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arxiv: 2605.16110 · v1 · pith:4UB3TFCDnew · submitted 2026-05-15 · ❄️ cond-mat.mtrl-sci · cs.IT· math.IT

Causation-guided mechanism identification and interpretable reduced-order modeling of damage-driving grain-boundary stress in creep

Weichen Kong , Yanwei Dai , Yinglin Zhang , Yinghua Liu This is my paper

Pith reviewed 2026-05-20 16:48 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cs.ITmath.IT
keywords stresscharacteristicsinterpretablecreepmachine-learningphysicalacrosscausation-guided
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The pith

Causation entropy analysis of mechanics-informed descriptors from dislocation-climb crystal-plasticity simulations identifies GB inclination angle, slip transmission, climb-related Schmid indicator, and elastic-modulus mismatch as the dominant factors controlling grain-boundary normal stress in crep

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

Creep is the gradual stretching of metal parts under steady high heat and load, a key failure mode in jet engines and power turbines. In polycrystalline superalloys the damage often starts at grain boundaries where local stresses concentrate. The authors simulated tiny clusters of a few grains with a crystal-plasticity model that includes dislocation climb, a mechanism that relaxes stress over time. From each simulation they extracted eighteen candidate descriptors grounded in geometry, crystal orientation, and elastic properties. They then used causation entropy, a statistical tool that estimates directed influence between variables, to rank which descriptors most strongly drive the normal stress on the boundary. Four stood out: the angle of the grain boundary itself, how easily slip can cross from one grain to the next, a climb-adjusted measure of resolved shear, and the difference in stiffness between neighboring grains. These four were combined into a compact regression equation that predicts boundary stress without rerunning the full simulation. The same equation remained useful under multiaxial loads and could be extended to three-grain setups with a simple nonlocal correction term.

Core claim

Among 18 physically motivated characteristics, the GB inclination angle, the slip transmission, the climb-related Schmid-type indicator, and the elastic-modulus mismatch are found to be dominant, revealing the coupled roles of interfacial geometry, crystallographic compatibility, creep stress relaxation, and micromechanical contrast.

Load-bearing premise

That the causation-entropy ranking performed on descriptors extracted from minimal grain-cluster simulations faithfully identifies causal mechanisms rather than correlations induced by the limited cluster size or by choices in the crystal-plasticity constitutive model.

read the original abstract

Grain-boundary (GB) local stress is central to the initiation and evolution of long-term creep damage in polycrystalline superalloys. Owing to the high-dimensional nonlinear relationships between the GB stress response and multiple crystallographic, microstructural, and micromechanical characteristics, it remains challenging to identify the key characteristics governing GB stress and to elucidate their mechanisms of influence. Dislocation-climb-affected crystal-plasticity finite-element simulations of minimal grain clusters are combined with an integrated causation-guided machine-learning framework, in which mechanics-informed descriptors are analyzed by causation entropy to identify governing mechanisms and then distilled into a reduced-order regression form for interpretable prediction of GB normal stress. Among 18 physically motivated characteristics, the GB inclination angle, the slip transmission, the climb-related Schmid-type indicator, and the elastic-modulus mismatch are found to be dominant, revealing the coupled roles of interfacial geometry, crystallographic compatibility, creep stress relaxation, and micromechanical contrast. The identified characteristics hierarchy and functional representation remain effective under multiaxial loading and can be extended to tricrystal systems through physically interpretable nonlocal augmentation when a purely local description becomes insufficient, demonstrating strong physical consistency and robust generalizability across physical conditions. The extracted candidate functions also improve surrogate-model performance across multiple machine-learning model classes, providing supporting evidence for the physical relevance and efficiency of the identified representation. The proposed methods demonstrate strong potential for the development of interpretable machine-learning models and for the study of microscale nonlocal damage.

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

3 major / 2 minor

Summary. The manuscript introduces a causation-guided framework that integrates dislocation-climb crystal-plasticity finite-element simulations of minimal grain clusters with causation entropy to rank 18 physically motivated descriptors for their influence on grain-boundary normal stress during creep. It identifies four dominant descriptors—GB inclination angle, slip transmission, climb-related Schmid-type indicator, and elastic-modulus mismatch—and distills them into an interpretable reduced-order regression model. The paper claims this hierarchy and functional form generalize across multiaxial loading conditions and can be extended to tricrystal configurations via nonlocal augmentation, while also enhancing surrogate model performance.

Significance. Should the causation-entropy ranking prove robust to variations in simulation setup, the results would offer valuable mechanistic understanding of how interfacial geometry, crystallographic compatibility, creep stress relaxation, and micromechanical contrast couple to drive GB stress concentrations. This could facilitate the development of efficient, physics-informed reduced-order models for predicting long-term creep damage in superalloys, with potential applications in materials design and component lifetime assessment.

major comments (3)
  1. [Simulation setup and descriptor extraction] The causation entropy ranking relies on data from minimal grain clusters; the manuscript does not test whether the identified dominant descriptors (GB inclination angle, slip transmission, climb-related Schmid-type indicator, elastic-modulus mismatch) maintain their ranking when cluster size is increased or when constitutive model parameters such as climb mobility are varied within plausible ranges.
  2. [Reduced-order regression] The reduced-order model is constructed from the same dataset used for the causation entropy ranking; additional details on data partitioning, cross-validation procedures, and quantitative error metrics (e.g., R² or RMSE on held-out data) are needed to rule out circularity or overfitting in the functional form and coefficients.
  3. [Generalizability section] Assertions that the identified characteristics hierarchy remains effective under multiaxial loading and extends to tricrystals are not supported by reported quantitative validation metrics or error bars, limiting the ability to assess the robustness of these claims.
minor comments (2)
  1. [Abstract] The abstract could more explicitly state the quantitative performance of the reduced-order model to strengthen the claims of generalizability.
  2. [References] Ensure all prior works on causation entropy applications in mechanics are cited to contextualize the novelty.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each of the major comments point by point below, providing clarifications and indicating the revisions made to strengthen the paper's rigor and transparency.

read point-by-point responses

  1. Referee: The causation entropy ranking relies on data from minimal grain clusters; the manuscript does not test whether the identified dominant descriptors (GB inclination angle, slip transmission, climb-related Schmid-type indicator, elastic-modulus mismatch) maintain their ranking when cluster size is increased or when constitutive model parameters such as climb mobility are varied within plausible ranges.

    Authors: Our use of minimal grain clusters is deliberate to isolate the local mechanisms at the grain boundary without interference from distant grains or complex interactions in larger aggregates. This setup enables a focused analysis of the causation entropy on the 18 descriptors. We recognize the value of testing robustness to larger cluster sizes and parameter variations such as climb mobility. However, these would require substantial additional computational resources and are proposed as directions for future research. In the revised manuscript, we have added a dedicated paragraph in the Methods and Discussion sections justifying the minimal cluster approach and discussing its limitations regarding generalizability to larger systems. revision: partial

  2. Referee: The reduced-order model is constructed from the same dataset used for the causation entropy ranking; additional details on data partitioning, cross-validation procedures, and quantitative error metrics (e.g., R² or RMSE on held-out data) are needed to rule out circularity or overfitting in the functional form and coefficients.

    Authors: We appreciate this point and have revised the manuscript to include a new subsection detailing the data partitioning (using an 80/20 train-test split), the cross-validation procedure (5-fold CV to evaluate model stability), and quantitative performance metrics on held-out data. These additions confirm that the reduced-order regression was validated independently to avoid circularity, with the causation entropy serving only for descriptor selection prior to fitting. The revisions ensure transparency and address potential concerns of overfitting. revision: yes

  3. Referee: Assertions that the identified characteristics hierarchy remains effective under multiaxial loading and extends to tricrystals are not supported by reported quantitative validation metrics or error bars, limiting the ability to assess the robustness of these claims.

    Authors: We have updated the Generalizability section to provide quantitative support for these claims. Specifically, we now include performance metrics such as mean absolute errors and correlation coefficients for the reduced-order model under different multiaxial loading conditions, along with error bars derived from ensemble simulations. For the tricrystal configurations, we report the quantitative improvement achieved by the nonlocal augmentation, including standard deviations across multiple grain orientations. These additions allow for a better assessment of the robustness and are supported by additional figures in the supplementary material. revision: yes

Circularity Check

1 steps flagged

Reduced-order regression fitted to same simulation data used for causation-entropy ranking

specific steps
  1. fitted input called prediction [Abstract]
    "mechanics-informed descriptors are analyzed by causation entropy to identify governing mechanisms and then distilled into a reduced-order regression form for interpretable prediction of GB normal stress. Among 18 physically motivated characteristics, the GB inclination angle, the slip transmission, the climb-related Schmid-type indicator, and the elastic-modulus mismatch are found to be dominant"

    Descriptors are computed directly from the same minimal-grain-cluster simulations; causation entropy ranks them on that data; the reduced-order regression is then fitted to reproduce GB stress values from the identical dataset, so the 'prediction' step is statistically forced by the input rather than derived from first principles or validated externally.

full rationale

The paper extracts 18 descriptors from dislocation-climb crystal-plasticity simulations of minimal grain clusters, applies causation entropy to rank them, and then distills a reduced-order regression for GB normal stress prediction. Because the regression coefficients and functional form are obtained from the identical dataset that supplied the ranked descriptors, the claimed 'interpretable prediction' reduces to a re-expression of relationships already present in the input data rather than an independent derivation or out-of-sample test. This matches the fitted-input-called-prediction pattern and produces partial circularity in the central claim of mechanism identification plus predictive modeling.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the fidelity of the minimal-cluster simulations and on the ability of causation entropy to isolate causal drivers; the reduced-order regression introduces fitted parameters whose values are not independently derived.

free parameters (1)
  • regression coefficients in the reduced-order model
    The distilled functional form for GB normal stress is obtained by regression on the simulation outputs after descriptor ranking.
axioms (1)
  • domain assumption Minimal grain clusters capture the essential local mechanics that govern GB stress in bulk polycrystals.
    Invoked when the authors extrapolate from small simulated clusters to general polycrystalline behavior.

pith-pipeline@v0.9.0 · 5805 in / 1490 out tokens · 153096 ms · 2026-05-20T16:48:43.333290+00:00 · methodology

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Works this paper leans on

4 extracted references · 4 canonical work pages

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    International Journal of Plasticity 61, 49 - 63

    Modelling the effect of elastic and plastic anisotropies on stresses at grain boundaries. International Journal of Plasticity 61, 49 - 63. Guo, H. - J., Ling, C., Busso, E.P., Zhong, Z., Li, D. - F., 2020. Crystal plasticity based investigation of micro - v oid evolution under multi - axial loading conditions. International Journal of Plasticity 129, 1026...

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    (Eds.), Engineering Materials 1 (Fifth Edition)

    Chapter 23 - Mechanisms of Creep, and Creep - Resistant Materials, in: Jones, D.R.H., Ashby, M.F. (Eds.), Engineering Materials 1 (Fifth Edition). Butterworth - Heinemann, pp. 381 - 394. Kong, W., Dai, Y ., Zhang, X., Liu, Y ., 2025. A dual - scale stochastic analysis framework for creep failure considering microstructural randomness. International Journa...

    work page 2025

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    International Journal of Plasticity 150

    Predicting grain boundary damage by machine learning. International Journal of Plasticity 150. Zhang, W., Wang, X., Wang, Y ., Yu, X., Gao, Y ., Feng, Z., 2020. Type IV failure in weldment of creep resistant ferritic alloys: II. Creep fracture and lifetime prediction. Journal of the Mechanics and Physics of Solids 134, 103775. Zhang, X., Oskay, C., 2016. ...

    work page 2020