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Cited by 3Mechanical Behavior of CompositesPolymer composites and self-healingFiber-reinforced polymer composites

Modeling of the Healing Process of Polycaprolactone‐Interleaved Carbon Fiber–Reinforced Composites

Open access
Magyar, Balázs, Czigány, Tibor, Török, Dániel, Marton, Gergő Zsolt, Balogh, Fanni, Szebényi, Gábor·2025·Polymer Composites
DOI 10.1002/pc.30070
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Abstract

Thermoplastic interlayer provides an excellent opportunity to heal/repair inhomogeneities or damage in composites. By melting the thermoplastic interlayer, the damage can be filled, thereby increasing the service life of the composite part. In this paper, we analyzed the healing process of carbon fiber–reinforced epoxy matrix composites with a thermoplastic, structured interlayer (created by FFF 3D printing method) during ENF tests. We observed the effect of the concentration of the interlayer and the applied surface pressure on the properties of the healing process. The results show that increasing interlayer content can improve maximal healing efficiency from 96.6% ± 0.3% (25 A/A%) to 98.8% ± 0.3% (100 A/A%). While healing pressure does not affect the healing efficiency significantly, it can reduce the optimal healing time. In all cases, healing efficiency has an optimum, after which increased healing time leads to a decrease. To gain a deeper understanding of the process, we have adapted a control theory model, which helps in the selection of optimal process parameters for healing, which can be utilized for other thermoplastic interlayer‐based healing methods.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper investigates healing of carbon fiber–reinforced epoxy composites with a 3D-printed polycaprolactone interlayer after end-notched flexure damage, varying PCL surface fill and healing pressure/time. It reports that healing efficiency increases with interlayer content, pressure mainly shortens the time to optimum, and efficiency decreases after an optimum due to PCL bleeding.

Key findings

  • Maximum healing efficiency increased with interlayer concentration: 96.6% ± 0.3% for 25 A/A%, 97.4% ± 0.2% for 50 A/A%, and 98.8% ± 0.3% for 100 A/A%.
  • Healing pressure did not significantly affect healing efficiency, but higher pressure reduced the time needed to reach maximum efficiency; at 10 bar, efficiency decreased after the maximum because molten PCL left the interface, with weight loss showing 25% of the PCL melted and left the specimen.
  • Healing efficiency showed an optimum followed by a decrease with longer healing time; at 10 bar, saturation was reached in 1 h, and an initial 10–15 s period occurred before thermoplastic bleeding began.
  • A control-theory model consisting of a proportional unit in parallel with a dead-time and proportional first-order unit could determine the time for maximum achievable healing efficiency, but not the later decrease caused by thermoplastic material leaving the system.

Methods

  • CFRP laminates with [0°6] layup were manufactured by vacuum infusion; PCL interlayers were printed by fused filament fabrication onto the middle carbon fabric at 25, 50, and 100 A/A% surface filling.
  • Initial damage was created by ENF tests until a 2.5% drop after maximum load, with ten specimens tested per surface filling ratio; specimens were then healed in a hot press at 65°C (above PCL Tm = 60°C, below epoxy Tg = 80°C) at 1, 2, and 10 bar for varying times, followed by a second ENF test.
  • Healing efficiency was calculated from initial and healed Mode II interlaminar fracture toughness; the healing process was modeled with a control-theory transfer function, with parameters fitted by ordinary least squares and surfaces fitted for dead time and time constant as functions of pressure and surface fill.

Limitations

  • Stated: the model is not suitable for modeling the decrease caused by melted thermoplastic material leaving the system, and at 10 bar it can only be used up to the maximum healing efficiency. The paper also states that only damaged resin can be mended; fractured fibers cannot be healed.
  • Evident from the text: the study is limited to one epoxy/PCL/carbon-fiber system, one fixed healing temperature (65°C), and Mode II ENF damage; the data are available from the corresponding author upon reasonable request.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1002/pc.30070

Cites

35 of 35 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

2 of 13 cited sources checked · 2 supported · 0 flagged

  • Premisecitation

    PCL can be used to create a weakened bond between matrix and reinforcement.

    “We used poly(ɛ-caprolactone) PCL as a surface modifier, which can be used to create a weakened bond between the matrix and the reinforcement.”
    Quote in the paperSubstantial claim1 of 1 sources checked
  • Premisecitation

    In each study, authors observed PCL filled cracks due to thermal expansion, different from composite.

    “In each study, the authors observed that the PCL filled the cracks due to its thermal expansion, which is different from that of the composite.”
    Quote in the paperNot a substantial claim1 of 3 sources checked
    • cites [21]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [22] source
    • cites [23] source
  • Findingown data

    Increasing interlayer content improves maximal healing efficiency, from 96.6% ± 0.3% at 25 A/A% to 98.8% ± 0.3% at 100 A/A%.

    “The results show that increasing interlayer content can improve maximal healing efficiency from 96.6% ± 0.3% (25 A/A%) to 98.8% ± 0.3% (100 A/A%).”
    Quote in the paperSubstantial claim
  • Findingnone given

    With 10 bar, healing efficiency vs time curve decreases after reaching maximum.

    “With 10 bar, the healing efficiency vs. time curve decreases after reaching η max .”
    Quote in the paperNot a substantial claim
  • Findingown data

    In all cases, healing efficiency has an optimum, after which increased healing time leads to a decrease.

    “In all cases, healing efficiency has an optimum, after which increased healing time leads to a decrease.”
    Quote in the paperSubstantial claim
  • May combine two claims. 25
  • Classified as probably not a substantial claim. 8

  • May combine two claims.

    Findingown data

    25% of PCL material in the system melted and left the specimen, significantly reducing thickness of boundary layer.

    “The decreasing weight of a test specimen shows that 25% of the PCL material in the system melted and left the specimen, significantly reducing the thickness of the boundary layer.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Reference samples without PCL interlayer separated completely and crack propagation was unstable.

    “In the case of reference samples (specimens without the PCL interlayer) the laminates separated completely, and crack propagation was unstable.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingnone given

    Under vacuum infusion conditions (0.8 bar, 3 h, 90°C), PCL was only partly dissolved in EP.

    “Under these conditions, PCL was only partly dissolved in the EP.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    In samples with larger interlayer content, the speed of efficiency decrease was faster and PCL left the system sooner.

    “In the case of samples with a larger interlayer content, the speed of this decrease was faster and the PCL left the system sooner.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In 3D printed interlayered specimens, crack propagation was stable and samples retained structural integrity after reaching maximal load capacity.

    “In contrast, in the 3D printed interlayered specimens, crack propagation was stable-after reaching maximal load capacity, the samples retained their structural integrity.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    The value of τ influences the time required to reach the maximal achievable healing efficiency and depends on time and surface filling.

    “Meanwhile, the value of τ influences the time required to reach the maximal achievable healing efficiency and depends on time and surface filling.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    Increasing interlayer content speeds up the recovery process and the derivative approaches 0 faster, so the system can reach maximum recovery for a given concentration level sooner.

    “By increasing the interlayer content, the recovery process speeds up and the derivative approaches 0 faster, that is the system can reach the maximum recovery for a given concentration level sooner.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The time derivative of healing shows negative values with decrease at 10 bar.

    “This is more noticeable in the derivative of the curve, where negative values also appear with the decrease.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    At the surface pressure of 1 bar, increasing interlayer content decreases the time requirement for the transient part (decreases D) and increases the maximal achievable healing efficiency (P2).

    “At the surface pressure of 1 bar, interlayer content changes dead time and P 2 .Increasing the interlayer content decreases the time requirement for the transient part (decreases D), and also increases the maximal achievable healing efficiency (P 2 ).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The value of P2 varies with different concentrations; increasing surface filling allows approaching the theoretically achievable 100% cure better.

    “The value of P 2 , which can be explained with the maximal achievable healing efficiency, varies with different concentrations, since none of the samples reached the theoretically achievable 100% cure, but by increasing surface filling, we were able to approach 100% better.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Pressure had a greater effect on the healing rate than the surface concentration of PCL; surface fill has a smaller effect than pressure; increasing pressure accelerates healing more.

    “The pressure had a greater effect on this rate than the surface concentration of PCL.It indicates that surface fill has a smaller effect than pressure.Increasing pressure accelerates healing more.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    With increasing pressure, dead time continuously decreases, and the time constant also decreases.

    “Similarly, to the curves of increasing surface fill, with increasing pressure, dead time continuously decreases, which is also true for the time constant (Figure 13c,d).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The time constant decreases significantly as pressure increases, so maximum efficiency is achieved in less time.

    “The time constant decreases significantly as the pressure increases, that is maximum efficiency is achieved in less time (Figure 11c,d).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given

    In methods requiring external intervention, basic rule for mending temperature is above melting temperature of thermoplastic healing material.

    “In the case of methods that require external intervention, the basic rule for mending temperature is that it should be above the melting temperature of the thermoplastic healing material.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationreasoning

    With the use of a model, the behavior of a system can be investigated regardless of concentration or healing pressure.

    “With the use of a model, the behavior of a system can be investigated regardless of concentration or healing pressure.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: During the healing process, the excitation is pressure and heat and the response is interlayer material filling cracks and separations over time.

  • May combine two claims.

    Interpretationnone given

    The adapted control theory model helps in selection of optimal process parameters for healing and can be utilized for other thermoplastic interlayer-based healing methods.

    “To gain a deeper understanding of the process, we have adapted a control theory model, which helps in the selection of optimal process parameters for healing, which can be utilized for other thermoplastic interlayer-based healing methods.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: During the healing process, the excitation is pressure and heat and the response is interlayer material filling cracks and separations over time.

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    The ENF test setup was selected because it provides similar delamination propagation as observed in bent structures with internal flaws.

    “The ENF test setup was selected because it provides similar delamination propagation, as observed in bent structures with internal flaws.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    The relevant literature does not include any detailed investigation of effects of different healing parameters, or any modeling of the healing process.

    “However, these studies do not include any detailed investigation of the effects of different healing parameters, or any modeling of the healing process, which could lead to a deeper understanding of the mechanisms and key affecting factors leading to the healing of the composites.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Hayes et al. found increasing temperature of mending increased healing efficiency of impact-bent epoxy-PBA blends, also true for composites Mode I.

    “Hayes et al. [19,20] found that by increasing the temperature of mending, the healing efficiency of the impact-bent epoxy resin-PBA blends increased, which is also true for the composites they examined with the Mode I tests.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [19] source
    • cites [20] source

  • May combine two claims.

    Interpretationreasoning

    Pressure accelerates reaction speed, so with higher pressures, cracks are filled more quickly.

    “The reason for this is that during the process, the pressure accelerates reaction speed, so with higher pressures, the cracks are filled more quickly.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Higher interlayer content shortens the necessary flow path, and cracks are filled faster thanks to excess material.

    “Furthermore, concentration also affects the previous two factors in a similar way: at higher interlayer content, the necessary flow path is shorter, and the cracks are filled faster thanks to the excess material.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    After mending, Wang et al. achieved healing efficiency of 42%.

    “After mending was done, a second G Ic test was carried out, where a healing efficiency of 42% was achieved.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [26] source

  • May combine two claims.

    Interpretationreasoning

    The initial proportional response occurs because the final failure did not occur during the first ENF tests, so the composites maintained integrity and could take up loads at the start of the next cycle, giving an initial G IIc value.

    “The reason for this is that the final failure did not occur during the first ENF tests, that is, the composites still maintained their integrity, so they were able to take up loads at the start of the next cycle, thus having an initial G IIc value.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    In each case, after exceeding the optimal healing time, healing efficiency decreases, which can be explained by the bleeding of PCL thermoplastic interlayer material.

    “In each case, after exceeding the optimal healing time, healing efficiency decreases, which can be explained by the bleeding of PCL thermoplastic interlayer material.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    At a pressure of 10 bar, the model can only be used within certain limits, up to the maximum healing efficiency, because the decrease observed in measurements caused by exiting melted thermoplastic interlayer material is not included in the model.

    “However, at a pressure of 10 bar, the model can only be used within certain limits, up to the maximum healing efficiency.This is due to the fact that the decrease observed in the measurements, which is caused by the exiting melted thermoplastic interlayer material, is not included in the model.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given

    The measurement procedure is based on observing the change in critical interlaminar fracture toughness, allowing the change in the healing process and its effectiveness to be followed.

    “The measurement procedure is based on observing the change in critical interlaminar fracture toughness; thereby, the change in the healing process and its effectiveness can be followed.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The model equation can determine the time required for the maximally achievable healing efficiency, but it is not suitable for modeling the decrease caused by the thermoplastic material leaving the system.

    “With the help of the equation, the time required for the maximally achievable healing efficiency can be determined, but it is not suitable for modeling the decrease caused by the thermoplastic material leaving the system.”
    • Also stated in: § 4 | Conclusion · plain
      “With the help of the equation, the time required for the maximal achievable healing efficiency can be determined, but it is not suitable for modeling the decrease caused by the melting of the thermoplastic material.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The healing response can be divided into several parts (proportional, dead time, transient).

  • May combine two claims.

    Interpretationreasoning

    In the case of the proportional term, only concentration dependence is observed; the maximum achievable healing efficiency only depends on the PCL present in the system, while pressure can only influence the speed of the reaction.

    “In the case of the proportional term, only concentration dependence is observed.The reason for this is that the maximum achievable healing efficiency only depends on the PCL present in the system; the pressure can only influence the speed of the reaction.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Furman et al., Meure et al., and Pingkarawat et al. achieved similar results using EMAA films in various tests, but different mending parameters.

    “Furman et al. [27], Meure et al. [28], and Pingkarawat et al. [29] achieved similar results using EMAA films in various tests, but in all papers different mending parameters were used.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [27] source
    • cites [28] source
    • cites [29] source

  • May combine two claims.

    Interpretationreasoning

    The transient occurs because the equilibrium state needs time after the end of the dead time; the stable state does not occur immediately.

    “This is because the equilibrium state needs time after the end of the dead time, that is, the stable state does not occur immediately.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    At t=0, a proportional unit (P1) immediately appears in the response to the jump excitation, followed by a dead time (D), after which the transient part appears (proportional first order unit with P2 and τ).

    “At t = 0, a proportional unit (P 1 ) immediately appears in the response to the jump excitation, which is followed by a dead time (D), after which the transient part appears, that is the proportional first order unit (with proportionality factor P 2 and time constant τ).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The healing response can be divided into several parts (proportional, dead time, transient).
31 of 31

  • The paper relies on this without support.

    CFRP systems tend to fail catastrophically without any sign before final failure.

    “Composite systems, which consist of carbon fiber (CF) and epoxy resin (EP) tend to fail catastrophically, without any sign before the final failure happens.”

  • The paper relies on this without support.

    PCL is soluble in the epoxy matrix and therefore does not create a new phase.

    “We chose PCL because it is soluble in the matrix, thus it does not create a new phase and it is easier to process than other thermoplastic additives.”

  • The authors state this as an assumption.

    During the healing process, the excitation is pressure and heat and the response is interlayer material filling cracks and separations over time.

    “During the healing process, the excitation is pressure and heat.The response to this is that the interlayer material fills the cracks and separations over time.”

  • The paper relies on this without support.

    Only damaged resin can be mended; fractured fibers cannot be healed.

    “It is important to note that with both autonomous and assisted methods, only the damaged resin can be mended; fractured fibers cannot be healed.”

  • The authors state this as an assumption.

    The healing response can be divided into several parts (proportional, dead time, transient).

    “The response can be divided into several parts.”
5 of 5

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Printed interlayer dimensions are assigned to the wrong table

    Minor

    The stated line widths and spacings appear in Table 2, not Table 1, which lists 3D-printing parameters.

  • Dead-time discussion cites an unrelated figure

    Minor

    The cited Figure 8 is captioned as showing exposed PCL at specimen edges, not dead time; its caption also identifies no panel b.

2 of 2

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
Magyar, B., Czigány, T., Török, D., Marton, G. Z., Balogh, F., & Szebényi, G.
Affiliations
Budapest University of Technology and Economics (HU)
Corresponding author
Szebényi, Gábor
ORCID
Venue
Polymer Composites
Publisher
Wiley
Published
2025-05-28
Volume
46
Issue
15
Pages
14422-14432
ISSN
  • 0272-8397 (ISSN-L)
  • 1548-0569
DOI
10.1002/pc.30070
OpenAlex
W4410832283
Semantic Scholar
7fd6868a61f1ea7e819360190989c755b265d4eb
Cited by
3
References
34
Citations by year
2026: 3
FWCI
1.01
Type
journal article
Language
en
Open access
Licence
Locations
  • Polymer Composites (publishedVersion, cc-by-nc-nd)
  • Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (submittedVersion)
Funders
  • Magyar Tudományos Akadémia
  • Nemzeti Kutatási Fejlesztési és Innovációs Hivatal (KDP‐2023)
Topics
  • Physical Sciences › Engineering › Mechanics of Materials › Mechanical Behavior of Composites
  • Physical Sciences › Materials Science › Polymers and Plastics › Polymer composites and self-healing
  • Physical Sciences › Engineering › Mechanical Engineering › Fiber-reinforced polymer composites
Keywords
self-healing composites, carbon/epoxy composites, polycaprolactone, healing efficiency, healing time, process parameter optimization

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