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Solder fatigue

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Solder Fatigue is the mechanical degradation of solder due to deformation under cyclic loading. This can often occur at stress levels below the yield stress of solder as a result of repeated temperature fluctuations, mechanical vibrations, or mechanical loads.


Overview

Solder is a metal alloy used to form electrical and mechanical interconnections between the component and printed circuit board (PCB) substrate in an electronic assembly. Although other forms of cyclic loading are known to cause solder fatigue, it has been estimated that the majority of electronic failures are thermo-mechanical driven due to temperature cycling. Under thermal cycling, stresses are generated in the solder due to coefficient of thermal expansion (CTE) mismatch. This causes the solder joints to experience non-recoverable deformation via creep and plasticity that accumulates and leads to degradation and eventual fracture. Historically, tin-lead solders were common alloys used in the electronics industry. Although they are still used in select industries and applications, lead-free solders have become significantly more popular due to RoHS regulatory requirements.

Much work has been done to characterize the creep-fatigue behavior of various solder alloys and develop predictive life damage models. This is done using a Physics of Failure approach. The fatigue life of a solder joint depends on several factors including: the alloy type and resulting microstructure, the joint geometry, the component material properties, the PCB substrate material properties, the loading conditions, and the boundary conditions of the assembly.

Thermo-Mechanical Solder Fatigue

During a product’s operational lifetime it undergoes temperature fluctuations from application specific temperature excursions and self-heating due to component power dissipation. Global and local mismatches of coefficient of thermal expansion (CTE) between the component, component leads, PCB substrate, and system level effects drive stresses in the interconnects (i.e. solder joints). Repeated temperature cycling eventually leads to thermomechanical fatigue.

The deformation characteristics of various solder alloys can be described at the microscale due to the differences in composition and resulting microstructure. Compositional differences lead to variations in phase(s), grain size, and intermetallics. This affects susceptibility to deformation mechanisms such as dislocation motion, diffusion and grain boundary sliding. During thermal cycling, solder grains will tend to coarsen as energy is dissipated from the solder structure. This growth eventually leads to crack initiation and propagation which can be described as accumulated fatigue damage.

The resulting bulk behavior of solder is described as viscoplastic (i.e. rate dependent inelastic deformation) with sensitivity to elevated temperatures. Most solders experience temperature exposures near their melting temperature (high homologous temperature) throughout their operational lifetime which makes them susceptible to significant creep. Several constitutive models have been developed to capture the creep characteristics of lead and lead-free solders. Creep behavior can be described in three stages: primary, secondary, and tertiary creep. When modeling solder, secondary creep, also called steady state creep (constant strain rate) is often the region of interest for describing solder behavior in electronics. Some models also incorporate primary creep. Two of the most popular models are hyperbolic sine models developed by Garofalo and Anand to characterize the steady state creep of solder. These model parameters are often incorporated as inputs in FEA simulations to properly characterize the solder response to loading.

Fatigue Models

Solder damage models take a physics of failure based approach by relating a physical parameter that is a critical measure of the damage mechanism process (i.e. inelastic strain range or dissipated strain energy density) to cycles to failure. The relationship between the physical parameter and cycles to failure typically takes on a power law or modified power law relationship with material dependent model constants. These model constants are fit from empirical testing and simulation for different solder alloys. For complex loading schemes, Miner's linear damage superposition law is employed to calculate accumulated damage.

Coffin-Manson Model

The generalized Coffin-Manson model considers the elastic and plastic strain range by incorporating Basquin’s equation and takes the form:

Δ ϵ 2 = σ f ′ − σ m E ( 2 N f ) b + ϵ f ′ ( 2 N f ) c {\displaystyle {\frac {\Delta \epsilon }{2}}={\frac {\sigma _{f}^{'}-\sigma _{m}}{E}}(2N_{f})^{b}+\epsilon _{f}^{'}(2N_{f})^{c}}

Here ∆ε ⁄ 2 represents the elastic-plastic cyclic strain range, E represents elastic modulus, σm represents means stress, and Nf represents cycles to failure. The remaining variables, namely σf,ε'f,b,and c are fatigue coefficients and exponents representing material model constants. The generalized Coffin-Manson model accounts for the effects of high cycle fatigue (HCF) primarily due to elastic deformation and low cycle fatigue (LCF) primarily due to plastic deformation.

Engelmaier Model

In the 1980s Engelmaier proposed a model, in conjunction with the the work of Wild, that accounted for some of the limitations of the Coffin-Manson model such as the effects of the frequency and temperature. His model takes a similar power law form:

N f ( 50 % ) = 1 2 ( Δ γ 2 ϵ f ′ ) 1 c {\displaystyle N_{f}(50\%)={\frac {1}{2}}({\frac {\Delta \gamma }{2\epsilon '_{f}}})^{\frac {1}{c}}}

c = − 0.442 − 6 ⋅ 10 − 4 T s + 1.74 ⋅ 10 − 2 ln ⁡ ( 1 + f ) {\displaystyle c=-0.442-6\cdot 10^{-4}T_{s}+1.74\cdot 10^{-2}\ln(1+f)}

Engelmaier relates the total shear strain (∆γ) to cycles to failure (Nf). ε'f and c are model constants where c is a function of mean temperature during thermal cycling (Ts) and thermal cycling frequency (f).

Δ γ = C ( L D h s ) Δ α Δ T {\displaystyle \Delta \gamma =C({\frac {L_{D}}{h_{s}}})\Delta \alpha \Delta T}

∆γ can be calculated as function of the distance from the neutral point (LD) solder joint height (hs), coefficient of thermal expansion (∆α), and change in temeprate (ΔT). In this case C is empirical model constant.

This model was initially proposed for leadless devices with tin-lead solder. The model has since been modified by Engelmaier and others to account for other phenomena such as leaded components, thermal cycling dwell times, and lead-free solders.

Darveaux Model

Darveaux proposed a model relating the quantity of volume weighted average inelastic work density, the number of cycles to crack initiation, and the crack propagation rate to the characteristic cycles to failure.

d a d N = K 3 Δ W a v g K 4 {\displaystyle {\frac {da}{dN}}=K_{3}\Delta W_{avg}^{K_{4}}}

N 0 = K 1 Δ W a v g K 2 {\displaystyle N_{0}=K_{1}\Delta W_{avg}^{K_{2}}}

N f = N 0 + a d a / d N = K 1 Δ W a v g K 2 + a K 3 Δ W a v g K 4 {\displaystyle N_{f}=N_{0}+{\frac {a}{da/dN}}=K_{1}\Delta W_{avg}^{K_{2}}+{\frac {a}{K_{3}\Delta W_{avg}^{K_{4}}}}}

In the first equation N0 represents the number of cycles to crack initiation, ∆W represents inelastic work density, K1 and K2 are material model constants. In the second equation, da/dN represents the crack prorogation rate, ∆W represents inelastic work density, K3 and K4 are material model constants. In this case the crack propagation rate is approximated to be constant. Nf represents the characteristic cycles to failure and a represents the characteristic crack length. Model constants can be fit for different solder alloys using a combination of experimental testing and Finite Element Analysis (FEA) simulation.

Blattau Model

Blattau proposed a modification to the Engelmaier model, replacing strain range with strain energy by calculating the shear stress in the solder. To do this the force applied on the solder joint is calcualted with the following equation:

α 1 − α 2 ⋅ Δ T ⋅ L D = F ⋅ ( L D E 1 A 1 + L D E 2 A 2 + h S A s G s + h c A c G c + ( 2 − ν 9 G b a ) ) {\displaystyle \alpha _{1}-\alpha _{2}\cdot \Delta T\cdot L_{D}=F\cdot ({\frac {L_{D}}{E_{1}A_{1}}}+{\frac {L_{D}}{E_{2}A_{2}}}+{\frac {h_{S}}{A_{s}G_{s}}}+{\frac {h_{c}}{A_{c}G_{c}}}+({\frac {2-\nu }{9G_{b}a}}))}

Here α is the CTE, T is temperature, LD is the distance to the neutral point, E is elastic modulus, A is the area, h is the thickness, G is shear modulus, ν is Poisson's ratio, and a is the edge length of the copper bond pad. The subscripts 1 refer to the component, 2 and b refer to the board, and s refer to the solder joint. The shear stress (∆τ) is then calculated by dividing this calculated force by the effective solder joint area. Strain energy is computed using the shear strain range and shear stress from the following relationship:

Δ W = 1 2 Δ γ Δ τ {\displaystyle \Delta W={\frac {1}{2}}\Delta \gamma \Delta \tau }

This approximates the hysteresis loop to be roughly equilateral in shape. Blattau uses this strain energy value in conjunction with model’s developed by Syed to related dissipated strain energy to cycles to failure.

Other Fatigue Models

Additional strain range and strain energy based models have been proposed by several others.

Vibration and Cyclic Mechanical Fatigue

While not as prevalent as thermo-mechanical solder fatigue, vibration fatigue and cyclic mechanical fatigue are also known to cause solder failures. Vibration fatigue is typically considered to be high cycle fatigue (HCF) with damage driven by elastic deformation. This can depend on the input excitation for both harmonic and random vibration. Steinberg developed a vibration model to predict time to failure based on the calculated board displacement. This model takes into account the input vibration profile such as the power spectral density or acceleration time history, the natural frequency of the circuit card, and the transmissibility. Blattau developed a modified Steinberg model that uses board level strains rather than displacement and has sensitivity to individual package types.

Additionally, low temperature isothermal mechanical cycling is typically modeled with a combination of LCF and HCF strain range or strain energy models. The solder alloy, assembly geometry and materials, boundary conditions, and loading conditions will affect whether fatigue damage is dominated by elastic (HCF) or plastic (LCF) damage. At lower temperatures and faster strain rates the creep can approximated to be minimal and any inelastic damage will be dominated by plasticity. Several strain range and strain energy models have been employed in this type of a case, such as the Generalized Coffin-Manson model. In this case, much work has been done to characterize the model constants of various damage models for different alloys.

Software Assisted Solder Fatigue Prediction

Sherlock is physics of failure based reliability tool developed by DfR Solutions that provides software assisted solder fatigue predictions. Users are able import their design (i.e. geometry and material properties of their PCB and components), boundary conditions, and loading conditions. Sherlock is then able to estimate times to failure under field or test conditions. This approach allows electronic manufacturers the ability to rapidly iterate their designs, assess the reliability of their products, and reduce the overall product cycle time.

See Also

References

  1. Wunderle, B. and B. Michel, “Progress in Reliability Research in Micro and Nano Region”, Microelectronics and Reliability, V46, Issue 9-11, 2006.
  2. http://www.dfrsolutions.com/hubfs/Resources/System_Level_Effects_on_Solder_Joint_Reliability.pdf
  3. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.115.7354&rep=rep1&type=pdf
  4. Garofalo, F. , 1965, Fundamentals of Creep and Creep-Rupture in Metals, Macmillan, New York.
  5. Anand, L., 1985, “Constitutive Equations for Hot Working of Metals,” J. Plasticity, 1(3), pp. 213–231
  6. Brown, S. B., Kim, K. H., and Anand, L., 1989, “An Internal Variable Constitutive Model for Hot Working of Metals,” Int. J. Plasticity, 5(2), pp. 95–130
  7. M. A. Miner, "Cumulative damage in fatigue," Journal of applied mechanics, vol. 12, pp. 159-164, 1945
  8. LF Coffin, “The Problem of Thermal Stress Fatigue in Austenitic Steels,” Special Technical Publication 165, ASTM, 1954, p. 31
  9. LF Coffin, “A study of the Effects of Cyclic Thermal Stresses on a Ductile Metal,” Trans. ASME, 76, 931–950 (August 1954).
  10. SS Manson, “Behavior of materials under conditions of thermal stress,” Proceedings of the Heat Transfer Symposium, University of Michigan Engineering Research Institute, Ann Arbor, Mich, pp. 9-75, 1953
  11. Dowling, N.E., Mechanical Behavior of Materials, 2nd Edition, Upper Saddle River, New Jersey, 1999.
  12. Basquin, O. H. (1910). "The exponential law of endurance test". Proceeding of the American Society for Testing and Materials. 10: 625–630.
  13. Engelmaier, W.; , "Fatigue Life of Leadless Chip Carrier Solder Joints During Power Cycling," Components, Hybrids, and Manufacturing Technology, IEEE Transactions on , vol.6, no.3, pp. 232- 237, Sep 1983
  14. Wild, R. N., “Some Fatigue Properties of Solders and Solder Joints,” IBM Tech. Rep. 73Z000421, January 1973.
  15. Darveaux, R., 1997, “Solder Joint Fatigue Life Model,” in Design & Reliability of Solder and Solder Interconnections, Proceedings of the ‘TMS, Orlando, Florida, February, 1997.
  16. Darveaux R (2000) Effect of simulation methodology on solder joint crack growth correlation. Electronic Components and Technology Conference, 2000 IEEE, pp 158–169
  17. http://www.dfrsolutions.com/hubfs/DfR_Solutions_Website/Resources-Archived/Publications/2005-2007/2006_Blattau_IPC_working.pdf
  18. ^ Syed, A., “Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints,” ECTC 2004, pp. 737-746 - corrected.
  19. S. Knecht and L. Fox, “Integrated matrix creep: Application to accelerated testing and lifetime prediction,” in Solder Joint Reliability Theory and Applications, J. H. Lau, Ed. New York: Van Nostrand Reinhold, 1991, ch. 16.
  20. A. Dasgupta, C. Oyan, D. Barker, and M. Pecht, “Solder creep-fatigue analysis by an energy-partitioning approach,” ASME J. Electron. Packaging. vol. 114, no. 2, pp. 152–160, 1992.
  21. Lee, W.W., Nguyen, L.T., and Selvaduray, G.S., “Solder joint fatigue models: review and applicability to chip scale packages.” Microelectronics Reliability 40 (2000) 231-244, 1999.
  22. Steinberg D.S. Vibration analysis for electronic equipment. John Wiley & Sons, 2000.
  23. http://resources.dfrsolutions.com/Guarantee-Reliability-with-Vibration-Simulation-and-Testing.pdf
  24. http://www.dfrsolutions.com/what-is-sherlock
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