Determination Of Shear Modulus Research Articles

Nonlinear inversion of the SH wave equation in a half-space for density and shear modulus determination

This paper deals with the problem of multi-parameter nonlinear inversion of the SH wave equation in an elastic half-space. A numerical approach combining Born iteration and a regularizing technique is presented for simultaneously reconstructing 2-D distributions of density and shear modulus in a scatterer embedded in a half-space. The well-to-well source–receiver scheme commonly used in geophysical exploration is considered in the model in which two incident frequencies are used to uncouple the parameters in frequency domain. The weighted residual method, along with bilinear interpolating functions, are used in the discretization procedure. Computer simulations have been conducted on several examples with different density and shear modulus configurations. The numerical results show that the approach proposed has a uniformly convergence for the given objects and has a feature of treating the limited-source well-to-well scheme that causes a more ill-conditioned equation in the inversion procedure.

Determination of shear modulus and Poisson's ratio of polymers and foams by the anticlastic plate-bending method

In this paper, results of research towards development of a test method for the determination of shear modulus and Poisson's ratio of polymers and structural foams are presented. Through this work, a test apparatus was developed which employed anticlastic plate bending behaviour; this device was used for calibration tests on steel and aluminium samples and for tests on a number of polymers, including high density Polyethylene (PE-HD), unplasticized Polyvinylchloride (PVC-U), Polymethylmethacrylate (PMMA) and rigid Polyurethane (PUR) foam. Long-term tests and temperature-dependent tests on PVC-U, PE-HD and PMMA samples were also performed. In some cases, results of the tests with the anticlastic bending method were compared with those obtained from tests carried out with the torsion pendulum method. For theoretical simulation, an analytical formula and a number of finite element analyses were performed. Through these simulations, values for the short-term, long-term and temperature-dependent shear modulus and Poisson's ratio of PE-HD, PMMA, PVC-U and PUR foam were obtained.

Determination of complex shear modulus with thickness shear mode resonators

The electrical response of polymer-coated acoustic wave sensors depends on changes in the surface mass loading and changes in viscoelastic properties of the coating material. In this paper we consider the acoustic behaviour and the electrical response of a thickness-shear mode resonator on changes in shear parameters of the coating material at its fundamental frequency as well as its third and fifth harmonics. The changes in material properties were induced by temperature changes. Both a glassy and a rubbery polymer were investigated. The complex shear parameter and dynamic glass transition temperature were calculated from impedance measurements.

Determination of polymer shear modulus with quartz crystal resonators

The dependence of the electrical response of polymer-coated acoustic wave sensors on the viscoelastic properties of the coating material is used for the determination of the complex shear parameter of thin polymer films. We discuss the acoustic behaviour and the electrical response of a coated quartz crystal vibrating in the thickness shear mode at its fundamental frequency as well as its third and fifth harmonic. The changes in material properties were induced by temperature changes. Both a glassy and a rubbery polymer consistency were investigated. We also discuss the concept of impedance analysis and parameter fitting to extract the coating shear parameters and we introduce a double layer concept for the direct calculation of the polymer shear parameters.

Viscoelastic properties of thin films studied with quartz crystal resonators

We discuss the possibility of determining shear moduli for thin polymeric films coated on quartz resonators by analysing the variation of normalized frequency shift δf/f with different harmonics. For sufficiently thick films, the elastic compliance can be deduced from the increase in δf/f with overtone order. However, a correction must be applied to account for a frequency dependence of the Sauerbrey factor relating frequency shift to film mass. Since the elastic effect scales with the square of the film mass, the correction is most important for thin films. Possible sources of frequency dependence of the Sauerbrey factor are the finite thickness of the electrodes, lateral stress components, and insufficient control of the electrical boundary conditions. In order to obtain the shear compliance, the frequency dependence of the Sauerbrey factor was measured and subtracted from the data on polymeric thin films. The correction procedure can be avoided by using electrodeless quartzes and exciting the vibration with external electrodes across an air gap. Since, in this case, the Sauerbrey factor is approximately constant, the shear compliance can be obtained directly from the variation of δf/f with overtone order.

Shear modulus—Measurement methodology with application to light-cured resin composites

Objectives. This study was conducted to test a novel methodology for shear modulus determination of light-cured resin composites. Methods. Using a butterfly-shaped specimen, a special loading device was able to apply pure uniform shear stress on a significant region of the specimen. Validation of the method was proven by photoelastic experiments. Shear modulus was directly obtained through shear stress-strain curve where the strains were measured by a shear strain gauge rosette. The composite materials analyzed were one microfill (Silux Plus, 3M Dental Products) and four hybrids (Brilliant, Coltene; Herculite XRV, Kerr; Z-100, 3M Dental Products; Graft LC, GC). Analysis of variance was used to evaluate the G modulus (P<0.01). Results. Modulus values varied between 2.54–8.01 GPa. The microfilled material presented the lowest value, and Graft LC presented the highest value. A statistically significant difference was found between all materials (p<0.01). Significance. The described methodology can also be applied to other restorative materials, as well as to adhesion strength measurements.

Vibration analysis and finite element modeling for determining shear modulus of pultruded hybrid composites

An impulse-frequency response vibration technique was employed for determining the shear modulus of glass/epoxy, graphite/epoxy and hybrid (glass-graphite/epoxy) pultruded cylindrical composite rods in torsion. The distribution of the fibers and matrix in the shell-core regions were examined microscopically and the volume fractions of the various constituents determined using the stereology point counting technique. Based on the examined cross-section finite element meshes were generated and analyzed for predicting the shear modulus of such composite rods. It was observed that there was close agreement between the finite element predictions and the experimentally obtained data for only some of the hybrid configurations. The nature of the pultrusion manufacturing process which causes variations in the fiber packing geometry in the shell and core regions of hybrids has been found to significantly influence the accurate prediction of shear modulus, using either analytical or finite element methods.

Determination of Shear Properties for RP Pultruded Composites

A complete understanding of the behavior of a structural system comprising RP components necessitates the determination of material properties for these components. Properties of interest include tensile, compressive, shear and bending stiffness and strength. This study focuses on the identification of a reliable test method for the determination of in-plane shear modulus and strength. Iosipescu shear tests and torsion tests were conducted on coupon samples. Results indicate that the torsion test is an easier and reliable method for the determination of shear modulus whereas the Iosipescu test should be used for the determination of shear strength.

Comparison of optical, needle probe and ultrasonic techniques for the measurement of articular cartilage thickness

Analysis of the mechanical properties of articular cartilage necessitates determination of thickness of the tested tissue. To evaluate the suitability of different methods for thickness measurements, the thickness of bovine and canine knee articular cartilage was determined with optical (stereomicroscopic), needle probe and ultrasonic techniques. The results obtained with the stereomicroscope and the needle probe showed high, linear correlations ( r = 0.97, n = 80). The mean thickness obtained with the needle was slightly higher than the optical thickness (0.88 ± 0.36 mm vs 0.85 ± 0.34 mm, mean ± S.D., n = 80, p < 0.01, matched-pairs Student t-test) or the ultrasonic thickness (0.93 ± 0.42 mm vs 0.87 ± 0.36 mm, n = 45, p < 0.05). The high scatter between optical and ultrasonic thickness, considered to be due to complex measurement geometry of canine knee articular cartilage, invaliditated the use of the A-mode, 10 MHz-ultrasonic device for thickness measurements. Based on the results of uncertainty analysis it is concluded that optical and needle probe methods can be used interchangeably when determining shear modulus of articular cartilage with indentation tests. However, if high area-aspect ratios (indenter radius-to-cartilage thickness ratios) are used in the indentation measurements uncertainty in shear modulus may be markedly increased due to possible errors in the measurement of cartilage thickness.

Simultaneous determination of in-plane shear and transverse moduli of unidirectional composite laminae at different strain rates and temperatures

A semi-empirical method is proposed for the extraction, simultaneously, of the transverse tensile and in-plane shear moduli of unidirectional laminae, at various strain rates and temperatures, from tests on symmetric and balanced ±65 ° angle-ply composite laminates. The extraction method is applied to data obtained from tests on Kevlar-49/epoxy and carbon/ epoxy filament-wound tubes which were subjected to internal pressure loading at three key temperatures of −45, 20 and 70 °C at different strain rates of up to 80/s. The combined effect of strain rate and temperature on these extracted properties is studied by applying strain rate temperature equivalence principles. It is found that the variation of the mechanical properties of the two materials with strain rate and temperature can be adequately described by semi-empirical equations similar to the Arrhenius and Williams-Landel-Ferry relationships, usually used for homogeneous solids.

The shear gage: For reliable shear modulus measurements of composite materials

A special strain gage called the ‘shear gage’ was developed for composite materials testing with notched shear specimens. The shear-gage records the average shear strain across the entire test section between the notches of the losipescu and compact shear specimens rather than just sampling the shear strain over a small region in the center of the test section. Hence, the shear stress/strain response is obtained by dividing the average shear stress (load divided by the cross-sectional area between the notches) by the average shear strain. By placing gages on both faces of the specimen, accurate and repeatable shear-modulus measurements can be made without prior knowledge of the shear strain or stress distributions. This scheme essentially integrates the shear strain through the entire test section. Knowledge of other material properties is not required to accurately determine shear modulus values. The shear gage was tested on a variety of composite and isotropic materials resulting in more reliable shear modulus determination and less scatter than previously possible.

Measurement of dynamic parameters of road pavement materials by the bender element and resonant column tests

Keywords: dynamics ; laboratory equipment ; laboratory tests ; sands ; stiffness ; vibration ... Show All

Improvement in the accuracy of determining shear moduli for orthotropic bars with twisting

A method is described for improving the accuracy of measuring shear moduli under twisting conditions taking account of the compliance of elements by testing an additional specimen.

Evaluation of test methods in the determination of in-plane shear modulus of poly(phenylene sulfide) matrix composites

An investigation was conducted to evaluate the validity of various test methods in the dtermination of in-plane shear moduli of semicrystalline, poly(phenylene sulfide) (PPS) thermoplastic composites. Materials studied included composites based on an orginal, non-optimized composite grade of PPS reinforced with carbon and glass fibers, and another based on the new improved, high-ductility, rapid crystallizing, composite grade of PPS along with optimally sized glass fiber reinforcement. Specimens were prepared in a matched die mold, either as-molded or annealed. It was found that shear test methods, such as ±45° in plane, Iosipescu, and 45° pff-axis tension, are validfor shear modulus measurements of PPS composites if the material has no internal stress cracks. For example, there was no significant difference for in-plane shear moduli determined from these three shear testsw for the improved, thoughened PPS composites. This was attributed to the thoughness and fast crystallization of the PPS composites. This was attributed to the thoughness and fast crystallization of the PPS matrix resin, and the strong fiber/maxtrix interface, however, the ±45° in-place shear test should be used with caution for certain thermoplastic composites,. Becuase of the ±45° lay-up, the annealed[±45]2s original PPS composite la, omates siffered jogj resodia; stresses and were observed to have stress-related cracks. Consequently, the measured shear moduli are lower than the true values. Since we have demostrated that some shear tests amy not be appropriate for modulus measurements of certain composites, it is important to choose the proper test method for the shear characterization of thermoplastic composites.

An Evaluation of the Iosipescu Specimen for Composite Materials Shear Property Measurement

A detailed evaluation of the suitability of the Iosipescu specimen tested in the modified Wyoming fixture is presented. A linear finite element model of the specimen is used to assess the uniformity of the shear stress field in the vicinity of the notch, and demonstrate the effect of the nonuniform stress field upon strain gage measurements used for the determination of composite shear moduli. Based upon test results from graphite epoxy laminates, the proximity of the load introduction point to the test section and the material orthotropy greatly influence the individual gage readings, however, shear modu lus determination is not significantly affected by the lack of pure shear. Correction factors are needed to allow for the nonuniformity of the strain field and the use of the average shear stress in the shear modulus evaluation. The correction factors are determined for the region occupied by the strain gage rosette. A comparison of the strain gage readings from one surface of a specimen with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to eccentric loading which induced twisting and spurious shear stress-strain curves. The discovery of specimen twisting explains the apparently inconsistent shear property data found in the literature. Recommendations for improving the reliability and accuracy of the shear modu lus values are made, and the implications for shear strength measurement discussed.

Evaluating the feasibility of using the asymmetric bending of a beam with V-shaped notches for the shear testing of multidimensional composites

The asymmetric bending of a beam with V-shaped notches has drawn the attention of researchers as a possible method for shear testing. The main shortcoming of this approach is the substantial effect of anisotropy of the elastic properties of the material on the stress distribution in the working section. However, several other features make the method attractive for testing composites with three-dimensional reinforcement schemes: simplicity of specimen preparation and testing; low consumption of materials; simultaneous determination of strength and shear modulus; the possibility of controlling the stress state in the working section by varying the geometry of the V-shaped notch and the test base. The given method is currently undergoing intensive experimental and theoretical study. It was shown that an increase in the angle and radius of the notch leads to a more uniform distribution of shear stress over the height of the working section on specimens made of anisotropic materials. Here, the normal stresses decrease. It was shown that the stress state in the zone between notches is significantly affected by the site of application of the internal load. It was shown that for an isotropic specimen with a base b equal to the specimen height, the contact stressmore » barely penetrates the region between notches. However, an increase in b leads to an increase in the bending stresses near the root of the notch. This may affect the determination of strength in shear. Using specimens of laminated composites with unidirectional and orthogonal schemes, workers determined the parameters of a V-shaped notch that correspond to the actual values of shear strength and shear modulus.« less

Simultaneous evaluation of bending and shear moduli of wood and the influence of knots on these parameters

This paper presents a method of simultaneous evaluation of bending and shear moduli of wooden beams. The method, which is based upon the measurement of two natural frequencies of a beam, is simple to perform. Existing techniques for determining shear moduli of wood based materials are either too cumbersome to carry out or prone to measurement errors. Using this method tests were conducted on matched groups of clear and knotty specimens. It was found that for clear specimens a value of 20 can be assumed for the E to G ratio. For specimens which contain knots the variation was so large that no corresponding figure can be suggested with confidence. But the ratio for knotty materials is though to be higher than 20.

Measurements of elastic constants of ceramic composites using ultrasonic plate mode antiresonances

With oblique incidence of an ultrasonic wave upon a thin anisotropic plate immersed in fluid, in general the quasilongitudinal, flexural, and quasi-SH vibrations are excited. At some angles of incidence, coherent interactions of these waves lead to antiresonance-type minima of the normal displacement on the back surface of the plate and therefore to minima of the transmission coefficient. At off-axis orientations of the thin anisotropic plate relative to the incidence plane, several minima may be found. One of them may be used for shear modulus measurement. The measurements have been performed on (1) a porous aluminum oxide membrane, which is transversely isotropic in the plane of the membrane, and (2) a unidirectional SiC/Al composite membrane, where the fibers lie in the plane of the plate. The elastic constants were extracted from the experimental data by a nonlinear least-squares optimization technique. It is demonstrated that the method gives very good results for determination of in-plane longitudinal and shear moduli.

Interpretation Procedure for Pressuremeter Tests in Sand

A new approach for the interpretation of pressuremeter tests in sands is proposed that permits the determination of shear strength characteristics, dilatancy properties, and shear modulus from the anlaysis of pressuremeter test results. A relatively simple soil model has been developed that takes into account the contracting or dilating behavior of the soil, or both, during the pressuremeter cavity expansion. The soil is assumed to be an elasto‐plastic material with a nonassociated flow rule. To evaluate the proposed interpretation procedure, laboratory cavity expansion tests on Fontainbleau sand specimens have been conducted in a specially designed hollow‐cylinder cell. The comparison between the sand properties (shear modulus, peak friction angle, dilation angle) derived from the cavity expansion tests and those obtained from conventional tests illustrates the applicability of the proposed interpretation procedure.

Shear Modulus of Soft Marine Clays

Abstract Instabilities occur frequently in ocean-bottom sediments where the deposition is faster than the consolidation of the material. Cyclic loading of waves contribute to the existing pore pressures within the sediment reducing the effective stresses. The sediment can lose strength and stability and flow in gullies of depth up to 30 m, on slopes less than 0.5 deg. One theory and some related experiments indicate that, depending on the depositional conditions and state of stress, the failure mechanism for such soft saturated marine clays may not necessarily require large straining of the material. Laboratory determination of low-strain shear behavior or shear modulus of soft marine clays can be complicated if high-frequency dynamic testing methods are utilized. Cyclic loading can promote fast degradation of moduli for these soils even at low strain amplitudes. A monotonic torsional shear device, namely a triaxial vane device, was equipped with a computer-aided data acquisition system to detect low-strain shear deformations under quasi-static loading conditions. The average range of electronically measured strain range was 10−4 to 1 percent, which was compatible with that of a high-frequency, low-strain dynamic testing method, namely, resonant column. Comparison of the dynamic and static moduli reduction curves of artificially prepared soft kaolinite specimens demonstrated the cyclic degradation effects on such clays. The relatively continuous, high-resolution low-strain static data indicated further gain in understanding of low-strain nonlinearity and yielding behavior of soft marine clays.