Challenges and opportunities in thermodynamic and kinetic modeling microalloyed HSLA steels using computational thermodynamics

Most High Strength Low-Alloy (HSLA) steels rely on the control of the carbonitrides of Ti, Nb and V to achieve their properties. To properly control the distribution and size of precipitates the knowledge of the thermodynamics of the Fe–C–N-(Ti,Nb,V) systems is essential. Furthermore, understanding the kinetics of dissolution and precipitation of the carbonitrides is fundamental to properly design these steels and their processing. In this work, we emphasize Ti and Nb behavior in HSLA steels. First, the thermodynamic information concerning the stability of their carbonitrides in steel is reviewed, highlighting the difficulties associated with the variable C/N ratio of the carbonitrides and with the fact that there is also miscibility between Ti, Nb and V in the carbonitrides of the “NaCl” structure. These difficulties make the use of the compound energy formalism (CEF) and of computational thermodynamics extremely recommended. To demonstrate this, some frequently used solubility products are compared to results obtained with current computational thermodynamics databases. Currently, many efforts have been made to model the kinetics of dissolution and precipitation of these particles in steel. We focus on the potential advantages of using computational thermodynamics methods both for diffusion and for nucleation, growth and coalescence, in special using software based on Kampmann-Wagner numerical (KWN) theory. The potential of these methods is demonstrated in some selected applications. We emphasize the importance of interfacial energy in these models. Frequently the interfacial energy is used as an adjustable parameter in these models. Even when this is done, the models can be very useful for steel and process design, as long as the user is aware of the limitations associated to the adjustment.     

Thermodynamic modeling of Ti–Cr–Mn ternary system

The Ti–Cr–Mn ternary system is one of the most important systems in the development of low cost titanium alloys. However, there are few reports of assessment for this system. In this paper, the previous works for the Ti–Cr–Mn system and the related binary sub-systems are reviewed. The thermodynamic parameters of TiMn₃ and TiMn₄ in the Ti–Mn system are reassessed in order to better describe the phase equilibrium involving TiMn₃ or/and TiMn₄ in the ternary system. Based on the Ti–Cr and the Cr–Mn systems modeled in the literature and the Ti–Mn system reassessed in this work, the Ti–Cr–Mn ternary system is assessed by means of the Calphad method using the ternary experimental data in the literature. The 1173 K and 1273 K isothermal sections are calculated. It is shown that the present calculated results are in good agreement with most of the experimental results.     

Study of diffusion mobilities of Nb and Zr in bcc Nb–Zr alloys

On the basis of the available thermodynamic parameters, the atomic mobilities of Nb and Zr in bcc Nb–Zr alloys are critically assessed as functions of temperatures and compositions by the CALPHAD method, where self-diffusion coefficients, impurity diffusion coefficients, tracer diffusion coefficients, interdiffusion coefficients and concentration curves are simultaneously optimized. Comparisons between the calculated and experimentally measured diffusion coefficients are made, where good agreement is evident. In addition, the obtained mobility parameters can reproduce a reasonable concentration profile for the Nb/Zr diffusion couple annealed at 1868 K for 5400 s.     

A thermodynamic model of the Z-phase Cr(V, Nb)N

Precipitation of large Z-phase particles, Cr(V, Nb)N, replacing fine MX carbonitrides, Nb(C, N) or V(N, C), has recently been identified as a major cause for premature breakdown in long-term creep strength of a number of new 9%–12% Cr martensitic steels, especially the high Cr variants.

A thermodynamic model of the Z-phase has been developed based on the regular solution model. The model predicts Z-phase to be stable and to fully replace the MX particles in most of the new 9%–12% Cr steels, which is in good agreement with experimental observations.

The rate of precipitation of Z-phase is a crucial factor for the long-term creep stability of these steels. Driving force calculations with the model allow estimates of the influence of the individual alloying elements on the rate of Z-phase precipitation, and can thus contribute useful information for alloy design to delay and retard Z-phase precipitation.

According to these calculations, particularly Cr has a strong accelerating effect on Z-phase precipitation.     

Modelling of interstitials in the bcc phase

There are several widespread thermodynamic datasets which produce a spurious bcc interstitial solution at high temperature and high X content (X is an interstitally dissolved element). The reason for this is the standard model for bcc interstitial solutions (M(V a,X)₃), which requires careful selection of optimising parameters to minimise spurious appearances of the bcc phase. In this work the model M(V a,X)₁ is suggested as an alternative. This model is much easier to handle and its parameters can be directly compared with those of the fcc phase. The two models are compared for the Fe–C and Nb–N systems. In the Fe–C system almost identical results are achieved. In Nb–N there are some differences for high N content, but there is no experimental data to clearly support any model.     

Development of hip joint prostheses with modular stems

Minimally invasive surgery for THR (Total Hip joint Replacement) is attractive for both surgeons and patients. Since such surgery needs an incision of only 3–4 inches around the hip joint for THR instead of the traditional, large incision of 10–12 inches, it causes less pain and enables early recovery for patients, besides facilitating THR for the operating surgeons. In this research, for minimally invasive THR, a unique type of a cementless stem, named a modular stem, is devised. It consists of two different parts in a stem that can be joined to and separated from each other. For actualizing the modular stem, Bio-CAD modeling technique is applied. The bony structure around the hip joint is three dimensionally reconstructed and its geometric solid model is fabricated. The geometric solid models of modular stems are designed and their prototypical models are fabricated using an acryl-based polymer. The geometric suitability of the prototypical modular stems is manually examined. The strength of the stem to sustain the applied load is evaluated using the finite element method. Finally, various sizes of actual modular stems with circular or rectangular cross-sections are fabricated using a biocompatible Ti alloy (Ti–6Al–4V). The developed modular stems will be used in the near future for minimally invasive THR surgery.     

Assessment of atomic mobilities for fcc Co–Ti–V alloys

Based on the experimental interdiffusion coefficients from our previous work and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Co, Ti and V in fcc Co–Ti–V alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformation) software. Askill's empirical relations were utilized to assess the self-diffusion coefficients of fcc Ti and fcc V. Comprehensive comparisons between the DICTRA-calculated diffusivities and the experimental data indicate that the presently obtained atomic mobilities can reproduce most of the diffusivities in binary and ternary systems. In addition, a further verification on the obtained atomic mobilities was carried out through comparing the DICTRA-simulated concentration profiles/diffusion paths of the diffusion couples with the corresponding experimental ones. This work contributes to the establishment of a kinetic database for multi-component cemented carbide.     

Thermodynamic modeling of the Al–Bi,Al–Sb,Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.