Dislocation strength

Appleton and Waddington [40] present experimental evidence that pulse duration also affects residual strength in OFHC copper. Samples shock loaded to 5 GPa for 1.2 ps pulse duration exhibit poorly developed dislocation cell structure with easily resolvable individual dislocations. When the pulse duration is increased to 2.2 ps (still at 5 GPa peak stress) recovered samples show an increase in Vickers hardness [41] and postshock electron micrographs show a well-developed cell structure more like samples shock loaded to 10 GPa (1.2 ps). In the following paragraphs we give several additional examples of how pulse duration affects material hardness. 

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... 

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

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. 

But crystals (like everything in this world) are not perfect they have defects in them. Just as the strength of a chain is determined by the strength of the weakest link, so the strength of a crystal - and thus of our material - is usually limited by the defects that are present in it. The dislocation is a particular type of defect that has the effect of allowing materials to deform plastically (that is, they yield) at stress levels that are much less than [Pg.95]

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... 

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... 

Explain what is meant by the ideal strength of a material. Show how dislocations can allow metals and alloys to deform plastically at stresses that are much less than the ideal strength. Indicate, giving specific examples, the ways in which metals and alloys may be made harder. 

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... 

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