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Chin. Phys. B, 2020, Vol. 29(10): 104602    DOI: 10.1088/1674-1056/abab6e

Multi-scale elastoplastic mechanical model and microstructure damage analysis of solid expandable tubular

Hui-Juan Guo(郭慧娟)1,2, Ying-Hua Liu(刘应华)1, Yi-Nao Su(苏义脑)2, Quan-Li Zhang(张全立)2, and Guo-Dong Zhan(詹国栋)3,
1 Department of Engineering Mechanics, AML, Tsinghua University, Beijing 100084, China
2 Drilling Mechanical Department, CNPC Engineering Technology R & D Company Limited, Beijing 102206, China
3 Drilling Technology Division, EXPEC Advanced Research Center, Saudi Arabia

We present an in-depth study of the failure phenomenon of solid expandable tubular (SET) due to large expansion ratio in open holes of deep and ultra-deep wells. By examining the post-expansion SET, lots of microcracks are found on the inner surface of SET. Their morphology and parameters such as length and depth are investigated by use of metallographic microscope and scanning electron microscope (SEM). In addition, the Voronoi cell technique is adopted to characterize the multi-phase material microstructure of the SET. By using the anisotropic elastoplastic material constitutive model and macro/microscopic multi-dimensional cross-scale coupled boundary conditions, a sophisticated and multi-scale finite element model (FEM) of the SET is built successfully to simulate the material microstructure damage for different expansion ratios. The microcrack initiation and growth is simulated, and the structural integrity of the SET is discussed. It is concluded that this multi-scale finite element modeling method could effectively predict the elastoplastic deformation and the microscopic damage initiation and evolution of the SET. It is of great significance as a theoretical analysis tool to optimize the selection of appropriate tubular materials and it could be also used to substantially reduce costly failures of expandable tubulars in the field. This numerical analysis is not only beneficial for understanding the damage process of tubular materials but also effectively guides the engineering application of the SET technology.

Keywords:  solid expandable tubular (SET)      material microstructure damage      multi-scale elastoplastic model      virtual failure  
Received:  27 March 2020      Revised:  10 May 2020      Published:  05 October 2020
PACS:  46.50.+a (Fracture mechanics, fatigue and cracks)  
  81.40.Np (Fatigue, corrosion fatigue, embrittlement, cracking, fracture, and failure)  
  89.30.aj (Oil, petroleum)  
  91.60.Ed (Crystal structure and defects, microstructure)  
Corresponding Authors:  Corresponding author. E-mail:   
About author: 
†Corresponding author. E-mail:
* Project supported by the National Major Science & Technology Project of China (Grant No. 2016ZX05020-003).

Cite this article: 

Hui-Juan Guo(郭慧娟), Ying-Hua Liu(刘应华), Yi-Nao Su(苏义脑), Quan-Li Zhang(张全立), and Guo-Dong Zhan(詹国栋)† Multi-scale elastoplastic mechanical model and microstructure damage analysis of solid expandable tubular 2020 Chin. Phys. B 29 104602

Fig. 1.  

Mechanical expansion specimen sampling: (a) expansion diagram; (b) expansion cone.

Pre-expansion/mm Cone OD/mm Expansion ratio/% Post expansion ID/mm Actual expansion ratio/% Shorting ratio/% Wall thickness reduction ratio/% Expansion pressure/MPa
Φ 203 × 10 200 9.29 203.11 11 3.13 6.4 17.8
Φ 203 × 10 211 15.30 214.07 16.98 4.54 9.7 24
Φ 203 × 10 215.5 17.76 218.53 19.4 5.00 11.1 26.3
Table 1.  

Geometric dimensions and expansion pressures of 20G SET before and after expansion.

Fig. 2.  

Sample selection, preparation, and shooting before and after the expansion of SET.

Fig. 3.  

Metallographic structure and grain size analysis of 20G SET before expansion. (a) Internal surface metallographic structure; (b) metallographic structure of the inner surface of the cross-section; (c) metallographic structure of the external surface of the cross-section; (d) external surface metallographic structure.

Fig. 4.  

Metallographic structures and crack morphologies of the expandable tubular after expansion under different expansion ratios and cutting quantities of the internal surfaces. (a) Expansion ratio: 9.29%, cut: 0 μm and 160.0 μm. (b) Expansion ratio: 15.30%, cut: 0 μm and 106.0 μm. (c) Expansion ratio: 17.76%, cut: 0 μm and 200.0 μm

Fig. 5.  

Metallographic, backscatter, and secondary electron scanning images of post-expansion SET at the expansion ratio of 17.76%. (a) Metallography of the uncorroded cross-section; (b) metallography of the corroded cross-section; (c) cross-sectional backscatter scanning image; (d) cross-sectional secondary electron scanning image; (e) metallography of the uncorroded longitudinal section; (f) metallography of the corroded longitudinal section; (g) longitudinal-sectional backscatter scanning image; (h) longitudinal-sectional secondary electron scanning image.

Yield strength Rp0.2/MPa Tensile strength Rm/MPa Elongation A/% Reduction of area Z/% Modulus of elasticity/GPa
Pre-expansion 290–310 460–470 35–37 61.5–62.5 206–208
Post-expansion 450–470 560–570 15–17 56–58.8 209–212
Table 2.  

Mechanical properties of the pre-expansion and post-expansion 20G tubular.

Fig. 6.  

Finite element model of expansion process. (a) Axisymmetric structure model; (b) complete 3D structure model.

Fig. 7.  

Stress field variables of axisymmetric model of the SET. (a) MISES diagram; (b) principal stress vector diagram.

Fig. 8.  

Accumulated plastic strain PEEQ diagram of the two models of the SET. (a) PEEQ diagram of the axisymmetric model at intermediate time point; (b) PEEQ diagram of the 3D structure model at the intermediate time point; (c) PEEQ diagram of the axisymmetric model at the final time point; (d) PEEQ diagram of the 3D structure model at the final time point.

Fig. 9.  

Contact forces on the inner surface of the 3D structure model of the SET. (a) Diagram of contact pressure; (b) diagram of contact status.

Fig. 10.  

Comparison of the relationship curves of the reaction force (RF) and displacement of the expansion cone in the 2D axisymmetric model and 3D structure model.

Fig. 11.  

Coupling diagram of boundary conditions of the macro-micromodel for the microstructures of the SET.

Fig. 12.  

Microstructural model of the two-phase heterogeneous material of the SET.

Fig. 13.  

Microstructure material constitutive model of expansion tube: (a) grain anisotropy of two-phase heterogeneous body and (b) elastoplasticity and damage model.

Component D1111 D2222 D3333 D1122 D1133 D2233 D1212 D1313 D2323 μa λa
Ferrite 265.6 166.2 259.8 111.6 117.9 117.3 84.2 84.8 77.7 69.8 97.2
Cementite 394.0 350.0 322.0 159.0 163.0 164.0 19.0 133.0 133.0 227.0 252.0
Table 3.  

Orthotropic elastic stiffness of the two-phase heterogeneous microstructure of expandable tubulars.

Fig. 14.  

Stress and strain field distribution results of virtual failure analysis of microstructure. (a) Overall MISES diagram; (b) MISES diagram of ferrite matrix phase; (c) MISES diagram of pearlite second phase; (d) Overall PEEQ diagram.

Fig. 15.  

Comparison of virtual failure analysis results of the microstructure from the numerical calculations and test results. (a) Stiffness decline degree of virtual failure (SDEG) diagram; (b) Analysis results of metallographic test.

Fig. 16.  

Diagram of damage initial criterion and evolution. (a) Ductile damage initial criterion (DUCTCRT) diagram; (b) shear damage initial criterion (SHRCRT) diagram.

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