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The purpose of this paper is to investigate the thermoelastic interactions in a homogeneous, transversely isotropic infinite medium with a spherical cavity in the context of two temperature Lord-Shulman (2TLS) generalized theory of thermoelasticity considering Eringen’s nonlocal theory and memory dependent derivative (MDD). Memory-dependent derivative is found to be better than fractional calculus for reflecting the memory effect which leads us to the current investigation.

The governing field equations of the problem are solved analytically using the eigenvalue approach in the transformed domain of Laplace when the cavity’s boundary is being loaded thermomechanically. Using MATLAB software the numerical solution in real space-time domain is obtained by Stehfest method.

Numerical results for the different thermophysical quantities are presented in graphs and the effects of delay time parameter, non-local parameter and two temperature parameters are studied thereafter. The outcomes of this study convince that the displacement u, conductive temperature ϕ, thermodynamic temperature θ are concave upward whereas radial stress τ_rr is concave downward for every choice of delay time parameter ω, two temperature parameter η and non-local parameter “ζ”. As a specific instance of our findings, the conclusions of an equivalent problem involving integer order thermoelasticity theory can be obtained, and the corresponding results of this article can be readily inferred for isotropic materials.

The novelty of this research lies in the adoption of generalized thermoelastic theory with memory dependent derivative and Eringen’s nonlocality for analyzing the thermoelastic interactions in an infinite body with spherical cavity by employing eigenvalue approach. It has applications to many thermo-dynamical systems.

The aim of this paper is to characterize the rheological properties of the flux media exposed to different levels of solicitation and to determine its influence on the rheology of the solder paste. The data obtained experimentally are fundamental for the development of numerical models that allow the simulation of the printing process of printed circuit boards (PCB).

Rheological tests were performed using the Malvern rheometer Bohlin CVO. These experiments consist of the analysis of the viscosity, yield stress, thixotropy, elastic and viscous properties through oscillatory tests and the capacity to recover using a creep-recovery experiment. The results obtained from this rheological analysis are compared with the rheological properties of the solder paste F620.

The results have shown that the flux is viscoelastic in nature and shear thinning. The viscosity does not decrease with increasing solicitations, except in the case where the flow is withdrawn directly from the bottle. Even if the solder paste shows a thixotropic behavior, this is not the case of the flux, meaning that this property is given by the metal particles. Furthermore, the oscillatory tests proved that the flux presents a dominant solid-like behavior, higher than the solder paste, meaning that the cohesive/tacky behavior of the solder paste is given by the flux.

To complement this work, printing tests are required.

This work demonstrates the importance of the rheological characterization of the flux in order to understand its influence in the solder paste performance during the stencil printing process.

The purpose of this paper is to study the rheological behaviours of lead‐free solder pastes used for flip‐chip assembly applications and to correlate rheological behaviours with the printing performance.

A range of rheological characterization techniques including viscosity, yield stress, oscillatory and creep‐recovery tests were carried out to investigate the rheological properties and behaviours of four different solder paste formulations based on no‐clean flux composition, with different alloy composition, metal content and particle size. A series of printing tests were also conducted to correlate printing performance.

The results show that in the viscosity test, all solder pastes exhibited a shear thinning behaviour in nature with different highest maximum viscosity. The yield stress test has been used to study the effect of temperature on the flow behaviour of solder pastes. A decrease in yield stress value with temperature was observed. The results from the oscillatory test were used to study the solid‐ and liquid‐like behaviours of solder pastes. Creep‐recovery testing showed that the solder paste with smaller particle size exhibited less recovery.

More extensive research is needed to simulate the paste‐roll, aperture‐filling and aperture‐emptying stages of the stencil printing process using rheological test methods.

Implementation of these rheological characterization procedures in product development, process optimization and quality control can contribute significantly to reducing defects in the assembly of flip‐chip devices and subsequently increasing the production yield.

The paper shows how the viscosity, yield stress, oscillatory and creep‐recovery test methods can be successfully used to characterize the flow behaviour of solder pastes and also to predict their performance during the stencil printing process.

A measurement method has been developed to reveal the viscosity change of solder pastes during stencil printing. This paper aimed to investigate thixotropic behaviour, the viscosity change of a lead-free solder paste (Type 4).

The viscosity change of the solder paste during stencil printing cycles was characterised in such a way that the time-gap between the printing cycles was modelled with a rest period between every rheological measurement. This period was set as 15, 30 and 60 s during the research. The Cross model was fitted to the measurement results, and the η₀ parameter was used to characterise the viscosity change. The number of printing cycles necessary for reaching a stationary state in viscosity was determined for various rest periods.

It was found that the decrease in zero-shear viscosity is significant (25 per cent) in the first cycles, and it starts to become stationary at the sixth-seventh cycles. This means a printing process can provide the appropriate deposits only after the 7th cycle with the investigated Type 4 solder paste.

Time-dependent rheological behaviour of solder pastes was studied in the literature, but only the viscosity change over continuous time at constant shear rates was examined. The time-gap between stencil printing cycles was not considered, and thixotropic behaviour of solder pastes was also neglected. Therefore, the authors developed a measurement set which is able to model the effect of time-gap between printing cycles on the viscosity change of solder pastes.

The purpose of this paper is to investigate how the formulation of a solder paste (with regards to the flux and particle size distribution (PSD)), can influence its creep and recovery performance.

New lead‐free paste formulations were characterised utilising viscometry and oscillatory methods, after which creep/recovery investigations were conducted to determine the recovery performance. Measurements were recorded using a rheometer with a parallel plate geometry of 40 mm and a sample height of 1 mm.

Results from the study highlighted that the formulation of a solder paste can have a significant impact on the creep/recovery measurements. Variations in flux and PSD highlighted a considerable difference in the recoverability of the solder pastes, in one instance demonstrating more than a 20 per cent increase in structural recovery.

More extensive research is needed relating to reduced PSDs, such as type 6 and 7 solder pastes, to fully understand their influence on the creep/recovery performance.

The results presented in this paper emphasise important information and investigational methods for research and development, and quality control.

The paper highlights how the composition of new paste formulations can influence the creep/recovery behaviour. It was found that the recoverability can be increased by careful selection of the flux and PSD, which in turn could reduce slumping influences in the print process. If used as a quality control tool, this paper may allow for the reduction in print defect occurrence.

The purpose of this paper is to suggest an analysis methodology for the stencil printing process and to obtain proper design parameters that guarantee the successful filling using suggested finite element analyses.

Filling performance of solder paste in the stencil printing process is highly dependent on material properties such as viscosity and surface tension together with process parameters such as squeegee angle and squeegee speed. In order to investigate the effects of process parameters on the filling performance, the pressure built‐up under the squeegee and the filling procedure of the solder paste into an aperture were analysed. Due to the limitations of the computational memory and time, the analysis domain was simplified. The pressure development under the squeegee was investigated for various values of squeegee angle and speed; then, the filling behaviour with the pressure boundary condition was analysed for only one aperture. Finally, the two analysis results were integrated to obtain the successful filling condition. In this analysis method, process parameters that guarantee filling performance were decided on.

It was shown that higher squeezing pressure develops as the squeegee angle decreases and the squeegee speed increases. The filling performance, however, improves as the squeegee angle and the squeegee speed decrease. This is because the pressure duration time decreases as the squeegee speed increases.

This study suggests a new design approach to obtain proper process design parameters for successful filling of solder paste into an aperture. The direct analysis of filling with squeegee movement is impossible due to limitations of computer memory and computation time. To overcome these limitations, a two steps analysis approach is proposed and can be effectively applied in the design of stencil screen printing.

In recent years, use of sensorless control methods for electrical motor-based variable speed drive systems has been increasing rapidly to compensate the increasing costs in industrial systems. Also, use of induction motors is popular for a long time to decrease the cost of these industrial systems. This study aims to design an effective controller to improve the sensorless speed control performance of induction motor. To achieve this, a conformable fractional order proportional integral (CFOPI) controller is designed.

The system is modeled based on small signal analysis by using the input–output data, experimentally. To do this, system identification toolbox of Matlab is used. The proposed controller is established on conformable fractional integral approach proposed by Khalil et al. (2014). CFOPI controller coefficients are optimized using particle swarm optimization method on the created small signal-based simulation model of the system to minimize the integral time absolute error. To prove the success of the proposed method, a traditional fractional order proportional integral (TFOPI) controller is tested under the same experimental system with the CFOPI controller.

TFOPI and CFOPI controllers are tested with the optimum parameters. Reference and actual speed trends are obtained for both methods. In induction motor start-up test, settling-times are measured as 8.73 and 8.44 s and steady-state oscillations are 2.66% and 0% (almost) for TFOPI and CFOPI controllers, respectively. In variable referenced speed tracking test, CFOPI performs well at all speed levels, while TFOPI fails to reach the reference speed at most speed levels.

Proposed CFOPI control method can be easily implemented in industrial systems, thanks to its simple algorithm. digital signal peripheral interface controller (dsPIC) based driver circuit with designed CFOPI controller used in this study can be applied directly to industrial systems such as elevators, conveyors, cranes and drills. Moreover, it can improve the performance of induction motor-based variable speed drive systems.

The proposed method provides robust performance for induction motor used in control systems. Additionally, it does this by using less complex algorithm written on the processors according to the traditional fractional order controllers.

There are several lead-free solder alloys available in the industry. Over the years, the most favorable solder composition of tin-silver-copper (Sn-Ag-Cu [SAC]) has been vastly used and accepted for joining the electronic components. It is strongly believed that the silver (Ag) content has a significant impact on the solder mechanical behavior and thus solder thermal reliability performance. This paper aims to assess the mechanical response, i.e. creep response, of the SAC solder alloys with various Ag contents.

A three-dimensional nonlinear finite element simulation is used to investigate the thermal cyclic behavior of several SAC solder alloys with various silver percentages, including 1%, 2%, 3% and 4%. The mechanical properties of the unleaded interconnects with various Ag amounts are collected from reliable literature resources and used in the analysis accordingly. Furthermore, the solder creep behavior is examined using the two famous creep laws, namely, Garofalo’s and Anand’s models.

The nonlinear computational analysis results showed that the silver content has a great influence on the solder behavior as well as on thermal fatigue life expectancy. Specifically, solders with relatively high Ag content are expected to have lower plastic deformations and strains and thus better fatigue performance due to their higher strengths and failure resistance characteristics. However, such solders would have contrary fatigue performance in drop and shock environments and the low-Ag content solders are presumed to perform significantly better because of their higher ductility.

Generally, this research recommends the use of SAC solder interconnects of high silver contents, e.g. 3% and 4%, for designing electronic assemblies continuously exposed to thermal loadings and solders with relatively low Ag-content, i.e. 1% and 2%, for electronic packages under impact and shock loadings.

The purpose of this paper is to present the establishment of a computational fluid dynamics model for investigating different non-Newtonian rheological models of solder pastes by simulating solder paste viscosity measurement. A combined material model was established which can follow the measured, apparent viscosity values with lower error.

The model included a parallel plate arrangement of rheometers. The diameter of the plate was 50 mm, whereas the gap between the plates was 0.5 mm. Only one quarter of the plate was modelled to enable using fine enough mesh, while keeping the calculation time low. Non-Newtonian properties were set using user defined function in Ansys, based on the Cross and Carreau–Yasuda material models. The viscosity values predicted by the mathematical models were compared to measured viscosity values of different types of solder pastes.

It was found that the Cross model predicts the apparent viscosity with a relatively high error (even approximately 50 per cent) at lower shear rates, whereas the Carerau–Yasuda model has higher errors at higher shear rates. The application of the proposed, combined model can result in a much lower error in the apparent viscosity between the calculated and measured viscosity values.

The error of Cross and Carreau–Yasuda material models has not been investigated yet in details. The proposed, combined material model can be applied for subsequent simulations via the described UDF, e.g. in the numerical modelling of the stencil printing. This can result in a more accurate modelling of the stencil printing process, which is inevitable considering the printing of solder paste for today fine-pitch, small size components.

Many e-commerce firms suffer from high returns because of inaccurate and incomplete product information. Omnichannel and bundling settings can help firms improve operational efficiency and lower returns costs. However, no studies have been conducted on omnichannel supply chains considering bundling strategies. The purpose of this study is to examine the comparison between test-in-store-and-buy-online (TSBO) and online retail, comparing manufacturers’ bundling with retailers’ bundling.

The supply chain discussed here consists of two competitive manufacturers and one retailer. The retailer sells both manufacturers' products online and displays one manufacturer's product in a showroom who bears the display cost. Stackelberg game theory is used to develop mathematical models that help manufacturers and retailers make the most effective decisions. Here, the manufacturer is the Stackelberg leader, while the retailer is the follower. Using the backward induction approach, the authors determined the optimal values for selling price, wholesale price and service effort level.

The results show that the total TSBO retailing profit under manufacturer bundling is highest when the second manufacturer integrates with the online retailer. The result additionally establishes that when the bundling cost exceeds a certain threshold (1.5), the total profit is higher for the non-integrated type of supply chain channel as compared to the integrated retailer bundling-based configuration.

The operations and logistics manager will likely undertake the TSBO omnichannel strategy during manufacturers bundling and retailer bundling under the integrated strategy.

The main contribution of the study is to examine the effect of TSBO retailing on supply chains profit and individual decision-making under different bundling strategies. The authors developed different mathematical models in the TSBO retailing and bundling context and extended the earlier work in the area of integration frame.