In the longitudinal direction of the sample, the total extension will be the sum of the extensions of the individual zones of different stress states in the tensile test with the lateral restriction (equation (3)), that is, the sum of the stresses in the two zones subjected to uniaxial stress of sample length b and one zone subjected to biaxial stress of sample length a (equation (4)), If there is a lateral restriction at the tensile stress of the material, then εy = 0 (no lateral deformation) and is also equal to the sum of deformations of all stress zones in the horizontal direction of the sample, followed by equation (5), Rearranging the above equation, equation (6) is obtained. Q6: State true or False. Since these angles are closer to the direction of the weft, where a small gap between the two distributions is also apparent throughout the whole extension range (Figure 6(b)), it can be concluded that the influence of the main weft direction influenced the difference between the distribution at these angles, and for these directions, the model should be adjusted by introducing the corrective factor. Curve slope change at the beginning of the extension is somewhat smaller. The measurement of Poisson’s ratio can be a delicate matter. This is generally accomplished using the tension-compression tests. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression. For tensile deformation, Poisson’s ratio is positive. However, in the case of extension outside the main axes, the Poisson’s ratio gains higher values up to 3.9. Again, the Poisson ratio will be the ratio of relative contraction to relative expansion, and will have the same value as above. We were getting ready to use some newly-purchased high heat extensometers for Poisson’s ratio measurements. Enter the strain in both directions into the formula to calculate the poisson’s ratio. Lengths a and b derive from the geometry of the cross-shaped sample and their values are a = 5 cm and b = 7.5 cm. 4.3 In this test method, the value of Poisson's ratio is obtained from strains resulting from uniaxial stress only. Indeed the study presented a novel approach to accurately determine the Poisson’s ratio using the thermal expansion properties of PDMS and an optical surface scanning device. In the direction of the weft, distributions of cross-shaped and adjusted module have sigmoid form whereby at the extension of 1%, modulus has minimum values of about 15 MPa; while the elongation increases the modules increase up to 120 MPa at 6.5% extension. Thus. For the calculation of Poisson’s ratios for cross-shaped samples through the model, the cross-shaped samples in plain and twill weaves with 20 threads/cm in both the directions were analyzed. The distribution of the modules in the directions with the same angular distance from the warp direction is very close to the point of being overlapping, suggesting the extreme orthotropy of the fabric woven in the plain weave. The tested fabrics were produced on the same weaving machine, woven from the same warp (same production lot) in two different weaves, plain weave and twill 2/2 weave. The properties of the material in these two main directions may differ, and therefore the elastic modulus may also be distinguished. The Poisson's ratio of a stable, isotropic, linear elastic material cannot be less than −1.0 nor greater than 0.5 due to the requirement that Young's modulus, theshear modulus and bulk modulus have positive values. View or download all content the institution has subscribed to. in which it appears a/(2b+a) as a geometric, corrective factor. Q8: What does the Poisson’s ratio 0.5 mean? In places where there is no interlacements between the warp and weft, threads are more mobile, which results in less stable structure of the fabric, and in these places, the contact area between the two thread systems is smaller. where α represents normal shear coefficient. This property is important for many engineering applications and computer simulations, and has been studied in many researches.1–9, The problem of determining Poisson’s fabric ratio is the subject of many researches. In 1992 she received her PhD degree for mechanical engineering on microturbines and micromotors. This could be due to the smaller compactness and diagonal geometry of the twill fabric, compared to plain fabric. If we had not checked the entire system we could have been issuing data that was about 25 percent lower than it should have been. The main advantage of this novel technique was that it only requires a profilometer, FEM simulations and numerical mathematics to determine the Poisson’s ratio, without any additional tensile testing setup or advanced tracking methods, in particular since tracking the transverse deformation of elastomers to such an accuracy is non-trivial. Please read and accept the terms and conditions and check the box to generate a sharing link. Poisson’s values in homogeneous, isotropic, elastic materials range between 0 and 0.5. Figures 8 to 10 show the distribution of elastic modules in the different directions of the twill weave K2/2, density 20/20 threads/cm for the cross-shaped sample, and the adjusted E* obtained from the model (equation (16)). The ratio of this lateral to longitudinal strain is defined as Poisson's ratio. The amount of deformation a material experiences due to an applied force is called strain. In the tensile test with lateral restriction, the lateral force is measured by means of a measuring device having a high rigidity relative to the test material itself, which means that the displacements achieved in the horizontal plane of the sample are very small. This results in equation (12), From equation (12), it is possible to express σy, that is, vTL which gives equation (13), By incorporating σy in equation (11), for the purposes of comparison of the uniaxial, ordinary tensile test, and the tensile test with lateral restriction, equation (14) is obtained, Then the relative extension of the complete sample (where l = 2b + a) is given by equation (15), The corrected elastic modulus from the tensile test with the lateral restriction comparing to the modulus of elasticity obtained from the ordinary, uniaxial tensile test is then described by equation (16).