Buckling of rolled thin sheets under residual stresses by ANM and Arlequin method
Source abstract
Abstract
We present a numerical technique to model the buckling of a rolled thin sheet. It consists in coupling, within the Arlequin framework, a three dimensional model based on 8-nodes tri-linear hexahedron, used in the sheet part located upstream the roll bite, and a well-suited finite element shell model, in the roll bite downstream sheet part, in order to cope with buckling phenomena. The resulting nonlinear problem is solved by the Asymptotic Numerical Method (ANM) that is efficient to capture buckling instabilities. The originalities of the paper ly, first in an Arlequin procedure with moving meshes, second in an efficient application to a thin sheet rolling process. The suggested algorithm is applied to very thin sheet rolling scenarios involving “edges-waves” and “center-waves” defects. The obtained results show the effectiveness of our global approach.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Vibration and Dynamic Analysis · Metal Forming Simulation Techniques · Numerical methods in engineering
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References (35)
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1. Abdelkhalek S, Zahrouni H, Potier-Ferry M, Legrand N, Montmitonnet P, Buessler P (2009) Coupled and uncoupled approaches for thin cold rolled strip buckling prediction. Int J Mater Form 2(1):833–83610.1007/s12289-009-0547-0 ↗
2. Marchand H (2000) Modélisation de la planéité en sortie de laminage des produits plats (Modelling flatness in flat rolling), Ph.D. thesis École nationale supérieure des mines de Paris
3. Hacquin A, Montmitonnet P, Guillerault J.-P. (1996) A steady state thermo-elastoviscoplastic finite element model of rolling with coupled thermo-elastic roll deformation. J Mater Process Technol 60(1):109–11610.1016/0924-0136(96)02315-1 ↗
4. Abdelkhalek S (2010) Un exemple de flambage sous contraintes internes: Étude des défauts de planéité en laminage á froid des tôles minces, Ph.D. thesis École nationale supérieure des mines de Paris
5. Fischer FD, Rammerstorfer FG, Friedl N, Wieser W (2000) Buckling phenomena related to rolling and levelling of sheet metal. Int J Mech Sci 42(10):1887–191010.1016/S0020-7403(99)00079-X ↗
6. Fischer FD, Friedl N, Noe A, Rammerstorfer FG (2005) A study on the buckling behaviour of strips and plates with residual stresses. Steel Res Int 76(4):327–33510.1002/srin.200506016 ↗
7. Rammerstorfer FG, Fischer FD, Friedl N (2001) Buckling of free infinite strips under residual stresses and global tension. J Appl Mech 68(3):399–40410.1115/1.1357519 ↗
8. Nakhoul R, Montmitonnet P, Potier-Ferry M (2015) Multi-scale method for modeling thin sheet buckling under residual stresses in the context of strip rolling. Int J Solids Struct 66:62– 7610.1016/j.ijsolstr.2015.03.028 ↗
9. Kpogan K (2014) Simulation numérique de la planéité des tôles métalliques formées par laminage, Ph.D. thesis, Université de Lorraine
10. Counhaye C (2000) Modélisation et contrôle industriel de la géométrie des aciers laminés à froid (modelling and industrial control of the geometry of cold rolled steels), Ph.D. thesis, Université de Liège
11. Roddeman D, Drukker J, Oomens C, Janssen J (1987) The wrinkling of thin membranes: Part i—theory. J Appl Mech 54(4):884–88710.1115/1.3173133 ↗
12. Abdelkhalek S, Montmitonnet P, Potier-Ferry M, Zahrouni H, Legrand N, Buessler P (2010) Strip flatness modelling including buckling phenomena during thin strip cold rolling. Ironmak Steelmak 37(4):290–29710.1179/030192310X12646889255708 ↗
13. Ben Dhia H (1998) Multiscale mechanical problems: the Arlequin method. C R Acad Sci IIB 326(12):899–904
14. Ben Dhia H, Rateau G (2005) The arlequin method as a flexible engineering design tool. Int J Numer Methods Eng 62(11):1442–146210.1002/nme.1229 ↗
15. Ben Dhia H, Rateau G (2001) Mathematical analysis of the mixed Arlequin method. C R Acad Bulg Sci I 332(7):649–65410.1016/S0764-4442(01)01900-0 ↗
16. Philippe S (2009) Développement d’une formulation arbitrairement lagrangienne eulérienne pour la simulation tridimensionnelle du laminage de produits plats, Ph.d. thesis École nationale supérieure des mines de Paris
17. Büchter N, Ramm E, Roehl D (1994) Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept. Int J Numer Methods Eng 37(15):2551–256810.1002/nme.1620371504 ↗
18. Simo J, Rifai M (1990) A class of mixed assumed strain methods and method of incompatible modes. Int J Numer Methods Eng 37:1595–163610.1002/nme.1620290802 ↗
19. Zahrouni H, Cochelin B, Potier-Ferry M (1999) Computing finite rotations of shells by an asymptotic-numerical method. Comput Methods Appl Mech Eng 175(1):71–8510.1016/S0045-7825(98)00320-X ↗
20. Bischoff M, Ramm E (2000) On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation. International journal of solids ans structures 37:6933–696010.1016/S0020-7683(99)00321-2 ↗
21. Azrar L, Cochelin B, Damil N, Potier-Ferry M (1993) An asymptotic numerical method to compute postbuckling behavior of elastic plates and shells. Int J Numer Methods Eng 36(8):1251–127710.1002/nme.1620360802 ↗
22. Tri A, Cochelin B, Potier-Ferry M (1996) Résolution des équations de navier stokes et détection des bifurcations stationnaires par une méthode asymptotique numérique. Revue européenne des éléments finis 5:415–44210.1080/12506559.1996.11509512 ↗
23. Boutyour E, Zahrouni H, Potier-Ferry M, Boudi M (2004) Bifurcation points and bifurcated branches by an asymptotic numerical method and padé approximants. Int J Numer Methods Eng 60(12):1987–201210.1002/nme.1033 ↗
24. Cadou JM, Potier-Ferry M, Cochelin B (2006) A numerical method for the computation of bifurcation points in fluid mechanics. Europeen journal of mechanics B: fluids 25:234–25410.1016/j.euromechflu.2005.07.002 ↗
25. Cochelin B (1994) A path-following technique via an asymptotic-numerical method. Comput Struct 53(5):1181–119210.1016/0045-7949(94)90165-1 ↗
26. Cochelin B, Damil N, Potier-Ferry M Méthode asymptotique numérique. Hermes-Sciences, Paris
27. Tri A, Zahrouni H, Potier-Ferry M (2014) Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems. Numerical methods for partial differential equations 30(3):978–99310.1002/num.21851 ↗
28. Rateau G (2003) Méthode Arlequin pour les problémes mécaniques multi-échelles: Applications á des problémes de jonction et de fissuration de structures élancées, Ph.D. thesis, École Centrale de Paris
29. Guidault P.-A., Belytschko T. (2007) On the L2 and the H1 couplings for an overlapping domain decomposition method using lagrange multipliers. Int J Numer Methods Eng 70(3):322–35010.1002/nme.1882 ↗
30. Roddeman D, Drukker J, Oomens C, Janssen J (1987) The wrinkling of thin membranes: Part I—theory. J Appl Mech 54(4):884–88710.1115/1.3173133 ↗
31. Abdelkhalek S, Montmitonnet P, Legrand N, Buessler P (2011) Coupled approach for flatness prediction in cold rolling of thin strip. Int J Mech Sci 53(9):661–67510.1016/j.ijmecsci.2011.04.001 ↗
32. Bush A, Nicholls R, Tunstall J (2001) Stress levels for elastic buckling of rolled strip and plate. Ironmak Steelmak 28(6):481–48410.1179/irs.2001.28.6.481 ↗
33. Hibbitt K (2001) Sorensen, ABAQUS/standard user’s Manual, Vol. 1, Hibbitt, Karlsson & Sorensen
34. Abdelkhalek S, Zahrouni H, Legrand N, Potier-Ferry M (2015) Post-buckling modeling for strips under tension and residual stresses using asymptotic numerical method. Int J Mech Sci 104:126–13710.1016/j.ijmecsci.2015.10.011 ↗
35. Friedl N, Rammerstorfer FG, Fischer FD (2000) Buckling of stretched strips. Comput Struct 78(1):185–19010.1016/S0045-7949(00)00072-9 ↗