Contribution of the microtexture evolution induced by plastic deformation on the resistance of a hot-rolled pipeline steel to flat cleavage fracture and to brittle delamination cracking

Abstract

This work focuses on the effects of plastic deformation on the anisotropy in resistance to cleavage cracking, with an application to the brittle delamination phenomenon observed in the ductile-to-brittle transition (DBT) of many pipeline steels. The microtexture of an as-received (AR) hot-rolled pipeline steel was first modified by cold-rolling (PS) and by a quenching + tempering treatment (QT). The resistance to cleavage fracture of the AR and modified materials was evaluated using the local approach to fracture. Cold-rolling strongly decreased the resistance to cleavage along the rolling plane, whereas the QT treatment decreased the anisotropy in critical cleavage fracture stress. Using a Griffith-inspired phenomenological approach, these evolutions were quantitatively related to the evolutions of microtexture. Using this approach, the resistance to delamination was correlated with the resistance to cleavage fracture along the rolling plane for the AR and PS materials. Detailed mechanical and microstructural analyses showed that plastic deformation experienced during the fracture test influenced both the anisotropy in cleavage fracture resistance and the delamination phenomenon in the DBT range. This work also shows that the critical cleavage fracture stress is not intrinsic to a given material; it may evolve with changes in microtexture and development of internal stresses during plastic deformation. The anisotropy of the warm prestress effect is also discussed.

Appendix: Description of constitutive models and calibration of model parameters

In any of these models, M, $\underline{\sigma }$ being the stress tensor and p being the equivalent plastic strain, the yield function was defined as:

$${f}^{M}\left(\underline{\sigma} , p\right)= {\sigma }_{eq}^{M}-R(p)$$

(3)

The equivalent stress, ${\sigma }_{eq}^{M}$, was expressed as follows:

$${\sigma}_{eq}^{M}=\frac{1}{2}{\left({\left|{\sigma}_{1}^{M}-{\sigma}_{2}^{M}\right|}^{a}+{\left|{\sigma}_{2}^{M}-{\sigma}_{3}^{M}\right|}^{a}+{\left|{\sigma}_{3}^{M}-{\sigma}_{1}^{M}\right|}^{a}\right)}^{1/a}\,\text{For}\,\text{the}\,\text{Hosford}\,\text{and}\,\text{Barlat}\,\text{yield}\,\text{criteria}$$

(4)

$${\sigma }_{eq}^{Hill}={\left(\frac{3}{2}\underline{{\sigma }_{dev}^{M}}:\underline{\underline{H}}:\underline{{\sigma }_{dev}^{M}}\right)}^{1/2}\,\text{For}\,\text{the}\,\text{Hill}\,\text{yield}\,\text{critirion}$$

(5)

In Eqs. (4) and (5), ${\sigma }_{1}^{M}\ge{\sigma}_{2}^{M}\ge{\sigma }_{3}^{M}$ are the eigenvalues of the generalized deviatoric part, $\underline{{\sigma }_{dev}^{M}}$, of $\underline{\sigma }$. $\underline{\underline{H}}$ is the fourth-order Hill tensor that was expressed as a 6 × 6 matrix using Voigt notation, with diagonal coefficients h₁ – h₆, non-diagonal coefficients being set to 0.

$\underline{{\sigma }_{dev}^{M}}$ was expressed as a linear function of $\underline{\sigma }$, as follows:

$$\underline{{\sigma }_{dev}^{M}}=\underline{\underline{S}}:\underline{\sigma }\,\text{with}\,\text{fourth-order}\,\text{tensor}\,\underline{\underline{S}}=\left(\begin{array}{cccccc}\frac{{c}_{2+}{c}_{3}}{3}& -\frac{{c}_{3}}{3}& -\frac{{c}_{2}}{3}& 0& 0& 0\\ -\frac{{c}_{3}}{3}& \frac{{c}_{3+}{c}_{1}}{3}& -\frac{{c}_{1}}{3}& 0& 0& 0\\ -\frac{{c}_{2}}{3}& -\frac{{c}_{1}}{3}& \frac{{c}_{1+}{c}_{2}}{3}& 0& 0& 0\\ 0& 0& 0& {c}_{4}& 0& 0\\ 0& 0& 0& 0& {c}_{5}& 0\\ 0& 0& 0& 0& 0& {c}_{6}\end{array}\right)\,\left(\text{in}\,\text{Voigt}\,\text{notation}\right)$$

(6)

The plastic strain tensor was determined using the normality rule applied to the yield function. The isotropic hardening contribution to the flow stress, R(p), was described using an initial yield strength parameter, R₀, a linear hardening contribution (involving a scalar parameter, H) and an exponential Voce-type term (involving two scalar parameters, Q and b):

$$ R(p) = R_{0} + Hp + Q\left( {1 - \exp \left( { - bp} \right)} \right) $$

(7)

In the Hill and Hosford-based models, material parameters c_i,i=1–6 were set to 1, leading to the usual definition of the stress deviator as used in the von Mises yield criterion. As a result, in addition to the fixed elastic stiffness parameters, respectively five, ten and eleven material constitutive parameters had to be determined for the models based on the Hosford, Hill, and Barlat yield criteria, respectively. The parameter identification procedure used in (Tankoua et al. 2018), using all available tensile tests on smooth and notched specimens, was also used to identify constitutive parameters of PS and QT materials. Details about numerical finite element calculation procedures are also reported in (Tankoua et al. 2018). Namely, for the PS material, data from uniaxial tensile tests along RD, TD, and ND and from the NT2 specimen along ND were used. For the QT material, data from the uniaxial test along ND and from the tests on NT2 specimens along RD, TD, and ND were used.

Optimised sets of parameters identified for all three materials are reported in Table 4. Model prediction are compared with experimental curves in the main body of this paper.

Table 4 Constitutive model parameters identified at − 60 °C for Steel PS and − 196 °C for Steel AR and Steel QT