In this paper, making use of the formula for rate process in formation of heterogeneous structures through three-dimensionally stressed fatigue in a previous paper, the relation of fatigue times in which heterogeneous structures caused through random-stressed fatigue and those through step-stressed fatigue become equal is discussed mathematically and experimentally. The results are as follows:
(1) The relation of fatigue times in which heterogeneous structures caused through step-stressed fatigue (by combination of arbitrary stress σ
i, arbitrary times _??_
tij, arbitrary temperature
Ti) and those through constant stressed fatigue (basic stress σ
0, basic temperature T
0=a
iT
i) become equal is given by the following formula:
t(σ
0)=∑<i>∑<j>exp[1/k•T
0{U
0(1-a
i)+α(a
iσ
2i-σ
20)}]•_??_t
ij(2) Fatigue curve for random-stressed fatigue (average stress σ, dispersion
S2) can be expressed by setting the fatigue time
t(σ) of constant stressed fatigue 1/
a times larger, where in
a=1/√<1-(2α•s
2/k•T
ran)>•exp{α•σ
2/k•T
ran(2α•s
2/k•T
ran-2α•s
2)}
and
U0 is activation energy, α is transformation parameter and
k is Boltzmann′s constant.
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