σ = 2 ⋅ 1220 K g ⋅ 9.8 π ( 0.004 ) 2 = 475.7 M P a {\displaystyle \sigma \ ={\frac {2\cdot 1220Kg\cdot 9.8}{\pi (0.004)^{2}}}=475.7MPa}
a c = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 38 M P a 1.5 ⋅ ( 475.7 + 4 ) M P a ) 2 ⋅ 1 π ⋅ 1000 = 0.88 m m {\displaystyle 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 = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 68 M P a 1.5 ⋅ ( 475.7 + 4 ) M P a ) 2 ⋅ 1 π ⋅ 1000 = 2.84 m m {\displaystyle 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 = d a A π m 2 ( 4 σ ) m ∫ a 0 a c 1 Y m a m 2 d a {\displaystyle 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 = a c 1 − m / 2 − a 0 1 − m / 2 A ⋅ ( π ⋅ Y ⋅ σ ) m ⋅ ( 1 − m / 2 ) {\displaystyle 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 = ( 2.84 ) 1 − 3 / 2 − ( 1 ) 1 − 3 / 2 2.71 ⋅ 10 − 10 ⋅ ( π ⋅ 1.5 ⋅ 8 M P a ) 3 ⋅ ( 1 − 3 / 2 ) ≃ 311867 c i c l e s {\displaystyle 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 c i c l e s ⋅ 1 s 2 c i c l e s ⋅ 1 h 3600 s ⋅ 1 d i a 24 h = 1.8 d i e s {\displaystyle 311867\ cicles\cdot {\frac {1s}{2cicles}}\cdot {\frac {1h}{3600s}}\cdot {\frac {1dia}{24h}}=1.8\ dies}
4 σ a = 4 σ 0 ( 1 − σ σ m a x ) {\displaystyle {\mathcal {4}}\sigma _{a}={\mathcal {4}}\sigma _{0}(1-{\frac {\sigma }{\sigma _{max}}})}
a σ _ m a x = 55 100 ⋅ 1420 M P a = 781 M P a {\displaystyle \sigma \_{max}={\frac {55}{100}}\cdot 1420MPa=781MPa}
σ _ m i n = 53 100 ⋅ 1420 M P a = 752.6 M P a {\displaystyle \sigma \_{min}={\frac {53}{100}}\cdot 1420MPa=752.6MPa}
Δ σ = σ _ m a x − σ _ m i n = 28.4 M P a {\displaystyle \Delta \ \sigma \ =\sigma \_{max}-\sigma \_{min}=28.4MPa}
a c = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 87.4 M P a 1.5 ⋅ 781 M p a ) 2 ⋅ 1 π ⋅ 1000 = 1.77 m m {\displaystyle 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 = ( 1.77 ) 1 − 2.7 / 2 − ( 1.45 ) 1 − 2.7 / 2 4.2 ⋅ 10 − 10 ⋅ ( π ⋅ 1.5 ⋅ 28.4 M P a ) 2.7 ⋅ ( 1 − 2.7 / 2 ) ≃ 3423 c i c l e s {\displaystyle 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 c i c l e s ⋅ 1 m i n 100 c i c l e s = 34.23 m i n u t s {\displaystyle 3423\ cicles\cdot {\frac {1min}{100cicles}}=34.23\ minuts}
a c = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 25 M P a 1 ⋅ 100 M p a ) 2 ⋅ 1 π ⋅ 1000 = 19.9 m m {\displaystyle 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 = ( 19.9 ) 1 − 3 / 2 − ( 4 ) 1 − 3 / 2 1 ⋅ 10 − 12 ⋅ ( π ⋅ 1 ⋅ 50 M P a ) 3 ⋅ ( 1 − 3 / 2 ) ≃ 792574 c i c l e s {\displaystyle 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}
∂ a ∂ N = A ⋅ 4 K m {\displaystyle {\frac {\partial a}{\partial N}}=A\cdot {\mathcal {4}}K^{m}}
σ = K I c Y π a {\displaystyle \sigma ={\frac {K_{Ic}}{Y{\sqrt {\pi a}}}}}
t = P ⋅ r σ {\displaystyle t={\frac {P\cdot r}{\sigma }}}
ϵ x = 4 d d 0 {\displaystyle \epsilon _{x}={\frac {{\mathcal {4}}d}{d_{0}}}}
4 d = d 0 ⋅ ϵ x = 10 m m ⋅ 2.31 ⋅ 10 − 3 = 0.0231 m m = 23.1 μ m {\displaystyle {\mathcal {4}}d=d_{0}\cdot \epsilon _{x}=10mm\cdot 2.31\cdot 10^{-3}=0.0231mm=23.1\mu m}
ϵ x = ϵ z ⋅ ν = 7 ⋅ 10 − 3 ⋅ 0.33 = 2.31 ⋅ 10 − 3 {\displaystyle \epsilon _{x}=\epsilon _{z}\cdot \nu =7\cdot 10^{-3}\cdot 0.33=2.31\cdot 10^{-3}}
ϵ z = σ E = 503 M P a 71.7 G P a = 7 ⋅ 10 − 3 {\displaystyle \epsilon _{z}={\frac {\sigma }{E}}={\frac {503MPa}{71.7GPa}}=7\cdot 10^{-3}}
F = σ ⋅ S 0 = 503 ⋅ 10 6 P a ⋅ ( π ⋅ ( 5 ⋅ 10 − 3 ) 2 ) = 39.5 K N {\displaystyle F=\sigma \cdot S_{0}=503\cdot 10^{6}\ Pa\cdot (\pi \cdot (5\cdot 10^{-3})^{2})=39.5\ KN}
σ = F S 0 = 2 ⋅ 1220 K g ⋅ 9.8 π ⋅ ( 4 ⋅ 10 − 3 ) 2 ) = 499.1 ⋅ 10 6 P a {\displaystyle \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}
σ m a x = 0.1 100 ⋅ σ + σ = 499.6 ⋅ 10 6 P a {\displaystyle \sigma _{max}={\frac {0.1}{100}}\cdot \sigma +\sigma =499.6\cdot 10^{6}Pa}
σ m i n = − 0.1 100 ⋅ σ + σ = 498.6 ⋅ 10 6 P a {\displaystyle \sigma _{min}=-{\frac {0.1}{100}}\cdot \sigma +\sigma =498.6\cdot 10^{6}Pa}
4 σ = σ m a x − σ m i n = 1 ⋅ 10 6 P a {\displaystyle {\mathcal {4}}\sigma =\sigma _{max}-\sigma _{min}=1\cdot 10^{6}Pa}
50 ⋅ c i c l e s s 3600 s h 24 h d i a 365 d i e s a n y = 1576.8 ⋅ 10 6 c i c l e s a n y {\displaystyle 50\cdot {\frac {cicles}{s}}{\frac {3600s}{h}}{\frac {24h}{dia}}{\frac {365dies}{any}}=1576.8\cdot 10^{6}{\frac {cicles}{any}}}
a c = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 28 M P a 1.3 ⋅ 499.6 M P a ) 2 ⋅ 1 π ⋅ 1000 = 0.59 m m {\displaystyle 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}
σ = K ⋅ σ = 3 ⋅ 170 M P a = 510 M P a {\displaystyle \sigma =K\cdot \sigma =3\cdot 170MPa=510MPa}
a c = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 28 M P a 1.25 ⋅ 510 M P a ) 2 ⋅ 1 π ⋅ 1000 = 0.61 m m {\displaystyle 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}
σ m a x = ( 60 100 + 3 100 ) ⋅ 1520 M P a = 957.6 ⋅ 10 6 P a {\displaystyle \sigma _{max}=({\frac {60}{100}}+{\frac {3}{100}})\cdot 1520MPa=957.6\cdot 10^{6}Pa}
σ m i n = ( 60 100 − 3 100 ) ⋅ 1520 M P a = 866.4 ⋅ 10 6 P a {\displaystyle \sigma _{min}=({\frac {60}{100}}-{\frac {3}{100}})\cdot 1520MPa=866.4\cdot 10^{6}Pa}
4 σ = σ m a x − σ m i n = 91.2 ⋅ 10 6 P a {\displaystyle {\mathcal {4}}\sigma =\sigma _{max}-\sigma _{min}=91.2\cdot 10^{6}Pa}
a c = ( K I c Y ⋅ σ ) 2 ⋅ 1 π = ( 120 M P a 1.15 ⋅ 957.6 M P a ) 2 ⋅ 1 π ⋅ 1000 = 3.78 m m {\displaystyle 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 = ( 3.78 ) 1 − 2.3 / 2 − ( 2.3 ) 1 − 2.3 / 2 3.8 ⋅ 10 − 15 ⋅ ( π ⋅ 1.15 ⋅ 91.2 M P a ) 2.3 ⋅ ( 1 − 2.3 / 2 ) ≃ 671 ⋅ 10 6 c i c l e s {\displaystyle 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}
800 ⋅ c i c l e s m i n u t 60 m i n u t s h ⋅ 800 h = 38.4 ⋅ 10 6 c i c l e s {\displaystyle 800\cdot {\frac {cicles}{minut}}{\frac {60minuts}{h}}\cdot 800h=38.4\cdot 10^{6}cicles}
ϕ f = ϕ i 1 − T F 100 {\displaystyle \phi _{f}=\phi _{i}{\sqrt {1-{\frac {TF}{100}}}}}
T F = 100 ⋅ ( A 0 − A f A 0 ) {\displaystyle TF=100\cdot ({\frac {A_{0}-A_{f}}{A_{0}}})}
σ = E ⋅ 4 l l 0 = F S 0 {\displaystyle \sigma =E\cdot {\frac {{\mathcal {4}}l}{l_{0}}}={\frac {F}{S_{0}}}}
L = L 0 ⋅ ( 1 + α ⋅ 4 T ) {\displaystyle L=L_{0}\cdot (1+\alpha \ \cdot {\mathcal {4}}T)}
R = V 2 P = 230 2 V 60 W = 882 Ω {\displaystyle R={\frac {V^{2}}{P}}={\frac {230^{2}V}{60W}}=882\Omega }
V f = 3 ⋅ V R O = 3 ⋅ 230 V = 130 V {\displaystyle V_{f}={\sqrt {3}}\cdot V_{RO}={\sqrt {3}}\cdot 230V=130V}
I = V R 0 R = 130 V 882 Ω = 147 m A {\displaystyle I={\frac {V_{R0}}{R}}={\frac {130V}{882\Omega }}=147mA}
I = V R 0 R = 230 V 882 Ω = 260 m A {\displaystyle I={\frac {V_{R0}}{R}}={\frac {230V}{882\Omega }}=260mA}