Modeling of Hydrogen Effects on the Thermomechanical Behavior of NiTi-Based Shape Memory Alloys

Abstract

NiTi Shape Memory Alloys (SMAs) orthodontic wires are subject to complex chemical loading in oral cavities. In the worst case, fractures are observed. Hydrogen effects are suspected, by analogy with the hydrogen embrittlement in Ti alloy systems. Several mechanisms have been observed for the case of steels, including hydride formations, hydrogen-enhanced-strain-induced vacancies (HESIV), hydrogen-enhanced-decohesion (HEDE), and hydrogen-enhanced-localized-plasticity (HELP). A degradation of the mechanical properties of NiTi arches appears due to the presence of hydrogen. Hydrogen atoms, which come from the chemical environment of buccal cavity, are supposed to diffuse in the interstitial sites naturally present in the crystallographic structure of NiTi SMAs as the same way than in steels. For instance, the maximum strain decreases, the area of the hysteresis becomes smaller with the increasing of hydrogen concentration in SMA archwires and fatigue life becomes shorter. Accounting for effects of hydrogen diffusion on the NiTi behavior, a coupled chemo-thermomechanical constitutive model needs to be formulated. The work of Lachiguer et al. (in: Smart Mater Struct 25(11):1–11, 2016) proposes material parameter dependencies to the normalized concentration of hydrogen in a NiTi constitutive law. The main limitation of this model is that the hydrogen concentration can only be considered as homogeneous. Nano-indentation tests carried out on NiTi wires charged with hydrogen highlighted an heterogeneous distribution of hardness (which is related to the hydrogen concentration). It becomes then necessary to take into account the gradient of hydrogen distribution. To this end, the weak form of equilibrium equations for each field (thermal, mechanical and chemical) through 2D domain is discretized and numerically solved by finite element method. A special finite element with coupled degrees of freedom (displacements, temperature, and hydrogen concentration) is developed and implemented in the Abaqus finite element software through the UEL subroutine. Numerical tests with complex loadings are carried out. Obtained results are discussed showing the relevance of the adopted approach.