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Cyclic mechanical behavior of thin layers of copper: A theoretical and numerical study

In printed circuit boards, thin copper layers are used as current paths. During the thermal loading of printed circuit boards, stresses arise due to the different coefficients of thermal expansion of the used materials. To be able to model the mechanical behavior of printed circuit boards under cyclic thermal loads, cyclic mechanical tests of thin copper foils under changing tensile and compression loads at different temperatures were conducted. From these experiments, the isotropic and kinematic hardening parameters were determined serving as material input data for a nonlinear isotropic/kinematic hardening model in the finite element analysis-software Abaqus. The kinematic hardening parameters were fitted in an optimization process. The isotropic hardening variables were determined based on the stress versus plastic strain relationship that was constructed incrementally from the available individual cycles. The so-obtained curve was found to be not unique, but to depend on the loading situation. Hence, different approaches for strain range memorization were evaluated. Since these approaches were developed for modeling strain-controlled tests, whereas the experimental data were obtained in a force-controlled way, a phenomenological formulation was developed and applied. The results of curvature measurements during thermal cycling were used for model validation. The experimental results and the numerical predictions are in good agreement.