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Tham khảo tài liệu 'mechanics.of.materials.saouma episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | heory 5 Figure 12.4 Influence of Atomic Misfit on Ideal Shear Strength and from basic elasticity T GYxy 12.21 and Fig. 12.4 Yxy x h. 9 Because we do have very small displacement we can elliminate x from TrnX sin 2nX 2nx yG XG max X X h Ttheo X 12.22-a 2nh 10 If we do also assume that X h and G E 2 1 V then theorE__E max - 12 1 v 18 12.23 12.2 Griffith Theory 11 Around 1920 Griffith was exploring the theoretical strength of solids by performing a series of experiments on glass rods of various diameters. He observed that the tensile strength ơt of glass decreased with an increase in diameter and that for a diameter ộ 10-000 in. ơt 500 000 psi furthermore by extrapolation to zero diameter he obtained a theoretical maximum strength of approximately 1 600 000 psi and on the other hand for very large diameters the asymptotic values was around 25 000 psi. 12 Griffith had thus demonstrated that the theoretical strength could be experimentally approached he now needed to show why the great majority of solids fell so far below it. 12.2.1 Derivation 13 In his quest for an explanation he came across Inglis s paper and his strike of genius was to assume that strength is reduced due to the presence of internal flaws. Griffith postulated that the theoretical strength can only be reached at the point of highest stress concentration and accordingly the far-field applied stress will be much smaller. 14 Hence assuming an elliptical imperfection and from equation theor _ rỉ-act a I V p 12.24 Victor Saouma Mechanics of Materials II Đ THEORETICAL STRENGTH of SOLIDS Griffith I lait Ơ is the stress at the tip of the ellipse which is caused by a lower far field stress ơcr . 15 Asssuming p a0 and since 2y a 1 for an ideal plate under tension with only one single elliptical flaw the strength may be obtained from theor Ex micro macro 12.25 hence equating with Eq. 12.9 we obtain theor iy act a Ơmax 2Ơcr X A1 ao a0 Macro Micro 12.26 16 From this very important equation we observe .