Theocharis Baxevanis

Finite element analysis of the plane strain crack-tip mechanical fields in pseudoelastic shape memory alloys

The plane strain mechanical fields near a stationary crack tip in a pseudoelastic shape memory alloy (SMA) are analyzed via the finite element method. The small scale transformation assumption is employed for the calculations using displacement boundary conditions on a circular region that encloses the stress-induced phase transformation zone. The constitutive law used adopts the classical rate-independent small strain flow theory for the evolution equations of both the transformation and plastic strains. Results on the size and shape of the stress-induced transformation and plastic zone formed near the stationary crack are obtained and a fracture toughness criterion based on the J-integral is discussed in view of the observed path-dependence of J. Moreover, the obtained results are discussed in relation to results for stationary cracks in conventional elastic–plastic materials.

A mode I fracture analysis of a center-cracked infinite shape memory alloy plate under plane stress

The problem of a center plane crack in an infinite, thin, pseudoelastic Shape Memory Alloy (SMA) plate subjected to an in-plane uniform tensile stress at infinity is analyzed. The analysis follows closely the Dugdale–Barenblatt model developed for conventional metals. It is found for low remote stress values—less than a critical value—that the SMA is not fully transformed in the vicinity of a crack tip. Closed form expressions for the size of the partial transformation zone, crack opening displacement and J-integral are given for this case. For remote stress levels above the critical value, the fully-transformed material near a crack tip is assumed to yield plastically. The sizes of the transformed (both partially and fully) and plastic regions are numerically evaluated by solving a system of integral equations and their sensitivity to the transformation characteristics (i.e., maximum transformation strain and temperature) is determined. Moreover, a relationship between the J-integral and the crack-tip opening displacement is derived. The results obtained are important in understanding the effect of stress-induced phase transformation in the fracture behavior of SMAs in the presence of static cracks, and subsequently in formulating conditions for initiation of crack propagation.

On the Fracture Toughness of Pseudoelastic Shape Memory Alloys

A finite element analysis of quasi-static, steady-state crack growth in pseudoelastic shape memory alloys is carried out for plane strain, mode I loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate. Results pertaining to the influence of forward and reverse phase transformation on the near-tip mechanical fields and fracture toughness are presented for a range of thermomechanical parameters and temperature. The fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip energy release rate. A substantial fracture toughening is observed, in accordance with experimental observations, associated with the energy dissipated by the transformed material in the wake of the growing crack. Reverse phase transformation, being a dissipative process itself, is found to increase the levels of toughness enhancement. However, higher nominal temperatures tend to reduce the toughening of an SMA alloy—although the material’s tendency to reverse transform in the wake of the advancing crack tip increases—due to the higher stress levels required for initiation of forward transformation. [DOI: 10.1115/1.4025139]

Fracture mechanics of shape memory alloys: review and perspectives

Shape memory alloys (SMAs) are intermetallic alloys displaying recoverable strains that can be an order of magnitude greater than in traditional alloys due to their capacity to undergo a thermal and/or stress-induced martensitic phase transformation. Since their discovery, the SMA industry has been dominated by products for biomedical applications with geometrically small feature sizes, especially endovascular stents. For such products the technological importance of fracture mechanics is limited, with the emphasis being placed on preventing crack nucleation rather than controlling crack growth. However, the successful integration of SMAs into commercial actuation, energy absorption, and vibration damping applications requires understanding and practice of fracture mechanics concepts in SMAs. The fracture response of SMAs is rather complex owing to the reversibility of phase transformation, detwinning and reorientation of martensitic variants, the possibility of dislocation and transformation-induced plasticity, and the strong thermomechanical coupling. Large-scale phase transformation under actuation loading paths, i.e., combined thermo-mechanical loading, and the associated configuration dependence complicate the phenomenon even further and question the applicability of single parameter fracture mechanics theories. Here, the existing knowledge base on the fracture mechanics of SMAs under mechanical loading is reviewed and recent developments in actuation-induced SMA fracture are presented, in terms of the micro-mechanisms of fracture, near-tip fracture environments, fracture criteria, and fracture toughness properties.

On the Effect of Latent Heat on the Fracture Toughness of Pseudoelastic Shape Memory Alloys

A finite element analysis of steady-state crack growth in pseudoelastic shape memory alloys under the assumption of adiabatic conditions is carried out for plane strain, mode I loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate and the fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip critical value. Results related to the influence of latent heat on the near-tip stress field and fracture toughness are presented for a range of parameters related to thermomechanical coupling. The levels of fracture toughness enhancement, associated with the energy dissipated by the transformed material in the wake of the growing crack, are found to be lower under adiabatic conditions than under isothermal conditions [Baxevanis et al., 2014, J. Appl. Mech., 81, 041005]. Given that in real applications of shape memory alloy (SMA) components the processes are usually not adiabatic, which is the case with the lowest energy dissipation during a cyclic loading–unloading process (hysteresis), it is expected that the actual level of transformation toughening would be higher than the one corresponding to the adiabatic case.

Predictive Modeling of the Constitutive Response of Precipitation Hardened Ni-Rich NiTi

The effective thermomechanical response of precipitation hardened near-equiatomic Ni-rich NiTi alloys is predicted on the basis of composition and heat treatment using a microscale-informed model. The model takes into account the structural effects of the precipitates (precipitate volume fraction, elastic properties, elastic mismatch between the precipitates and the matrix, and coherency stresses due to the lattice mismatch between the precipitates and the matrix) on the reversible martensitic transformation under load as well as the chemical effects resulting from the Ni-depletion of the matrix during precipitate growth. The post-aging thermomechanical response is predicted based on finite element simulations on representative microstructures, using the response of the solutionized material and time–temperature–martensitic transformation temperature maps. The predictions are compared with experiments for materials of different initial compositions and heat treatments and reasonably good agreement is demonstrated for relatively low precipitate volume fractions.

Stable Crack Growth During Thermal Actuation of Shape Memory Alloys

A finite element analysis of crack growth is carried out in shape memory alloys subjected to thermal variations under plane strain, mode I, constant applied loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate which is modeled using the virtual crack closure technique. The load level, applied at a high temperature at which the austenite phase is stable, is assumed sufficiently low so that the resulting crack-tip energy release rate is smaller than the critical value but sufficiently high so that the critical value is reached during cooling, initiating crack growth (Baxevanis and Lagoudas in Int J Fract 191:191–213, 2015). Stable crack growth is observed, mainly associated with the shielding effect of the transformed material left in the wake of the advancing crack. Results pertaining to the near-tip mechanical fields and fracture toughness are presented and their sensitivity to phase transformation metrics and bias load levels is investigated.

Stable crack growth during actuation in shape memory alloys

A finite element analysis of crack growth is carried out in an in nite center-cracked shape memory alloy plate subjected to thermal variations under plane strain mode I constant applied loading. Crack is assumed to propagate when the energy release rate reaches a material specific critical value. The virtual crack growth technique is employed to calculate the energy release rate, which was shown to increase an order of magnitude at constant applied loading as a result of phase transformation induced by thermal variations.1 A fracture toughening is observed associated with the energy dissipated by the transformed material in the wake of the growing crack and its sensitivity over key thermomechanical parameters is presented.

On the Experimental Evaluation of the Fracture Toughness of Shape Memory Alloys

A methodology for measuring the fracture toughness of shape memory alloys (SMAs) from a single compact tension (CT) nominally isothermal load-load line displacement record is proposed. The methodology uses J-integral as the fracture criterion, relies on the ASTM standards E1820 modified to accommodate the Young’s moduli mismatch between the austenite and martensite phases. Finite element analysis (FEA) is employed to validate the methodology while experimental data from CT specimens are interpreted accordingly. The fracture toughness of martensitic equiatomic NiTi at room temperature is much higher than the phenomenological value reported on the basis of linear elastic fracture mechanics.

Full-Field Micromechanics of Precipitated Shape Memory Alloys

A full-field micromechanics approach is developed to predict the effective thermomechanical response of precipitation-hardened near-equiatomic Ni-rich NiTi alloys on the basis of composition and heat treatment. The microscale-informed model takes into account the structural effects of the precipitates (precipitate volume fraction, elastic properties, and coherency stresses due to the lattice mismatch between the precipitates and the matrix) on the reversible martensitic transformation under load as well as the chemical effects resulting from the Ni depletion of the matrix during precipitate growth. The post-aging thermomechanical response is predicted based on finite element simulations on representative microstructures, using the response of the solutionized material and time–temperature–martensitic transformation temperature maps. The predictions are compared with experiments for materials of different initial compositions and heat treatments and reasonably good agreement is demonstrated. The proposed methodology can be in principle extended to predict the post-aging thermomechanical response of other shape memory alloy systems as well.