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Analysis of Young's modulus for Carboniferous sedimentary rocks and its relationship with uniaxial compressive strength using different methods of modulus determination

Małkowski P., Ostrowski Ł., Brodny J.

Journal of Sustainable Mining

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2018

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Vol. 17, iss. 3

145--157

EN

Young’s modulus (E) is one of the basic geomechanical parameters used in rock engineering in practice. It is determined based on uniaxial compressive test (UCS). However, according to International Society of Rock Mechanics it can be calculated by three different ways: as the tangent, secant and average modulus. The results from each method are significantly different. The UCS tests was carried out on 237 rock specimens with the slenderness ratio 2 of Carboniferous claystones, mudstones and sandstones. The axial deformation was always measured automatically by the displacement measurement device (LVDT) built into the testing machine and connected to the hydraulic piston. Then the Young’s modulus was calculated for each test by all three methods. The analysis of the results is presented in this paper to show the difference between all the three moduli calculated for each specimen, and to recommend the best method of Young’s modulus determination. First, the typical range of the elastic linear deformability for the chosen rock types was determined as 25-75% of the peak strength at confidence interval 95% for these sedimentary rocks. The modulus value distributions obtained from each calculation method were compared using statistical parameters: mean value, median, minimum, maximum, standard deviation, mean difference at confidence interval 95%, and non-uniformity coefficient. The proportions between average-secant modulus (Eav/Esec) and average-tangent modulus (Eav/Etan) for the rock samples were estimated. For the studied rocks the obtained values were: 1.10-1.32% for Eav/Esec, 1.08-1.25% for Etan/Esec and 1.01-1.06 for Eav/Etan (for Etan with the range of 20-80% of peak strength). These values show low coherence between secant and average modulus (ca. 23% difference) and good consistency of average and tangent modulus. Based on the analysis, tangent Young’s modulus is recommended as the guiding one at the constant range of 30-70% of the ultimate stress. Secant Young’s modulus, as it comprises not only elastic strain but the pore compaction as well, should be named as modulus of deformability. This conclusion was further confirmed by the regression analysis between UCS and E. The highest regression coefficients and the lowest standard error of the regression was obtained for tangent Young’s modulus determination method. In addition, modulus ratio MR for claystones, mudstones and sandstones was studied and determined as 274, 232 and 223 respectively.

2

Determination of the elasticity range of paper

Szewczyk W.

Fibres & Textiles in Eastern Europe

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2010

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Vol. 18, no. 1 (78)

98--103

EN

This research work presents a method for the determination of the limit of elasticity of paper considered as a variable dependent on stress and the time of its duration. For plane stress it was found that in the case of a low share of permanent strain in the total strain, we can assume that the highest value of its share appears on one of the principal axes of stress. Such an assumption allowed to use a one-dimensional rheological model to define the permanent range in a two dimensional state of stresses for paper.

PL

W ramach pracy zaproponowano sposób wyznaczania granicy sprężystości papieru, traktowanej jako zmienna zależna od wartości naprężeń i czasu ich działania. Dla płaskich stanów naprężeń, występujących w płaszczyźnie papieru wykazano, że w przypadku małego udziału odkształceń trwałych w całkowitych można przyjąć, że największa wartość udziału odkształceń trwałych w całkowitych występuje dla jednego z kierunków naprężeń głównych. Takie założenie, pozwoliło na wykorzystanie jednowymiarowego modelu reologicznego do określenia zakresu sprężystości w dwukierunkowym stanie naprężeń papieru.

3

Coherence Analysis of the Charasteristics of Wound Woolen Yarn Deformation

Radivojevic D., Stamenkovic M., Stepanovic J., Trajkovic D.

Fibres & Textiles in Eastern Europe

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2008

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Vol. 16, no. 4 (69)

29--33

EN

In the winding process, on its way from the spinning tube to the bobbin, yarn was exposed to different influences that caused various tensions in different sectors. The increase in the tension force brought about a decrease in the linear density of all the wound yarns. All of this influenced the resulting tension with which the yarn was wound onto the bobbin. After two weeks, the deformation characteristics of these yarns were examined. Also determined were values of the breaking forces and relative elongation at break for all the linear density. On the basis of a F-ε curve, elasticity limits were defined as well as the yield point of the wound yarns analysed. Making use of the recommendations of some investigators, it was possible to project the breaking forces, elasticity limit force and forces at the yield point. The quality control of raw materials, process control and yarn quality control are a necessary help for the technologist to establish a well-set winding process. It is only on the basis of the exact parameters provided by such controls that it becomes possible to intervene correctly and in time in order to achieve optimal results and obtain good quality wound yarn.

PL

W procesie przewijania, przędza na drodze od cewki przędzalniczej do nawoju poddana jest różnorodnym wpływom, które powodują powstanie zróżnicowanych naprężeń przędzy na jej długości. Wzrost naprężeń powoduje zmniejszenie się masy liniowej przędzy dla wszystkich przewijanych przędz. Wpływa to na wynikowe naprężenia przędzy nawijanej na nawój. Charakterystyki deformacji przędzy były badane w dwa tygodnie po nawinięciu. Określano również wartości siły zrywającej i względnego wydłużenia dla wszystkich badanych mas liniowych. Na podstawie krzywych siła-wydłużenie określano granice elastyczności oraz parametry pełzania. Na podstawie rekomendacji pewnych badaczy można przewidywać siłę zrywającą, granice elastyczności i parametry pełzania. Kontrola jakości surowca i otrzymywanej przędzy oraz parametrów procesu są niezbędną pomocą dla technologa w celu określenia prawidłowych nastaw procesu przewijania. Jedynie na podstawie w ten sposób ściśle określonych parametrów istnieje możliwość odpowiedniej ingerencji w proces w celu otrzymania optymalnych rezultatów nawijania i dobrej jakości nawijanej przędzy.