Solder Joint Fatigue

Solder Joint Fatigue

Engelmaier-Wild Model, Norris-Landzberg Acceleration and the Test Plan

What the tool estimates

A surface-mount component and the board it is soldered to expand at different rates. Every thermal cycle therefore pushes the farthest solder joints back and forth by the mismatch displacement L_D Δα ΔT, and solder, which operates above half its absolute melting temperature even at room temperature, creeps and relaxes under that displacement until the strain is almost entirely inelastic. The joints fail by creep-fatigue after a number of cycles that depends on the strain range, on how much of the stored elastic energy relaxes during each dwell (the dwell time and the mean temperature), and on the solder alloy. The tool evaluates that life with the Engelmaier-Wild creep-fatigue model in the form published in IPC-SM-785 (1992), compares a field cycle with an accelerated test cycle, and derives the test that stands for the design life. It is a first-pass, closed-form screening method: finite-element creep analysis is the next step for a critical design, and the IPC-SM-785 caveats repeated below say where the closed form should not be trusted.

Thermal cycles

The field cycle is described by the board temperatures at the two dwells, T_S,lo and T_S,hi, and, when the component dissipates power, by its own temperatures T_C,lo and T_C,hi. The two members then do not see the same swing, and the model uses the equivalent temperature swing ΔT_e = |α_S ΔT_S − α_C ΔT_C| / Δα, with Δα = |α_C − α_S|, which is the swing that would give the same mismatch displacement without power. The mean cyclic solder-joint temperature is T_SJ = ¼ (T_C,hi + T_S,hi + T_C,lo + T_S,lo). The dwell time t_D is the half-cycle time at temperature available for stress relaxation; a product switched on in the morning and off at night has a dwell of about 715 minutes, an accelerated test 10 to 15 minutes. The cycle time is 2 t_D + 2 t_R with t_R the ramp, and sets the cyclic frequency used by the Norris-Landzberg equation (cycles per day). The test cycle is unpowered: component and board are at the chamber temperature. The test board may have a different CTE from the product board (IPC-SM-785 recommends a larger mismatch to increase the acceleration), so the test has its own Δα.

Presets: the IPC-9701 Table 4.1 conditions TC1 (0 to 100 °C, the preferred reference), TC2 (−25 to 100), TC3 (−40 to 125), TC4 (−55 to 125) and TC5 (−55 to 100 °C) with their 10-minute dwells (the standard limits the ramp rate to 20 °C/min and fixes no ramp time; 10 minutes is entered), and the IPC-SM-785 Table 1 test of 0 to 100 °C with 15-minute dwells at 24 cycles per day.

Cyclic shear strain range

Leadless attachments (leadless ceramic chip carriers, chip resistors and capacitors, and, by the usual practice, BGA and CSP solder balls) are stiff enough for the joint stress to exceed the solder yield strength, and the shear strain is the mismatch displacement of the farthest joint divided by the joint height (IPC-SM-785 eq. 3):

Δγ = F (L_D / h) Δα ΔT_e

L_D is the maximum distance from the neutral point (the component centre, where the displacement is zero) to a solder joint, measured to the joint centre: half the diagonal between the corner joints of a square array, half the pad-centre distance of a two-terminal chip component. h is the solder-filled gap between the component metallization and the pad, not the fillet height. F is an empirical "non-ideal" factor for second-order effects (cyclic warpage, transients, non-ideal joint geometry, brittle intermetallics, the solder's own mismatch with the materials it wets): 1.0 to 1.5 for column-like leadless joints, 0.7 to 1.2 for leadless joints with fillets (castellated chip carriers and chip components), about 1 for compliant leads. The handbook's own example uses 0.7 for a chip capacitor and 1.0 for a leaded chip carrier.

Compliant-lead attachments keep the joint stress below the solder yield strength, so the fatigue damage is governed by the stress-strain product rather than by the displacement alone (eq. 4):

Δγ = F K_D (L_D Δα ΔT_e)² / ((200 psi) A h)

K_D is the diagonal flexural stiffness of the unconstrained lead in the direction of the neutral point (strain-energy methods or finite elements; Kotlowitz 1989 gives compliance metrics for gull-wing, J and clip leads), A the effective minimum load-bearing joint area (about two-thirds of the solder-wetted lead area projected onto the pad), h about half the stencil thickness, and 200 psi (1.38 MPa) the scaling stress of the model. The cyclic shear stress range Δτ = K_D L_D Δα ΔT_e / A should stay below about twice the solder shear yield strength (IPC-SM-785 puts τ_y at 250 to 500 psi); above that the lead is too stiff for this form and underpredicts the life, and the leadless form gives the other bound. The 200 psi constant and the square of the displacement are Engelmaier's calibration, not a derivation; the handbook states them without proof.

Fatigue ductility exponent and cycles to failure

The Coffin-Manson relation written for the solder's shear strain, N_f(50 %) = ½ (Δγ / (2 ε′_f))^1/c, gives the mean (median) cycles to failure. Wild's isothermal fatigue tests on SnPb joints at 25 and 100 °C and 4 to 300 cycles per hour gave Engelmaier a fatigue ductility coefficient 2 ε′_f = 0.65 and an exponent that depends on the mean temperature and on the time available for stress relaxation (eq. 5):

c = −0.442 − 6 × 10⁻⁴ T_SJ + 1.74 × 10⁻² ln(1 + 360 / t_D)

with T_SJ in °C and t_D in minutes. A short dwell (incomplete relaxation) makes c less negative and the life for a given strain longer: that is the physical content of the acceleration transform. The tool writes the exponent as c = −(c₀ + c₁ T_SJ) + c₂ ln(1 + t₀/t_D) so that other alloys can be entered. Engelmaier's 2010 IPC APEX paper gives tentative parameters for lead-free solders, fitted to accelerated-test results from several sources rather than to isothermal fatigue data like Wild's: SAC405/305 ε′_f 0.425, c₀ 0.480, c₁ 9.3 × 10⁻⁴, c₂ 1.92 × 10⁻², t₀ 500; SAC205 ε′_f 0.250 and SAC105 0.225 with the same exponent; SnAg 0.275, 0.430, 6.3 × 10⁻⁴, 1.82 × 10⁻², 400. The paper warns that they may be adjusted when independent temperature and dwell data exist, and that for benign conditions the SAC405/305 life comes out up to a factor of 3 below SnPb.

The spread of failures over a population follows a two-parameter Weibull distribution: N_f(x %) = N_f(50 %) [ln(1 − 0.01 x) / ln 0.5]^1/β, and F(N) = 1 − 0.5^(N/N_f50)β is the fraction failed after N cycles. IPC-SM-785 suggests β = 4 for leadless and 2 for compliant-leaded attachments when no test data exist; a measured slope from the test is better. The design passes when N_f(x %) is at least the design life N = years × cycles per year at the acceptable failure fraction x (Table 1 of the handbook: 1 % for consumer products, 0.1 % computers and automotive, 0.01 % telecommunications and military avionics, 0.001 % commercial aircraft and space).

Acceleration factor

Engelmaier's acceleration transform (eqs. 12 to 15) applies the model to the field and to the test and divides: N_f(2, 50 %) = ½ [(2 N_f(1, 50 %))^c(1) ΔD(2)/ΔD(1)]^1/c(2) with the damage term ΔD = Δγ / (2 ε′_f). The geometry, F and the ductility coefficient cancel in the ratio; the strain ratio (Δα ΔT_e for leadless, its square for leaded joints), the two dwell times and the two mean temperatures do not. Because the exponent differs between the conditions the transform is not a constant factor, and the acceleration factor AF = N_f(field, 50 %)/N_f(test, 50 %) printed by the tool holds for the strain level of the case. In time the acceleration is AF × f_test/f_field (eq. 11).

Norris-Landzberg (1969) wrote the Coffin-Manson ratio directly in terms of the cycle parameters, from IBM flip-chip data: AF = N_field/N_test = (ΔT_t/ΔT_f)ⁿ (f_f/f_t)^m exp[(E_a/k)(1/T_max,f − 1/T_max,t)], temperatures in kelvin, with n = 1.9, m = 1/3 and E_a/k = 1414 K for eutectic SnPb. It is the acceleration equation referenced by JEDEC JESD47 and JESD94. For SAC solder, Pan et al. (2005) fitted n = 2.65, m = 0.136 and E_a/k = 2185 K to CBGA, CSP and TSOP tests; Vasudevan and Fan (2008) fitted 17 industry data pairs and found the SnPb constants adequate (n = 1.9, m = 0.33, E_a/k = 1414 K), with a mean error under 6 %. The tool shows all three. When the test board has a different CTE from the product board the plain ΔT ratio understates the test's severity; the tool then applies the equation to the strain driver Δα ΔT_e, as the distance-to-neutral-point form of the equation used at JPL scales ΔT by the DNP for a changed package, and prints the plain ΔT value for comparison. Neither constant set contains the geometry, so Norris-Landzberg cannot predict a life without a test result; it compares two cycles of the same assembly.

Test cycles that stand for the design life

The mean field life the product needs is N / w_x with w_x the Weibull factor from the median to the x % life. Carried to the test condition by eq. 12 it becomes the equivalent mean test cycles N(test, 50 %), the quantity tabulated in IPC-SM-785 Table 2 for the handbook's use categories; divided by the test's cycles per day it gives the test duration. A test does not have to run until half the samples fail: eq. 17 gives the failure-free cycles that confirm the failure fraction x at the design life with n individually monitored samples, N(test, n) = N(test, 50 %) [ln(1 − 1/n) / ln 0.5]^1/β (0.46 N(test, 50 %) for 32 leadless samples, 0.21 for 32 leaded samples). The Norris-Landzberg plan divides the required mean field life by AF_NL instead. A measured median test life is carried the other way: first corrected for the daisy-chain partition (eq. 16, N_f(component) = N_f(chain) (1/m)^1/β, where m is the number of monitored partitions per component, or 1/k for a chain of k components), then transformed to the field by eq. 12 and multiplied by w_x.

The default case

The default inputs are the step-by-step example of IPC-SM-785 Appendix A: a CC1820 chip capacitor (α_C = 6.8 ppm/°C, L_D = 0.080 in, h = 0.005 in, F = 0.7, β = 4) on a low-CTE board (10.5 ppm/°C) in a Navy computer that cycles daily between 25 and 85 °C (t_D = 715 min) for a 10-year life (N = 3,650) at 0.5 % acceptable failures, tested on an FR-4 board (16.0 ppm/°C) at 0 to 100 °C with 15-minute dwells, 24 cycles per day. The handbook prints Δα = 3.7 ppm/°C, N_f(50 %) = 73,000 and N_f(0.5 %) = 21,400 cycles for this swing (149,000 and 43,300 for its 45 to 85 °C swing), a test life of 6,310 cycles for chains of 8 capacitors, 10,612 per component, and the same 73,000 and 21,400 cycles when that test result is carried to the field; the page reproduces each of these. The handbook's leaded example (a 68 I/O LCCC with K_D = 52 lb/in, L_D = 0.674 in, A = 6 × 10⁻⁴ in², dissipating 0.8 W so that the component runs 8 °C above the board) is reproduced in the tool's test script; the handbook prints its joint area as 6 × 10⁻⁶ in², a misprint, since its printed lives follow only from 6 × 10⁻⁴ in².

Limits

The model is for uncoated attachments of near-eutectic SnPb solder, the lead-free parameters being tentative. IPC-SM-785 lists its caveats: lives below about 1,000 cycles, strain ranges above about 10 %, leads stiffer than about 500 lb/in, temperatures outside the range of Wild's tests (the exponent extrapolates below room temperature and above 125 °C), and very short dwells are outside the fitted range; the tool prints a note when a case reaches one of them. The model treats the joint as a column of uniform shear strain and ignores the fillet, the pad size and the board's local stiffness (later strain-energy models such as Blattau's add them), takes the cycle as a steady state (vibration, shock and thermal transients are separate analyses), and the Norris-Landzberg constants for lead-free solder remain a matter of published disagreement. For a given design the test result, carried to the field by the transform, is better evidence than the model's own prediction: in the handbook's example the two agree within 1 %, but Engelmaier's F factor exists to absorb the difference.