tailieunhanh - Engineering Materials 2E VOLUME1 Episode 5

Tham khảo tài liệu 'engineering materials 2e volume1 episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 92 Engineering Materials 1 Fig. . Reduction in area at break The maximum decrease in cross-sectional area at the fracture expressed as a percentage of the original cross-sectional area. Strain after fracture and percentage reduction in area are used as measures of ductility . the ability of a material to undergo large plastic strain under stress before it fractures. chapter 9 Dislocations and yielding in crystals Introduction 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 strength of a perfect crystal As we showed in Chapter 6 on the modulus the slope of the interatomic forcedistance curve at the equilibrium separation is proportional to Young s modulus E. Interatomic forces typically drop off to negligible values at a distance of separation of the atom centres of 2r0. The maximum in the force-distance curve is typically reached at separation and if the stress applied to the material is sufficient to exceed this maximum force per bond fracture is bound to occur. We will denote the stress at which this bond rupture takes place by Ỡ the ideal strength a material cannot be stronger than this. From Fig. T Ee _ E 2Ỡ E - - r0 4 E Ỡ 8 More refined estimates of Ỡ are possible using real interatomic potentials Chapter 4 they give about E 15 instead of E 8. Let us now see whether materials really show this strength. The bar-chart Fig. shows values of Ơy E for materials. The heavy broken line at the top is

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