Browsing by Subject "Inhomogeneous deformation"
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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, DesiderioNearly 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.Item On the effect of Lüders bands on the bending of steel tubes(2011-12) Hallai, Julian de Freitas; Kyriakides, S.; Engelhardt, Michael D.; Landis, Chad M.; Liechti, Kenneth M.; Ravi-Chandar, KrishnaswaIn several practical applications, hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2-3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1-4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. It starts with the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2 to 14.7 and Lüders strains of 1.8% to 2.7%. In all cases, the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues, the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends, the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. This class of problems is analyzed using 3D finite elements while the material is modeled as an elastic-plastic solid with an “up-down-up” response over the extent of the Lüders strain, followed by hardening. The analysis reproduces the main features of the mechanical behavior provided the unstable part of the response is suitably calibrated. The uniform curvature elastic regime terminates with the nucleation of localized banded deformation. The bands appear in pockets on the most deformed sites of the tube and propagate into the hitherto intact part of the structure while the moment remains essentially unchanged. The Lüders-deformed section has a higher curvature, ovalizes more than the rest of the tube, and develops wrinkles with a characteristic wavelength. For every tube D/t there exists a threshold of Lüders strain separating the two types of behavior. This bounding value of Lüders strain was studied parametrically.