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.

An investigation of austenite grain growth (AGG) during the isothermal heat treatment of low-alloy steel is conducted. The goal is to uncover the effect of time, temperature, and initial grain size on SA508-III steel grain growth. Understanding this relationship enables the optimization of the time and temperature of the heat treatment to achieve the desired grain size in the studied steel. A modified Arrhenius model is used to model austenite grain size (AGS) growth distributions. With this model, it is possible to predict how grain size will change depending on heat treatment conditions. Then, the generalized reduced gradient (GRG) optimization method is employed under adiabatic conditions to characterize the model’s parameters, providing a more precise solution than traditional methods. With optimal model parameters, predicted AGS agree well with measured values. The model shows that AGS increases faster as temperature and time increase. Similarly, grain size grows directly in proportion to the initial grain size. The optimized parameters are then applied to a practical case study with a similar specimen size and material properties, demonstrating that our approach can efficiently and accurately predict AGS growth via GRG optimization.

An implicit, elastoplastic, finite element method (FEM) with multi-body treatment function was applied to accurately analyze the real-world shaft clinching of a duplex-pair tapered roller (DPTR) wheel-bearing unit (WBU) under minimal assumptions during modeling. The inner races were viewed as elastoplastically deformable and were fitted to the hub shaft before clinching by imposing a thermal load reflecting the mechanical load of press-fitting. The forming roller (i.e., the power source) was considered to be force-prescribed, similar to the approach on real shop floors. The predictions focused on the homogenizing stage, during which the two inner races bear the preload. At this time, local plastic deformation occurred at the end of the hub shaft and in the armpit area and the cavity was either maintained or enlarged. The predicted cavity size in case of force-prescribed forming roller increased, compared with the velocity-prescribed forming roller. The residual stress became axisymmetric and was divided into two parts by the cavity. These findings allow engineers to control the pre-stresses imparted to the inner races of tapered roller bearing assemblies.

In this paper, elastic, rigid-viscoplastic and elastoplastic finite element analyses of typical metal forming processes or structural problems of multi-body cases occurring in metal forming are conducted to present their mechanical characteristics together with validation of the numerical approaches. Theoretical backgrounds are briefly introduced with an emphasis on the contact condition treatment of moving or deformable bodies. The application problems in metal forming are classified into three categories namely typical multi-deformable body case, mechanically coupled case between material and dies and bonded material group case. Mechanics of overloaded ball bearing problem, typical assembling processes, coupled material and dies problem, bolt-and-nut assembling process, composite material forming, and structural analysis problem of assembled die are solved. The predictions are discussed to validate their accuracy and to extract valuable engineering insights.

Control of carbide morphology during heat treatment plays a decisive role in achieving stable dimensions, improved cutting performance, and reliable mechanical properties in precision steel components. In this work, a computational approach is developed to analyze the spheroidization behavior of cementite in eutectoid Fe-0.8 wt.% C steel subjected to cyclic thermal processing. The model, implemented within a finite element method (FEM) framework, links the transient local temperature history to temperature-dependent spheroidization kinetics. The kinetic formulation is physically motivated by established mechanisms of cementite spheroidization, including carbon diffusion and curvature-driven reduction of interfacial energy; however, carbon concentration and interface curvature are not explicitly solved as independent FEM field variables. Instead of relying on empirical correlations, the transformation kinetics are described through physically based rate equations that account for temperature dependence and accumulated thermal exposure. A morphology evolution parameter is introduced to quantitatively represent the transition from lamellar pearlite to spheroidal carbide particles during repeated heating cycles. Numerical predictions indicate that cyclic reheating enhances the transformation rate due to progressive lamella fragmentation and increased interfacial stability, leading to accelerated approach toward equilibrium morphology. The simulated evolution trends are consistent with reported experimental behavior, confirming the validity of the modeling strategy. This study demonstrates the feasibility of integrating microstructural kinetics into process simulation platforms, providing a practical tool for optimizing heat-treatment schedules in precision manufacturing applications while minimizing experimental iterations.