Identification and doing without it, V: A formal mathematical analysis for a case of mix-up of individuals, and of recovery from failure to attain identification

Identification, when sought, is not necessarily obtained. Operational guidance that is normatively acceptable may be necessary for such cases. We proceed to formalize and illustrate modes of exchanges of individual identity, and provide procedures of recovery strategies in specific prescriptions from an ancient body of law for such situations when, for given types of purposes, individuals of some relevant kind had become intermixed and were undistinguishable. Rules were devised, in a variety of domains, for coping with situations that occur if and when the goal of identification was frustrated. We propose or discuss mathematical representations of such recovery procedures.

Thixotropic studies of lead-based solder, lead-free solder and conductive adhesive pastes

The stencil printing process is an important process in the assembly of Surface Mount Technology (SMT)devices. There is a wide agreement in the industry that the paste printing process accounts for the majority of assembly defects. Experience with this process has shown that typically over 60% of all soldering defects are due to problems associated with the flow properties of solder pastes. Therefore, the rheological measurements can be used as a tool to study the deformation or flow experienced by the pastes during the stencil printing process. This paper presents results on the thixotropic behaviour of three pastes; lead-based solder paste, lead-free solder paste and isotropic conductive adhesive (ICA). These materials are widely used as interconnect medium in the electronics industry. Solder paste are metal alloys suspended in a flux medium while the ICAs consist of silver flakes dispersed in an epoxy resin. The thixotropy behaviour was investigated through two rheological test; (i) hysteresis loop test and (ii) steady shear rate test. In the hysteresis loop test, the shear rate were increased from 0.001 to 100s-1 and then decreased from 100 to 0.001s-1. Meanwhile, in the steady shear rate test, the materials were subjected to a constant shear rate of 0.100, 100 and 0.001s-1 for a period of 240 seconds. All the pastes showed a high degree of shear thinning behaviour with time. This might be due to the agglomeration of particles in the flux or epoxy resin that prohibits pastes flow under low shear rate. The action of high shear rate would break the agglomerates into smaller pieces which facilitates the flow of pastes, thus viscosity is reduced at high shear rate. The solder pastes exhibited a higher degree of structural breakdown compared to the ICAs. The area between the up curve and down curve in the hysteresis curve is an indication of the thixotropic behavior of the pastes. Among the three pastes, lead-free solder paste showed the largest area between the down curve and up curve, which indicating a larger structural breakdown in the pastes, followed by lead-based solder paste and ICA. In a steady shear rate test, viscosity of ICA showed the best recovery with the steeper curve to its original viscosity after the removal of shear, which indicating that the dispersion quality in ICA is good because the high shear has little effect on the microstructure of ICA. In contrast, lead-based paste showed the poorest recovery which means this paste undergo larger structural breakdown and dispersion quality in this paste is poor because the microstructure of the paste is easily disrupted by high shear. The structural breakdown during the application of shear and the recovery after removal of shear is an important characteristic in the paste printing process. If the paste’s viscosity can drop low enough, it may contribute to the aperture filling and quick recovery may prevent slumping.

Numerical and experimental studies of a substructural identification strategy

For structural health monitoring it is impractical to identify a large structure with complete measurement due to limited number of sensors and difficulty in field instrumentation. Furthermore, it is not desirable to identify a large number of unknown parameters in a full system because of numerical difficulty in convergence. A novel substructural strategy was presented for identification of stiffness matrices and damage assessment with incomplete measurement. The substructural approach was employed to identify large systems in a divide-and-conquer manner. In addition, the concept of model condensation was invoked to avoid the need for complete measurement, and the recovery process to obtain the full set of parameters was formulated. The efficiency of the proposed method is demonstrated numerically through multi-storey shear buildings subjected to random force. A fairly large structural system with 50 DOFs was identified with good results, taking into consideration the effects of noisy signals and the limited number of sensors. Two variations of the method were applied, depending on whether the sensor could be repositioned. The proposed strategy was further substantiated experimentally using an eight-storey steel plane frame model subjected to shaker and impulse hammer excitations. Both numerical and experimental results have shown that the proposed substructural strategy gave reasonably accurate identification in terms of locating and quantifying structural damage.

Influence of solder paste components on rheological behaviour

Rheological properties of solder pastes are very important for a high quality surface mount technology process. The stencil/screen printing process of solder pastes is one of the most critical steps in the SMT assembly process, as most of the assembly defects can often be shown to originate from paste rheology and associated poor printing performance. This paper concerns an investigation of the effect of solder paste composition on the rheological properties and behaviour of four different solder pastes. We report on the evaluation of three different paste formulations based on the no-clean flux composition, with different alloy composition, metal content and particle size using a range of rheological characterisation techniques - including viscosity measurements, yield stress, oscillatory and creep-recovery tests. Our results show that in the viscosity test, all solder pastes exhibited a shear thinning behaviour in nature with different highest maximum viscosity. In the region of shear thinning behaviour the paste 3 delivered the best results. Viscosity test helps to understand the solid and cohesive behaviour of solder pastes. Good solid and cohesive behaviour indicates a good paste roll and helps to avoid paste bleeding. The yield stress test has been used to study the effect of temperature on the flow behaviour of solder pastes. Yield stress was measured for a range of temperature from 15deg C to 35deg C with an increment of 5degC. The result indicated a decreasing of the yield stress point if the temperature was increased. Paste 4 has shown the minimum dependence on temperature. The oscillatory test has been used to find out the linear visco-elastic range and to study the solid and liquid like behaviours of solder pastes. Paste 1 indicated the biggest linear visco-elastic region (LVR) and the highest value of G' and G" which means solder paste 1 will be needed a higher squeegee pressure in the printing process. In the creep recovery test paste 4 showed the best- - recovery and the lowest values of creep and recovery compliance which indicated a good printing behaviour. The test also has showed the solder paste with smaller particle size exhibit less recovery