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Related Concept Videos

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

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When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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Temperature Dependent Deformation01:12

Temperature Dependent Deformation

146
In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
261
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

276
One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
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Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

184
When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...
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Dislocation random walk under cyclic deformation.

Atsushi Kubo1, Emi Kawai1, Takashi Sumigawa2

  • 1Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.

Physical Review. E
|July 18, 2024
PubMed
Summary

This study introduces a random walk model to predict dislocation diffusion under cyclic loading. The model accurately estimates dislocation diffusion coefficients, validated by molecular dynamics simulations in copper.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Dislocation motion is crucial for understanding material behavior under cyclic loading.
  • Existing models may not fully capture the stochastic nature of dislocation dynamics.
  • Accurate prediction of dislocation diffusion is vital for fatigue life assessment.

Purpose of the Study:

  • To develop a novel random walk model for dislocation diffusion under cyclic loading.
  • To analytically derive the diffusion coefficient and probability distribution of dislocation motion.
  • To validate the model using molecular dynamics simulations.

Main Methods:

  • Modeling dislocation behavior as a series of one-dimensional random walks (binomial stochastic processes).
  • Analytical derivation of dislocation motion probability distribution and diffusion coefficient per cycle.
  • Validation against molecular dynamics simulations of copper under cyclic deformation.

Main Results:

  • An analytical equation for the diffusion coefficient of dislocations under cyclic loading was derived.
  • The random walk model demonstrated good agreement with molecular dynamics simulation results.
  • The model successfully links macroscopic loading conditions to microscopic material properties.

Conclusions:

  • The developed random walk model provides a robust theoretical framework for dislocation diffusion under cyclic loading.
  • The model's validation confirms its utility in predicting material response to cyclic stress.
  • This approach offers a computationally efficient alternative for simulating dislocation dynamics.