Mecânica da Fratura Linear-2023-2

Tabelas e Gráficos Mecânica da Fratura Linear Universidade Tecnológica Federal do Paraná Propriedades de alguns materiais 578 Chapter 11 Fatigue Crack Growth Table 11.2 Constants for the Walker Equation for Several Metals Material Yield Toughness Walker Equation Man-Ten steel RQC-100 steel AISI 4340 steel (σu = 1296 MPa) 17-4 PH steel (H1050, vac. melt) 2024-T3 Al2 7075-T6 Al2 σo MPa (ksi) KIC (ksiv/in) 2001 (182) 1501 (136) 130 (118) 1201 (109) 34 (31) 29 (26) C0 mm/cycle (MPav)m 3.28 x 10−9 8.01 x 10−11 5.11 x 10−10 3.29 x 10−9 1.42 x 10−10 2.71 x 10−8 C0 in/cycle (ksiv/in)m 1.74 x 10−10 4.71 x 10−12 2.73 x 10−11 1.63 x 10−9 7.85 x 10−10 1.51 x 10−9 m 3.13 4.24 3.24 2.44 3.59 3.70 γ (R ≥ 0) 0.928 0.719 0.420 0.790 0.680 0.641 γ (R < 0) 0.220 0 0 — 0 0 363 (52.6) 778 (113) 1255 (182) 1059 (154) 353 (51.2) 523 (75.9) Table 8.1 Fracture Toughness and Corresponding Tensile Properties for Representative Metals at Room Temperature (a) Steels AISI 1144 ASTM A470-8 (Cr-Mo-V) ASTM A517-F AISI 4130 18-Ni maraging air melted 18-Ni maraging vacuum melted 300-M 650°C temper 300°C temper (b) Aluminum and Titanium Alloys (L-T Orientation) 2014-T651 2024-T351 2024-T851 2219-T851 7075-T6 7075-T651 7475-T7351 Ti-6A1-4V annealed Sources: Data in [Barsom 87] p. 172, [Boyer 85] pp. 6.34, 6.35, and 9.8. [MIL-HDBK 941] pp. 3.10–3.12 and 5.3, and [Ritchie 77]. Toughness KIC MPa√ m (ksiv/in) 24 (22) 33 (30) 33 (30) 35 (31) 26 (23) 28 (25) 40 (36) 50 (45) (60) 112 (102) 160 (157) (42) 45 (41) 144 (131) (38) 60 (55) (60) (60) (112) (160) (165) (42) (45) 140 Yield σo 540 (60) 880 (55) 1180 (170) 1050 (110) 1310 (190) 1240 (180) (138) 590 (59) 590 (60) 470 (47) 470 (47) 880 (60) (47) 770 (60) MPa (ksi) (85) 780 (90) (174) (122) (173) (183) (172) 410 (60) 420 (62) 540 (88) 600 (112) 840 900 894 660 730 780 1340 1190 640 580 840 530 620 835 Membros em tração Values for small a/b and limits for 10% accuracy: (a) K = Sig sqrt pi a (a/b ≤ 0.4) (b) K = 1.12 Sq sqrt pi a (a/b ≤ 0.6) (c) K = 1.12 Sq sqrt pi a (a/b ≤ 0.13) Expressions for any a = a/b: (a) F = \frac{1 - 0.5 \alpha + 0.326 \alpha^2}{\sqrt{1 - \alpha}} (h/b ≥ 1.5) (b) F = (1 + 0.122 \cos^4 \frac{\pi \alpha}{2}) \sqrt{\frac{2}{\pi \alpha}} \tan \frac{\pi \alpha}{2} (h/b ≥ 2) (c) F = 0.265 (1 - \alpha)^4 + \frac{0.857 + 0.265 \alpha}{(1 - \alpha)^{3/2}} (h/b ≥ 1) (diagrams and graph omitted) Membros em Flexão Values for small a/b and limits for 10% accuracy: (a, b) K = 1.12 Sg sqrt pi a (a/b ≤ 0.4) Expressions for any a = a/b: (a) F = \sqrt{\frac{2}{\pi \alpha}} \tan \frac{\pi \alpha}{2} \left[0.923 + 0.199 \left(1 - \sin \frac{\pi \alpha}{2}\right)^4 \right] \frac{1}{\cos \frac{\pi \alpha}{2} } (large h/b) (b) F is within 3% of (a) for h/b = 4, and within 6% for h/b = 2, at any a/b: F =\frac{1.99 - \alpha (1 - \alpha) (2.15 - 3.93 \alpha + 2.7 \alpha^2)}{\sqrt{\pi (1 + 2 \alpha) (1 - \alpha)^{3/2}}} (h/b = 2) (diagrams and graph omitted) Eixos em cargas combinadas (a) Axial load P: S_g = P/πb², F = 1.12 (10%, a/b ≤ 0.21) (b) Bending moment M: S_g = 4M/πb³, F = 1.12 (10%, a/b ≤ 0.12) (c) Torsion T, K = K_III: S_g = 2T/πb³, F = 1.00 (10%, a/b ≤ 0.09) K = FS_g√πa α = a/b β = 1 - α F = 1/2β¹.⁵ [1 + 1/2β + 3/8β² - 0.363β³ + 0.731β⁴] F = 3/8β².⁵ [1 + 1/2β + 3/8β² + 5/16β³ + 35/128β⁴ + 0.537β⁵] F = 3/8β².⁵ [1 + 1/2β + 3/8β² + 5/16β³ + 35/128β⁴ + 0.208β⁵] Cargas combinadas – trinca circular K = FS√πa S = St (tension, P) S = Sb (bending, M) Case St Sb F for small a Limits for ±10% on F (a) P/4bt — 2/π = 0.637 a/t < 0.4, a/b < 0.5 (b) P/2bt 3M/bt² 0.728 a/t < 0.4, a/b < 0.3 (c) P/bt 6M/bt² 0.722 a/t < 0.35, a/b < 0.2 (d) 4P/πd² 32M/πd³ 0.728 a/d < 0.2 or 0.351 Note: 1Different limits for tension or bending, respectively. 𝐾(𝜃) – Cargas combinadas e trinca circular Forças de abertura de trinca - Tração Compact Tension – ASTM E399 K = F_P P/√t√b h/b = 0.6 F_P = 2 + α (1 - α)³/² (0.886 + 4.64α - 13.32α² + 14.72α³ - 5.6α⁴) (a/b ≥ 0.2) Open Hole Tension K = F_d S / \pi \sqrt{\ell},\;\quad d = \frac{\ell}{a} = \frac{\ell}{c + \ell} F_d = 0.5(3 - d)[1 + 1.243(1 - d)^3] K = F_d S / \pi \ell\quad\; \text{K}_A = 1.12\; k_t \; S / \pi \ell\;\text{,}\quad k_t = 3\;\text{,}\quad \text{F} = 1 \quad K_B = FS / \pi a\; \quad \text{K} = F_d\; S/\pi \ell\; \quad \ell = \ell' Demais casos https://asmedigitalcollection.asme.org/ebooks/book/188/The- Stress-Analysis-of-Cracks-Handbook-Third