Table Of ContentMechanical Engineering Series
Frederick F. Ling
Series Editor
AdvisoryBoard
Applied Mechanics FA Leckie
University ofCalifornia,
Santa Barbara
Biomechanics V.c. Mow
Columbia University
ComputationalMechanics H.T.Y. Yang
Purdue University
DynamicSystemsand Control K.M. Marshek
University ofTexas, Austin
Energetics J.R. Welty
Oregon State University
MechanicsofMaterials I. Finnie
UniversityofCalifornia, Berkeley
Processing K.K. Wang
Cornell University
ThermalScience A.E. Bergles
Rensselaer PolytechnicInstitute
Tribology W.O. Winer
Georgia InstituteofTechnology
Peter A. Engel
Structural Analysis
of Printed Circuit
Board Systems
With 192 Figures
Springer Science+Business Media, LLC
Peter A. Engel
Department of Mechanical and Industrial
Engineering
State University of New York at Binghamton
Binghamton, NY 13902-6000 USA
Series Editor
Frederick F. Ling
Ernest F. Gloyna Regents Chair in Engineering
Department of Mechanical Engineering
The University of Texas at Austin
Austin, TX 78712-1063 USA
and
William Howard Hart Professor Emeritus
Department of Mechanical Engineering,
Aeronautical Engineering and Mechanics
Rensselaer Polytechnic Institute
Troy, NY 12180-3590 USA
Library of Congress Cataloging-in-Publication Data
Engel, Peter A.
Structural analysis of printed circuit board systems/Peter A.
Engel.
p. cm. - (Mechanical engineering series)
Inc1udes bibliographical references and indexes.
ISBN 978-1-4612-6945-8 ISBN 978-1-4612-0915-7 (eBook)
DOI 10.1007/978-1-4612-0915-7
1. Printed circuits - Design and construction. 2. Structural
analysis (Engineering) 1. Title. II. Series: Mechanical
engineering series (Berlin, Germany)
TK7868.P7E53 1993
621.3815'31 - dc20 92-21531
Printed on acid-free paper.
© 1993 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 1993
Softcover reprint of the hardcover 1s t edition 1993
AII rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer Science+Business Media, LLC), except for brief
excerpts in connection with reviews or scholarly analysis.
Use in connection with any form of information storage and retrieval, electronic adaptation,
computer software, or by similar or dissimilar methodology now known or hereafter developed
is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if
the former are not especially identified, is not to be taken as a sign that such names, as
understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by
anyone.
Production managed by Hal Henglein; manufacturing supervised by Vincent R. Scelta.
Typeset by Macmillan India Ltd., Bangalore, India.
9 8 7 6 5 4 3 2 1
ISBN 978-1-4612-6945-8
To Fanya
Preface
Electronics,avionics,and opto-electronicspackagingdemanda greatdealof
mechanical design skill for achieving sound and reliable products. This
mechanicalengineeringactivity has thus become acrucialcontributor to the
computer, telecommunications, aerospace, and other industries.
Traditionally, printed circuit cards are categorized as "second level
packaging"since they supportthechipcarrier(the"firstlevel package"). The
cards are, most often, further connected to larger "boards" and the latter to
frames, constituting the higher levels (third and fourth) ofpackaging. These
manifold interactions make the realm of printed circuit card and board
systemsoneofthemoststructurallyfundamental andfascinatingareasinthe
electronics hardware hierarchy. A multiplicity of thermal stress, handling,
and vibration problems arise here in transient, repetitive, or steady state
form. On their successful solution depends the manufacturing, testing, and
operational life ofthe product.
This book was written with a focus on the mechanical principles involved
in the system components and their assembly. The author's thinking in this
field was nurtured by his many years ofwork on industrial design, develop
ment, testing,analysis, and consulting inelectronics and avionics packaging.
Much ofthe book involves his own research.
Some words must be said right at the outset about terminology, which
varies widely in the area to be treated. Printed circuit boards are also often
called"printedwiringboards"- theacronym PWBoccursinmanyajournal
articletitle.Thesizedistinctionbetween"cards"andthelarger,thicker(more
multilayered) "boards" also enters the semantics syndrome.
Module, component, chip carrier and package are some of the names
appended to first level structuresattached to cards and boards. In this work,
the term moduleisadoptedin mostcases,althoughexceptionsmaybemade,
especially when a quoted work employs a different terminology. One must
realize that terminology is also a function oflocality, company, or industry
and, as such, a matter of professional traditions. The author hopes that his
readers will find his choices reasonable.
vii
VllI Preface
A special note is due regarding the roles offinite element method versus
classical theory and experiment. There is no clear "winner" here in general.
Finite element solutions must have confirmation by simplified or approxim
ateanalytical methods. Such"classical"methods havealways beenneededin
engineering for basic understanding to fall back on. The author emphasizes
the use of the latter, and attempts to show the direction to develop them
further as the need arises. Because finite element problems can also be
extremely demanding in memory for complex multileaded, multimodule
systems,computationalproceduressimplifyingthe tasksoffinding leadforce
distributions, structural stiffness, and solderjointstress are required. Experi
mental stress analysis in these highly miniaturized components, using ingen
ious applications ofstrain gauging, holography, and Moire techniques, for
example, is on the rise. There is no more convincing, albeit far from cheap,
proof of understanding a mechanical system than through experiments. In
general, it is one of the author's basic views that electronics packaging
structuraldesign mustcontain all three phases: analysis,finite elements, and
experiment.
This book is intended as a statement and discussion ofstructural princi
ples, and the ensuing solution methods are applied to various circuit board
systems. It is for use in the research laboratory, design office, by testing
agencies, and in university curricula. Fundamental mechanical engineering
concepts are stressed, with the mathematical handling corresponding to a
senior or first year graduate level.
The subject matter is introduced in Chapter 1, dedicated to classical
structural analysis concepts and methods. Beams (for example, those sup
ported on elastic foundations), plates, thermal stresses, plasticity, and other
topics arediscussed, in connection with typical circuit-board problems. This
comes in handy for reference in later chapters on that type ofcomponent.
Chapter 2 is a concise wrapup of finite element structural analysis.
Theoretical fundamentals and examples are shown, referred to the circuit
board subject matter.
The physical properties of various components, cards, modules, leads,
solder joints, and their testing methods are described in Chapter 3. Some
mechanical data (e.g., for modulus, creep, and fatigue) are graphed and
tabulated, ready to furnish input for later analytical treatment.
Chapter4isdevoted to thefundamentally important leadlesschipcarrier.
Hall's analysis of solder forces and his constitutive solder equations are
described.
Thermal stresses in pin-grid arrays are analyzed in Chapter 5. The
"primary" system of forces arises on a single pin (the corner pin is highest
stressed) subjected to thermal mismatch between the module and card. A
basicingredientistheroleofsolderasanelasticfoundation. InChapter6,the
finite tlexibilities of the module and card are also included, furnishing a
"secondary" force system, and tending to relieve some ofthe stresses gener
ated by the primary mechanism.
Preface
IX
Flexural treatment ofsimple compliant leaded, surface mounted systems,
called "local assemblies," is the subject of Chapter 7. The latter are the
"building blocks" of populated circuit cards, and their solution facilitates
computation of more complex assemblies (module clusters) discussed in
Chapter 8. Such technological entities as double sided, stacked, and hybrid
configurations are also treated here.
Chapter 9 introduces a simplified analysis of a circuit card subjected to
twist. At first, a single module attachment is treated. Next, an approximate
engineering computational procedure for highly populated circuit cards is
given. An analytical torsional stiffness and lead force computation method
is expounded in Chapter 10, for elastic systems. Experimental work on
torsional testers, and the fatigue ofinterconnecting leads resulting from this
type ofloading, is shown.
Thermal stress analysis in compliant leaded modules is the subject of
Chapter 11. Structural analysis methods are given, and finite element treat
ment is exemplified by Lau's modeling ofJ- and gullwing leads. The cyclic
thermal fatigue analysis procedures of Engelmaier and his co-workers and
their "figure ofmerit" calculation are introduced.
Chapter 12 is concerned with dynamic analysis. This is crucial to
avionics packaging problems. For vibration analysis, module-populated
systemscan berepresented by"smearing"or"lumping"techniques. Random
vibration testing and the fragility (damage boundary) method are
described. The analysis of a mixed thermal/vibrational fatigue problem is
exhibited.
Plated holes (PTH and vias) are featured in Chapter 13. PTHs have two
major failure mechanisms. The "global" (module-to-card) stressing tends to
cause longitudinal cracks in the solder; their self-strain relieving tendencies
arediscussed. The secondfailure mechanism is the "z-directional mismatch"
betweenboardandcopper barrel. Experienceon thefailure phenomena, and
work on through-holes and on vias by experimental, analytical, and finite
element methods, are discussed.
The book concludes with a description, in Chapter 14, of the assembly
structuralanalysis workfor the IBM 9370cardenclosuresystem.Thedesign
of the frame, boards, and their stiffeners required excessive rigidity to
promote a sizable wipe during insertion ofcards into a zero insertion force
connector. The actuation of a card is analyzed for its role on the other
contacts; tribological analysis of the multilayer plated contacts is also
featured.
This book initiated from the author's work and consulting experience at
the IBM Endicott Development Laboratory. He fondly recalls the fun of
sharing work with R.G. Bayer, W.L. Brodsky, D.V. Caletka, W.T. Chen,
E.Y. Hsue, C.K. Lim, M.R. Palmer, N.G. Payne, D.L. Questad,D.H. Strope,
M.D. Toda, A.K. Trivedi, T.E. Wray, and many others. He has also learned
muchfrom discussions with manyeminentcolleagues,suchasJ.H. Lau,B.G.
Sammakia, and E. Suhir,just to name a few.
x Preface
The author taught some ofthe material in graduate courses at the State
UniversityofNew York at Binghamton; he warmly recalls the interest ofhis
students. Special thanksgo tostudentswhoworked with theauthoronsome
of the topics involved in the book. They include T. Albert, B. Banerjee,
A.R. Chitsaz, Y. Ling, T.M. Miller, R. Prasanna, A. Sahay, J.T. Vogelmann,
J.R. Webb, K.R. Wu, and Q. Yang. The author thanks his colleagues J.M.
Pitarresi and V. Prakash for"their useful comments on the manuscript.
A word of indebtedness is due to several professional societies and
publishers who permitted reproduction of some illustrations in this book.
The American Society of Mechanical Engineers (ASME) has spearheaded
efforts to promote electronics packaging advances in the mechanical engi
neering area; their conferences and their Transaction Journal of Electronic
Packaging rallied much initiative. The Institute ofElectrical and Electronic
Engineers (IEEE) has sponsored conferences and a great deal of research,
such as the task force on compliant leaded structures. The International
Electronic Packaging Society (IEPS) and International Society of Hybrid
Microelectronics (ISHM) have done much for the discipline. Quotations in
this book werealsotakenfrom conferencesandpublicationsofthe American
Society ofMetals, the Institute ofEnvironmental Research, National Elec
tronic Packaging Conferences (NEPCON), and the journals Circuit WorId,
Connection Technology, the IBM Journal of Research and Development,
Solid State Technology, and Soldering and Surface Mount Technology.
Last, but not least, the author thanks his wife for the inspiration she was
always ready to give.
Binghamton, New York Peter A. Engel
November, 1992
Contents
Preface. . . . . VB
Nomenclature. xvii
Chapter 1. Elements of Structural Analysis 1
1. Rods. . . . . 1
2. Beams. . . . . . . . . . . . . . . . . 1
2.1. Flexure. . . . . . . . . . . . . . 1
2.2. Beams on Elastic Foundation. 2
2.3. Torsion. 5
2.4. Frames . . . . . . . . 5
3. Plates. . . . . . . . . . . . 6
3.1. Cylindrical Bending. 6
3.2. Pure Bending . . . . 8
3.3. Circular Plates. . . . 9
3.4. Rectangular Plates in Flexure. 11
4. Thermal Stress. . . . . . . . . . . . 12
4.1. One-Dimensional Treatment: Bimaterial Rods. 12
4.2. Timoshenko's Formula for Thermal Bending ofBimaterial
Circular Plates. . . . . . . . . . . . . 13
5. Plastic Beam Deformation. . . . . . . . 14
6. Energy Methods in Structural Analysis. 16
7. Experimental Methods ofAnalysis 17
7.1. Load Testers. . . . . . . . . 17
7.2. Strain Gauges. . . . . . . . . . 17
7.3. Capacitance Measurement. . . 17
7.4. Fiberoptic ProbejPhotodiode Measurement. 18
7.5. Photoelasticity. . . . . . . . . 18
7.6. Holographic Interferometry. 18
7.7. Piezo-electric Stress Sensors. 18
7.8. Moire Interferometry. . . . . 18
7.9. Electrical Resistance Method. 19
References. . . . . . . . . . . . . . . . . 19
XI
xii Contents
Chapter 2. Finite Element Analysis. 21
1. Preliminaries . . . . . . . . . . . 21
2. Direct Stiffness Matrix Approach . 22
3. The Principle ofMinimum Potential Energy 25
4. Element Types . . . . . . . . . . . . 28
5. Finite Element Dynamic Analysis. 31
6. Stress and Strain Calculations . . . 32
7. Structural Codes . 33
8. Steps in the Use of Finite Element Analysis. 34
References . 34
Chapter 3. Components, Data, and Testing. 35
1. Modules. . . . . . . . . . . 35
2. Circuit Cards and Boards. . . . . . . . . 41
2.1. General Description . . . . . . . . . 41
2.2. Properties of Laminated Construction. 43
3. Pin Leads ofPGA Modules. . . . . . . . . 47
4. Strength ofCompliant Leads in Surface-Mount Construction 49
5. Stiffness ofCompliant Leads. 53
6. Solder Strength. 54
References. . . . . . . . . . . . . . 59
Chapter 4. Leadless Chip Carriers. 61
1. Loads and Materials. . . . . . 61
2. Thermal Stress Analysis. . . . 63
3. The Influence ofSolder Joint Shape. 69
4. Constitutive Equation for Solder Mount. 72
5. Conclusions. . . . . . . . 74
6. Exercises and Questions. 75
References. . . . . . . . . . . 75
Chapter 5. Thermal Stress in Pin-Grid Arrays:
Primary Analysis ofPins . . . . . . . 77
1. Introduction. . . . . . . . . . . . . . . . . . . 77
2. Elastic Foundation Modulus ofa Soldered Pin. 78
3. Elastic Foundation Treatment for the Embedded Pin. 84
4. Solder Pressure Calculation . . . 87
5. Plastic Analysis ofthe Pin . . . . 88
6. Axial Pin Force Due to Flexure. 92
7. A Magnified-Scale Experiment. 94
8. Conclusions. . . . . . . . 95
9. Exercises and Questions. 96
References. . . . . . . . . . . 96
