• Macromolecular Research
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• v.9 no.3
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• pp.164-170
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• 2001

Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for the simplified differential version of these constitutive equations. It is proved that they are globally Hadamard stable except for the case of maximum constant backbone stretch (λ = q) with arm withdrawal s$\_$c/ neglected, as long as the orientation tensor remains positive definite or the smooth strain history in the now is previously given. However this model is dissipative unstable, since the steady shear How curves exhibit non-monotonic dependence on shear rate. This type of instability corresponds to the nonlinear instability in simple shear flow under finite amplitude disturbances. Additionally in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady now curves, the constitutive equations will possibly violate the positive definiteness of the orientation tensor and thus become Hadamard unstable.

• Journal of the Microelectronics and Packaging Society
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• v.17 no.2
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• pp.21-28
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• 2010

Creep behaviors of the solder balls in a flip chip package assembly during thermal cycling test is investigated.. A material models used in the finite element analysis are viscoplastic model introduced by Anand and creep model called partitioned model. Experiment of two temperature cycles using moir$\acute{e}$ interferometry is conducted to verify the reliability of material models for the analysis of thermo-mechanical behavior. Bending deformations of the assemblies and average strains of the solder balls due to temperature change and dwell time are investigated. The results show that time-dependent shear strain of solder by the partitioned model is in excellent agreement with those by moir$\acute{e}$ interferometry, while there is considerable difference between results by Anand model and experiment. In this paper, the partitioned model is employed for the time-dependent creep analysis of the FC-PBGA package. It is also shown that the thermo-mechanical stress becomes relaxed by creep behavior at high temperature during temperature cycles.

• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.505-518
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• 2000

A major cause of premature debonding of tension face plates is shear peeling (Jones et al. 1988, Swamy et al. 1989, Ziraba et al. 1994, Zhang et al. 1995), that is debonding at the plate ends that is associated with the formation of shear diagonal cracks that are caused by the action of vertical shear forces. It is shown in this paper how side plated beams are less prone to shear peeling than tension face plated beams, as the side plate automatically increases the resistance of the reinforced concrete beam to shear peeling. Tests are used to determine the increase in the shear peeling resistance that the side plates provide, and also the effect of vertical shear forces on the pure flexural peeling strength that was determined in the companion paper. Design rules are then developed to prevent premature debonding of the plate ends due to peeling and they are applied to the strengthening and stiffening of continuous reinforced concrete beams. It is shown how these design rules for side plated beams can be adapted to allow for propped and unpropped construction and the time effects of creep and shrinkage, and how side plates can be used in conjunction with tension face plates.

• Journal of the Microelectronics and Packaging Society
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• v.17 no.3
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• pp.33-41
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• 2010

Crack propagation mechanisms of Sn-3.0Ag-0.5Cu solder were studied in strain controlled push-pull creepfatigue conditions using the fast-fast (pp) and the slow-fast (cp) strain waveforms at 313 K. Transgranular cracking was found in the pp strain waveform which led to the cycle-dominant crack propagation and intergranular cracking in the cp strain waveform that led to the time-dominant crack propagation. The time-dominant crack propagation rate was faster than the cycle-dominant crack propagation rate when compared with J-integral range which resulted from the creep damage at the crack tip in the cp strain waveform. Clear recrystallization around the crack was found in the pp and the cp strain waveforms, but the recrystallized grain size in the cp strain waveform was smaller than that in the pp strain waveform. The cycle-dominant crack propagated in the normal direction to the specimen axis macroscopically, but the time-dominant crack propagated in the shear direction which was discussed in relation with shear micro cracks formed at the crack tip.

• Steel and Composite Structures
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• v.43 no.6
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• pp.809-819
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• 2022

This paper proposes a method to predict the deflection of prestressed concrete (PC) beams with corrugated steel web (CSW) under constant load concerning time-dependent variation in concrete material. Over time, the top and bottom concrete slabs subjected to asymmetric compression experience shrinkage and creep deformations. Here, the classical Euler-Bernoulli beam theory assumption that the plane sections remain plane is not valid due to shear deformation of CSW. Therefore, this study presents a method based on the first-order shear deformation to find the long-term deflection of the composite beams under bending by considering time effects. Two experimental prestressed beams of this type were monitored under their self-weight over time, and the theoretical results were compared with those data. Additionally, 3D analytical models of the experimental beams were used according to material properties, and the results were compared with two previous cases. There was good consistency between the analytical and numerical results with low error, which increased by wave radius. It is concluded that the proposed method could reliably be used for design purposes.

• Journal of the Microelectronics and Packaging Society
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• v.12 no.1 s.34
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• pp.47-52
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• 2005

Worldwide movement for prohibition of Pb usage drives imminent implementation of Pb-free solders in microelectronic packaging industry. Reliability information of Pb-free solders has not been completely constructed yet. One of the potential reliability concerns of Pb-free solders is allotropic transformation of Sn known as tin pest. Volume increase during the formation of tin pest could deteriorate the reliability of solder joints. It was also reported that the addition of soluble elements (i.e. Pb, Bi, and Sb) into Sn can effectively suppress the tin pest. However, the mechanical properties of the tin pest resistant alloys have not been studied in detail. In this study, lap shear creep test was conducted with Sn and Sn-0.7Cu based solder alloys doped with minor amount of Bi or Sb. Shear strain rates of the alloy were generally higher than those of Sn-3.5Ag based alloys. Rupture strains and corresponding Monkman- Grant products were largest for Sn-0.5Bi alloy and smallest for Sn-0.7Cu-0.5Sb alloy. Rupture surface Sn-0.5Bi alloy showed highly elongated $\beta$-Sn globules necked to rupture by shear stresses, while elongation of $\beta$-Sn globules of Sn-0.7Cu-0.5Sb alloy was relatively smaller.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.461-473
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• 2000

This paper deals with a numerical model for the time-dependent analysis of steel and concrete composite beams with partial shear connection. A linear partial interaction theory is adopted in formulation of structural slip behavior, and the effect of concrete creep and shrinkage are considered. The proposed model is effective in simulating the slip behavior, combined with concrete creep and shrinkage, of multi-span continuous composite beams. Finally, correlation studies and several parameter studies are conducted with the objective to establish the validity of the proposed model.

• Journal of Mechanical Science and Technology
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• v.19 no.7
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• pp.1432-1440
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• 2005

High-temperature rupture behavior of 5083-Al alloy was tested for failure at 548K under multiaxial stress conditions: uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times were compared for uniaxial, biaxial, and triaxial stress conditions with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the von Mises effective and principal facet stresses give good correlation for the material investigated, and these parameters can predict creep life data under the multiaxial stress states with the rupture data obtained from specimens under the uniaxial stress. The results suggest that the creep rupture of this alloy under the testing condition is controlled by cavitation coupled with highly localized deformation process, such as grain boundary sliding. It is also conceivable that strain softening controls the highly localized deformation modes which result in cavitation damage in controlling rupture time of this alloy.

• Geomechanics and Engineering
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• v.29 no.1
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• pp.41-51
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• 2022

Tunneling in rocks having the time-dependent behavior, causes some difficulties like tunnel convergence and, as a result, pressure on concrete lining; and so instability on this structure. In this paper the time-dependent behaviour of squeezing phenomenon in a large cross section tunnel was investigated as a case study: Alborz tunnel. Then, time-dependent behaviour of Alborz tunnel was evaluated using FLAC2D based on the finite difference numerical method. A Burger-creep viscoelastic model was used in numerical analysis. Using numerical analysis, the long-time effect of squeezing on lining stability was simulated.This study is done for primary lining (for 2 years) and permanent lining (for 100 years), under squeezing situations. The response of lining is discussed base on Thrust Force-Bending Moment and Thrust Force-Shear Force diagrams analysing. The results determined the importance of consideration of time-dependent behaviour of tunnel that structural forces in concrete lining will grow in consider with time pass and after 70 years can cause instability in creepy rock masses section of tunnel. To show the importance of time-dependent behavior consideration of rocks, elastic and Mohr-Coulomb models are evaluated at the end.

• Journal of the Microelectronics and Packaging Society
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• v.10 no.3
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• pp.29-35
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• 2003

The Sn-based lead-free solders with varying microstructure were prepared by changing the cooling rate from the melt. Bulky as-cast SnAg, SnAgCu, and SnCu, alloys were cold rolled and thermally stabilized before the creep tests so that there would be very small amount of microstructural change during creep (TS), and thin specimens were water quenched from the melt (WQ) to simulate microstructures of the as-reflowed solders in flip chips. Cooling rates of the WQ specimens were 140∼150 K/sec, and the resultant $\beta-Sn$ globule size was 5∼10 times smaller than that of the TS specimens. Subsequent creep tests showed that the minimum strain rate of TS specimens was about $10_2$ times higher than that of the WQ specimens. Fractographic analyses showed that creep rupture of the TS-SnAgCu specimens occurred by the nucleation of voids on the $Ag_3Sn$ Sn or $Cu_6Sn_5$ particles in the matrix, their subsequent growth by the power-law creep, and inter-linkage of microcracks to form macrocracks which led to the fast failure. On the other hand, no creep voids were found in the WQ specimens due to the mode III shear rupture coming from the thin specimens geometry.