Elastic-plastic stress distribution in the rotating annular disk with variable thickness

Summary The plane state of stress in a rotating annular disk with variable thickness is studied. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening.

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Die elastisch-pastische Spannungsverteilung in einem rotierenden Kreisring mit veränderlicher Dicke

Übersicht Der ebene Spannungszustand in einem rotierenden Kreisring mit veränderlicher Dicke und aus Material mit linearer Verfestigung wird unter Zugrundelegung der Trescaschen Fließbedingung und der zugehörigen Fließregel untersucht.

     

Elastic-plastic strain and stress distribution in notched plates under plane stress

An experimental solution is presented for the plane state of stress in an elastic-plastic isotropic solid obeying the Mises yield condition. The elastic and plastic strains were determined by using birefringent coatings cemented on the surface of the model. Normal incidence of circularly polarized light yielded the difference of principal strains at the model-coating interface. Linearly polarized light gave the directions of principal strains.The values of ϵ_z-principal strains, normal to the surface of the plate, were determined from an analogy relating this strain to another potential field. The values of ϵ_z-strains together with data from the birefringent coatings yielded enough information for the explieit analytic solution of the elastic-plastic plane stress problem. The stress-components were determined by means of the Prandtl-Reuss stress-strain relations in a step-by-step process of loading. It was assumed that stresses and strains remained constant during each step and they only changed when the next step started. This method may have a general applicability to any plane-stress restricted plasticity problem, provided that convenient formulae are established satisfying the yield condition of the material and the associated flow rule. The method was applied to the solution of a series of plane-stress problems of restricted plasticity. Thin flat plates containing symmetrical deep notches with circular roots subjected to a uniform tension were considered and their elastoplastic stress and strain distribution was evaluated. Four cases were solved for various flank angles between 0 and 120°, the minimum width of the plates remaining constant. The influence of the flank angle on the shape of the spreading plastic zones was determined and the critical loads for incipient plastic flow were evaluated.     

Elastic-plastic deformation of the rotating solid disk

Summary The plane state of stress in a rotating circular disk of elastic-plastic material with linear strain hardening is studied based on Tresca's yield condition and its associated flow rule. The plastic core consists of two parts with different forms of the yield condition. By specializing the results to perfectly plastic material, the usual statically determinate stress distribution is recovered but, since the plastic strain at the axis becomes infinite, these stresses are not meaningful.

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Die elastisch-plastische deformation der rotierenden vollscheibe

Übersicht Der ebene Spannungszustand in einer rotierenden Kreisscheibe aus elastisch-plastischem Werkstoff mit linearer Verfestigung wird berechnet unter Zugrundelegung der Trescaschen Fließbedingung und der zugehörigen Fließregel. Der plastische Kern setzt sich zusammen aus zwei Teilen, in denen die Mießbedingung verschiedene Formen annimmt. Durch Grenzwertbildung werden die Ergebnisse auf idealplastisches Verhalten spezialisiert; man findet die übliche statisch bestimmte Spannungsverteilung. Da diese aber mit unbeschränkten plastischen Dehnungen an der Scheibenachse verbunden ist, können die Spannungen nicht sinnvoll sein.

     

Plastic limit state of a thin hollow disk under thermomechanical loading

This paper considers the plastic limit state of a thin hollow axisymmetric disk subjected to thermomechanical loading with a uniform pressure distribution on the inner contour and a temperature increasing during deformation. A semi-analytical solution of the formulated boundary-value problem is obtained. Qualitative features of the behavior of the solution with a loss of the load-carrying capacity of the disk are investigated.     

Evaluating the limiting state of materials with asymmetric cyclic loading and a complex stress state

Conclusion In order to construct models of the limiting state in asymmetric cyclic loading, it is best to use the representation of a unique limit curve that is invariant to the time to failure and type of stress state. Isotropic metallic materials were used as an example to show that such a curve does exist and is described satisfactorily by an exponential cosine function.The models constructed above were used to calculate the limiting state for several steels and alloys acted upon by the combinations of cyclic bending and cyclic torsion, static bending and cyclic torsion, and static torsion and cyclic bending. Results were also calculated for materials with stress raisers. The calculated data were compared with experimental findings and were shown to agree satisfactorily with the latter.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 2, pp. 67–79, February, 1995.     

Analysis of stress concentration around a spheroidal cavity under asymmetric dynamic loading

The fracture and fatigue properties of porous materials are strongly influenced by stress concentrations around the pores. In addition, failure of structural components initiates at locations of high stress concentration which is often caused by holes, inclusions or other discontinuities. In view of this, the stress concentration around a spheroidal cavity embedded in an elastic medium is studied under dynamic loading conditions. While solutions abound for static loads, only limited solutions exist for dynamic loads. The stress field around a spheroidal cavity is determined by using a hybrid methodology that combines the finite element technique with a spherical wave function expansion method. The stress concentrations within the matrix are found to be dependent on the frequency of excitation, aspect ratio of the cavity and the Poisson’s ratio of the matrix. The study reveals that dynamic stress concentrations can reach much higher values than those encountered under static loading.     

Elastic-plastic deformations of thickwalled circular cylinders under transient heating and combined axial tension and torsion loads

The method of successive elastic solutions has been used to predict the stress-strain history of a thick-walled circular cylinder when it is subjected to rapid heating on its outer surface together with various combinations of axial tension and torsion. The extent of the zones of plasticity is calculated for both a constant yield stress and for a yield stress which reduces with increase of temperature.     

Fracture of sedimentary rocks under a complex triaxial stress state

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.     

Dynamic and static asymmetric response of a layered thick disk

Treated is the asymmetric static and dynamic response of a stack of layered thick disks from external load. Variables of the three-dimensional equations are separated assuming approximate simple supports along the cylindrical perimeter, yielding non-orthogonal eigenfunctions. This also couples the truncated set of radial wave numbers. Applying a radial transform to all variables eliminates radial dependence producing a diagonal eigenproblem in all coupled axial wave numbers. Comparing 3-D and 2-D asymmetric models of industrial glass disks reveals that the 3-D resonances are close to their 2-D counterparts adopting the Mindlin model. A Fourier analysis of a specific asymmetric line-load from pressure or thermal expansion produces a scale factor to static stress from a limited number of asymmetric solutions each with a different circumferential wave number.