Effect of solute interaction on interfacial segregation and grain boundary embrittlement in binary alloys

The effect of solute interaction on interfacial segregation and intergranular embrittlement is modeled on the basis of the combined Fowler and Rice–Wang approaches in a binary system using the chosen values of standard thermodynamic parameters of interfacial segregation and varied values of the binary interaction coefficients. It is clearly shown that attractive interaction strengthens interfacial segregation and substantially enhances intergranular embrittlement, while repulsive interaction exhibits an opposite effect. This finding is demonstrated in the available literature data.     

Influence of precipitation and segregation on hydrogen embrittlement in aged 9Cr–1Mo steel

Abstract

A study is reported of temper embrittlement and hydrogen embrittlement in a series of model 9Cr–1Mo steel alloys in which the levels of silicon and phosphorus have been varied to separate the formation of the brittle intermetallic (Laves) phase from the segregation of phosphorus during aging. Phosphorus segregation was mildly detrimental to ductility properties, Laves phase formation was more detrimental, and their effects combined produced the most severe loss in ductility. Hydrogen effects were additive to those of aging. In unaged material without silicon enrichment, only M₂₃C₆ precipitates were detected, with little phosphorus segregation. With silicon enrichment, phosphorus segregation to lath and grain boundaries was enhanced. This enhancement increased the susceptibility of the materials to hydrogen embrittlement, promoting transgranular cleavage and chisel fracture. In aged material, the high phosphorus alloys showed some grain boundary segregation, but only limited interaction with hydrogen. In the high silicon alloys, the formation of Laves phase was most evident. This enhanced hydrogen embrittlement resulted in extensive chisel, transgranular cleavage, and some intergranular fracture. In the high silicon high phosphorus alloy, both Laves phase formation and phosphorus segregation were evident. This resulted in enhanced susceptibility to hydrogen embrittlement, producing intergranular fracture. Thus, silicon controls the susceptibility to hydrogen embrittlement in unaged alloy by promoting phosphorus segregation and in aged alloy by promoting Laves phase formation. In the aged alloy, segregation of phosphorus can enhance the effect of silicon.

MST/1785     

Finite element simulation of complex interfacial segregation phenomena in dilute alloys

Segregation of trace elements on a surface, at grain boundaries or more generally in any interface can have important consequences: adhesion of thin films, catalytic activity, embrittlement of steels by P or of nickel alloys by S, reinforcement of nickel alloys by B, etc. Segregation kinetics can be simulated by a finite element (FE) approach, by implementing the Darken–Du Plessis equation at the interface and Fick’s diffusion laws in the bulk. It is then possible to simulate segregation kinetics in non-isothermal conditions, and to couple segregation and macroscopic heat transfer calculations. A previously developed model is here adapted to the case of complex interfacial segregation phenomena: (i) segregation of a single species with a solute–solute or solute–solvent interaction, (ii) co-segregation of two species with a site competition in the interface, and (iii) segregation of a single species at an interface between two phases. Results are compared with available experimental data.     

Effect of boron on phosphorus-induced temper embrittlement

Combined equilibrium and non-equilibrium grain boundary segregation of solute atoms in dilute ternary alloys is modelled through consideration of site competition between two solutes. Model predictions are made for a low-alloy steel containing boron. The predicted results indicate that the kinetics of phosphorus segregation are dramatically facilitated by quenched-in vacancies, and the magnitude of the segregation, however, is substantially suppressed by the competition of boron with phosphorus for segregation sites, and in turn the phosphorus-induced embrittlement may be alleviated.     

Combined equilibrium and non-equilibrium segregation treatment of temper embrittlement in low alloy steels

Abstract

Embrittlement is an important factor for low alloy ferritic steels used for components and structures in the power and petrochemical industries when exposed to a higher temperature. The embrittlement may be classified into non-hardening embrittlement and hardening embrittlement. The non-hardening embrittlement, for example temper embrittlement, originates from grain boundary segregation of impurity elements such as phosphorus. To predict this segregation behaviour, a model is established by simplifying a low alloy steel as a dilute Fe–C–Mo–P quaternary alloy and modifying previous models. This model is applied to segregation predictions in a 2.25Cr–1Mo steel subjected to a complex heat treatment cycle.     

Upper and lower bounds for evaluation of nonlinear fracture parameters

Bound theorems for estimating small strain nonlinear fracture parameters are proposed. It is found that the lower bound for the J-integral can be obtained by a compatible displacement finite element method. On the other hand, the upper bound of the I1-integral, which is the dual counterpart of the J-integral, can be obtained by an equilibrium finite element method. To verify the theorems and avoid the difficulty of designing equilibrium finite element models, the popular Pian–Sumihara hybrid stress model is modified by incorporating a penalty-equilibrium constraint. Moreover, an incremental formulation of the I1-integral for nonlinear finite element computation is developed. Numerical examples on different crack and loading configurations are presented. All the results indicate the validity of the theorems.     

Elastic–plastic analysis of interaction between an interfacial crack and a subinterfacial microcrack in bi-materials

In the present work the finite element method is used to analyze the effect of interaction between an interfacial crack and a microcrack in ceramic/aluminum bi-materials. The behaviour is analyzed by the determination of the J integral, the plastic zone at the tips of the interfacial crack and the microcrack. The effects of longitudinal and transversal distance between the tips of the two cracks and the rotation of the microcrack are examined. The obtained results allow us to deduce a correlation between the position of the microcrack and the J integral and the plastic zone.The obtained results shows that the J integral at the interfacial crack tip reaches a maximum value when the microcrack is moved in the vicinity of the interfacial crack. With this distance the effect of interaction is marked more; the stress field at the microcrack tip and that of the interfacial crack generates only one plastic zone at the interfacial crack tip. The maximum size of the plastic zone is localised at the interfacial crack tip. Those of the two tips of the microcrack are very weak and even negligible in front of the zone plasticized at the interfacial crack tip.     

Hydrogen and temper embrittlement in 9Cr–1Mo steel

Abstract

The synergism between hydrogen embrittlement and temper embrittlement has been investigated in a 9Cr–1Mo martensitic steel. Measurements of tensile ductility were used to monitor the development of embrittlement with increasing hydrogen content in material as tempered and aged for up to 5000 h at 500 or 550°C. A detailed examination was made of associated changes in fracture mechanism, precipitate microstructure, and interfacial and precipitate chemistry. A strong interaction between hydrogen and temper embrittlement was observed. Both types of embrittlement in isolation reduced tensile ductility by promoting a ductile interlath fracture mechanism: ‘chisel fracture’. Hydrogen and temper embrittlement acted synergistically to reduce ductility further by the promotion of brittle intergranular fracture and transgranular cleavage. The dominant factor controlling the interaction was the precipitation of a brittle intermetallic Laves phase containing phosphorus in solution. Phosphorus segregated to interfaces was considered to make an important, but secondary, contribution to the embrittlement observed.

MST/791     

Interfacial segregation and grain boundary embrittlement: An overview and critical assessment of experimental data and calculated results

One of the most dangerous technical failures of materials is intergranular brittle fracture (temper embrittlement) as it proceeds very quickly and its appearance is often hardly predictable. It is known that this phenomenon is closely related to the chemistry of grain boundaries and to the difference of the segregation energies of the grain boundaries and the free surfaces (Rice–Wang model). To elucidate the effect of individual solutes on embrittlement of various materials such as steels and nickel-base superalloys, grain boundary and surface segregation was extensively studied in many laboratories. As a result, numerous data on surface and grain boundary segregation have been gathered in literature. They were obtained in two main ways, by computer simulations and from experiments. Consequently, these results are frequently applied to quantify the embrittling potency of individual solutes. Unfortunately, the values of the segregation energy of a solute at grain boundaries as well as at the surfaces obtained by various authors sometimes differ by more than one order of magnitude: such a difference is unacceptable as it cannot provide us with representative view on the problem of material temper embrittlement. In some cases it seems that these values do not properly reflect physical reality or are incorrectly interpreted. Due to the above mentioned large scatter of the segregation and embrittlement data a critical assessment of the literature results is highly needed which would enable the reader to avoid both the well known and less well known pitfalls in this field. Here we summarize the available data on interfacial segregation and embrittlement of various solutes in nickel and bcc iron and critically discuss their reliability, assessing also limitations of individual approaches employed to determine the values of segregation and strengthening/embrittling energies, such as density functional theory, Monte Carlo method, molecular statics and dynamics and tight binding on the theoretical side, and Auger electron spectroscopy, 3D tomographic atom probe, and electron microscopy techniques on the experimental side. We show that experimental methods have serious limitations which can be overcome by accepting reasonable assumptions and models. On the other hand, the theoretical approaches are limited by the size of the computational repeat cell used for the calculations of the segregation energy. In both cases, a careful critical analysis of the available segregation energy and/or enthalpy reflecting physical reality allows to assess the reliability of these values and their applicability in analysis of intergranular brittle fracture in steels and nickel-base alloys.     

Dynamic J integral, separated dynamic J integral and component separation method for dynamic interfacial cracks in piezoelectric bimaterials

First, the near-tip stress and electric displacement fields are analytically solved for a dynamically propagating interfacial crack in a piezoelectric bimaterial. Second, from the rate formulation of the energy balance in a piezoelectric material, the path independent dynamic J integral is derived, which has the physical significance of the energy release rate. Using the present near-tip analytical solutions, the relationships between the dynamic J integral and the stress and electric displacement intensity factors are also obtained. It is shown that the path independent dynamic J integral contains the static J integral and the dynamic J integral for elastic materials, and static J integral for piezoelectric materials as special cases. Third, for an interfacial crack in a piezoelectric bimaterial, the path independent separated dynamic J integrals are derived, which have the physical significance of energy flow rates into the propagating interfacial crack tip from the individual material sides or, equivalently, the separated dynamic energy release rates. Fourth, to accurately evaluate mixed-mode stress and electric displacement intensity factors, the component separation method of the dynamic J integral is developed. Finally, the finite element analyses of a static stationary interfacial crack in a piezoelectric bimaterial subject to mechanical, electrical and combined loading are carried out to demonstrate the applicability of the generalized (dynamic) J integral and the separated J integral, and the component separation method.     

Hydrogen and temper embrittlement interactions in fatigue of 2·25Cr–1Mo steel

Abstract

The influence of strength, precipitate microstructure, temper embrittlement, and environment on fatigue crack growth in 2·25Cr–1 Mo steel has been investigated. Particular attention was paid to the interaction between hydrogen embrittlement and temper embrittlement in fatigue. A range of tempered and aged conditions was examined in air, vacuum, and gaseous hydrogen environments at growth rates between 10^?10 and 10^?5 m/cycle. In this paper, discussion focuses on effects observed in hydrogen. Gaseous hydrogen was found to encourage crack growth by promoting intergranular fracture, which peaked at intermediate growth rates, and by reducing the general plasticity associated with transgranular fracture at high growth rates. Mechanisms underlying these effects, which involve stress-driven hydrogen segregation and the facilitation of crack-tip dislocation emission, are considered in detail. Reversible temper embrittlement encouraged crack growth at near-threshold and intermediate rates in hydrogen by increasing susceptibility to intergranular fracture. The magnitude of this effect was directly related to the degree of intergranular phosphorus enrichment, thus clearly demonstrating synergy between hydrogen embrittlement and temper embrittlement in fatigue. In contrast, one-step temper embrittlement encouraged transgranular crack growth in hydrogen only at high growth rates. This is considered to result from a concentration of slip on glide planes intersecting the crack tip under the combined influences of hydrogen and an increasingly dense precipitate microstructure.

MST/583     

Theoretical evaluation of equilibrium partition coefficients of solute elements in Fe–C–base quaternary and muIticomponent systems

Abstract

The coefficients of equilibrium partition of solute elements between austenite and liquid iron were evaluated thermodynamically for Fe–C–base quaternary systems. The validity of the calculation was examined in comparison with the measured coefficients of solute elements in some quaternary systems. The equilibrium partition coefficient of the third element i in an Fe–C–base quaternary system is affected by two factors: the effects of the fourth element j on the interaction between carbon and the third element and the interaction between the third and fourth elements. Most of the combinations of the third and fourth elements in Fe–C–i–j quaternary systems showed a relatively small interaction between the elements i and j except the combination of chromium and titanium, which exhibited an explicit influence of titanium on the partition coefficient of chromium. It was concluded that the partition coefficients in Fe–C–base multicomponent systems differed little from those in Fe–C–base ternary systems, with a few exceptions.

MST/220     

Partitioning of titanium during solidification of aluminium alloys

Abstract

The purpose of the present work is to compare the segregation behaviour of Ti solute in low solute alloys, such as nominally pure Al, and high solute alloys typical of Al–Si casting alloys. Microprobe measurements of Ti segregation within grains show that, under the solidification conditions employed, the measured partition coefficient of Ti in pure Al is 6.7 compared with the phase diagram prediction of ～7.5. Similar measurements in an Al–7Si–0.3Mg alloy resulted in a partition coefficient of 3.2. Based on the measured partition coefficients, this translates into a reduction in the growth restriction factor (a measure of the segregating power of solute elements) from 8.75 K in pure Al to 3.36 K in Al–7Si–0.3Mg with an addition of 0.05 wt-%Ti. This may explain why Ti in solution is a less effective grain refiner in casting alloys than in low solute content wrought alloys. In addition, the measured Ti segregation profiles were compared with predicted profiles based on the Scheil or similar solidification relationships. It was found that the predictions of the Scheil equation produced a good fit with the measured Ti segregation profiles once it was adapted for the geometrical nature of dendritic solidification.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

Precipitation–segregation mechanism for high temperature temper embrittlement of steels revealed by Auger electron spectroscopy and internal friction measurements

Abstract

A precipitation–segregation mechanism of high temperature (reversible) temper embrittlement has been suggested on the basis of Auger electron spectroscopy, internal friction measurements, and scanning and transmission electron microscopy (SEM, TEM) of 0·3C–Si–Mn–Cr steel after various heat treatments. It was found that P segregation takes place during heating for quenching and tempering. The intensity of P segregation does not change when the steel transforms from a ductile (600°C tempered for 2 h with water cooling) to a brittle (600°C tempered with furnace cooling) state. Isothermal aging at 500°C for 200 h leads to further segregation of P, but the intensity remains unchanged after a reductilising treatment (600°C reheating for 2 h with water cooling). (The term reductilising is used to describe the treatment employed to attempt to return the material to its original ductile state.) The internal friction measurements and TEM examinations indicated that the temper embrittlement of the steel is always accompanied by precipitation of very fine particles of Fe₃C(N) causing dead pinning of dislocations within the grains while the reductilised state corresponds to the re-solution of these fine particles back into the a solid solution which explains the reversibility of the phenomenon. Therefore, the P segregation is a necessary factor for grain boundary fracture of the steel in the temper embrittled state, but is still not sufficient for the actual appearance of this mode of fracture. The leading factor is the precipitation of Fe₃C(N) particles on dislocations and a precipitation–segregation mechanism is suggested which can be used to explain all the specific features of high temperature temper embrittlement.

MST/707     

Combined quenching and tempering induced phosphorus segregation to grain boundaries in 2·25Cr–1 Mo steel

Abstract

Combined quenching and tempering induced phosphorus segregation to prior austenite grain boundaries in α 0·077 wt-%P doped 2·25Cr–1Mo steel was examined using field emission gun scanning transmission electron microscopy. The results indicate that combined equilibrium and non-equilibrium phosphorus segregation may play an important part in temper embrittlement of the steel caused by direct tempering after quenching. Non-equilibrium segregation requires the formation of sufficient quantities of vacancy–impurity complexes and their migration to grain boundaries is of great importance in the segregation. For this reason, the mechanism for migration of the complexes is discussed in detail.

MST/3419     

Effect of phosphorus segregation and Ni2Cr formation on hydrogen embrittlement in 70Ni–30Cr alloys

Abstract

The effects of aging at 773 K on hydrogen embrittlement in Ni–30Cr (wt-%) alloys having two levels of P have been investigated by considering the grain-boundary segregation of impurity atoms and the Ni₂ Cr ordered-phase formation. Aging at 773K suppressed intergraular fracture and reduced the susceptibility to hydrogen embrittlement in the low-P alloy. Such behaviour can be explained in terms of the grain-boundary strengthening caused by the segregation of C atoms. During aging at 773 K, the Ni₂Cr ordered phase formed and the deformation mode changed from wavy slips to coplanar slip with paired dislocations, and then to coplanar slip with microtwins. In the low-P alloy, this change of deformation mode induced step-like cracks which may have occurred by the separation of either the {111} slip planes or the microtwin interfaces. In the high-P alloy, aging for short times caused C segregation to the grain boundaries which suppressed intergranular fracture. However, aging for longer times induced drastic intergranular hydrogen embrittlement because of the grain-boundary segregation of P atoms, which offset the effect of the boundary strengthening caused by C atoms.

MST/177     

Critical time and temper embrittlement isotherms

Abstract

The critical time in a non-equilibrium segregation isotherm will induce a critical time in the relative temper embrittlement isotherm, at which when a steel is held, a maximum extent of embrittlement will occur. This suggestion has been confirmed for the non-equilibrium cosegregation to grain boundaries of Ti, Sb, and Ni in low carbon Ni–Cr steels and for phosphorus non-equilibrium segregation to grain boundaries in some steels.     

Kinetics of cold work embrittlement in rephosphorised,interstitial free steels

Abstract

The kinetics of cold work embrittlement, associated with grain boundary segregation of P in batch annealed interstitial free steels, was determined from the temperature–time cycle of the batch annealing process. The grain boundary segregation predictions were subsequently extended to a hypothetical optimised steel chemistry, where C effectively displaced P from the grain boundary through a site competitive interaction process. The P–C, site competitive process was expected to minimise the cold work embrittlement phenomena experienced in interstitial free steels. From a comparison of grain boundary P segregation, it was possible to draw conclusions concerning the minimum grain boundary P level that can be achieved through appropriate modification of the batch annealing cycle or by optimisation of the steel chemistry.     

Statistical analysis of phosphorus segregation on intergranular fracture facets in pressure vessel steels

Abstract

A533B and C–Mn steels, widely used as nuclear pressure vessel steels, have been aged at 520°C after tempering at 650°C for various periods of time to produce different levels of embrittlement resulting from the segregation of P to grain boundaries. Metallographic observation and tensile test results showed that the embrittlement heat treatment did not have significant influence on the microstructures or tensile properties of the steels. P segregation at grain boundaries and on intergranular facets was investigated using field emission gun transmission electron microscopy and Auger electron spectroscopy. After such treatment, enhanced segregation was found to be a linear function of the square root of embrittling time. Statistical analysis of the AES measurements indicated that there is a minimum segregation level for intergranular fracture to occur.