# Browsing by Subject "Shape memory alloys"

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Item Evolution of localization in NiTi shape memory alloys and its effect on structures(2016-05) Bechle, Nathan Joseph; Kyriakides, S.; Landis, Chad M; Liechti, Kenneth M; Ravi-Chandar, Krishnaswa; Kovar, DesiderioShow more Nearly equiatomic NiTi can be strained to several percent and fully recover upon unloading (pseudoelastic behavior). This property is derived from solid-state transformations between the austenitic (A) and martensitic (M) phases, which can be induced by either changes in temperature or stress. In concert with prior results in tension, stress-induced phase transformation leads to localized deformation associated with the nucleation and propagation of the M-phase during loading and the A-phase during unloading. By contrast, it is demonstrated that under compression, transformation stresses are higher, strains are smaller, and the deformation is essentially homogeneous. This tension-compression asymmetry and unstable material behavior have an effect on the response and stability of NiTi structures. This is demonstrated with pure bending of tubes, and axial compression of cylindrical shells. Pure bending results in localization that leads to the coexistence of two curvature regimes. In the axial compression of the shell, transformation induces buckling and collapse, both of which are recoverable upon unloading. A requirement for the analysis and design of such structures is constitutive models that capture the material instability and asymmetry. Furthermore, the extensions of these material nonlinearities to the multiaxial setting must be addressed. To this end, results from a series of experiments on pseudoelastic NiTi tubes loaded under combined axial load and internal pressure are presented in which radial stress paths in the axial-hoop stress space were traced. Stereo digital image correlation was used to monitor the evolution of transformation-induced deformation. Results spanning axial-to-hoop stress ratios from -1.0 to uniaxial tension revealed that, but for a narrow region near equibiaxial tension, transformation leads to localized helical deformation bands with helix angles that vary with the stress ratio, while the stresses remain nearly constant. In the vicinity of equibiaxial tension, the material exhibits hardening and homogeneous deformation. Loci of the transformation stresses, while exhibiting minor anisotropy, traced an elongated non-Mises trajectory in the axial-hoop stress space. By contrast, the transformation strains exhibit significant anisotropy between axial and hoop dominant stress paths. Moreover, strains around the equibiaxial stress state, where material hardening and homogeneous deformation was observed, are significantly smaller than in the rest of the stress space. The strain anisotropy has a corresponding reflection on the energy dissipated during transformation with axial dominant stress paths dissipating significantly more energy than hoop dominant ones, with less dissipation observed in the neighborhood of equibiaxial stress.Show more Item Extraction of the underlying material response of pseudoelastic NiTi and its application in numerical simulations(2023-08) Greenly, Jacob Louis; Kyriakides, S.Show more In certain temperature regimes NiTi exhibits pseudoelasticity, meaning that after being loaded to strains of 6-7% it can return to its original configuration. This behavior is produced by the reversible solid-state phase transformation between the austenitic (A) and martensitic (M) phases. During isothermal tensile testing the response produces a closed hysteresis that traces two stress plateaus corresponding to localization and propagation of transformation front(s). Hallai and Kyriakides (2013) extracted the underlying up-down-up material response during the A [rightwards arrow symbol] M transformation from an experiment on a laminate composed of an unstable NiTi core and hardening facestrips. In these experiments, the laminates were plastically deformed to a strain of about 6%. To obtain the underlying response during the reverse M [rightwards arrow symbol] A transformation, the laminate must be reverse loaded back to zero, resulting in compressive forces in the hardening facestrips which ultimately lead to the laminate buckling. This thesis presents a new experimental setup to prevent buckling by laterally supporting the laminate during reverse loading. From this test, the complete underlying NiTi response is extracted and exhibits the expected softening branches during both the A [rightwards arrow symbol] M and M [rightwards arrow symbol] A transformations, with each branch having a Maxwell stress similar to the corresponding experimental plateau stress level. The full response is used to calibrate a custom constitutive model that produces a fit based completely on a measured response for the first time. Simulations of the isothermal tensile tests using this fit capture the measured response and localized deformation pattern to the greatest extent thus far. The fit is also used to conduct a parametric study on the effect the hardening facestrip thickness has on the overall laminate response, and possible changes to aid future users of this method are identified. The new method presented can replace the previously empirical model calibration method and enable more confident modeling of the unstable behavior of SMA structures through the use of measured data.Show more Item Localization instabilities in pseudoelastic NiTi tubes under multiaxial stress states(2022-07-01) Kazinakis, Karlos Thomas Leonidas; Kyriakides, S.; Landis, Chad M.; Kovar, Desiderio; Liechti, Kenneth M.; Ravi-Chandar, KrishnaswamyShow more Nearly equiatomic NiTi has a unique property called pseudoelasticity in that strain of several percent is recoverable at room temperatures. This characteristic is attainable due to solid-state transformations between the austenite and martensite phases. It is well established that the transformation in tension is associated with localization during the loading/unloading stress plateaus of its hysteresis. By contrast, the transformation in compression is essentially homogeneous and occurs at much higher stresses and lower strains. Recently conducted biaxial experiments on NiTi tubes revealed, in addition to tension/compression asymmetry, an inherent anisotropic behavior. The interaction of these material nonlinearities with geometric instabilities results in challenging structural problems and the need for adept constitutive models is vital. Hence, a J₂-type kinematic hardening model was developed by our group, which incorporates asymmetry and is now extended to include anisotropy. Two numerical studies of NiTi tubular structures incorporate this framework within a finite element analysis aiming to reproduce the experimental responses and the transformation-induced strain patterns. The first problem investigates the buckling and collapse of a thin-walled NiTi tube under pure bending. The analysis captures the moment-end rotation response and the distinct diamond patterns that develop demonstrating how their interaction with ovalization leads to buckling and collapse. Parametric sensitivity studies illustrate the roles of the diameter-to-thickness ratio, geometric imperfections, and some key aspects of the model to the stability of the structure. The second problem examines thin-walled NiTi tubes under combined axial force and internal pressure. The simulations reproduce well the stress-average strain responses and the transformation stress loci, while for hoop dominant stress paths the extents of the transformation strains are somewhat overpredicted. The evolution of localization in the form of high or low strain helical bands, the variation of helix angles with the stress ratio, and the dissipated energy compare favorably. The hardening response and essentially homogeneous deformation exhibited in the neighborhood of the equibiaxial stress state is reproduced, but with reduced hardening and weak deformation patterns. The special case of equibiaxial tension is studied further as it highlights the effects of asymmetry and anisotropy in the constitutive model on structural behaviorsShow more Item Phenomenological constitutive modeling and numerical analysis of fracture toughness for shape memory alloys(2022-05-02) Alsawalhi, Mohammed Yousuf; Landis, Chad M.; Foster, John T; Ravi-Chandar, Krishnaswamy Ravi; Mear, Mark E; Kyriakides, SteliosShow more Nickel titanium (NiTi) alloys possess unique characteristics that provide them the ability to recover large mechanical strains up to 8%. Pseudoelasticity and the shape memory effect are phenomena associated with SMA behavior. Shape recovery is driven by thermomechanical loading/unloading during the martensitic phase transformation. NiTi behavior also exhibits the property of asymmetry in transformation stress and transformation strain between the tension and compression responses as a result of forward and reverse phase transformations, as well as the reorientation and detwinning of the martensite phase. Furthermore, the process of heat generation during phase transformation near a crack tip effects the local temperature variations and thus the fracture toughness of the material. A new thermomechanical constitutive modeling approach for shape memory alloys (SMAs) that undergo a martensite to austenite phase transformation is presented. The novelty of this new formulation is that a single transformation surface is implemented in order to capture the main aspects of SMAs including forward transformation, reverse transformation, and martensite reorientation. Specific forms for the transformation surface and the transformation potential are devised and results for the behaviors captured by the model are provided for a range of thermomechanical loadings. The validity of the model is assessed with experimental studies of complex thermomechanical proportional and non proportional load paths at different temperatures using numerical simulations. The phenomenological constitutive model is implemented in finite element calculations and applied to the pseudoelastic and shape memory effects of a beam in pure bending. Fracture analysis is implemented within finite element computations to model the toughening due to the austenite to martensite phase transformation and martensite reorientation during steady mode I crack growth. Several dimensionless parameters relating the thermomechanical parameters of the constitutive model, the crack growth velocity, and the prevailing sample temperature are identified and applied to study the thermomechanical crack tip fields and the toughening enhancement due to the forward and reverse phase transformations in the vicinity of the crack tip. The first part of this dissertation involves validation of the model by comparisons of numerical simulations with experimental data and by developing consistent tangent moduli and applying the model to simple structural analysis of pure beam bending. First, uniaxial tensile and compressive stress-strain responses are simulated at four different temperatures: below the martensite finish temperature, between the martensite start and austenite start temperatures, between the austenite start and austenite finish temperatures, and above the austenite finish temperature. The numerical model reproduces the major aspects of the experimental measurements including the stress and strain levels. The transformation stress and transformation strain asymmetry between the tensile and compressive responses is also implemented in the model. The second problem investigates the performance of the model for a NiTi tube under a square axial-shear strain load path. The asymmetric model outperforms the symmetric model by reproducing the main features observed in the experiments. However, there is a notable difference in the magnitudes of stresses, mainly the shear stress, due to the anisotropy of the SMA material which is not accounted for in this model. The third problem examines the behavior of the constitutive model for tension-torsion of SMA wires for temperatures at the martensite and austenite phases. Again, the asymmetric model performs better than the symmetric model in terms of fitting the model response to the experimental measurements. The exclusion of anisotropy from the constitutive model has noticeable impact on the axial strain behavior at high temperatures. Lastly, the final problem investigates the pseudoelastic and shape memory behaviors of a beam under pure bending. The analysis in each case captures the moment-curvature and the temperature-curvature responses, as well as the axial stress distribution through the cross-section of the beam. The asymmetric model produced asymmetry in the axial stress distribution that fits the behavior of real SMAs. The second part of this dissertation involves fracture computations to analyze the toughening due to the stress-induced martensitic transformation and martensite reorientation during steady mode I crack growth. First, analyses are performed on the sizes and shapes of the various transformed zones near the crack tip for a range of temperatures analyzed. Secondly, the uniaxial stress-strain response is impacted by the thermomechanical parameters in the constitutive model which results in a relatively strong dependence of the transformation toughening on the material parameters. Next, numerical simulations are used to illustrate the effects of crack growth speed and heat capacity on the toughening. Finally, different sample temperatures show the strong impact on the toughness enhancement due to phase transformation. The last part of this dissertation discusses different approaches for material modeling, including different formulations associated with the transformation potentials and the associated integration routines. The first approach introduces a new internal variable that is a function of the other two in an attempt to control the pure shear stress-strain response as being a mixture between the tensile and compressive responses. The second approach introduces two stress invariants that are a linear or non-linear combination of the strain invariant. Here the objective is to control how fast the strain invariant goes towards uniaxial tension in a pure shear loading in order to allow the pure shear response to be a controlled mixture between the tensile and compressive responses as opposed to having similar behavior to the tensile response. The last approach for the integration algorithm utilizes a classical elastic prediction-transformation correction return mapping. This method simplifies the number of unknowns solved in the integration routine to just one. Therefore, a 1-D Newton-Raphson (NR) scheme is used which allows for more robust numerical calculations.Show more