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arxiv: 1907.10135 · v1 · pith:NBEBZSYGnew · submitted 2019-07-23 · ⚛️ physics.app-ph

A Study on the Multi-axial Fatigue Failure Behavior of Notched Composite Laminates

Yao Qiao , Antonio Alessandro Deleo , Marco Salviato This is my paper

Pith reviewed 2026-05-24 16:58 UTC · model grok-4.3

classification ⚛️ physics.app-ph
keywords composite laminatesmulti-axial fatiguenotched compositesdamage mechanismsstiffness degradationS-N curvesmicro-computed tomographyquasi-isotropic and cross-ply
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0 comments X

The pith

Damage progression under multi-axial fatigue in notched composites differs substantially from the quasi-static case.

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

The paper tests notched quasi-isotropic and cross-ply composite laminates under combined tension-shear loading applied either once or repeatedly. Measurements of S-N curves and stiffness loss, together with micro-CT images of internal damage, show that the sequence and location of matrix cracks, delaminations, and fiber breaks change when the same peak loads are applied cyclically rather than statically. A reader would care because real structures experience both loading types, yet most fatigue models assume damage paths remain the same. The data also map how notch shape and the ratio of normal to shear stress alter the observed differences. The authors conclude that efficient fatigue models must therefore track the transition in damage behavior as a function of load type, local multi-axiality, size, geometry, and stacking sequence.

Core claim

Investigation of the S-N curves and stiffness degradation, and the analysis of the damage mechanisms via micro-computed tomography clarified the effects of the multi-axiality ratio and the notch configuration. Furthermore, it allowed to conclude that damage progression under fatigue loading can be substantially different compared to the quasi-static case. Future efforts in the formulation of efficient fatigue models will need to account for the transition in damaging behavior in the context of the type of applied load, the evolution of the local multi-axiality ratio, the structure size and geometry, and stacking sequence.

What carries the argument

Micro-computed tomography imaging of damage mechanisms combined with S-N curves and stiffness degradation, evaluated across multi-axiality ratios and notch configurations in two laminate layups.

If this is right

  • Fatigue models must incorporate a transition in damaging behavior when the load changes from quasi-static to cyclic.
  • The evolution of the local multi-axiality ratio during loading affects which damage mechanisms dominate.
  • Structure size, geometry, and stacking sequence must be treated as variables that can shift the fatigue damage path.
  • The reported S-N data and CT images supply calibration and validation targets for such models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Design allowables for notched regions may need separate static and fatigue values rather than a single knockdown factor.
  • Size-effect studies performed only under static loading may not predict fatigue notch sensitivity correctly.
  • Extending the same CT-based comparison to other fiber architectures could test whether the transition is universal.

Load-bearing premise

The tested laminate layups, notch geometries, and specific multi-axial loading ratios are representative enough that the observed difference in damage progression generalizes beyond these particular specimens and test conditions.

What would settle it

Observation of identical damage sequences and locations in additional layups or loading ratios when the same peak multi-axial stresses are applied statically versus cyclically would falsify the claim of substantial difference.

Figures

Figures reproduced from arXiv: 1907.10135 by Antonio Alessandro Deleo, Marco Salviato, Yao Qiao.

Figure 1
Figure 1. Figure 1: (a) Test setup and Arcan rig used for the multi-axial tests. Geometry of notched specimens used [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Normalized S-N curves for unnotched quasi-isotropic and cross-ply specimens under tensile [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Nominal normal stress vs. nominal normal strain obtained from the multi-axial quasi-static tests [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Nominal shear stress vs. nominal shear strain obtained from the multi-axial quasi-static tests on [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Nominal normal stress vs. nominal normal strain obtained from the multi-axial quasi-static tests [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Nominal shear stress vs. nominal shear strain obtained from the multi-axial quasi-static tests on [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Failure envelopes of notched [0/90]2s and [+45/90/ − 45/0]s specimens under multi-axial quasi￾static loading conditions. Note that the nominal normal and shear strength are defined as Pmaxcosθ/[(w−a)t] and Pmaxsinθ/[(w − a)t] and the multiaxiality ratio is defined as λ = arctan(τN /σN ). 0 4 8 12 16 20 1 10 100 1000 10000 100000 0 5 10 15 20 1 10 100 1000 10000 100000 0 5 10 15 20 25 30 1 10 100 1000 10000… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of structural stiffness vs. number of cycles measured during the multi-axial fatigue tests [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of structural stiffness vs. number of cycles measured during the multi-axial fatigue tests [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of structural stiffness vs. number of cycles measured during the multi-axial fatigue [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Evolution of structural stiffness vs. number of cycles measured during the multi-axial fatigue [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The percentage of stiffness degradation right before catastrophic failure vs. multiaxiality ratio [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Analysis of main fatigue damage mechanisms before final failure by micro-computed tomography. [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The evolution of the total crack volume and delamination area for the [0 [PITH_FULL_IMAGE:figures/full_fig_p027_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Analysis of main fatigue damage mechanisms before final failure by micro-computed tomography. [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The evolution of the total crack volume for notched [+45/90/ [PITH_FULL_IMAGE:figures/full_fig_p028_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: S-N curves vs. multiaxiality ratio measured from the multi-axial fatigue tests on notched quasi [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Number of cycles to failure vs. multiaxiality ratio for notched quasi-isotropic and cross-ply [PITH_FULL_IMAGE:figures/full_fig_p030_18.png] view at source ↗
read the original abstract

Composite structures must endure a great variety of multi-axial stress states during their lifespan while guaranteeing their structural integrity and functional performance. Understanding the fatigue behavior of these materials, especially in the presence of notches that are ubiquitous in structural design, lies at the hearth of this study which presents a comprehensive investigation of the fracturing behavior of notched quasi-isotropic [+45/90/$-$45/0]$_{s}$ and cross-ply [0/90]$_{2s}$ laminates under multi-axial quasi-static and fatigue loading. The investigation of the S-N curves and stiffness degradation, and the analysis of the damage mechanisms via micro-computed tomography clarified the effects of the multi-axiality ratio and the notch configuration. Furthermore, it allowed to conclude that damage progression under fatigue loading can be substantially different compared to the quasi-static case. Future efforts in the formulation of efficient fatigue models will need to account for the transition in damaging behavior in the context of the type of applied load, the evolution of the local multi-axiality ratio, the structure size and geometry, and stacking sequence. By providing important data for model calibration and validation, this study represents a first step towards this important goal.

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

0 major / 3 minor

Summary. The paper presents an experimental investigation into the multi-axial fatigue failure behavior of notched composite laminates, specifically quasi-isotropic [+45/90/-45/0]s and cross-ply [0/90]2s layups. It employs S-N curves, stiffness degradation monitoring, and micro-computed tomography to compare damage under quasi-static versus fatigue loading, concluding that damage progression can be substantially different in the fatigue case and providing data for future model calibration.

Significance. If the observations hold, the work supplies useful experimental data on how multi-axiality ratio, notch configuration, and load type affect damage mechanisms in notched composites. The micro-CT analysis strengthens the mechanistic insights, and the modest existential claim is directly tied to the reported contrasts. This supports the need for fatigue models to incorporate load-type transitions.

minor comments (3)
  1. [Abstract] Abstract: 'lies at the hearth of this study' is a typographical error and should read 'heart'.
  2. [Methods/Results] The manuscript would benefit from explicit statements of sample sizes, number of replicates per condition, and any statistical measures used to support the S-N curve and stiffness degradation trends.
  3. [Figures] Figure captions and axis labels should be checked for consistency with the multi-axiality ratios and notch geometries described in the text.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The referee's summary accurately captures the experimental focus on multi-axial fatigue versus quasi-static damage in the two laminate types, the use of S-N curves, stiffness monitoring, and micro-CT, as well as the implications for future modeling.

Circularity Check

0 steps flagged

Purely observational experimental study; no derivations or models present

full rationale

The paper reports experimental S-N curves, stiffness degradation measurements, and micro-CT damage observations for two specific laminate layups under multi-axial quasi-static and fatigue loading. No equations, fitted parameters, predictive models, or derivation chains appear in the abstract or described content. Conclusions are limited to direct observational contrasts (damage progression 'can be substantially different'), with no reduction of any claim to its own inputs by construction, self-citation, or renaming. This matches the default expectation of no circularity for non-modeling experimental work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

No mathematical model, free parameters, or new entities are introduced; the work rests on standard domain assumptions of composite materials testing.

axioms (1)
  • domain assumption Standard assumptions in composite laminate testing including uniform ply properties, accurate multi-axial load application, and micro-CT resolution sufficient to capture dominant damage modes.
    Implicit in the experimental description and conclusions drawn from S-N curves and micro-CT analysis.

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