Effect of Mechanical Cycling at Elevated Temperatures on The Constitutive Properties and Microstructure of Lead Free Solder Alloys

Solder joints in electronic packages often experience fatigue failures due to cyclic mechanical stresses and strains in fluctuating temperature environments. These stresses and strains are induced by mismatches in coefficients of thermal expansion, and lead to damage accumulation that contributes to crack initiation, crack propagation, and eventually to failure. In this study, we have tried to compare the effects of elevated mechanical cycling on SAC305 and SAC+Bi (SAC_Q). Initially, small uniaxial cylindrical samples of both alloys were prepared and reflowed in a reflow oven. These samples were then mechanically cycled for various durations at testing temperatures of 100 °C. The measured cyclic stress-strain curves were used to characterize the evolution of the hysteresis loop properties (peak stress, hysteresis loop area, and plastic strain range) with high temperature mechanical cycling. In addition, uniaxial tensile tests and creep tests were also conducted on specimens that had been previously mechanically cycled for various durations (e.g 0, 50, 100, 200, and 300 cycles) at an elevated temperature. This allowed us to study the evolution of the constitutive behavior of the solder alloys that occurred during the high temperature mechanical cycling due to the fatigue damage that builds up in the specimens. The reductions in the properties that occur during high temperature mechanical cycling were also correlated with the corresponding changes in the microstructure of the specimens. Rectangular cross-sectioned samples of the two lead free solder alloys were polished and selected regions indented to track the changes in the microstructure of a fixed region with mechanical cycling at T = 100 °C. Using the results of this study, we are working to develop better fatigue criteria for lead free solders which are subjected to variable temperature applications.

APPLICATION OF ACOUSTIC PULSE ECHO-METHOD FOR THE INVESTIGATION OF DYNAMIC AND STRUCTURAL DYSLOCATION CHARACTERISTICS OF CRYSTALS

The multifunctional pulse equipment allowіng to use the method of amplitude-independent internal friction in the frequency range 7.5 to 232.5 MHz is described. Equipment gjves the possibility to investigate the peculiarities of the process of phonon-dislocation interaction in crystals, to carry out thermoactivation analysis of the process of dislocation of the dislocations about the stoppers under the action of temperature and elastic loading, to study processes of dislocation and mechanical relaxation in loaded samples in the quasi-elastic and plastic strain range.

Low-Cycle Fatigue Life of Continuously Cyclic-Hardening Material

A general fatigue life equation is derived by modifying the Tanaka-Mura-Wu dislocation pile-up model for variable strain-amplitude fatigue processes, where the fatigue crack nucleation life is expressed in terms of the root mean square of plastic strain range. Low-cycle fatigue tests were conducted on an austenitic stainless steel. At 400 ? and 600 ?, the material exhibits continuously cyclic-hardening behaviour. The root mean square of plastic strain ranges is evaluated from the experimental data for each test condition at strain rates ranging from 0.0002/s to 0.02/s. The variable-amplitude Tanaka-Mura-Wu model is found to be in good agreement with the LCF data, which effectively proves Miner's rule on the stored plastic strain energy basis.

The Shear Stress Determination in Tubular Specimens under Torsion in the Elastic–Plastic Strain Range from the Perspective of Fatigue Analysis

The comparison of shear stress determination methods in tubular specimens under torsion is presented in this paper. Four methods were analyzed: purely elastic solutions, purely plastic solutions, the midsection approach, and the Chaboche nonlinear kinematic hardening model. Using experimental data from self-designed and conducted fatigue experiments, an interesting insight on this problem was obtained that is not often tackled in the literature. It was shown that there are differences in determined shear stress values, and their level depends on a few factors. The midsection approach and purely plastic solution gave values of surface shear stress very close to the values obtained using the Chaboche nonlinear kinematic hardening model for high strain levels. The purely elastic solution gave proper results for the low strain ranges, close to the cyclic yield limit. Since none of the methods can be trusted in the full range of loading, an important conclusion from these analyses regards the formulated ranges of their applicability. It was also shown that the calculated values of shear stress and plastic and elastic strain energy density determined on this basis have a strong impact on fatigue life predictions. Finally, the influence of predicted values of shear stresses on the interpretation of cyclic hardening phenomena was also presented.

RAYLEIGH SURFACE WAVES IN ASSESSING THE STATE OF METAL STRUCTURES

The paper is dedicated to search for an ultrasonic sensing method to identify the state of a material that makes it possible to classify the structure to be diagnosed as the structure of which state is associated with occurrence of plastic strains. We examined the effect of C275 steel’s uniaxial strain-stress state on velocity of an elastic Rayleigh wave. Elastic waves were generated by piezoelectric transducers using oscillation frequencies of 2, 5, and 10 MHz. Transmitting and receiving transducers have been fitted in a single block and permanently spaced 50 mm apart. The transmitting transducer was excited using А1214 test instrument. The sensing pulse was taken up using Tektronix TDS2022 oscilloscope with maximum time resolution of 2 ns. Delay of the received signal relative to the initial position of the informative point (pulse’s zero crossing) has been chosen as a numerical indicator of elastic wave velocity variations caused by strain. Rise in delay value at permanent space between transmitting and receiving transducers is indicative of decrease in sensing pulse velocity and vice versa. For pure elastic strains the difference between delays (velocities) of the waves propagating parallel and perpendicular to stress acting in a material under load is proportional to the acting stress. For plastic strains the dependence of acoustic anisotropy (difference between delays) on the applied stress is non-linear and drops with rise in stress. Delay variations in the elastic range do not depend on the sensing pulse frequency. As to the plastic strain range we observe a significant dependence of velocity on frequency. Due to the results obtained we propose to use the dependence on Rayleigh wave velocity as a diagnostic symptom of a material under plastic strains.

Determination of Surface Stresses in X20Cr13 Steel by the Use of a Modified Hardness Measurement Procedure with Vickers Indenter

The paper presents a method for estimating the value of equibiaxial stress in a surface layer of a material by using a modified hardness measurement procedure with a Vickers indenter. A certain characteristic parameter was defined and related to the surface stress. A hybrid approach, based on experimental tests and accompanied by the complementary results obtained by the finite element modelling of X20Cr13 steel in elastic–plastic range, confirmed a linear relationship between the value of the characteristic parameter and the magnitude of equibiaxial stress at the surface. This linear relationship was valid in both elastic and elastic–plastic strain range beyond the yield stress of the material.

Low-Cycle Fatigue Life of Continuously Cyclic-Hardening Material

A general fatigue life equation is derived by modifying the Tanaka-Mura-Wu dislocation pile-up model for variable strain-amplitude fatigue processes, where the fatigue crack nucleation life is expressed in terms of the root mean square of plastic strain range. Low-cycle fatigue tests were conducted on an austenitic stainless steel. at 400°C and 600°C, the material exhibits continuously cyclic-hardening behaviour. The root mean square of plastic strain ranges is evaluated from the experimental data for each test condition at strain rates ranging from 0.0002/s to 0.02/s. The variable-amplitude Tanaka-Mura-Wu model is found to be in good agreement with the LCF data, which effectively proves Miner’s rule on the stored plastic strain energy basis.

Decomposed Collaborative Modeling Approach for Probabilistic Fatigue Life Evaluation of Turbine Rotor

To improve simulation accuracy and efficiency of probabilistic fatigue life evaluation for turbine rotor, a decomposed collaborative modeling approach is presented. In this approach, the intelligent Kriging modeling (IKM) is firstly proposed by combining the Kriging model (KM) and an intelligent algorithm (named as dynamic multi-island genetic algorithm), to tackle the multi-modality issues for obtaining optimal Kriging parameters. Then, the decomposed collaborative IKM (DCIKM) comes up by fusing the IKM into decomposed collaborative (DC) strategy, to address the high-nonlinearity problems for accelerating simulation efficiency. Moreover, the DCIKM-based probabilistic fatigue life evaluation theory is introduced. The probabilistic fatigue life evaluation of turbine rotor is regarded as case study to verify the presented approach; the evaluation results reveal that the probabilistic fatigue life of turbine rotor is 3296 cycles. The plastic strain range ∆εp and fatigue strength coefficient σf′ are the main affecting factors to fatigue life, whose effect probability are 28% and 22%, respectively. By comparing with direct Monte Carlo method, KM method, IKM method and DC response surface method, the presented DCIKM is validated to hold high efficiency and accuracy in probabilistic fatigue life evaluation.