Solving systems of nonlinear equations is perhaps one of the most difficult problems in all of numerical computations, especially in a diverse range of engineering applications. The convergence and performance characteristics can be highly sensitive to the initial guess of the solution for most numerical methods such as Newton’s method. However, it is very difficult to select reasonable initial guess of the solution for most systems of nonlinear equations. Besides, the computational efficiency is not high enough. Aiming at these problems, an improved particle swarm optimization algorithm (imPSO) is proposed, which can overcome the problem of selecting reasonable initial guess of the solution and improve the computational efficiency. The convergence and performance characteristics of this method are demonstrated through some standard systems. The results show that the improved PSO for solving systems of nonlinear equations has reliable convergence probability, high convergence rate, and solution precision and is a successful approach in solving systems of nonlinear equations.

Nickel-based superalloys are widely used in thermal power, nuclear power, aerospace and other fields due to their excellent properties. Since the deformation resistance of Ni–Cr–Co superalloy is large and the forming range is narrow, the hot deformation behavior of Ni–Cr–Co superalloy was studied by hot compression experiments on a Gleeble-3800 under different deformation conditions (deformation temperature: 950–1200 °C, strain rate: 0.01–10 s⁻¹, and deformation: 60 %). The modified Johnson–Cook, modified Zerilli–Armstrong and strain compensated Arrhenius models were constructed based on the stress–strain curves corrected for friction and temperature. The correlation coefficient (R) and average absolute relative error (AARE) were compared to verify the accuracy of the model. The results showed that the strain compensated Arrhenius model had high accuracy, the modified Zerilli–Armstrong had high accuracy in predicting the flow behavior above 1100 °C, while the modified Johnson cook had high accuracy only under the reference conditions. Electron back-scattered diffraction analysis showed that high-angle grain boundaries formed when the low-angle grain boundaries piled up to a certain extent, which is beneficial for refining the as-cast microstructure, and the increase in strain rate was beneficial for refining the microstructure and promoting the occurrence of recrystallization.

The viscoplastic self‐consistent (VPSC) model is used to establish a combination of different deformation mechanisms. By using this model, axial tension and compression tests of extruded AZ31 magnesium alloy at room temperature are simulated. The influence of secondary deformation mechanism (prismatic <a> slip, pyramidal <c + a> slip, and compression twin) on mechanical response and texture evolution is expounded. Increased activity of the prismatic <a> slip is conducive for the improvement of flow stress in mechanical response during axial tension and for the splitting of pole densities in the {0002} pole figure during axial compression. However, increased activity of the pyramidal <c + a> slip causes the basal texture to transfer to the extrusion direction in the {0002} pole figure during axial compression. The compression twinning has a negligible influence on the plastic deformation and mechanical response of AZ31 magnesium alloy during axial tension and compression. However, the compression twinning should be included in VPSC modeling to predict the texture evolution accurately.

Cuboid samples with significant initial texture differences were cut from extruded AZ31 Mg alloy samples, whose long axis and bar extrusion direction ED were 0° (sample E0), 45° (sample E45), and 90° (sample E90). The relationship among the initial texture, deformation mechanism, mechanical properties, and texture evolution of the AZ31 Mg alloy was investigated systematically using a compression test, microstructure characterization, and the Viscoplastic Self-Consistent (VPSC) model. Results revealed a close relationship among them. By influencing the activation of the deformation mechanism, the deformation under different initial textures resulted in obvious mechanical anisotropy. Compared with E0 and E90, the initial texture of E45 was more conducive to the improvement of reforming ability after pre-compression. Meanwhile, the initial texture significantly affected the microstructure characteristics of the material, especially the number and morphology of the {10–12} tensile twins. Texture results showed that the priority of deformation mechanism depended on the initial texture and led to the difference in texture evolution.

In order to analyze the influence of technical parameters on work roll axial force of four-high continuous variable crown (CVC) mill, the deformation analyzing model with top roll system and strip was established based on influence function method. Then a CVC work roll curve designing scheme was proposed and it was carried out on some cold rolling mill considering the requirement of comprehensive work roll axial force minimization. The status of comprehensive work roll axial force is improved considering the rolling schedule that is beneficial to the roller bearing. Corresponding to the newly designed work roll contour, the backup roll end chamfer was designed considering comprehensive performance of interroll stress concentration, comprehensive work roll axial force, and strip shape control ability. The distribution of roll wear with newly designed backup roll contour is more even according to the field application data. The newly established roll configuration scheme is beneficial to four-high CVC mill.