Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length

Analyses of longitudinal fracture behavior of inhomogeneous beams which have continuously varying sizes of the cross-section along the beam length are carried-out. Beams of a rectangular cross-section are studied. It is assumed that beams exhibit continuous (smooth) material inhomogeneity along the width and height of the cross-section. A longitudinal crack located arbitrary along the beam height is analyzed. First, a cantilever beam with linearly varying width and height along the beam length is considered. The material of the beam has non-linear elastic mechanical behavior. The external loading consists of one bending moment applied at the free end of the lower crack arm. The fracture behavior is analyzed in terms of the strain energy release rate assuming that the modulus of elasticity is distributed continuously in the beam cross-section. The balance of the energy is considered in order to derive the strain energy release rate. A solution to the strain energy release rate is obtained also by considering the complementary strain energy for verification. The longitudinal fracture behavior of the inhomogeneous non-linear elastic cantilever beam configuration is studied also for the cases when the variation of the width and height of the cross-section is described by sine and power laws.      &nbsp

Longitudinal Fracture Analysis of an Inhomogeneous Stepped Rod with Two Concentric Cracks in Torsion

Analysis of the longitudinal fracture behaviour of an inhomogeneous stepped rod with two concentric longitudinalcracks is developed. The stepped rod has circular cross-section and exhibits continuous material inhomogeneity in radial direction.The material has non-linear elastic mechanical behaviour. The rod is subjected to torsion. The two cracks present concentriccircular cylindrical surfaces. Thus, the fronts of the cracks are circles. The fracture is studied in terms of the strain energy releaserate by considering the complementary strain energy stored in the rod. Solutions to the strain energy release rate are derived atdifferent lengths of the two cracks. The balance of the energy is analyzed in order to verify the solutions. It is shown that thesolutions can be applied also when the stepped rod is inhomogeneous in both radial and length directions. The solutions are usedin order to evaluate the influences of the locations of the two concentric cracks in radial direction and the material inhomogeneityin radial and length directions on the longitudinal fracture behaviour of the stepped rod

Modelling Creep Behaviour of Superheater Materials

AbstractThe energy demand of human being is ever increasing. The naturally available energy resources are in a crude form and need conversion to one which is readily available for end use. Power plants play the role of this conversion process. Majority of the conversion processes take place at severe conditions of very high temperature and high pressure. Hence, power plant components always exhibit inelastic behaviours like creep and fatigue. The design of such components should take these inelastic behaviours in to consideration. This work focuses on modelling the creep behaviour of superheater materials. Specifically, creep constitutive model of T91 steel which is commonly used for constructing superheater tubes is developed and validated with results from experimental work. Then a material user subroutine has been written to incorporate the model in commercial software ABAQUS

Zu einigen Aspekten der klassischen Kontinuumsmechanik und ihrer Erweiterungen

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On the Analytical Estimation for Isotropic Approximation of Elastic Properties applied to Polycrystalline Cubic Silicon used at Solar Cells

The present contribution is concerned with the effective mechanical parameters of polycristalline silicon used for solarcells. Thereby, an analytical scheme for the prediction of elastic properties of polycrystals is reviewed, applied and verified.Emphasis is on first-order bounds and derived estimates. Based on cubic symmetry of a single crystal the projector representationis exploited for the description of the constitutive equations. The elasticity tensor is developed for several assumptions whichstem from rather classical homogenization schemes. This results in a rational representation and determination of linear elasticmaterial parameters of a homogeneous, macroscopically isotropic comparison material. The analytically determined parametersare compared to experimental data. It is found that the present procedure reproduces the experimental results in very closeproximity

Grundlagen einer verallgemeinerten halbmomentenfreien Schalentheorie für dünnwandige, anisotrope Konstruktionen

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Konzepte der Schädigungsmechanik und ihre Anwendung bei der werkstoffmechanischen Bauteilanalyse

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Anisotrope Stabschalenmodelle mit nichtsymmetrischem Wandaufbau

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Inelastic Deformation of Conductive Bodies in Electromagnetic Fields

Inelastic deformation of conductive bodies under the action of electromagnetic fields is analyzed. Governing equations for non-stationary electromagnetic field propagation and elastic-plastic deformation are presented. The variational principle of minimum of the total energy is applied to formulate the numerical solution procedure by the finite element method. With the proposed method, distributions of vector characteristics of the electromagnetic field and tensor characteristics of the deformation process are illustrated for the inductor-workpiece system within a realistic electro-magnetic forming process

On the Derivation of Hooke’s Law for Plane State Conditions

We discuss the derivation of Hooke’s law for plane stress and plane strain states from its general three-dimensional representation. This means that we consider the anisotropic case to ensure a certain generality of our representation. Thereby, two approaches are examined, namely the tensorial representation involving fourth-order tensors over a three-dimensional vector space, and the Voigt-Mandel-Notation involving second-order tensors over a six-dimensional vector space. The latter reduces to a vector-matrix notation common in engineering applications. It turns out that both approaches have their merits: The tensorial approach is easier to handle symbolically, the matrix approach is easier to handle numerically. Both procedures are applicable for arbitrary material symmetries. Finally, we answer the question why a material under the assumptions of a plane stress state behaves softer and why it behaves stiffer under a plane strain state compared to the three-dimensional state