Stress field
Encyclopedia
A stress field is a region in a body for which the stress
is defined at every point. Stress fields are widely used in fluid dynamics
and materials science
.
Intuitively, one can picture the stress fields as the stress
created by adding an extra half plane of atoms to a crystal
. The bonds are clearly stretched around the location of the dislocation
and this stretching causes the stress field to form. Atomistic bonds farther and farther away from the dislocation center are less and less stretched which is why the stress field dissipates as the distance from the dislocation center increases. Each dislocation within the material has a stress field associated with it. The creation of these stress fields are a result of the material trying to dissipate mechanical energy that is being exerted on the material. By convention these dislocations are labeled as either positive or negative depending on whether the stress field of the dislocation is mostly compressive or tensile.
By modeling or dislocations and their stress fields as either a positive (compressive field) or negative (tensile field) charges we can understand how dislocations interact with each other in the lattice. If two positive fields come in contact with one another they will be repelled by one another. On the other hand if two opposing charges come into contact with one another they will be attracted to one another. These two interactions will both strengthen the material in different ways. If two positively charged fields come in contact and are confined to a particular region, excessive force is needed to overcome the repulsive forces so the dislocations can move past one another.If two oppositely charged fields come into contact with one another they will merge with one another to form a jog. A jog can be modeled as a potential well that traps dislocations. Thus a larger than normal external force is needed to force the dislocations apart. Since dislocation motion is the primary mechanism behind plastic deformation, increasing the stress required to move dislocations directly increases the yield strength of the material.
The theory of stress fields can be applied to various strengthening mechanisms
for materials. Stress fields can be created by adding different sized atoms to the lattice (solute strengthening). If a smaller atom is added to the lattice a tensile stress field is created. The atomistic bonds are longer due to the smaller radius of the solute atom. Similarly if a larger atom is added to the lattice a compressive stress field is created. The atomistic bonds are shorter due to the larger radius of the solute atom. The stress fields created by adding solute atoms form the basis of the material strengthening process that occurs in alloy
s.
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
is defined at every point. Stress fields are widely used in fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
and materials science
Materials science
Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates...
.
Intuitively, one can picture the stress fields as the stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
created by adding an extra half plane of atoms to a crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
. The bonds are clearly stretched around the location of the dislocation
Dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...
and this stretching causes the stress field to form. Atomistic bonds farther and farther away from the dislocation center are less and less stretched which is why the stress field dissipates as the distance from the dislocation center increases. Each dislocation within the material has a stress field associated with it. The creation of these stress fields are a result of the material trying to dissipate mechanical energy that is being exerted on the material. By convention these dislocations are labeled as either positive or negative depending on whether the stress field of the dislocation is mostly compressive or tensile.
By modeling or dislocations and their stress fields as either a positive (compressive field) or negative (tensile field) charges we can understand how dislocations interact with each other in the lattice. If two positive fields come in contact with one another they will be repelled by one another. On the other hand if two opposing charges come into contact with one another they will be attracted to one another. These two interactions will both strengthen the material in different ways. If two positively charged fields come in contact and are confined to a particular region, excessive force is needed to overcome the repulsive forces so the dislocations can move past one another.If two oppositely charged fields come into contact with one another they will merge with one another to form a jog. A jog can be modeled as a potential well that traps dislocations. Thus a larger than normal external force is needed to force the dislocations apart. Since dislocation motion is the primary mechanism behind plastic deformation, increasing the stress required to move dislocations directly increases the yield strength of the material.
The theory of stress fields can be applied to various strengthening mechanisms
Strengthening mechanisms of materials
Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the...
for materials. Stress fields can be created by adding different sized atoms to the lattice (solute strengthening). If a smaller atom is added to the lattice a tensile stress field is created. The atomistic bonds are longer due to the smaller radius of the solute atom. Similarly if a larger atom is added to the lattice a compressive stress field is created. The atomistic bonds are shorter due to the larger radius of the solute atom. The stress fields created by adding solute atoms form the basis of the material strengthening process that occurs in alloy
Alloy
An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...
s.