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Research Papers

# Exploitation of Large Recoverable Deformations Using Weaved Shape Memory Alloy Wire-Based Sandwich Panel ConfigurationsOPEN ACCESS

[+] Author and Article Information
Ashish Mohan

Research and Development
Establishment (Engineers),
Defence R&D Organization,
Pune 411 015, India
e-mail: ashish_uor@rediffmail.com

Sivakumar M. Srinivasan

Department of Applied Mechanics,
Chennai 600 036, India
e-mail: mssiva@iitm.ac.in

Makarand Joshi

Research and Development
Establishment (Engineers),
Defence R&D Organization,
Pune 411 015, India
e-mail: meenmak@hotmail.com

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 31, 2016; final manuscript received December 23, 2016; published online February 9, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021014 (Feb 09, 2017) (5 pages) Paper No: MATS-16-1158; doi: 10.1115/1.4035765 History: Received May 31, 2016; Revised December 23, 2016

## Abstract

A new class of truss structure based on superelastic shape memory alloy (SMA) wire has been developed by weaving superelastic SMA wire through two perforated facesheets. A gap was maintained between the facesheets while weaving and the ends of wire forming the truss legs are anchored in each facesheet. The resulting structure has a modified pyramidal configuration and is capable of undergoing large recoverable deformations typical of superelastic SMA. A four-unit cell truss specimen has been tested under static load cycles to investigate the compressive response. The truss specimen underwent a hysteretic loop and demonstrated minimal permanent deformation closely resembling the behavior of bulk SMA. A finite element model of the truss was generated and the analysis results were compared with the experimental response. The present work is an attempt to demonstrate an SMA-based truss structure having energy absorption capabilities with minimum permanent deformation. These truss structures may be applied for damage mitigation in composites subjected to impact and blast loads.

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## Introduction

Lattice truss core-based sandwich structures have been the focus of numerous studies by various research groups [16]. Haydn Wadley [1] discussed different methods for fabrication of various truss topologies. He also investigated the structural performance of cellular metal sandwich structures and demonstrated that truss core-based sandwich panels sustain static design loads at weights greatly superior to stochastic foams and competitive with the lightest known (honeycomb core) systems. Lim and Kang [2] fabricated tetrahedral and Kagome truss cores from metal wires by tri-axial weaving. They evaluated the equivalent properties of such cores analytically and compared with experimental results. The failure mechanism under compressive loading was also studied. Lee and Kang [3] fabricated wire-woven bulk Kagome (WBK) using helical wires and brazed at joints and carried out experimental and numerical studies. They observed that WBK truss strength was comparable to that of ideal Kagome. Zhang et al. [4] investigated sandwich structures with carbon fiber reinforced plastic (CFRP) facesheets and aluminum pyramidal truss core. The core was made by snap-fitting individual strands and bonding them to the facesheet. Quasi-static compression tests were conducted to get stress–strain curves and to evaluate energy absorption mechanism. Low velocity impact tests were carried out to investigate damage resistance. George et al. [5] developed sandwich panels with facesheets as well as pyramidal core made of CFRP and studied their failure under quasi-static shear loading. Xiong et al. [6] investigated two-layer pyramidal-core sandwich panels under quasi-static compression and low velocity impact. They observed better energy absorbing capability per unit mass compared to glass fiber woven textile truss core.

Among other cellular structures, Shaw et al. [7] have demonstrated superelastic SMA-based honeycomb structures. These honeycombs exhibited enhanced shape recovery compared to monolithic SMA.

A common aspect of the response of truss structures fabricated with conventional metals and CFRP is that they undergo permanent (plastic) deformations when stressed beyond their elastic limits. Plastic deformation in turn helps in energy absorption under impact and blast loading conditions. However, this permanent deformation in the structure reduces their postimpact strength and stiffness rendering them unusable postimpact. SMA-based honeycomb structures, on the other hand, demonstrated significant shape recovery by undergoing reversible hysteretic phase transformation. The shape recovery through reversible hysteretic phase transformation suggests that SMA-based structures can be employed for energy absorption applications with minimum permanent deformation. This is evident from the stress–strain curve for superelastic NiTi (a nickel–titanium alloy is the most common SMA) shown in Fig. 1.

The present work aims to combine the advantages of truss structures with the adaptive nature of superelastic SMA by developing truss structures made from SMA wires. The compressive response of SMA truss, which is indicative of energy absorption capacity, is investigated.

The organization of the paper is as follows: The basic concept of SMA truss is presented in Sec. 2. The fabrication process and experimental investigations are explained in Sec. 3. The finite element analysis (FEA) is presented in Sec. 4. Section 5 details the experimental and simulation results, comparison between them, and discussion on major observations. The paper concludes with a summary of the major findings of the work in Sec. 6.

## Concept

Shape memory alloy are readily available in the form of wires. A novel fabrication approach employing superelastic SMA wires for constructing truss structure is developed. The technique requires two facesheets with a specific pattern of holes. A gap is maintained between the facesheets and SMA wires are weaved through them to realize the truss. Unlike other metal wires, the superelastic nature of SMA wires prevents any kinking during weaving. A typical cross section with one complete weaving cycle is shown in Fig. 2(a).

The bend radius, r, is decided by wire diameter, dw, and maximum strain, εmax, in bend region. This (εmax) is the strain generated on the top and bottom surfaces (tensile and compressive) of wire when it is bend to attain the radius r. Based upon height H, facesheets thickness t and required truss angle θ, all other geometric parameters required for fabricating the truss, i.e., facesheet hole diameter, d, spacing s, height of bend from facesheet, h and length L can be obtained as follows: Display Formula

(1)$r=dw2(1εmax−1)$
Display Formula
(2)$d=tcotθ+dwcscθ$
Display Formula
(3)$s=2r sin θ$
Display Formula
(4)$h=r(1−cos θ)$
Display Formula
(5)$L=2(Hcotθ+s+dwcscθ)$

The holes pattern can be decided depending upon the desired truss configuration. In order to anchor the bend in the facesheet, a plate with higher thickness T, shown in Fig. 2(b), was chosen and a counter hole of diameter D was made on the outer face. The counter hole depth was kept sufficient to accommodate the complete bend. This slot was filled with adhesive after completion of weaving resulting in a flat top surface.

## Experimentation

###### Fabrication Methodology.

A four-cell pyramidal truss was realized based upon the concept presented above. SMA wire with the following properties was used for construction of the truss: alloy composition—50.8Ni49.2Ti (%); Austenite modulus—70 GPa; Martensite modulus—28 GPa; plateau stress (loading)—470 MPa; plateau stress (unloading)—210 MPa; plateau strain—6%; ultimate tensile strength—1550 MPa. Pyramidal truss has four legs and therefore requires two wire bends to cross over each other as shown in Fig. 2(b). The two Aluminum plates with holes and counter holes constituting the facesheets are shown in Figs. 3(a) and 3(b). The facesheets were maintained 10 mm apart (H-2t) using a nut-bolt arrangement and SMA wire of diameter 0.8 mm was weaved through it as shown in Fig. 3(c). An inclination angle, “θ” of “tan−1(10/8)” was chosen. After completion of weaving, all the counter holes were filled with adhesive to anchor the wire ends resulting in desired truss configuration. The nut-bolt arrangement was removed after the adhesive cures to achieve the free standing truss. The resulting four-unit cell pyramidal truss structure is shown in Fig. 3(d).

###### Compressive Testing.

The compressive response of the four-cell truss specimen has been studied under static cyclic loading on a servohydraulic universal testing machine. The test arrangement is shown in Fig. 4. The truss was subjected to a deformation of 1 mm, which is 10% of effective truss height at a loading frequency of 2 min/cycle. Around five loading cycles were passed to allow for settling of the truss, if any, followed by which the load-deformation data was recorded. The effect of repeated cycling was studied by subjecting the truss to five continuous cycles.

## Finite Element Analysis

A finite element model of a single cell truss, representing one-fourth of the specimen, was generated using abaqus finite element code [8]. The SMA wire was modeled using three-dimensional linear beam elements while the cylindrical blocks of adhesive were modeled with linear brick elements. abaqus [8] has built-in constitutive model of superelastic SMA, which was directly used for the analysis. There could be residual stresses generated in bend region of SMA wire during fabrication. In this work, these have not been considered in the analysis. The aluminum facesheets were not modeled and in-plane constraint was applied to the peripheral nodes of the adhesive blocks to account for them. The bottom face nodes of lower blocks were constrained against any vertical deformation. The model had a total of 192 beam elements and 9120 brick elements. The SMA wires were extended into the adhesive blocks to match the degrees-of-freedom of beam (SMA) and brick (adhesive block) elements. The meshed model is shown in Fig. 5.

A nonlinear static analysis is performed applying a downward deformation of 1 mm on the top midnode of the upper block in 100 equal increments. The entire deformation is recovered back in a subsequent step in another 100 equal increments.

## Results and Discussion

The specimen under maximum vertical deformation is shown in Fig. 6(a) and the corresponding deflection contour is shown in Fig. 6(b). Figure 6(a) shows the buckling of multiple truss legs which is also captured in the simulation. However, simulation being the ideal scenario depicts symmetric bending of all truss legs. The specimen, on the other hand, being a fabricated structure, demonstrates an unsymmetric behavior. Upon removal of loading, a small kink in a few truss legs was observed indicating that the strain exceeded the maximum recoverable strain in those legs.

The load-deformation plots from the experiments and analysis results are compared in Fig. 7, with the simulation loading amplified four times to achieve equivalent load for a four cell specimen. The experimental plot of four-cell SMA truss resembles the behavior of bulk SMA closely. There is, however, a 24% drop in load at 1 mm deflection as compared to the peak load. This drop is due to the coupled effect of buckling of truss legs and stiffness reduction because of the austenite to martensite transformation of SMA. The unloading response is closer to bulk SMA behavior. The residual deformation is also observed to be less than 10% of the applied deformation.

The simulation plot demonstrates a significant drop in peak load indicating a dominant buckling effect along with austenite to martensite transformation. The unloading curve depicts an increase in load because of straightening of truss legs. The residual strain is not captured by material model in abaqus [8] so the specimen returns to its original position.

The comparison of experimental and simulation results shows a close match between the initial stiffness of the two results. The peak load observed in simulation is, however, 33% higher than that observed in actual testing. In simulation, all legs carry equal loads and buckle simultaneously resulting in higher peak load and sharp drop in load. The specimen, due to fabrication nonuniformities, has unequally loaded legs, which undergo buckling at different instants; hence, a gradual load reduction and higher load at 1 mm deflection as compared to simulation.

During unloading, the differently strained legs recover gradually and unequally; therefore, the behavior is governed by reverse transformation. In simulation, all legs recover from buckling simultaneously, thereby resulting in increase in load. The effect of buckling can be reduced by reducing the truss height or by restraining the lateral deflection of truss legs at midheight.

The effect of continuously cycling is studied by subjecting the specimen to five continuous cycles and the load-deformation curves are shown in Fig. 8. The loading curve stabilizes within a few cycles and the buckling becomes less prominent gradually. The unloading curve stabilizes faster and the residual deformation also remains less than 10% of applied deformation.

In order to study the effect of truss height on compressive response, single cell truss models with heights varying from 4 mm to 12 mm in steps of 2 mm were generated. Each model was subjected to a loading–unloading cycle with peak deformation equal to 10% of the truss height. A comparative load-deflection plot for these cases is shown in Fig. 9. The areas of hysteresis loop for these cases, for unit deflection, are compared in Fig. 10.

The curves demonstrate that buckling of truss legs dominate the response for truss heights of 8 mm and beyond. When the truss height is below 8 mm, the truss behavior is closer to bulk SMA behavior. There is marked reduction in hysteresis loop area due to buckling of truss legs as depicted in Fig. 9. Hence, the effectiveness of SMA truss can be improved by reducing buckling of truss legs. However, it must be appreciated that the finite element model is a simplified representation of the specimen and hence the actual response may vary a little. Nonetheless, it proves that this SMA truss is capable of undergoing reversible transformation under compressive loading.

## Conclusion and Future Work

A new concept of truss structure realized using SMA wires is presented. A four-cell truss specimen is fabricated and its compressive response is studied experimentally. The response depicts deformation recovery through the combined effect of buckling and austenite–martensite transformation. The buckling behavior is found to reduce gradually upon static cycling and the response stabilizes after 4–5 cycles.

Finite element analysis is performed on a single cell specimen in abaqus [8] FEA package using in-built superelastic SMA constitutive model. The model predicts the initial stiffness closely but the peak load is observed to be 33% higher than test result. The buckling is also more prominent in simulation results. A lower experimental load is due to fabrication-related imperfections, which cannot be modeled. The effect of truss height is studied by modeling trusses with varying heights. It is observed that buckling has negligible effect for truss of 6 mm or less.

The SMA truss demonstrated deformation recovery by undergoing hysteresis loop with less than 10% residual deformation. The truss can therefore be utilized for energy absorption applications such as impact and blast loading. The hysteretic recovery will lead to reduced structural damage.

It is planned to investigate the shear and bending response of this truss. Pyramidal trusses with reduced height will be fabricated and thoroughly characterized. In addition to this, other competing truss configurations will also be attempted.

## References

Wadley, H. N. G. , 2006, “ Multifunctional Periodic Cellular Metals,” Philos. Trans. R. Soc., A, 364(1838), pp. 31–68.
Lim, J.-H. , and Kang, K.-J. , 2006, “ Mechanical Behavior of Sandwich Panels With Tetrahedral and Kagome Truss Cores Fabricated From Wires,” Int. J. Solids Struct., 43(17), pp. 5228–5246.
Lee, Y.-H. , and Kang, K.-J. , 2009, “ A Wire-Woven Cellular Metal—Part I: Optimal Design for Applications as Sandwich Core,” Mater. Des., 30(10), pp. 4434–4443.
Zhang, G. , Wang, B. , Ma, L. , Xiong, J. , and Wu, L. , 2013, “ Response of Sandwich Structures with Pyramidal Truss Cores Under the Compression and Impact Loading,” Compos. Struct., 100, pp. 451–463.
George, T. , Deshpande, V. S. , and Wadley, H. N. G. , 2013, “ Mechanical Response of Carbon Fiber Composite Sandwich Panels With Pyramidal Truss Cores,” Composites, Part A, 47, pp. 31–40.
Xiong, J. , Vaziri, A. , Ma, L. , Papadopoulos, J. , and Wu, L. , 2012, “ Compression and Impact Testing of Two-Layer Composite Pyramidal-Core Sandwich Panels,” Compos. Struct., 94(2), pp. 793–801.
Shaw, J. A. , Grummon, D. S. , and Foltz, J. , 2007, “ Superelastic NiTi Honeycombs: Fabrication and Experiments,” Smart Mater. Struct., 16(1), pp. S170–S178.
ABAQUS, 2012, “ ABAQUS/Standard User's Manual, Version 6.12-1,” Dassault Systemes Simulia Corp., Providence, RI.
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## References

Wadley, H. N. G. , 2006, “ Multifunctional Periodic Cellular Metals,” Philos. Trans. R. Soc., A, 364(1838), pp. 31–68.
Lim, J.-H. , and Kang, K.-J. , 2006, “ Mechanical Behavior of Sandwich Panels With Tetrahedral and Kagome Truss Cores Fabricated From Wires,” Int. J. Solids Struct., 43(17), pp. 5228–5246.
Lee, Y.-H. , and Kang, K.-J. , 2009, “ A Wire-Woven Cellular Metal—Part I: Optimal Design for Applications as Sandwich Core,” Mater. Des., 30(10), pp. 4434–4443.
Zhang, G. , Wang, B. , Ma, L. , Xiong, J. , and Wu, L. , 2013, “ Response of Sandwich Structures with Pyramidal Truss Cores Under the Compression and Impact Loading,” Compos. Struct., 100, pp. 451–463.
George, T. , Deshpande, V. S. , and Wadley, H. N. G. , 2013, “ Mechanical Response of Carbon Fiber Composite Sandwich Panels With Pyramidal Truss Cores,” Composites, Part A, 47, pp. 31–40.
Xiong, J. , Vaziri, A. , Ma, L. , Papadopoulos, J. , and Wu, L. , 2012, “ Compression and Impact Testing of Two-Layer Composite Pyramidal-Core Sandwich Panels,” Compos. Struct., 94(2), pp. 793–801.
Shaw, J. A. , Grummon, D. S. , and Foltz, J. , 2007, “ Superelastic NiTi Honeycombs: Fabrication and Experiments,” Smart Mater. Struct., 16(1), pp. S170–S178.
ABAQUS, 2012, “ ABAQUS/Standard User's Manual, Version 6.12-1,” Dassault Systemes Simulia Corp., Providence, RI.

## Figures

Fig. 1

Stress–strain curve of typical superelastic SMA

Fig. 2

(a) Cross section with wire weaved through the two facesheets and (b) view at wire bend with cylindrical slot in the facesheet

Fig. 3

(a) Top facesheet, (b) bottom facesheet, (c) cross-sectional view, and (d) SMA truss after fabrication

Fig. 4

Test bed with specimen

Fig. 5

(a) SMA wire elements and (b) finite element model of single cell truss

Fig. 6

(a) Specimen under maximum deformation and (b) deflection contour

Fig. 7

Comparison of load-deformation response between experimental and simulation results

Fig. 8

Continuous static cycling of truss specimen for five cycles

Fig. 9

Comparison between different height trusses for same percentage vertical deflection

Fig. 10

Comparison of hysteresis loop area per unit deflection for different height trusses

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