Precipitation Strengthening - Theory

Theory

The primary species of precipitation strengthening are second phase particles. These particles impede the movement of dislocations throughout the lattice. You can determine whether or not second phase particles will precipitate into solution from the solidus line on the phase diagram for the particles. Physically, this strengthening effect can be attributed both to size and modulus effects, and to interfacial or surface energy.

The presence of second phase particles often causes lattice distortions. These lattice distortions result when the precipitate particles differ in size and crystallographic structure from the host atoms. Smaller precipitate particles in a host lattice leads to a tensile stress, whereas larger precipitate particles leads to a compressive stress. Dislocation defects also create a stress field. Above the dislocation there is a compressive stress and below there is a tensile stress. Consequently, there is a negative interaction energy between a dislocation and a precipitate that each respectively cause a compressive and a tensile stress or vice versa. In other words, the dislocation will be attracted to the precipitate. In addition, there is a positive interaction energy between a dislocation and a precipitate that have the same type of stress field. This means that the dislocation will be repulsed by the precipitate.

Precipitate particles also serve by locally changing the stiffness of a material. Dislocations are repulsed by regions of higher stiffness. Conversely, if the precipitate causes the material to be locally more compliant, then the dislocation will be attracted to that region.

Furthermore, a dislocation may cut through a precipitate particle. This interaction causes an increase in the surface area of the particle. The area created is

where, r is the radius of the particle and b is the magnitude of the burgers vector. The resulting increase in surface energy is

where is the surface energy. The dislocation can also bow around a precipitate particle.

Read more about this topic:  Precipitation Strengthening

Other articles related to "theory":

Feudalism - Etymology
... The most widely held theory is put forth by Marc Bloch ... This Germanic origin theory was also shared by William Stubbs in the nineteenth century ... Another theory was put forward by Archibald R ...
J. Philippe Rushton - Work and Opinions - Application of r/K Selection Theory To Race
... book Race, Evolution, and Behavior (1995) uses r/K selection theory to explain how East Asians consistently average high, blacks low, and whites in the ... He first published this theory in 1984 ... He theorizes that r/K selection theory explains these differences ...
Falsifiability - The Criterion of Demarcation
... It is useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess the theory ... Popper claimed that, if a theory is falsifiable, then it is scientific ... thus it leaves us with the Duhemian problem of what constitutes a 'whole theory' as well as the problem of what makes a statement 'meaningful' ...
Zermelo Set Theory
... Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory ...
Minimax
... Minimax (sometimes minmax) is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a ... Originally formulated for two-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves ...

Famous quotes containing the word theory:

    The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.
    Giuseppe Mazzini (1805–1872)

    If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.
    Albert Einstein (1879–1955)

    Hygiene is the corruption of medicine by morality. It is impossible to find a hygienest who does not debase his theory of the healthful with a theory of the virtuous.... The true aim of medicine is not to make men virtuous; it is to safeguard and rescue them from the consequences of their vices.
    —H.L. (Henry Lewis)