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Fatigue strength of unwelded components

Values for calculation

$ \{e_n\in\mathbb{R}\mid e_n>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ e_n $ $ \mathrm{mm} $
$ \{Δσ_{eq}\in\mathbb{R}\mid Δσ_{eq}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ Δσ_{eq} $ $ \mathrm{MPa} $
$ \{σ_{eq\ max}\in\mathbb{R}\} $
This set includes all real numbers.
$ σ_{eq\ max} $ $ \mathrm{MPa} $
$ \{\overline{σ}_{eq}\in\mathbb{R}\} $
This set includes all real numbers.
$ \overline{σ}_{eq} $ $ \mathrm{MPa} $
$ \{T^*\in\mathbb{R}\mid T^*\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T^* $ $ \mathrm{°C} $
$ \{R_z\in\mathbb{R}\mid R_z>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ R_z $ $ \mathrm{μm} $
$ R_{p0.2/T^*} $ $ \mathrm{MPa} $
$ R_{p1.0/T^*} $ $ \mathrm{MPa} $
$ R_{m/20} $ $ \mathrm{MPa} $
$ R_{m/T^*} $ $ \mathrm{MPa} $
$ Δσ_D $ $ \mathrm{MPa} $
$ Δσ_{Cut} $ $ \mathrm{MPa} $

Calculation

Proof strength

$\text{if }\ R_{p1.0/T^*}> 0$
$\text{if }\ R_{p1.0/T^*}> 0$
Equations in LaTeX code
\text{if }\ R_{p1.0/T^*}> 0
$$R_p=R_{p1.0/T^*}$$
$R_p=R_{p1.0/T^*}$
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R_p=R_{p1.0/T^*}
$\text{else}$
$\text{else}$
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\text{else}
$$R_p=R_{p0.2/T^*}$$
$R_p=R_{p0.2/T^*}$
Equations in LaTeX code
R_p=R_{p0.2/T^*}

Tensile strength

$\text{if }\ R_{m/T^*}> 0$
$\text{if }\ R_{m/T^*}> 0$
Equations in LaTeX code
\text{if }\ R_{m/T^*}> 0
$$R_m=R_{m/T^*}$$
$R_m=R_{m/T^*}$
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R_m=R_{m/T^*}
$\text{else}$
$\text{else}$
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\text{else}
$$R_m=R_{m/20}$$
$R_m=R_{m/20}$
Equations in LaTeX code
R_m=R_{m/20}

Coefficient $ F_e $

$\text{if }\ e_n> 150$
$\text{if }\ e_n> 150$
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\text{if }\ e_n> 150
$$F_e=\left(\cfrac{25}{150}\right)^{0.182}$$
$F_e=\left(\cfrac{25}{150}\right)^{0.182}$
Equations in LaTeX code
F_e=\left(\cfrac{25}{150}\right)^{0.182}
$\text{else}$
$\text{else}$
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\text{else}
$$F_e=\left(\cfrac{25}{e_n}\right)^{0.182}$$
$F_e=\left(\cfrac{25}{e_n}\right)^{0.182}$
Equations in LaTeX code
F_e=\left(\cfrac{25}{e_n}\right)^{0.182}

Temperature correction factor

$\text{if }\ T^*\le 100$
$\text{if }\ T^*\le 100$
Equations in LaTeX code
\text{if }\ T^*\le 100
$$f_{t^*}=1$$
$f_{t^*}=1$
Equations in LaTeX code
f_{t^*}=1
$\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{ferritic material}$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{ferritic material}$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{ferritic material}
$$f_{t^*}=1.03-1.5\cdot 10^{-4}\cdot T^*-1.5\cdot 10^{-6}\cdot {T^*}^2$$
$f_{t^*}=1.03-1.5\cdot 10^{-4}\cdot T^*-1.5\cdot 10^{-6}\cdot {T^*}^2$
Equations in LaTeX code
f_{t^*}=1.03-1.5\cdot 10^{-4}\cdot T^*-1.5\cdot 10^{-6}\cdot {T^*}^2
$\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{austenitic material}$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{austenitic material}$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{austenitic material}
$$f_{t^*}=1.043-4.3\cdot 10^{-4}\cdot T^*$$
$f_{t^*}=1.043-4.3\cdot 10^{-4}\cdot T^*$
Equations in LaTeX code
f_{t^*}=1.043-4.3\cdot 10^{-4}\cdot T^*
$\text{else}$
$\text{else}$
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\text{else}
$$f_{t^*}=1$$
$f_{t^*}=1$
Equations in LaTeX code
f_{t^*}=1

Thickness correction factor in unwelded components

$\text{if }\ e_n\le 25$
$\text{if }\ e_n\le 25$
Equations in LaTeX code
\text{if }\ e_n\le 25
$$f_e=1$$
$f_e=1$
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f_e=1
$\text{else if }\ N\geq 2\cdot 10^6$
$\text{else if }\ N\geq 2\cdot 10^6$
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\text{else if }\ N\geq 2\cdot 10^6
$$f_e=F_e$$
$f_e=F_e$
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f_e=F_e
$\text{else}$
$\text{else}$
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\text{else}
$$f_e=F_e^{\left(0.1\cdot\ln{N}-0.465\right)}$$
$f_e=F_e^{\left(0.1\cdot\ln{N}-0.465\right)}$
Equations in LaTeX code
f_e=F_e^{\left(0.1\cdot\ln{N}-0.465\right)}

Coefficient $ F_s $

$$F_s=1-0.056\cdot\left(\ln{R_z}\right)^{0.64}\cdot\ln{R_m}+0.289\cdot\left(\ln{R_z}\right)^{0.53}$$
$F_s=1-0.056\cdot\left(\ln{R_z}\right)^{0.64}\cdot\ln{R_m}+0.289\cdot\left(\ln{R_z}\right)^{0.53}$
Equations in LaTeX code
F_s=1-0.056\cdot\left(\ln{R_z}\right)^{0.64}\cdot\ln{R_m}+0.289\cdot\left(\ln{R_z}\right)^{0.53}

Surface finish correction factor

$\text{if }\ R_z< 6$
$\text{if }\ R_z< 6$
Equations in LaTeX code
\text{if }\ R_z< 6
$$f_s=1$$
$f_s=1$
Equations in LaTeX code
f_s=1
$\text{else if }\ N\geq 2\cdot 10^6$
$\text{else if }\ N\geq 2\cdot 10^6$
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\text{else if }\ N\geq 2\cdot 10^6
$$f_s=F_s$$
$f_s=F_s$
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f_s=F_s
$\text{else}$
$\text{else}$
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\text{else}
$$f_s=F_s^{\left(0.1\cdot\ln{N}-0.465\right)}$$
$f_s=F_s^{\left(0.1\cdot\ln{N}-0.465\right)}$
Equations in LaTeX code
f_s=F_s^{\left(0.1\cdot\ln{N}-0.465\right)}

Mean stress sensitivity factor

$$M=0.00035\cdot R_m-0.1$$
$M=0.00035\cdot R_m-0.1$
Equations in LaTeX code
M=0.00035\cdot R_m-0.1

Reduced mean equivalent stress for elastic-plastic conditions

$\text{if }\ \overline{σ}_{eq}> 0$
$\text{if }\ \overline{σ}_{eq}> 0$
Equations in LaTeX code
\text{if }\ \overline{σ}_{eq}> 0
$$\overline{σ}_{eq,r}=R_p-\cfrac{Δσ_{eq}}{2}$$
$\overline{σ}_{eq,r}=R_p-\cfrac{Δσ_{eq}}{2}$
Equations in LaTeX code
\overline{σ}_{eq,r}=R_p-\cfrac{Δσ_{eq}}{2}
$\text{else if }\ \overline{σ}_{eq}< 0$
$\text{else if }\ \overline{σ}_{eq}< 0$
Equations in LaTeX code
\text{else if }\ \overline{σ}_{eq}< 0
$$\overline{σ}_{eq,r}=\cfrac{Δσ_{eq}}{2}-R_p$$
$\overline{σ}_{eq,r}=\cfrac{Δσ_{eq}}{2}-R_p$
Equations in LaTeX code
\overline{σ}_{eq,r}=\cfrac{Δσ_{eq}}{2}-R_p
$\text{else}$
$\text{else}$
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\text{else}
$$\overline{σ}_{eq,r}=0$$
$\overline{σ}_{eq,r}=0$
Equations in LaTeX code
\overline{σ}_{eq,r}=0

Mean stress correction factor

$\text{if }\ Δσ_{eq}> 2\cdot R_p$
$\text{if }\ Δσ_{eq}> 2\cdot R_p$
Equations in LaTeX code
\text{if }\ Δσ_{eq}> 2\cdot R_p
$$f_m=1$$
$f_m=1$
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f_m=1
$\text{else if }\ N> 2000000$
$\text{else if }\ N> 2000000$
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\text{else if }\ N> 2000000
$$f_m=-0.0003405\cdot \overline{σ}_{eq}+1.006$$
$f_m=-0.0003405\cdot \overline{σ}_{eq}+1.006$
Equations in LaTeX code
f_m=-0.0003405\cdot \overline{σ}_{eq}+1.006
$\text{else if }\ \left|σ_{eq\ max}\right|< R_p\geq \overline{σ}_{eq}\geq\cfrac{\cfrac{Δσ_{eq}}{f_u}}{2\cdot\left(1+M\right)}$
$\text{else if }\ \left|σ_{eq\ max}\right|< R_p\geq \overline{σ}_{eq}\geq\cfrac{\cfrac{Δσ_{eq}}{f_u}}{2\cdot\left(1+M\right)}$
Equations in LaTeX code
\text{else if }\ \left|σ_{eq\ max}\right|< R_p\geq \overline{σ}_{eq}\geq\cfrac{\cfrac{Δσ_{eq}}{f_u}}{2\cdot\left(1+M\right)}
$$f_m=\cfrac{1+M/3}{1+M}-\cfrac{M}{3}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq}}{\cfrac{Δσ_{eq}}{f_u}}\right)$$
$f_m=\cfrac{1+M/3}{1+M}-\cfrac{M}{3}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq}}{\cfrac{Δσ_{eq}}{f_u}}\right)$
Equations in LaTeX code
f_m=\cfrac{1+M/3}{1+M}-\cfrac{M}{3}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq}}{\cfrac{Δσ_{eq}}{f_u}}\right)
$\text{else if }\ \left|σ_{eq\ max}\right|> R_p\geq \overline{σ}_{eq,r}\geq\cfrac{\cfrac{Δσ_{eq}}{f_u}}{2\cdot\left(1+M\right)}$
$\text{else if }\ \left|σ_{eq\ max}\right|> R_p\geq \overline{σ}_{eq,r}\geq\cfrac{\cfrac{Δσ_{eq}}{f_u}}{2\cdot\left(1+M\right)}$
Equations in LaTeX code
\text{else if }\ \left|σ_{eq\ max}\right|> R_p\geq \overline{σ}_{eq,r}\geq\cfrac{\cfrac{Δσ_{eq}}{f_u}}{2\cdot\left(1+M\right)}
$$f_m=\cfrac{1+M/3}{1+M}-\cfrac{M}{3}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq,r}}{\cfrac{Δσ_{eq}}{f_u}}\right)$$
$f_m=\cfrac{1+M/3}{1+M}-\cfrac{M}{3}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq,r}}{\cfrac{Δσ_{eq}}{f_u}}\right)$
Equations in LaTeX code
f_m=\cfrac{1+M/3}{1+M}-\cfrac{M}{3}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq,r}}{\cfrac{Δσ_{eq}}{f_u}}\right)
$\text{else if }\ \left|σ_{eq\ max}\right|< R_p$
$\text{else if }\ \left|σ_{eq\ max}\right|< R_p$
Equations in LaTeX code
\text{else if }\ \left|σ_{eq\ max}\right|< R_p
$$f_m=\left[1-\cfrac{M\cdot\left(2+M\right)}{1+M}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq}}{\cfrac{Δσ_{eq}}{f_u}}\right)\right]^{0.5}$$
$f_m=\left[1-\cfrac{M\cdot\left(2+M\right)}{1+M}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq}}{\cfrac{Δσ_{eq}}{f_u}}\right)\right]^{0.5}$
Equations in LaTeX code
f_m=\left[1-\cfrac{M\cdot\left(2+M\right)}{1+M}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq}}{\cfrac{Δσ_{eq}}{f_u}}\right)\right]^{0.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_m=\left[1-\cfrac{M\cdot\left(2+M\right)}{1+M}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq,r}}{\cfrac{Δσ_{eq}}{f_u}}\right)\right]^{0.5}$$
$f_m=\left[1-\cfrac{M\cdot\left(2+M\right)}{1+M}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq,r}}{\cfrac{Δσ_{eq}}{f_u}}\right)\right]^{0.5}$
Equations in LaTeX code
f_m=\left[1-\cfrac{M\cdot\left(2+M\right)}{1+M}\cdot\left(\cfrac{2\cdot \overline{σ}_{eq,r}}{\cfrac{Δσ_{eq}}{f_u}}\right)\right]^{0.5}

Overall correction factor applied to unwelded components

$$f_u=f_s\cdot f_e\cdot f_m\cdot f_{t^*}$$
$f_u=f_s\cdot f_e\cdot f_m\cdot f_{t^*}$
Equations in LaTeX code
f_u=f_s\cdot f_e\cdot f_m\cdot f_{t^*}

Allowable number of cycles obtained from the fatigue design curves

$\text{if }\ \cfrac{Δσ_{eq}}{f_u}\geq Δσ_D$
$\text{if }\ \cfrac{Δσ_{eq}}{f_u}\geq Δσ_D$
Equations in LaTeX code
\text{if }\ \cfrac{Δσ_{eq}}{f_u}\geq Δσ_D
$$N=\left(\cfrac{46000}{\cfrac{Δσ_{eq}}{f_u}-0.63\cdot R_m+11.5}\right)^2$$
$N=\left(\cfrac{46000}{\cfrac{Δσ_{eq}}{f_u}-0.63\cdot R_m+11.5}\right)^2$
Equations in LaTeX code
N=\left(\cfrac{46000}{\cfrac{Δσ_{eq}}{f_u}-0.63\cdot R_m+11.5}\right)^2
$\text{else if }\ Δσ_{Cut}< \cfrac{Δσ_{eq}}{f_u}< Δσ_D$
$\text{else if }\ Δσ_{Cut}< \cfrac{Δσ_{eq}}{f_u}< Δσ_D$
Equations in LaTeX code
\text{else if }\ Δσ_{Cut}< \cfrac{Δσ_{eq}}{f_u}< Δσ_D
$$N=\left(\cfrac{2.69\cdot R_m+89.72}{\cfrac{Δσ_{eq}}{f_u}}\right)^{10}$$
$N=\left(\cfrac{2.69\cdot R_m+89.72}{\cfrac{Δσ_{eq}}{f_u}}\right)^{10}$
Equations in LaTeX code
N=\left(\cfrac{2.69\cdot R_m+89.72}{\cfrac{Δσ_{eq}}{f_u}}\right)^{10}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$N={INF} $$
$N={INF} $
Equations in LaTeX code
N={INF}
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