The diffusion and trapping of hydrogen in steel
TL;DR: In this paper, the mobility of dissolved hydrogen in an iron lattice having a population of extraordinary, or trapping, sites for hydrogen is analyzed under the assumption of local equilibrium between the mobile and the trapped populations.
About: This article is published in Acta Metallurgica.The article was published on 1970-01-01. It has received 1323 citations till now. The article focuses on the topics: Population & Hydrogen.
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01 Jan 1987
TL;DR: In this article, a boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed and the effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework.
Abstract: A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from initial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a "ductile" or "brittle" manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids. 1 Introduction The nucleation of voids from inclusions and second phase particles plays a key role in limiting the ductility and toughness of plastically deforming solids, including structural metals and composites. The voids initiate either by inclusion cracking or by decohesion of the interface, but here attention is confined to consideration of void nucleation by interfacial decohesion. Theoretical descriptions of void nucleation from second phase particles have been developed based on both continuum and dislocation concepts, e.g., Brown and Stobbs (1971), Argon et al. (1975), Chang and Asaro (1978), Goods and Brown (1979), and Fisher and Gurland (1981). These models have focussed on critical conditions for separation and have not explicitly treated propagation of the debonded zone along the interface. Interface debonding problems have been treated within the context of continuum linear elasticity theory; for example, the problem of separation of a circular cylindrical inclusion from a matrix has been solved for an interface that supports neither shearing nor tensile normal tractions (Keer et al., 1973). The growth of a void at a rigid inclusion has been analyzed by Taya and Patterson (1982), for a nonlinear viscous solid subject to overall uniaxial straining and with the strength of the interface neglected. The model introduced in this investigation is aimed at describing the evolution from initial debonding through complete separation and subsequent void growth within a unified framework. The formulation is a purely continuum one using a cohesive zone (Barenblatt, 1962; Dugdale, 1960) type model for the interface but with full account taken of finite geometry
1,848 citations
TL;DR: In this paper, the effects of hydrogen on the physical and mechanical properties of iron and steel are reviewed and a new mechanism for the cold work peak for hydrogen in iron is considered.
Abstract: The effects of hydrogen on the physical and mechanical properties of iron and steel are reviewed. A new mechanism for the cold work peak for hydrogen in iron is considered. Together, internal friction and mechanical properties indicate that hydrogen softens iron by enhancing screw dislocation mobility at room temperature but hardens iron by core interactions at low temperatures. No single mechanism exists for the degradation of the properties of steel by hydrogen. Instead a complex process involving many of the proposed mechanisms as contributing factors is shown to account for most degradation phenomena.
1,596 citations
TL;DR: The relative amount of trapped hydrogen and the activation energy for its evolution from various lattice defects in iron were calculated by monitoring the pressure change caused by release of hydrogen from charged specimens heated at uniform heating rates as discussed by the authors.
Abstract: The relative amount of trapped hydrogen and the activation energy for its evolution from various lattice defects in iron were calculated by monitoring the pressure change caused by release of hydrogen from charged specimens heated at uniform heating rates. Hydrogen release peaks were observed at 385 K, 488 K, and 578 K, respectively, when the hydrogen charged specimen were heated at 2.6 K per minute. Analysis suggests that the peak at 385 K corresponds to hydrogen release from grain boundaries, and the peak at 488 K corresponds to release from dislocations, while the peak at 578 K results from release from micro voids. The activation energies for evolution of trapped hydrogen were determined experimentally from measured peak temperatures at different heating rates and were found to be 17.2 KJ/mol, 26.8 KJ/mol, and 35.2 KJ/mol, respectively, in grain boundaries, dislocations, and microvoids. It was also observed that most of hydrogen is trapped on dislocations if the density of specimen is greater than 98.95 pct, and in microvoids if less than 98.95 pct.
523 citations
TL;DR: In this paper, Oriani's equilibrium theory is used to relate the hydrogen in traps (micro-structural defects) to concentration in normal interstitial lattice sites (NILS), and the resulting non-linear transient hydrogen diffusion equations are integrated using a modified backward Euler method.
Abstract: T he hydrogen transport problem is studied in conjunction with large deformation elastic—plastic behavior of a material. Oriani's equilibrium theory is used to relate the hydrogen in traps (micro-structural defects) to concentration in normal interstitial lattice sites (NILS). The resulting non-linear transient hydrogen diffusion equations are integrated using a modified backward Euler method. Coupled diffusion and plastic straining is analysed with this numerical procedure in the area around a blunting crack tip. A uniform NILS concentration as dictated by Sievert's law at the pressure and temperature of interest is used as initial condition throughout the body. The crack is initially blunted by plane strain mode I (tensile) loading. The finite element results show that hydrogen residing at NILS is generally very small in comparison with the population that develops in trapping sites near the crack surface. That is, lattice diffusion delivers the hydrogen but it is predominantly the trapping that determines its distribution at temperatures of interest. The predominance of trapped hydrogen over lattice concentration prevails even in the case when hydrogen migrates under steady state conditions. Hence, the hydrostatic stress effect is less important than traps created by plastic straining as far as the creation of high total hydrogen concentration is concerned. The trapping site locations and the temperature determine the amounts and locations of high hydrogen concentrations. Consequently, ahead of a blunting crack tip, the total hydrogen concentration and plastic strain diminish with distance from the crack tip whereas the hydrostatic stress rises. This would seem to have significant consequences for fractures induced by the presence of hydrogen.
493 citations
TL;DR: In this article, a kinetic model for the transport of hydrogen, as Cottrell atmospheres on dislocation, at a rate appreciably in excess of that for lattice diffusion is presented.
Abstract: A kinetic model is presented for the transport of hydrogen, as Cottrell atmospheres on dislocation, at a rate appreciably in excess of that for lattice diffusion. The particular destinations for the hydrogen which are modeled here are ductile fracture initiation sites such as inclusions and microvoids. The functional predictions of the mechanism are shown to be consistent with available experimental evidence on ductile fracture behavior in the presence of hydrogen.
469 citations
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01 Jan 1956
TL;DR: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Abstract: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained
20,495 citations
TL;DR: In this article, the existence of a chemical potential of a mobile component everywhere within a solid within a generalized stress system is demonstrated, as well as also the presence of an immobile component of a stressed body at appropriate interfaces.
Abstract: The validity of the concept of a chemical potential of a component of an olastically stressed body is discussed. The existence of a chemical potential of a mobile component everywhere within a solid under a generalized stress system is demonstrated, as is also the existence of a chemical potential of an immobile component of a stressed body at appropriate interfaces. The theorem, that the work required for a closed reversible isothermal cycle is zero, is used to develop a general equation for the chemical potential. This is μ = μ\" + w —W, where μ\" is the chemical potential in the unstressed state, w is the partial molar strain energy and W is the total work done on the stressed body per molo addition of the component. This relation is applied to various systems such as an interstitial solute in a solid under externally applied stresses, iron carbide precipitated in iron, and other precipitates in solid matrices. The equilibrium variation of concentration with position is evaluated for cases of inhomogeneous stress systems. The existence of a free energy function for a stressed body is demonstrated; however, it is differentiable only with respect to mobile components. Introduction The thermodynamics of stressed solids has attracted sporadic interest since the original work of Gibbs1 (1876). Wabbubton2 (1946) considered the absorption of water by rigid gels in which a nonhydrostatic stress system can develop as a result of the absorption. 1 J. Willard Gibbs, \"The Collected Works\", Vol. I, Longmans, Green and Co., New York 1928. 2 F. W. Warburton, Proc. physic. Soc. 58 (1946) 585. Z. physik. Chem. Neue Folge, Bd. 49, Heft 3/4 is 272 J. C. M. Li, . A. Oriani and L. S. Darken Gurney3 (1947) treated the cases of a stressed solid phase consisting of two components one of which is mobile and a pure fluid phase consisting wholly of that mobile component, and of a stressed onecomponent solid phase coexisting with a two-component fluid phase. Gurney applied his relations to the swelling of wood by the absorption of water. Flood4 (1958) considered the change due to stress in the thermodynamic potential of only a one-component solid, obtaining results at variance with those of Gibbs. Callen5 (1960) has presented formal relations between stress and various thermodynamic parameters. Yang, Hobne, and Pound6 (1962) applied Gibbs' method to the case of a mobile component in an elastic body under homogeneous stress. The purpose of the present work is to avoid the basic assumption implicit in the work both of Callen and of Gubney—the existence of a free energy function for a stressed body such that the chemical potential of each component is the partial derivative of that function with respect to the number of moles of that component. It will be shown that in general such a function does not exist for a stressed body; notwithstanding this, Gurney's deduced relations for specific cases involving homogeneously stressed bodies are correct. Another motivation in our work is to extend the definition and the utility of the chemical potential to the case of a mobile component in an inhomogeneously stressed body. The procedure will consist of demonstrating the existence of a uniform chemical potential, μ , for a mobile component at equilibrium in an inhomogeneously stressed, multi-phase body, developing a way based on Moutier's theorem for the evaluation of μ , and applying the result to some known and some hitherto untreated situations. The range of validity of the chemical potential of an immobile component in a stressed solid will also be discussed. Chemical Potential of a Mobile Component in a Stressed System Let us consider a thought experiment performed on an isothermal two-component system of special type. In this two-component system 3 C. Gurney, Proc. physic. Soc. 59 (1947) 629. 4 E. A. Flood, Cañad. J. Chem. 36 (1958) 1332. 5 . B. Callen, \"Thermodynamics\", John Wiley & Sons, Inc., New York 1961. 6 Ling Yang, G. T. Horne and G. M. Pound, \"Proceedings of a Symposium, Physical Metallurgy of Stress Corrosion Cracking, Pittsburgh 1959\", Interscienco Publishers, Inc., New York 1959, p. 29. The Thermodynamics of Stressed Solids 273 one component, , is considered to be mobile and the other, /, immobile ; an interstitial system such as that of hydrogen in iron may be considered representative. Let us now consider a unit cube (or rectangular parallelepiped) of such material and apply pressures Px, Py, Pz (or tensions) to it by means of a fluid in which the mobile component has a finite solubility, but which fluid has a vanishingly small solubility in the solid (alternatively the cube may be regarded as plated with a thin layer of material which is impervious to all substances involved except to the mobile component). For mechanical equilibrium, the pressures on opposite sides are equal. A two-dimensional section of the arrangement is shown in Fig. 1.
446 citations
180 citations
TL;DR: In this article, a constant heat-flow calorimeter was used to measure the enthalpy of the pearlite-austenite transformation as a function of pearlite spacing in the iron-carbon and copper-aluminum eutectoids.
100 citations