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A dynamic closure criterion for central defects in heavy plate during hot rolling

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Abstract

A new continuous velocity field used to analyze central defect closure for heavy plate rolling is proposed by modifying a two-dimensional velocity field. By using the proposed velocity field and mean yield criterion (or called MY criterion for short), the internal deformation energy rate is obtained. With co-line vector inner-product method, the frictional energy rate is then integrated. Ultimately, an analytical solution of the rolling torque and rolling force is obtained by minimizing the total energy rate with respect to neutral angle. Based on the assumption that when a central defect tends to be closed the stress state coefficient will obtain its critical value, a mathematical expression of critical shape factor together with a dynamic closure criterion for rectangular shape defects are derived. It is found that the critical shape factor is a function of initial plate thickness, relative reduction, work roll radius, and friction factor. The effects of independent rolling parameters such as plate thickness, relative reduction, work roll radius, and friction factor on the critical shape factor are discussed systematically. The results show that the increases in relative reduction, work roll radius and friction factor benefit defect closure, while a large value of initial plate thickness induces central burst formation. In addition, the proposed criterion is validated by comparison with available theoretical results and very good agreement is found.

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Abbreviations

\(h_{x} ,h_{m}\) :

Half of plate thickness and half of average plate thickness in roll gap

\(h_{0} ,h_{1}\) :

Half of initial and final plate thickness at inlet and outlet, respectively

\(h_{t}\) :

Total average thickness of rolling plate, \(h_{t} = 2h_{m}\)

\(h_{x}^{{\prime }} ,h_{x}^{{\prime \prime }}\) :

The first and second order derivatives of \(h_{x}\)

h :

Plate thickness

\(h_{{\alpha_{n} }}\) :

Half of plate thickness at the location of neutral point

\(l_{0} ,l\) :

Contact lengths without central defect and with central defect, respectively

b :

Plate width

\(\theta\) :

Bite angle

\(\sigma_{s}\) :

Yield stress

k :

Yield shear stress

\(v_{x} ,v_{y} ,v_{z}\) :

Velocity components in x, y, z directions

\(\dot{\varepsilon }_{ij}\) :

Strain rate

\(D\left( {\dot{\varepsilon }_{ij} } \right)\) :

Specific plastic work rate

\(x_{a} ,x_{b}\) :

Vertical distances between the central defect and the entry section

\(\Delta h\) :

Half of absolute reduction

\(v_{R}\) :

Roll circumferential velocity

\(\tau_{f}\) :

Frictional shear stress on plate surface

\(\Delta v_{f}\) :

Discontinuous quantity of tangential velocity

\(v_{0}\) :

Inlet velocity of plate

\(\alpha ,\beta ,\gamma\) :

Direction angles formed by \(\tau_{f}\) and the coordinate axes in x, y, z directions, respectively

\(N_{d}\) :

Internal strain energy rate

\(N_{f}\) :

Friction energy rate

\(N_{s}\) :

Shear energy rate

\(U\) :

Flow volume per second of deformation part

\(\alpha_{n}\) :

Neutral angle

\(x_{n}\) :

Location of neutral point, \(x_{n} = l - R\sin \alpha_{n}\)

\(\varPhi\) :

Total energy rate

\(M_{\hbox{min} }\) :

Minimum value of roll torque

\(F_{\hbox{min} }\) :

Minimum value of separating force

\(n_{\sigma }\) :

Stress state coefficient

m :

Friction factor

χ :

Lever arm ratio

\(\Delta ,\Delta_{c}\) :

Actual and critical shape factors

r :

Relative reduction

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Acknowledgments

The authors wish to acknowledge the National Natural Science Foundation of China (Grant No. 51504156), the Basic Research Program of Jiangsu Province (Grant No. BK20140334), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 14KJB460024) and the Project Funded by China Postdoctoral Science Foundation (Grant No. 2014M561707). The authors also wish to acknowledge valuable suggestions from reviewers.

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Authors and Affiliations

  1. Shagang School of Iron and Steel, Soochow University, Suzhou, 215021, China

    Shun Hu Zhang, Jian Zhou & Xin Yi Wang

  2. School of Chemical and Environmental Engineering, Soochow University, Suzhou, 215123, China

    Shun Hu Zhang & Xiao Dong Chen

  3. State Key Lab of Rolling and Automation, Northeastern University, Shenyang, 110819, China

    De Wen Zhao

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  1. Shun Hu Zhang
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  2. Xiao Dong Chen
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  3. Jian Zhou
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  5. Xin Yi Wang
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Correspondence to Shun Hu Zhang.

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Zhang, S.H., Chen, X.D., Zhou, J. et al. A dynamic closure criterion for central defects in heavy plate during hot rolling. Meccanica 51, 2365–2375 (2016). https://doi.org/10.1007/s11012-016-0371-9

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