Conserved Quantities for the General Linear Heat Equation

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions

On the classification of 2 (1 )n n   dimensional non-linear Klein-Gordon equation via Lie and Noether approach

A complete group classification for the Klein-Gordon equation is presented. Symmetry generators, up to equivalence transformations, are calculated for each f (u) when the principal Lie algebra extends. Further, considered equation is investigated by using Noether approach for the general case n  2. Conserved quantities are computed for each calculated Noether operator. At the end, a brief conclusion is presented

Erosion Corrosion Behavior of Nanostructure Commercial Pure Titanium in Simulated Body Fluid

To date, ECAP technique have been successfully employed to produce Ultra-fine/Nanostructure grain materials, but some materials such as hexagonal closed-packed (HCP) alloys are difficult to process by ECAP at room temperature. In this work, Transmission Electron Microscopy (TEM), Vickers hardness test and Torsion test were employed to confirm the attainment of ultrafine/nanostructured grain (UFG/NSG) commercial pure titanium (CP-Ti) Titanium fabricated by ECAP as a sever plastic deformation process. The samples were pressed by ECAP (route BC) up to four passes at elevated temperature (400° C). Finally, the Erosion-Corrosion (E-C) behavior of ultrafine/nanostructured grain (UFG/NSG) Titanium in a simulated body fluid were investigated through weight loss measurement

Surface Modelling of Nanostructured Copper Subjected to Erosion-Corrosion

The last decade has witnessed considerable advancements in nanostructured material synthesis and property characterization. However, there still exists some deficiency in the mechanical and surface property characterization of these materials. In this paper, the erosion corrosion (E-C) behavior of nanostructured copper was studied. The nanostructured copper was produced through severe plastic deformation (SPD) by applying four passes of equal channel angular pressing (ECAP). The combined effects of the testing time, impact velocity, and concentration of erosive solid particles (i.e., sand concentration) on the E-C behavior of nanostructured copper were then examined. Based on a defined domain for the testing time, impact velocity, and sand concentration, E-C tests were performed for numerous combinations of test points via the slurry pot method. The test points were selected using the face-centered center composite design of experiments to enable visualization of the test results through surface plots. The extent of E-C on the test specimens was determined by measuring the mass loss. Polynomial regression and Kriging were used to fit surfaces to the experimental data, which were subsequently used to generate surface plots. The results showed that the E-C of nanostructured copper is best described by a quadratic function of testing time, velocity, and erosive solid particle concentration. The results also revealed that E-C increases with an increasing testing time, impact velocity, and erosive solid particle concentration. In addition, it was observed that the effect of the erosive solid particles on E-C is further intensified by an increased impact velocity

Effect of Equal Channel Angular Pressing (ECAP) on Erosion-Corrosion of Pure Copper

During the past few decades, ultrafine-grained materials (UFG) have experienced rapid development. Enhanced mechanical and surface properties, such as strength, ductility and erosion-corrosion (E-C) resistance by refining the grain to ultra-fine/nanometer size has been achieved. The equal channel angular pressing (ECAP) is a popular severe plastic deformation (SPD) method to fabricate UFG bulk materials. In this research, the E-C behavior of commercial annealed pure copper subject to four passes of ECAP have been investigated. Hardness measurement of the copper specimen after four passes of ECAP showed an increase of 200% on the hardness value as compared with annealed condition. Simulated seawater was used as an E-C medium. The effect of different E-C parameters such as time, slurry flow velocity, impact angle, and solid particle concentration on ECAP process is studied. The results showed that ECAP enhances the E-C resistance of copper, and this behavior improves with increasing the pass number. Generally, a 30% rise in resistance to E-C was achieved after four ECAP passes as compared to coarse grain copper for the parameters studied in this work. Optical microscopy was used to examine the microstructure and material removal mechanism of the annealed copper. Scanning electron microscopy (SEM) was used to validate the reduction of grain size due to ECAP process. Furthermore, examination of the surface roughness of the copper at different ECAP passes showed that for the same E-C condition the increment of ECAP passes leads to a smoother surface

Influence of V and Zn in FeCrCuMnTi High-Entropy Alloys on Microstructures and Uniaxial Compaction Behavior Prepared by Mechanical Alloying

The densification behavior of FeCrCuMnTi (HEA1), FeCrCuMnTiV (HEA2), and FeCrCuMnTiVZn (HEA3) equiatomic high-entropy alloys (HEAs) was explored using different uniaxial quasi-static controlled compaction (1 mm/min). These HEAs were synthesized by mechanical alloying (MA, speed: 300 rpm, BPR: 10:1, time: 25 h). Various phase formations, structural characteristics (crystallite size, lattice strain, and lattice constant), thermo-dynamic calculations, powder surface morphologies, detailed microstructural evolutions, and chemical compositions were examined using X-ray diffraction, high-resolution scanning electron microscopy, and high-resolution transmission electron microscopy. The XRD results revealed the formation of multiple solid solutions (FCC, BCC, and HCP) due to the variation in entropy, and the presence of high-strength elements (Cr, Ti, and V) in the developed HEA alloys. The synthesized powders were consolidated into bulk green samples with different compaction pressures starting from 25 to 1100 MPa under as-milled and milled under stress recovery conditions (150 °C, 1 h). The incorporation of V in the FeCrCuMnTi HEA resulted in improved densification due to a greater reduction in particle size, and high configurational entropy. Furthermore, the stress-recovered powder samples produced more relative density owing to the elimination of lattice strain. Several linear and non-linear compaction models were applied to predict densification behavior. The non-linear Cooper and Eaton model produced the highest regression coefficients compared to the other models

Erosion Corrosion Behavior of Nanostructure Commercial Pure Titanium in Simulated Body Fluid

To date, ECAP technique have been successfully employed to produce Ultra-fine/Nanostructure grain materials, but some materials such as hexagonal closed-packed (HCP) alloys are difficult to process by ECAP at room temperature. In this work, Transmission Electron Microscopy (TEM), Vickers hardness test and Torsion test were employed to confirm the attainment of ultrafine/nanostructured grain (UFG/NSG) commercial pure titanium (CP-Ti) Titanium fabricated by ECAP as a sever plastic deformation process. The samples were pressed by ECAP (route BC) up to four passes at elevated temperature (400° C). Finally, the Erosion-Corrosion (E-C) behavior of ultrafine/nanostructured grain (UFG/NSG) Titanium in a simulated body fluid were investigated through weight loss measurement

Strain Behavior of Nickel Alloy 200 during Multiaxial Forging through Finite Element Modeling

Multiaxial forging (MAF) is one of the appealing methods of severe plastic deformation (SPD) techniques to fabricate ultrafine-grained (UFG) materials. In this study; the influence of process parameters such as strain rate; friction; and initial temperature has been assessed through finite element simulation of Nickel 200 alloy. The Johnson⁻Cook equation was applied in simulating the MAF process. The homogeneous microstructure of a material processed by MAF is an important requirement to obtain uniform mechanical and other properties. The uniformity in properties was evaluated by the investigation of the hardness measurements; effective strain (ES), and inhomogeneous factor (IF) or coefficient of standard deviation. The results showed that the inhomogeneous factor decreases with an increase in strain rate and decrease in temperature. It was found that a more homogeneous structure is observed with an increasing number of MAF cycles and the strain rate strain. Furthermore; the average grain size reduced from 850 nm to 220 nm after three cycles of MAF. Finally; experimental work was performed to validate the results