• PDF / 822,709 Bytes
• 32 Pages / 439.37 x 666.142 pts Page_size
• 22 Downloads / 210 Views

DOWNLOAD

REPORT

---

Thick-Walled Circular Cylinders in the Linear Elastic-Perfectly Plastic State After Loading Beyond the Elastic Range

7.1 General and Scope Tests carried out on thick-walled circular cylinders under internal pressure demonstrate unequivocally that failure occurs at pressures corresponding to maximum nominal elastic stresses that are not only much above the material’s yield strength, but also exceed its failure strength. This is due to the fact that if the equivalent stress calculated with a yield theory at the inner radius, where the material is at greatest risk, locally exceeds the material’s elastic limit, the stress field will be profoundly changed. In particular, there will be a more uniform redistribution of stresses, together with a reduction in their concentrations near geometric discontinuities such as notches, holes, flanged connections, etc. In addition, once the pressure has been released, a circular cylinder stressed beyond yielding will have residual internal stresses that in the subsequent pressure cycles will be superposed on the stresses resulting from the pressure loads. As these residual stresses are generally compressive, the designer can use them to advantage in reducing the maximum tensile stresses due to the working pressure (Faupel and Furbeck, 1953, Faupel 1955). Analyzing the stress state in a circular cylinder loaded beyond yielding until the material reaches the fully plastic state is of considerable importance for highly stressed tubular structures, for proof testing to failure and interpreting the results, and for reducing stress intensification effects in machine parts and structures by creating an appropriate residual state of coaction in the material. This analysis, conducted with the usual assumptions of axisymmetry and a generalized plane strain state, so that the problem is mono-dimensional, leads to closed form solutions even without making rough simplifications concerning the material’s stress– strain curve (Crossland and Bones 1955 and 1958, Faupel 1956, Gormann 1967, Capurso 1971, Franciosi 1979, Liguori 1983). However, to gain a better grasp of the strain mechanics occurring in a circular cylinder under a pressure that stresses it beyond the elastic range, from the onset of yielding up to ultimate stress, it is best to proceed step by step. Accordingly, it will first be assumed that the stress–strain curve is that of a linear elastic-perfectly plastic material (material with behavior perfectly elastic up to yield point and V. Vullo, Circular Cylinders and Pressure Vessels, Springer Series in Solid and Structural Mechanics 3, DOI: 10.1007/978-3-319-00690-1_7,  Springer International Publishing Switzerland 2014

179

180

7

Thick-Walled Circular Cylinders

perfectly plastic up to failure). Subsequently, we will renounce this restrictive assumption and take this curve to be the far more general one for an elasto-plastic material with nonlinear strain hardening (Batdorf and Budiansky 1949, Westergard 1952, Hoffmann and Sachs 1953, Goodier and Hodge 1958, Smith and Sidebottom 1