We show that a single degree of freedom system with a rigid cubic characteristic of the restoring force (known in the physical literature on nonlinear vibrations as “Duffing oscillator”) is a suitable analytical (“mathematical”) model that can be used, when appreciable reactive in-plane (“membrane”) forces occur, to evaluate the dynamic response of a printed circuit board (PCB) subjected to a drop or a shock impact. When modeling such a response either of the PCB itself, or of a surface mounted device (SMD) package, including ball-grid-array (BGA) or pad-grid-array (PGA) structure, on a board level, there is an obvious incentive in trying to simplify the modeling by substituting an impact load of finite duration with an instantaneous impulse. On the other hand, when there is an intent to replace drop tests with shock tests, one has to properly “tune” the shock tester, so that to adequately mimic the drop test conditions. In this analysis we obtain exact solutions to the Duffing equation for the cases of an instantaneous impulse and for a suddenly applied and suddenly removed constant loading. We use these solutions to determine the error (in terms of the predicted amplitudes and accelerations) from substituting an impact load of finite duration with an instantaneous impulse. We consider an elongated PCB, which is currently employed in the Nokia accelerated test vehicle (experimental setup). The PCB’s short edges are simply supported, while its long edges are support-free. The in-plane reactive forces arise because the PCB’s short edges (supports) cannot get closer during its impact induced vibrations. We have determined, based on the obtained model, that the nonlinear system in question is, in general, less sensitive to the duration of the applied load than a linear system, and that this sensitivity decreases with an increase in the degree of the nonlinearity. Since the nonlinear frequency is strongly dependent on the magnitude of the applied load, we suggest that the nonlinear analysis be carried out prior to the assessment of the possible error in a modeling or a testing effort.

View full abstract

The objective of the present paper is to propose a method for detecting inside corrosions at actual finned tubes in air-cooled heat exchanger by applying an Electro-Magnetic Acoustic Transducer(EMAT),where axial shear resonance waves using electromagnetic acoustic resonance (EMAR) in EMAT can detect the corrosions. The accuracy for measuring the corrosions in the finned tubes with the nominal diameter of 1 inche in which artificial flaws have been fabricated is investigated. Furthermore, the measurements in site are carried out and comparison is made between the measured results and the actual situations. As the result, (1) It is shown that an artificial flaw (slit 2mm in width, 10mm in length, 0.7mm in depth) is able to be detected clearly at the finned tubes. (2)It is shown that the artificial flaws can be detected even though the filling rate of the probe of EMAT is around 87%. (3) From the measurement results, it is found that corroded parts which is located far from the EMAT can be detected and the location of the flaw also be detected. It is can be conclude that the present method is an outstanding inspection method for detecting inside corrosions at actual finned tubes.

View full abstract

This paper studies the creep-fatigue crack growth in Sn-3.0Ag-0.5Cu lead-free solder. Strain controlled push-pull low cycle crack growth tests were performed using fast-fast (pp), fast-slow (pc), slow-fast (cp), and slow-slow (cc) strain waveforms at 313K. The fastest crack growth rate was found in the pc waveform, followed by the cp, cc and pp waveforms. Crack growth rates in the pp waveform were well correlated with the cyclic J-integral range and fatigue J-integral range and those in the pc, cp and cc waveforms with the creep J-integral range. No creep-fatigue interaction was found in the correlation of the crack growth rate with the J-integral ranges. The crack grew perpendicular to the specimen axis in the pp waveform. In the cases of the pc, cp and cc waveforms, the crack grew in the perpendicular direction to the specimen axis initially and branched in the direction about 45 degrees to the specimen axis.

View full abstract

An analytical model for describing the mechanical behavior of a bolted joint subjected to a transverse load has been theoretically formulated. This paper focuses on the load-displacement relation. The transverse displacement is separated into five factors: (a) bolt bending due to a transverse force acting on the thread surface, (b) bolt bending due to the thread-surface reaction moment, (c) inclination of the bolt head, (d) thread surface slip, and (e) bearing surface slip. Contact force and slip displacement are newly modeled in order to describe (d) and (e). Contact surfaces are discretized into meshes. The contact force acting on each mesh is formulated by taking into account the helical profile of the thread. The slip criterion is judged according to the Coulomb friction law. In order to maintain a mechanical equilibrium, the contact force and contact state are calculated in a self-consistent manner. As for the interaction between the thread and bearing surfaces, torque induced on the thread surface is transmitted to the bearing surface in a model of bolt torsion, relevant to the loosening rotation. The mechanism by which the reaction moment, which affects (b) to (e), is induced on the thread and bearing surfaces is also investigated. We found that the inclination of the bolt affects the reaction moment during localized thread-surface slip, while the transverse displacement of the bolt affects that during the complete thread-surface slip. The reaction moment is formulated to be proportional to the stiffness of the thread and bearing surfaces. Finally, our analytical model is applied to an M16 bolted joint and confirmed that our model agree well with the FEM result.

View full abstract

Cavitation erosion is one of the major problems to be solved in hydraulic machinery. Propellers of high speed boats require a light weight metallic material for their improved high performance. This example tells us that solutions are the developments of way for the improvement of cavitation erosion resistance of light weight metallic material. Coatings on aluminum alloy can enhance the cavitation erosion resistance. This study discussed the cavitation erosion behavior of 6061 aluminum alloy coated with TiAlN thin film. TiAlN coatings were deposited by DC magnetron sputtering method at various nitrogen partial pressures of the coating process using Ti based alloy cathode. The composition of target material was 90wt%Ti, 6wt%Al and 4wt%V. Using the TiAlN coated 6061 aluminum alloy specimen, cavitation erosion tests were carried out to investigate its resistance to the ultrasonic cavitation erosion. Prior to and after the tests, the specimen surfaces were analyzed by using the surface analysis techniques such as micro-hardness test, AFM, SEM, GXRD and scratch test to measure the microstructure of thin film and bonding properties of the applied TiAlN coatings to the substrate material. An improvement in cavitation erosion resistance could be seen with TiAlN coating on 6061 aluminum alloy. Especially, the coating at a nitrogen flow rate of 0.85 sccm or more were very effective in reducing the surface cavitation erosion from the ultrasonic cavitation. In the observation of surface damages during the cavitation erosion tests, the surface cracks in TiAlN were created by the bending of TiAlN coating which were resulted from the plastic deformation of the soft substrate material of aluminum alloy. Once the cracks initiate, drastic delaminations of TiAlN from the substrate material occured. The mean depth erosion rate (MDER) could be evaluated by critical and delamination loads measured by scratch test.

View full abstract