Tension Cylinder Research Articles

Initiation of damage in a class of polymeric materials embedded with multiple localized regions of lower density

Fatigue and damage are the least understood phenomena in the mechanics of solids. Recently, Alagappan et al. (“On a possible methodology for identifying the initiation of damage of a class of polymeric materials”, Proc R Soc Lond A Math Phys Eng Sci 2016; 472(2192): 20160231) hypothesized a criterion for the initiation of damage for a certain class of compressible polymeric solids, namely that damage will be initiated at the location where the derivative of the norm of the stress with respect to the stretch starts to decrease. This hypothesis led to results that were in keeping with the experimental work of Gent and Lindley(“Internal rupture of bonded rubber cylinders in tension. Proc. R. Soc. Lond. A 1959; 249, 195–205 :10.1098) and agrees qualitatively with the results of Penn (“Volume changes accompanying the extension of rubber”, Trans Soc Rheol 1970; 14(4): 509–517) on compressible polymeric solids. Alagappan et al. considered a body wherein there is a localized region in which the density is less than the rest of the solid. In this study, we show that the criterion articulated by Alagappan et al. is still applicable when bodies have multiple localized regions of lower density, thereby lending credence to the notion that the criterion might be reasonable for a large class of bodies with multiple inhomogeneities. As in the previous study, it is found that damage is not initiated at the location where the stresses are the largest but instead at the location where the densities tend to the lowest value. These locations of lower densities coincide with locations in which the deformation gradient is very large, suggesting large changes in the local volume, which is usually the precursor to phenomena such as the bursting of aneurysms.

On the Global Stability of Compressible Elastic Cylinders in Tension

Consider a three-dimensional, homogeneous, compressible, hyperelastic body that occupies a cylindrical domain in its reference configuration. We identify a variety of hypotheses on the structure of the stored-energy function under which there exists an axisymmetric, homogeneous deformation that globally minimizes the energy. For certain classes of energy functions the uniqueness of this minimizer is also established. The primary boundary condition considered is the extension of the cylinder via the prescription of its deformed axial length, but the biaxial extension of the curved surface is also briefly considered. In particular, the results contained in this paper give conditions on the stored-energy function under which material instabilities, such as necking or the formation of shear bands, are not energy favorable.

Failure tests on full-scale models of grout laminated wood decks

Grout laminated wood decks (GLWDs), representing the third generation of stressed wood decks, comprise either laminates or logs trimmed to obtain two parallel faces. The logs or laminates, running along the span, are held together by means of transverse internal grout cylinders that may be in either compression or tension. Two full-scale models of GLWD were constructed at Dalhousie University, Halifax, one with grout cylinders in compression and the other with the cylinders in tension. Service load tests conducted in Halifax showed that the former deck had better load distribution characteristics. Two years after the tests in Halifax, the models were shipped to The University of Manitoba in Winnipeg, where they were tested to failure under a central patch load. Because of miscommunication with the supplier, the logs of the GLWD with grout cylinders in compression were also trimmed to the third face that was kept at the bottom of the deck. The failure tests showed that despite its superior load distribution characteristics, the deck with grout cylinders in compression failed at a significantly lower load than the GLWD with cylinders in tension. It is argued that a planar surface in the logs at the flexural tension face not only reduces their flexural stiffness but also brings the defects of wood to the surface with maximum stress. The deck with the flat bottom surface underwent tension failure of the most heavily loaded logs, whereas the deck with the intact round surface of the logs at both top and bottom failed by horizontal splitting of all the logs.Key words: articulated plate, bridge deck, grout laminated deck, orthotropic plate, timber.

On the buckling of cylindrical shells with through cracks under axial load

Presence of cracks or similar imperfections can considerably reduce the buckling load of a shell structure. In this paper, the buckling of cylindrical shells with through cracks has been studied. A general finite element model has been proposed, verified and applied to some novel cracked shell buckling problems for which documented results are not available. A special purpose program has been developed for generating finite elements models of cylindrical shells with cracks of varying length and orientation. The buckling behavior of cracked cylinders in tension and compression has been studied. The results of the analysis are presented in parametric form when it seems to be appropriate. Sensitivity of the buckling load to the crack length and orientation has also been investigated.

A Systematic Method to Determine Optimal Specimen Geometry for Measuring Concrete Fracture Properties by the Peak-Load Method

Abstract The peak-load method is a simple method for determining the fracture properties KIcS and CTODc of the two-parameter fracture model of concrete. With this method, the fracture properties can be determined from the measured peak loads of several different (or distinct) specimens. Specimens can be made distinct in specimen shape, size, notch length, and loading configuration. To quantitatively identify the degree of specimen distinction, a variable named specimen distinction number is proposed. When test specimens are considerably distinct, random experimental errors have negligible effect, and determination KIcS and CTODc is of high accuracy. Thus test specimens can be optimized to obtain the most accurate values of the fracture properties. A previous experimental program found that change in specimen shape (e.g., a hole drilled at the axis of splitting tension cylinder) can largely expand the specimen distinction. An experimental program reported in this paper shows that changing loading configurations of beams (or prisms) from bending to eccentric compression can also largely enhance the specimen distinction and therefore provide KIcS and CTODc determination of high accuracy.

Splitting tension tests to determine concrete fracture parameters by peak-load method

Abstract An experimental program confirms that the peek-load method can be successfully applied to splitting tension tests to determine fracture parameters KIcS and CTODc of the two-parameter fracture model from the measured peak loads. The peak-load method requires distinct specimens. It is found that a hole drilled at the axis of splitting tension cylinder can largely expand the specimen distinction. Combination of tests on splitting tension cylinders with and without a hole raises the reliability of the KIcS and CTODc values determined by the peak-load method.

Plastic Yielding in Ice Single Crystals

Stress-strain relations in single crystals were investigated using ice cylinders in tension. The cylinders were deformed at strain rates varying from 8×10-6 min-1 to 4×10-4 min-1 and at temperatures between -15 and -40°C. The stress-strain curves obtained showed large yield drops and the amount of the drop increased with an increase in the deformation rate or with decreasing temperature. The stress-strain curves of ice single crystals from those of materials such as LiF, Ge, InSb etc., which also show large yield drops in that the slope of initial, linear portion of the curves varies with the strain rate and with temperature. Another characteristic feature of the curves is that past the yield point the curves do not show minimums. This indicates that ice crystals do not work-harden. The maximum stress τmax, and the slope of the initial, linear portion M=(dτ/dε)i are taken as characteristic parameters of the curves. Their dependence on temperature and strain rate are given as follows: M=(M0+D\\dotε exp (E1/RT) and τmax∝\\dotε1/m exp (E2/RT) where m=1.53 and E1=8.4 Kcal/mole and E2=10.4 Kcal/mole Values for the activation energy E2 and m indicate that the results are in good agreement with those expected from interpretations of creep experiments based on Johnston's theory of movement and multiplication of dislocations. Specific features of the stress-strain curves are also discussed in terms of a special characteristic of ice crystals.

Internal Rupture of Bonded Rubber Cylinders in Tension

Abstract An unusual rupture process is described. It consists of the sudden appearance of internal cracks in bonded rubber cylinders at a well-defined and comparatively small tensile load. The cracks occur in all the vulcanizates examined, and in particularly weak rubbers are found to cause failure. Their appearance may also lead to marked changes in the load-deflection relationship. A theoretical treatment is presented on the basis of a proposed criterion for crack formation. It is assumed that they form when the negative hydrostatic pressure component of the applied stress reaches a critical value. It is shown by means of the theory of large elastic deformations that a critical value of the negative pressure exists at which any cavity in the rubber will burst, and the calculated value is shown to be in satisfactory agreement with experiment. Moreover, the theory successfully predicts the observed dependence of the cracking stress on the Young's modulus of the rubber, its virtual independence of the rubber strength and extensibility, and the general form of the observed variation of cracking stress and crack disposition with the thickness of the testpiece.

Internal rupture of bonded rubber cylinders in tension

An unusual rupture process is described. It consists of the sudden appearance of internal cracks in bonded rubber cylinders at a well-defined and comparatively small tensile load. The cracks occur in all the vulcanizates examined, and in particularly weak rubbers are found to cause failure. Their appearance may also lead to marked changes in the load-deflexion relationship. A theoretical treatment is presented on the basis of a proposed criterion for crack formation. It is assumed that they form when the negative hydrostatic pressure component of the applied stress reaches a critical value. It is shown by means of the theory of large elastic deformations that a critical value of the negative pressure exists at which any cavity in the rubber will burst, and the calculated value is shown to be in satisfactory agreement with experiment. Moreover, the theory successfully predicts the observed dependence of the cracking stress on the Young’s modulus of the rubber, its virtual independence of the rubber strength and extensibility, and the general form of the observed variation of cracking stress and crack disposition with the thickness of the test-piece.