Fracture micro mechanics of polymer materials

Transcription

1 Fracture micro mechanics of polymer materials

2 Series on Fatigue and Fracture VOLUME I S. Kocanda - Fatigue failure of metals VOLUME II V. S. Kuksenko and V. P. Tamuzs - Fracture micromechanics of polymer materials

3 Fracture micromechanics of polymer materials V. s. Kuksenko and V. P. Tamuzs II 1981 SPRlNGER-SCIENCE+BUSINESS MEDIA, B.Y.

4 Library of Congress Catalog Card Number: ISBN ISBN (ebook) DOI / Copyright 1981 by Springer Science+Business Media Dordrecht Originally published by Martinus Nijhojj Publishers by, The Hague in 1981 Softcover reprint of the hardcover 1 st edition 1981 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer-Science+Business Media, B. V.

5 Fatigue and fracture Editorial Board Editor-in-Chief: Members: Professor George C. Sih Lehigh University Bethlehem, Pa. USA Dr. David Broek Battelle Columbus Laboratories Columbus, Ohio USA Professor Dominique Francois Universite de Technologie de Compiegne Compiegne, France Professor Hiroyuki Okamura University of Tokyo Tokyo, Japan Dr. Erwin Sommer Institut fiir Festkorpermechanik Freiburg, West Germany Dr. Harry C. van Elst Metal Research Institute TNO Apeldoorn, The Netherlands

6 Fatigue and Fracture Fatigue and fracture encompass a great many disciplines involving physics, chemistry, continuum mechanics, materials testing and structural analysis. Because of the large number of publications, the analytical and experimental complexities, and the variety of phenomena and materials encountered, it becomes necessary to provide a medium for disseminating pertinent technical material, data, and information on an organized basis. This new series is devoted to the advancement of theoretical knowledge and practical understanding of fatigue and fracture. It intends to strike a balance between material evaluation and structrual design. The ever-increasing demand for high performance structures has necessitated the revision of existing technical principles and the development of new ones. Admittedly, the problem of material failure cannot be completely avoided and will very likely always be with us. Encouraged, however, are contributions to the fundamental understanding and practical application of procedures for design, material selection and fabrication which, when combined into an integrated whole, should provide a better means of evaluating the safety and or reliability of modern engineering structures. The editorial board VII

7 Contents Foreword Preface to the English edition Editors preface XII XIV XV 1 Changes in the mechanical properties of polymer and composite materials during the fatigue process 1.1 A brief survey of literature Principles of experimental study 5 The measurement of strains, energy dissipation and temperature Changes in the deformation properties of fiberglass plastics during cyclic loading The energy dissipation in glass laminate during cyclic tension - compression 16 Shape and magnitude of the hysteresis loops 16 The ratio of mechanical to thermal losses of energy 17 The dependence of L~ W on durability Changes in the mechanical properties and temperature during cyclic loading of thermoplastic polymer materials Fatigue of fiberglass plastics under repeated impact loads Recording of damage processes in fiberglass plastics by acoustic emission technique 29 2 The observations of continuum ruptures in polymers under load X-ray scattering on density heterogeneities 2.2 Equipment for the measurement of small angle X-ray scattering 2.3 Experimental data processing 2.4 Separation of sub micro crack scattering Regularities of submicrocrack origination in loaded polymers 3.1 The sizes and shapes of submicrocracks 3.2 Comparison of the shapes of submicro- and macrocracks 3.3 Accumulation of submicrocracks under different loading conditions 3.4 Submicrocrack concentrations in the prerupturing state 3.5 The effect of submicrocracks on the deformation of polymers Structural conditions for submicrocrack generation Structure of directed crystalline polymers and their behavior under load Properties of amorphous interlayers in directed crystalline polymers 98 IX

8 Contents 4.3 Comparison of sizes of structural elements and submicrocracks Structural peculiarities of submicrocrack formation in non-directed polymers Molecular mechanism of submicrocrack generation Thermoftuctuational nature of submicrocrack formation Ruptures of chemical bonds in loaded polymers The role of chain processes in the origination of submicrocracks The effect of ionizing radiations on the rate of submicrocrack origination Localization of the fracture process The concentration criterion for interaction and coalescence of submicrocracks Enlargement of sub microcracks The role of surface in fracture localization The effect of sub microcracks on the origination and development of microand macrocracks Localization levels and the main principles of polymer fracture micromechanics A statistical model of the fracture of polymer materials Some statistical theories of short-term strength Fracture models under uniaxial loading 170 The measure of material damage 170 Lifetime analysis with statistical overstress distribution The statistical model of fracture kinetics to materials with heterogeneous structure Principle hypotheses of the model Calculation and discussion of results 8 Theory of scattered fracture at the complex stress state 189 x 8.1 Some variants of the volume fracture theory and their connection with the theory of plasticity 189 Historic information 189 The theory of long-term strength considering damage accumulation A proposed variant of the phenomenological theory of fatigue and fracture 200 Basic hypotheses 200 Sphere function approximations by three-dimensional tensors 202 Dependence of sphere functions on the stress tensor 209 Local failure conditions Strength at the complex stress state 211 Application of the failure criterion max D, = I 211 Failure analysis under complex loading 216 Examples of long-term strength calculations by using the failure criterion I,D, ds = Calculating elasticity constants of damaged materials 227 A general scheme for calculating changes in mechanical properties of a damaged material 227 Calculating the elastic properties of a damaged material containing defects in the form of penny-shaped cracks

9 Contents 8.5 Relating the proposed theory to other strength theories The Afanasyev's theory The Hsiao's theory 8.6 Development of the fracture theory of anisotropic media Spherical invariants of an anisotropic medium Specific cases of anisotropic media Applications of the criterion max D z = I to anisotropic media Fracture of polymer and composite materials during high speed tension 9.1 Problems and testing techniques 255 Statement of the problem 255 Static test techniques of uniaxial tension and specimen shapes 256 High-speed testing techniques of one-dimensional tension Comparison of long- and short-term strength of fiberglass reinforced plastics Fracture of oriented materials during tension 263 Experimental results and statement of the problem 263 Calculation model of fracture to oriented polymers Analysis of the temperature field during vibrational loading with consideration given to scattered damage Statement of the problem Solution for a specimen with uniform temperature distribution Solutions to an infinite cylinder with convection on the lateral surface References Index XI

10 Foreword Within the last two decades fracture theory has been one of the most rapidly advancing fields of continuous media mechanics. Noteworthy success has been achieved in linear fracture mechanics where the propagation of the macrocrack in elastic materials is under study. However, fracture of materials is by no means a simple process since it involves fracture of structural elements ranging from atomic sizes to macrocracks. To obtain all information about how and why materials fail, all stages of the process must be studied. For a long time both mechanical engineers and physicists have been concerned with the problem of the fracture of solids. Unfortunately, most of their work has been independent of the others. To solve the problem not only requires the minds and work of mechanical engineers and physicists but chemists and other specialists must be consulted as well. In this book we will consider some conclusions of the "physical" and "mechanical" schools acquired by the A. F. Joffe Physics-Technical Institute of the USSR Academy of Sciences in Leningrad and the Institute of Polymer Mechanics of Latvian SSR Academy of Sciences in Riga. The methods for studying the phenomena of fracture applied at both Institutes are different yet complimentary to one another; the materials tested are also sometimes different. Whatever the differences are, a common point for both authors is conformity of their views on the fracture processes outlined in the monograph as follows: 1) Fracture of materials is not a solitary and instantaneous event but rather a process in time; 2) A certain preparatory phase usually preceeds the macrocrack propagation-volume fracture of the material; 3) The volume fracture is a defect accumulation process - microcrack sizes are determined by the main structural element sizes of the material, followed by further enlargement and coalescence of these defects. Although the book deals mostly with polymeric materials it is our belief that many other materials also display fracture characteristics similar to those discussed. The book considers the fracture of highly-oriented crystalline polymers, amorphous polymers and polymer-based composite materials. XII

11 Foreword These materials were studied using different methods since there are different defect sizes which have accumulated in materials under load. Thus, while sub microcracks in oriented films of crystalline polymers are most successfully observed by the small-angle x-ray scattering method, the acoustic emission method or the measurement of the materials mechanical properties' variations and direct microscopy are preferred for composite materials. We are of the opinion that the above given fracture features revealed primarily in simple tension should be also principally found, with certain deviations, in other types of loading. The tests considered in the book refer to creep and constantly increasing load conditions, and cyclic fatigue. The methods applied vary accordingly. For example, acoustic emission can be efficiently used to state the damage level in fiberglass plastics under creep conditions, while the measurement of the changes in the cyclic modulus, energy dissipation and selfheating temperature of a specimen are more efficient under cyclic load. The mathematical model of volume fracture given in this book involves the following major aspects: - direct calculation of the random process of nucleation and development of defects in uniaxial loading in a nonuniform medium with inhomogeneities being of a size characteristic for the material: - description of the material volume fracture taking into account orientation of defects, complex stress state and the fracture features under particular types of loads, such as selfheating of the specimen under cyclic load and additional orientation in high-speed tension. Chapter I, VII-X were written by V. P. Tamuzs and II-VI by V. S. Kuksenko respectively. We find that this monograph does not include all aspects of fracture micro mechanics since many problems in question are presently still underway. We thank you in advance for any critical remarks. Please, forward them to either the or Institute of Polymer Mechanics, Latvian SSR Academy of Sciences 23 Aizkraukles Street , Riga USSR A. F. Joffe Physics-Technical Institute USSR Academy of Sciences 26 Politechnicheskaya Street , Leningrad USSR The authors XIII

12 Preface to English edition The main objective of fracture micro mechanics of solids is to disclose basic regularities that define transition from a microscopic (molecular, supermolecular) level to much higher scales of the failure process, macrofracture included. The progress made in this respect has been reported in a number of publications scattered in various, mainly Soviet, periodicals and then generalized in this monograph. The authors are happy about the appearance of the English edition of the book which, no doubt, will facilitate further discussion on the problems related. The experimental and theoretical results which have been obtained in the later period of our investigations and, therefore, could not be included in this book indicate that the revealed laws are applicable not only to polymeric materials but also to other heterogenous solids, such as metals, rocks, modern composites, etc. Since the fracture micromechanics allows us to describe the mechanical behavior of materials with respect to their primary structures and, consequently, to explain and predict the macroscopic fracture, the authors remain hopeful that a closer look at the problems will enhance the interest to this significant research field. The authors wish to thank Professor G. Sih for his great concern in our work and support to the issue of this edition. The authors are grateful to A. Tarvids, L. Kulimanina and N. Aleksandrova for their help in the translation, and to I. Vilks and M. Smalka for technical assistance. XIV

13 Editor's preface Polymers are firmly established as materials of choice in many fields of engineering. Their applications are increasing at such a rate that engineers need a better understanding of their physical properties. Apart from the problem of correlating mechanical behavior with chemical composition, there is much to be done in understanding the phenomena of failure or fracture. The discrepancy between strength as calculated from conventional theories and as measured in tests is largely due to the presence of defects in the specimens that were not considered in the theoretical analyses. Real materials are known to contain mechanical imperfections that are either inherent in the material, as in crystal defects, or introduced in mechanical handling or fabrication, when they take the form of scratches, cracks, etc. Unlike metals, polymers respond to stress in a variety of ways with elongation at fracture ranging from one percent to several thousand percent. The applied stresses at fracture can also vary from 10 to "10 3 MPa while cracks in some polymers may travel rapidly at near sonic velocities, and in others so slowly that little change can be detected in many hours. The occurrence of this extended time-scale phenomenon can also be affected by environment, which mayor may not cause chemical degradation of the polymer. To distinguish real changes in material properties from material damage due to formation of sub micro- or micro-cracks requires careful scrutiny in analytical modeling. As the available experimental evidence is examined in the light of the fracture mechanics discipline, there is good reason for regarding the different forms of time-dependent failure or fracture not as unrelated independent events, but rather as different aspects of a single phenomenon. To bring some order to this broad range of responses to stress by different polymers, the authors V. P. Tamuzs and V. S. Kuksenko have provided a wide variety of theoretical and experimental results in a well-organized form for the reader. They view the phenomenon of fracture as a process of defect nucleation and accumulation at the submicro-, micro- and macro-scale resulting in the eventual separation of material. Both crystalline and amorphous polymers with defects are investigated in simple and complex stress states. Fiberglass reinforced polymers are also xv

14 Editor's preface treated. It is not surprising that the authors describe many of the failure or fracture characteristics displayed by polymers as analogous to those of other materials. In particular, crystalline polymers and metals have certain obvious similarities and differences in behavior patterns. The book also contains valuable descriptions of the X-ray scattering method for detecting microcracks and the acoustic emission technique for measuring the level of damage in fiber reinforced polymers. Although much of the material in the book is still rather qualitative and a detailed understanding of polymer fracture is still lacking, the authors are to be complimented for having made a logical approach to the subject. The book contains many informative data and ideas that should stimulate researchers to make further advances in the field of polymer fracture. It should be a most welcome addition to the libraries and those individuals who study and/or perform research in fracture mechanics. Bethlehem, Pennsylvania January 1981 G. C. Sih Editor-in-Chief XVI