Constitutive models of creep for lead-free solders

The constitutive modeling of creep has been extensively studied due to the important of the creep failure mode in solder joints. However, there are very few studies that considered room temperature aging contributions in their creep modeling studies. This study investigated constitutive modeling of creep of solders by taking into account the possible contribution room temperature aging. Lead-free solder (Sn–4.0Ag–0.5Cu) was found to have a higher creep resistance than Sn–Pb solder at the same stress level and testing temperature. The higher creep resistance was contributed by the second phase intermetallic compounds, Ag₃Sn and Cu₆Sn₅. The precipitation of these intermetallic compounds can significantly block the movement of dislocations and increase the creep resistance of the material. Constitutive models of creep for both lead-free and Sn–Pb eutectic solders were constructed based on the experimental data. The activation energy for SAC405 is much higher than that of Sn–Pb, which also indicates that SAC405 possesses higher creep resistance. The constitutive models can be used in finite element analysis of actual electronic packages to predict solder joint failure. The creep mechanisms of both lead-free and Sn–Pb eutectic solders were also extensively discussed in this dissertation. Dislocation gliding and climb is believed to be the major failure mode at high stresses, while lattice diffusion and grain boundary diffusion is believed to be the major failure mode at low stress levels. Grain boundary sliding is believed to contribute to creep deformation at both high-stresses and low-stresses. For eutectic Sn–Pb, superplastic deformation is a major the creep mechanism at low-stresses and high-temperatures.     

Compressive creep behavior in air of a slightly porous as-sintered polycrystalline α-alumina material

Compressive creep tests in air have been performed on a polycrystalline submicron as sintered and slightly porous α-alumina material. Two different deformation mechanisms, depending on the applied stress and creep temperature, have been identified when the grain size becomes higher than a critical value 〈G ^*〉. For low temperatures and/or low applied stresses, deformation occurs by grain boundary sliding accommodated by an in-series “interface reaction/diffusion of Al³⁺ cations” process, with the limiting step being the interface reaction. In this case increased densification of the samples is observed after creep, compared to the as-sintered ones. In contrast, for high temperatures and/or high-applied stresses, deformation occurs by grain boundary sliding accommodated by the relocation and growth of preexisting cavities, the growth step being also controlled by the diffusion of Al³⁺ cations. In this case, a marked decrease of the relative density is measured on the crept samples compared to the as-sintered ones. Using these results, it is possible to identify the optimal conditions for superplastic forming of previously as-sintered parts, leading to shaped objects with an increased final density.     

Creep behavior of AZ31 magnesium alloy in low temperature range between 423 K and 473 K

The deformation behavior of coarse-grained AZ31 magnesium alloy was examined in creep at low temperatures below 0.5 T _m and low strain rates below 5 × 10⁻⁴ s⁻¹. The creep test was conducted in the temperature range between 423 and 473 K (0.46–0.51 T _m) under various constant stresses covering the strain rate range 5 × 10⁻⁸ s⁻¹–5 × 10⁻⁴ s⁻¹. All of the creep curves exhibited two types depending on stress level. At low stress (σ/G < 4 × 10³), the creep curve was typical of class I behavior. However, at high stresses (σ/G > 4 × 10³), the creep curve was typical of class II. At the low stress level, deformation could be well described by solute drag creep whereas at the high stress level, deformation could be well described by dislocation climb creep associated with pipe diffusion or lattice diffusion. The transition of deformation mechanism from solute drag creep to dislocation climb creep, on the other hand, could be explained in terms of solute-atmosphere-breakaway concept.     

Studies on high temperature deformation behaviour of 3Y-TZP ceramics

The present work reports the results on the deformation behaviour of ZrO₂-3 mol% Y₂O₃ (3Y-TZP) ceramics which were prepared by pressureless sintering at 1400°C. Dense, cylindrical samples were subjected to uniaxial compression tests under a constant stress of 15 MPa in the temperature range of 1200–1400°C. The ceramics exhibit considerable ductility, attaining over 60% true strain without any edge cracking. Microstructural changes due to interaction of grain boundary viscous phase with the ultrafine and equiaxed grains were analyzed by transmission electron microscopy. Results show the grain boundary sliding accompanied by a diffusion accommodation process as the predominant deformation mechanism in these ceramics.     

Superplastic power-law creep of Sn–40%Pb–2.5%Sb peritectic alloy

The power law-creep behavior of superplastic Sn–40Pb–2.5Sb alloys with different grain sizes has been investigated at room temperature. Stress exponent values for these alloys have been determined by indentation creep, conventional creep and uniaxial tension tests in order to evaluate the correspondence of indentation creep results with conventional tests. In all cases, the indentation results were in good agreement with each other and with those of the tensile and conventional creep tests. The average stress exponent values of about 2.6 and 3.0 corresponding to the strain rate sensitivity (SRS) indices of 0.33–0.39, depending on the grain size of the materials, indicate that the grain boundary sliding is the possible mechanism during creep deformation of Sn–Pb–Sb alloys. Within limits, the indentation tests are thus considered useful to acquire information on the creep behavior of small specimens of these soft tin–lead–antimony alloys at room temperature. It is also demonstrated that the indentation creep test provides a convenient method to measure SRS and thereby to assess the ability of a material to undergo superplastic deformation.     

Creep deformation mechanism of magnesium-based alloys

Two heat-resistant magnesium alloys AJC421 and Mg-2Nd were prepared. Both as-cast Mg-2Nd and AJC421 alloys exhibited good creep resistance in comparison with commonly used magnesium alloys. The improvement in creep properties through Nd addition to pure magnesium is attributed to both solid solution and precipitation hardening. The stress exponents of 4.5–5.5 and activation energies of 70.0–96.0 kJ/mol obtained from the as-cast Mg-2Nd alloy at low temperatures and low stresses indicate the five power law can be used for predicting the creep mechanism. The additions of alkaline earth elements Sr and Ca into Mg–Al alloys suppress the discontinuous precipitation of Mg₁₇Al₁₂ and form thermal-stable intermediate phases at grain boundaries, leading to effective restriction to grain boundary sliding and migration. However, the mechanism responsible for creep deformation of Mg–Al based alloys with Ca and Sr additions is not consistent with the results of microstructure observations performed on the alloys before and after creep tests.     

High temperature creep of ultrafine-grained Fe-doped MgO polycrystals

Creep deformation in ultrafine-grained (0.1 to 1μm) Fe-doped magnesia polycrystals is studied in compression, at temperatures of 700 to 1050° C, and constant loads of 50 to 140 MPa. The stress exponent observed to be nearly unity and the strong grain size sensitivity (ė∼d ^−2.85) suggest that diffusional creep mechanisms dominate the deformation. In the grain size range of the present study the grain boundary diffusion contribution is significantly more important than lattice diffusion. Magnesium is tentatively identified as the rate-controlling species along grain boundaries from an analysis of the diffusivities inferred from the present work and from other authors for Fe-doped magnesia. Associated with the CNRS.     

Stress relaxation following heating of nanocrystalline nickel

Stress relaxation of nanocrystalline nickel within the range of temperatures from 523 to 673K (0.17–0.27·T_m) in the regime of uniaxial compression is studied. The results obtained for nickel with more coarse grains are given for comparison. An average strain rate of nanocrystalline nickel within the investigated range of temperatures is 1.75·10⁻⁵–3.03· 10⁻⁵s⁻¹. The presence of two types of stress relaxation dependencies is shown. The most probable mechanism of plastic strain is grain boundary sliding controlled by grain boundary diffusion for 623–673K. At lower test temperatures, 523–573K, a plastic strain occurs by the powder law creep according to the Weertman model.     

Analysis of Coble creep in cylindrical and cubic crystals

Abstract

An analysis is made of the rate of creep by the stress induced diffusion of vacancies along surfaces or grain boundaries of crystals of cylindrical and cubic shape, developed from the original proposal by Coble of the significance of this creep mode. It is shown that complete analytical solutions can be obtained, satisfying all physical conditions of the problem. The creep rate ε by this mechanism at a temperature T in a cylinder of length L and diameter D subjected to a stress σ along its axis is given by ε = 64D8_g wσΩ/kTLD²[1 + (4L/3D)], where D_g is the, self-diffusion coefficient in a layer at the surface or grain boundary of width w, Ω is the atomic volume and k is Boltzmann's constant. In the case of a cube of side L subject to stress σ perpendicular to a pair of faces, the creep rate ε = 16D_gwσΩ/kTL³.

MST/251     

Thermal strain in lead thin films II: strain relaxation mechanisms

A deformation mechanism map was constructed to study the mechanisms of strain relaxation in lead thin films which were deposited on oxidized silicon wafers at room temperature and which were then thermally cycled between room temperature and liquid helium temperature. The stress level, which was calculated from the strain measured by an X-ray diffraction technique, was plotted on the map. By comparing the calculated and experimental stress levels the following observations were obtained. In the cooling process the strain was relaxed rapidly in a field of dislocation glide mechanism for films of greater than 0.2 μm thickness. In the heating process most of the strain was again believed to be relaxed by the glide mechanism. For a film 0.5 μm thick the stress (after the primary relaxation was completed) was found to be (1–1.5) × 10⁹ dyn cm^-2 for the cooling process and (0.17–0.24) × 10⁹ dyn cm^-2 for the heating process at temperatures around 200–280 K. Slow secondary relaxations were observed after the primary relaxations were completed. The measured compressive strain relaxation rate at room temperature was very close to the rate calculated on the assumption of grain boundary diffusion creep. This suggested that the secondary relaxation mechanism of compressive strain was grain boundary diffusion creep at temperatures near room temperature. These suggestions were supported by scanning electron microscopy observations in which dislocation slip lines were observed inside grains and hillocks were observed on grain boundaries.     

A research on the creep properties of titanium matrix composites rolled with different deformation degrees

(TiB + La₂O₃)/Ti composites were in situ synthesized and deformed with different deformation degrees. The influence of TiB whisker orientation and grain refinement on the creep properties of titanium matrix composites (TMCs) are discussed. The creep test reveals that the steady state creep rate of TMCs first decreases and then increases with the increase of deformation degree, which can be attributed to competing effects: TiB whisker rotating to the rolling direction, α plate grain boundary hindering and pinning dislocations can all decrease the creep rate, however, dislocation movement on the α plate grain boundary and dislocation emitting from the α plate grain boundary can both increase the creep rate.     

Diffusive relaxation of stress concentrations at grain boundary cavities in elevated temperature creep

This work deals with certain aspects of elevated temperatures creep cavitation of grain boundaries under cyclic and rapidly applied loading. The response of partially damaged materials (where damage is represented as crack-like cavities on the grain boundaries) following load alterations at temperatures in the vicinity of 0.5 T_m or higher is analyzed. The interaction between grain boundary diffusion and elastic deformation is important in alleviating local stress concentrations under these conditions. The stress levels considered are assumed to be low enough that plastic deformation is significant. Diffusive processes contribute to high temperature creep rupture by material redistribution from the void surfaces to the grain boundaries, and any non-uniform matter accommodation along the grain boundaries is accomplished by elastic deformation under the conditions assumed. The same material redistribution mechanism dominates in the stress relaxation process. The analysis of the stress and displacement fields is based on consideration of the coupled elasticity-diffusion boundary value problem, which leads to an integral equation. On the basis of the solution obtained, the detailed analysis of the process under cyclic, step and ramp loadings is given. For suddenly applied loading the results demonstrate that the elastic stress concentration is effectively relaxed by diffusion after t = 0.05τ where $\text{τ ≈}\text{L}{}^3\text{DE}$, L is half of the distance between adjacent tips of neighboring cracks along the grain boundary, E is Young's modulus, and D is diffusion parameter relating volumetric flux along the grain boundary to the stress gradient. By t = 0.25τ the stress distribution becomes essentially identical to that calculated for rigid grains, i.e. diffusion has become the dominant process and elastic deformability of the adjoining grains is then irrelevant.     

The effect of creep deformation on the stability of intergranular carbide dispersions in an austenitic stainless steel

The stability of intergranular TiC in a 20% Cr-30% Ni, Ti stabilized stainless steel and the transformation of TiC to M₂₃C₆, has been investigated as a function of creep deformation over a wide range of stresses at 800° C. It was found that diffusion creep does not make a significant contribution to the general ageing process or to the transformation of TiC to M₂₃C₆. However, dislocation creep strongly accelerates this transformation and increases the general rate of coarsening of intergranular carbides. It is concluded that this acceleration occurs through the combined action of an increase in the number of available nucleation sites (extrinsic grain boundary dislocations) and dislocation enhanced diffusion.     

Room-temperature indentation creep of lead-free Sn–Bi solder alloys

Creep behavior of the lead-free Sn–Bi alloys with bismuth contents in the range of 1–5 wt.% was studied by long time Vickers indentation testing at room temperature. The materials were examined in the homogenized cast and wrought conditions. The stress exponents, determined through different indentation methods, were in good agreement. The exponents of 13.4–15.3 and 9.2–10.0, found respectively for the cast and wrought conditions, are close to those determined by room-temperature conventional creep testing of the same material reported in the literature. Due to the solid solution hardening effects of Bi in Sn, creep rate decreased and creep resistance increased with increasing Bi content of the materials. Cast alloys, with a rather coarser grain structure and some Bi particles at the grain boundaries, showed typically higher resistance to indentation creep compared to the wrought materials. These two factors have apparently resulted in a less tendency of the material for grain boundary accommodated deformation, which is considered as a process to decrease the creep resistance of soft materials.     

Creep behaviour of equiaxed fine-grain γ-TiAl-based alloy prepared by powder metallurgy

In this study, γ-TiAl-based alloy with chemical composition of Ti–45Al–5Nb (in at.-%) fabricated by powder metallurgy method was crept at 700°C under 200–500?MPa. The creep properties and the microstructure after creep tests were investigated. The results showed that the γ-TiAl-based alloy was composed of equiaxed γ-TiAl grains and α ₂-Ti₃Al grains with average sizes of 1.4 and 0.5?μm, respectively. The creep resistance deteriorated generally with increased applied stresses. The typical intergranular fracture characteristics were observed though the grains were small. The calculated stress exponent and activation energy revealed the main creep mechanism of grain boundary sliding. Furthermore, twinning and dynamic recrystallisation also led to the creep deformation.     

Ultrafine-grained nickel refined by dislocation activities at intermediate strain rate impact: deformation microstructure and mechanical properties

This article presents an application of the impact-induced deformation in effective grain refinement in polycrystalline nickel. Ultrafine-grained microstructure was processed by means of Dynamic Plastic Deformation at room temperature using a falling impactor with a maximum impact velocity of 10 m s⁻¹. The commercially pure (98.4 wt%) starting material was characterised by a coarse-grained (~25 μm) microstructure. Electron backscattering diffraction and transmission electron microscopy studies showed that the initial equiaxed grains evolved into a laminar structure of submicron size narrow domains delineated by high-angle grain boundaries. The texture after deformation exhibits preferential orientations including a strong 〈220〉 fibre texture. The mechanical behaviour under quasi-static compression at room temperature and at a strain rate of 2 × 10⁻³ s⁻¹ was investigated in directions parallel and perpendicular to the impact axis. Stress–strain responses showed an increased yield strength (440–520 MPa) compared with the initial state (90 MPa). The strain-hardening behaviour was found to strongly depend on the orientation of the compression axis.     

Microstructure and fracture-mechanical properties of carbon derived Si3N4 + SiC nanomaterials

The microstructure and basic mechanical properties, as hardness, fracture toughness, fracture strength and subcritical crack growth at room temperature were investigated and creep behavior at high temperatures was established. The presence of SiC particles refined the microstructure of Si₃N₄ grains in the Si₃N₄ + SiC nanocomposite. Higher hardness values resulted from introducing SiC nanoparticles into the material. A lower fracture toughness of the nanocomposite is associated with its finer microstructure; crack bridging mechanisms are not so effective as in the case of monolithic Si₃N₄. The strength value of the monolithic Si₃N₄ is higher than the characteristic strength of nanocomposites. Fractographic analysis of the fracture surface revealed that a failure started principally from an internal flaw in the form of cluster of free carbon, and on large SiC grains which degraded strength of the nanocomposite. The creep resistance of nanocomposite is significantly higher when compared to the creep resistance of the monolithic material. Nanocomposite exhibited no creep deformation, creep cracks have not been detected even at a test at 1400 °C and a long loading time, therefore the creep is probably controlled mainly by diffusion. The intergranular SiC nanoparticles hinder the Si₃N₄ grain growth, interlock the neighboring Si₃N₄ grains and change the volume fraction, geometry and chemical composition of the grain boundary phase.     

High ductilities in physically vapor-deposited nickel

Two thick films of physically vapor-deposited Ni were prepared on either side of the Movchan-Demchishin T₁ transition temperature. Both deposits were fine grained and columnar, but the lower temperature deposit contained a fine dispersion of pores. During high temperature deformation, the fully dense deposit behaved erratically owing to abnormal grain growth. The porous deposit transformed to a microstructure consisting of fine equiaxed grains interspersed with voids. This transformed structure deforms by grain boundary sliding. The measured activation energy is 116 kJ mol^?1 corresponding to grain boundary self-diffusion. The creep stress exponent is found to be 3, and the grain size exponent is -1. This porous physically vapor-deposited Ni attains steady state elongations that are far superior to those of conventionally processed or larger-grained Ni.     

Microstructure and elevated temperature properties of a refractory TaNbHfZrTi alloy

Compression properties of a refractory multi-component alloy, Ta₂₀Nb₂₀Hf₂₀Zr₂₀Ti₂₀, were determined in the temperature range of 296–1473 K and strain rate range of 10⁻¹–10⁻⁵ s⁻¹. The properties were correlated with the microstructure developed during compression testing. The alloy was produced by vacuum arc melting, and it was hot isostatically pressed (HIPd) and homogenized at 1473 K for 24 h prior to testing. It had a single-phase body-centered cubic structure with the lattice parameter a = 340.4 pm. The grain size was in the range of 100–200 μm. During compression at a strain rate of έ = 10⁻³ s⁻¹, the alloy had the yield strength of 929 MPa at 296 K, 790 MPa at 673 K, 675 MPa at 873 K, 535 MPa at 1073 K, 295 MPa at 1273 K and 92 MPa at 1473 K. Continuous strain hardening and good ductility (ε ≥ 50%) were observed in the temperature range from 296 to 873 K. Deformation at T = 1073 K and έ ≥ 10⁻³ s⁻¹ was accompanied by intergranular cracking and cavitation, which was explained by insufficient dislocation and diffusion mobility to accommodate grain boundary sliding activated at this temperature. The intergranular cracking and cavitation disappeared with an increase in the deformation temperature to 1273 and 1473 K or a decrease in the strain rate to ~10⁻⁵ s⁻¹. At these high temperatures and/or low-strain rates the alloy deformed homogeneously and showed steady-state flow at a nearly constant flow stress. Partial dynamic recrystallization, leading to formation of fine equiaxed grains near grain boundaries, was observed in the specimens deformed at 1073 and 1273 K and completed dynamic recrystallization was observed at 1473 K.     

Effect of heat treatment on precipitation behaviour and high temperature strength in a wrought Co-base superalloy

The effects of solution and ageing temperatures on the grain boundary reaction as well as on matrix precipitation in the interior of the grains were investigated using wrought Co-base superalloy HS-21. The grain boundary reaction occurred during furnace-cooling after solution-heating. The phase that precipitated in the grain boundary reactions nodule was M₂₃C₆ carbide. It also occurred during ageing after solution treatment, but the extent of it was considerably influenced by cooling procedure after solution heating. The activation energy of the grain boundary reaction was 244 kJ mol^–1 for the early stage of the grain boundary reaction in HS-21 alloy, and was considered to be the activation energy of grain boundary diffusion of chromium. The extent of the matrix precipitation that occurred during ageing was also influenced by the cooling procedure. Creep rupture tests were carried out at 1088 K in air. An excellent combination of long rupture life and large ductility was attained on a specimen, which involved both the grain boundary reaction nodules (about 7% in area fraction) and the matrix precipitates. The improvement of creep rupture properties results from the retardation of brittle intergranular fracture, which is achieved by grain boundary serration owing to the grain boundary reaction and by the increase of strength in the interior of grain due to the matrix precipitation.