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Related Concept Videos

Strain-Energy Density01:20

Strain-Energy Density

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Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
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Plasticity00:58

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Plasticity is the property where an object loses its elasticity and undergoes irreversible deformation, even after the deformation forces are eliminated. If a material deforms irreversibly without increasing stress or load, then this is called ideal plasticity. For example, when a force is applied to an aluminum rod, it changes its shape, but it does not return to its original shape once the force is removed. Plastic deformation or ductility is thus a permanent deformation or change in the...
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Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

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A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
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Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
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Plastic Behavior01:21

Plastic Behavior

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A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and...
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Elastic Strain Energy for Shearing Stresses01:20

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Determining the Mechanical Strength of Ultra-Fine-Grained Metals
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Size-dependent energy in crystal plasticity and continuum dislocation models.

Sinisa Dj Mesarovic1, Samuel Forest2, Jovo P Jaric3

  • 1School of Mechanical and Materials Engineering , Washington State University , Pullman, WA 99164, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|March 21, 2015
PubMed
Summary
This summary is machine-generated.

This study questions the justification of phenomenological size-dependent plasticity models. It proposes a coarsening method, revealing that unifying length scales simplifies models but sacrifices accuracy in plastic dissipation at interfaces.

Keywords:
coarseningcrystal symmetriesgeometrically necessary dislocationsmaterial length scalesmesoscale models

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Computational Materials Science

Background:

  • Recent advancements in discrete dislocation mechanics enable mesoscale modeling of plasticity.
  • Size-dependent plasticity is crucial for understanding material behavior at smaller scales.

Purpose of the Study:

  • To investigate the physical justification of phenomenological size-dependent energy expressions in plasticity.
  • To develop methods for computing size-dependent energy from dislocation mechanics in anisotropic crystals.

Main Methods:

  • Analysis of material and slip system symmetries to evaluate phenomenological models.
  • Development of a coarsening method based on dislocation interaction energy for physical expression computation.
  • Investigation of elastically anisotropic crystal behavior.

Main Results:

  • The phenomenological quadratic form of Nye's dislocation density tensor cannot be generally justified from dislocation mechanics.
  • A coarsening method reveals that physical and phenomenological expressions can be equivalent only if the multiplicity of characteristic lengths is ignored.
  • Plastic dissipation at interfaces shows strong dependence on the embedded length scale.

Conclusions:

  • The assumption of a single length scale governing crystal plasticity simplifies models but may not fully capture complex behaviors.
  • Dislocation mechanics provides a foundation for understanding size-dependent energy, but approximations are necessary for practical mesoscale models.