The goal of the present work is to identify and model the elastic-viscoplastic behavior of electrodeposited copper films under tension-compression loadings. From the experimental point of view, as proposed in the literature, a film of copper is electrodeposited on both sides of an elastic compliant substrate. The overall specimen is next subjected to tensile loading-unloadings. As the substrate remains elastic, the elastic-plastic response of copper under cyclic loading is experimentally determined. A clear kinematic hardening behavior is captured. To model the mechanical response, a new elastic-viscoplastic self-consistent scheme for polycrystalline materials is proposed. The core of the model is the tangent additive interaction law proposed in (Molinari, 2002). The behavior of the single grain is rate dependent where kinematic hardening is accounted for in the model at the level of the slip system. The model parameters are optimized via an evolutionary algorithm by comparing the predictions to the experimental cyclic response. As a result, the overall response is predicted. In addition, the heterogeneity in plastic strain activity is estimated by the model during cyclic loading.
The elastic orthotropic behavior of thin woven composites is studied combining a numerical and experimental strategy. For thin materials, in-plane properties are measured by classical tensile tests and digital image correlation. The out-of-plane properties are derived performing finite element simulations at the level of the internal structure of the laminate. Indeed, the glass fiber arrangement in the yarn and the weaving pattern are defined based on microtomography and SEM observations. So a representative unit cell is found. A statistical approach is further proposed to derive the behavior of the warp and fill yarns, since the fiber position may fluctuate between yarns. For the considered laminate, the matrix (resin and ceramic inclusion) behavior is unknown and difficult to measure. Therefore an inverse method is proposed. By comparing with measured in-plane elastic moduli, behaviors of the matrix, of yarns and of the laminate are defined. The present homogenization strategy is exemplified by laminates used in printed circuit boards for high frequency applications. This approach has also been applied to investigate the evolution of the elastic moduli of the laminate with temperature. Those information, usually not available in the literature, are important when dealing with reliability of printed circuit boards during thermal cycles.
The elastic-plastic and low-cycle fatigue behaviors of copper films are studied experimentally and identified for further simulation works. A rolled annealed copper grade is considered here, as it is often used in flexible printed circuit boards for its mechanical resistance to high elongations. During operation, the printed circuit board (PCB) will undergo various loadings, whether purely mechanical or environmental. These loadings can lead to the fracture of copper and thus to the disconnection of the electrical signal in the PCB. Copper has a low yield stress, so it undergoes easily plastic deformation. In the present work, a predominant kinematic hardening has been observed experimentally and modeled with the combined hardening model of Lemaitre-Chaboche. The fatigue behavior has been identified on cyclic loadings at different strain amplitudes. A Coffin-Manson model has been adopted to reproduce experimental data. Identified behaviors have been introduced in a numerical simulation of a flexible PCB under cyclic bending/reverse bending, in order to estimate its mechanical reliability.
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