Proceedings of COBEM 2011 Copyright c 2011 by ABCM 21st International Congress of Mechanical Engineering October 24-28, 2011, Natal, RN, Brazil Limit Analysis for Porous Materials in Plane Strain Fabio da Costa Figueiredo, ffi[email protected] CEFET-RJ, Departamento de Engenharia Mecânica - Av.Maracanã, 229 - Rio de Janeiro, RJ, Brazil UFRJ-COPPE, Programa de Engenharia Mecânica - Av. Brigadeiro Trompowski,s/n, Centro de Tecnologia, bloco G - Rio de Janeiro, RJ, Brazil Lavínia Borges, [email protected] UFRJ-COPPE, Programa de Engenharia Mecanica - Av. Brigadeiro Trompowski,s/n, Centro de Tecnologia, bloco G - Rio de Janeiro, RJ, Brazil Abstract. On plasticity theory two methods are widely used to solve structural analysis problems: the incremental method and direct method. Unlike incremental method, in direct method there is no need to analyze the structure behavior during each load step in order to compute critical states and collapse mechanisms. The shakedown and limit analysis are the main representatives of the direct methods. In this paper, from maximum plastic dissipation principle and the set of admissible stress fields, a limit analysis formulation for porous materials is proposed.In order to model a problem in plasticity, the choice of an appropriate yielding function is mandatory. For ductile materials, the stress deviatory dependent von Mises criterion is largely used. However for porous materials, like soils, ceramic materials and powder metals, the von Mises criteria does not consider the main variables that describes his mechanical behavior such as friction angle, cohesion and the porosity. Moreover, those materials are pressure dependents and the stress invariant I 1 must be taken into account. Thus, a J 2 and I 1 dependent yield function is proposed and it takes into account all the described porous materials properties. Depending on these properties, a critical porosity is calculated and the yield function may assume an elliptical or an hyperbolic shape.The problem of interest is a plane strain and applying the normality rule, one normal strain component is made null and the stress in that direction is derived, function of others components. This kind of problem is applied to describe among others, indentation problems and scratch tests on porous materials. In indentation tests, a rigid indenter is punched against the tested material. In scratching tests, an indenter made of rigid material is dragged on the material tested surface. Controlled forces are applied and the penetration depth remains constant. Both tests are realized on nanoscale and the main objectives of them is to get the hardness of porous materials. Keywords: limit analysis, porous materials, strain plane. 1. INTRODUCTION In oil industry, due the necessity of extracting oil from deep waters, subsea pipes are submitted to severe mechanical efforts. In deep waters, pipes are submitted to high external pressure and eventually to high temperatures and since the pipe is not free, i.e., there are supports and anchors restraining movements, compressive forces are developed due to water column pressure and pipe thermal expansion. Under these conditions, compressive stresses may reach a critical magnitude and buckling may occur, leading to a catastrophic failure and causing structure collapse. On the other hand, buckling is not a problem if it is controlled and induced on pipes in order to relief high stresses. Buckling occurrence, among many variables, depends on friction between pipe-soil and this interaction must be un- derstood. In pipe buckling two situations may occur: the pipe can get out from the trench or it can drag the amount of soil around his vicinity. To model this problem, the pipe is described as a rigid structure dragging a soft material (soil). This may be idealized as a scratch test problem, where a rigid indenter is dragged into a material. The indentation problem, where a indenter is pressed against a surface is also studied. Both problems are solved using plasticity theory and limit analysis method by an algorithm developed by Borges (1991). Limit analysis is a direct method and there is no need to analyze the structure behavior during each load step. The results required are the collapse factor α, the stress and velocity fields and the plastic multiplier λ. Modeling the mechanical behavior of porous materials is a difficult task since many variables are involved. The de- velopment of plasticity studies on porous materials have wide applications like material hardness determination using nondestructive methods by indentation or scratch tests. Porous materials comprise soils (sand, clay), ceramics or even metallic powder, where the metal is physically divided into many small particles, then passing through compression and sintering processes. Indentation tests are very useful in civil engineering and geotechnics in piling problems. As another application of indentation problems, Cariou (2006) by means of nanoindentation techniques identifies mechanical proper- ties in cohesive-frictional porous materials. Due to heterogeneity of sedimentary rocks, the application of nanoindentation has provided a new versatile tool to test in situ phase and structures of geomaterials that cannot be recapitulated ex situ in bulk form. This technique requires a rigorous indentation analysis to translate indentation data into meaningful me- chanical properties. The application of this technique is also made by Sorelli et al. (2008). Similarly to indentation tests, scratch tests are also used as an alternative way of measuring mechanical properties as adhesion of coatings or strength of
Limit Analysis for Porous Materials in Plane Strain
Jun 24, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
