Behavior of Integral Curves of the Quasilinear Second Order Differential Equations

AbstractThis paper deals with certain classes of Cauchy's solutions of quasilinear second order differential equations in general form, Van der Pol's differential equation, which is used in the theory of electric circuits, and Lagerstorm's differential equations, which is used in asymptotic treatment of viscous flow past a solid at low Reynolds number. Behaviour of integral curves in the neighbourhoods of an arbitrary or integral curve is considered. Obtained results establish sufficient conditions for the existence and asymptotic behaviour of the observed equations. The obtained results contain the answer to the question on approximation of solutions whose existence is established. The errors of the approximation are defined by functions that can be sufficiently small. The qualitative analysis theory and topological retraction methods were used

Influence of feed rate on damage development in hot ring rolling

AbstractAs an incremental forming process of bulk metal, ring rolling provides a cost effective process route to manufacture seamless rings. Applications of ring rolling cover a wide range of products in aerospace, automotive and civil engineering industries. Under some process conditions, defects such as porosity can sometimes be found in hot rolled rings, which are manufactured from high alloyed steel ingots having macro segregations. For the reduction of the waste of material and improvement of product quality, a better understanding of the relations between segregation levels in the ingot, process parameters in the hot ring rolling and the occurrence of porosity is needed. In this research, a coupled thermo-mechanical multi-stage finite element model is used to simulate the hot ring rolling process including preform forging. The deformations, stresses and strains from the preforming steps are included as initial conditions for the rolling stage. Subroutines are implemented to represent the control algorithm for the motion of the rolls. A damage indicator is implemented in the material model. Simulations with different feed rate curves are carried out in order to see the influence on the occurrence of porosity. Hot ring rolling experiments in an industrial rolling mill are conducted to validate the numerical study. The results of simulation and experiment show good agreement

Characteristics of Desalination Brine and Its Impacts on Marine Chemistry and Health, With Emphasis on the Persian/Arabian Gulf: A Review

At a time when worldwide water shortage is increasing, seawater is being viewed as an inexhaustible supply of freshwater via the process of seawater desalination. As a result, seawater desalination is becoming more popular, especially in areas where freshwater is scarce, such as the Middle East and North Africa (MENA), which accounts for half of all global saltwater desalination activities. To enhance the efficiency of saltwater desalination, thermal and membrane-based desalination technologies are continually being developed and hybridized systems established. Brine is an unavoidable product of seawater desalination and is commonly disposed of in oceans and seas, where it has negative effects on the surrounding marine environment and its biodiversity due to the resultant increased salinity and temperature, as well as the presence of chemicals. Furthermore, the quality and amount of brine are influenced by several parameters, including the input quality and quantity, the desalination process, and the discharge method. The intensity of brine’s influence on the marine biota is determined by a number of factors; nevertheless, marine species differ in their tolerance to brine’s effects. Desalination technology is improving to maximize water recovery and reduce the volume of brine produced, with the objective of eventually reaching zero liquid discharge and limiting harmful effects on the marine environment. Meanwhile, proper systems for analyzing the effects of seawater desalination facilities on the marine ecology must be implemented. This review study will look at all of the factors that determine the physicochemical features of desalination brine, with a focus on its impact on marine chemistry and biodiversity. More crucially, the most cutting-edge brine management methods will be investigated for long-term desalination and a healthy marine ecosystem.This report was made possible by the NPRP award [NPRP11S-0110-180248] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors

Modelling of Inelastic Effects in Metal Sheets and Identification of Material Parameters

The continuum modelling of the macroscopic behaviour of metallic sheets and the identification of corresponding material parameters for models selected are dealt with in the thesis. Thermodynamics with internal variables provides a framework for the derivation of the models. Inelastic effects, such as mixed plastic hardening, and either isotropic or anisotropic ductile damage are included in the models. For isotropic damage, represented by a scalar variable, the effective stress concept is combined with the principle of strain equivalence. The extension to anisotropy is affected by replacing the strain equivalence principle with the elastic energy equivalence. A second-order damage tensor is shown to give rise to a degradation of elastic stiffness. The elasticity law assumes material isotropy, since there is no damage in the initial undamaged state. The concept of small elastic and large plastic deformations is applied to Belytcshko shell elements. The plastic yield criterion is evaluated in the space of the real stresses, which simplifies the numerical algorithm. A limitation of the model is that damage propagates only during plastic hardening. Since cyclic loading causes opening and closing of microcracks, the microcrack reopening and closing mechanism is intended to model the corresponding damage growth. Accordingly, damage propagates mainly in the tensile state. The incorporation of the dynamic yield surface ensures an upper asymptotic limit to the viscoplastic stress state. The time integration of the constitutive models is done by using the Backward Euler method in combination with the Newton-Raphson iteration technique. These algorithms are later implemented as user material subroutines in the explicit Finite Element program LS-DYNA. Three experimental methods are used to identify material parameters: uniaxial tension tests at different strain rates, a three-point cyclic bending test, and continuous uniaxial tension loading and unloading of metal sheets. Since steel alloys exhibit strain-rate dependence, stress-strain curves from uniaxial tension tests at different strain rates are used for calibration of the viscoplastic material parameters. The three-point cyclic bending test methodology is assessed for identification of material hardening parameters. Continuous uniaxial loading and unloading of metal sheets was performed with the objective of identifying the isotropic growth of damage. This identification technique is based on the coupling between damage propagation and degradation of the elastic properties of a material

Modelling of Inelastic Effects in Metal Sheets and Identification of Material Parameters

The continuum modelling of the macroscopic behaviour of metallic sheets and the identification of corresponding material parameters for models selected are dealt with in the thesis. Thermodynamics with internal variables provides a framework for the derivation of the models. Inelastic effects, such as mixed plastic hardening, and either isotropic or anisotropic ductile damage are included in the models. For isotropic damage, represented by a scalar variable, the effective stress concept is combined with the principle of strain equivalence. The extension to anisotropy is affected by replacing the strain equivalence principle with the elastic energy equivalence. A second-order damage tensor is shown to give rise to a degradation of elastic stiffness. The elasticity law assumes material isotropy, since there is no damage in the initial undamaged state. The concept of small elastic and large plastic deformations is applied to Belytcshko shell elements. The plastic yield criterion is evaluated in the space of the real stresses, which simplifies the numerical algorithm. A limitation of the model is that damage propagates only during plastic hardening. Since cyclic loading causes opening and closing of microcracks, the microcrack reopening and closing mechanism is intended to model the corresponding damage growth. Accordingly, damage propagates mainly in the tensile state. The incorporation of the dynamic yield surface ensures an upper asymptotic limit to the viscoplastic stress state. The time integration of the constitutive models is done by using the Backward Euler method in combination with the Newton-Raphson iteration technique. These algorithms are later implemented as user material subroutines in the explicit Finite Element program LS-DYNA. Three experimental methods are used to identify material parameters: uniaxial tension tests at different strain rates, a three-point cyclic bending test, and continuous uniaxial tension loading and unloading of metal sheets. Since steel alloys exhibit strain-rate dependence, stress-strain curves from uniaxial tension tests at different strain rates are used for calibration of the viscoplastic material parameters. The three-point cyclic bending test methodology is assessed for identification of material hardening parameters. Continuous uniaxial loading and unloading of metal sheets was performed with the objective of identifying the isotropic growth of damage. This identification technique is based on the coupling between damage propagation and degradation of the elastic properties of a material