Modeling creep and creep recovery of 332 aluminum alloy using fractional calculus

Wang, Fan; Huang, Yang

doi:10.1007/s11043-021-09528-7

Cited by 3 publications

(2 citation statements)

References 30 publications

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“…By means of the superposition principle, 45,46 the creep model can be used to capture the creep recovery process…”

Section: Analysis Based On Creep Recovery Behaviormentioning

confidence: 99%

“…By means of the superposition principle, 45,46 the creep model can be used to capture the creep recovery process

ε (t) = ε (t) U (t) - ε (t - t_{1}) U (t - t_{1}),

Where

t_{1}

is the beginning time when the applied load is removed,

U (t)

and

U (t - t_{1})

are the unit step function. The recovery phase can be described by

ε_{R} (t) = [J (t) - J^{'} (t - t_{1})] σ_{0},

in which

J (t) = w + d [1 - E_{α} (- {((), vt)}^{α})]

is the creep compliance.…”

Section: Model Development and Variable‐order Function Analysismentioning

confidence: 99%

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Analysis of the variable‐order fractional viscoelastic modeling with application to polymer materials

Han

Yin

Gao

2023

Polymers for Advanced Techs

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The variable-order fractional (VOF) operator has been extensively employed to depict complex physical phenomena of viscoelastic materials, during which the reasonable form of the proper variable-order (VO) function will significantly affect the applicability and accuracy of proposed fractional model. To this regard, this work aims to provide a technical guidance for VO function selection in VOF viscoelastic modeling. In this paper, we develop a VOF model based on the classical Zener model, the suitable VO function form and the applicability of VOF model are investigated by means of characterizing the stress relaxation and creep recovery behaviors, in which the monotonicity of VO functions (decreasing or increasing) are discussed in detail.The results demonstrate that the stress relaxation and creep recovery responses have a realistic physical meaning only when the VOF rheological model with a monotonically decreasing VO function. Furthermore, three definitions of VOFD are also considered to determine the optimal VO function form and the reasonability of the proposed model is validated by fitting the experimental data of polymer matric materials. The analysis found that the decreasing exponential VO function exhibits good prospects in describing the time-dependent behaviors, and it was found that the V2 and V3 definition types performed better. The results also show that the proposed model has unique advantage compared to the other existing viscoelastic models.Finally, the proposed VOF model is employed to predict the viscoelastic behavior to test the model's predictive ability.

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“…By means of the superposition principle, 45,46 the creep model can be used to capture the creep recovery process…”

Section: Analysis Based On Creep Recovery Behaviormentioning

confidence: 99%

“…By means of the superposition principle, 45,46 the creep model can be used to capture the creep recovery process

ε (t) = ε (t) U (t) - ε (t - t_{1}) U (t - t_{1}),

Where

t_{1}

is the beginning time when the applied load is removed,

U (t)

and

U (t - t_{1})

are the unit step function. The recovery phase can be described by

ε_{R} (t) = [J (t) - J^{'} (t - t_{1})] σ_{0},

in which

J (t) = w + d [1 - E_{α} (- {((), vt)}^{α})]

is the creep compliance.…”

Section: Model Development and Variable‐order Function Analysismentioning

confidence: 99%

Analysis of the variable‐order fractional viscoelastic modeling with application to polymer materials

Han

Yin

Gao

2023

Polymers for Advanced Techs

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A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined

Li,

2023

Chaos, Solitons & Fractals

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Constitutive modeling for the flow stress behaviors of alloys based on variable order fractional derivatives

Meng

Cao

Zhang

2022

Mater. Res. Express

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During hot working, alloys may experience three kinds of flow stress behaviors, including strain hardening, strain softening, or steady flow, because of the competition of work hardening and thermal softening. Modelling the flow stress behaviors plays an essential role in understanding the mechanical properties of alloys. In this paper, the variable order fractional model is provided to describe the flow stress behaviors of alloys. The variation of the fractional order between 0 and 1 can reflect the mechanical property changing between solids and fluids. By assuming that the fractional order varies linearly with time, the proposed model can describe both the strain softening and strain hardening behaviors of alloys. The model fitting results are compared to the experimental data of A356 alloy for strain softening and Cu-Cr-Mg alloy for strain hardening under different temperatures and strain rates. It is validated that the variable order fractional model can accurately describe the flow stress behaviors of alloys. Furthermore, the rule of the variable order is also discussed to analyze its overall values and the changes before and after the yield point. It is concluded that the variation of the fractional order can intuitively reveal the changes in mechanical properties in the flow stress behaviors of alloys, including both strain softening and strain hardening.

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Modeling creep and creep recovery of 332 aluminum alloy using fractional calculus

Cited by 3 publications

References 30 publications

Analysis of the variable‐order fractional viscoelastic modeling with application to polymer materials

Analysis of the variable‐order fractional viscoelastic modeling with application to polymer materials

A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined

Constitutive modeling for the flow stress behaviors of alloys based on variable order fractional derivatives

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