Homologous Temperature Research Articles

Phase-field crystal study of grain-boundary premelting

We study the phenomenon of grain-boundary premelting for temperatures below the melting point in the phase-field crystal model of a pure material with hexagonal ordering in two dimensions. We investigate the structures of symmetric tilt boundaries as a function of misorientation $\ensuremath{\theta}$ for two different inclinations and compute in the grand canonical ensemble the ``disjoining potential'' $V(w)$ that describes the fundamental interaction between crystal-melt interfaces as a function of the premelted layer width $w$, which is defined here in terms of the excess mass of the grain boundary via a Gibbs construction. The results reveal qualitatively different behaviors for high-angle grain boundaries that are uniformly wetted, with $w$ diverging logarithmically as the melting point is approached from below, and low-angle boundaries that are punctuated by liquid pools surrounding dislocations, separated by solid bridges. The latter persist over a superheated range of temperature. This qualitative difference between high- and low-angle boundaries is reflected in the $w$ dependence of the disjoining potential that is purely repulsive [${V}^{\ensuremath{'}}(w)l0$ for all $w$] for misorientations larger than a critical angle ${\ensuremath{\theta}}_{c}$, but switches from repulsive at small $w$ to attractive at large $w$ for $\ensuremath{\theta}l{\ensuremath{\theta}}_{c}$. In the latter case, $V(w)$ has a minimum that corresponds to a premelted boundary of finite width at the melting point. Furthermore, we find that the standard wetting condition ${\ensuremath{\gamma}}_{\text{gb}}({\ensuremath{\theta}}_{c})=2{\ensuremath{\gamma}}_{\text{sl}}$ gives a much too low estimate of ${\ensuremath{\theta}}_{c}$ when a low-temperature value of the grain-boundary energy ${\ensuremath{\gamma}}_{\text{gb}}$ is used. In contrast, a reasonable lower-bound estimate can be obtained if ${\ensuremath{\gamma}}_{\text{gb}}$ is extrapolated to the melting point, taking into account both the elastic softening of the material at high homologous temperature and local melting around dislocations.

On interfacial velocities during abnormal grain growth at ultra-high driving forces

Interfacial velocities during grain growth studies of nanocrystalline materials have been investigated. Two types of interfacial velocity parameters were developed in Ni and Ni–Co alloys. The first was a transformation-averaged parameter based on the time to consume the nanocrystalline matrix by abnormal grain growth. The second was a time-averaged parameter based on the rate of size increase of the largest growing grains. Despite the ultra-high driving force and rapid loss of nanostructure during annealing, the averaged grain boundary velocities are considerably lower than reported velocities during recrystallization in high purity systems for the same homologous temperature. It was found that the time-averaged abnormal growth front velocity decreased with increasing migration distance, which was interpreted in terms of a dynamic sulfur segregation model.

Asperity contacts at the nanoscale: Comparison of Ru and Au

We develop and validate an interatomic potential for ruthenium based on the embedded atom method framework with the Finnis/Sinclair representation. We confirm that the potential yields a stable hcp lattice with reasonable lattice and elastic constants and surface and stacking fault energies. We employ molecular dynamics simulations to bring two surfaces together, one flat and the other with a single asperity. We compare the process of asperity contact formation and breaking in Au and Ru, two materials currently in use in microelectromechanical system switches. While Au is very ductile at 150 and 300 K, Ru shows considerably less plasticity at 300 and 600 K (approximately the same homologous temperature). In Au, the asperity necks down to a single atom thick bridge at separation. While similar necking occurs in Ru at 600 K, it is much more limited than in Au. On the other hand, at 300 K, Ru breaks by a much more brittle process of fracture/decohesion with limited plastic deformation.

Texture and High-Angle Boundary Formation during Deformation Processing

Among the phenomena leading to formation of high-angle boundaries during deformation processing at low homologous temperatures is the subdivision of prior grains and formation of deformation bands. Evidence for this phenomenon during processing of AA2004, a superplastic aluminum alloy, is reviewed; fragmentation of deformation bands leads to equiaxed grains and high-angle boundaries that support superplasticity. In addition to subdivision, groups of grains undergo lattice rotation toward one or the other variant of the β orientation fibers during plane-strain deformation of pure aluminum by ambient temperature rolling. The formation of equiaxed grains from banded structures during simple shear by equal channel angular pressing (ECAP) is also considered.

Temperature-Level Effect on Solder Lifetime During Thermal Cycling of Power Modules

In this paper, we show that, during thermal cycling, the solder lifetime of power modules is not only dependent on temperature variation, but we also highlight the influence of some other key parameters such as upper and lower dwell temperature levels. In particular, we show the influence of these parameters on the solder crack initiation and propagation in the solder layer between the direct copper bonding and base plate of high-power insulated gate bipolar transistor modules. For this purpose, both experimental and numerical investigations have been carried out. Concerning thermal cycling tests, three temperature profiles have been done: -40degC/120degC, 40degC/120degC, and -40degC/40degC. Results have shown that stress values in the solder are monitored by the low temperature level and that the strain is monitored by the high-level one. We observed that the relative magnitude of strain variations is larger than that of stress variation. In order to understand experimental results, finite-element simulations with various high and low temperatures have been performed. Results have pointed out that the solder exhibits two different mechanical behaviors, depending on whether the upper dwell temperature (Tmax) exceeds or not a homologous temperature of approximately 0.74 T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> . When Tmax is below this value, shear strain variations remain in relatively small range values, and shear stress variations have a linear dependence with the temperature variation. In these conditions, only energy-based models should be used for solder lifetime estimation. On the contrary, when Tmax is above 0.74 T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> , shear stress variations reach a saturation value while inelastic shear strains increase significantly. Therefore, in these conditions, either strain- or energy-based models could be used for solder lifetime estimation. Finally, the thermal cycling behaviors of a lead-free solder (SnAg3Cu0.5) and a lead-based one (SnPb37) are numerically compared.

Cyclic stability of ultrafine-grained interstitial-free steel at elevated temperatures

The fatigue performance of an ultrafine-grained interstitial-free steel was investigated at elevated temperatures up to a homologous temperature of 0.39. The significantly altered cyclic stability under combined thermal-mechanical loading is attributed to localized grain growth.

An evidence of high strain rate superplasticity at intermediate homologous temperatures in an Al–Zn–Mg–Cu alloy processed by high-pressure torsion

A commercial Al–Zn–Mg-Cu alloy, 7075 Al, was processed by high-pressure torsion in unconstrained conditions at room temperature to five complete turns under load of 6 GPa. Microstructural characterization was performed by transmission electron microscopy in the peripheral region of the processed samples, showing equiaxed and submicron grain sizes of 100–150 nm. Vickers microhardness measurements revealed large strengthening at ambient temperature as a consequence of the grain refinement. Small punch testing, having the same axial symmetry as high-pressure torsion processing, was performed to evaluate the mechanical properties at intermediate temperatures. The processed disks showed high strain rate superplasticity at 250 and 300 °C.

The role of Harper–Dorn creep at high temperatures and very low stresses

Creep experiments were conducted on single crystals of very high purity aluminum to evaluate the validity of the Harper–Dorn region of flow which occurs at very low stresses and high homologous temperatures. The results confirm the existence of a different flow process under these conditions but with a stress exponent closer to ∼3 rather than 1. Measurements show that the dislocation density within this low stress region varies with stress in a manner consistent with the behavior anticipated from an extrapolation of data reported in the regime of conventional power-law creep at high stresses. All of the experimental results are in reasonable agreement with earlier published data, including with the original data of Harper and Dorn when their results are plotted without incorporating a threshold stress.

A novel low-temperature solder based on intermetallic-compound phases: Alloy design, high-homologous temperature properties, and reliability

A novel low-temperature solder that consists entirely of two phases of intermetallic compounds has been developed as a reliable low-temperature interconnect. The new solder can be reflowed below 125°C and yet exhibits excellent mechanical properties at homologous temperatures exceeding 0.9. Specifically, the new solder exhibits creep resistance an order of magnitude greater than conventional low-temperature solders, and strength retention ability exceeding that of Sn-4%Ag-0.5%Cu (SAC405) at the same homologous temperatures.

Influence of Severe Thermomechanical Treatment on Formation of Nanocrystalline Structure in Ni 718 and Ni 718Plus Alloys and their Mechanical Properties

The influence of severe thermomechanical treatment via multiple forging on the formation of a nanocrystalline (NC) structure in bulk samples of Alloy 718 and ATI 718Plus has been investigated. It was observed that a step-wise decrease of processing temperature from 950 down to 575°C allowed the refinement of the initial coarse grain structure to a NC state. Investigations of structural changes in the deformed samples have shown that extending the temperature interval of dynamic recrystallization to low homologous temperatures resulted in the formation of a fine-grained recrystallized structure. The temperature of NC structure formation in ATI Alloy 718Plus was 50-100°С higher than that required for alloy 718. This was due to the presence of the additional γ′-phase, which increased the recrystallization temperature. This decreased the total strain required to produce NC structure, as compared with Alloy 718. It was observed that increasing the total strain and decreasing temperatures step-wise during deformation via multiple forging resulted in a uniform structure across the cross-section of the samples. The room temperature mechanical properties of the investigated alloys with various grain sizes are also compared.

Microstructure Modification

Pressure and temperature in internal combustion engines have rapidly increased during the past 15 years. Operating at maximum temperatures of up to 420 °C in series production engines (which is equivalent to a homologous temperature of 0.92!), light vehicle diesel pistons for modern passenger vehicles probably represent aluminium’s most challenging hightemperature application. To meet these requirements, Federal Mogul has developed the process of local remelting for critical piston regions. The technical benefit of the remelt process has been proven by engine validation.

Material flow stress and failure in multiscale machining titanium alloy Ti-6Al-4V

Titanium Ti-6Al-4V alloy is a typical difficult-to-machine material due to its unique physical and mechanical properties. The material properties of Ti-6Al-4V play an important role in process design and optimization. However, the dynamic mechanical behavior is poorly understood and accurate predictive models have yet to be developed. This work focuses on the dynamic mechanical behavior of machining Ti-6Al-4V beyond the range of strains, strain rates, and temperatures in conventional materials testing. The flow stress characteristics of strain hardening and thermal softening can be predicted by the Johnson–Cook model coupled with the adiabatic condition. The predicted flow stresses at small strains agree very well with those from the split Hopkinson pressure bar (SHPB) tests, while the predicted flow stresses at large strains also agree with the calculated flow stresses based on the cutting tests with a suitable depth of cut. Heat fraction and temperature parameter control the range of thermal softening and the decrease rate of flow stress. The material may exhibit super plasticity at a small depth of cut with a large radius of the cutting edge in micromachining. Strain rate is one important factor for material fracture close to the cutting edge. The failure strain increases linearly with the increase of homologous temperature, while it only increases slightly with the strain rate.

Improvement of the fatigue performance of an ultrafine-grained Nb–Zr alloy by nano-sized precipitates formed by internal oxidation

The formation of nano-sized precipitates in an ultrafine-grained Nb–Zr alloy was investigated. ZrO2 precipitates induced by internal oxidation during heat treatment at low homologous temperatures significantly intensify the hardness of the surface layer without deterioration of the surface quality, and thus significantly improve the fatigue performance.

On the Onset of a Steady State in Body-Centered Cubic Iron during Severe Plastic Deformation at Low Homologous Temperatures

Armco Iron was severely deformed by means of a high-performance, high-pressure torsion (HPT) tool at a hydrostatic pressure of 5.4 GPa at low homologous temperatures, Tm, between 0.08 and 0.40 Tm. The flow stress was estimated from the measured torque during severe plastic deformation (SPD). At all investigated deformation conditions, a saturation in the flow stress at large strains without any decline was obtained. It is shown that this occurrence of a “steady state” at low homologous temperatures is significantly influenced by the deformation parameters, whereby an increase in deformation temperature or a decrease in strain rate results in a decrease in onset strain and an increase in flow stress in both the steady state and the size and aspect ratio of the structural elements. The Zener–Hollomon parameter is used to analyze the mechanical and microstructural properties as a function of the processing parameters; this shows that the investigated range of deformation conditions is divided into two regimes. For comparable high-deformation temperatures, the occurrence of a steady state is ascribed to a process similar to geometric dynamic recrystallization (DRX). Possible reasons for the occurrence of a different behavior in the low homologous temperature regime are discussed; the size of the crystallites formed during straining by the subdivision of the initial grains is considered to play an important role.

On the evolution of free volume during the deformation of metallic glasses at high homologous temperatures

Recently a finite-deformation and coupled thermo-mechanically-based theory for metallic glasses has been developed by Thamburaja and Ekambaram [Thamburaja, P., Ekambaram, R., 2007. Coupled thermo-mechanical modelling of bulk-metallic glasses: theory, finite-element simulations and experimental verification. J. Mech. Phys. Solids 55, 1236–1273], and implemented in the ABAQUS/Explicit (2007) finite-element program. In this work, we use the aforementioned constitutive model and its numerical algorithm to study the deformation behavior of a Pd-based metallic glass near its glass transition temperature. At a temperature of 564 K, the material parameters in the constitutive model were fit to the simple tension stress–strain curves and the steady-state free volume concentrations data for a variety of applied strain-rates obtained from De Hey et al. [De Hey, P., Sietsma, J., Van Den Beukel, A., 1998. Structural disordering in a amorphous Pd–Ni–P induced by high temperature deformations. Acta Mater. 46, 5873–5882]. With the model calibrated, the simple tension steady-state stresses and free volume concentrations data for a variety of applied strain-rates at temperatures of 556 K and 549 K (De Hey et al.) were predicted to be in good accord by the constitutive model. Furthermore, the experimental stress–strain curves for samples annealed for different times before the tensile tests were carried out under a particular strain-rate (De Hey et al.) were also well-predicted by the constitutive model. Finally we also perform numerical simulations to show that at a given temperature below the glass transition temperature, metallic glasses which show shear localization behavior as a result of being tested in the fully-annealed condition can be made to deform more homogeneously by first pre-deforming the specimen under high strain-rates at temperatures within the supercooled liquid region before being tested again at temperatures below the glass transition temperature.

The reaction pathway and rate-limiting step of dehydrogenation of the LiHN 2 + LiH mixture

The reaction pathway and rate-limiting step of dehydrogenation of the LiNH 2 + LiH mixture have been investigated. The study reveals that dehydrogenation of the LiNH 2 + LiH mixture is diffusion-controlled and the rate-limiting step is NH 3 diffusion through the Li 2NH product layer outside the LiNH 2 shrinking core. This phenomenon is explained based on a model describing the major steps of the dehydriding reaction of the mixture, and related to the evidence obtained from X-ray diffraction and specific surface area measurements of the mixture before and after isothermal hydrogen uptake/release cycles at high homologous temperatures.

A novel low-temperature solder based on intermetallic-compound phases with superior high-homologous temperature properties

A novel low-temperature solder which consists entirely of two phases of intermetallic compounds is reported. The new solder can be reflowed below 125 °C and yet maintains high-temperature mechanical properties at homologous temperatures exceeding 0.9. Specifically, the new solder exhibits creep resistance and high-temperature retention capability exceeding those of conventional low-temperature solders, and its strength even exceeds that of Sn–4%Ag–0.5%Cu (SAC405) at the same homologous temperatures. This intermetallic solder also exhibits room-temperature ductility comparable to conventional solders. Drastic enhancement of wettability is achieved with addition of active metals.

Reappraising elastic thickness variation at oceanic trenches

We reassess the variation of elastic thickness as a function of lithospheric plate age using a global database of bathymetric and free‐air gravity profiles which are perpendicular to oceanic trenches. As in many previous studies, our starting point is the well‐known floating elastic plate model. In order to remove the influence of short‐wavelength features not associated with lithospheric bending, adjacent profiles from 10‐Myr bins have been stacked together to construct average profiles with standard deviations. Each average profile was then inverted in a two‐stage procedure. First, singular value decomposition was used to determine two unknown flexural parameters, together with a regional slope and offset, for any given elastic thickness. This procedure was repeated for a range of elastic thicknesses. Second, residual misfit was plotted as a function of elastic thickness, and the global minimum was identified. This two‐stage procedure makes no prior assumptions about magnitude of the load, size of the bending moment, or whether the elastic plate is broken/continuous. We obtained excellent fits between theory and observation for both bathymetric and gravity profiles from lithosphere with an age range of 0–150 Ma. The shape of the residual misfit function indicates the degree of confidence we have in our elastic thickness estimates. The lower limit of elastic thickness is usually well determined but upper limits are often poorly constrained. Inverse modeling was carried out using a range of profile lengths (250–300, 500, and 700 km). In general, our estimates show no consistent increase of elastic thickness as a function of plate age. This surprising result is consistent with recent reassessments of elastic thickness beneath seamounts and implies either that elastic thickness is independent of plate age or that elastic thickness cannot be measured with sufficient accuracy to reveal such a relationship. Modeling of short free‐air gravity profiles (250–300 km) does tentatively suggest that elastic thickness increases linearly from 5 to 10 km between 0 and 20 Ma and from 10 to 15 km between 20 and 150 Ma. This variation roughly matches the depth to the 200°C isotherm which corresponds to an homologous temperature of 0.4 for wet peridotite. Unfortunately, for longer profile lengths, there is no temporal dependence, and elastic thicknesses vary considerably for all plate ages. Bathymetric profile modeling yields similar results although uncertainties are larger.

Local Strain Measurement in Hot Deformed Microstructures

The deformation of metals at high homologous temperatures typical of industrial forming processes such as hot rolling is investigated using an electron micro-lithography technique enabling strain measurements at the scale of the microstructure of these metals. Grids with a typical 5 μm pitch have been laid on the surface of an aluminium alloy and a stainless steel deformed by plane strain compression at 400oC and 850oC respectively. In-plane strain values can be computed from the displacements of the intersections of the grids. Strain maps can then be plotted over representative areas of the microstructures together with strain distributions within each phase of the microstructure. Results obtained for a commercial high-purity aluminium alloy with 5% magnesium show a strong localisation of deformation at triple points with a local equivalent strain value of 1.7 for a 0.22 applied strain at 400oC. As for the two-phase stainless steel deformed to a strain of 0.3, results show a high heterogeneity of deformation within each phase with a localisation of deformation into bands in the ferrite phase and local values reaching more than two times the applied compression.

Thermal structure and seismicity of subducting lithosphere

It has recently been suggested that the mechanical behaviour of the oceanic and continental uppermost mantle depends on temperature alone, and that there is no strong evidence for compositional effects. It seems in the majority of cases that, if uppermost mantle temperatures exceed 600 °C, any deformation that occurs does so in the absence of significant seismicity. This observation apparently applies irrespective of whether that mantle material underlies an ocean or a continent. This paper investigates whether the same behaviour exists for earthquakes occurring in descending lithospheric slabs, namely whether there is some limiting temperature above which deformation occurs without significant seismicity, and whether that limiting temperature is consistent with the behaviour seen in the uppermost mantle beneath oceans and continents. By re-examining the thermal structure in subducting slabs, accounting for the temperature dependence of the relevant physical parameters, teleseismically recorded seismicity is shown to be limited to material having potential temperatures less than ∼570–600 °C, or homologous temperatures less than ∼0.42. The exceptions to this pattern occur in the subhorizontally subducting regions of the Nazca Plate, in which temperatures are probably affected by the relatively cold overriding plate.