Usuario:Bloody Guardian/Pruebas

$\sigma \ ={\frac {2\cdot 1220Kg\cdot 9.8}{\pi (0.004)^{2}}}=475.7MPa$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {38MPa}{1.5\cdot (475.7+4)MPa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=0.88mm$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {68MPa}{1.5\cdot (475.7+4)MPa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=2.84mm$

$N_{f}={\frac {da}{A\pi ^{\frac {m}{2}}({\mathcal {4}}\sigma )^{m}}}\int _{a_{0}}^{a_{c}}{\frac {1}{Y^{m}a^{\frac {m}{2}}}}\,da$

$N_{f}={\frac {a_{c}^{1-m/2}-a_{0}^{1-m/2}}{A\cdot ({\sqrt {\pi }}\cdot Y\cdot \sigma \ )^{m}\cdot (1-m/2)}}$

$N_{f}={\frac {(2.84)^{1-3/2}-(1)^{1-3/2}}{2.71\cdot 10^{-10}\cdot ({\sqrt {\pi }}\cdot 1.5\cdot 8MPa)^{3}\cdot (1-3/2)}}\simeq \ 311867cicles$

$311867\ cicles\cdot {\frac {1s}{2cicles}}\cdot {\frac {1h}{3600s}}\cdot {\frac {1dia}{24h}}=1.8\ dies$

${\mathcal {4}}\sigma _{a}={\mathcal {4}}\sigma _{0}(1-{\frac {\sigma }{\sigma _{max}}})$

a $\sigma \_{max}={\frac {55}{100}}\cdot 1420MPa=781MPa$

$\sigma \_{min}={\frac {53}{100}}\cdot 1420MPa=752.6MPa$

$\Delta \ \sigma \ =\sigma \_{max}-\sigma \_{min}=28.4MPa$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {87.4MPa}{1.5\cdot 781Mpa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=1.77mm$

$N_{f}={\frac {(1.77)^{1-2.7/2}-(1.45)^{1-2.7/2}}{4.2\cdot 10^{-10}\cdot ({\sqrt {\pi }}\cdot 1.5\cdot 28.4MPa)^{2.7}\cdot (1-2.7/2)}}\simeq \ 3423\ cicles$

$3423\ cicles\cdot {\frac {1min}{100cicles}}=34.23\ minuts$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {25MPa}{1\cdot 100Mpa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=19.9mm$

$N_{f}={\frac {(19.9)^{1-3/2}-(4)^{1-3/2}}{1\cdot 10^{-12}\cdot ({\sqrt {\pi }}\cdot 1\cdot 50MPa)^{3}\cdot (1-3/2)}}\simeq \ 792574\ cicles$

${\frac {\partial a}{\partial N}}=A\cdot {\mathcal {4}}K^{m}$

$\sigma ={\frac {K_{Ic}}{Y{\sqrt {\pi a}}}}$

$t={\frac {P\cdot r}{\sigma }}$

$\epsilon _{x}={\frac {{\mathcal {4}}d}{d_{0}}}$

${\mathcal {4}}d=d_{0}\cdot \epsilon _{x}=10mm\cdot 2.31\cdot 10^{-3}=0.0231mm=23.1\mu m$

$\epsilon _{x}=\epsilon _{z}\cdot \nu =7\cdot 10^{-3}\cdot 0.33=2.31\cdot 10^{-3}$

$\epsilon _{z}={\frac {\sigma }{E}}={\frac {503MPa}{71.7GPa}}=7\cdot 10^{-3}$

$F=\sigma \cdot S_{0}=503\cdot 10^{6}\ Pa\cdot (\pi \cdot (5\cdot 10^{-3})^{2})=39.5\ KN$

$\sigma ={\frac {F}{S_{0}}}={\frac {2\cdot 1220Kg\cdot 9.8}{\pi \cdot (4\cdot 10^{-3})^{2})}}=499.1\cdot 10^{6}Pa$

$\sigma _{max}={\frac {0.1}{100}}\cdot \sigma +\sigma =499.6\cdot 10^{6}Pa$

$\sigma _{min}=-{\frac {0.1}{100}}\cdot \sigma +\sigma =498.6\cdot 10^{6}Pa$

${\mathcal {4}}\sigma =\sigma _{max}-\sigma _{min}=1\cdot 10^{6}Pa$

$50\cdot {\frac {cicles}{s}}{\frac {3600s}{h}}{\frac {24h}{dia}}{\frac {365dies}{any}}=1576.8\cdot 10^{6}{\frac {cicles}{any}}$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {28MPa}{1.3\cdot 499.6MPa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=0.59mm$

$\sigma =K\cdot \sigma =3\cdot 170MPa=510MPa$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {28MPa}{1.25\cdot 510MPa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=0.61mm$

$\sigma _{max}=({\frac {60}{100}}+{\frac {3}{100}})\cdot 1520MPa=957.6\cdot 10^{6}Pa$

$\sigma _{min}=({\frac {60}{100}}-{\frac {3}{100}})\cdot 1520MPa=866.4\cdot 10^{6}Pa$

${\mathcal {4}}\sigma =\sigma _{max}-\sigma _{min}=91.2\cdot 10^{6}Pa$

$a_{c}=({\frac {K_{I}c}{Y\cdot \sigma \ }})^{2}\cdot {\frac {1}{\pi }}=({\frac {120MPa}{1.15\cdot 957.6MPa}})^{2}\cdot {\frac {1}{\pi }}\cdot 1000=3.78mm$

$N_{f}={\frac {(3.78)^{1-2.3/2}-(2.3)^{1-2.3/2}}{3.8\cdot 10^{-15}\cdot ({\sqrt {\pi }}\cdot 1.15\cdot 91.2MPa)^{2.3}\cdot (1-2.3/2)}}\simeq \ 671\cdot 10^{6}cicles$