The pure titanium, as a biomaterial destined for production of load-demanding prostheses, requires thermo-mechanical processing to increase its strength. The most common way to achieve this is the method of grain fragmentation. Thermo-mechanical deformation of titanium is a complex process, which makes it very difficult to describe it by means of constitutive equations. Such constitutive relations are very useful as they can be implemented in the finite element method tools in order to simulate and optimize the whole process. Cylindrical specimens were compressed at elevated temperatures on a thermo-mechanical simulator. The tests were performed at four different strain rates (from 10\(^{\mathrm {-2}}\) s\(^{\mathrm {-1}}\) to 10 s\(^{\mathrm {-1}})\) and at 775 K and 875 K temperatures. The collected data allowed us to create strain–stress graphs characterizing the process. Observations on the scanning electron microscope and scanning transmission electron microscope were done as well as the electron backscatter diffraction analysis, revealing significant grain fragmentation. The aim of the studies described in the paper was to verify and select a proper mathematical model for the process of titanium grain fragmentation obtained in a thermoplastic process. Four different constitutive models were considered. The calculation of theoretical stress values based on the Arrhenius-type equation, Anand viscoplastic model, Johnson–Cook model and Khan Huang-Liang model was done and compared to experimental results. The theoretical curves were generated and fitted to experimental, which made it possible to calibrate the constants in the mathematical models. The curve-fitting analyses showed that the Anand constitutive model described the titanium behaviour best.

纯钛作为一种用于生产高负荷假体的生物材料，需要进行热机械加工以提高其强度。实现此目的的最常见方法是晶粒破碎方法。钛的热机械变形是一个复杂的过程，因此很难通过本构方程来描述它。这种本构关系非常有用，因为它们可以在有限元方法工具中实现，以模拟和优化整个过程。在高温机械模拟器上，将圆柱形样品在高温下压缩。测试是在四种不同的应变率下进行的（从10 \（^ {\ mathrm {-2}} \） s \（^ {\ mathrm {-1}} \）到10 s \（^ {\ mathrm { -1}} \）到10 s \（^ {\ mathrm {- 1}}）\）以及775 K和875 K的温度。收集的数据使我们能够创建表征过程的应变-应力图。进行了扫描电子显微镜和扫描透射电子显微镜的观察以及电子背散射衍射分析，显示出明显的晶粒碎裂。本文所述研究的目的是为热塑性工艺中获得的钛晶粒破碎过程验证并选择合适的数学模型。考虑了四个不同的本构模型。进行了基于Arrhenius型方程，Anand粘塑性模型，Johnson-Cook模型和Khan Huang-Liang模型的理论应力值的计算，并与实验结果进行了比较。产生了理论曲线，并拟合到实验中，这样就可以校准数学模型中的常数。曲线拟合分析表明，Anand本构模型最能描述钛的行为。