Analytical description of the bending behaviour of NiTi shape-memory alloys

Plietsch, R.; Bourauel, Christoph; Drescher, Dieter; Nellen, B.

doi:10.1007/bf00366873

Cited by 14 publications

(7 citation statements)

References 10 publications

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“…Despite the myriad of applications that employ superelastic SMA in bending, and despite the number of SMA bending models (we found 13) (Atanacković and Achenbach, 1989;Thier et al, 1991;Pelton et al, 1994;Plietsch et al, 1994;Berg, 1995b;Auricchio and Sacco, 1997;Raniecki et al, 2001;Rejzner et al, 2002;Purohit and Bhattacharya, 2002;Liew et al, 2004;Rajagopal and Srinivasa, 2005;Buratti, 2005;De la Flor et al, 2010), few careful pure-bending experiments exist in the literature. Traditional 4-point bending fixtures operate under the assumptions of small beam displacements and rotations, which are easily violated when used with slender SMA specimens.…”

Section: Introductionmentioning

confidence: 82%

Tension, compression, and bending of superelastic shape memory alloy tubes

Reedlunn

Churchill

Nelson

et al. 2014

Journal of the Mechanics and Physics of Solids

176

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While many uniaxial tension experiments of shape memory alloys (SMAs) have been published in the literature, relatively few experimental studies address their behavior in compression or bending, despite the prevalence of this latter deformation mode in applications. In this study, superelastic NiTi tubes from a single lot of material were characterized in tension, compression, and pure bending, which allowed us to make direct comparisons between the deformation modes for the first time. Custom built fixtures were used to overcome some long-standing experimental difficulties with performing well-controlled loading and accurate measurements during uniaxial compression (avoiding buckling) and large-rotation bending. In all experiments, the isothermal, global, mechanical responses were measured, and stereo digital image correlation (DIC) was used to measure the evolution of the strain fields on the tube's outer surface.As is characteristic of textured NiTi, our tubes exhibited significant tension-compression asymmetry in their uniaxial responses. Stress-induced transformations in tension exhibited flat force plateaus accompanied by strain localization and propagation. No such localization, however, was observed in compression, and the stress "plateaus" during compression always maintained a positive tangent modulus. While our uniaxial results are similar to the observations of previous researchers, the DIC strain measurements provided details of localized strain behavior with more clarity and allowed more quantitative measurements to be made. Consistent with the tension-compression asymmetry, our bending experiments showed a significant shift of the neutral axis towards the compression side. Furthermore, the tube exhibited strain localization on the tension side, but no localization on the compression side during bending. This is a new observation that has not been explored before. Detailed analysis of the strain distribution across the tube diameter revealed that the traditional assumption of elementary beam theory, that plane sections remain plane, does not hold. Yet when the strain was averaged over a few diameters of axial length, the tensile and compressive responses input into elementary beam theory predicted the global bending response with reasonable accuracy. While it is encouraging that a simple model could predict the moment-curvature response, we recommend that beam theory be used with caution. The averaged strain field can under/over predict local strains by as much as two-fold due to the localized deformation morphology.

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Section: Introductionmentioning

confidence: 82%

Tension, compression, and bending of superelastic shape memory alloy tubes

Reedlunn

Churchill

Nelson

et al. 2014

Journal of the Mechanics and Physics of Solids

176

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“…In terms of analytical solutions for the bending problem, Thier et al (1991), Plietsch et al (1994), Auricchio andSacco (1997, 2001), Purohit and Bhattacharya (2002), Rajagopal and Srinivasa (2005), Eshghinejad and Elahinia (2011), Rizzoni et al (2013) and Mirzaeifar et al (2013) have studied PE beams. Furthermore, neglecting phase transformation hardening, Atanackovic and Achenbach (1989) have derived an analytical moment-curvature relation for PE beams based on a one-dimensional (1D) constitutive equation.…”

Section: Introductionmentioning

confidence: 99%

An analytical study on the bending of prismatic SMA beams

Ostadrahimi¹,

Arghavani²,

Poorasadion³

2015

Smart Mater. Struct.

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In this study, an analytical solution is presented for pure bending of shape memory alloy (SMA) beams with symmetric cross section as well as symmetric behavior in tension and compression. To this end, a three-dimensional constitutive equation is reduced to one-dimensional form and employed to study the bending response of SMA beams at high (pseudo-elasticity) and low (shape memory effect) temperatures. An analytical expression for bending stress as well as polynomial approximation for shear stress and deflection are obtained. Derived equations for bending are employed to analyze an SMA beam with rectangular cross section and results are compared with those of the finite element method. The results of this work show good agreement when compared with experimental data and finite element results. Furthermore, the existence of several zero-stress fibers during unloading of SMA beams at low temperature is demonstrated.

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“…Rogers [6], and Brinson [7] has been developed to describe the uniaxial tensile thermomechanical behaviour of the oneway shape memory effect while Thier [8], Plietsch [9] and Rahman [10] worked on the bending vs. external loading behaviour of SMA. For our application, the generated force behaviour in the bending configuration (to enable revolute joint motion) is the most important parameter which we are interested in characterizing and hence it is one of the primary focus of this paper.…”

Section: Introductionmentioning

confidence: 99%

Towards a MR image-guided SMA-actuated neurosurgical robot

Koltz

Simard

et al. 2011

2011 IEEE International Conference on Robotics and Automation

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We present our work towards the development of a MR image-guided SMA-actuated neurosurgical robot. We used two antagonistic SMA wires as actuators for each joint in the robot, so that each joint can be actuated independently. We also modeled and tested the force behaviour of SMA wires in the bent configuration, which can be used as a guideline for SMA actuator selection. Due to the size scale of the robot, it is impossible to have individual position sensors at each joint and hence we rely primarily on vision feedback to control the joint motion of the robot. The images used to control the robot in this paper were obtained from a camera with the goal of eventually using MR images to control the end-effector motion. We then developed a control strategy and a switching circuit to control multiple links simultaneously and independently using only one power supply. Experimental results from our current prototype of a 3-DOF robot showed that we can actuate the robot and hence observe joint motion in a gelatin slab. We also did a series of experiments inside the MRI to show that the robot is fully MRI-compatible and creates no significant image distortion in the MR images.

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Analytical description of the bending behaviour of NiTi shape-memory alloys

Cited by 14 publications

References 10 publications

Tension, compression, and bending of superelastic shape memory alloy tubes

Tension, compression, and bending of superelastic shape memory alloy tubes

An analytical study on the bending of prismatic SMA beams

Towards a MR image-guided SMA-actuated neurosurgical robot

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