Thermal creep and fracture behaviors of the lead-free Sn–Ag–Cu–Bi solder interconnections under different stress levels

In our previous study, the creep behavior of the lead-free Sn–Ag–Cu–Bi solder joints has been proven to follow the Arrhenius power-law relationship, and the thermal fatigue behavior of the solder joints exhibits the typical creep deformation characteristics with a superposition of the pulsating features. In this study, the thermal creep and fracture behaviors of the lead-free Sn–Ag–Cu–Bi solder interconnections were characterized under different stress levels, with a systematical comparison to that of a traditional Sn60Pb40 near-eutectic solder. The results show that the creep strain rate of both solder connections follows Weertman-Dorn equation, and the calculated creep stress exponent for two solders is reasonably close to other published data. The SEM inspection and analysis of fractographies of creep fractured solder joints manifest that the creep failure of the lead-free Sn–Ag–Cu–Bi solder joint shows obviously intergranular fracture mechanism, while the Sn60Pb40 joint ruptures dominantly by a transgranular sliding mechanism.     

Analysis of Garofalo equation parameters for an ultrahigh carbon steel

Isothermal stress–strain curves data from torsion tests conducted at high temperature (950–1200 °C) and strain rates (2–26 s⁻¹) were analyzed in an ultrahigh carbon steel (UHCS) containing 1.3%C. The sine hyperbolic Garofalo equation was selected as an adequate constitutive equation for the entire range of the forming variables considered. The Garofalo parameters were assumed strain dependent allowing the prediction of stress–strain curves under transient and steady-state conditions. The average relative errors obtained were below 3% in stress. In addition, the creep deformation mechanisms in the UHCS were analyzed from the Garofalo equation parameters. For this aim, the stress exponent of the Garofalo equation was, for the first time, related to that of the power law equation. The results show that the controlled deformation mechanism at steady state is lattice diffusion-controlled slip creep.     

Plane stress creep of damaged plates

Creep of plates that undergo damage due to in-plane mechanical loads is discussed. A method for solving the initial boundary value problem of creep is based on combined application of R-functions, Ritz, and Runge-Kutta-Merson methods. Solution structures have been obtained for main types of boundary conditions. The influence of a material’s heteroresistance and damage parameter on the creep and creep-rupture strength of a plate with a circular opening is studied. __________ Translated from Problemy Prochnosti, No. 6, pp. 51–60, November–December, 2007.     

Creep and creep-rupture strength of gas turbine components in view of nonuniform temperature distribution

The conventional model of Kachanov-Rabotnov-Hayhurst continuum fracture mechanics is extended to cover the case of variable temperature and strain hardening. The creep and damage rates are assumed to depend on temperature. The resulting model for nonisothermal creep and damageability is implemented in a finite-element code of the general-purpose software package ABAQUS. The mathematical model is tested on an axisymmetric problem for a gas turbine body. __________ Translated from Problemy Prochnosti, No. 5, pp. 37–44, September–October, 2008.     

The effectiveness of coincidence site lattice criteria in predicting creep cavitation resistance

The coincidence site lattice (CSL) concept is often used in microstructural characterization by researchers studying grain boundary engineering as a method for improving the performance of polycrystalline materials. It is assumed that a high degree of shared lattice sites in the boundary between two grains will result in improved mechanical properties. For practical application of the CSL concept to experimental results, a maximum deviation from ideal CSL orientation relationships must be defined to distinguish potential CSL boundaries from random boundaries that are not likely to exhibit “special” properties. Several different maximum deviation criteria have been proposed in the literature. In this study, four of these criteria are investigated for their effectiveness in predicting the creep cavitation resistance of boundaries of different CSL character in three model alloys: pure Cu, Cu-Bi, and Cu-Sb. Bi and Sb strongly segregate to Cu grain boundaries and are detrimental to creep life. The experimental observations are compared to simulation results for a non-textured polycrystal. It is observed that only boundaries related to cubic annealing twins (Σ3 and Σ9) exhibit special resistance to creep cavitation, that boundaries with Σ > 3 are affected by the presence of segregants, and that the fraction of non-Σ(3,9) boundaries tracks closely with what would be expected from a random polycrystal. It is shown that more restrictive criteria result in more reliable characterization of the fraction of cavitation-resistant boundaries only because they exclude more non-Σ(3,9) boundaries from the analysis.     

Constitutive models of creep for lead-free solders

The constitutive modeling of creep has been extensively studied due to the important of the creep failure mode in solder joints. However, there are very few studies that considered room temperature aging contributions in their creep modeling studies. This study investigated constitutive modeling of creep of solders by taking into account the possible contribution room temperature aging. Lead-free solder (Sn–4.0Ag–0.5Cu) was found to have a higher creep resistance than Sn–Pb solder at the same stress level and testing temperature. The higher creep resistance was contributed by the second phase intermetallic compounds, Ag₃Sn and Cu₆Sn₅. The precipitation of these intermetallic compounds can significantly block the movement of dislocations and increase the creep resistance of the material. Constitutive models of creep for both lead-free and Sn–Pb eutectic solders were constructed based on the experimental data. The activation energy for SAC405 is much higher than that of Sn–Pb, which also indicates that SAC405 possesses higher creep resistance. The constitutive models can be used in finite element analysis of actual electronic packages to predict solder joint failure. The creep mechanisms of both lead-free and Sn–Pb eutectic solders were also extensively discussed in this dissertation. Dislocation gliding and climb is believed to be the major failure mode at high stresses, while lattice diffusion and grain boundary diffusion is believed to be the major failure mode at low stress levels. Grain boundary sliding is believed to contribute to creep deformation at both high-stresses and low-stresses. For eutectic Sn–Pb, superplastic deformation is a major the creep mechanism at low-stresses and high-temperatures.     

Superplastic power-law creep of Sn–40%Pb–2.5%Sb peritectic alloy

The power law-creep behavior of superplastic Sn–40Pb–2.5Sb alloys with different grain sizes has been investigated at room temperature. Stress exponent values for these alloys have been determined by indentation creep, conventional creep and uniaxial tension tests in order to evaluate the correspondence of indentation creep results with conventional tests. In all cases, the indentation results were in good agreement with each other and with those of the tensile and conventional creep tests. The average stress exponent values of about 2.6 and 3.0 corresponding to the strain rate sensitivity (SRS) indices of 0.33–0.39, depending on the grain size of the materials, indicate that the grain boundary sliding is the possible mechanism during creep deformation of Sn–Pb–Sb alloys. Within limits, the indentation tests are thus considered useful to acquire information on the creep behavior of small specimens of these soft tin–lead–antimony alloys at room temperature. It is also demonstrated that the indentation creep test provides a convenient method to measure SRS and thereby to assess the ability of a material to undergo superplastic deformation.     

Computer simulation of the processes of mechanical shaping of three-dimensional shells under the conditions of creep. Part 1

We study the problem of complex numerical simulation of changes in the properties of materials as functions of time, temperature, and the level of irreversible strains as a part of the problem of numerical simulation of mechanical shaping of three-dimensional shells under the conditions of creep. The fact that the quantities appearing in the equations of state of the material are adequate is verified by using a variable reference configuration. The possibility of application of the deduced laws of state is corroborated by good agreement between the results of numerical analysis of tension and compression of specimens under large creep strains and the experimental data. Kiev State Engineering University of Building and Architecture, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 52–58, July–August, 1997.     

A new model for the analysis of composite steel – concrete slab and beam structures with deformable connection

 In this paper a solution to the bending problem of reinforced concrete slabs stiffened by steel beams with deformable connection including creep and shrinkage effect is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface producing lateral deflection and inplane deformation to the plate and lateral deflection and axial deformation to the beams are related with the interface slip through the shear connector stiffness. Any distribution of connectors along the interface and any linear or non-linear load–slip relationship or partial shear connection for the shear connectors can be handled. The creep and shrinkage effect relative with the time of the casting and the time of the loading of the plate is taken into account. The solution of the arising plate and beam problems, which are nonlinearly coupled, is achieved using the analog equation method (AEM). The adopted model compared with those ignoring the inplane forces and deformations, approaches more reliable the actual response of the plate–beams system. Moreover, it permits the evaluation of the shear forces at the interfaces, the knowledge of which is very important in the design of composite steel–concrete structures. Received: 21 June 2002 / Accepted: 5 March 2003     

Microstructural evolution during creep of a hot extruded 2D70Al-alloy

Microstructural evolution during creep of a hot extruded Al–Cu–Mg–Fe–Ni (2D70) Al-alloy was investigated in this study using transmission electron microscopy (TEM). The samples for creep test were carried out two-stage homogenization, followed by extruding. The creep ultimate strength dropped and the temperature increased gradually from 312 to 117 MPa and from 423 to 513 K, respectively. The microstructural observation for the crept samples showed that the S′ phase coarsened with increased creep temperature and the aging precipitates transformed from S″ phase to S′ phase during creep process. Meanwhile, excess solute atoms in supersaturated solid solution dynamically precipitated to further form finer S′ phase and S″ phase, which pinned the dislocations and impeded the dislocation movements. Large amount of dislocations piled up around the micron-scale Al₉FeNi phase, and a lot of dislocation walls were generated along 〈220〉 orientation. S phase accumulates around these defects. The interaction between dislocations and precipitates was beneficial for the improved performances at elevated temperature.     

Creep and fatigue behaviors of the lead-free Sn–Ag–Cu–Bi and Sn60Pb40 solder interconnections at elevated temperatures

Creep and fatigue behaviors of the interconnections soldered by the lead-free Sn–Ag–Cu–Bi solder were investigated at different elevated temperatures (with the homologue temperature in the range of 0.71– 0.82), with a comparison to that of a traditional Sn60Pb40 solder. The results show that the lead-free Sn–Ag–Cu–Bi solder shows a superior anti-creep performance over the Sn60Pb40 solder, in terms of a much lower creep strain rate and a vastly elongated creep fracture lifetime; in the secondary creep regime, the calculated creep-activation energy for two solders is reasonably close to other published data. In addition, it has also been shown that the joints soldered by the lead-free Sn–Ag–Cu–Bi solder exhibits a superb fatigue property.     

Time-dependent creep stress redistribution analysis of thick-walled functionally graded spheres

Time-dependent creep stress redistribution analysis of thick-walled spheres made of functionally graded material (FGM) subjected to an internal pressure and a uniform temperature field is performed using the method of successive elastic solution. The material creep and mechanical properties through the radial graded direction are assumed to obey a simple power-law variation. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are time, temperature and stress dependent. Using the equations of equilibrium, compatibility and stress–strain relations a differential equation, containing creep strains, for radial stress are obtained. Ignoring creep strains, a closed-form solution for initial thermoelastic stresses at zero time is presented. It has been found that the material in-homogeneity parameterβ has a substantial effect on thermoelastic stresses. From thermoelastic analysis the material identified by β=2 in which a more uniform shear stress distribution occurs throughout the thickness of the FGM sphere is selected for time-dependent stress redistribution analysis. Using the Prandtl–Reuss relations and Norton’s creep constitutive model, history of stresses and strains are obtained. It has been found that radial stress redistributions are not significant, however, major redistributions occur for circumferential and effective stresses. It has also been concluded that stresses and strains are changing with time at a decreasing rate so that there is a saturation condition beyond which not much change occurs. Indeed after 50 years the solution approaches the steady-state condition.     

Dependence of the period of subcritical growth of a creep fatigue crack on the duration of loading cycles

We construct the kinetic equation for the period of growth of a creep fatigue crack. By using the experimental data, it is shown that this equation correctly describes the behavior of the crack. It follows from the solution of Sack’s problem that the larger the duration of the loading cycle T, the more pronounced the effect of creep and, hence, the smaller the residual service life of the structure.     

Thermostable scintillation detector

A design of a scintillation detector of ionizing radiation based on a Tl-activated NaI single or polycrystal is proposed. The detector is equipped with a unique compensator of inconsistent variations of the axial dimensions of the scintillator and its container. Khar’kov Institute of Electrification and Mechanization of Agriculture, Khar’kov, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 4, pp. 577–581, July–August, 1996.     

Creep and fracture behavior of as-cast Mg–11Y–5Gd–2Zn–0.5Zr (wt%)

The tensile-creep and creep–fracture behavior of as-cast Mg–11Y–5Gd–2Zn–0.5Zr (wt%) (WGZ1152) was investigated at temperatures between 523 and 598 K (0.58–0.66T _m) and stresses between 30 and 140 MPa. The creep stress exponent was close to five, suggesting that dislocation creep was the dominant creep mechanism. The activation energy for creep (233 ± 18 kJ/mol) was higher than that for self-diffusion in magnesium, and was believed to be associated with cross-slip, which was the dominant thermally-aided creep mechanism. This was consistent with the surface observations, which suggested non-basal slip and cross-slip were active at 573 K. The minimum creep rate and fracture time values fit the original and modified Monkman–Grant models. In situ creep experiments highlighted the intergranular cracking evolution. The creep properties and behavior were compared with those for other high-temperature creep-resistant Mg alloys such as WE54-T6 and HZ32-T5.     

Analytic description of the formation of pores under conditions of steady-state creep of metals

On the basis of a generalization of the synthetic theory of plasticity and creep, the process of formation of pores in a metal is analytically described under conditions of steady-state creep. The relations between the volume of micropores and the steady-state creep strain are deduced for different levels of stresses. The accumulated analytic results are in good agreement with the experimental data. __________ Translated from Problemy Prochnosti, No. 1, pp. 107–113, January–February, 2007.     

Prediction of the corrosion cracking of structures under the conditions of high-temperature creep

On the basis of the continual model of corrosion crack growth proposed earlier and the well-known incremental-type creep theory, we make an attempt to predict the corrosion cracking of structures under the conditions of high-temperature creep. We propose the mathematical statement of the problem taking into account the influence on corrosion cracking of the properties of corrosive media and the redistribution of stresses in time caused by creep. The Bubnov–Galerkin method is applied for the solution of this problem. An example of prediction of the phenomenon of corrosion cracking in the case of creep of a pipe under the action of internal pressure is analyzed.     

Higher-order crack-tip creep stress fields in materials under biaxial loading

We have developed and implemented a method for calculating the fields of parameters of the crack-tip creep stress-strain state by taking direct account of the higher-order terms. The paper presents some calculated data on the fields of crack-tip stresses, creep strain rates, and amplitude ratios in the creep case. The influence of loading biaxiality on redistribution of stresses between the creep stages and on the constraint parameters in failure is assessed. Translated from Problemy Prochnosti, No. 6, pp. 25–43, November–December, 2008.