Determination Of Dynamic Elastic Modulus Research Articles

Determination of dynamic elastic modulus of materials under a state of simple stresses by using electrodynamic actuators in beam-type mechanical elements

The dynamic elastic modulus is an important parameter for the study of solid mechanical elements. Even though there exist several well-established standardized methods that allow determining this parameter under a state of simple stresses, some of these may require sophisticated laboratory equipment or involve the use of multiple devices (impulser, sensor transducer…). The main purpose of this work is to propose an alternative approach that uses a single electrodynamic actuator both as an impulse exciter and vibration sensor simultaneously. By generating a random signal excitation and measuring the electrical input impedance of the actuator when coupled to a beam-type cylindrical element, the fundamental flexural mode of vibration of the latter can be identified and the dynamic elastic modulus of its material determined in a simple and straightforward manner. Preliminary experiments were performed over different size beams with rectangular cross-sections made of natural stone, marble, wood, and aluminium. Results were compared to those obtained using the standardized procedure described in the ASTM E1876 for the same specimens, these showing a good agreement in terms of dynamic elastic modulus.

Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Rectangular Timoshenko Prisms

AbstractIn this paper, the exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions is determined with an accurate shear shape factor. The exact soluti...

Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Timoshenko Rods

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

Evaluation of residual mechanical properties of steel fiber-reinforced reactive powder concrete after exposure to high temperature using nondestructive testing

Abstract Reactive powder concrete (RPC) is classified as ultra-high performance concrete, owing to its superior strength, excellent durability and high fracture energy. However, RPC may also be severely affected by devastating fire exposures. This paper presents the variations in residual mechanical properties of RPC after exposure to high temperature. The strength of RPC after cooling was also assessed by nondestructive tests (NDTs). The ultrasonic pulse velocity (UPV) method and resonance frequency (RF) method were used. The samples were subjected to the target temperature of 120℃, 300℃, 500℃, 700℃ and 900℃. The heating was continued for further 3 hours so that steady state condition was achieved. The available equations have been used for determination of dynamic elastic modulus of RPC using UPV and RF measurements. The residual mechanical properties, RF and UPV were plotted as a function of temperature. The result shows that the residual strength increases from room temperature to 300℃. However, above 300℃, it’s decreasing gradually. Various comparisons have been made between residual mechanical strength versus UPV and RF measurements. Relationships have been proposed among residual mechanical properties versus NDTs values. These relationships can be employed for post-fire strength assessment of RPC structures.

Determination of dynamic elastic modulus of polymeric materials using vertical split Hopkinson pressure bar

This paper is focused on the determination of dynamic elastic modulus of polymer materials under high strain rate loading using the split Hopkinson pressure bar (SHPB) technique. Experiments conducted on the epoxy specimen by the traditional SHPB and the proposed vertical SHPB equipment demonstrates that the vertical SHPB can give more accurate measurements. The related factors, namely, the effect of stress inequilibrium in specimen, indentation in bars due to specimen and the tilt between specimen and bars, are extensively studied. It is concluded through theoretical analysis and numerical calculations that the influence of stress inequilibrium becomes negligible after two characteristic times. The numerical study on the indentation effect shows that the bar to specimen specific elastic modulus ratio and specific diameter ratio are critical to the level of influence on indentation. However, polymers with low elastic modulus values can still be accurately measured regardless of the indentation displayed. The numerical investigation on tilt effect indicates that the imperfect contact condition severely affects the accuracy of measured elastic modulus. This issue can be rectified by the newly proposed vertical SHPB. It can improve the contact conditions between bars and specimen significantly and offer acceptable accurate measurements for the dynamic elastic modulus of polymeric materials.

Comparison of Nondestructive Evaluation Findings, Constrained and Unconstrained Wave Speeds, Dynamic Moduli, and Poisson’s Ratio of Core Specimens from a Concrete Structure Damaged by Fire

This article discusses the use of nondestructive and subsequent laboratory materials testing techniques in evaluation of extent of fire damage to a precast prestressed parking structure. The nondestructive and laboratory testing findings were used in determination of extent of fire damage to concrete and potential effects on the prestressing tendons. The in-situ nondestructive testing phase consisted of scanning affected areas using ultrasonic pulse velocity through concrete members and use of impact echo on a confirmatory limited basis. Subsequently, cores were removed and tested for resonant frequency-based dynamic modulus in accordance with ASTM C 215. Upon determination of dynamic elastic modulus of the entire core per ASTM C 215, the cores were sawn into 25-mm (1-in.) disks. Young’s modulus of individual disks was determined by utilizing nondestructive measurement of resonant frequency. Determination of Young’s modulus at small depth increments permitted assessment of the heat-induced damage gradient into the concrete and more importantly at the level of the prestressing tendons. The data from multiple techniques provided a means of comparison between constrained in-situ ASTM C 597 pulse velocity to unconstrained compression wave velocity obtained from ASTM C 1383, and an estimated unconstrained compression wave velocity based on dynamic modulus based on disks. The results of these comparisons should be of value to practicing engineers utilizing these techniques in forensic evaluations.

Damage assessment in cellulose–cement composites using dynamic mechanical characteristics

This paper reports on an experimental investigation of test methods that can detect damage in cement composites, incorporating cellulose macro-nodule fibers, subjected to freezing/thawing and immersion in hot water. Conventional methods of ascertaining damage, such as porosity and flexural strength testing, were carried out, along with dynamic mechanical testing for determination of elastic modulus and damping capacity. Increase in porosity and reduction in flexural strength (as compared to normally cured specimens) were observed for low fiber volume composites subjected to freezing and thawing, whereas no significant changes were observed for specimens with higher fiber volumes. Determination of dynamic elastic modulus and specific damping capacity at regular intervals of exposure showed that the high volume of porous macro-nodules in the mixture prevented damage due to freezing and thawing by acting as stress release sites. No appreciable change in porosity and flexural strength was observed for specimens continuously exposed to hot water; however, reduction in relative modulus and increase in damping capacity was observed. The changes in these system properties suggest that a certain degree of damage might be occurring under sustained hot water exposure, which the determination of porosity and flexural strength could not capture. Using a stiffness-loss map, it is shown in this paper that the damping characteristic is more sensitive than the stiffness in detecting damage as a result of continuous exposure to hot and wet conditions.

The Modeling and Determination of Dynamic Elastic Modulus of Metal Matrix Composites

The Modeling and Determination of Dynamic Elastic Modulus of Metal Matrix Composites

Modelling and determination of dynamic elastic modulus of magnesium based metal matrix composites

The aim of the present study was to determine the elastic modulus of magnesium based composites containing different volume fractions of SiC particulate using an innovative suspended beam type impact based technique. This applies classical vibration theory, which relates the resonant frequency of the test specimens to the geometry and material properties of the metal matrix composites. The elastic modulus values were determined from the funda mental resonant frequency obtained from the experiment and density measurements. In addition, a finite element model was proposed for determining the dynamic elastic modulus of MMCs with different SiC reinforcement content using the first natural frequency corresponding to the flexural mode. The elastic modulus values obtained from the finite element model were in close agreement with the values obtained from the impact based experiments and in better agreement than those from theoretical methods such as the shear lag, Eshelby, and Halpin–Tsai models.

The modeling and determination of dynamic elastic modulus of magnesium based metal matrix composites

The aim of the present study was to determine elastic modulus of the magnesium-based composites containing different volume fraction of SiC particulates using an innovative free-free beam type impact based technique. This technique is based on classical vibration theory, by which the geometry and material properties of the metal matrix composites are related to resonant frequency of the test specimen. With the fundamental resonant frequency obtained from the experiment and density determined by the Archimedes' principle, the elastic modulus values were determined. In addition, a finite element model is proposed for different SiC weight percentage samples for the determination of dynamic elastic modulus using the first natural frequency corresponding to the flexural mode. The elastic modulus values obtained using finite element method were found to be in close agreement with the values obtained from the impact based experiments and in better agreement when compared to theoretical methods such as Halpin-Tsai method. Both the theoretical approaches, in common, exhibit the increasing trend of elastic modulus value with an increase in weight percentage of SiC particulates.

A note on the measurement of damping in vibrating rods

The theory of the determination of dynamic elastic modulus and damping from observations of the resonance curves of thin rods vibrating longitudinally or in torsion is discussed. Formulae are derived for these quantities in terms of resonance frequency and bandwidth for cases where the higher-order harmonics are used and where the damping is neither very small nor independent of frequency. A formula given by Lethersich and Pelzer in this Journal(5) is amended.