Fig 5 low amplitude load region
in low-high sequence. (A), The definition of load region. (B), Influence
of preload on the residual fatigue life
As shown in Fig 5(A), σH and σL are the
maximum and minimum strengthening stress, respectively; σ is the stress
level of preload. Its influence on residual fatigue life can be omitted
for loads lower than the minimum strengthening stress. In the
strengthening region, the residual fatigue life can be improved when the
number of preload cycles is within the appropriate range. Several
investigations29,38,55 confirmed this phenomenon and
suggested that σH is slightly below the fatigue limit.
For loads over the σH, the residual fatigue life firstly
increases and then decreases with the number of preload cycles. This
opinion is supported by the test results exhibiting the strengthening
effect in Fig 2. In fact, for loads over the fatigue limit, the finite
fatigue life makes it inevitable that the damaging effect is dominated
when the number of cycles exceeds a specific value. The strengthening
effect is also affected by the stress level of the preload. Two-level
tests on various materials indicated that the strengthening effect
decreases with increasing stress level of the preload. Ishihara et
al.45 conducted two-level load tests on S45C steel
with preload stresses of 400 MPa and 500 MPa, respectively. The former
loading condition corresponds to a significant strengthening effect,
while the latter one can be ignored. The test results for DTD683
steel17 and Maraging steel49 also
show this trend. In Li et al.’s study44, two-level
load tests with different stress levels were conducted on K417 alloy. It
was found that the residual fatigue life fraction decreased from 5.37 to
2.33 with increasing preload stress. Only the damaging effect can be
observed when the preload stress σa1 is equal to or
higher than the subsequent stress σa2. The relationship
betweenn 1/Nf 1 andn 2/Nf 2must follow Miner’s rule when σa1 equals
σa2.
In the Chaboche model, the damage evolution in the low-high loading path
is shown in Fig 6. For materials exhibiting the strengthening effect, it
can be assumed that the fatigue resistance is improved after low
amplitude loading, i.e., the damage growth rate is reduced. The
expression of the damage rate can be modified from Equation to:
where q is a factor characterizing the strengthening effect and
can be referred to as the “strengthening factor.”