Static Analysis of the Effect of Shape Memory Alloy in Laminated Beam

Article History: Received: 10 November 2020; Revised: 12 January 2021; Accepted: 27 January 2021; Published online: 05 April 2021 Abstract: This study deals with the effect of shape memory alloy in carbon/epoxy laminated beam. In this study we analyses static response of laminated beam under the load of 10 KN at the mid span of the beam. In this study a cantilevered beam of dimension 1000mm length, 100mm width and 30mm height which is divided in 3 layers of 10mm each is considered. The study includes three cases. In first case all the 3 layers of beam is laminated with carbon/epoxy. In second case the top and the bottom layers are laminated with carbon/epoxy and middle layer is2qw laminated with shape memory alloy. In the third case the top and the bottom layers are laminated with shape memory alloy while the middle with carbon/epoxy. Loading and boundary conditions are same for all the three cases. All the analysis is done using ANSYS workbench 15.0


Introduction
Shape memory alloy is a material, which keeps its shape in memory and can be made to return to its actual shape after getting deformation if subjected to an appropriate thermal process [1]. The phase change occurs in SMA's over a range of temperature [2]. The recovery of strains imparts to the material at a low temperature, as a result of heating is called Shape Memory Effect and the formation of stress induced (at higher temperature) Martensite from Austenite (at low temperature) phase result in a phenomenon called pseudo-elasticity [3]. In the past few decades SMA is receiving more attention in research area. Many researchers have been working on the application of unique properties of SMA like shape memory effect and pseudo elasticity in various engineering applications [4]. Many researchers have contributed to the wide accessible literature on the study of experimental and observational behavior of SMA [5]. There are many approaches that have been evolved to mark the constitutive behavior of these materials [6]. Beams are important element of structures and are widely used in machinery, aerospace and in light weight structures. In their service life they are subjected to various static as well as dynamic loads of certain frequency of vibrations which leads to their failure [7]. Vibration analysis has become important in the design and development of such engineering systems [8]. This study deals with the effect of shape memory alloy in carbon/epoxy laminated beam. In this study we analyses the static response of laminated beam under the load of 10 KN at the mid span of the beam [9].

Materials and Methods
The properties of shape memory alloy and carbon/epoxy are given in the Table 1  Properties of Carbon/Epoxy are given in Table 2. Shape memory alloys are extensively used in several domains of engineering to handle a set of applications, which are given in figure 1. These alloys can be utilized either as independent or as a reinforcement in composites based on the application. The SMAs are commercially available in sets of geometries like wires, rods, ribbon, springs, foils, and also as foams. The sintered NiTi alloy foam of high porosity (71-87%) are being examined to be comparable with the intended performance of human bone. Application domain of shape memory alloys are shown in Figure 1.

Figure 1. Application domain of shape memory alloys
Usually, pre-strained SMAs are used in such a way that on heating more than the austenite finish temperature, the material changes back to its actaul dimensions resulting from restoration. A rise in pre-strain leads to a parallel increase in stress related to the slip and dislocation motion. According to ASTM E3098, the process adopted for pre-straining the SMA has been briefly given in Figure 2.

Modeling and Simulation
For modeling and analysis of laminated beam with SMA and carbon-epoxy, ANSYS Workbench 15.0 version is to be used which is based on Finite Element Method (FEM). ANSYS 15.0 has innovative features for composites, bolted connections and improved mesh tools. The ANSYS Workbench platform provides a comprehensive and integrated system. ANSYS workbench provides higher productivity in product development simulation because it has an in-built application and access to Multiphysics and system level application. The equation of motion of Composite laminated plate with and with no cutouts is resolved employing FEM tool (ANSYS) in the form of the equation of motion for a laminate with cutouts is hard to be visualized and hence any FEM tool is the only probable solution for the analysis of the vibration features of laminate with cutouts. The ANSYS 15 finite element program was considered for free vibration of the orthotropic (Composite) Laminated plate. To this end, the key points were first generated and later line segments were created. Multiple layers are specified along with the Orientation and thickness. The lines were merged to form an area. At last, this area was shaped to model the laminated plate. Schematic of static analysis is shown in Figure 3.

Geometry
In this work a cantilevered beam of dimension 1000mm length, 100mm width and 30mm height which is divided in 3 layers of 10mm each is considered. The figures below show the geometry of the beam.  Figure 4 shows the Isometric view of the geometry of the beam. Isometric projection is a technique used for visually defining 3-D objects in 2-D in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes seem to be equally contracted and the angle between any two of them is 120 degrees.   Figure 6 shows the Elevation view of a 3-D object from the view of a vertical plane along an object. Otherwise said, an elevation is a side view as seen from the front, back, left or right sides.

Meshing
The figure 7below shows the meshing of the laminated beam. Here rectangular mechanical mashing is done for both static as well as harmonic analysis.

Loading and boundary conditions
Loading Condition is shown in figure 8. The loading and boundary conditions used for all 3 cases are given as below: 1. In static analysis a concentrated load of 10 KN at the mid of the beam is considered. 2. Boundary conditions are one end is fixed and another end free.

Case.1
In case-1 all the three layers of beam is laminated with carbon/epoxy for both static as well as harmonic response analysis.

Case.2
In second case the top and the bottom layers are laminated with carbon/epoxy and middle layer is laminated with shape memory alloy.

Case.3
In the third case the top and the bottom layers are laminated with shape memory alloy while the middle with carbon/epoxy.

Results and Discussion
Following figures and graphs shows the maximum total deformation, maximum stress, and maximum strain for all three cases full carbon/epoxy laminated beam, with SMA at Centre, and with carbon-epoxy at Centre       Table 3 shows the Maximum deformation, Maximum Equivalent von-mises stress and maximum Equivalent von-mises strain in all the three cases.  Figure 18 shows the Max total deformation when full beam is laminated with carbon/epoxy Figure 19. Max stress when full beam is laminated with carbon/epoxy, when SMA at Centre and when carbon/epoxy at Centre Figure 19 shows the Max stress when full beam is laminated with carbon/epoxy, when SMA at Centre and when carbon/epoxy at centre  Figure 20 shows the max strain when full beam is laminated with carbon/epoxy, when SMA at Centre and when carbon/epoxy at Centre

Conclusions
When we use SMA at Centre there is decrease in deformation by 17.7%, increase in stress by 90.13 %, decrease in strain by 19 %, as compared to full carbon/epoxy laminated beam. When we use carbon epoxy at center there is decrease in deformation by 81.79%, increase in stress by 8.2429 %, decrease in strain by 86.58 %, decrease in deformation by 77.77 % as compared to full carbon/epoxy laminated beam. When we use carbon/epoxy at Centre there is decrease in stress by 43.07 %, decrease in strain by 83.433 % as compared to SMA at Centre. From the above observation we can conclude that shape memory alloy increases the strength

Future Scope
In future we can use other fiber materials to enhance the properties of the laminate and we can perform Fatigue as well as free and forced vibration analysis using same composite.