Chemical Change in Deforming Materials

by Brian Bayly

Overview

This book is the first to detail the chemical changes that occur in deforming materials subjected to unequal compressions. While thermodynamics provides, at the macroscopic level, an excellent means of understanding and predicting the behavior of materials in equilibrium and non-equilibrium states, much less is understood about nonhydrostatic stress and interdiffusion at the chemical level. Little is known, for example, about the chemistry of a state resulting from a cylinder of deforming material being more strongly compressed along its length than radially, a state of non-equilibrium that remains no matter how ideal the cylinder's condition in other respects. M. Brian Bayly here provides the outline of a comprehensive approach to gaining a simplified and unified understanding of such phenomena. The author's perspective differs from those commonly found in the technical literature in that he emphasizes two little-used equations that allow for a description and clarification of viscous deformation at the chemical level. Written at a level that will be accessible to many non-specialists, this book requires only a fundamental understanding of elementary mathematics, the nonhydrostatic stress state, and chemical potential. Geochemists, petrologists, structural geologists, and materials scientists will find Chemical Change in Deforming Materials interesting and useful.

Product Details

ISBN-13:	9780195361889
Publisher:	Oxford University Press
Publication date:	01/21/1993
Series:	Oxford Monographs on Geology and Geophysics , #21
Sold by:	Barnes & Noble
Format:	eBook
File size:	4 MB

About the Author

Rensselaer Polytechnic Institute

Table of Contents

	Symbols	xv
	Note on diffusion coefficients used	xviii
1.	Overview and preview of conclusions	3
	Preview of conclusions	5
	An overview of the overview	10
I	Fundamentals
2.	Chemical potential	15
	Definition of free energy	15
	Definition of chemical potential	15
	Properties of [mu]	16
	Nonequilibrium states	19
3.	Disequilibrium 1: Potential gradients and flows	22
	Gradient of pressure or concentration	22
	Gradients in potential	24
Appendix 3A	Diffusion at an interface	27
4.	Disequilibrium 2: Associated equilibrium states	30
	Diffusion in a long bar	30
	Associated equilibrium states	33
	Indeterminacy and dependence on history	33
5.	Disequilibrium 3: Internal variables	36
	An example	36
	Internal and spatial variables combined	38
6.	Nonhydrostatic stress	40
	Principal directions and stresses	40
	Stress relations in the principal planes	43
	Tensile stresses	45
	Shear stresses	45
7.	Change of shape and change of volume	47
	Strain and strain rate	47
	Change of shape and change of volume	49
	Summary	52
	Shear strains	52
8.	Conservation	54
	Conservation statements	54
	Self-diffusion	57
	Conservation and strain	58
	Summary	59
Appendix 8A	Proof of the stress relation (8.10)	60
Appendix 8B	Conservation: a numerical example	62
Appendix 8C	Invariants	63
9.	Chemical potential under nonhydrostatic stress	66
	Associated equilibrium states	66
	Sine-wave, Mohr-circle, and ellipsoid representations	69
	Numerical examples	71
	Summary	71
II	Simultaneous Deformation and Diffusion
10.	Introduction	75
	Historical review: descriptions of diffusive mass transfer accompanying deformation	77
11.	Deformation and diffusion compared	82
	Preliminary sketches	83
	Continuum behavior using wafers	86
	Questions about validity	90
	Summary and conclusions	93
Appendix 11A	Other harmonic stress fields	94
Appendix 11B	Gibbsian argument for multivalued potentials	96
12.	Deformation and diffusion: quantitative relations	100
	Relation of L[subscript 0] to N and K	100
	Change of shape and diffusive mass transfer combined	101
Appendix 12A	A material's characteristic length	105
Appendix 12B	Harmonically varying stress field with nonspecial wavelength	107
III	Application: Movements Along One Direction
13.	Two phases and one component	113
	Initial conditions and assumptions	114
	Solution	116
	Discussion	120
	Summary	126
Appendix 13A	Plane strain at an interface	126
14.	One phase and two components	129
	Initial conditions and assumptions	129
	Solution	133
	Discussion	136
	Summary	139
15.	Compounds of the type (A, B)X	141
	Theory	141
	A nonzero constriction rate	147
	Binary materials reconsidered	148
	Summary	150
16.	Two phases and two components	152
	Exponential change of composition and stress	152
	A nonzero constriction rate	157
	Behavior affected by K[superscript *]: a stationary interface	160
	Behavior affected by K[superscript a]: a moving interface	165
	Review	167
Appendix 16A	Magnitudes of e[subscript 0] and [delta]p	170
17.	Summary	174
	Preface	174
	Core	177
	Postscript	183
IV	Extensions
18.	Cylindrical inclusions	187
	Deformation of a cylinder with no diffusion	187
	Deformation of a cylinder with diffusion	191
	Materials of formula (A, B)X	193
	Summary	196
	Wet granular aggregates	196
19.	Review of strategies	199
	Simple binary materials	199
	Questions of scale	201
	A material's characteristic length and microstructure	203
	Summary	205
	Invariants	205
20.	Further extensions	208
	Unsteady behavior	208
	Poorly correlated materials and the factor f	213
	Anisotropic materials	215
Appendix 20A	Unsteady behavior, a numerical example	216
	References and notes	218
	Index	221