The influence of phosphorus segregation to particle/matrix interfaces on ductile fracture in a high strength steel

Hippsley, C. A.; Druce, S.G.

doi:10.1016/0001-6160(83)90132-3

Cited by 36 publications

(22 citation statements)

References 15 publications

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“…The inverse relation gives the strain in terms of the stress [6] where S ijkl are the components of the elastic compliance tensor. Mechanical equilibrium requires the divergence of the stress tensor to vanish: [7] The elastic fields are obtained by solving Eq. [7], along with the appropriate mechanical boundary conditions, for a given interstitial field.…”

Section: A Elasticitymentioning

confidence: 99%

“…Mechanical equilibrium requires the divergence of the stress tensor to vanish: [7] The elastic fields are obtained by solving Eq. [7], along with the appropriate mechanical boundary conditions, for a given interstitial field. If the interstitial composition field is a function of position, becomes an implicit function of position through its dependence on the composition.…”

Section: A Elasticitymentioning

confidence: 99%

“…[7], comprise a set of coupled equations for the four fields y (1) , y (2) , y (3) , and ij . These fields are coupled through the compositional strain tensor.…”

Section: Stress-induced Interstitial Redistributionmentioning

confidence: 99%

“…The actual solution, obtained by numerical solution of the mechanical and thermodynamic equilibrium conditions of Eqs. [7] and [21], is given by the solid curve. Three common approximations to the equilibrium compositions are also shown.…”

Section: Estimates Of Stress-induced Composition Changementioning

confidence: 99%

“…For example, dislocations, [1,2] precipitates, [3] interfaces, [4] and cracks [5,6] can redistribute solute atoms owing to the elastic interaction between the defect and the compositional strain of the component species. This interaction can have a significant influence on the mechanical [7] and electrical [8] properties of the crystal. The body-centered-cubic (bcc) crystal contains two substitutional atoms and six octahedral sites for interstitials per cubic unit cell.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of stress-induced interstitial redistribution in body-centered cubic metals

Johnson

Huh

2003

Metall Mater Trans A

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of a nonhydrostatic stress field, which would entail an interaction between the individual components of the applied stress tensor and the compositional strain tensor, would then conceivably have a much larger effect on the equilibrium distribution of the interstitial atoms than would be anticipated on the basis of a dilatational distortion or isotropic compositional strain, which would interact only with the trace of the stress tensor.Chou et al. [11] and Zhang et al. [12,13,14] have recognized the importance of the interaction between an applied nonhydrostatic stress field and the inherent tetragonal nature of the compositional strain in bcc metals. They derived equations for hydrogen redistribution around crack tips in bcc iron with various loading conditions and predicted hydrogen enhancement ratios of 30 or more above the far-field hydrogen composition and significantly in excess of predictions made assuming an isotropic compositional strain for the interstitial. [9] Zhang and Hack also predict that a correct accounting of the tetragonal distortion can lead to qualitative differences in the hydrogen redistribution. For example, they calculate hydrogen enhancement in the vicinity of a crack tip with pure mode III loading, even though there is no hydrostatic component of the crack stress field.Although such predictions of interstitial solute redistribution based entirely on the interaction of the external field and the compositional strain tensor are insightful, they suffer from an inconsistency in that the interstitial composition field itself generates a nonlocal stress field that interacts with the applied stress field. This interaction generates a compositional self-stress, which tends to inhibit further solute redistribution. Calculation of equilibrium solute profiles that neglect the compositional self-stress, therefore, tend to overestimate solute redistribution.Larché and Cahn recognized that neglecting the compositional self-stress in the determination of the elastic field yielded estimates of solute redistribution in the presence of a material defect that were not correct to even first order in the change in the composition. [15] Assuming a large, binary substitutional crystal with isotropic elastic constants, they linearized the mechanical and chemical equilibrium conditions to obtain a prediction for solute enhancement that is correctA set of open-system elastic constants used to approximate the redistribution of interstitial atoms among the three different interstitial sublattices in a body-centered cubic (bcc) metal is derived accounting for the tetragonal nature of the compositional strain in the presence of a nonhydrostatic stress. Predictions of the stress-induced composition change are calculated and compared to the actual solution and to two other approximation schemes, one based on a hydrostatic compositional strain and one based on ignoring the compositional self-stress. The open-system elastic constants give a qualitatively and quantitatively accurate representation of the composition cha...

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Section: A Elasticitymentioning

confidence: 99%

Section: A Elasticitymentioning

confidence: 99%

“…[7], comprise a set of coupled equations for the four fields y (1) , y (2) , y (3) , and ij . These fields are coupled through the compositional strain tensor.…”

Section: Stress-induced Interstitial Redistributionmentioning

confidence: 99%

Section: Estimates Of Stress-induced Composition Changementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Thermodynamics of stress-induced interstitial redistribution in body-centered cubic metals

Johnson

Huh

2003

Metall Mater Trans A

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Fracture Toughness and Hydrogen‐Assisted Crack Growth in Engineering Alloys

Knott

1994

Hydrogen Effects in Materials

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Phosphor in Eisen und Stahl – Ein Überblick über grenzflächenanalytische Untersuchungen am Max‐Planck‐Institut für Eisenforschung zum Segregationsverhalten des Phosphors an äußeren und inneren Grenzflächen von Eisen und Stahl

Viefhaus

Richarz

1995

Materials & Corrosion

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stitutionelle Mischkristallharter des Eisens [2], was potentiell fur Eisen eine gunstige Beeinflussung ist. Andererseits aber weist Phosphor eine starke Tendenz auf, sich bei erhohter Temperatur durch Diffusion an aurjeren und inneren Grenzflachen anzureichern (Obefflachen-und Korngrenzensegregation) und sowohl die Grenzflacheneigenschaften als auch das mechanische Verhalten deutlich zu verandern [3-71. Der wesentliche Grund fur die Anlarjversprodung von Eisen-, Nickelund Chrombasislegierungen liegt in der Segregation von Metalloidatomen (Zinn, Antimon und Phosphor als Verunreinigungen) an die Korngrenzen. Obgleich Phosphor nicht das 0947-5 11 719510505-0306$5.00+.25/0 0 VCH Verlagsgesellschaft mbH, D-6945 1 Weinheim, 1995

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The influence of phosphorus segregation to particle/matrix interfaces on ductile fracture in a high strength steel

Cited by 36 publications

References 15 publications

Thermodynamics of stress-induced interstitial redistribution in body-centered cubic metals

Thermodynamics of stress-induced interstitial redistribution in body-centered cubic metals

Fracture Toughness and Hydrogen‐Assisted Crack Growth in Engineering Alloys

Phosphor in Eisen und Stahl – Ein Überblick über grenzflächenanalytische Untersuchungen am Max‐Planck‐Institut für Eisenforschung zum Segregationsverhalten des Phosphors an äußeren und inneren Grenzflächen von Eisen und Stahl

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