Crystal Elasticity. Pascal Gadaud

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       to Philippe M.†for having conveyed to me histaste for experimental work andhopefully some of his skill

       to Jacques W.for having transmitted to me hisscientific curiosity even if itmay involve calling everythinginto question every morning

       Series Editor

       Gilles Pijaudier-Cabot

      Crystal Elasticity

      Pascal Gadaud

      First published 2022 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

      Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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      © ISTE Ltd 2022

      The rights of Pascal Gadaud to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

      Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.

      Library of Congress Control Number: 2022933477

      British Library Cataloguing-in-Publication Data

      A CIP record for this book is available from the British Library

      ISBN 978-1-78630-822-1

      Introduction

      The first part of this book focuses on the description of crystal elasticity. This field became fully established at the beginning of the 20th century. Its ancestral branches can be referred to as “crystallosapiens” and “elastosapiens”.

      The ancestor of the first branch can be considered the mineralogist René Just Haüy, the father of geometric crystallography in the 18th century, who observed the features of the cleavage of crystals such as calcite and deduced that they were made up of small orderly stacks, which he named integrant molecules. The concept of atomic lattice dates back to the 19th century, when it was introduced by Gabriel Delafosse, one of Haüy’s disciples. Shortly afterwards, Auguste Bravais formulated the hypothesis of a lattice structure of crystals based on the principles of geometry, according to which he listed 14 different types of crystal lattices that accounted for crystal anisotropy and symmetry properties. Finally, at the beginning of the 20th century, Max von Laue used X-ray diffraction to experimentally confirm Bravais’ works.

      As for the second branch, its forerunner is beyond any doubt Robert Hooke, who in the 17th century established the linear relation between force and displacement in a loaded spring. Then, the notions of stress and deformation were formulated by Thomas Young at the beginning of the 19th century. Soon afterwards, Augustin-Louis Cauchy established the 3D formalism for the generalized Hooke’s law using the notion of elastic constants and tensor calculus applied to the mechanics of continuous media.

      As this brief history indicates, by the beginning of the 20th century, the conditions were met for a wide and varied descent.

First of all, Clarence Zener rigorously quantified the elastic anisotropy of cubic symmetry, a concept that will be constantly revisited in this part of the book. For other symmetries, different approaches were also proposed.

      Experimental characterization also improved. While simple quasi-static tests, such as the tensile test, were previously used to characterize elasticity, dedicated physical methods involving volume or surface elastic waves were used for more precise measurements of macroscopic