No description available.

No description available.

No description available.

No description available.

No description available.

Many metals used in modern engineering exhibit anisotropy. A common assumption when modelling anisotropic metals is that the level of anisotropy is fixed throughout the calculation. As it is well understood that processes such as cold rolling, forging or shock loading change the level of anisotropy, it is clear that this assumption is not accurate when dealing with large deformations. The aim of this project was to develop a tool capable to predict large deformations of a single crystal or crystalline aggregate of a metal of interest and able to trace an evolution of anisotropy within the material. The outcome of this project is a verified computational tool capable of predicting large deformations in metals. This computational tool is built on the Crystal Plasticity Finite Element Method (CPFEM). The CPFEM in this project is an implementation of an existing constitutive model, based on the crystal plasticity theory (the single crystal strength model), into the framework of the FEA software DYNA3D® . Accuracy of the new tool was validated for a large deformation of a single crystal of an annealed OFHC copper at room temperature. The implementation was also tested for a large deformation of a polycrystalline aggregate comprised of 512 crystals of an annealed anisotropic OFHC copper in a uniaxial compression and tension test. Here sufficient agreement with the experimental data was not achieved and further investigation was proposed in order to find out the cause of the discrepancy. Moreover, the behaviour of anisotropic metals during a large deformation was modelled and it was demonstrated that this tool is able to trace the evolution of anisotropy. The main benefit of having this computational tool lies in virtual material testing. This testing has the advantage over experiments in time and cost expenses. This tool and its future improvements, which were proposed, will allow studying evolution of anisotropy in FCC and BCC materials during dynamic finite deformations, which can lead to current material models improvement.

In real conditions, a great majority of machine and elements and parts are subjected to cyclic deformation. There is no possibility to improve their quality, to increase their reliability and durability without good knowledge of working condition and materials feature. During cyclic loading, stresses can overpass proportionality limits. It causes residual stresses which reduce durability of elements to limited number of loading cycles. Such a loading is called low cycle loading. Usually it happens in small volumes of material, concentration zones, welded joints so on. In this work, main cyclic elastic plastic characterestics of materials are presented and explained. It also contains experimental and analytical methods of estimation that characteristics and detail research of experimental cyclic stress strain curve approximation methods.

[pt] Este trabalho apresenta a abordagem do problema de análise de tensões e deformações em estruturas elasto-plásticas através de técnicas de programação matemática, e alguns métodos de solução deste problema. A determinação da evolução das tensões e deformações que ocorrem em uma estrutura de material elasto-plástico, submetida à um programa de carga que evolui no tempo, é definida por um sistema de equações e inequações obtidas a partir das equações constitutivas do material e das equações de compatibilidade e de equilíbrio da estrutura, formuladas em taxas. Este sistema é equivalente as condições necessárias de Kuhn-Tucker para a minimização de um funcional quadrático com restrições de igualdade e desigualdade. Para a solução deste problema de otimização através de técnicas numéricas, que permitem determinar a cada incremento de carga a evolução das tensões e deformações na estrutura, adota-se uma formulação incremental do problema elasto-plástico, própria para o tratamento numérico. / [en] This thesis presents the analysis of the stresses and strains in elastic-plastic structures, using a mathematical programming approach and some solution techniques for this problem. The evolution of the stresses and strains occuring in one elastic-plastic structure, loaded by a time varying load, is defined by a system of equations and inequations obtained from the constitutive relations of the material and from the compatility and equilibrium conditions of the structure, expressed in terms of rates. This system is equivalent to the Kuhn-Tucker conditions needed for the minimization of a quadraditic funtional with equality and inequality constraints. An incremental formulation for the elastic-plastic problem is adoted to solve this optimization problem by numerical techniques, enabling the determination of stresses and strains evolution in the structure due to finite load increments.

No description available.

Experimental studies have shown that the yield strength of many important engineering materials such as polymers, ceramics and metallic glasses is dependent on hydrostatic stress. In addition, these materials may also exhibit plastic dilatancy. These deviations from the assumptions of classical plasticity theories have also been observed for some metallic alloys, although to a lesser extent compared to non-metals. In pressure independent plastic solids, it has been found that the level of crack tip constraint can affect the near-tip stress and deformation fields and hence the fracture resistance. The objective of the present work is to study the effects of pressure sensitive yielding, plastic dilatancy and constraint loss on the ductile fracture processes under mode-I conditions. Further, the three-dimensional (3D) structure of elastic-plastic near-crack front fields in a pressure independent plastic solid under mixed mode (combined modes I and II) loading is also examined. A finite element study of 3D crack tip fields in pressure sensitive plastic solids under mode-I, small scale yielding (SSY) conditions is first carried out. The material is assumed to obey a small strain, Extended Drucker-Prager (EDP)yield criterion. The roles of pressure sensitive yielding, plastic dilatancy and yield locus shape on the 3D plastic zone development and near-crack front fields are systematically investigated. It is found that while pressure sensitivity leads to a significant drop in the hydrostatic stress all along the 3D crack front, it enhances the plastic strain and crack opening displacements. However, plastic incompressibility results in elevation of both near-tip hydrostatic stress and notch opening. The implications of these observations on micro-void growth and interaction near a notch tip are studied in detail subsequently. The effects of constraint loss on void growth near a notch tip under mode-I loading in materials exhibiting pressure sensitive yielding and plastic dilatancy are investigated by performing large deformation elastic-plastic finite element analyses. To this end, two-dimensional (2D)plane strain and 3Dmodified boundary layer formulations are employed by prescribing the elastic K-T field as remote boundary conditions. The results are generated for different combinations of K (or J ) and T -stress. The material is assumed to obey a finite strain, EDP yield condition. The distributions of hydrostatic stress and plastic strain in the ligament connecting the notch and a nearby void (cylindrical or spherical) as well as the growth of the notch and the void are studied. The results show that void growth with respect to J is enhanced due to pressure sensitivity, and more so when the plastic flow is non-dilatational, which corroborates with the trends exhibited by the 3D crack tip fields. However, the evolution of ductile fracture processes like void growth, plastic strain localization and ligament length reduction with respect to J is retarded in the case of spherical voids. Further, irrespective of pressure sensitivity, loss of crack tip constraint can significantly slow down void growth. The effects of pressure sensitive yielding and plastic dilatancy on near-tip void growth and multiple void interaction mechanisms in single edge notched bend (SENB) and center cracked tension (CCT) specimens which display high and low constraint levels, respectively, are investigated next. It is observed that the latter mechanism which is favored by high initial porosity is further accelerated by pressure sensitive yielding and high constraint. The predicted resistance curves based on a simple void coalescence mechanism show enhancement in fracture resistance when constraint level is low and when pressure sensitivity is suppressed. Finally, detailed elastic-plastic finite element simulations are carried out using a boundary layer (SSY) formulation to investigate the 3D nature of near-crack front fields in a von Mises solid under mixed mode (combined modes I and II)loading. The plastic zones and radial, angular and thickness variations of the stresses are studied corresponding to different levels of remote elastic mode mixity and applied load, as measured by the plastic zone size with respect to the plate thickness. The 3D results are compared with those obtained from 2D simulations and asymptotic solutions to establish the validity of 2D plane stress and plane strain approximations near a crack front. It is found that, in general, plane stress conditions prevail at a distance from the crack front exceeding half the plate thickness, although it could be slightly smaller for mode-II predominant loading.