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Effects of thermal misfit strains on dielectric features for sandwich structural barium strontium titanate (BST) thin films on metal plates were investigated via a modified thermodynamic model. When TEC of substrates is closer to that of BST, larger permittivity and tunability can be received. The tendency of permittivities and tunabilities of such films as a function of TEC of substrates agrees with that of single compositional BST films and compositionally graded BST multilayer films. The highest tunability reaches 60% at the biasing field of 300 kV/cm when the films are onto Ti metal. Moreover, Ba[Formula: see text]Sr[Formula: see text]TiO3/Ba[Formula: see text]Sr[Formula: see text]TiO3/Ba[Formula: see text]Sr[Formula: see text]TiO3 structure can obtain higher tunability than Ba[Formula: see text]Sr[Formula: see text]TiO3/Ba[Formula: see text]Sr[Formula: see text]TiO3/Ba[Formula: see text]Sr[Formula: see text]TiO3 structure, while Ba[Formula: see text]Sr[Formula: see text]TiO3/Ba[Formula: see text]Sr[Formula: see text]TiO3/Ba[Formula: see text]Sr[Formula: see text]TiO3 films show better compatible composition range for relatively larger tunability. Dielectric properties of sandwich-like BST films in some references can also be analyzed based on our calculated results.

Misfit strain, polarization, permittivity, and tunability of Ba x Sr1−x TiO3 (BST) thin films on various substrates with varied buffer layers are calculated by a modified thermodynamic model. The lattice parameters of the LaAlO3 (LAO), CaTiO3 (CT), BaZr0.25Ti0.75O3 (BZT), and MgO buffer layers grow consecutively as does the thermal expansion coefficient (TEC) of the Si, Ti, Ni, and stainless steel (SS) substrates. When the TEC of substrates is bigger (such as Ni, SS) than that of the films, introducing buffer layers with larger lattice parameters (such as BZT, MgO) can improve the permittivity and tunability. Conversely, inserting buffer layers with smaller lattice parameters (such as LAO, CT) can enhance the dielectric response when the TEC of substrates is smaller (such as Si, Ti) than that of the films. The relationship between the TEC of substrate and the lattice parameter of buffer layer is primarily linear for achieving high tunability. According to several references, introducing LaNiO3 buffer layers can significantly increase the tunability of BST solid solutions prepared on Si‐based substrates, which is in line with the estimated rule. This law offers a guide for choosing the best substrate and buffer layer when producing BST films with strong dielectric response.

Misfit strain, lattice parameter, polarization, permittivity, and tunability of Ba[Formula: see text]Sr[Formula: see text]TiO3 thin films onto Ba[Formula: see text]Sr[Formula: see text]TiO3-buffered stainless steel (SS) substrates are computed via a modified phenomenological model. When the Ba/Sr ratio of Ba[Formula: see text]Sr[Formula: see text]TiO3 buffer layer grows, the permittivity and tunability first increase and then decrease with the maximum at [Formula: see text] = 0.75. The highest tunability of such films prepared by the sol-gel technique can reach 32.5% at the electric field of 320 kV/cm when [Formula: see text] = 0.8. The strains are qualitatively analyzed through combining XRD, Raman, and theoretical calculation. The computed data are generally supported by experimental lattice parameters, permittivities, and tunabilities, which show that polycrystalline BST thin films with smaller compressive strain obtain higher dielectric response, and that inserting buffer layer could regulate the strains and dielectric properties of BST thin films.

Cold roll forming, as a metal plastic forming process, is still mainly used in industrial production by the trial-and-error method, which wastes a lot of time and materials. In this paper, the C-channel steel is taken as the research object. First, the empirical equations of forming passes are verified and analyzed, then the cold roll forming model of C-channel steel is established, the forming quality of each pass and the stress-strain distribution of the whole sheet metal are analyzed, and the validity of the model is verified by experiments. The residual stresses of the web zone and flange of the finished product were measured. The results show that the empirical formulas are still not universal and the forming quality of the bite zone is poor. It needs to be adjusted by improving the distribution of deformation. The external surface of the C-channel steel is undertensile stress, while the internal surface is undercompressive stress, and the residual stresses of the flange are far greater than those of the web zone. The research provides a reference for the design of the bite zone and the number of forming passes.