Shape of a mechanical hysteresis loop for metallic materials under harmonic stresses below the fatigue limit. Part 1. Experimental method

Bovsunovsky, A.

doi:10.1007/bf02767590

Cited by 1 publication

(8 citation statements)

References 3 publications

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“…By differentiating the strain:

\overset{ε}{true} ((), t) = 2 italicπf ε_{a} ([], \cos ((), 2 italicπft) \cos φ + \sin ((), 2 italicπft) \sin φ)

Considering the product between Equations 2 and 4, it is possible to assess the mechanical energy rate

\overset{W}{true}

that is the derivative along the time of work increment of the external forces treated as a scalar product of the instantaneous values of stress and strain, 11,13,16,17 also called instantaneous power density 10 :

\overset{W}{true} ((), t) = σ ((), t) \overset{ε}{true} ((), t) = σ_{m} 2 italicπf ε_{a} ([], \cos ((), 2 italicπft) \cos φ + \sin ((), 2 italicπft) \sin φ) + σ_{a} 2 italicπf ε_{a} ([], \sin ((), 2 italicπft) \cos ((), 2 italicπft) \cos φ + \sin {(2 πft)}^{2} \sin φ)

By considering that the system pulsation is ω = 2πf , and the relation between σ max , σ m , σ a , and R , and by considering that ε a = σ a / E , 15 it is possible to write:

\overset{W}{true} ((), t) = ω \frac{1 - R^{2}}{4 E} {σ_{italicmax}}^{2} ([], \cos ((), ωt) \cos φ + \sin ((), ωt) \sin φ) + normalω \frac{{((), 1 - R)}^{2}}{4 E} {σ_{italicmax}}^{2} ([], \sin ((), ωt) \cos ((), ωt) \cos φ + \sin {(italicωt)}^{2})

…”

Section: Theorymentioning

confidence: 99%

“…The energy during a cyclic process,

\overset{W}{true}

, can be defined by considering stress and strain over the time 10,11,13,16,17 :

σ ((), t) = σ_{m} + σ_{a} \sin ((), 2 italicπft)

ε ((), t) = ε_{m} ((),, R, σ_{m}) + ε_{a} ((),, R, σ_{a}) \sin ((), 2 italicπft - φ)

where σ m , σ a , ε m , and ε a are mean and amplitude of the stress, mean and amplitude of the strain, φ the phase shift between stress and strain, and f the loading frequency. As it is possible to observe ε m and ε a values are clearly dependent on stress ratio ( R ) and stress amplitude.…”

Section: Theorymentioning

confidence: 99%

“…Referring to mechanical energy input, the aim is to assess the area under the hysteresis loop that represents the dissipated energy, by investigating the constitutive stress–strain law 9–11,13,16,17 or by modeling the strain hardening behavior 7,11 . Both approaches require the definition of a model and the experimental assessment of coefficients (i.e., hardening coefficients) that depend on imposed loading, fatigue regime, material.…”

Section: Introductionmentioning

confidence: 99%

“…The dissipated energy in the material (cyclic plastic energy) because of mechanical loading is related to the number of cycles for failure and can be used as a damage parameter for the material fatigue life estimation 4–6 . Such an energy dissipation is of critical importance for setting up energy‐based fatigue life prediction approaches 10–14 based on the assessment of mechanical energy input 10–19 or heat converted energy by measuring the material surface temperature 20–30 …”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10] The dissipated energy in the material (cyclic plastic energy) because of mechanical loading is related to the number of cycles for failure and can be used as a damage parameter for the material fatigue life estimation. [4][5][6] Such an energy dissipation is of critical importance for setting up energy-based fatigue life prediction approaches [10][11][12][13][14] based on the assessment of mechanical energy input [10][11][12][13][14][15][16][17][18][19] or heat converted energy by measuring the material surface temperature. [20][21][22][23][24][25][26][27][28][29][30] Even if many efforts have been made to better understand the relationships between surface thermal measurements and heat converted energy, and in turn between heat converted energy and intrinsic dissipations, how they vary depending on loading conditions is still unclear.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the relationship between mechanical energy rate and heat dissipated rate during fatigue for a C45 steel depending on stress ratio

Finis

Palumbo

Galietti

2021

Fatigue Fract Eng Mat Struct

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This work deals with the analysis in the frequency domain of the temperature signal and mechanical energy rate of C45 steel under two different fatigue stepwise loading series at stress ratios of 0.1 and −1. It was first investigated the energy distribution among the harmonic components of the signals to understand possible variations caused by a different stress ratio. In addition, the second amplitude harmonic (SAH) of heat dissipated and mechanical energy rates have been considered in the analysis, and their relationship was investigated. It has been shown as it depends only on the material, and hence, it is valid whatever the kind of the test is without any assumption on the energy supplied to the material or material hysteresis loop stabilization. The adopted approach allows the analysis of intrinsic dissipations by means of rapid, full‐field, and contactless techniques without any specific requirement on loading condition or temperature signal stabilization.

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“…By differentiating the strain:

\overset{ε}{true} ((), t) = 2 italicπf ε_{a} ([], \cos ((), 2 italicπft) \cos φ + \sin ((), 2 italicπft) \sin φ)

Considering the product between Equations 2 and 4, it is possible to assess the mechanical energy rate

\overset{W}{true}

\overset{W}{true} ((), t) = σ ((), t) \overset{ε}{true} ((), t) = σ_{m} 2 italicπf ε_{a} ([], \cos ((), 2 italicπft) \cos φ + \sin ((), 2 italicπft) \sin φ) + σ_{a} 2 italicπf ε_{a} ([], \sin ((), 2 italicπft) \cos ((), 2 italicπft) \cos φ + \sin {(2 πft)}^{2} \sin φ)

By considering that the system pulsation is ω = 2πf , and the relation between σ max , σ m , σ a , and R , and by considering that ε a = σ a / E , 15 it is possible to write: