• Journal of Powder Materials
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• v.4 no.2
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• pp.83-89
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• 1997

A finite element analysis to solve the coupled thermomechanical problem in the plane strain upsetting of the porous metals was performed. The analysis was formulated using the yield function advanced by Lee and kim and developed using the thermo-elasto-plastic time integration procedure. The density and temperature dependent thermal and mechanical properties of porous metals were considered. The internal heat generation by the plastic deformation and the changing thermal boundary conditions corresponding to the geometry were incorporated in the program. The distributions of the stress, strain, pressure, density and temperature were predicted during the free resting period, deformation period and dwelling period of the forging process.

• Structural Engineering and Mechanics
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• v.73 no.4
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• pp.407-426
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• 2020

In this present paper, a semi-analytical mesh-free method is employed for the three-dimensional free vibration analysis of a bi-directional functionally graded piezoelectric circular structure. The dependent variables have been expanded by Fourier series with respect to the circumferential direction and have been discretized through radial and axial directions based on the mesh-free shape function. The current approach has a distinct advantage. The nonlinear Green-Lagrange strain is employed as the relationship between strain and displacement fields to observe thermal impacts in stiffness matrices. Nevertheless, high order terms have been neglected at the final steps of equations driving. The material properties are assumed to vary continuously in both radial and axial directions simultaneously in accordance with a power law distribution. The convergence and validation studies are conducted by comparing our proposed solution with available published results to investigate the accuracy and efficiency of our approach. After the validation study, a parametric study is undertaken to investigate the temperature effects, different types of polarization, mechanical and electric boundary conditions and geometry parameters of structures on the natural frequencies of functionally graded piezoelectric circular structures.

• Computers and Concrete
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• v.1 no.2
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• pp.189-209
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• 2004

Several extensions to the Thelandersson phenomenological model for concrete under transient high temperatures are explored. These include novel expressions for the temperature degradation of the elastic modulus and the temperature dependency of the coefficient of the free thermal strain. Furthermore, a coefficient of thermo mechanical strain is proposed as a bi-linear function of temperature. Good qualitative agreement with various test results taken from the literature is demonstrated. Further extensions include the effects of plastic straining and temperature dependent Poisson's ratio. The models performance is illustrated on several simple benchmark problems under uniaxial and biaxial stress states.

• Journal of Welding and Joining
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• v.19 no.4
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• pp.406-412
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• 2001

This study is focussed on the numerical prediction of the thermal fatigue life of a ${\mu}BGA$(Micro Ball Grid Array) solder joint. Numerical method is used to perform three-dimensional finite element analysis for Sn-37mass%Pb. Sn-3.5mass%Ag solder alloys during the given thermal cycling. Strain values, along with the result of mechanical fatigue tests for solder alloys were then used to predict the solder joint fatigue life using the Coffin-Manson equation. In this study, a practical correlation for the prediction of the thermal fatigue life is suggested by using the dimensionless variable $\gamma$. As a result. it could be found that Sn-3.5mass%Ag has longer fatigue life than Sn-37mass%Pb in low cycle fatigue. In addition. the result with ${\gamm}ashow$a good agreement with the FEA results.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.5
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• pp.134-139
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• 2007

This paper presents a computer-based analysis on the thermal shock characteristics of Pb-free solder joints and UBM in flip chip assemblies. Among four types of popular UBM systems, TiW/Cu system with 95.5Sn-3.9Ag-0.6Cu solder joints was chosen for simulation. A simple 3D finite element model was first created only including silicon die, mixture between underfill and solder joints, and substrate. The displacements due to CTE mismatch between silicon die and substrate was then obtained through FE analysis. Finally, the obtained displacements were applied as mechanical loads to the whole 2D FE model and the characteristics of flip chip assemblies were analyzed. In addition, based on the hyperbolic sine law, the accumulated creep strain of Pb-free solder joints was calculated to predict the fatigue life of flip chip assemblies under thermal shock environments. The proposed method for fatigue life prediction will be evaluated through the cross check of the test results in the future work.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.6
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• pp.117-125
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• 1998

The paper attempts to estimate the incubation time of a cavity in the interface between a power law creep particle and an elastic matrix subjected to a uniaxial stress. Since the power law creep particle is time dependent, the stresses in the interface relax. The volume free energy associated with Helmholtz free energy includes strain energies caused by applied stress and dislocations piled up in interface(DPI). The energy due to DPI is found by modifying the result of Dundurs and Mura[4]. The volume free energies caused by both applied stress and DPI are a function of the cavity size(r) and elapsed time(t) and arise from stress relaxation in the interface. Critical radius $r^*$ and incubation time $t^*$ to maximise Helmholtz free energy is found in present analysis. Also, kinetics of cavity formation are investigated using the results obtained by Riede [7]. The incubation time is defined in the analysis as the time required to satisfy both the thermodynamic and kinetic conditions. Through the analysis it is found that 1) strain energy caused by the applied stress does not contribute significantly to the thermodynamic and kinetic conditions of a cavity formation, 2) in order to satisfy both thermodynamic and kinetic conditions, critical radius $r^*$ decreases or holds constant with increase of the time until the kinetic condition(eq. 2.3) is satisfied. there for the cavity may not grow right after it is formed, as postulated by Harris [15], and Ishida and Mclean [16], 3) the effects of strain rate exponent (m), material constant $\sigma$0, volume fraction of the particle to matrix(f)and particle size on the incubation time are estimated using material constants of the copper as matrix.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.1856-1863
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• 2004

In the last 50 years, lead-contained solder materials have been the most popular interconnect materials used in the electronics industry. Recently, lead-free solders are about to replace lead-contained solders for preventing environmental pollutions. However, the reliability of lead-free solders is not yet satisfactory. Several researchers reported that lead-contained solders have a good fatigue property. The others published that the lead-free solders have a longer thermal fatigue life. In this paper, the reason for the contradictory results published on the estimation of fatigue life of lead-free solder is investigated. In the present study, fatigue behavior of 63Sn37Pb, and two types of lead-free solder joints were compared using pseudo-power cycling testing method, which provides more realistic load cycling than chamber cycling method does. Pseudo-power cycling test was performed in various temperature ranges to evaluating the shear strain effect. A nonlinear finite element model was used to simulate the thermally induced visco-plastic deformation of solder ball joint in BGA packages. It was found that lead-free solder joints have a good fatigue property in the small temperature range condition. That condition induce small strain amplitude. However in the large temperature range condition, lead-contained solder joints have a longer fatigue life.

• Journal of the Korean Society of Safety
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• v.30 no.6
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• pp.7-11
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• 2015

The present study investigates the impact shear strength of thermal aged Sn-3Ag-0.5Cu lead-free solder joints at impact speeds ranging from 0.5 m/s to 2.5 m/s. The specimens were thermal aged for 24, 100, 250 and 1000 hours at $100^{\circ}C$. The experimental results demonstrate that the shear strength of the solder joint decreases with an increase in the load speed and aging time. The shear strength of the solder joint aged averagely decreased by 43% with an increase in the strain rate. For the as-reflowed specimens, the mode II stress intensity factor ($K_{II}$) of interfacial IMC between Sn-3.0Ag-0.5Cu and a copper substrate also was found to decrease from $1.63MPa.m^{0.5}$ to $0.97MPa.m^{0.5}$ in the speed range tested here. The degradations in the shear strength and fracture toughness of the aged solder joints are mainly caused by the growth of IMC layers at the solder/substrate interface.

• Korean Journal of Metals and Materials
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• v.47 no.8
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• pp.500-507
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• 2009

Pb-free solder has recently been used in electronics in efforts to meet environmental regulations, and a number of Pb-free solder alloy choices beyond the near-eutectic SnAgCu solder are now available. With increased demand for thin and portable electronics, the high cost of alloys containing significant amounts of silver and their poor mechanical shock performance have spurred the development of low Ag SnAgCu solder, which provides improved mechanical performance at a reasonable cost. Although low Ag SnAgCu solder exhibits significantly higher fracture resistance under high-strain rates, little thermal fatigue data exist for this solder. Therefore, it is necessary to investigate thermal fatigue reliability of low Ag SnAgCu solder under variation of thermal stress in order to allow its implementation in electronic products with high reliability requirements. In this study, the reliability of Sn0.3Ag0.7Cu(SAC0307), a low Ag solder alloy, is discussed and compared with that of Sn3Ag0.5Cu(SAC305). Three sample types and six samples size are evaluated. Mechanical properties and microstructure of the solder joint are investigated under thermal shock cycles. It was observed that the mechanical strength of SAC0307 dropped slightly with thermal cycling relative to that of SAC305. This reveals that the failure mode of SAC0307 is different from that SAC305 under this critical condition.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.2
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• pp.82-88
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• 2007

Thermal Buckling and free vibration analyses of multi-layered composite conical shells based on a layerwise displacement theory are performed. The Donnell's displacement-strain relationships of conical shell structure are applied. The natural frequencies are compared with the ones existing in the previous literature for laminated conical shells with several cone semi-vertex angles. Moreover, the thermal buckling behaviors of the laminated conical shell are investigated to consider the effect of the semi-vertex angle, subtended angle, and radius to thickness ratio on the structural stability.