PSI - Issue 42

Martin Matušů et al. / Procedia Structural Integrity 42 (2022) 102 – 109 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3.3. Limiting energy for the Fargione method The Fargione method (Fargione (2001)) is based on an assumption illustrated with the help of Fig. 3b. Fargione claims that the area under the temperature evolution curve over imposed number of cycles is a constant value independent of the load amplitude. This constant value is referred to as the limiting energy Φ and it is defined by the following formula:

s  =  = 

.

T dN const

(5)

N

f

Fargione (2001) assumes that there is a second phase of steady temperature response, which can be described by ∆ T s , see Fig. 3a. However, in the experiments presented here, no stabilized ∆ T s is observed in the second phase, and the temperature is growing with the R s rate; see Fig. 4. Since Fargione assumed that the specimen spends nearly the entirety of its useful life in the second phase, he could simplify Eq. (5) to

(6)

.

f N const =

   

s

Using this simplified formula, the number of cycles relevant to the load level can be found by the specific response of ∆ T s obtained for a substantially smaller number of applied cycles. Because ∆ T s is the response to cyclic loading at a specific stress level, the fatigue curve can be approximated from an experimental test with a subsequently increasing stress amplitude for which the relation between the acting stress and the response in ∆ T s is observed. The question investigated in this paper is whether Φ can be assumed to be a constant for this specific material and setup conditions. The answer is negative; see the output for series A01-A04 in Fig. 7. The limiting energy parameter is highly dependent on the loading amplitude in the presented setup. The limiting energy for A01-A03 ranges from 1e5 to 1e7 K·cycles. From the observed results, only the limiting energy of specimen type A04 could be claimed to be close to a constant value.

Fig. 7 Evolution of limiting energy at given amplitudes of stress of all series A01-A04.

Even if the observation had confirmed that the limiting energy is constant, a serious modification of the solution would have to be proposed to approximate the second phase of temperature evolution to use the limiting energy parameter to approximate the fatigue curve. The limiting energy is highly affected by the absence of the phase with a constant temperature response. The authors assume that this type of response could likely be caused by the conduction