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Quantification and microstructural origin of the anisotropic nature of the sensitivity to brittle cleavage fracture propagation for hot-rolled pipeline steels

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Abstract

This work proposes a quantitative relationship between the resistance of hot-rolled steels to brittle cleavage fracture and typical microstructural features, such as microtexture. More specifically, two hot-rolled ferritic pipeline steels were studied using impact toughness and specific quasistatic tensile tests. In drop weight tear tests, both steels exhibited brittle out-of-plane fracture by delamination and by so-called “abnormal” slant fracture, here denoted as “brittle tilted fracture” (BTF). Their sensitivity to cleavage cracking was thoroughly determined in the fully brittle temperature range using round notched bars, according to the local approach to fracture, taking anisotropic plastic flow into account. Despite limited anisotropy in global texture and grain morphology, a strong anisotropy in critical cleavage fracture stress was evidenced for the two steels, and related through a Griffith-inspired approach to the size distribution of clusters of unfavorably oriented ferrite grains (so-called “potential cleavage facets”). It was quantitatively demonstrated that the occurrence of BTF, as well as the sensitivity to delamination by cleavage fracture, is primarily related to an intrinsically high sensitivity of the corresponding planes to cleavage crack propagation across potential cleavage facets.

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Abbreviations

BTF:

Brittle tilted fracture

RD:

Rolling direction of the steel plate

TD:

Transverse direction of the steel plate

ND:

Normal direction of the steel plate

\(\theta \)-Plane:

Plane tilted by \(40{^{\circ }}\) around RD with respect to the rolling plane, along which BTF propagates

\(\theta \)-Direction:

Normal to the \(\theta \)-plane

Anti-\(\theta \)-plane:

Plane tilted by \(40{^{\circ }}\) around TD with respect to the rolling plane

Anti-\(\theta \)-direction:

Normal to the anti-\(\theta \)-plane

PCF :

Potential cleavage facet, estimated from microtexture analyses

\(PCF_{eff\_s}^d\) :

Effective PCF size normal to the given loading direction d and relative to given steel S

\(\alpha ^{a,b}\) :

Misorientation angle between \(\langle {001}\rangle \) directions of grain a and adjacent grain b that are closest to the loading direction

\(\alpha _c\) :

Critical value of \(\alpha ^{a,b}\) used in the determination of PCFs

\(\beta ^{a,b}\) :

Misorientation angle between adjacent grains a and b

\(\beta _c\) :

Critical value of \(\beta ^{a,b}\) used in the determination of PCFs

\(\sigma _{c\_s}^d\) :

Critical cleavage fracture stress estimated from notched tensile tests along loading direction d of steel S

\(\sigma _{G\_s}^d\) :

Critical cleavage fracture stress estimated from the Griffith-inspired approach along loading direction d of steel S

a :

Exponent coefficient used for the calculation of \({\underline{\sigma }}_{\textit{eq}}\)

\({\underline{\sigma }}^{\textit{dev}}\) :

Modified deviator of the stress tensor \({\underline{\sigma }}\)

\({\underline{\sigma }}_{\textit{eq}}\) :

Equivalent stress of the stress tensor \({\underline{\sigma }}\)

\(\omega ^{i}\) :

Minimum angle between the loading direction and a \(\langle {001}\rangle \) direction of grain i

\(\omega _c\) :

Critical value of \(\omega ^{i}\) used in the determination of PCFs

\(c^{i}\) :

Coefficients of the tensor used for the calculation of \({\underline{\sigma }}^{\textit{dev}}\)

\(R_0, H,Q,b\) :

Hardening parameters of the Voce equation

\(\sigma _{a}\), \(\sigma _{b}\), \(T_{0}\) :

Parameters of the \(R_{0}\) versus temperature dependence equation

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Acknowledgements

Financial support from the French Agency for Research and Technology (ANRT) under CIFRE Grant No. 2011/1199 is gratefully acknowledged. Fruitful discussions with Dr M. Mazière (MINES ParisTech) and technical help from A. Laurent and A. Meddour (MINES ParisTech) and from Frank Rootsaert, Martin Liebeherr, Andries De Geest and Nuria Sanchez (OCAS) are gratefully acknowledged.

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Author notes

  1. F. Tankoua

    Present address: CEA Saclay, DEN/DANS/DM2S/SEMT/LISN, 91191, Gif-sur-Yvette, France

Authors and Affiliations

  1. MINES ParisTech, MAT-Centre des Matériaux, PSL Research University, UMR CNRS 7633, BP 87, 91003, Evry Cedex, France

    F. Tankoua, J. Crépin & A.-F. Gourgues-Lorenzon

  2. ArcelorMittal Global R&D Gent, Pres. J.F. Kennedylaan 3, 9060, Zelzate, Belgium

    P. Thibaux & S. Cooreman

Authors
  1. F. Tankoua
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  2. J. Crépin
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  3. P. Thibaux
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  4. S. Cooreman
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  5. A.-F. Gourgues-Lorenzon
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Correspondence to A.-F. Gourgues-Lorenzon.

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Appendix: Determination of the tilt and twist components of a cleavage crack deviation to cross a cleavage facet boundary

Appendix: Determination of the tilt and twist components of a cleavage crack deviation to cross a cleavage facet boundary

Let us consider a first facet with normal \({{\varvec{n}}}_{\mathbf{1}}\) that has been created by a cleavage crack. The local orientation of the facet boundary is b. Let us consider that the closest possible crack propagation plane in the adjacent grain has normal \({{\varvec{n}}}_{\mathbf{2}}\). In the general case, b is neither parallel (pure tilt) nor perpendicular (pure twist) to the cross-product \({{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{n}}}_{\mathbf{2}}\). The situation is illustrated in Fig. 14. The orientation of facets 1 and 2 is schematized on both sides of the facet boundary, to better illustrate the calculation procedure.

Let \({{\varvec{p}}} = {{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{b}}}\) be the direction belonging to facet 1 and perpendicular to boundary b. The tilt component is calculated in the auxiliary plane \(P_{\textit{tilt}}\), containing both p and \({{\varvec{n}}}_{\mathbf{1}}\) (its normal is direction b). It is the angle between the so-called ti direction (belonging to both \(P_{\textit{tilt}}\) and cleavage facet 2: \({{\varvec{ti}}} = {{\varvec{n}}}_{\mathbf{2}} \times {{\varvec{b}}}\)) and direction p. Mathematically, it is expressed as follows:

$$\begin{aligned} \hbox {tilt}\_\hbox {component}=\hbox {cos}^{-1}\left( {\frac{({{{\varvec{n}}}_{\mathbf{2}} \times {{\varvec{b}}}}) \cdot ({{{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{b}}}})}{|{{{\varvec{n}}}_{\mathbf{2}} \times {{\varvec{b}}}}| \cdot |{{{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{b}}}}|}} \right) \end{aligned}$$
(6)

The twist component is calculated in the auxiliary plane \(P_{\textit{twist}}\), containing both b and \({{\varvec{n}}}_{\mathbf{1}}\) (its normal is direction p). Let tw be the direction common to both plane \(P_{\textit{twist}}\) and facet 2, i.e., \({{\varvec{tw}}} = {{\varvec{p}}} \times {{\varvec{n}}}_{\mathbf{2}}\), which can be rewritten as \({{\varvec{tw}}} = ({{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{b}}}) \times {{\varvec{n}}}_{\mathbf{2}}\). The twist component is the angle between tw and direction b, mathematically expressed as:

$$\begin{aligned} \hbox {twist}\_\hbox {component}=\hbox {cos}^{-1}\left( {\frac{({( {{{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{b}}}}) \times {{\varvec{n}}}_{\mathbf{2}}}) \cdot {{\varvec{b}}}}{|{({{{\varvec{n}}}_{\mathbf{1}} \times {{\varvec{b}}}}) \times {{\varvec{n}}}_{\mathbf{2}}}| \cdot |{{\varvec{b}}}|}} \right) \nonumber \\ \end{aligned}$$
(7)

The values of tilt and twist components measured from quantitative fractography data are reported in Fig. 9 of the main text.

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Tankoua, F., Crépin, J., Thibaux, P. et al. Quantification and microstructural origin of the anisotropic nature of the sensitivity to brittle cleavage fracture propagation for hot-rolled pipeline steels. Int J Fract 212, 143–166 (2018). https://doi.org/10.1007/s10704-018-0297-4

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