Raymond A. Fournelle

Cyclic stress strain relations and strain-controlled fatigue of 4140 steel

Abstract The strain controlled low cycle fatigue properties and cyclic stress-strain response of a 4140 steel were investigated as functions of tempering temperature. While as-quenched 4140 steel specimens showed cyclic hardening, tempering at 200°C or higher resulted in cyclic softening which was a maximum for 400°C tempering. The hardening in the quenched steel was attributed to dynamic strain aging. Cyclic softening for the 400 and 550°C tempers resulted in part from rearrangement of the dislocation substructure and reduction of dislocation density as shown by transmission electron microscope. Mechanical removal of the yield point also contributed to cyclic softening and was the dominant mode for specimens tempered at 650°C. Removal of the yield point was attributed to an increase in the number of mobile dislocations. On tempering at 650°C, a failure of the Coffin-Manson relation was observed. Agreement was obtained when the plastic strain amplitude was plotted vs cycles to crack initiation rather than cycles to failure. For tempering at 350°C and higher, it is suggested that the endurance limit is essentially equal to the cyclic yield stress.

Discontinuous coarsening of lamellar cellular precipitate in an austenitic Fe-30 wt%Ni-6wt.%Ti alloy—I. Morphology

Abstract The morphology of discontinuous coarsening of lamellar cellular precipitate in an austenitic Fe-30 wt.%Ni-6 wt.%Ti alloy aged at temperatures ranging from 400 to 900°C has been studied by light microscopy, electron microscopy and X-ray diffraction. Aging at all temperatures resulted in decomposition of the austenite by a cellular precipitation into alternate lamellae of depleted austenite and Ni3Ti. This reaction was followed by a second cellular or discontinuous coarsening reaction which decomposed the first lamellar product into a coarse lamellar structure of the same two phases. At all aging temperatures, the lamellar spacings and growth rates of the second cellular reaction were larger and slower, respectively, than those of the first. The second cells also always contained more Ni3Ti than the first cells.

A numerical method for predicting intermetallic layer thickness developed during the formation of solder joints

A numerical, method has been developed for calculating the thickness of intermetallic layers formed in substrate-solder systems during the soldering process. As input, the method requires the temperature-time profile for the soldering process and the isothermal liquid state growth rate parameters for the growth of the intermetallic layer. These usually consist of a growth constant, ko, and an activation energy, Q. The method allows one to predict the thickness of a layer at any time during the soldering process. As such, it can be used in industrial solder processing to enhance the reliability and lifetime of solder joints by allowing control of the thickness of intermetallic layers. The validity of the method is demonstrated for intermetallic growth between copper and 62Sn-36Pb-2Ag solder. The kinetic parameters for the chosen model system were experimentally determined and isothermal intermetallic layer growth between molten solder and copper was found to follow a t0.25 dependence on time t. The growth rate increased with increasing temperature according to an Arrhenius dependence in the temperature range 187 to 258°C with Q = 7.04 kJ/mol and ko = 7.75 μm/min0.25.

A high temperature lattice parameter and dilatometer study of the defect structure of nonstoichiometric cerium dioxide

Abstract The defect structure of CeO 2− x has been investigated over the composition range from CeO 2 to CeO 1.8 and 900°C using the combined techniques of high temperature dilatometric length change and X-ray lattice parameter measurements. The oxygen partial pressure associated with the nonstoichiometric composition was controlled by passing different ratios of H 2 /He mixtures through a constant temperature water bubbler and was monitored constantly with a YSZ oxygen sensor. The difference between the percent expansion for the dilatometric and X-ray lattice parameter measurements was zero, which indicated that the predominant defects of the CeO 2- x are oxygen vacancies.

Cellular precipitation and discontinuous coarsening of cellular precipitate in an Al-29 at.% Zn alloy

Abstract The morphology and growth kinetics of cellular precipitation and discontinuous coarsening of the cellular precipitate in an Al-29 at.% Zn alloy have been investigated at temperatures ranging from 323 to 523 K (50 to 250°C) by light microscopy, electron microscopy and X-ray diffraction. At all aging temperatures the alloy was observed to decompose completely by a cellular precipitation reaction which resulted in a fine lamellar structure of aluminium rich and zinc rich solid solutions. The first cell lamellar structure was then decomposed at all aging temperatures by a second cellular or discontinuous coarsening reaction. The discontinuous coarsening reaction occurred at a much slower rate than the first cellular reaction and resulted in a much coarser lamellar structure. Lattice parameter measurements showed the aluminum rich phase in the cellular precipitate to have a composition far from equilibrium while that in the product of discontinuous coarsening was close to equilibrium. Analysis of the growth kinetics of both the cellular precipitation and the discontinuous coarsening suggested that they were controlled by grain boundary diffusivity.

Discontinuous coarsening of lamellar cellular precipitate in an austenitic Fe-30 wt.%Ni-6 wt.%Ti alloy—II. Growth kinetics

Abstract The growth kinetics of discontinuous coarsening of lamellar cellular precipitate in an austenitic Fe-30 wt.%Ni-6 wt.%Ti Alloy aged at temperatures ranging from 400 to 900°C have been studied by light and electron microscopy measurements of cell growth rate and lamellar spacing. Analysis of the growth kinetics shows that the Livingston-Cahn [1] model is not obeyed with the reason being that not all of the available volume free energy is used in the first reaction. A theory which considers the volume free energy remaining after the first reaction is presented. According to this theory, the growth rate of the coarsening reaction in this system is controlled by grain boundary diffusivity, Db. and depends on the growth rate, V1, and lamellar spacing, λ1, of the first cellular precipitation reaction according to the following equation: V 2 = − V 1 λ 1 2 λ 2 2 + 8D b δ RTλ 2 2 (ΔF 0 + 2σv λ 2 ) .

Discontinuous precipitation and coarsening in Al-Zn alloys

Abstract The morphology and kinetics of discontinuous precipitation (DP) and discontinuous coarsening (DC) in solution treated and isothermally aged Al-Zn alloys containing 39.3 and 59.3 at.% Zn have been investigated at temperatures ranging from 323 to 523 K by light microscopy, electron microscopy and X-ray diffraction. At all aging temperatures the supersaturated α solid solution was observed to decompose rapidly by DP into a lamellar mixture of solute depleted α phase and β phase precipitate. DP occurred so rapidly in the 59.5 at.% Zn alloy that the heat of transformation raised the temperature of the alloy significantly. With further aging a slower DC reaction transformed the lamellar DP into a coarser lamellar structure of the same two phases; however, the composition of the α phase of the DC was closer to the equilibrium solvus composition than that of the DP. With still further aging a second, much slower DC reaction was observed to decompose the lamellar product of the first DC reaction in the 59.5 at.% Zn alloy into a still coarser lamellar structure. Analysis of the kinetics of both the DP and DC reactions showed them to be controlled by boundary diffusion in the advancing reaction interface. Reaction front migration rates for both DP and DC increased markedly with increasing Zn content. This increase seems to be associated partially with an increase in boundary diffusivity with increasing Zn content.

On the thermodynamic driving force for diffusion-induced grain boundary migration, discontinuous precipitation and liquid film migration in binary alloys

Abstract An expression for the net thermodynamic driving force (free energy change per unit distance of reaction front migration per unit area of reaction front) for the migration of reaction fronts during diffusion-induced grain boundary migration (DIGM), discontinuous precipitation (DP) and liquid film migration (LFM) in binary alloys is determined from a two-dimensional model which considers individual segments of the migrating reaction front as open systems which can receive solute and solvent atoms from or give them up to the surrounding material. In the case of DIGM and DP the reaction front is treated as a separate grain boundary phase of thickness δ. In the case of LFM it is treated as a liquid film of thickness δ. The magnitude of the force on the reaction front is calculated for DIGM in AuCu and for LFM in NiMo using available thermodynamic data. Finally, a criterion for the stability of a reaction front, when a small change in composition across a reaction front occurs and the reaction front composition is slightly changed, is established which shows that a driving force for reaction front migration can develop spontaneously as the result of solute and solvent diffusion along it, as long as the curvature of the free energy curve for the reaction front is positive.

Discontinuous coarsening of discontinuous precipitate in a Ni-7.5 at.% In alloy

Abstract The morphology and growth kinetics of the discontinuous coarsening of discontinuous precipitate in a Ni-7.5 at.% In alloy have for the first time been investigated at temperatures ranging from 667 to 1030 K by light and scanning electron microscopy and X-ray diffraction. At all aging temperatures the alloy was observed to decompose completely by discontinuous precipitation into a fine lamellar structure of nickel rich solid solution and θ (Ni 3 In) precipitate phase. This lamellar structure was then decomposed at all aging temperatures by a discontinuous coarsening reaction. This reaction occurred at a much slower rate than the first reaction and resulted in a much coarser lamellar structure of the same phases. Lattice parameter measurements showed the Ni rich solid solution in the product of the first reaction to be far from equilibrium while that of the second reaction was close to equilibrium. Analysis of the growth rates, lamellar spacings and phase compositions for both the discontinuous precipitation and discontinuous coarsening reactions showed that they were controlled by grain boundary diffusion. In analyzing the results a generally applicable procedure for calculating the driving force is presented. In this calculation the solid solution is treated as a regular solution and the actual thermodynamic data are used for the precipitate phase. The driving forces calculated in this way should be more reliable than those calculated with the approximations based on Raoults and Henrys laws.

Diffusion induced grain boundary migration of symmetric and asymmetric 〈011〉 {011} tilt boundaries during the diffusion of Zn into Cu

Diffusion induced grain boundary migration (DIGM) of symmetric and asymmetric 〈011〉{011} tilt boundaries during the diffusion of Zn into Cu bicrystals having misorientation angles θ ranging from 10° to 172° was studied over the temperature range from 623 to 773 K using light microscopy and electron probe microanalysis. All boundaries except for the low angle (θ < 15°) and coherent Σ3 twin boundaries exhibited DIGM with the migration being randomly distributed on both sides of the originally symmetric boundaries and in preferred directions for the asymmetric boundaries. Symmetric Σ19a boundaries exhibited a unique faceted form of DIGM in which all boundary migration resulted in triangular shaped alloyed regions having {111} and {113} habit planes in the neighboring grains. At 693 K the average migration rates of the grain boundaries during DIGM as well as calculated grain boundary diffusivities exhibited a strong dependence on misorientation angle with some coincident site boundaries such as the Σ9 boundaries exhibiting high migration rates and others such as the incoherent Σ3 twin boundaries exhibiting low migration rates. For asymmetric Σ19a boundaries the migration rate at 693 K was observed to increase with increasing asymmetry. Grain boundary diffusivity values calculated for Σ19a, Σ9 and 45° high angle grain boundaries over the temperature range from 627 to 773 K agreed well with the values reported for Zn tracer diffusion in stationary Cu grain boundaries.