Solder fatigue

The generalized Coffin–Manson[11][12][13][14] model considers the elastic and plastic strain range by incorporating Basquin's equation[15] and takes the form:

${\displaystyle {\frac {\Delta \epsilon }{2}}={\frac {\sigma _{f}^{'}-\sigma _{m}}{E}}(2N_{f})^{b}+\epsilon _{f}^{'}(2N_{f})^{c}}$

Here ∆ε ⁄ 2 represents the elastic-plastic cyclic strain range, E represents elastic modulus, σ_m represents means stress, and N_f represents cycles to failure. The remaining variables, namely σ_f,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.

In the 1980s Engelmaier proposed a model,[16] in conjunction with the work of Wild,[17] 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:

${\displaystyle N_{f}(50\%)={\frac {1}{2}}({\frac {\Delta \gamma }{2\epsilon '_{f}}})^{\frac {1}{c}}}$

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

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

${\displaystyle \Delta \gamma =C({\frac {L_{D}}{h_{s}}})\Delta \alpha \Delta T}$

∆γ can be calculated as function of the distance from the neutral point (L_D) solder joint height (h_s), coefficient of thermal expansion (∆α), and change in temperature (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. While initially a substantial improvement over other techniques to predict solder fatigue, such as testing and simple acceleration transforms, it is now generally acknowledged that Engelmaier and other models that are based on strain range do not provide a sufficient degree of accuracy.

Darveaux[18][19] 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.

${\displaystyle N_{0}=K_{1}\Delta W_{avg}^{K_{2}}}$

${\displaystyle {\frac {da}{dN}}=K_{3}\Delta W_{avg}^{K_{4}}}$

${\displaystyle N_{f}=N_{0}+{\frac {a}{da/dN}}=K_{1}\Delta W_{avg}^{K_{2}}+{\frac {a}{K_{3}\Delta W_{avg}^{K_{4}}}}}$

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. N_f 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.

The Darveaux model has been found to be relatively accurate by several authors.[20][21] However, due to the expertise, complexity, and simulation resources required, its use has been primarily limited to component manufacturers evaluating component packaging. The model has not received acceptance in regards to modeling solder fatigue across an entire printed circuit assembly and has been found to be inaccurate in predicting system-level effects (triaxiality) on solder fatigue.[22]

The current solder joint fatigue model preferred by the majority of electronic OEMs worldwide is the Blattau model, which is available in the Sherlock Automated Design Analysis software. The Blattau model is an evolution of the previous models discussed above. Blattau incorporates the use of strain energy proposed by Darveaux, while using closed-form equations based on classic mechanics to calculate the stress and strain being applied to the solder interconnect.[23] An example of these stress/strain calculations for a simple leadless chip component is shown in the following equation:

${\displaystyle (\alpha _{1}-\alpha _{2})\cdot \Delta T\cdot L_{D}=F\cdot ({\frac {L_{D}}{E_{1}A_{1}}}+{\frac {L_{D}}{E_{2}A_{2}}}+{\frac {h_{S}}{A_{s}G_{s}}}+{\frac {h_{c}}{A_{c}G_{c}}}+({\frac {2-\nu }{9G_{b}a}}))}$

Here α is the CTE, T is temperature, L_D 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:

${\displaystyle \Delta W={\frac {1}{2}}\Delta \gamma \Delta \tau }$

This approximates the hysteresis loop to be roughly equilateral in shape. Blattau uses this strain energy value in conjunction with models developed by Syed[24] to relate dissipated strain energy to cycles to failure.

The Norris–Landzberg model is a modified Coffin–Manson model.[25][26]

Additional strain range and strain energy based models have been proposed by several others.[24][27][28]