Skip to main content
Log in

Modeling of plasticity and fracture behavior of X65 steels: seam weld and seamless pipes

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

A non-associated/associated flow rule coupled with an anisotropic/isotropic quadratic yield function is presented to describe the mechanical responses of two distinct X65 pipeline steels. The first as a product of the cold-rolling forming (UOE) process also known as seam weld pipes and the second as a result of high temperature piercing process called seamless tube manufacturing. The experimental settings consist of a wide range of sample types, whose geometric characteristics represent different state of stresses and loading modes. For low to intermediate stress triaxiality levels, flat specimens are extracted at different material orientations along with notched round bar samples for high stress triaxialities. The results indicate that despite the existing differences in plasticity between materials due to anisotropy induced processes, material failure can be characterized by an isotropic weighting function based on the modified Mohr–Coulomb (MMC) criterion. The non-associated flow rule allows for inclusion of strain directional dependence in the definition of equivalent plastic strain by means of scalar anisotropy (Lankford) coefficients and thus keeping the original capabilities of the MMC model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

Download references

Acknowledgements

The work reported herein was supported by MIT Industrial Fracture Consortium—Phase III with collaboration of RWTH Aachen University and Tenaris Co. The authors are in debt with Professor Yuanli Bai and Dr. Yueqian Jia from University of Central Florida for the fruitful discussions and comments done along the execution of this work. Mr. Michal Bardadyn is also acknowledged for his support in performing tests and post-processing of measured data.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcelo Paredes.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A: Numerical procedure and FE models

A detailed 3D finite element models were developed for numerical analysis for all specimen geometries selected. Exploiting symmetry conditions of them only 1/8 of tensile specimens and 1/2 of special butterfly specimen were modeled. Orthogonal symmetric planes of FE models were constrained with zero normal displacement. A typical FE model is shown in Fig. 12 of a NRB specimen with two different radii. The model is meshed with trilinear eight cubic elements (C3D8R from Abaqus library) with reduced integration and hourglass control, being the more refined those allocate in the critical region near the center specimen with a characteristic length of \(200~\upmu \hbox {m}\). Monotonic quasi-static loading conditions are applied on each FE model similar to those conditions imposed on tests. The principal axes of anisotropy are assumed to be aligned with the material coordinates, in this case the pipe, such as: longitudinal (\(\hbox {e}_{1} - 0^{\circ }\)), hoop (\(\hbox {e}_{2} - 90^{\circ }\)) and through thickness (\(\hbox {e}_{3}\)) direction.

The constitutive model of plasticity and fracture was implemented into a VUMAT user-defined subroutine. Explicit time integration scheme with finite strain setting is employed for taking account nonlinear geometric changes and mass scaling factor to reduce computation time.

Appendix B: The state of stress characterization

The stress triaxiality (\(\eta \)) and the Lode angle (\(\bar{\theta }\)) parameters are defined in terms of the invariants of the Cauchy stress tensor \({\varvec{\sigma }}\) in the form

$$\begin{aligned} \eta =\frac{\sigma _m }{\bar{\sigma }} \end{aligned}$$
(B.1)

where, \(\sigma _m =-1/3\hbox {tr}{\varvec{\sigma }}\) is the mean stress and \(\bar{\sigma } =\sqrt{1/2{{\varvec{S}}}:{{\varvec{S}}}}\) is the von Mises equivalent stress. S stands for the deviatoric stress tensor, which is defined as

$$\begin{aligned} {{\varvec{S}}}={\varvec{\sigma }} -({\hbox {tr}\ {\varvec{\sigma }}})\mathbf{1} \end{aligned}$$
(B.2)

1 is the fourth order identity tensor. Likewise, the normalized Lode angle (simply called Lode angle) is represented as the normalized third invariant of the Cauchy stress deviator

$$\begin{aligned} \bar{\theta }=1-\frac{6\theta }{\pi } \qquad -1\le \bar{\theta }\le 1, \end{aligned}$$
(B.3)

where \(\theta \) is the actual Lode angle, which is defined as

$$\begin{aligned} \theta =\frac{1}{3}\cos ^{-1}\left( {\frac{27}{2}\frac{\det {{\varvec{S}}}}{\left[ {1/2\,{{\varvec{S}}}:{{\varvec{S}}}} \right] ^{3/2}}}\right) 0\le \theta \le \pi /3,\nonumber \\ \end{aligned}$$
(B.4)

The corresponding strain to fracture in plane stress condition is calculated by setting \(\sigma _3 =0\) and substituting into Eq. B.2 and Eq. B.4 to obtain a functional relation between the stress triaxiality and Lode angle parameter in the form

$$\begin{aligned} -\frac{27}{2}\eta \left( {\eta ^{2}-\frac{1}{3}}\right) =\sin \left( {\frac{\pi }{2}\bar{\theta }}\right) \end{aligned}$$
(B.5)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paredes, M., Lian, J., Wierzbicki, T. et al. Modeling of plasticity and fracture behavior of X65 steels: seam weld and seamless pipes. Int J Fract 213, 17–36 (2018). https://doi.org/10.1007/s10704-018-0303-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-018-0303-x

Keywords

Navigation