Structural Integrity: Theory and Experiment PDF
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Structural Integrity Structural Integrity Theory and Experiment edited by E. S. FOLIAS UniversityafUtah Salt Lake City, Utah, U.S.A. Reprinted from International Journal of Fracture, Vol. 39, Nos. 1-3 (1989) Kluwer Academic Publishers Dordrecht / Boston / London ISBN -13: 978-94-010-6906-9 e-ISBN-13: 978-94-009-0927-4 DOl: 10.1007/978-94-009-0927-4 Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing progranunes of D. Reidel, Martinus Nijhoff, Dr W. Junk: and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. All Rights Reserved © 1989 by Kluwer Academic Publishers Softcover reprint of the hardcover 1s t edition 1989 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the copyright owners. TABLE OF CONTENTS F.W.B. van Eysinga: Preface - 25th Anniversary Issue vii Editorial Committee: Foreword - Professor M.L. Williams at 65 ix K.B. Broberg: The near-tip field at high crack velocities C.W. Smith, J.S. Epstein and M. Rezvani: Measurement of dominant eigenvalues in cracked body problems 15 E.S. Folias: On the stress singularities at the intersection of a cylindrical inclusion with the free surface of a plate 25 Dang Dinh Ang and Alain Pham Ngoc Dinh: Some viscoelastic wave equations 35 W.L. Ko: Application of fracture mechanics and half-cycle theory to the prediction of fatigue life of aerospace structural components 45 H.W. Liu: Fatigue crack growth by crack tip cyclic plastic deformation: the unzipping model 63 E. von Meerwall and F.N. Kelley: Use of parametric models in designing polymeric materials to specifications 79 R.J. Farris and M.S. Vratsanos: Impulse viscoelasticity: a new method to study poly- merization of thermosets 93 L.C. Vanyo: Effect of crosslink type on the fracture of natural rubber vulcanizates 103 A.S. Krausz and K. Krausz: The conceptual physical framework of stochastic fracture kinetics III Dang Dinh Ang, T. Folias, F. Keinert and F. Stenger: Viscoelastic flow due to penetra- tion: a free boundary value problem 121 F.E. Penado and E.S. Folias: The three-dimensional stress field around a cylindrical inclusion in a plate of arbitrary thickness 129 J.G. Williams and M.N.M. Badi: The effect of damping on the spring-mass dynamic fracture model 147 R.A. Schapery: On the mechanics of crack closing and bonding in linear viscoelastic media 163 G.P. Anderson and K.L. DeVries: Predicting strength of adhesive joints from test results 191 R.G. Stacer and H.L. Schreuder-Stacer: Time-dependent autohesion 201 K.M. Liechti, E.D. Becker, C. Lin and T.H. Miller: A fracture analysis of cathodic delamination in rubber to metal bonds 217 G. Ravichandran and W.G. Knauss: A finite elastostatic analysis ofbimaterial interface cracks 235 ''L-' - "" lA ~~. .J4.1 -1 '~ ,,.:".; ..0 " :-' ~I ~~ 1 • 'l<,1. t . I --- ---- - -- Some of the attendees at the University of Utah meeting honoring Professor M. L. Williams on the occasion of his 65th anniversary. VB Preface It is propitious that the 25th year of publication of the International Journal of Fracture should coincide with the opportunity to support the recognition by the Society of Engineer ing Science of the 65th birthday of the Founding Editor-in-Chief, Professor M.L. Williams. At its 24th Annual Meeting at the University of Utah in September 1987, the Organizing Committee of the Society chose to honor Professor Williams by reserving several sessions for contributions from his colleagues working in the mechanics of fracture and associated mechanical property-structure relationships. We are therefore pleased to welcome Professor E.S. Folias, Professor of Mechanical Engineering, University of Utah, and a member of the Editorial Committee as the Guest Editor for the first three issues of Volume 39 of the Journal. We have also noted that the University of Utah was one of the three homes for the Journal, sandwiched between the original home at the California Institute of Technology in 1965 and its current location at the University of Pittsburgh. In observing these dual anniversaries, the publishers not only enthusiastically support the presentation of these special papers, but also wish to extend to Professor Williams our own best wishes on his personal anniversary, and to thank him and all the authors, reviewers, and particularly M.e. Williams, J.L. Swedlow and the Regional Editors for their respective contributions as we observe this 25th milestone. F. W.B. van Eysinga Dordrecht, The Netherlands President January 1989 Kluwer Academic Publishers Group Professor M. L. Williams International Journal of Fracture 39: ix-xiv (1989) © Kluwer Academic Publishers, Dordrecht IX Foreword It has been a pleasure for a few of us in various capacities and with different knowledge bases to join in organizing and presenting a tribute to our colleague and friend on the occasion of his 65th birthday. Professor Williams has contributed his talents over a diverse range of activity spanning the academic, industrial, and public service arenas while maintaining an enviable sense of humor and sense of proportion. In this volume we focus mainly upon his technical work and merely note for the record that the observance in Salt Lake City was suitably accompanied by a very non-technical evening session enlivened by appropriate anecdotes from the past which were contributed by the many colleagues and friends of the "roastee. " Max Lea Williams, Jr. was born on 22 February 1922 in Aspinwall, Pennsylvania, a suburb of Pittsburgh. He spent his early years in that vicinity and ultimately attended the Carnegie Institute of Technology, now Carnegie Mellon University, from which he graduated in 1942, having received a degree in mechanical engineering (aeronautics option). During his college days he was quite active in extra curricular activities, one of them interestingly enough being editor of the Carnegie Technical, the monthly engineering school publication - perhaps portending his editorship of the International Journal of Fracture. Upon graduation he was called to active duty with the Air Force and served approximately four years, first as a squadron engineering officer in the 15th Air Force, and then as a flight test engineer at Wright Field in Dayton, Ohio. The practical field maintenance experience coupled with the subsequent opportunity to flight test a wide variety of Air Force experi mental aircraft at the Dayton center for technical research, development, and evaluation had a strong influence on his later career. He flew, for example, in the Northrop Flying Wing and the C-74 Douglas Globemaster, which was a forerunner of the present day large cargo aircraft. This personal experience with rapidly changing designs, many influenced by the emergence of supersonic flight which had not been usually presented in pre-war aeronautics courses, motivated his return to post-graduate studies. He therefore entered the graduate program at the Gugenheim Aeronautical Laboratory of the California Institute of Technol ogy (GALCIT) in 1946, originally only for a master's degree, but his residence there eventually extended to 20 years. He joined the faculty in 1948 as a part-time lecturer in flight testing and systems engineer ing and graduated in 1950 with a doctorate in aeronautics. His work was based upon a major research program of Professor E.E. Sechler's dealing with one of the early research investiga tions into the stress analysis of swept aircraft and missile wings [1]. With the missile wing idealized as a swept plate with reentrant corners, the study led naturally to research into the stress state at angular corners and ultimately produced an extensive series of papers on stress singularities, the best known being the two on stresses in the vicinity of angular corners of thin plates subjected to bending [2] and stretching [3]. From this work came the limit case when the angular corner was reduced to a zero opening angle, or crack, which was the first of many contributions by Dr. Williams to the mechanics offracture. His 1957 paper [4] in the Journal of Applied Mechanics developed the now called x Foreword "Williams series" for analyzing symmetrically and anti-symmetrically loaded plates. The latter paper also predicted the characteristic "bug-eye" photoelastic fringe pattern to be expected at crack tips as well as the angular orientation about the tip at which various maximum and minimum critical stresses and strain energies would occur, e.g. the maxi mum principal tensile stress would occur at ± 60 degrees either side of the direction of the original crack when subjected to symmetrical loading. Also, the two principal stresses at the crack tip were equal, thus suggesting a decreased amount of yielding and a higher degree of applicability of the elastic solution near the (locally yielded) crack tip. Another interesting outgrowth was the direct interpretation of the stress intensity factor in terms of the local (elliptical) radius of curvature at the tip [5]. Eigenfunction expansions, or Williams series, were also to prove useful in numerical analysis; first in collocation analysis of fracture geometries and second in finite element analysis using the singular crack tip elements. While much of his analytical work at the time related to fracture, Dr. Williams also published a pair of papers stimulated by concern in the aircraft industry for blast and thermal loading in skin panels [6, 7]. By considering (infinite) thin plate strips loaded by varying pressure and arbitrary temperature distribution through the thickness he deduced a straight-forward exact solution for this geometrical limit case of the von Karman non-linear large deflection equations, supplemented with the necessary thermal terms derived from a variational formulation of the minimum potential energy. Interestingly enough, his direct solution, presented in graphical, parametric form for easy design use, circumvented the cumbersome development of the special case treated by Timoshenko in Chapter I of his classical text, Theory of Plates and Shells (1940). In 1959, Dr. Williams published another classic paper, also dealing with stress sin gularities, which produced a local crack tips singularity of the (sometime) oscillating type between dissimilar media [8]. His result arose from a geophysics seminar presented at Caltech and subsequently sparked personal interest in the mechanics of adhesive fracture and different bonding orientations [9], as well as stimulating many extensions in the literature, including the astute observation of A.H. England that if elastic displacement oscillations were to actually occur the faces would interact! Practically speaking the extent of the oscillating effect is confined to the tip region, probably within any yielded region. The foregoing analytical papers at Caltech were complemented by a parallel series of experimental works, frequently utilizing a modified Ellis million frame per second camera constructed at GALCIT [10]. Blast loading around underground structures and their shock isolation was modelled photoelastically by Arenz [11] and high speed crack propagation in steel photographed by W.M. Beebe, M.E. Jessey, H.W. Liu, and S.R. Valluri [12]. At almost the same time, and in support of analytical work on solid propellant rocket motor design, Dr. Williams applied a photoelastic testing device used by A.J. Durelli to publish, with D.D. Ordahl, the first series of parametric stress concentration factors for pressurized solid rocket grains [13, 14] and followed up with a similar series for thermally loaded grains using a Weibull deformeter and exploiting the Biot-Muskhelishvili displacement dislocation principle. By the late 1950's, his research group was becoming well established in the fracture field and was unique in its interest in fracture phenomena regardless of the material. At about this time, the USSR launched Sputnik and stimulated enhanced international interest in Foreword Xl rocketry. Inasmuch as solid propellant rocket grains are composed of filled, rubbery, viscoelastic materials in which cracks could cause catastrophic fracture, this aeronautical design generated considerable special interest which had to start with a knowledge of mechanical properties and materials characterization before fracture behavior could be assessed in an orderly way. The GALCIT interest in solid rocket structural integrity attracted industrial sponsorship which, in 1961, led to the popular and well circulated GALCIT 61-5 report [15] co-authored with P.J. Blatz and R.A. Schapery. This period was one of intense activity and the contributions had a strong influence on the early direction of structural integrity analysis in the rocket industry because the personal research of Dr. Williams, his Research Fellows, and senior graduate students was reinforced by their vigorous participa tion in various joint industry-government-academic working committees, steering groups, e.g. JANAF Solid Propellant Information Agency, as well as their being frequent lecturers at many industrial short courses. Just last year, Dr. Williams and Professor J.E. Fitzgerald, a former colleague at Utah and now at the Georgia Institute of Technology, were honored by the American Institute of Aeronautics and Astronautics (AIAA) for their achievements in rocket structural integrity. One of the last major papers given by Dr. Williams from his Caltech position was an invited presentation to the AIAA in 1966 on practical engineering stress analysis methods of linear viscoelastic materials [16]. This summary and survey paper covered material characterization, stress analysis and experimental methods as known at the time. Space does not permit a commentary in depth on the entire scope of the GALCIT group's activity, particularly outside the rocket area described above, but one gains an appreciation of the breath of interest from the subject matter of several of the dissertations: photoelastic material characterization by R.J. Arenz, fracture micro-mechanisms by W.G. Knauss, large deformation phenomena by W.L. Ko and G.H. Lindsey, fundamental thermodynamic interpretation of fracture by R.A. Schapery, numerical analysis techniques in the work of J.L. Swedlow, that of E.S. Folias on the effect of single and double curvature on fracture initiation, and work on dynamic fracture by D.O. Ang, which complemented the experi mental work of W.M. Beebe, and in 1959 related closely to the Broberg running crack problem of the same time period. In addition, there were also many contributions from national and international visitors, such as the joint papers with Professor Takeshi Kunio of Keio University on solid rocket design [17, 18]. As a final comment regarding Professor Williams' 20 year period at Caltech, it is perhaps not surprising in view of the group's fracture activity, its collegiality, and its diversity that, in conjunction with Dr. Williams and Dr. Swedlow being Founder Members of the International Conference on Fracture (lCF), Caltech was a natural choice and Professor Williams an obvious person to accept Professor Takeo Y okobori's challenge to initiate the first technical journal dealing solely with the mechanics offracture. As mentioned earlier, the first issue of the International Journal of Fracture (Mechanics), a quarterly at the time, came off the press, from an antecedent of the present publisher, in March 1965. It was in 1965 that Professor Williams somewhat reluctantly, we believe, left the research culture of Caltech to become Dean of the College of Engineering at the University of Utah. With increased administrative duties, his research role, while still technical, became more that of a supporter and collaborator, particularly to Professor K.L. DeVries and his students. On the public service side, Professor Williams became increasingly active and held several committee memberships, most notably on the Biomaterial Research Advisory
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