If the temperature gradient inside the solid at the heat transfer surface is determined from experimental measurements, the heat flux can be calculated as a product of the thermal conductivity of the solid and the temperature gradient at the surface. Due to the practical difficulty involved in the exact measurement of surface temperature or surface temperature gradient, it has been suggested that the surface conditions be estimated from temperature measurements made at some convenient point inside the solid. Such a problem is termed the inverse problem of heat conduction, wherein the temperature history at an interior point is prescribed and the surface conditions are calculated from the solution of the transient heat conduction equation satisfying the prescribed interior conditions. This is in contrast to the direct problem of heat conduction, where the boundary conditions are prescribed at the surfaces and the interior conditions are calculated.

For a novel friction welding process, the objective was to calculate the surface heat flux evolution, q(t), at the friction surface using the temperature measurements during the welding experiment at a place away from the interface. The inverse problem was solved by minimizing an objective function, the least-squares of norms of measured and predicted temperature vectors.

Comparison between capabilities and model requirements of two thermal models: Inverse method and Friction theory

By a 3-D coupled thermo-mechanical finite element (FE) model, the temperature profile, axial shortening and flash formation at the joint interface of a novel friction welding process was analyzed. With a thermal phase transformation FE model, the volume fractions of the final microstructure constituents and the size of the heat affected zone (HAZ) were also predicted. The predicted HAZ width, upset, thermal history, and final microstructure are verified successfully on the experimental measurements.

Based on the estimated heat generation obtained from an inverse heat transfer analysis, two FE simulations are carried out. First, in the coupled thermal-mechanical FE model, the peak (interface) temperature, thermal history, flash formation and axial shortening are successfully analyzed. Then, with the thermal phase transformation FE analysis, the final microstructure constituents after welding and the size of the HAZ are predicted.

The phase field approach is an attractive mesoscale method for modeling different types of microstructure evolution processes, including austenite decomposition. A particular advantage of phase field models (PFMs) is that they can easily handle time-dependent growth geometries with complex pattern formations making PFMs a powerful modeling technique to simulate microstructure evolution with complex morphologies, e.g., banded structures. A challenge in PFMs is the simulation of the nucleation of a new phase. Several attempts have been made in order to incorporate nucleation into the phase field formulation.

Microstructural banding is a phenomenon that is of increasing concern in advanced high strength low-carbon steels because of higher alloying levels. The phenomenon has been known for more than half a century. The root cause of banding is microsegregation of substitutional alloying elements during dendritic solidification. The alloying elements with low partition ratios, i.e., less than unity (e.g. P, Nb, Si, Mn and Cr) are rejected from the first formed δ-ferrite dendrites during casting process, which results in the formation of interdendritic regions of high solute content. The segregation is aligned into longitudinal bands during hot rolling, and upon subsequent cooling of the steel from the austenitic (γ) condition alternating bands of pro-eutectoid ferrite (α) and pearlite (or martensite) are formed. From technological standpoint, ferrite/pearlite banding may cause hydrogen induced cracking and may lead to a reduction in the impact toughness, if the steel is heat treated in the inter-critical region (α+γ) with subsequent rapid cooling. However, other parameters such as austenite grain size and cooling rate from austenite region also influence the development of microstructural banding, i.e. the formation of pearlite, bainite or martensite bands within the ferrite matrix.

A phase field model is employed to simulate the microstructural banding phenomena in a C-Mn steel. 2D PF simulations with a periodic Mn band structure have been used to quantify the effects of microsegregation level, cooling rate, prior austenite grain size, and band thickness on microstructural band formation.

The segregation of carbon to lattice defects has substantial influence on the properties of martensitic steels. An assessment in the framework of the CALPHAD (CALculation of PHAse Diagrames) technique has been carried out, which, in combination with software for Gibbs Energy minimization, can be used to predict phase stabilities in general alloy systems of technical relevance. The model allows expressing the trapped carbon phenomenon within a quantitative framework, which is an important issue in many steel-production scenarios where heavily dislocated martensite is present during quenching or deformation processes.

The new model is implemented in the software MatCalc, which is used to simulate the influence of defects on solute trapping and cementite precipitation during tempering.

A model is proposed and formulated in the framework of the CALPHAD technique, which accounts for the influence of lattice defects on carbide formation in steel. In the model, the defect sites are represented by an additional sublattice, which represents a superior attractor for carbon compared to cementite. The proposed model, which is convenient for multicomponent, multiphase systems, has been implemented in the software MatCalc. The model can calculate the fraction of carbon atoms that are trapped by the defects as well as the amount of free carbon available in the martensite for carbide formation. It is demonstrated that high defect densities provide a sufficient number of stressed sites that can trap a significant fraction of carbon atoms. Simultaneously, the driving force for cementite formation decreases drastically such that cementite formation is suppressed.