tailieunhanh - Introduction to Elasticity Part 12

Tham khảo tài liệu 'introduction to elasticity part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Note that this result is different than the Tresca case in which we had k ƠY 2. The von Mises criterion can be plotted as a yield locus as well. Just as the Tresca criterion it must pass through ƠY on each axis. However it plots as an ellipse rather than the prismatic shape of the Tresca criterion see Fig. 7 . Figure 7 Yield locus for the von Mises criterion. Effect of hydrostatic pressure Since in the discussion up to now yield has been governed only by shear stress it has not mattered whether a uniaxial stress is compressive or tensile yield occurs when Ơ aY. This corresponds to the hydrostatic component of the stress p ơx ơy ơz 3 having no influence on yield which is observed experimentally to be valid for slip in metallic systems. Polymers however are much more resistant to yielding in compressive stress states than in tension. The atomistic motions underlying slip in polymers can be viewed as requiring free volume as the molecular segments move and this free volume is diminished by compressive stresses. It is thus difficult to form solid polymers by deformation processing such as stamping and forging in the same way steel can be shaped this is one reason the vast majority of automobile body panels continue to be made of steel rather than plastic. Figure 8 Effect of pressure on the von Mises yield envelope. 6 This dependency on hydrostatic stress can be modeled by modifying the yield criterion to state that yield occurs when Tmax or ƠM To Ap 3 where T0 and A are constants. As p increases the hydrostatic component of stress becomes more positive the shear stress needed for yield becomes greater as well since there is less free volume and more hindrance to molecular motion. The effect of this modification is to slide the von Mises ellipse to extend less into the I quadrant and more into the III quadrant as shown in Fig. 8. This shows graphically that greater stresses are needed for yield in compression and lesser stresses in tension. Figure 9 A craze in .