# 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, 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 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, KrishnaswaShow more In 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.Show more Item On the multiaxial crushing of low-density open-cell foams(2020-05) Yang, Chenglin, Ph. D.; Kyriakides, S.; Huang, Rui; Kraynik, Andrew M.; Liechti, Kenneth M.; Ravi-Chandar, KrishnaswamyShow more Under uniaxial compression deformation in low-density foams localizes into narrow bands of crushed cells. Crushing spreads at nearly constant stress with crushed and relatively undeformed material coexisting. The material returns to homogeneous deformation with increasing stress when the crushing has spread over the whole specimen. The present study investigates how this partially unstable behavior of low-density foams transfers to the multiaxial setting as follows: (i) The crushing behavior of random foams is investigated under “true” triaxial loadings. A micromechanically accurate cubical model of an Al-alloy open-cell foam with relative density of 0.08 is crushed by a numerical true triaxial apparatus in three directions for three families of radial displacement paths. For all paths studied, the foam traces the same three regime behavior observed under uniaxial compression. Local cell crushing developed in narrow bands of cells at boundaries and subsequently propagate to the rest of the domain until the whole domain is crushed. (ii) A plasticity model is presented with a Drucker-Prager type yield function coupled with a non-associated flow rule. An essential component of the modeling effort is the introduction of a softening branch to the material stress-strain response. The constitutive model is incorporated in a cubical finite element model to simulate true triaxial crushing tests performed on the random foam in the continuum setting. Small geometric imperfections are used to trigger localized deformation in the form of planar bands of high strain. The bands broaden with the stresses tracing plateaus. For all loading paths, the calculated crushing responses reproduce those of the random foam very well. The study clearly demonstrates that the homogenized model captures the partially inhomogeneous crushing behavior of foams. (iii) The same random foam model is crushed under displacement controlled axial compression at different levels of external pressure. The study shows that such foams deform inhomogeneously under this triaxial loading also. The level of external pressure tends to lower the limit stress, the stress plateau, and the rest of the response. This behavior is subsequently simulated at the continuum level. It is demonstrated that the homogenized model again captures the three-regime response of the random foamShow more