We focus on the importance of accurately describing the flow behaviors of metallic materials to be cold formed; we refer to several valuable examples. We review the typical experimental methods by which flow curves are obtained, in addition to several combined experimental-numerical methods. The characteristics of four fundamental flow models including the Ludwik, Voce, Hollomon, and Swift models are explored in detail. We classify all flow models in the literature into three groups, including the Ludwik and Voce families, and blends thereof. We review the experimental and numerical methods used to optimize the flow curves. Representative flow models are compared via tensile testing, with a focus on the necking point and pre- or post-necking strain hardening. Several closed-form function models employed for the non-isothermal analyses of cold metal forming are also examined. The traditional bilinear C-m model and derivatives thereof are used to describe the complicated flow behaviors of metallic materials at cold forming temperatures, particularly in terms of their applications to metal forming simulations and process optimization.

A practical method for adjusting and optimizing isothermal transformation (IT) diagrams using the Jominy test is presented. The method is based on a finite-element optimization procedure, which iteratively minimizes the error between the target phase fractions and the corresponding finite-element solutions at the sample points using an optimization tool. A standard Jominy test of AISI 52100 bearing steel is used to investigate the feasibility and reliability of the method. Three optimization parameters for each IT diagram curve are mathematically applied to the modified Kirkaldy model. These parameters are the design variables in the optimization. The curves obtained from the modified Kirkaldy model are used as the initial guesses in the optimization and they approach the experimental IT diagram by minimizing the error. Good agreement is observed between the optimized diagram and the experimental diagram reported in the literature. The predicted phase fractions using the experimental IT diagram, the IT diagram obtained from the modified Kirkaldy model, and those obtained from the optimized model are compared and demonstrate that the adjustment or optimization procedure significantly improves the accuracy of the predicted phase fraction of the model. The applicability of the method is investigated in a practical case study.

In this study, plastic flow behaviors of aluminum alloys at elevated temperatures are studied to establish the engineering foundation of hot metal forming of aluminum alloys. Various material models of characterizing the flow behaviors for metal forming application are introduced and they were evaluated, comparing the experimental flow curves with the fitted flow curves (of Arrhenius model, improved Johnson-Cook model and Hensel-Spittel model and its variant) found from the related literature together with flow curves of the piecewise bilinear C-m model (power law model), the Ebrahimi et al. model and improved Ebrahimi et al. model (called PLF model). It has been shown that the accuracy of flow stress modelling is much dependent on the number of material constants and that the piecewise bilinear C-m model is the most attractive in terms of accuracy as well as practicability.

A study on the optimal design of preforms has previously been actively conducted as a method to solve defects such as voids and flash in forged products. However, previous research has generally been performed through deterministic optimization for ideal cases that do not take manufacturing tolerances into account. As a result, the application of such optimal designs in actual processes may be limited due to various factors such as material manufacturing tolerances and the machining environment of preforms. Therefore, this study conducted reliability-based optimization considering tolerances in billets and preforms. The objective of the study was to optimize the design of a bearing hub and minimize defects in the final product. When comparing deterministic optimization and reliability-based optimization, the former showed relatively superior results in terms of defect indicators but had a higher occurrence of voids and lower forming loads, increasing the probability of void occurrence. On the other hand, the reliability-based optimization showed relatively lower performance in quality improvement indicators, but it successfully met the target reliability of 99% by reducing the probability of defect occurrence. These results were derived using an approximate model based on the Kriging method, providing an optimal design that is practical and effective in actual manufacturing processes.