force P = 0.9 N (0.2 lb). This is still in the linear range as shown in Fig. 7; however, w p = 1 mm (P = 8.9 N or 2.19 lb) would already begin to cause some nonlinear geometric effect. As the load (i.e., torque) rises faster from here on, w p = 2.5 mm is expected to correspond to a larger than linear increment; however, the experimentally observed increase of torsional stiffness was much less than found by finite elements.

The data indicate that if the bare card stiffness is approxi- mately by a second-order relationship

P = A W ~ + BW;

P = CWP + Dw;

(4)

and the module-reinforced card, likewise:

(5)

then C can be obtained from one experiment as a constant. Furthermore, the curvature of P( w p ) does not change, because it is due to nonlinear deformation of the circuit card alone, and not caused by nonlinearities in the module or leads; consequently,

D = B. (6)

In fact, from the data (Fig. 6), A = 6.5 N/mm, B = 2 N/mm2; from Fig. 7, C = 10 N/mm, and, confirming (6), D = B = 2 N/mm2.

The parameters of Table I led to a ratio f = 0.1, so that for w p = 1 mm a comer lead force F,,, = 0.89 N (0.2 lb) would result. For the nonlinear geometrical effect, however, the maximum lead force is expected to grow proportionally to P, and not to w p , so that at w p = 2.5 mm, from (5 ) and (6), we get

Fm, = f[(10)(2.5) + (2)(2.5>2] = 3.75N(0.8431b).

In the range of the displacements w p employed in the fatigue tests (Fig. S), the gullwing leads are subjected to substantial plastic deformations; this is easily shown. A section modulus of S = 0.00128 mm3 and an eccentricity of e = 0.6 mm are estimated, resulting in the elastically computed bending stress 0.6F/0.00128 = 469F MPa; this will certainly exceed yield, IS E 140 MPa for w p over 1 mm. As an elastoplastic response, the stress will be redistributed in the leads; fatigue damage, cracking, and eventual failure follow during cycling.

Fig. 11 shows the fatigue curve for gullwing leads corre- sponding to Fig. 9, where w p has been transformed to F,, by the above analytical procedure, including the large deflection relations. The range of the curve corresponds to low-cycle fatigue, which may be compared with the higher 103-107 cycle range tested in an earlier work [6]. In that investigation, pairs of leads were bonded from above and below to the faces of the tester. It is remarked that similar observations were made in

Page 6: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

~

582 IEEE TRANSACTIONS ON COMPONENTS, HYBRIDS, AND MANUFACTURING TECHNOLOGY, VOL. 16, NO. 6, SEPTEMBER 1993

GULLWING FATIGUE DATA - MAX. LEAD FORCE DISPLACEMENT CONTROLLED FATIQUE ANALYSIS

1 , I 4.448

I I I I I , , 0.1 ‘ m WO K)o

NUMBER OF -E8 (NI

Fig. 11. Gullwing maximum lead force fatigue data.

[6] about gullwings fatiguing through the lead portions, while J-leads failed through the solder joints.

No attempt was made to vary the applied loading frequency, which would have a possible effect on the fatigue strength. Especially in the case of the J-leads that failed through the solder, a larger fatigue strength is expected at higher frequencies.

VIII. CONCLUSIONS

The Engel-Ling structural analysis method was found to correspond closely to finite element computations of compliant leaded systems. It facilitated computation of maximum lead forces and torsional stiffness; the lead force distribution in closely spaced gullwing leaded ceramic modules was nearly linear.

Large displacements added significant torsional rigidity to the assembly, tending to proportionally increase lead forces. Fatigue curves of gullwing leaded and J-leaded modules were generated by a torsional apparatus devised for circuit card systems.

APPENDIX

A. Notation of Engel-Ling Theory

The displacement at point (z, y) of a square plate of size L and constants (0, v), due to an antisymmetrical configuration of four pairs of point forces, each applied symmetrically with respect to the diagonal (z = E , y = 77) and (z = 77, y = E ) is written in the five-parameter form w(v; I , 77; 2, y). Here z, y are nondimensionalized coordinates z = X / ( L / 2 ) , y =

Lead force solutions are effected by stipulating compati- bility of module, card, and lead displacements, W = w + F / K . The respective plate displacements from pairs of forces F(<, 7) can be written as

Y / ( L / 2 ) .

w = w(v; E , 77; 5 , y) = c lzy + c22y(z + Y) (AI)

where the Ritz coefficients are

c1 = “ [(6 + v) + 6(1 - v ) ( 2 - E - 77)] (A2) (1 - ~)(6 + V ) and

The plate displacement from a force applied along the diagonal can be written as

w W ( V ; E ; 5 , 1 ~ ) = clzy + C ~ X ~ ( Z + y), (A4)

where the Ritz coefficients are

and

The lead forces Fi are then computed from simultaneous algebraic equations, expressing the compatible displacements of module, lead, and card at each lead location. Note that, to obtain the physical displacements of the nodule, a factor a2 / ( 4 O m ) must multiply the nondimensional displacement w(v,; 5, 77; z, y). For the card, the corresponding factor is L2/(4Dc>.

ACKNOWLEDGMENT

The authors thank B. G . Sammakia and D. V. Caletka of the IBM Endicott Laboratory for supplying and evaluating some useful test materials.

REFERENCES

[ l ] P. A. Engel and Y. Ling, “Torsion of elastically coupled plates with applications to electronic packaging,” in Proc. ASMEIJSME Elecrronic Packaging Con$, Milpitas, CA, Apr. 1992, pp. 575-581.

[2] W. Engelmaier, “Surface mount solder joint long-term reliability: De- sign, testing, prediction,” Soldering and Surface Mount Technology, no. 1, pp. 14-22, 1989.

[3] J-P. M. Clech, W. Engelmaier, R. W. Kotlowitz, and J. A. Augis, “Surface mount solder attachment reliability figures of merit-Design for reliability tools,” in Proc. SMART V Conf., New Orleans, LA, 1989.

[4] H. D. Solomon, “Low cycle fatigue of surface mounted chip car- riedprinted wiring board joints,” in Proc. 39th ECTC Con$, 1989, pp. 277-292.

[5] D. Barker, J. Vodzak, A. Dasgupta, and M. Pecht, “Combined vibra- tional and thermal solder joint fatigue-A generalized strain versus life approach,” ASMEJ. Electronic Packaging, vol. 112, no. 2, pp. 12%134, 1990.

[6] P. A. Engel, D. V. Caletka, and M. R. Palmer, ‘‘Stiffness and fa- tigue study for surface mounted moduleflead/card systems,” ASME J. Electronic Pachging, vol. 113, no. 2, pp. 129-137, 1991.

[7] P. A. Engel and J. T. Vogelmann, “Approximate structural analysis of circuit card systems subjected to torsion,” ASME J. Electronic Packaging, vol. 114, no. 3, pp. 203-210, 1992.

[8] J. H. Lau, “Static and dynamic analyses of surface mount component leads and solder joints,” Solder Joint Reliability; Theory and Applica- tions, J. H. Lau, Ed. New York: Van Nostrand Reinhold, 1991, Chap. 15.

[9] R. W. Kotlowitz, “Comparative compliance of generic lead designs for surface mounted components,” IEPS J . , vol. 10, no. 1, pp. 7-19, 1988.

[lo] P. A. Engel, StructuralAnalysis of Printed Circuit Board Systems. New York: Springer Verlag, 1993.

[ I l l S. P. Timoshenko and S . Woinowski-Krieger, Theory of Plates and Shells, 2nd ed. New York: McGraw-Hill, 1959.

Page 7: Torsional stiffness and fatigue study of surface-mounted compliant leaded systems

ENGEL AND MILLER TORSIONAL STIFFNESS AND FATIGUE STUDY OF LEADED SYSTEMS 583

Peter A. Engel received the B.E. degree from Vanderbilt University, the M.S. degree from Lehigh University, and the Ph.D. degree from Come11 Uni- versity (1968) in theoretical and applied mechanics.

He has extensive industrial background, having worked at Boeing (Saturn Division) and IBM (En- dicott Laboratory). He is a Professor of Mechanical Engineering at SUNY Binghamton at present.

Dr. Engel is technical editor of the Journal of Electronic Packaging (ASME). He is author of the books Impacr Wear of Materials and Structural

Analysis of Printed Circuir Board by Systems and of over 80 papers.

Timothy M. Miller received the B.S. degree in mechanical engineering and the M.S. degree in mechanics and design from the State University of New York at Binghamton in 1989 and 1992, respectively.

Currently, he is a finite element analysis engineer at Dresser-Rand, Painted Post, NY.