# Fatigue strength of unwelded components

## Values for calculation

$e_n$ $\mathrm{mm}$
$Δσ_{eq}$ $\mathrm{MPa}$
$σ_{eq\ max}$ $\mathrm{MPa}$
$\overline{σ}_{eq}$ $\mathrm{MPa}$
$T^*$ $\mathrm{°C}$
$R_z$ $\mathrm{μm}$
$R_{p0.2/T^*}$ $\mathrm{MPa}$
$R_{p1.0/T^*}$ $\mathrm{MPa}$
$R_{m/20}$ $\mathrm{MPa}$
$R_{m/T^*}$ $\mathrm{MPa}$
$Δσ_D$ $\mathrm{MPa}$
$Δσ_{Cut}$ $\mathrm{MPa}$

## Calculation

### Proof strength

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

### Tensile strength

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

### Coefficient $F_e$

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

### Temperature correction factor

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

### Thickness correction factor in unwelded components

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

### Coefficient $F_s$

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

### Surface finish correction factor

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

### Mean stress sensitivity factor

$$M=0.00035\cdot R_m-0.1$$

### Reduced mean equivalent stress for elastic-plastic conditions

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

### Mean stress correction factor

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

### Overall correction factor applied to unwelded components

$$f_u=f_s\cdot f_e\cdot f_m\cdot f_{t^*}$$

### Allowable number of cycles obtained from the fatigue design curves

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