Coupled thermo-chemo-mechanical phase field-based modelling of hydrogen-assisted cracking in girth welds

Abstract

A new computational framework is presented to predict the structural integrity of welds in hydrogen transmission pipelines. The framework combines: (i) a thermo-mechanical weld process model, and (ii) a coupled deformation-diffusion-fracture phase field-based model that accounts for plasticity and hydrogen trapping, considering multiple trap types, with stationary and evolving trap densities. This enables capturing, for the first time, the interplay between residual stresses, trap creation, hydrogen transport, and fracture. The computational framework is particularised and applied to the study of weld integrity in X80 pipeline steel. The focus is on girth welds, as they are more complex due to their multi-pass nature. The weld process model enables identifying the dimensions and characteristics of the three weld regions: base metal, heat-affected zone, and weld metal, and these are treated distinctively. This is followed by virtual fracture experiments, which reveal a very good agreement with laboratory studies. Then, weld pipeline integrity is assessed, estimating critical failure pressures for a wide range of scenarios. Of particular interest is to assess the structural integrity implications of welding defects present in existing natural gas pipelines under consideration for hydrogen transport: pores, lack of penetration, imperfections, lack of fusion, root contraction, and undercutting. The results obtained in hydrogen-containing environments reveal an important role of the weld microstructure and the detrimental effect of weld defects that are likely to be present in existing natural gas pipelines, as they are considered safe in gas pipeline standards.

Figures (10)

• Figure 1: Temperature dependence of relevant material properties. (a) Thermal properties: coefficient of thermal expansion ($\alpha$), thermal conductivity ($k$), and specific heat ($c$). (b) Mechanical properties: Young's modulus ($E$), initial yield strength ($\sigma_{y0}$) and density $\rho$; a tilde is used to denote the temperature-dependent parameter.
• Figure 2: Schematic representation of the boundary value problem considered: a 4-pass girth weld, with weld angle $\varphi$ and HAZ width $L_{\text{HAZ}}$, in a pipeline with inner radius $r_i$ and thickness $t_{\text{pipe}}$. The pipeline is made of X80 pipeline steel and assumed to transport hydrogen at a pressure $p_{H_2}$. A 2D axisymmetric model is employed, with a gradually refined mesh with a maximum element size of $h_{\text{max}}$, in the edges of the domain, and a minimum element size of $h_{\text{min}}$, in the weld region. The longitudinal axis of the pipeline, which corresponds to the axis of symmetry in the model, is represented with a dashed line.
• Figure 3: Welding process modelling and resulting fields. (a) Sequence of steps for the first welding pass, showing the evolution of thermal profiles and maximum principal stresses ($\sigma_I$): (Step 1) Apply Torch, (Step 2) Hold Torch, (Step 3) Pause Torch, and (Step 4) Cool-down. (b) Evolution of the temperature in a node located in the heat-affected zone (HAZ) at a distance of 3 mm from the fusion line. (c) Residual stress distribution at the end of the welding process, represented by contours of equivalent plastic strain ($\varepsilon_{p}$) and maximum principal stress ($\sigma_I$) values along the weld longitudinal direction, sampled at different relative depths of the pipe thickness: 0.1$t_{\text{pipe}}$, 0.5$t_{\text{pipe}}$, and 0.9$t_{\text{pipe}}$.
• Figure 4: Determining the hydrogen degradation law from experimental toughness versus H$_2$ pressure data from the literature Marchi2011Marchi2022Shang2021. The normalised toughness versus lattice hydrogen content data is very well approximated ($R^{2}=0.992$) with the degradation law, Eq. (\ref{['eq:DegradationLaw']}), upon the assumption of the following degradation coefficients: $\xi=0.12$, $\eta=9$, and $b=0.8$.
• Figure 5: Computational predictions of crack growth resistance (J-R) curves for the three regions of the X80 pipeline steel weld: BM, WM, and HAZ. The numerical results, obtained with a boundary layer model, show a very good agreement with the experimental data from Ref. Yang2015.