Dislocations yield strength

A crystal yields when the force xh (per unit length) exceeds /, the resistance (a force per unit length) opposing the motion of a dislocation. This defines the dislocation yield strength... 

Figure 7.6 shows the relationship between the meehanieal threshold and the separation between pinning points for dislocation segments. The mechanical yield strength is controlled by the largest separation, Hence, behind... 

In the last chapter we examined data for the yield strengths exhibited by materials. But what would we expect From our understanding of the structure of solids and the stiffness of the bonds between the atoms, can we estimate what the yield strength should be A simple calculation (given in the next section) overestimates it grossly. This is because real crystals contain defects, dislocations, which move easily. When they move, the crystal deforms the stress needed to move them is the yield strength. Dislocations are the carriers of deformation, much as electrons are the carriers of charge. 

The result is work-hardening the steeply rising stress-strain curve after yield, shown in Chapter 8. All metals and ceramics work-harden. It can be a nuisance if you want to roll thin sheet, work-hardening quickly raises the yield strength so much that you have to stop and anneal the metal (heat it up to remove the accumulated dislocations) before you can go on. But it is also useful it is a potent strengthening method, which can be added to the other methods to produce strong materials. 

Ty is the quantity we want the yield strength of bulk, polycrystalline solids. It is larger than the dislocation shear strength Tj (by the factor 3) but is proportional to it. So all the statements we have made about increasing apply unchanged to... 

When other elements dissolve in a metal to form a solid solution they make the metal harder. The solute atoms differ in size, stiffness and charge from the solvent atoms. Because of this the randomly distributed solute atoms interact with dislocations and make it harder for them to move. The theory of solution hardening is rather complicated, but it predicts the following result for the yield strength... 

The yield strength and toughness of Dural differ enormously in these three conditions (slow-cooled, quenched, and quenched and aged) the last gives the highest yield and lowest toughness because the tiny particles obstruct dislocations very effectively. 

All real metals contain dislocations even a well-annealed metal would typically contain 10 dislocations per square millimetre, while a heavily cold-worked metal could contain up to lO Vmm. At first sight this is an anomaly dislocations were postulated to account for the low yield strength of metals, and whereas an annealed material with a low dislocation density is weak, a cold-worked metal with a high dislocation density is strong. The answer lies in the fact that when the dislocation density is low, the dislocations are generally too far apart to interact with each other very often and are more free to move under the influence of a low applied stress. On the... 

Beyond point E, the material begins to plasticly deform, and at point Y the yield point is achieved. The stress at the yield point corresponds to the yield strength, Oy [see Eq. (5.20)]. Technically, point Y is called the upper yield point, and it corresponds to the stress necessary to free dislocations. The point at which the dislocations actually begin to move is point L, which is called the lower yield point. After point L, the material enters the ductile region, and in polycrystalline materials such as that of Eigure 5.26, strain hardening occurs. There is a corresponding increase in the stress... 

By necessity, the treatment of solid state kinetics has to be selective in view of the myriad processes which can occur in the solid state. This multitude is mainly due to three facts 1) correlation lengths in crystals are often much larger than in fluids and may comprise the whole crystal, 2) a structure element is characterized by three parameters instead of only by two in a liquid (chemical species, electrical charge, type of crystallographic site), and 3) a crystal can be elastically stressed. The stress state is normally inhomogeneous. If the yield strength is exceeded, then plastic deformation and the formation of dislocations will change the structural state of a crystal. What we aim at in this book is a strict treatment of concepts and basic situations in a quantitative way, so far as it is possible. In contrast, the often extremely complex kinetic situations in solid state chemistry and materials science will be analyzed in a rather qualitative manner, but with clearcut thermodynamic and kinetic concepts. 

Dislocations as introduced in Section 3.2 have been postulated in order to explain the low yield strength of a crystal (if we compare it to the theoretical shear strength). Likewise, cracks are postulated in order to explain fracturing of crystals well below the theoretical tensile strength of the atomic bonds. Pre-existing cracks can easily magnify low applied stresses at their tips to the maximal atomic bond strength. 

---