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A novel precipitation kinetics model for fast-aging process of Al–Zn–Mg–Cu alloy

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Abstract

In this paper, a set of novel thermo-mechanical coupling kinetics models were developed for the fast aging process of Al–Zn–Mg–Cu alloy. The precipitates models in this paper described the continuous growth behavior of precipitates in the two-step aging, by introducing temperature dependent constants, the contribution of each aging step in the two-step aging process was quantitatively characterized; the analytical formula for the critical temperature of instantaneous nucleation during the aging process was derived; providing a pre-aging time threshold in the competition mechanism, which for the inhibition of precipitates nucleation on dislocations in secondary aging. Subsequently, associated above models with macroscopic material strength, the yield strength of 7075 aluminum alloy after fast aging was predicted. Through the quantitative verification by mechanical properties experiments, the model values have a good agreement with the experimental ones, and the errors are below 8%.

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All the relevant experimental and computational data for the manuscript can be provided upon request.

Abbreviations

\({{\varvec{C}}}_{{\varvec{i}}}\) :

Initial concentration of solutes in the matrix

\({{\varvec{C}}}_{{\varvec{s}}}\) :

Concentration of solutes in the matrix when the precipitates are completely dissolved

\({{\varvec{C}}}_{{\varvec{e}}{\varvec{q}}}\) :

Equilibrium concentration of solutes in the matrix during single-step aging

\({{\varvec{C}}}_{{\varvec{e}}{\varvec{q}}1}\) :

Equilibrium concentration of solutes in the matrix during aging

\({{\varvec{C}}}_{{\varvec{e}}{\varvec{q}}2}\) :

Equilibrium concentration of solutes in the matrix during secondary aging

\({\varvec{C}}({\varvec{t}})\) :

Concentration of solutes in the matrix during single-step aging

\({\varvec{C}}({{\varvec{t}}}_{10})\) :

Concentration of solutes in the matrix after the pre-aging time of \({t}_{10}\)

\({\varvec{\sigma}}\) :

Flow stress

\({{\varvec{\sigma}}}_{0}\) :

Initial stress

\({{\varvec{\sigma}}}_{{\varvec{s}}{\varvec{s}}}\) :

Solid solution stress

\({{\varvec{\sigma}}}_{{\varvec{d}}}\) :

Dislocation stress

\({{\varvec{\sigma}}}_{{\varvec{p}}{\varvec{p}}{\varvec{t}}}\) :

Precipitation stress

\({{\varvec{\sigma}}}_{{\varvec{p}}{\varvec{p}}{\varvec{t}}{\varvec{m}}}\) :

Precipitation stress in matrix

\({{\varvec{\sigma}}}_{{\varvec{p}}{\varvec{p}}{\varvec{t}}{\varvec{d}}}\) :

Precipitation stress on dislocations

\({{\varvec{\sigma}}}_{{\varvec{d}}{\varvec{f}}}\) :

Flow stress with deformation

\({{\varvec{\sigma}}}_{{\varvec{n}}{\varvec{d}}{\varvec{f}}}\) :

Flow stress without deformation

\({\varvec{T}}\) :

Single-step aging temperature

\({{\varvec{T}}}_{1}\) :

Pre-aging temperature

\({{\varvec{T}}}_{2}\) :

Secondary aging temperature

\({{\varvec{T}}}_{{\varvec{s}}}\) :

Aging temperature at which all precipitates are dissolved without deformation

\(\mathbf{D}\) :

Solute atomic diffusion coefficient in matrix during single-step aging

\({\mathbf{D}}_{1}\) :

Solute atomic diffusion coefficient in matrix during pre-aging

\({\mathbf{D}}_{2}\) :

Solute atomic diffusion coefficient in matrix during secondary aging

\({\varvec{t}}\) :

Single-step aging time

\({{\varvec{t}}}_{1}\) :

Pre-aging time

\({{\varvec{t}}}_{2}\) :

Secondary aging time

\({{\varvec{t}}}_{0}\) :

Any aging time when a batch of precipitates begins to nucleate

\({{\varvec{t}}}_{01}\) :

Any pre-aging time when a batch of precipitates begins to nucleate

\({{\varvec{t}}}_{10}\) :

Pre-aging time at the end of pre-aging

\({{\varvec{\tau}}}_{0}\) :

Time-dependence constant in single-step aging

\({{\varvec{\tau}}}_{1}\) :

Time-dependence constant in pre-aging

\({{\varvec{\tau}}}_{2}\) :

Time-dependence constant in secondary aging

\({{\varvec{\uptau}}}_{{\varvec{e}}{\varvec{q}}}\) :

Equivalent time-dependence parameter without deformation at the temperature of secondary aging

\({{\varvec{f}}}_{1}\) :

Volume fraction of precipitates in pre-aging

\({{\varvec{f}}}_{10}\) :

Equilibrium volume fraction of precipitates in pre-aging

\({{\varvec{f}}}_{20}\) :

Equilibrium volume fraction of precipitates in secondary aging

\({{\varvec{f}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}\) :

Volume fraction of precipitates when the solutes dissolved completely

\({{\varvec{Q}}}_{{\varvec{s}}}\) :

Diffusive energy of solute atoms in aging

\(\boldsymbol{\Delta }{{\varvec{G}}}_{{\varvec{m}}}\) :

Free energy of precipitates growth in matrix

\(\boldsymbol{\Delta }{{{\varvec{G}}}_{{\varvec{d}}}}^{\boldsymbol{*}}\) :

Free energy of precipitates nucleation on dislocations

\(\boldsymbol{\Delta }{\varvec{g}}\) :

Precipitate driving force in single-step aging

\(\boldsymbol{\Delta }{{\varvec{g}}}_{1}\) :

Precipitate driving force in pre-aging

\(\boldsymbol{\Delta }{{\varvec{g}}}_{2}\) :

Precipitate driving force in secondary aging

\(\boldsymbol{\Delta }{{\varvec{g}}}_{{\varvec{d}}}\) :

Precipitate driving force of precipitates around dislocations

\(\boldsymbol{\Omega }\) :

Super-saturation of solutes in matrix during single-step aging

\({\boldsymbol{\Omega }}_{1}\) :

Super-saturation of solutes in matrix during pre-aging

\({\boldsymbol{\Omega }}_{2}\) :

Super-saturation of solutes in matrix during secondary aging

\(\mathbf{\varphi }\) :

Aspect ratio of plate-like precipitates during single-step aging

\({\mathbf{\varphi }}_{1}\) :

Aspect ratio of plate-like precipitates during pre-aging

\({\mathbf{\varphi }}_{2}\) :

Aspect ratio of plate-like precipitates during secondary aging

\({{\varvec{r}}}^{\boldsymbol{*}}\) :

Nucleation radius of precipitates during single-step aging

\({{{\varvec{r}}}_{1}}^{\boldsymbol{*}}\) :

Nucleation radius of precipitates during pre-aging

\({{{\varvec{r}}}_{2}}^{\boldsymbol{*}}\) :

Nucleation radius of precipitates during secondary aging

\({{{\varvec{r}}}_{{\varvec{d}}1}}^{\boldsymbol{*}}\) :

Nucleation radius of precipitates around dislocations

\({{{\varvec{r}}}_{{\varvec{d}}2}}^{\boldsymbol{*}\boldsymbol{*}}\) :

Clustering radius of precipitates on dislocations before nucleation

\({{{\varvec{r}}}_{{\varvec{d}}2}}^{\boldsymbol{*}}\) :

Nucleation radius of precipitates on di Slocations

\({\varvec{r}}\) :

Growth radius of precipitates during single-step aging

\({{\varvec{r}}}_{1}\) :

Growth radius of precipitates during pre-aging

\({{\varvec{r}}}_{2}\) :

Growth radius of precipitates during secondary aging

\({{\varvec{N}}}_{1}\) :

Number of precipitates during pre-aging

\(\boldsymbol{\alpha }\) :

Contribution factor of \({\tau }_{eq}\) in the two-step aging

\({\varvec{\upmu}}\) :

Shear modulus

\({\varvec{\upupsilon}}\) :

Poisson’s ratio

\({\varvec{\upgamma}}\) :

Surface energy of precipitates

\(\mathbf{b}\) :

Bergs vector

\(\mathbf{R}\) :

Gas constant

\(\mathbf{k}\) :

Boltzmann constant

\({\mathbf{v}}_{\mathbf{a}\mathbf{t}}\) :

Solute atomic volume

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Acknowledgments

The authors duly acknowledge the financial support from the National Natural Science Foundation of China (Grant no. 51975440); the National Key R&D Program of China (No. 2020YFA0714900); the 111 Project (Grant no. B17034); and the Innovative Research Team Development Program of Ministry of Education of China (Grant no. IRT_17R83).

Funding

Funding was provided by the financial support from the National Natural Science Foundation of China (Grant no. 51975440).

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Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China

    Pu Zhou, Yanli Song, Jue Lu, Lin Hua & Lvyong Huang

  2. Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan, 430070, China

    Yanli Song & Lin Hua

  3. Hubei Research Center for New Energy & Intelligent Connected Vehicle, Wuhan University of Technology, Wuhan, 430070, China

    Yanli Song & Lin Hua

Authors
  1. Pu Zhou
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  2. Yanli Song
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  3. Jue Lu
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  4. Lin Hua
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  5. Lvyong Huang
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Contributions

PZ: Conceptualization, Methodology, Data adjustment, Writing original draft. YS: Writing—Review & Editing, Supervision, Project administration, Funding acquisition. JL: Writing—Review & Editing. LH: Supervision. LH: Investigation.

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Correspondence to Yanli Song or Lin Hua.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “A novel precipitation kinetics model for fast-aging process of Al–Zn–Mg–Cu alloy”.

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Zhou, P., Song, Y., Lu, J. et al. A novel precipitation kinetics model for fast-aging process of Al–Zn–Mg–Cu alloy. Journal of Materials Research 39, 928–943 (2024). https://doi.org/10.1557/s43578-024-01281-0

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