####
J. Japan Inst. Metals, Vol. 15, No. 9 (1951),

pp. 402-407

##
On the Relation between Structure and Strength (II) On the Fatigue Failure of Steel and Cast Iron

**
F. Matsumoto
**

#### Abstract:

The author proposed the general formula for the fatigue strength as follows:

σ_{nW}=σ_{n}-k_{1}τ, ·····(1) |

where σ_{nW} and σ_{n} mean the fatigue strength,respectively,with or without diminishing the effect caused by repeated load having the stress difference τ in shearing,and k_{1} is a coefficient depending on micro-slip-path besides τ. In other words, σ_{n} correspends to the separating strength discussed Previously.

For steel,k_{1} is about 2.8~3.3 and σ_{t} is equal to (2.3 ~ 2.7)σ_{u},where σ_{u} indicates the fatigue limit in single blow tension. Furthermore,the following expressions were derived, respectively: σ_{W},fatigue limit in tension and compression=(0.53 ~ 0.68)σ_{u}, σ_{W}', fatigue limit in bending: (1.1 ~ 1.3)σ_{W}, τ_{u}, fatigue limit in single flow torsion: σ_{W}, and τ_{W}, fatigue limit in double blow torsion=(0.3 ~ 0.4)σ_{u}. With the same conception, for cast iron, σ_{u}', σ_{W}', σ_{W}'', τ_{u}' and τ_{W}' which correspond to σ_{u}, σ_{W}, σ_{W}', τ_{u} and τ_{W} respectively, for steel, were expressed using stress concentration factor α_{kt} (in tension) or α_{kt} (in shearing), correcting factor k_{2} against k_{1} and factor δ in bending. For an example, for σ_{W}' the following formula was derived :
α_{kt}σ_{W}'=σ_{t}-k_{1}k_{2}(σ_{kt}/2+α_{ks}/2)σ_{W}' ·····(2) |

For steel containing x% of carbon, an approximation was put forward empirically as follows:
σ_{Wx}'=(0.6 ~ 0.9){σ_{fs}+(σ_{ps}-σ_{fs})(x/0.9)^{2/3}} ·····(3) |

where σ_{fs} and σ_{ps} indicate the yceld
point of firrite and pearlite, respectively. This idea could be applied also to
the carburized steel, which is considered to be composed of harder outer case
and softer inner part. Furthermore, the author discussed the outer notch effect
on fatigue.

(Received 1950/12/18)

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