Elasto-plastic materials with lattice defects modeled by second order deformations with non-zero curvature

2010 ◽  
pp. 61-75
Author(s):  
Sanda Cleja-Ţigoiu
Keyword(s):  
Second Order ◽  
Lattice Defects ◽  
Zero Curvature ◽  
Plastic Materials

scholarly journals Kinetic Modelling of Biodegradability Data of Commercial Polymers Obtained under Aerobic Composting Conditions

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 54-68
Author(s):  
Ilenia Rossetti ◽  
Francesco Conte ◽  
Gianguido Ramis
Keyword(s):  
Kinetic Data ◽  
Kinetic Modelling ◽  
Kinetic Equations ◽  
Second Order ◽  
Aerobic Biodegradation ◽  
First Order ◽  
First Order Kinetics ◽  
Plastic Materials ◽  
Partial Degradation ◽  
Commercial Polymers

Methods to treat kinetic data for the biodegradation of different plastic materials are comparatively discussed. Different samples of commercial formulates were tested for aerobic biodegradation in compost, following the standard ISO14855. Starting from the raw data, the conversion vs. time entries were elaborated using relatively simple kinetic models, such as integrated kinetic equations of zero, first and second order, through the Wilkinson model, or using a Michaelis Menten approach, which was previously reported in the literature. The results were validated against the experimental data and allowed for computation of the time for half degradation of the substrate and, by extrapolation, estimation of the final biodegradation time for all the materials tested. In particular, the Michaelis Menten approach fails in describing all the reported kinetics as well the zeroth- and second-order kinetics. The biodegradation pattern of one sample was described in detail through a simple first-order kinetics. By contrast, other substrates followed a more complex pathway, with rapid partial degradation, subsequently slowing. Therefore, a more conservative kinetic interpolation was needed. The different possible patterns are discussed, with a guide to the application of the most suitable kinetic model.

Elasto-Plastic Models with Continuously Distributed Dislocations and Disclinations

2012 ◽  
Vol 504-506 ◽  
pp. 125-130
Author(s):  
Sanda Cleja-Tigoiu
Keyword(s):  
Mathematical Model ◽  
Evolution Equations ◽  
Second Order ◽  
Lattice Defects ◽  
Screw Dislocations ◽  
Crystalline Materials ◽  
Distributed Dislocations

The paper deals with a mathematical model able to describe the presence of lattice defects of the crystalline materials, such as dislocation and disclination. Within the constitutive framework of second order plasticity developed by the author, the evolution equations to describe the disclinations that are compatible with the screw dislocations are derived.

Zero Curvature Method and Protection Criterion Against Plastic Collapse

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Cheng-Hong Duan ◽  
Yu Sun ◽  
Ming-Wan Lu
Keyword(s):  
Limit Load ◽  
Plastic Collapse ◽  
Computing Process ◽  
Perfectly Plastic ◽  
Zero Curvature ◽  
Plastic Materials ◽  
Definition Of ◽  
Strain Strengthening

A zero curvature method to estimate the limit load is introduced in detail, and a uniform computing process for computerization of the zero curvature method is presented. A new protection criterion against plastic collapse is proposed. A lot of examples are performed and discussed. The zero curvature load determined by the zero curvature method is a preferable definition of the limit load for perfectly plastic materials or the plastic load for strain strengthening materials. Both advantages of the ASME VIII-2 code and the EN-13445 standard are absorbed in the new protection criterion.

Strain Gradient Effect in Finite Elasto-plastic Damaged Materials

2010 ◽  
Vol 20 (4) ◽  
pp. 484-514 ◽  
Author(s):  
Sanda Cleja-Ţigoiu ◽  
Victor Ţigoiu
Keyword(s):  
Plastic Deformation ◽  
Free Energy ◽  
Strain Gradient ◽  
Evolution Equations ◽  
Free Energy Density ◽  
Second Order ◽  
Structural Defects ◽  
Plastic Behavior ◽  
Plastic Materials ◽  
Isothermal Processes

In this article we propose a strain gradient model for elasto-plastic materials in which there exist zones with structural inhomogeneities, characterized by nonlocal deformations. We assume the existence of an anholonomic configuration, called damaged configuration, which is associated with the second-order plastic deformation. We proved how the damage may be coupled to the second-order plasticity introducing a tensorial damage variable, Qd, as a measure of the nonmetricity of the plastic Bilby-type part of the connection, which characterizes peculiar structural defects. The constitutive and evolution equations are subjected to be compatible with the principle of the imbalanced free energy, which is applied for isothermal processes. The free energy density function Ψ, is represented as a function of second-order elastic deformation and it depends on the damaged configuration, K, through the second-order plastic deformation. At the level of plastically deformed configuration, the effects of macro- and microforces are cumulated into the internal power. Two possible nonlocal evolution equations to describe plastic behavior are derived as a consequence of balance equation for microforces. Finally, we look at the influence of the strain gradient in a simple model.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Contrast in Scanning Images of Thin Crystals

1972 ◽  
Vol 30 ◽  
pp. 520-521
Author(s):  
S. Kimoto ◽  
H. Hashimoto ◽  
S. Takashima ◽  
R. M. Stern ◽  
T. Ichinokawa
Keyword(s):  
Crystal Surface ◽  
Solid Angle ◽  
Incident Angle ◽  
Intensity Variation ◽  
Lattice Defects ◽  
Scanning Microscope ◽  
Electron Detector ◽  
Backscattered Electrons ◽  
Electron Image ◽  
Backscattered Electron

The most well known application of the scanning microscope to the crystals is known as Coates pattern. The contrast of this image depends on the variation of the incident angle of the beam to the crystal surface. The defect in the crystal surface causes to make contrast in normal scanning image with constant incident angle. The intensity variation of the backscattered electrons in the scanning microscopy was calculated for the defect in the crystals by Clarke and Howie. Clarke also observed the defect using a scanning microscope.This paper reports the observation of lattice defects appears in thin crystals through backscattered, secondary and transmitted electron image. As a backscattered electron detector, a p-n junction detector of 0.9 π solid angle has been prepared for JSM-50A. The gain of the detector itself is 1.2 x 104 at 50 kV and the gain of additional AC amplifier using band width 100 Hz ∼ 10 kHz is 106.

Crystal structure-size relationship in ultrafine metallic particles

1989 ◽  
Vol 47 ◽  
pp. 266-267
Author(s):  
Jun Liu ◽  
Mehmet Sarikaya ◽  
Ilhan A. Aksay
Keyword(s):  
Ultrafine Particles ◽  
Carbon Film ◽  
Lattice Defects ◽  
Careful Examination ◽  
Seeded Growth ◽  
Gold Particles ◽  
Metallic Particles ◽  
Interfacial Structures ◽  
Typical Particle ◽  
Many Particles

Ultrafine particles usually have unique physical properties. This study illustrates how the lattice defects and interfacial structures between particles are related to the size of ultrafine crystalline gold particles.Colloidal gold particles were produced by reducing gold chloride with sodium citrate at 100°C. In this process, particle size can be controlled by changing the concentration of the reactant. TEM samples are prepared by transferring a small amount of solution onto a thin (5 nm) carbon film which is suspended on a copper grid. In this work, all experiments were performed with Philips 430T at 300 kV.With controlled seeded growth, particles of different sizes are produced, as shown in Figure 1. By a careful examination, it can be resolved that very small particles have lattice defects with complex interfaces. Some typical particle structures include multiple twins, resulting in a five-fold symmetry bicrystals, and highly disordered regions. Many particles are too complex to be described by simple models.

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