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A general model for prediction of deformation from initial residual stress

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Abstract

This paper studied the influence of the initial residual stress on the dimensional stability of manufactured components. Although residual stresses are assumed to be in self-equilibrium within a solid that is not subjected to an external load, most manufactured products will be affected by external forces during service. Therefore, this study allowed for the combined effects of the initial residual stress and external forces on the excessive deformation of a prestressed body. On the basis of the virtual work principle, we developed a new analytical model for predicting the excessive deformation of a prestressed body under an applied load. The proposed model was validated by means of the finite difference method, and we made a comparison with an existing model from the literature, which was developed to predict the excessive deformation of a thin aluminum plates with the machining-induced residual stress. The computational results showed that the proposed method had 10% greater predictive accuracy than previous models available in the work.

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Abbreviations

T 0 :

Residual stress the second Piola-Kirchhoff stress tensor in the undeformed frame

N :

Outward unit normal vector of area element in the undeformed frame

E :

Strain tensor the undeformed frame

σ :

The Cauchy stress in the deformed/current frame

e :

Euler strain tensor in the deformed/current frame

I :

Identity matrix

F :

The material deformation gradient tensor

I :

The displacement in the deformed/current frame

f(x) :

Body force in the deformed/current frame

g(x) :

Surface force in the deformed/current frame

τ :

The applied stress unrelated to the residual stress

Ω :

The total stress in the loaded but undeformed frame

T :

The initial stress in the deformed frame

t :

The applied stress in the deformed frame

n :

Outward unit normal vector of area element in the deformed frame

W :

Strain energy density function

C IJKL :

Moduli

ci :

Coefficient

h :

Depth

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Funding

This work was funded by the National High Technology Research and Development Program of China (No. 2012AA040702, No. 2012AA040703).

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Authors and Affiliations

  1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, 1037 Luoyu Road, Hongshan District, Wuhan, 430074, Hubei, China

    Yamin Zhu, Kuanmin Mao & Xunxing Yu

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  1. Yamin Zhu
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  2. Kuanmin Mao
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Correspondence to Kuanmin Mao.

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Zhu, Y., Mao, K. & Yu, X. A general model for prediction of deformation from initial residual stress. Int J Adv Manuf Technol 109, 1093–1101 (2020). https://doi.org/10.1007/s00170-020-05683-2

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