Jumping Over Thermal Cycles Accelerates Thermomechanical Fatigue Simulations

Although you are probably not aware of them, dozens of electronic control units (ECUs) — printed circuit boards (PCBs) in metal or plastic housings — exist in your car to control and monitor the operation and safety of your vehicle’s many control systems. These units must work for the lifetime of your car, during which time they are subjected to many heating and cooling cycles. The most obvious cycle occurs when you start your car after it has cooled at night. It heats up as the car runs and then cools again when you shut it off. That’s one “ambient” temperature cycle.

Additional so called “active” thermal cycles can occur locally within specific electronic components on the PCB. For instance, a MOSFET transistor draws a lot of current and heats up the PCB near its location, causing additional thermal cycling. These complex temperature distributions can cause local thermomechanical strain because differences in temperature across the PCB result in differential expansion of the board. Because the board is constrained by its housing, this can lead to bending of the board, putting additional strain on the solder joints that connect the components to the board. If one solder joint fails, it can have a domino effect as the stress that the failed joint once absorbed is transferred to nearby solder joints. This can affect the reliability of the whole system.

In order to support the ECU reliability design, physical temperature cycling of ECUs in climate chambers is preceded with ECU simulation in early design phase. While simulation is clearly the more efficient method, until recently it had many limitations. The widely used power law based approach — simulation of only few cycles and prognosis of solder joints lifetime — has many shortcomings, where no absolute lifetime prediction or the damage driven load relocation and its nonlinear evolution are captured. Youssef Maniar and Marta Kuczynska, engineers at Robert Bosch GmbH in Germany, have developed an accurate nonlinear damage model able to predict absolute lifetime of solder connections. The problem they faced, absolute lifetime prediction, involves simulation of all cycles imposed to the components, and the computational effort is therefore extensive. Then, about two years ago, they read an academic paper that described a way to “jump” over some cycles to accelerate simulation. They approached Ansys about implementing this innovative calculation method into Ansys Mechanical, and Ansys was happy to do so.

“We are now saving two-thirds of our CPU time to simulate a lifetime of thermal cycles without sacrificing accuracy,” says Maniar, corporate research and advance engineering at Bosch.

Cyclic jump simulation.

The basics of the “jump”

The mathematics behind the ability to jump over a large number of simulated thermomechanical cycles to dramatically accelerate the simulation time without sacrificing accuracy is involved, but the software essentially looks at the slope or “gradient” of certain solution variables (e.g., stress) versus time plot on the fly to determine when it can skip over the next n number of cycles. The maximum value of n must be defined by the simulation engineer before the run. The simulation engineer also inputs other parameters beforehand to impose limits on the software to optimize the run.

“The software is deciding the jump size on its own based on the evolution of internal variables, but it still needs controlling inputs from the user,” says Kuczynska, a reliability simulation engineer at Bosch Automotive Electronics. The software must calculate at least three intermediate cycles between jumps, but this number can be adjusted by the simulation engineer. “So, the algorithm performs the jump and then calculates user defined number of consecutive cycles to estimate the slope again to determine whether to keep simulating cycles or allow another jump.”

The gradient of the data indicates whether the system is stable at that point or changing rapidly. If it is changing rapidly, simulating more intermediate cycles is essential. If it is stable, another jump might be beneficial in speeding up the simulation.

The simulation engineer has to understand the system to decide the proper ratio of simulated cycles to skipped cycles, which can involve some trial and error in the beginning.

“If the load amplitude is not very high you can allow the jump algorithm to skip many more cycles,” Kuczynska says.

Implementing the “jump”

Initially, Bosch engineers took the initiative to implement the jump themselves by writing their own algorithms. It was a successful proof-of-concept, but it was not user-friendly. Basically, it involved running the simulation in Ansys Mechanical, then leaving the Ansys platform, performing the jump in the Bosch software, then restarting the simulation in Mechanical again.

“This version was just for testing purposes,” Kuczynska says. “How is it working? Should this be the strategy we use to increase the numerical efficiency?”

Once they had determined that the new method was working, they approached Ansys about incorporating it into Mechanical. The Ansys team jumped at the opportunity.

Two years and two algorithms later, the jump capability is part of the commercial release of Mechanical. The first algorithm produced was not optimal, so the Bosch and Ansys teams continued to work together until they got it right. The second algorithm was exactly what they wanted.

“We had two years of great discussions with Ansys, going back and forth to fine-tune the algorithm so that it worked as we envisioned it,” says Maniar. “It was very important to have this conversation on a high technical level between Bosch and Ansys engineers.”

Kuczynska is especially impressed with the resulting algorithm after comparing the “jumped” results with simulation of full loading history.

“I’m astonished how intelligent the jump is,” she says. “Skipping over a large number of thermal cycles is bound to introduce some error because we are performing an extrapolation. But after those consecutive cycles that it calculates afterwards, the software converges to the full simulation results and we see that the accuracy of the prediction is really astonishing.”

Future applications

Having demonstrated that the jump technique works for predicting the operational lifetime of solder joints in automotive applications due to thermomechanical fatigue, Bosch engineers are eager to extend the technique to predict other damage mechanisms. Materials experience a continuous change in properties over time and temperature cycles, including other aging processes, such as thermal induced oxidation of polymers, that can lead to stiffening and deterioration of electronic components.

“This simulation technique could be used to predict any cyclic nonlinear material evolution within the system,” Kuczynska says. “It triggers the development of new methods. I mean, previously we never dreamed about being able to target simulation based absolute lifetime prognosis of different kinds of cyclic aging mechanisms. Now we have that chance.”

The jump technique will also be valuable for new automotive applications under development.

“Due to autonomous driving and the electrification of the automobile industry, we are encountering new load cases and lots of innovative components,” Maniar says. “This means we have new electronic systems to investigate and having an accelerated simulation testing method like this will be even more important to the development process.”

Maniar and Kuczynska, along with colleagues Alexander Kabakchiev and Masoomeh Bazrafshan at Bosch and Peter Binkele and Siegfried Schmauder at the Institute for Materials Testing, Materials Science and Strength of Materials at the University of Stuttgart, Germany, have published a paper describing their findings titled “Nonlocal Damage Modeling of Solder Joint Failure Under Thermomechanical Cyclic Loading” as part of the Proceedings of the ASME 2021 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems.

Bosch and Ansys are currently working together on a technical paper describing this new cycle jump technique for publication in a journal, so others can benefit from this innovative simulation technique.