Thermal Fatigue of a Surface Mount Resistor

A surface mount resistor is subjected to thermal cycling. The difference in the thermal expansion between the materials introduces thermal stresses in the structure. The solder, connecting the resistor to the printed circuit board, is seen as the weakest link in the assembly. Because the operating temperature is high when compared to the melting point of the solder, creep deformation occurs. In order to ensure the structural integrity of the component, a fatigue analysis is performed where the life predictions from two different fatigue models are compared.

Model Definition

A resistor is fastened on a printed circuit board (PCB) with SnAgCu solder. The solder is connected to the printed circuit board through two copper pads and to the resistor through a NiCr conductor. In reality there are additional thin films around the resistor but they are disregarded in current analysis. A sketch of the surface mount assembly is shown in Figure 1.

Figure 1: Schematic description of the surface mount resistor.

The resistor is made out of alumina and has dimensions 3.2 mm x 0.55 mm. It is covered on both edges with a 0.025 mm layer of NiCr conductor. The thin layer continues 0.325 mm along the lower and the upper side of the resistor. The printed circuit board is large in comparison with the resistor and is here modeled 0.8 mm thick. It has two copper pads on the top side that are 0.025 mm thick and 1.05 mm wide. The thickness of the solder fillet between the copper pads and the NiCr conductor is 0.05 mm. The remaining shape of the solder joint varies greatly between each examined solder joint and is here modeled with two representative roundings.

Because the out-of-plane dimension is 1.55 mm, which is significant in comparison with the size of the resistor, the model is simulated in 2D, assuming plane strain conditions.

The elastic properties of the materials are summarized in Table 1.

Table 1: Elastic and thermal material properties.
Material	Young’s Modulus (GPa)	Poisson’s ratio	Coefficient of Thermal expansion (ppm/°C)
PCB laminate	22	0.4	21
Copper	141	0.35	17
SnAgCu	50	0.4	21
NiCr	170	0.31	13
Alumina	300	0.22	8

The SnAgCu solder material exhibits creep behavior, which can be modeled by a Garofalo model where creep rate is described with

(1)

where

is the creep strain tensor, T is the temperature, σe is the equivalent stress, R is the universal gas constant, and sij is the deviatoric stress tensor.

The thermal load during an operating cycle is prescribed as a temperature which varies between 20 °C and 70 °C. Each temperature change takes 2 minutes and is followed by a 3 minutes dwell. This means that one fatigue cycle requires 10 minutes, see Figure 2.

Figure 2: Temperature load.

Since the solder material is nonlinear, see Equation 1, simulation of several cycles may be required before a stable cycle is obtained.

Two fatigue models are evaluated. The first is a strain-based Coffin-Manson type model with the equivalent creep strain as the damage controlling mechanism, and the second is an energy-based Morrow type model with the dissipated creep energy as the damage controlling mechanism. The material constants for the Coffin-Manson model are εf’=0.281 and c=-0.51. The material constants for the Morrow type model are Wf’=55.0 J/m3 and m=-0.69.

Results and Discussion

The difference in the elastic and thermal properties introduces thermal stresses in the device. Although they are not very high, the solder experiences significant inelastic strains. In Figure 3 accumulated equivalent creep strain after six cycles is shown.

Figure 3: Creep strains in the solder joint.

The highest strains occur in the thin solder layer just below the resistor. It is mainly the shear strain component which contributes to the equivalent creep strain in that layer. The slightly higher values around the edge are also affected by modeling of a sharp corner. With a fillet instead, the strains will be somewhat lower. Nevertheless, the location of highest strain agrees well with the crack path in real applications.

In order to evaluate fatigue, it is important to obtain a stable load cycle. In applications involving solder joints, either inelastic strain or dissipated energy are typically used to predict fatigue. The change of creep strain during the first six cycles is therefore evaluated at a point just below the resistor, slightly shifted to the right form the sharp corner. The position of this point can be debated. It is however located in the area where the largest strains occur, and is therefore seen as the critical point. In Figure 4, the equivalent creep strain and the shear creep strain components are shown.

Figure 4: Creep strain development in a critical point below the resistor.

The dissipated energy represents a combined contribution of changes in stresses and strains during a cycle and is in Figure 5 shown with a shear hysteresis. The shear component has been chosen since it gives the dominating contribution to the equivalent creep strain in the critical point.

Figure 5: Shear hysteresis evaluated in a critical point just below the resistor.

It is clear from the two last figures that the first cycle is not representative for fatigue analysis, since its response differs significantly from the one experienced in the following cycles. Even after six cycles, the stress-strain loop has not stabilized. The temperature cycling can by extended with additional cycles to evaluate whether the state stabilizes further or not. Under some conditions, it may happen that the hysteresis loop is moving in stress-strain space. In this example additional cycles are not simulated since the difference in the creep strain and the dissipated energy between cycle five and six is small. Assuming that the consecutive cycles follow the trend and deform less as, well as dissipate less energy, the fatigue analysis based on the results of the sixth cycle gives a conservative fatigue prediction.

The fatigue life based on the Coffin-Manson model is shown in Figure 6, and the fatigue life based on the Morrow model is shown in Figure 7.

Figure 6: Fatigue life based on the creep strain.

Figure 7: Fatigue life based on the dissipated energy.

Fatigue based on strain gives lifetime of about 800 cycles, while the energy prediction gives 1400 cycles.

Fatigue_Module/Energy_Based/surface_mount_resistor

Modeling Instructions

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Geometry 1

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Interpolation 1 (int1)

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Browse to the model’s Application Libraries folder and double-click the file surface_mount_resistor_thermal_load_cycle.txt.

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Argument	Unit
t	min

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Function	Unit
thermLC	degC

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Materials

PCB

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Property	Variable	Value	Unit	Property group
Young’s modulus	E	22[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.4	1	Young’s modulus and Poisson’s ratio
Density	rho	0	kg/m³	Basic
Coefficient of thermal expansion	alpha_iso ; alphaii = alpha_iso, alphaij = 0	21e-6	1/K	Basic

Copper

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Property	Variable	Value	Unit	Property group
Young’s modulus	E	141[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.35	1	Young’s modulus and Poisson’s ratio
Density	rho	0	kg/m³	Basic
Coefficient of thermal expansion	alpha_iso ; alphaii = alpha_iso, alphaij = 0	16.6e-6	1/K	Basic

Solder

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Property	Variable	Value	Unit	Property group
Young’s modulus	E	50[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.4	1	Young’s modulus and Poisson’s ratio
Density	rho	0	kg/m³	Basic
Coefficient of thermal expansion	alpha_iso ; alphaii = alpha_iso, alphaij = 0	21e-6	1/K	Basic
Creep rate coefficient	A_gar	262000	1/s	Garofalo (hyperbolic sine)
Reference stress	sigRef_gar	39.1[MPa]	N/m²	Garofalo (hyperbolic sine)
Stress exponent	n_gar	6.19	1	Garofalo (hyperbolic sine)

NiCr

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Property	Variable	Value	Unit	Property group
Young’s modulus	E	170[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.31	1	Young’s modulus and Poisson’s ratio
Density	rho	0	kg/m³	Basic
Coefficient of thermal expansion	alpha_iso ; alphaii = alpha_iso, alphaij = 0	13e-6	1/K	Basic

Alumina

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Property	Variable	Value	Unit	Property group
Young’s modulus	E	300[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.22	1	Young’s modulus and Poisson’s ratio
Density	rho	0	kg/m³	Basic
Coefficient of thermal expansion	alpha_iso ; alphaii = alpha_iso, alphaij = 0	8e-6	1/K	Basic