Related Experiment Video
Updated: May 7, 2026
09:06
Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
Published on: March 24, 2019
Yield-strain and shear-band direction in amorphous solids under two-dimensional uniaxial loading
Ashwin J1, Oleg Gendelman, Itamar Procaccia
1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
Summary
This study presents a microscopic theory for plastic instability in amorphous solids. It explains how loading conditions dictate shear band angles and yield strain, aligning with experimental data.
Area of Science:
- Materials Science
- Solid Mechanics
- Condensed Matter Physics
Background:
- Amorphous solids exhibit plastic instability, leading to shear localization and potential fracture.
- Yield strain, yield stress, and shear band orientation depend significantly on external loading conditions.
Purpose of the Study:
- To develop a microscopic theory for plastic instability in 2D athermal amorphous solids under quasistatic strain.
- To derive analytic formulas for yield strain and shear band angles based on loading conditions.
Main Methods:
- Utilizing a microscopic theory for 2D athermal amorphous solids.
- Modeling nonaffine displacement fields with quadrupolar Eshelby inclusions representing elementary plastic events.
- Analyzing the influence of external loading conditions on theoretical predictions.
Main Results:
- Analytic formulas derived for yield strain and shear band angles under various loading conditions.
- Demonstrated that external loading conditions determine eigenvalues of Eshelby inclusions, which govern plastic events.
- Theoretically predicted shear band angles are confined between 30° and 60° with respect to the principal stress axis.
Conclusions:
- The developed microscopic theory successfully explains shear localization phenomena in amorphous solids.
- The theory provides a framework for predicting yield strain and shear band orientation.
- Experimental data validate the theoretical prediction of shear band angles ranging from 30° to 60°.
More Related Videos
Related Concept Videos
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
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.
01:20Shearing Strain
The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
01:29Three-Dimensional Analysis of Strain
Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
01:20Normal Strain under Axial Loading
Normal strain under axial loading is an important concept in the field of mechanics of materials. Axial loading implies the application of a force along the axis of a material, like a column or bar. This force can either compress or stretch the material. In the context of axial loading, normal strain is the deformation experienced by the material in the direction of the loading force. It's calculated as the change in length divided by the original length of the material. This unitless ratio...
01:12Transformation of Plane Strain
When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
01:24Stress-Strain Diagram - Ductile Materials
The stress-strain relationship in ductile materials such as structural steel or aluminium is intricate and progresses through several stages. When a specimen is loaded, it initially exhibits a linear length increase, depicted by a steep straight line on the stress-strain diagram. It indicates the material is elastically deforming and will return to its original shape once unloaded. However, when a critical stress value is reached, plastic deformation begins. This stage sees substantial...