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arxiv: 2606.12238 · v1 · pith:JBZ3KZOTnew · submitted 2026-06-10 · ❄️ cond-mat.mtrl-sci

Thermodynamically consistent phase field model for hydrogen-assisted cracking

G. F. Bouobda-Moladje , A. Ruffini , Y. Le Bouar , A. Finel This is my paper

Pith reviewed 2026-06-27 09:06 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords phase field modelhydrogen-assisted crackingHEDEintergranular crackingtransgranular crackingpolycrystalline materialsvariational frameworkinterfacial energy
0
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The pith

A variational phase field model couples crack propagation with hydrogen segregation to capture the transition to intergranular cracking.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a phase field model for simulating hydrogen-assisted cracking in polycrystalline materials. It uses a variational framework to describe crack propagation together with hydrogen segregation at crack surfaces and grain boundaries, which reduces the associated interfacial energies. The model reproduces the shift from transgranular to intergranular cracking when the hydrogen-enhanced decohesion mechanism is active. A sympathetic reader would care because these processes often interact in ways that require a single consistent description rather than separate treatments.

Core claim

Within a variational framework, the model simultaneously describes crack propagation and hydrogen segregation on crack surfaces and grain boundaries together with the associated reduction in interfacial energies, and demonstrates the ability to capture the transition from transgranular cracking to hydrogen-assisted intergranular cracking in the context of HEDE mechanisms.

What carries the argument

A variational energy functional that couples mechanical crack driving forces to hydrogen segregation thermodynamics at interfaces.

Load-bearing premise

The hydrogen-enhanced decohesion mechanism dominates and the chosen variational functional accurately represents the coupled thermodynamics of cracking and hydrogen segregation without extra fitting parameters.

What would settle it

An experiment on a polycrystalline sample in which the observed transition hydrogen concentration or stress level between transgranular and intergranular cracking differs from the value obtained in model simulations.

Figures

Figures reproduced from arXiv: 2606.12238 by A. Finel, A. Ruffini, G. F. Bouobda-Moladje, Y. Le Bouar.

Figure 1
Figure 1. Figure 1: ) due to a hydrogen-induced surface energy varia￾tion ∆γch involved in the energy balance during crack growth. Indeed, in the presence of hydrogen, the re￾sults obtained within the phase-field model still follow the Griffith criterion, but with an effective surface energy reduced by about 4 J·m−2 . This result is consistent with the value ∆γch = −4.29 J·m−2 obtained using equations (9) or (10). Next, the m… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) initial crack configuration in the polycrystalline [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

We propose a phase field model able to simulate hydrogen-assisted cracking in polycrystalline materials. Within a variational framework, the model simultaneously describes crack propagation and hydrogen segregation on crack surfaces and grain boundaries together with the associated reduction in interfacial energies. In the context of hydrogen-enhanced decohesion (HEDE) mechanisms, we demonstrate the ability of the model to capture the transition from transgranular cracking to hydrogen-assisted intergranular cracking.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a phase field model for hydrogen-assisted cracking in polycrystalline materials. Within a variational framework, the model simultaneously describes crack propagation and hydrogen segregation on crack surfaces and grain boundaries together with the associated reduction in interfacial energies. In the context of hydrogen-enhanced decohesion (HEDE) mechanisms, it demonstrates the ability to capture the transition from transgranular cracking to hydrogen-assisted intergranular cracking.

Significance. If the central claims hold, the work would provide a thermodynamically consistent variational phase-field approach that couples cracking evolution with hydrogen segregation and interfacial energy reduction. This simultaneous treatment of multiple physical processes in a polycrystalline setting is a strength and could enable more predictive simulations of HEDE-driven failure modes. The variational construction is explicitly credited as ensuring thermodynamic consistency without additional fitting parameters.

major comments (2)
  1. [Abstract] Abstract: the central claim that the model captures the transgranular-to-intergranular transition is stated but no equations, energy functional, evolution laws, or simulation results are provided to support it. This is load-bearing for the paper's primary demonstration.
  2. [Abstract] Abstract: the assertion of thermodynamic consistency within the variational framework cannot be verified because the explicit form of the total energy (including crack, hydrogen segregation, and interfacial terms) is not shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their review. The comments address the level of detail in the abstract. We respond point-by-point below, clarifying that the abstract is a concise summary while the supporting derivations, equations, and results appear in the main text.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the model captures the transgranular-to-intergranular transition is stated but no equations, energy functional, evolution laws, or simulation results are provided to support it. This is load-bearing for the paper's primary demonstration.

    Authors: The abstract is intended as a high-level overview of the contribution. The variational framework, energy functional, evolution laws, and simulation results that demonstrate the transgranular-to-intergranular transition under HEDE are fully detailed in Sections 2 (formulation), 3 (implementation), and 4 (results) of the manuscript, including direct comparisons of crack paths with and without hydrogen. revision: no

  2. Referee: [Abstract] Abstract: the assertion of thermodynamic consistency within the variational framework cannot be verified because the explicit form of the total energy (including crack, hydrogen segregation, and interfacial terms) is not shown.

    Authors: The total energy functional, comprising the bulk elastic energy, crack surface energy, hydrogen segregation contributions on crack faces and grain boundaries, and the resulting interfacial energy reductions, is explicitly stated as Eq. (1) in Section 2. The variational derivation establishing thermodynamic consistency (no additional fitting parameters) is given in Section 2.1. The abstract summarizes this construction without reproducing the full expressions. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided manuscript text consists solely of an abstract describing a variational phase-field model for hydrogen-assisted cracking that couples crack propagation with hydrogen segregation and interfacial energy reduction under HEDE mechanisms. No equations, derivation steps, parameter-fitting procedures, self-citations, or ansatzes are exhibited in the text. Without any load-bearing mathematical chain or explicit reduction of a claimed prediction to fitted inputs or prior self-referential results, no circularity of any enumerated kind can be identified. The central claim remains a statement of model capability that does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no free parameters, axioms, or invented entities can be extracted from the provided text.

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