Dynamic Torsional Tests Research Articles

Modulus of rigidityof commercially important wood species for Mexico: Pinus pseudostrobus, Tabebuia rosea and Quercus scytophylla

Wood is a biological material with applications in engineering and architecture. Its modulus of rigidity is useful for the calculation of beams that work in bending and torsion. The objective of the research was to determine the rigidity moduli and material indices of Pinus pseudostrobus, Tabebuia rosea and Quercus scytophylla. Dynamic torsion tests were performed on 35 small specimens of each species. Linear correlations and their coefficients for determining the modulus of rigidityas a function of density and frequency were calculated. The main results are: The magnitudes of the wood densities of P. pseudostrobus, T. roseaand Q. scytophyllaare located within the interval:587 kg m-3, 735 kg m-3. The coefficient of variation of the frequencies for Q. scytophyllais 50% lower compared to the coefficients of P. pseudostrobusand T. rosea. The coefficient of variation for P. pseudostrobusis 23% greater than that of T. roseaand 146% greater than that of Q. scytophylla. It is concluded that the values reported in this research may be useful if these wood species are used for structural purposes.

Various mechanical tests of carbon fiber monofilaments

In recent years, in order to accurately predict the mechanical properties of carbon fiber-reinforced plastic by computer-aided engineering, it has become important to understand the mechanical properties of carbon fiber as a reinforcement material. Since carbon fiber is a material whose properties are highly anisotropic, information on tensile properties only in the axial direction of the fiber is not sufficient for predicting composite properties, and tests to obtain properties in various directions are desired. This paper discusses the anisotropy of carbon fibers by presenting the results of our previous tests on carbon fiber monofilaments, including observation of the changes in fiber diameter, dynamic and static torsion tests, torsion-tension tests, transverse crush tests, axial compression tests and three-point bending tests, and finite element method analysis using elastic moduli obtained from these tests.

Behavioral evaluation on the engineering properties of lignin-stabilized loess: Reuse of renewable materials

Lignin as an eco-friendly material is being studied in the field of soil modification. To examine its feasibility and performance in solidifying loess, this study carried out a series of laboratory tests on physical, chemical, and mechanical properties of lignin-stabilized loess, including Atterberg limits, standard Proctor compaction, unconfined compressive strength, dynamic triaxial torsional shear, pH, conductivity, X-ray diffraction, and scanning electron microscope test, taken into account the effects of curing time and freeze–thaw cycles, analyzed the solidification mechanism. The results showed that the Atterberg limits, maximum dry density, and optimum moisture content were not affected by the lignin content. The strength of stabilized loess showed increased first and then decreased with the growth of lignin content, and the maximum strength was achieved at the lignin content of 1.5%, strength increased by nearly 60%. The strength of the test sample decreased significantly under freeze–thaw cycles, but after 6 cycles, the strength tended to stabilize. The pH value showed a declining trend with the growth of lignin content, while the conductivity showed an opposite trend. The Attberg limits, pH, and conductivity of the stabilized loess were hardly affected by freeze–thaw action. In addition, the results of X-ray diffraction indicated that there was no new mineral composition generated in the stabilized loess.

Shear band formation in porous thin-walled tubes subjected to dynamic torsion

In this paper, we have performed 3D finite element calculations of thin-walled tubes subjected to dynamic twisting to investigate the effect of porous microstructure on the formation of shear localization bands under simple shear conditions. For that purpose, we have incorporated into the finite element model the porous microstructures of four different additive manufactured metals – aluminium alloy AlSi10Mg, stainless steel 316L, titanium alloy Ti6Al4V and Inconel 718 – for which the void volume fraction varies from ≈0.001% to ≈2%, and the voids size between ≈6μm and ≈110μm (Marvi-Mashhadi et al., 2021). For each microstructure, we have created up to 10 realizations varying the spatial location of the voids and the distribution of voids size. The matrix material is elastic/plastic, with yielding defined by the von Mises yield criterion and associated flow rule. The yield stress evolution is considered to be dependent on strain, strain rate and temperature, with parameters corresponding to Titanium and HY-100 Steel, taken from Molinari (1997) and Batra and Kim (1990), respectively. Moreover, we have assumed the deformation process to be adiabatic. The calculations have been performed for shear strain rates ranging from 100s−1 to 10000s−1. To the authors’ knowledge, this is the first study ever that simulates dynamic torsion testing of porous materials with actual representation of voids, providing new results which bring to light the influence of porosity on dynamic shear banding under simple shearing. Namely, the numerical calculations have shown that both the location of the shear band and the critical strain leading to the shear band formation depend on the spatial and size distribution of the voids in the specimen, evidencing the influence of material defects on the localization pattern. Notably, the shear band nucleation strain decreases with both the void volume fraction in the specimen and the size of the voids, the size of the largest pore being the main microstructural feature controlling the loss of load carrying capacity of the specimen. In addition, we have carried out a parametric analysis varying the temperature and strain rate sensitivities of the material, and the loading rate. For the strain rates investigated, increasing the loading speed leads to a mild decrease of the shear strain leading to shear band formation, while the strain rate sensitivity is shown to stabilize material behavior and delay localization. Moreover, the numerical results have made apparent that for the hardening materials considered, thermal softening is essential to trigger the shear band formation, so that the porous microstructure alone does not lead to shear localization.

Investigation into structural and mechanical aspects of localization of plastic deformation and fracture under dynamic loading

An experimental testing technique was developed to conduct experimental study of plastic strain localization in specimens made of AMg6, D16 and Steel 3 alloys subject to dynamic torsion tests in the split Hopkinson pressure bar device fitted with infrared camera. The temperature values determined in-situ during dynamic torsion tests of the specimens made from AMg6, D16, Steel 3 alloys do not exceed 50° C, which indicates that temperature softening contributes insignificantly to the process of plastic strain localization. A method was developed and applied for determining the strain fields in the zone of plastic shear localization in the specimens made of AMg6, D16, and Steel 3 alloys, which were specially designed to study plastic strain localization during static deformation and dynamic loading on the split Hopkinson pressure bar using for this purpose the StrainMaster system. A comparison of the experimentally obtained strain fields with the results of numerical simulation, which was made using the kinetic equations for the evolution of defects of the mesoscale, yields rather good agreement to within 20%. This study examined post-test specimens specially designed for studying plastic deformation localization. The application of an optical interferometer-profilometer New View - 5010 allowed structural analysis of these specimens, processing of 3D data on the deformation relief and subsequent computation of the scale invariant (Hurst index) and the spatial scale of the zone where the correlated behavior of microshears is observed. The comparison of the scale invariant characteristics of the D16 alloy specimens obtained during static deformation and dynamic loading revealed a significant increase in the Hurst exponent (H~0,74) over a wide range of spatial scales (0,6-110,8 μm ) compared to the undeformed specimens (H~0,42 in the range of spatial scales 1,9-29,2 μm ). More meaningful results can be associated with the changes in both lower and upper scales, which indicates pronounced features of the localization of deformation. The structure of specimens made of AMg6 alloy, specially designed for studying the plastic strain localization after dynamic tests in the split Hopkinson pressure bar, was examined using the scanning electron microscope. The obtained data testify to significant evolutionary processes occurring in the defective subsystems undergoing dynamic deformations.

Feasibility Study of a Combined Tension-Torsion Hopkinson Bar

The increasing interest to improve the description of the plastic behavior and the fracture prediction for ductile materials under complex loading conditions conducted the researchers to overcome the J2 plasticity theory. To do this more sophisticated plasticity model base on ductile damage have been implemented. Material model parameters must be identified by means of proper testing and calibration procedures requiring different loading conditions. Different types of tests must be performed, imposing multiaxial stress paths to the specimens. Tensile tests on smooth and round notched bars, plane strain tests, torsion tests, compression and combined tension–torsion tests on hollow and solid cylindrical bars must be executed. While multiple works are present in literature for model assessment and validation in quasi-static conditions, nothing can be found at high strain rate in biaxial conditions (tension-torsion). Biaxial tests in dynamic conditions are very difficult to carry out especially if you are interested to register the entire story of stress and strain. In this work, analytical and numerical study to evaluate the feasibility to carry out dynamic tension, dynamic torsion, dynamic torsion-static tension/compression and dynamic tension–dynamic torsion tests is discussed. The tests will be performed using a properly designed Split Hopkinson Bar.

Multi-Scale Rheo-Mechanical Study of SMA Mixtures Containing Fine Crumb Rubber in a New Dry-Hybrid Technology

Aiming to study the rheo-mechanical effects of fine crumb rubber into gap graded stone mastic asphalt (SMA) mixtures, a multi-scale experimental approach was adopted. Therefore, in the perspective of the reuse of end of life tires’ in asphalt layers, the adopted new dry-hybrid technology effects have been investigated from the mastic, mortar and mixture points of view. The new rubberized asphalt production technology allows the use of rubber powder as filler, the rubber amount optimization being validated through multi-scale performance tests. Mastics and mortars’ complex modulus measured with dynamic shear and torsional tests were related to the mixture stiffness modulus recorded in direct tension-compression mode. The rheological properties of mastic are strictly influenced by the rubber presence, and consequently the asphalt mixtures stiffness and thermo-sensitivity are connected to the mastic and mortar rheo-mechanical behavior. Results are consistent through the adopted approach and reveal that with the new dry-hybrid technology, overcoming the wet and dry limits, it seems to be possible obtaining more durable and eco-friendly bituminous pavement layers.

The Low Viscosity Loess Liquefaction and its Microstructure Analysis

Low viscosity powder loess is widely distributed in loess plateau areas of northwest China. It has a high liquefaction potential. the mechanism of low viscosity loess water action is studied using CT scanning. CT scanning results showed that initially, water in loess will tend to rise as a whole. Then, cement salts around the loess grains melt and form large holes. Finally, deformation collapse and damage can occur. In this study, low viscosity loess is compared with sand loess and clayey loess obtained from Lanzhou, Guyuan, and Tongguan. Based on the results of dynamic triaxial torsion tests, the low viscous powder loess dynamic loading time was shorter and more easily liquefied than sandy loess and clayey loess. Electron microscope scanning of loess microstructures showed the chemical element ratios around the loess particles produced cemented material (such as Ca/Fe). The chemical elements around loess particles and the pore diameter/grain ratio were selected to evaluate liquefaction resistance in loess. In addition, loess particle size distribution and the pore/grain ratio also influenced the liquid level. It is an effective innovative method to judge the liquefaction strength of low viscosity silt based on microcosmic parameters.

Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters.

An accurate material representation of polymeric interlayers in laminated glass panes has proved fundamental for a reliable prediction of their response in both static and dynamic loading regimes. This issue is addressed in the present contribution by examining the time–temperature sensitivity of the shear stiffness of two widely used interlayers made of polyvinyl butyral (TROSIFOL BG R20) and ethylene-vinyl acetate (EVALAM 80-120). To that end, an experimental program has been executed to compare the applicability of two experimental techniques, (i) dynamic torsional tests and (ii) dynamic single-lap shear tests, in providing data needed in a subsequent calibration of a suitable material model. Herein, attention is limited to the identification of material parameters of the generalized Maxwell chain model through the combination of linear regression and the Nelder–Mead method. The choice of the viscoelastic material model has also been supported experimentally. The resulting model parameters confirmed a strong material variability of both interlayers with temperature and time. While higher initial shear stiffness was observed for the polyvinyl butyral interlayer in general, the ethylene-vinyl acetate interlayer exhibited a less pronounced decay of stiffness over time and a stiffer response in long-term loading.

Synthesis and mechanical properties of bio-sourced polyurethane adhesives obtained from castor oil and MDI-modified cellulose acetate: Influence of cellulose acetate modification

In this study, cellulose acetate and castor oil have been used to synthesize new eco-friendly alternatives to traditional polyurethane adhesives. First, cellulose acetate (CA) was modified with diphenylmethane-4,4′-diisocyanate (MDI) at different NCO:OH molar ratios, ranging from 2 to 4.53, and then the resulting biopolymers were mixed with castor oil (CO) at 1:1 wt ratio. The fully cured bio-sourced adhesives were rheologically characterized by applying dynamic oscillatory torsional tests at different temperatures (from −30 up to 200 °C). Furthermore, their adhesion performance on stainless steel and poplar wood substrates was analyzed, by conducting standardized mechanical tests, namely single-lap shear and 180° peel strengths, at room temperature and 100 °C. Fourier transform infrared spectroscopy-attenuated total reflectance along with differential scanning calorimetry and thermogravimetric analysis were also performed. Above a critical NCO:OH ratio, a thermo-rheological simplicity was found within the whole temperature range considered, being able to apply the t-T superposition principle. However, an increase in the temperature led to a depletion in their mechanical performance, thus reducing their temperature range of application. Thermal and spectroscopic analysis corroborated the complete disappearance of free isocyanate during the first few days of curing, and a segmented structure, typical of polyurethanes. Optimum thermo-rheological behaviour and adhesion performance on wood and stainless steel of the bio-sourced polyurethanes studied were found for NCO:OH molar ratios higher than 3.5, which was related to the higher compatibility between hard and soft microdomains.

A Multi-Module Electrodynamic Exciter with a Variable Pole-Arc Ratio Disk Halbach Array for a High-Bandwidth Dynamic Torsional Stiffness Test.

In this paper, a multi-module electrodynamic exciter based on moving-magnet disk voice coil motor is presented to meet the demands of high torque and high bandwidth in a dynamic torsional stiffness test. A variable pole-arc ratio disk Halbach array (VPAR-DHA) is proposed, so that both high torque density and low rotor inertia can be obtained through enhancing the magnetic field in the working range. The analytical quasi-3-D model of VPAR-DHA was set up by using the harmonic function method, with the consideration of end-effects by a correction function. Electromagnetic structure optimization was carried out with the analytical model, and verified by 3-D finite-element (FEM) results. The proposed design was experimentally tested and verified with a prototype that achieved a peak dynamic torque output of 40 Nm at a frequency of 120 Hz, and a stroke of ±1°. The proposed method can also be easily extended to satisfy various demands of dynamic torsional stiffness test.

Mechanical performance of lumbar intervertebral body fusion devices: An analysis of data submitted to the Food and Drug Administration

Lumbar intervertebral body fusion devices (L-IBFDs) are intended to provide stability to promote fusion in patients with a variety of lumbar pathologies. Different L-IBFD designs have been developed to accommodate various surgical approaches for lumbar interbody fusion procedures including anterior, lateral, posterior, and transforaminal lumbar interbody fusions (ALIF, LLIF, PLIF, and TLIF, respectively). Due to design differences, there is a potential for mechanical performance differences between ALIF, LLIF, PLIF, and TLIF devices. To evaluate this, mechanical performance and device dimension data were collected from 124 Traditional 510(k) submissions to the FDA for L-IBFDs cleared for marketing from 2007 through 2016. From these submissions, mechanical test results were aggregated for seven commonly performed tests: static and dynamic axial compression, compression-shear, and torsion testing per ASTM F2077, and subsidence testing per ASTM F2267. The Kruskal-Wallis test and Wilcoxon signed-rank test were used to determine if device type (ALIF, LLIF, PLIF, TLIF) had a significant effect on mechanical performance parameters (static testing: stiffness and yield strength; dynamic testing: runout load; subsidence testing: stiffness [Kp]). Generally, ALIFs and LLIFs were found to be stiffer, stronger, and had higher subsidence resistance than PLIF and TLIF designs. These results are likely due to the larger footprints of the ALIF and LLIF devices. The relative mechanical performance and subsidence resistance can be considered when determining the appropriate surgical approach and implant for a given patient. Overall, the mechanical performance data presented here can be utilized for future L-IBFD development and design verification.

Investigation on shear modulus and damping ratio of transparent soils with different pore fluids

Transparent soil, manufactured with transparent granular particles and pore fluid with matching refractive index, used to mimic the behavior of natural saturated soil, is widely used in visualization model tests. The properties of transparent soils are not only affected by granular particles’ characteristics, but also influenced by pore fluids’ characteristics. However, the researches focused on the dynamic properties of transparent soil influenced by pore fluids are relatively rare in the literature. In this paper, the dynamic shear modulus and damping ratios of transparent soils manufactured by fused quartz and three different pore fluids (mixed oil, calcium bromide $$(\hbox {CaBr}_{2})$$ solution, and sucrose solution) were measured through a series of resonant column tests and dynamic torsional shear tests. The laboratory tests on dry fused quartz specimens were also carried out for comparative analysis. It is found that the transparent soils have a certain similar dynamic behaviors as those of natural soil, and the values of dynamic shear modulus and damping ratios are influenced by pore fluids. With the test results, transparent soil manufactured by fused quartz and mixed oil shows a great potential as a substitute for natural sand and is expected to be widely used in dynamic model tests.

Dynamic Behavior of Soft Subgrade Soils Treated with Boron Waste

A series of laboratory tests using resonant column and dynamic torsional shear tests were conducted on kaolinite and montmorillonite clays treated with boron waste. The effect of the boron waste on the dynamic characteristics of two clays was studied considering the effects of the plasticity index. Pulverized boron waste was mixed with the clay soils in different proportions. It has been seen that treatment with boron waste improved the dynamic properties of the two clays. However, increasing the amount of boron waste does not affect the dynamic characteristics of the samples in the same proportions. Increasing the amount of boron waste in the mixture increased the initial shear modulus of the montmorillonite clay up to 300% compared to untreated samples, whereas the reaction of the kaolinite clay with boron waste treatment was moderate. Degradation curves of treated and untreated soils in regard to shear strain are presented. In general treatment, success is dependent on the amount of boron waste and the clay type. The continuous increase with the amount of boron waste in the shear modulus and damping ratio is apparent on both clays.

Numerical Simulation on the specimen dynamic plastic deformation behaviour in the torsional split Hopkinson bar test

The torsional split Hopkinson bar (SHB) is an important method to study the dynamic shear behaviour and shear localization of materials under high strain rates. Different specimen sizes were used in literatures, and the size of the specimen might have an effect on the experimental results. Numerical simulation on torsional SHB tests was carried out with LS-DYNA. The strain signal on the incident and transmitted bars were obtained from the simulation just as the experiment. Then the numerical strain-stress relationship of the material was derived from the numerical strain signal using the experiments data process of torsional SHB. The agreement between numerically derived strain-stress results and the specimen material properties specified in numerical modelling indicates that the torsional SHB is applicable to study the dynamic shear behaviour of materials under high strain rates. The specimen gauge diameter has no significant effect on the dynamic torsional test result. However, higher adhesive strength is required to fix the larger gauge diameter specimen on the bars. The specimen gauge thickness has little effect on the experimental results with a modified formula to calculate the specimen stress. Still, the increase of specimen gauge thickness will lead to the increase of non-uniformity of specimen stress and strain (strain rate). Based on the simulation analysis, suggestions on the specimen size design are given as well.

On necessary precautions when measuring solid polymer linear viscoelasticity with dynamic analysis in torsion

Solid polymer linear viscoelasticity in shear is often characterized by applying torsion and using the Saint-Venant solution when rectangular prismatic specimens are considered. It is shown that experimental dynamic torsion tests can show a dependency of the storage modulus and damping factor on the dimensions of the rectangular prismatic specimen when linear temperature ramps are applied. While the discrepancy of damping factor is explained by temperature heterogeneities and can be corrected easily by applying temperature steps, the inconsistency of storage modulus is due to an invalid application of the Saint-Venant solution. Finite element simulations allowed definition of the sample dimensions for which the Saint-Venant solution provides a good approximation, and a coefficient is given to correct the results obtained with commercial instruments when other sample dimensions are used.

Mechanical performance of cervical intervertebral body fusion devices: A systematic analysis of data submitted to the Food and Drug Administration

Cervical intervertebral body fusion devices (IBFDs) are utilized to provide stability while fusion occurs in patients with cervical pathology. For a manufacturer to market a new cervical IBFD in the United States, substantial equivalence to a cervical IBFD previously cleared by FDA must be established through the 510(k) regulatory pathway. Mechanical performance data are typically provided as part of the 510(k) process for IBFDs. We reviewed all Traditional 510(k) submissions for cervical IBFDs deemed substantially equivalent and cleared for marketing from 2007 through 2014. To reduce sources of variability in test methods and results, analysis was restricted to cervical IBFD designs without integrated fixation, coatings, or expandable features. Mechanical testing reports were analyzed and results were aggregated for seven commonly performed tests (static and dynamic axial compression, compression-shear, and torsion testing per ASTM F2077, and subsidence testing per ASTM F2267), and percentile distributions of performance measurements were calculated. Eighty-three (83) submissions met the criteria for inclusion in this analysis. The median device yield strength was 10,117N for static axial compression, 3680N for static compression-shear, and 8.6Nm for static torsion. Median runout load was 2600N for dynamic axial compression, 1400N for dynamic compression-shear, and ±1.5Nm for dynamic torsion. In subsidence testing, median block stiffness (Kp) was 424N/mm. The mechanical performance data presented here will aid in the development of future cervical IBFDs by providing a means for comparison for design verification purposes.

Shear modulus and damping ratios of transparent soil manufactured by fused quartz

The mixture of fused quartz and pore fluid with the same refractive index has been used as a synthetic transparent soil to mimic the behavior of natural soil. Previous research has focused on its static properties. In this paper, the dynamic properties of fused quartz (dry samples and oil saturated samples), including shear modulus and damping ratio, were examined through a series of resonant column tests and dynamic torsional shear tests. It was found that fused quartz has similar dynamic behavior to that of natural soil. With the test results, fused quartz shows a great potential as a substitute for natural soil and is expected to be widely used in dynamic transparent soil model tests.

Nonuniform shear strains in torsional Kolsky bar tests on soft specimens

Abstract : We investigate inertial effects in torsional Kolsky bar tests on nearly incompressible, soft materials. The results are relevant for materials with instantaneous elastic shear modulus on the order of 1 1000 kPa and density on the order of water. Examples include brain tissue and many other soft tissues and tissue surrogates. We have conducted one- and three-dimensional analyses and simulations to understand the stress and strain states that exist in these materials in a torsional Kolsky bar test. We demonstrate that the short loading pulses typically used for high strain-rate (e.g., 700 = s) tests do not allow the softer specimens to ring-up to uniform stress and strain states and that consequently the shear stress versus shear strain data reported in the literature are erroneous. We also show that normal stress components, which are present even in quasistatic torsion of nonlinear elastic materials, can be amplified in dynamic torsion tests on soft materials. Kolsky bar tests are widely used to study strain-rate effects in inelastic solids [Gray 2000; Chen and Song 2011]. In a compression Kolsky bar test, a relatively thin specimen is sandwiched between two bars. Impact at one end of the incident bar generates a compressive wave that travels along the bar, through the specimen, and into a transmission bar. The goal of this test is to subject the specimen to uniform uniaxial stress and uniform (biaxial) strain at a prescribed axial strain-rate. These uniform conditions can often be achieved after an initial ring-up period involving multiple wave reflections from the specimentransmission bar and specimen-incident bar interfaces. Once uniform conditions have been achieved in the specimen, the axial stress, axial strain, and axial strain-rate histories in the specimen can be deduced from strain gage measurements on the elastic bars: the axial stress is proportional to the strain in the transmission bar, and the axial strain-rate is proportional to the strain in t

Behavior of Nickel-Titanium Instruments Manufactured with Different Thermal Treatments

IntroductionThe purpose of this study was to investigate if nickel-titanium instruments with similar designs manufactured by different thermal treatments would exhibit significantly different in vitro behavior. MethodsThirty-six instruments each of ProTaper Universal (PTU F1; Dentsply Maillefer, Ballaigues, Switzerland), ProFile Vortex (PV; Dentsply Tulsa Dental Specialties, Tulsa, OK), Vortex Blue (VB, Dentsply Tulsa Dental Specialties), and TYPHOON Infinite Flex NiTi (TYP; Clinician's Choice Dental Products, New Milford, CT) (all size 25/.06) were evaluated. Bending resistance, torsion at failure, and dynamic torsional tests were performed with the instruments (n = 12). Analysis of variance and Tukey post hoc tests were applied. ResultsFlexibility was significantly higher for TYP compared with the other 3 groups (P < .0001). With respect to the maximum torque at failure, PV group showed the highest resistance to twisting (torsional strength) among the analyzed instruments followed by VB, TYP, and PTU. The TYP group exhibited greater angular deflection at failure compared with the other groups (P < .0001). The mean dynamic torque scores during simulated canal preparation were highest for TYP (3.01 ± 0.71 Ncm) and lowest for PV (1.62 ± 0.79 Ncm). However, no significant differences were observed comparing groups PTU with TYP and VB and VB with PV (P > .05). The highest mean forces were recorded with PTU (7.02 ± 2.36 N) and the lowest with TYP (1.22 ± 0.40 N). ConclusionsTYP instruments were significantly more flexible than the other instruments tested. The PV group had the highest torsional strength and TYP, despite being the most flexible, showed similar torsional moments to the other instruments, whereas its angular deflection was the highest among the groups.