Plastic Deformation Kinetics of 95.5Sn4Cu0.5Ag Solder Joints

1995 ◽  
Vol 117 (2) ◽  
pp. 100-104 ◽  
Author(s):  
Z. Guo ◽  
Yi-Hsin Pao ◽  
H. Conrad
Keyword(s):  
Plastic Deformation ◽  
Shear Stress ◽  
Shear Rate ◽  
Solder Joints ◽  
Deformation Kinetics ◽  
Constant Shear ◽  
Controlling Mechanism ◽  
Deformation Equation ◽  
Kinetics Of ◽  
Constant Shear Rate

The plastic deformation kinetics of 95.5Sn4Cu0.5Ag solder joints were determined in monotonic loading shear over the temperature range of 25°–150°C using three types of tests: (a) constant shear rate, (b) constant shear stress (creep), and (c) differential tests (changes in shear rate or temperature during an otherwise isothermal constant shear rate test). The deformation kinetics were evaluated in terms of the Dorn high temperature plastic deformation equation γ˙p=A(μb/kT)D(b/d)P(τ/μ)n where γ˙p is the shear rate, μ the shear modulus, b the Burgers vector, D the appropriate diffusion coefficient, d the grain size and τ the shear stress. A, p, and n are constants whose values depend on the rate controlling mechanism. It was found that n increased with stress from ~4 at 2 MPa to ~20 at 25 MPa, relatively independent of temperature. The activation ΔH was determined to be 21.1 ± 2 kcal/mole. The constant A, however, decreased with temperature from a value of ~1018 at 25°C to ~1010 at 150°C. The values of n and ΔH suggest that dislocation glide and climb is the rate controlling mechanism and hence that p ≈ 0. It is speculated that the large decrease in A with temperature may be the result of an effect on the microstructure.

scholarly journals Aging, Rejuvenation and Thixotropy in Complex Fluids: Time-dependence of the Viscosity at Rest and under Constant Shear Rate or Shear Stress

2008 ◽  
Vol 18 (5) ◽  
pp. 53298-1-53298-13
Author(s):  
Daniel Quemada
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Volume Fraction ◽  
Complex Fluids ◽  
Transient Behaviour ◽  
Volume Fractions ◽  
Constant Shear ◽  
Constant Shear Stress ◽  
Constant Shear Rate ◽  
Viscosity Changes

Abstract Complex fluids exhibit time-dependent changes in viscosity that have been ascribed to both thixotropy and aging. However, there is no consensus for which phenomenon is the origin of which changes. A novel thixotropic model is defined that incorporates aging. Conditions under which viscosity changes are due to thixotropy and aging are unambiguously defined. Viscosity changes in a complex fluid during a period of rest after destructuring exhibit a bifurcation at a critical volume fraction ϕc2. For volume fractions less than ϕc2 the viscosity remains finite in the limit t →∞. For volume fractions above critical the viscosity grows without limit, so aging occurs at rest. At constant shear rate there is no bifurcation, whereas under constant shear stress the model predicts a new bifurcation in the viscosity at a critical stress σB, identical to the yield stress σy observed under steady conditions. The divergence of the viscosity for σ≤σB is best defined as aging. However, for σ > σB, where the viscosity remains finite, it seems preferable to use the concepts of restructuring and destructuring, rather than aging and rejuvenation. Nevertheless, when a stress σA(≤σB) is applied during aging, slower aging is predicted and discussed as true rejuvenation. Plastic behaviour is predicted under steady conditions when σ > σB. The Herschel-Bulkley model fits the flow curve for stresses close to σB, whereas the Bingham model gives a better fit for σ >> σB. Finally, the model’s predictions are shown to be consistent with experimental data from the literature for the transient behaviour of laponite gels.

Shear Flow and Large Amplitude Oscillation Shear Study of Solutions of Aggregating Micellar Casein Particles

2008 ◽  
Vol 18 (2) ◽  
pp. 23050-1-23050-7 ◽  
Author(s):  
Anne Pitkowski ◽  
Taco Nicolai ◽  
Dominique Durand
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Shear Flow ◽  
Heating Temperature ◽  
Constant Shear ◽  
Micellar Casein ◽  
Large Amplitude Oscillation ◽  
Increasing Temperature ◽  
Small Shear ◽  
Constant Shear Rate

Abstract Small micellar casein particles were formed in aqueous solutions of native casein after addition of polyphosphate. These so-called submicelles aggregated and gelled with a rate that increased with increasing temperature. The evolution of the viscosity during this process was determined at constant shear rate or shear stress. When applying a small shear stress the viscosity increased strongly until the shear rate became immeasurably slow, but when the applied shear stress exceeded a critical value (σc) the aggregates broke up and the viscosity reached a maximum. At longer times the viscosity decreased rapidly at first, followed by a very slow decrease. σc was independent of the shear rate and heating temperature, but increased strongly with increasing casein concentration. At constant shear rate the stress remained close to σc, but fluctuated irregularly. After cessation of shear flow, gels were formed rapidly. Oscillation shear measurements for σ > σc showed a strongly non-linear response at the time of maximum viscosity.

ELECTRO-MAGNETORHEOLOGICAL FLUIDS DISPERSING ZEOLITE PARTICLES CONTAINING IRON

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2405-2411 ◽  
Author(s):  
A. SHIBAYAMA ◽  
T. MIYAZAKI ◽  
K. YAMAGUCHI ◽  
K. MURAKAMI ◽  
T. FUJITA
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Shear Rate ◽  
Electric Field ◽  
Electric Fields ◽  
Fluid Viscosity ◽  
Magnetic Field Direction ◽  
Constant Shear ◽  
Stress Curve ◽  
Constant Shear Rate

Some functional fluids that respond to both magnetic and electric fields have been prepared and their characteristics are described. In this study, an electro-magnetorheological fluid (EMRF) dispersing zeolite particles containing metallic iron by reducing precipitated magnetite has been investigated. When the viscosity is measured by cone plate viscometer and cylindrical viscometer, electric and magnetic fields are applied both between cone and plate or two cylinders. In case of cone plate, the shear stress at constant shear rate increased with the increase of both magnetic field and electric field. On the other hand when the viscosity is measured by cylindrical viscometer, the shear stress at constant shear rate increased with the increase of electric field, however, the increase rate of shear stress by magnetic field is very small. In this case the magnetic field direction is perpendicular to electric field. The EMRF has typical characteristics to respond with magnetic and electric field. The shear stress of EMRF in electric field is stronger than that of magnetic field. Additionally, the inflection and peak point in the shear rate-shear stress curve are appeared and the behaviors of the clusters in the electric field are observed. The experimental results suggested that the fluid viscosity (shear stress/shear rate) is affected by the arrangement of clusters parallel or perpendicular to the direction of the EMRF flow.

scholarly journals Mechanical Properties of Paste Slurry under Constant Shear Rate in Initial Structure Failure Process

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Chaoqun Dai ◽  
Aixiang Wu ◽  
Yan Qi ◽  
Zhiqiang Chen ◽  
Bin Li
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Initial Stress ◽  
Mass Concentration ◽  
Model Equation ◽  
Failure Process ◽  
Initial Structure ◽  
Structural Failure ◽  
Constant Shear ◽  
Constant Shear Rate

At constant shear rate, the process of deformation of the paste slurry is divided into two stages: one is the initial structural failure process with increasing shear stress; the other is the thixotropic process with decreasing shear stress after yielding. Based on experiments, the mechanical response characteristics of the paste slurry in the initial structural failure process under different shear rate conditions were studied in this paper. At the same time, according to the Maxwell model, the stress-time model equation describing the initial structure failure stage of the paste was deduced and the constant shearing test was carried out on the paste slurry at different mass concentrations; the model equation was used to fit the test data of the initial stress increment stage. The results showed that the model equation had higher prediction accuracy and better popularity. In the initial structural failure stage, the paste had a nonlinear stress-time relationship. At different shear rates (0.05, 0.5, and 1 s−1), the lower the rotation speed, the smoother the curve, and the slurry at various stages in the yielding process could be more clearly reflected; in the range of low constant shear rate (0.03, 0.05, and 0.07 s−1), the initial stress and yield stress of the paste increased with the increase of shear rate at the same mass concentration, and the time to yield was shorter. The yield stress increased exponentially with mass concentration.

scholarly journals Computer aided optimisation of a constant shear-rate micro-channel contraction

2009 ◽  
Vol 50 ◽  
pp. 1004
Author(s):  
Simon Higgins ◽  
Gregory J Sheard ◽  
Andreas Fouras ◽  
Kerry Hourigan
Keyword(s):  
Shear Rate ◽  
Micro Channel ◽  
Constant Shear ◽  
Computer Aided ◽  
Constant Shear Rate

ELECTRORHEOLOGY OF DISPERSIONS OF BaxSr(1-x)TiO3 IN SILICONE OIL UNDER AC OR DC ELECTRIC FIELD

2012 ◽  
Vol 26 (14) ◽  
pp. 1250081 ◽  
Author(s):  
GLAUBER M. S. LUZ ◽  
ANTONIO J. F. BOMBARD ◽  
SILVIO L. M. BRITO ◽  
DOUGLAS GOUVÊA ◽  
SHEILA L. VIEIRA
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Electric Field ◽  
Silicone Oil ◽  
Ferroelectric Materials ◽  
Dc Electric Field ◽  
Ac Fields ◽  
Er Fluid ◽  
Constant Shear Rate

Electrorheology (ER) of ferroelectric materials such as nanometric BaTiO 3 is still not fully understood. In this paper, nanoparticles of Ba x Sr (1-x) TiO 3 (where x = 0.8, 0.9 or 1.0) were synthesized using the method of Pechini, calcinated at 950°C, and after, lixiviated under pH 1 or pH 5. A controlled stress rheometer (MCR-301) was used to make the ER characterization of dispersions made of Ba x Ti 1-x O 3 in silicone oil (30% w/w), where (a) shear stress as a function of DC electric field (under constant shear rate) or (b) shear stress as a function of shear rate (under constant AC or DC electric field) were measured. We observed that electrophoresis occurred under electric field DC, creating a concentration gradient which induced phase separation in ER fluid. On the other hand, under AC fields above 1 kV/mm, the ER effect is stronger than for DC field, and almost without electrophoresis. Furthermore, there is an AC frequency, dependent on the disperse phase, where the ER effect has a maximum.

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