The Thermodynamics of Stressed Solids

Li, J. C. M.; Oriani, R. A.; Darken, L. S.

doi:10.1524/zpch.1966.49.3_5.271

Cited by 472 publications

(142 citation statements)

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“…(8.44) Subtracting (8.44) from (8.43), and neglecting In (I -c,), one gets This is the boundary condition used by Herring (his eq (2» for the partial differential eq (8.42) since our P equals his -P zz • The stress equilibrium equation is the same, and he implicitly used condition (8.37) to get the rate of displacement of the interface (e.g., to go from (3) to (4) in his paper). Thus within the assumptions explicitly spelled out at the beginning of this section, we recover Herring's equations and boundary conditions.…”

Section: The Partial Differential Equationmentioning

confidence: 98%

“…A very good example of the kind of equilibrium Gibbs was able to calculate is the bending of a damp wooden beam in which the water redistributes at equilibrium and affects the compliance. Li, Darken, and Oriani [3] pointed out that mobile interstitials in metals at temperatures where the substitutional atoms did not move was a valid metallurgical example of a Gibbs solid with a fluid component. An example of the equilibria of a dissolving Gibbs solid occurs in stressed electrodes.…”

Section: What Is a Solid?mentioning

confidence: 99%

“…Making the usual small strain approximations, and an expansion of the strain around To =0 produces the constant chemical-potential form of Hooke's law (5.2) The coefficients of the stress have been called opensystem compliances, S * and are related to the constant composition compliances S by 3) where (aM 12 /ac)T mn is evaluated at Tmn =0 and where all the quantities except Va are functions of c. The second order terms that are neglected in this expansion have been discussed [15]. Introducing the notation for substitutional binary solutions, the open systems compliances, for isotropic solids are given by…”

Section: Open-system Elastic Constantsmentioning

confidence: 99%

“…2) where J is the determinant of F. In the small strain approximation, the displacement tensor is given, to first order in the derivatives Uti, by [11] (A2. 3) where E is the small strain tensor, (eq (3.1)), n the small rotation tensor, and I the unit tensor. To the same approximation, its inverse is given by (A2.4)…”

Section: Appendix 2 the Boundary Conditions For Coherent Phase Changmentioning

confidence: 99%

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The Interactions of Composition and Stress in Crystalline Solids

Lärché¹,

Cahn²

1984

J. RES. NATL. BUR. STAN.

105

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The thermodynamics of stressed crystals that can change phase and composition is examined with particular attention to hypotheses used and approximations made, Bulk and surface conditions are obtained and for each of them practical expressions are given in terms of experimentally measurable quantities. The concept of open-system elastic constants leads to the reformulation of internal elastochemical equilibrium problems into purely elastic problems, whose solutions are then used to compute the composition distribution. The atmosphere around a dislocation in a cubic crystal is one of several examples that are completely worked out. The effects of vacancies and their equilibrium within a solid and near surfaces are critically examined, and previous formulas are found to be first order approximations. Consequences of the boundary equations that govern phase changes are studied with several examples. Finally, problems connected with diffusional kinetics and diffusional creep are discussed.

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Section: The Partial Differential Equationmentioning

confidence: 98%

Section: What Is a Solid?mentioning

confidence: 99%

Section: Open-system Elastic Constantsmentioning

confidence: 99%

Section: Appendix 2 the Boundary Conditions For Coherent Phase Changmentioning

confidence: 99%

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The Interactions of Composition and Stress in Crystalline Solids

Lärché¹,

Cahn²

1984

J. RES. NATL. BUR. STAN.

105

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“…Hydrogen will segregate to regions of high tensile lattice strain (6). Therefore, the increase in hydrogen volubility in Type 21-6-9 stainless steel compared to Type 304L stainless steel is probably due to hydrogen segregation into the tensile strain field associated with the nitrogen atoms.…”

Section: Effects Of Nitrogenmentioning

confidence: 99%

Hydrogen solubility in austenitic stainless steels

Caskey

Sisson

1981

Scripta Metallurgica

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Hydrogen volubility was directly measured in specimens of Types 304L, 21-6-9, and modified A-286 austenitic stainless steels saturated with hydrogen at 69 MPa pressure at 470 K. Nitrogen in Type 21-6-9 stainless steel and precipitate morphology in the modified Type A-286 stainless steel altered the hydrogen volubility. Cold work and surface treatment had only minor effects on hydrogen volubility in the three stainless steels.

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Dissolution response of hydroxyapatite coatings to residual stresses

Han

2001

J. Biomed. Mater. Res.

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The effect of residual stress on the dissolution of hydroxyapatite (HA) coatings was investigated. The examined coatings of 80-, 110-, and 200-microm thickness were prepared by a plasma-spraying technique under identical conditions. Residual stresses in the coatings were measured with a hole-drilling method. Dissolution of the coatings was monitored along with an examination of the phase composition. The results showed that both tensile residual stress and amorphous HA existed throughout the entire depth of the coatings and tended to increase from the surface to the interface of the coating and substrate. The thicker the coatings were, the higher the maximum residual stress was. Correspondingly, the pH value and calcium concentration of the solutions tended to increase with the coating thickness. On the basis of these phenomena and a thermodynamic analysis of the dissolution of the HA subjected to stresses, we concluded that besides structural effects, residual stress was also an important intrinsic factor influencing dissolution of HA coatings, and the dissolution can be delayed or even restrained by compressive residual stress.

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The Thermodynamics of Stressed Solids

Cited by 472 publications

References 0 publications

The Interactions of Composition and Stress in Crystalline Solids

The Interactions of Composition and Stress in Crystalline Solids

Hydrogen solubility in austenitic stainless steels

Dissolution response of hydroxyapatite coatings to residual stresses

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