Stress relaxation in Tin-Lead solders

Materials Science and Engineering, 38 (1979) 241 - 247

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© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

Stress Relaxation in Tin-Lead Solders E. BAKER

School of Mechanical Engineering, N.S. W. Institute of Technology, Sydney (Australia) (Received January 9, 1978; in revised form October 26, 1978)

SUMMARY

Compressive stress relaxation in four hypereutectic tin-lead alloys was studied to establish parameters for an analytical model which can be used at very low strain rates. The experimental results exhibited little experimental scatter and were consistent between all the tests. At these low strain rates the activation enthalpy and the stress exponent were found to be 67 kJ mol -z and 3.4 respectively. These values were found to be independent of both temperature and composition. In addition a unique stress relaxation relation was found which correlated the data for all the alloys tested.

recoverable strain. Consequently the rate of plastic deformation of the material during stress relaxation is n o t zero b u t a function of stress, temperature and time. The deformation mechanisms within the material that occur during stress relaxation are the same as those occurring during creep for the same strain rates. The stress relaxation and creep behaviour of eutectic S n - P b has been investigated extensively (e.g. refs. 3 - 5) and a survey of much of this w o r k is contained in ref. 5. Most studies use a mathematical model for creep and stress relaxation which incorporates the Arrhenius model to describe the effect of temperature. These models often use an empirical power law to predict the effect of stress on the plastic strain rate of the material, i.e.

1. INTRODUCTION

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The long term behaviour of materials under load is of increasing importance to the mechanical designer. For example, miniaturization in electronics has led to the increased use of plastics and low-melting-point metals as load-carrying members [1, 2]. Consequently creep and stress relaxation in these assemblies will redistribute the loads and deform the assembly. The designer must ensure that this time-dependent deformation will n o t interfere with the functioning of the assembly during its design life. To achieve this goal, however, the designer must have accurate long term experimental data and reliable models for his materials. Stress relaxation is the time-dependent deformation of a material under constant constraint (i.e. total strain) conditions. Although the total strain is constant througho u t the stress relaxation test, the plastic (or permanent) strain within the material increases with time at the expense of the

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where A is a constant for any given test conditions, n is the stress e x p o n e n t and Ah a is the activation enthalpy for the material. For eutectic S n - P b solder most experimental studies (e.g. refs. 3 - 5) have found that when the plastic strain rate is below 10 -5 s-z the stress e x p o n e n t is between 2 and 4 and the activation enthalpy is between 63 and 84 kJ mol -z. For strain rates above 10 -~ s-z, the stress e x p o n e n t appears to increase to between 6 and 10 [4]. Mohamed and Langdon [ 5] reported the results of creep tests which showed a sigmoidal relation between strain rate and stress for a eutectic S n - P b solder. Their tests showed that at strain rates between 10 -5 and 10 -3 s- z , the stress exponent attained a minimum value of 1.65 and the activation enthalpy was of the order of 59 kJ mol-z. The stress relaxation tests reported by Murty [4] contained t o o much

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experimental scatter to verify this sigmoidal relationship. However, Murty did obtain nearly the same stress exponent in the lowstrain-rate region as Mohamed and Langdon. The purpose of the present study was to extend the work reported in ref. 3 to other S n - P b alloys. The test m e t h o d used in ref. 3 was designed to simulate the stress-strain conditions that would exist in a specific soldered structure. The results of those tests were needed to determine the appropriate temperature cycle to be used in acceleratedlife tests of that soldered structure. For these life tests it was assumed that small variations in the proportions of tin and lead in the solder would not affect the activation enthalpy significantly. The present investigation was c o n d u c t e d to see if that assumption was correct.

2. E X P E R I M E N T

New high stiffness stress relaxation rigs were used in these tests that had been specifically designed to measure stress relaxation in plastics and low-melting-point alloys. In the tests described in ref. 3 it was believed that when the load was applied the deflection in the Instron universal testing machine might have been significant relative to the total deflection of the specimen. The presses used in the present study were designed to have a large stiffness so that the deflection of the system under maximum load conditions (i.e. less than 1300 N) was negligible compared with the deflection of the test specimen. Also since the entire apparatus was contained within the oven no temperature gradients existed at the grips. These temperature gradients can often be encountered at the grips used in tensile tests. The test specimens were right-circular cylinders 1.4 cm in diameter and 1.4 cm long. (The shape of the test specimen was dictated by the application [2, 3] .) Since the ratio of length to diameter was only 1, the end constraints on the specimen had a significant effect on the stress distribution within the specimen. Consequently some parts of the specimen were in shear as well as compression. Four specimens were tested simultaneously to ensure that the test conditions were

identical for all specimens. The temperature measured on one specimen and the load-cell outputs from all four rigs were monitored continuously. The load was applied with a high precision screw on the rigs that made it possible to estimate the compressive strain of the specimen by the angle of rotation of the screw. Thus it was possible to estimate the elastic modulus of the material from the load change and the screw travel during loading and unloading of the specimen. The length of a single test varied from a minimum of 16 h for the high temperature tests to several weeks for the tests conducted at room temperature. The measured temperature variation during any test was less than -+0.5 °C at the high temperatures and -+1 °C at room temperature. In an earlier study of Pb-60%Sn alloy it was found that the effect of prior testing was n o t significant provided the total accumulated strain in the specimen did n o t exceed 5%*. Consequently it was possible to use the same test specimen for the entire series of isothermal tests on one alloy. Thus errors due to system calibration, misalignment of the system, flaws within the specimen etc. would be consistent for each specimen throughout the entire series of tests. In any case the variations between the stress relaxation curves obtained under the same test conditions from different specimens were so small as to indicate that these potential sources of error were n o t in fact significant.

3. A N A L Y S I S A N D D I S C U S S I O N

3.1. Activation enthalpy Figure 1 shows the family of stress relaxation curves obtained for each S n - P b alloy as a function of temperature and time. The following m e t h o d was used to obtain the activation enthalpy from these data. (1) The stress relaxation curves in Fig. 1 were shifted along the time axis to form a universal curve for each composition. The shift factors F(t) for each temperature were determined from the ratio of the time taken to relax to some arbitrary stress to the time *As a c h e c k the first test o f each series was repeated at the end o f the test series a n d n o differe n c e s could be seen b e t w e e n the t w o sets o f results.

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The activation enthalpy obtained from this plot is 67 kJ mo1-1. Figure 2 shows that the same straight line correlated the data for all three Sn-Pb alloys tested. Consequently the activation enthalpy appears to be independent of composition for these alloys. This value of the activation enthaipy is significantly lower than the value reported in ref. 4. This difference is probably due to differences in the test methods used in the two experiments. In ref. 4 a double-shear creep test was used. In double-shear tests the loads are not coaxial so bending m a y be a factor. Also, as mentioned earlier, in the compression tests used here end effects would probably have a significant influence on the test results.

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To show all of the experimental scatter on a single figure the shift factors were calculated for all tests using the same activation enthalpy. For this activation enthalpy (67 kJ tool-1) and for a reference temperature o f 40 °C the shift factor equation becomes

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3.2. Stress exponent The analysis given in ref. 4 was used to determine the stress exponent n from the stress relaxation data in Fig. 3. This method can be used to find the stress exponent if a log-log plot of the stress relaxation data against time (Fig. 3) approaches a straightline asymptote. The universal curve for Pb37% Sn solder in Fig. 3(b) does appear to approach a straight-line asymptote for shifted times greater than 2 × 105 s. The slope of the line shown in Fig: 3(b) indicates that the stress exponent n for this material is 3.4 for strain rates between 7 × 10 - s s- i and 10 -s s-1. Although this linear region appears to extend over a decade, it is still possible that the slope has not quite attained its maximum value and the stress exponent n obtained from this slope may still be a little high. The creep tests on a eutectic solder reported in ref. 5 found the stress exponent to be 3.0 at a strain rate of 1 0 - 7 s - 1 . The agreement between the values of the stress exponent obtained from these two Sn-Pb alloys using different test methods is quite

*The 6 0 / 4 0 S n - P b data are from stress relaxation tests that were conducted in 1972 partly on an Instron universal testing machine [ 3 ]. The stiffness o f the Instron machine and the other test rigs used in those experiments was probably less than what is required for this type o f test and would have contributed to some small errors in the shape o f the final stress relaxation curve. Consequently these results are less reliable than the results o f the present study.

good. The asymptote corresponding to a stress exponent of 3.4 has also been drawn on each of the universal curves in Fig. 3 and the data do seem to fit reasonably well. These results show that over the range of compositions and temperatures tested the stress exponent is independent of both composition and temperature. This agrees with earlier creep tests by Mohamed and Langdon [5] who found that n was independent of temperature for eutectic Pb-Sn at these low creep rates. Their results indicated that the dominant creep mechanism at these low strain rates was lattice self-diffusion.

3.3 Effect o f composition on stress relaxation The universal curves in Fig. 3 show that the stress-relaxation curves are similar for all the compositions tested. This similarity indicates that it may be possible to correlate the universal curves for different compositions using a time-scale shift factor similar to the one used to correlate data taken at different temperatures. Figure 4 shows the results obtained by superposing all the universal curves obtained from the three alloys studied here. These superposed curves do appear to form a unique universal curve. In Fig. 5, the time-scale shift factors used to correlate the different alloy compositions are shown to be an exponential function of composition. The figure shows that, as the percent tin in the alloy increases, more time is required to reach the same relaxed state, which indicates that the stress relaxation in these alloys is mainly influenced by the lead-rich a-portion of the alloy and that the tin-rich ~-portion may behave as a relaxation inhibitor. The results shown in Figs. 2, 4 and 5 enable the designer to generate an approximate stress-relaxation curve for any intermediate Sn-Pb alloy (between 29% and 60% Sn) without having to conduct a single test. Also, if life tests are to be accelerated by increasing either the temperature or the stress, the acceleration factor obtained from these tests is independent of composition.

4. CONCLUSIONS Compressive stress relaxation was studied in four hypereutectic Sn-Pb alloys. The main

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goal of the study was to establish parameters for an analytical model that would be valid at very low strain rates. Stress relaxation tests were chosen since the strain rates attained under these test conditions are significantly lower than those normally obtained with other techniques. Compact high stiffness test rigs were used which had been specially designed for this type of test. The data exhibited a high level of consistency between the various tests. Nearly identical stress relaxation curves were found

at each temperature. In addition when the same activation enthalpy was used to calculate all of the temperature acceleration factors for each alloy, the universal curves obtained showed little experimental scatter. Both the activation enthalpy and the stress exponent were independent of temperature and composition for all of the hypereutectic alloys tested. The activation enthalpy and the stress exponent were found to be 67 kJ mo1-1 and 3.4 respectively. This indicates that the a-lead region of the material dominates the stress relaxation behaviour in these hypereutectic alloys. Finally a unique stress relaxation relation was found which correlated the data from all the tests. Thus tests conducted on one alloy can be used to predict the behaviour of another alloy under different test conditions.

5. A C K N O W L E D G M E N T S

The author wishes to acknowledge I. Hanson and K. McDonald for their assistance in developing the test rigs used in this experiment. In addition he is particularly indebted to A. Lah for his technical assistance both during the tests and during the preparation of this paper.

247 REFERENCES

1 E. Baker, Some effects of temperature on material properties and device reliability, IEEE Trans. Parts Hybrids Packag., PHP 8 (4) (1972) 4 - 14. 2 E. Baker, Understanding cyclical thermal stresses -the key to improving accelerated-life testing, Insul./Circuits, 21 ( 1 1 ) ( O c t . 1 9 7 5 ) 4 9 -57.

3 E. Baker and T. J. Kessler, The influence of temperature on stress relaxation in a chill-cast, t i n lead solder, IEEE Trans. Parts Hybrids Packag., PHP 9 (4) (1973) 243 - 246. 4 G. S. Murty, Stress relaxation in superplastic materials, J. Mater. Sci., 8 (1973) 611 - 614. 5 F. A. Mohamed and T. G. Langdon, Creep hehaviour in superplastic Pb-62% Sn eutectic, Philos. Mag., 32 (1975) 697 - 709.