Phenomenological constitutive modeling and numerical analysis of fracture toughness for shape memory alloys
Creators: name: Alsawalhi, Mohammed Yousuf
name: 0000-0001-7729-800X
Publisher: name: The University of Texas at Austin
Year: 2022
Subjects: Shape memory alloys
Constitutive modeling
Phase transformation
Fracture toughness
Fracture mechanics

description: 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.