Machines and Robots Driven by Muscle Like Acting NiTi Alloys

1. Introduction

 A The research presented has the aim to show that better optimized systems based on Shape Memory Alloys (SMAs) can be designed using muscles working as biomimetic model. In particular the Skeletal muscles and the antagonistic pairs have been used as biomechanical model, they are the voluntary muscles that allow the body to move and they make up 40% of an organism’s body mass (Lindstedt, 2016).

Skeletal muscles are held to the bones by tendons, which role is to transfer the force generated by the muscles contraction to the bone joint. Tendons are made of robust tissue and they work as special viscoelastic connectors between bone and muscle. For an adduction movement in a joint, contraction and shortening of the muscle generates a force that is applied on a lever system that causes the joint adduction movements. To recover its initial position, the reciprocal muscle on the other side of the joint contracts and shortens. As described by Biewener and Roberts (2000), muscles are normally coupled in opposition so that movements of joints are driven by a mechanism in which one group of muscles contracts while another group relaxes or lengthens (Aversa et al., 2017 a-e, 2016 a-o; Petrescu et al., 2017, 2016 a-e; Petrescu and Petrescu; Petrescu).

Basically antagonistic pairs are muscles where one moves the bone in one direction and the other moves it back the other way in transmission of nerve impulses to the muscles. In the adduction movement of a human arm, the agonist biceps shortens and bends the forearm on the elbow joint, conversely, on arm abduction movement; the antagonist triceps shortens and returns the forearm to its original position. In general, the muscle that applies the force needed for a movement is only one of agonist-antagonistic pairs and, in particular, there is always a selective stimulation driven by the brain that acts on the muscle that contracts or shortens (agonist), while the behaviour of the reciprocal is passive, it works roughly like a brake (antagonist). The active muscle for a specific movement is always the one that contracts (Yang et al., 2013).

A unique class of Smart Materials that has in common with muscles the capability to react to an impulse (thermal in this case) with a change of shape and thus also with a contracting movement if necessary is that of Shape Memory Alloys (Van Humbeeck, 2010; Meisel et al., 2014; Melton and Mercier, 1980).

This analogy between muscles contraction and extension and the ability of this class of intermetallic alloys to undergo contraction and extension (superelasticity) under the effect of thermal and mechanical stimulation, allow us to derive a biomechanically inspired machine based on these materials.

U.S. Naval Ordnance Laboratory discovered shape Memory Effect for the first time during 1960s. The researcher of the Laboratory found this effect in a 1 to 1 alloy of Nickel and Titanium, but only nowadays, a higher spread for biomedical field, actuators, couplings and surgical instruments. Anyhow, applications of SMAs for industrial or product design are still so poorly spread and SMAs potentialities are only rarely and weakly exploited.

Nickel-Titanium alloys are intermetallic compounds (Otsuka and Ren, 1999) and they able to show thermal shape memory effect, namely, to return to their original shape on heating even when largely deformed (up to 10%).

The Stress-Strain-Temperature diagram of Fig. 1 resumes the thermo-mechanical behaviour of these NiTi based materials.

The NiTi alloy assumes, at higher temperatures, an interpenetrating simple body centred cubic structure known as Austenite (Meisel et al., 2014).

When brought at lower temperatures (treatment A in Fig. 1 and 2), this intermetallic alloy freely solid-solid transforms to a constrained and more complex face-centred tetragonal crystalline structure identified as Martensite.

The Body-Centred Cubic (BCC) crystal structure of Austenite (Xiangyang et al., 2003) shows only one possible crystallographic habit that can be got at equilibrium (high temperatures state 1 in Fig. 1) that is identified as B2 type (Fig. 2). On cooling, Austenite crystals undergo a constrained solid-solid diffusionless transformation to metastable Martensite. After Otsuka and Ren (1999) it has been recognized that, in binary TiNi transformation proceeds from the parent BCC structure (B2 type in Fig. 2) to martensitic FCC lattices. The body-centred cubic parent austenitic phase (B2) may transform by a diffusionless local shear mechanism into an orthorhombic or monoclinic martensite phases. The later martensite lattice is a monoclinic B19′ phase (Otsuka et al., 1971; Knowles and Smith, 1981; Miyazaki et al., 1984; Matsumoto et al., 1987), which has been justified as a monoclinic alteration of the B19 orthorhombic structure (Fig. 2).

The transition amongst these structures needs small thermal activation because involves diffusionless transformation and easily results in the restrained and rapid rearrangement of atomic positions.

For this crystalline conformation, however, two differently oriented crystallographic variants with small energetic differences exist. These two configurations consist of the twinned (B19 in Fig. 2) and detwinned (B19’ in Fig. 2) rearrangements of atomic planes without crystal plane slip (states 2 and 6 of Fig. 1). Due to thermodynamic considerations, the twinned structure freely occurs in unstressed conditions (state 2).

The Martensite is described to be crystallographically reversible, which involves that a given plate undergo a backward reverse shear upon heating.

Normally, the Martensite forms, on cooling, only under Ms, however, it could even occur at temperatures higher than Ms if a stress is applied (Yang and Wayman, 1999).

The Martensite formed in these conditions is named Stress-Induced Martensite (SIM).

It can be deduced that the prevailing driving force for Martensitic transformation above Ms is not thermal but mechanical (transformations B in Fig. 1 and 2). Above the temperature where Martensitic transformation starts (Ms), the stress required to produce SIM progressively increases with increasing temperature (Šittner et al., 2014).

where, P is the pressure, T is the temperature and ΔH is the latent heat of phase change (that can be determined by DSC analysis) and ΔV is the volume change of the phase change (the volume change for NiTi Austenitic to Martensitic phases may be calculated from the dimension of the crystalline units, namely a cube of 0.3015 nm for Austenite to the 0.4622×0.4120×0.3015 nm for the Martenisite (orthotrombic or nonoclinic).

Moreover, it has been theoretically predicted (Clasius Claypeiron Equation 2) and experimentally determined (Šittner et al., 2014) that the level of mechanical loading necessary to create Stress Induced Martensite (SIM) growths linearly with temperature. These reversible solid-state phase transformations are known as a martensitic transformation that requires to occur, depending on temperature, mechanical loading stresses between 70 to 140 MPa (Duerig et al., 1990).

According to Equation 2 the stress drops to zero at the temperature Ms.

The difficulty to stress induce Martensite continues to increase with temperature until Md, above which the critical stress required to induce Martensite is greater than the stress required to move the dislocations (not reversible plastic deformation).

Therefore the temperature range for SIM is from Ms to Md. For a number of SMA systems, the agreement in the temperature dependence of the stress to form SIM according to the Clausius-Clayperon equation is quite striking.

The equation works equally well for the non-isothermal case, i.e., the case where temperature was held constant while the stress needed to form Martensite was measured.

Super-elasticity occurs when a material is deformed above As, but still below Md. In this range, Martensite could be stabilized with the application of stress, but becomes unstable upon removal of stress.

By mechanical stretching (treatment B in Fig. 1 and 2), in fact, the SMA is deformed to a larger extent (states 3 to 4 in Fig. 1 and structures B19 and B19’ in Fig. 2). This pseudo-plastic deformation is enabled by reorientation of crystallographic variants in the cold temperature phase following twinned (B19) to de-twinned (B19’) martensite transformations. Consequently, the deformation persists after load removal (from state 2 to 3 in Fig. 1). On re-heating, process C in Fig. 1 and 2, the material progressively transforms to Austenite B2 crystal lattice (from state 6 to intermediate state 7 and final state 1 in Fig. 1) recovering its initial shape.

During this shape recovery, large strain changes and large forces are generated that are of particular benefit for the development of temperature-activated actuators.

As reported on the temperature axis of Fig. 1, the four characteristic temperatures of SMAs are Mf (Martensite finish), Ms (Martensite start) on cooling and As (Austenite start) and Af (Austenite finish) on heating.

When SMA is heated, it starts to change into Austenite phase at As and it completes the transition at Af temperature; similarly, on cooling, it starts the transformation to Martensite at Ms temperature and it completes the transition at Mf temperature.

However, for some NiTi alloy compositions, an intermediate phase, called R-phase with rhombohedral structure, could also manifest, in this case the characteristics temperatures are indicated as Rs and Rf. This event manifests itself by thermal events that can be measured in Differential scanning Calorimetry. The calorimetric analysis has been run on our samples to identify not only austenitic than martensitic characteristic temperatures but also the occurrence of the intermediate rhombohedral lattices.

The SMAs can exhibit two kind of Shape Memory Effect (SME), defined as one-way and two-way effects. For one-way effect we mean the SMAs ability to remember and resume the macroscopic shape associated with austenitic phase when heated up to Af temperature; for two-way effect, instead, we mean the first ability described added to the capability to recover also the macroscopic shape associated with martensitic phase when cooled up to Mf temperature.

To get one or two-way memory effect, in order to program pre-set shapes for martensitic and austenitic phases, thermo-mechanical treatments are required (Naresh et al., 2016).

The basic idea of this paper on how and why to use the biomechanical model of muscles working is discussed in the next paragraphs.

 

1. Materials, Methods and Procedures

 

Materials

In order to experiment and develop the biomimetic model aimed to the optimization of systems based on SMAs wires Dinalloy Inc.

Flexinol is a SMA with Nickel and Titanium as main chemical constituents.

Apparatus and Procedures

Differential Scanning Calorimetry (DSC)

Thermocalorimetric analyses have been carried out on NiTi alloys. The DSC technique determines the temperature and the heat flows associated with material transitions as a function of time and temperature. It also provides quantitative data on endothermic (heat absorption) and exothermic (heat evolution) processes of materials during physical transitions (Ziólkowski, 2012; Shaw et al., 2008).

The thermocalorimetric characterization has been carried out in a nitrogen atmosphere by a Mettler ADSC Differential Scanning Calorimeter equipped with a liquid nitrogen cooling unit in the range of temperatures between -30 and 120°C. Temperature scans were carried out at 5°C/min. For sample stabilization, isothermal scan were run at 500°C, heat flux were recorded up the final apparent equilibrium (heat flux = 0). The high temperature treatment induces the crystal structure atoms to re-arrange into the most compact and regular pattern possible finally resulting in a rigid cubic austenite phase (Kauffman and Mayo, 1993). A typical DSC thermogram performed on a specimen of Flexinol wire (0.25 mm of diameter, 4,00 mg) has been reported in Fig. 3.

 

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