Strain circumferential

The torsion-tube test described by Whitney, Pagano, and Pipes [2-14] involves a thin circular tube subjected to a torque, T, at the ends as in Figure 2-29. The tube is made of multiple laminae with their fiber directions aligned either all parallel to the tube axis or all circumferentially. Reasonable assurance of a constant stress state through the tube thickness exists if the tube is only a few laminae thick. However, then serious end-grip difficulties can arise because of the flimsy nature of the tube. Usually, the thickness of the tube ends must be built up by bonding on additional layers to introduce the load so that failure occurs in the central uniformly stressed portion of the tube (recall the test specimen criteria). Torsion tubes are expensive to fabricate and require relatively sophisticated instrumentation. If the shearing strain y 2 is measured under shear stress t.,2, then... 

Peel Strength. Samples were prepared by cutting 2.5" (63.5 mm) wide radial sections, bead to bead. The sample was then sectioned into two 1.25" (31.75 mm) radial strips, which were each cut circumferentially at the centerline of the tread resulting in four test specimens (2-SS and 2-OSS). Each sample was cut with a razor knife for a length of 1" (25.4 mm) from the skim end of the test strip, midway between the belts, to facilitate gripping the ends in the T-2000 stress-strain tester jaws. The sides of each specimen were scored midway between the belts, to a depth of 1/8" (3.175 mm) radially from the end of the gripping surface to the end of belt 2 in the shoulder area, providing a 1" wide peel section. The peel test was performed at 2"/min (50.8 mm/min) at 24°C. 

The radial (diametrical strain) will be the same as the circumferential strain e2. For any shell of revolution the dilation can be found by substituting the appropriate expressions for the circumferential and meridional stresses in equation 13.36. 

Figure 5.127 Effect of strain on elastic fraction of aorta in the circumferential (solid triangles) and axial (open squares) directions, as well as on skin (open circles). Reprinted, by permission, from F. H. Silver and D. L. Christiansen, Biomaterials Science and Biocompatibility, p. 202. Copyright 1999 by Springer-Verlag.

For thin-walled cylinders subject to in-plane (axial and circumferential) loading and axial torsion, Whitney and Halpin [8] have developed an analytic solution for strains. Their analysis is valid in the central region of the cylinder, end support effects are neglected. 

Consider now the circumferential normal strain rate ree By definition... 

By symmetry, the two principal directions of stress (and strain) are in the meridian direction, Tin, and the circumferential direction 7133. The third principal stress is zero. Show that if body and acceleration forces are neglected, the following equilibrium equations are obtained for thin membranes ... 

There are several ways to bond strain gauge elements. In Figure 3.139, the working element is a tube closed on one end, with the other end open to the process pressure. Four strain gauges are bonded to the outside of this tube. Two of the elements are strained under pressure, and two are not because they are mounted longitudinally and circumferentially. 

Figure 6.1. Stress-strain curve for aorta. Tensile stress-strain curve for human thoracic aorta in the circumferential direction obtained at a strain rate of 50% per minute. At strains less than 0.2, the elastic fibers dominate the behavior, whereas above 0.2, alignment of collagen fibers occurs. (Adapted from Silver, 1987.)...

Figure 8.3. Strain dependence of elastic fraction of connective tissues using a sequential incremental loading program, the elastic fraction as a function of strain (%) for (A) aorta tested in the circumferential (A) and axial directions ( ), and skin (O), (B) pericardium ( ), psoas major tendon (A), and dura mater (O). (From Dunn and Silver, 1983.)...

Active stresses exerted by smooth muscle cells appear to increase the internal stresses that exist in vessel wall. The effects of passive and active muscular contraction on the residual stress in the wall have been considered. Their results suggest that basal muscle tone, which exists under physiological conditions, reduces the strain gradient in the arterial wall and yields a near uniform stress distribution. Increased muscular tone that accompanies elevated blood pressure tends to restore the distribution of circumferential strain in the arterial wall, and to maintain the flow-induced wall shear stress at normal levels. It appears that the active stresses exerted by smooth muscle cells may balance the tension within the vessel wall in a similar manner to the way that active fibroblast tension balances the stress in the dermis. 

The exact calculation of radial and circumferential stresses in each layer requires the solution of N+2 linear equations in N-r2 unknowns, namely the N-H radial displacements of the layer boundaries, and the longitudinal strain of the vessel. We simplify by assuming that the internal pressure is applied only to the steel shell, and that the other layers follow the expansion of the steel. We also assume a condition of plane stress that is, no stress in the axial direction of the cylindrical vessel. We also consider the layer as being flat when layer stresses are being computed. 

Tji Temperature at outside of layer n T Average temperature in a lining 5t Temperature drop across a layer A Change in a parameter when conditions change S Circumferential stress e Circumferential strain d Thickness, inches W Width of brick or mortar, inches... 

The law has been found that in cylinders of metal, the circumferential strain on the different pai-ts varies inversely as the squares of the distances of the parts from the axis. According to this ratio a two-inch gun with two inches of metal, will be internally fractured l>efore the exterior receives one-twelfth part of the strain causing the fracture. Of course increasing the thickness still more would add very little to its strength. 

How then are we to equalize this immense circumferential strain which possesses the same ratio of inequality in all solid masses of metal ... 

Fig. 10. Results of FliM calculations of the spherical indentation surface profile (a), radial (b) and circumferential (c) surface strains versus radial distance from the centre of the indent for a piecewise linear work hardening (tangent modulus Et - 0.1 E for , < 0.02 and Er -- 0.0044 E for e, >0.02 (full line) T = 0.1 E (dashed line) E - 180 GPa, v =- 0.3,...

By inserting the calculated substrate strain, es, into formulas (1) and (2), one finds a decrease of the stress in the scale with distance from the periphery of the indent according to the decrease of es. For the example of the piling-up of the surface, a circumferential tensile stress arises, and for the example of the sinking-in a radial tensile stress. Correspondingly, in the former case radial cracks are expected, and in the latter case circumferential cracks. The tensile stresses calculated at positions, which correspond to the observed tip of radial cracks and of the outermost circumferential-tike... 

A power law strain-energy function expressed in terms of circumferential, longitudinal and transmural extension ratios (A,i, A.2, and k ) was used [111] to describe the biaxial properties of sheep myocardium 2 weeks after experimental myocardial infarction, in the scarred infarct region ... 

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