Computational study of the effect of core skin structure on the mechanical properties of carbon nanofibers

C O M P U T A T I O N & T H E O R Y

Computational study of the effect of core–skin

structure on the mechanical properties of carbon

nanofibers

Miao He1, Kaushik Joshi1, and Leonid V. Zhigilei1,*

1

Department of Materials Science and Engineering, University of Virginia, 395 McCormick Road, Charlottesville, VA 22904-4745, USA

Received:4 March 2021 Accepted:29 May 2021 Published online: 11 June 2021

Ó

ABSTRACT

The effect of the core–skin structure on the mechanical properties of carbon nanofibers is investigated in large-scale molecular dynamics simulations of tensile deformation of carbon nanofibers with the core–skin and homogeneous structures. Contrary to an established notion of the deleterious effect of the skin layer on the strength of carbon fibers, the presence of a high-quality skin layer is found to increase both the Young’s modulus and tensile strength of the nano-fiber. A detailed analysis of the fracture process indicates that the nanofiber strengthening is related to the ability of skin layer to suppress crack nucleation at the core–skin interface. The computational predictions suggest that the design of new approaches to carbon fiber manufacturing and processing leading to the generation of a high-quality skin layer while avoiding the introduction of structural defects at the core–skin interface may yield a significant enhancement of the mechanical properties of carbon fibers.

Handling Editor: Avinash Dongare.

Address correspondence toE-mail: [email protected]

https://doi.org/10.1007/s10853-021-06221-5

GRAPHICAL ABSTRACT

Introduction

Carbon fibers and their composites are well estab-lished as an important class of engineering materials featuring excellent mechanical properties, high ther-mal conductivity, low weight, and good thermo-chemical stability [1–3]. In particular, the high strength-to-weight ratio of carbon fibers makes them increasingly attractive for automotive applications [4, 5], where the rapidly growing demand for improving the vehicle fuel efficiency and satisfying the stringent emission standards cannot be addressed with traditional structural materials based on metals. The mechanical properties of carbon fibers are strongly correlated with characteristics of their microstructure, which are largely controlled by the choice of precursors and processing conditions.

A variety of cross-sectional structures and align-ments of graphitic layers observed in carbon fibers produced from different precursors and with differ-ent processing parameters includes a promindiffer-ent class of core–skin structures featuring distinct microstruc-ture of the central parts (core) and outer layers (skin) of the carbon fibers [6–11]. The skin layers usually consist of multilayer graphitic crystallites aligned along the perimeter of the core and exhibit a higher degree of graphitization and structural ordering as compared to the core regions. In addition to carbon fiber manufacturing conditions, the thickness and structure of the graphitic skin layer can be controlled by post-processing, e.g., by high-temperature

treatment [12, 13] combined with tension [14] or by applying laser processing at different power densities [11], thus suggesting an approach for modifying the mechanical properties of the core–skin carbon fibers, as well as the fiber-matrix interfaces in nanocom-posites [15,16].

appearance of microcracks, however, is not inherent to the formation of the skin layer, as the latter can be produced not only in the course of the fiber manu-facturing but also created in a controlled manner through post-processing by mechanical, thermal or chemical treatment, laser irradiation, etc.

The generation of structural defects can be drasti-cally reduced and the strength significantly increased with the decrease of the size of the carbon fibers [19] down to nanoscale, as has been demonstrated in a series of recent studies [20–23]. The superior prop-erties of carbon nanofibers (CNFs), with diameters of tens to hundreds of nanometers, have largely been attributed to the elimination of large structural defects and formation of highly uniform microstruc-ture of the nanofibers. In particular, the elimination of the core–skin composite/gradient structure of CNFs [24] has been considered to be one of the key pre-requisites for achieving the improved mechanical properties [20,21,23].

In the present paper, we test the universality of the common assumption of the detrimental effect of the skin region on the mechanical properties of CNFs by performing large-scale atomistic simulations of CNFs with and without a skin layer. The results of the simulations suggest that the presence of an idealized graphitic multilayer skin region covering a core consisting of a mixture of turbostratic, amorphous, and graphitic carbon can result in simultaneous increase in the fracture strength and Young’s modu-lus of the carbon nanofiber. The predictions of the atomistic simulations are used for design and parametrization of a continuum-level core–skin model connecting the relative sizes of the core and skin regions with the Young’s modulus of the core– skin carbon fiber.

Results and discussion

Generation of the model carbon nanofibers

The mechanical properties of CNFs with and without the graphitic skin layer are investigated in this study using large-scale molecular dynamics (MD) simula-tions. This computational technique has been suc-cessfully applied to analysis of chemical reactions leading to the formation of carbon fiber microstruc-ture from molecular precursors [25–32], oxidation of carbon fibers [33], as well as the elementary processes

involved in mechanical deformation of carbon fibers [27, 28, 34–37]. The high computational cost of MD simulations, however, prevents application of this technique for direct evaluation of the mechanical properties of fibers with heterogeneous microstruc-ture, such as the ones of core–skin carbon fibers. Therefore, we explore the effect of the skin layer on the mechanical properties of carbon fibers using an idealized model of a CNF with diameter of * 20 nm, which is comparable to but smaller than the thinnest CNFs manufactured and studied in experiments [20–24].

The model core–skin CNF system is illustrated in Fig.1, where the atoms belonging to the core and the skin are colored with different colors. The core, shown by green color in Fig. 1, is represented by a cylindrical segment with a length of 54.1 nm along the nanofiber axis, diameter of 19.5 nm, and periodic boundary conditions applied in the axial direction. The structure of the core is cut from a bulk carbon

fiber sample with dimension of

kinetic Monte Carlo and MD simulations [26,32,33], where perfect alignment of graphene sheets along the fiber axis is enforced by the combination of small sizes of the computational cells and periodic bound-ary condition applied along the fiber axis. In contrast to these studies, the structure of the core of the CNF is fully three-dimensional and features a complex interconnected arrangement of curled graphene sheets fused together with amorphous regions (see Fig.1d, e).

The skin layer wrapping around the fiber core was generated using visual molecular dynamics code [39] with an algorithm designed for construction of multi-walled carbon nanotubes. We chose the chirality of the inner, middle, and outer layers as (150,150), (155,155), and (160,160), respectively, so that the interlayer spacing, * 3.4 A˚ , is similar to that of phite. The CNF core, inner, middle, and outer gra-phene sheets contain 1,468,642, 132,000, 136,400, and 140,800 atoms, respectively, and are colored in green, blue, yellow, and red in Fig.1. The periodic bound-ary condition is applied along the CNF axis.

To evaluate the effect of the skin layer on the mechanical properties, a cylindrical CNF system of the same dimensions as the core–skin structure but with homogeneous core structure extending throughout the nanofiber cross section, i.e., without the skin layer, has been created. This system consists

of 1,758,582 atoms and has a diameter of 21.4 nm. Finally, a hollow cylindrical system that only consists of the three-monolayer-thick skin is also constructed as baseline system for parametrization of the contin-uum-level model discussed in the next section.

To obtain the fully relaxed computational systems for mechanical testing, a MD procedure of energy minimization followed by room temperature (300 K) equilibration was applied to all of the initial config-urations. The equilibrated CNF systems were also heated to 2500 K, annealed for 250 ps, and cooled back to room temperature. This annealing cycle resulted in the formation of cross-links between the fiber core and different skin layers in the core–skin sample, and the reactive interaction between unsat-urated carbon atoms present on the free surface of the initial skinless CNF. The final configuration of the core–skin CNF is shown in Fig.1, where the cross-links formed during the annealing cycle are depicted by gray bars in the enlarged view of the surface region provided in Fig.1c.

The preparation of the final microstructures was done in MD simulations performed with the reactive bond-order AIREBO-M potential [40] implemented within the LAMMPS MD suite [41]. To evaluate the mechanical properties of each structure, MD simu-lations were performed by stretching the systems along the fiber axis (x-direction) at an engineering Figure 1 Orthogonal a and cross-sectional b, d views of the

annealed and relaxed core–skin CNF, with atoms belonging to the CNF core, inner, middle, and outer skin monolayers colored green, blue, yellow, and red, respectively. Enlarged views of regions

strain rate of 4 9 108s-1. While this strain rate is substantially higher than the experimental values, the scission and rearrangement of strong carbon bonds are not affected by thermal fluctuations at 300 K, making the process of mechanical deformation and fracture insensitive to the strain rate. Indeed, an MD simulation study of the mechanical deformation of diamond, graphene, and carbon nanotubes [42] did not reveal any significant effect of the strain rate on the stress–strain curves as long as the strain rate stays below 22 9 108s-1.

The tensile testing simulations are performed with a more computationally expensive [43] ReaxFF interatomic potential [29, 44, 45], which provides a more realistic, as compared to the AIREBO-M potential, description of the bond rearrangement and scission during the irreversible (plastic) deformation and fracture (see Supplementary Information for additional discussion of problems preventing the use of AIREBO-M in the simulations of fracture of carbon nanofibers). The ReaxFF force field used in this paper is parameterized for C/H/O/N chemistry [29] and has been successfully applied to simulation of dif-ferent steps in the carbon fiber formation [28–31].

Mechanisms of deformation and fracture

of carbon nanofibers

The stress–strain curves obtained in MD simulations of tensile testing performed for the three

computational systems, i.e., the core–skin CNF, the CNF without the skin, and the three-monolayer-thick skin alone are shown in Fig.2. The strain depicted in Fig.2 is the true normal strain calculated as e¼ ln 1 þ eð eÞ, where ee is the engineering normal

strain defined as the system elongation divided by the initial length along the fiber axis. The stress shown in Fig. 2 is the true normal stress calculated based on the instantaneous cross-sectional area. For the core–skin CNF and CNF without the skin, the cross section is approximated as a circle with a radius equal to the average distance of atoms of the outer skin monolayer (for the core–skin CNF) or the out-most 32,800 atoms (for the CNF without the skin) from the nanofiber axis. For the hollow cylindrical system consisting of three graphene sheets, the cross-sectional area is calculated as S ¼ p R2

o Rð i dÞ2

h i

, where Roand Riare the average distances of atoms of

the outer and inner graphene skin monolayers from the tube axis, respectively, and d ¼RoRi

2 is the

aver-age interlayer separation.

The curves obtained for the core–skin CNF and the hollow skin structure are characterized by two elastic regimes separated by stress plateaus. The plateau is much wider for the skin structure and is barely vis-ible for the core–skin CNF. As demonstrated by the detailed analysis provided in Supplementary Infor-mation, the appearance of the plateau is related to the peculiarities of the elastic deformation of the gra-phitic skin layer predicted by the ReaxFF potential for high levels of strain. In particular, it is found that the skin layer undergoes a transition to a high-bond-length structure in the range of strain associated with the stress plateau. Similar structural changes and stress plateaus have been reported in earlier MD simulations of graphene and carbon nanotubes per-formed with the ReaxFF potential [42,46], but are not observed in simulations performed with bond order Brenner and AIREBO potentials [47,48]. The plateau appears at strain levels exceeding those accessible in experiments [21, 22], which prevents experimental verification of this behavior. The absence of experi-mental validation and the sensitivity of the appear-ance of the stress plateau to the type of interatomic potential used in the simulations leaves the possibil-ity that the plateau is an artifact resulting from the functional form and parameterization of the ReaxFF potential. The appearance of the plateau, however, has a minor effect on the prediction of the strength Figure 2 Stress–strain curves predicted in atomistic simulations

and Young’s modulus of the carbon nanofibers and does not affect any of the conclusions derived from the simulation results.

The nonlinearity of interatomic interaction poten-tial and the transition to the high-bond-length struc-ture within the stress plateau region result in a noticeable increase in stiffness of the hollow skin system as the values of strain increase past the pla-teau regime (Fig.2). This stiffening is reflected by *10% increase in the Young’s modulus fitted to the MD data in the low (0–4.4%) and high (6.3–11.8%) strain ranges, given in Table 1. The stress–strain curves for the core–skin CNF and the skinless system are also exhibiting the nonlinear behavior, even though the stress plateau is very small or absent in the curves obtained for these two systems. The elastic deformation for these systems can also be character-ized by two values of the Young’s modulus calcu-lated for the low- and high-strain stages of the deformation, and they are listed in Table 1. The nonlinear elastic deformation in these cases can be explained by the mostly reversible structural rear-rangements in the complex nanostructure of CNFs leading to the effective enhancement of the Young’s modulus at higher values of the tensile strain.

The values of the Young’s modulus of the three-monolayer-thick skin layer, 737–813 GPa, are similar to those calculated in this work with the same ReaxFF potential for a monolayer graphene sheet, 704–797 GPa. The values of the tensile strength and fracture strain of the skin layer, obtained in the tensile testing simulation performed until the three gra-phene monolayers break, are 192.6 GPa and 28.7%, respectively. These values are significantly higher than the corresponding values for the CNF systems and are out of range of Fig.2, which illustrates the stress–strain behavior of the skinless and core–shell CNF systems. The Young’s modulus and tensile

strength of the skin layer predicted by the ReaxFF force field are in a good agreement with the results of earlier MD simulations of graphene [49] and nan-otubes [50, 51] performed with classical bond-order potentials, but are below the values predicted by ab initio density functional theory methods [49, 52–54]. The Young’s modulus of the skinless CNF, 251–360 GPa, is within the range of experi-mental values reported for PAN-based carbon fibers, *200–600 GPa [19, 55], and agrees well with the highest experimental values reported for CNFs [21–23,56]. The core–skin CNF exhibits the values of the Young’s modulus intermediate between those of the hollow skin and skinless configurations. This observation is consistent with experimental results reported for larger micron-scale carbon fibers, which suggest that the formation of the core–skin structure leads to an increase in the Young’s modulus of the fiber [11,13].

In contrast to the elastic modulus, the tensile strength of the skinless CNF, * 35 GPa, is about five times higher than the highest values achieved in the experimental studies. The fracture strain of the skin-less CNF, 11.3%, is also significantly higher than that of the experimental CNF samples, which is typically below 3% [21,23, 56]. The large difference between experimental results and computational predictions can be attributed to the presence of much larger pores, microcracks, and inclusions [19,20,55] leading to the stress concentration in the experimental sam-ples. Indeed, small-angle X-ray scattering probing of real PAN-based carbon fibers [34, 57, 58] and PAN fibers prior to the carbonization [59] reveal elongated voids with length ranging from * 20 to 200 nm preferentially aligned along fiber axis. As expected, the stress concentration is observed to increase and the tensile strength to decrease with increasing misorientation of the voids with respect to the fiber

Table 1 Mechanical properties predicted in atomistic simulations of tensile deformation of three

computational systems: CNF without a skin layer, skin layer represented by a hollow cylindrical system consisting of three graphene sheets, and core–skin CNF

CNF without skin 3-monolayer skin core–skin CNF

Strength (GPa) 34.8 192.6 47.4

Fracture strain (%) 11.3 28.7 12.8

Stage I Range of strain 0–4.9% 0–4.4% 0–4.9%

Young’s modulus (GPa) _{251.1 (E}I

c) 736.8 (EIs) 307.5 (EI) Stage II Range of strain 5.4%–10.4% 6.3%–11.8% 5.4%–11.8%

Young’s modulus (GPa) 360.1 (EII

axis [58]. In the computational nanofiber, the longest void dimension does not exceed 8 nm, and the voids are well aligned along the fiber axis [27]. As a result, the stress concentration is largely eliminated and simulated nanofiber exhibits the limiting strength characteristic of homogeneous predominantly tur-bostratic structure of the nanofiber. Note that the tensile strength measured in experiments is defined by the largest void present in the macroscopic fiber subjected to tensile testing. As a result, for the same nominal structure, the strength can be expected to increase logarithmically with the length of the fiber [60].

The observation of a higher tensile strength of the core–skin CNF as compared to the structurally homogeneous skinless core structure (Fig.2 and Table 1), however, contradicts an established notion of deleterious effect of the skin layer on the strength of conventional [9, 11, 13, 17, 55] and nanoscale [20,21, 23] carbon fibers. The additional increase of the tensile strength to * 47 GPa in the core–skin system demonstrates that the formation of a high-quality skin layer may increase not only the elastic modulus but also the strength of the fiber. This observation goes against the accepted view that the carbon fiber microstructure optimization should always aim at achieving the structural uniformity and avoiding formation of core–skin or gradient microstructures [20, 55]. Note that the increase in strength is observed despite the strong radial heterogeneity in the elastic properties of the nanofi-ber, typically discussed as the main reason for the reduced fracture strength of the core–skin fibers. Indeed, a large mismatch in the elastic properties between the core and the shell is well reproduced by the model, as the Young’s modulus of the core is more than twice lower than that of the skin, see Table1.

In order to reveal the origin of strengthening of a CNF by a skin layer consisting of three perfect gra-phene sheets, we performed a detailed comparative analysis of the fracture process in the skinless and core–skin CNF systems. The formation and propa-gation of cracks leading to the fracture of the two CNF systems are illustrated by a series of snapshots of atomic configurations shown in Fig.3 for the skinless CNF and in Figs.4 and 5 for the core–skin CNF. The snapshots in Figs.3 and 4 are colored according to the local atomic axial stress. The atomic stresses are calculated using the average atomic

volume in the computational system, 11.15 A˚3, and are averaged over neighboring atoms located within a cutoff distance of 7 A˚ .

The analysis of the stress distribution in the skin-less CNF undergoing tensile deformation reveals a heterogeneous stress distribution within the nanofi-ber, with many nanoscale regions of high stress appearing in the interior and on the surface of the nanofiber. For example, the regions with local axial stress level approaching 90 GPa can be seen as red regions in Fig. 3a, which shows the snapshot of the nanofiber deformed to the strain of 11.34% and the average axial stress of 34.8 GPa. Interestingly, the regions of the high stress localization do not remain static during the deformation but continuously ‘‘mi-grate’’ as a result of local load redistribution caused by heterogeneous elastic and plastic deformation. The fracture starts at e = 11.34% from one of the high stress spots on the surface outlined by the black circle in Fig. 3a. The onset of fracture leads to the relaxation of local stress around the emerging crack, which propagates through the nanofiber cross section until the complete break of the system (Fig.3b-f).

In the core–skin CNF, the initiation of the fracture is observed at e = 12.8%, i.e., a substantially higher strain as compared to the skinless nanofiber. As can be seen from the snapshots shown in Fig.4, where only the CNF core and the inner monolayer are shown while the middle and outer skin monolayers are blanked, the fracture starts from appearance of a crack at the core–skin interface (Fig.4a), leading to the stress relaxation around the emerging crack. The crack propagates through the CNF core as deforma-tion continues, leading to the eventual separadeforma-tion of the system into two parts connected by several fila-ments, as shown in Fig. 4f. The filaments undergo thinning and completely break with further increase of the strain.

load redistribution from the outer part of the CNF core, which is reflected in the variation of the local stress across the skin monolayer clearly visible in Fig.4a–e. The load redistribution at the core–skin interface inhibits the nucleation of cracks and increases the overall strength of the nanofiber. Note that the strengthening mechanisms revealed in the present study do not rely on the idealized defect-free nature of the skin layer used in the simulations, as a more realistic skin layer composed of graphitic crystallites aligned along the perimeter of the core can be expected to partake in the local load

redistribution and to inhibit the crack nucleation on the surface of the core.

Although the fracture of the core starts at e = 12.8% and is almost complete at e = 13.03%, the middle and outer monolayers of the skin layer remain intact during this process. The middle monolayer fractures only at e = 13.33% (Fig.5a), while the outer mono-layer fractures and rapidly crumples when the strain reaches 13.6% (Fig.5d, e). The larger fracture strain of the skin layer is not surprising, given the fact that the skin layer can withstand strains up to 28.7% when loaded in the absence of the core (Fig.2and Table1). Figure 3 Snapshots of atomic

configurations of the skinless CNF shown for different values of tensile strain: e = 11.34%a, e = 11.38% b, e = 11.43%c, e = 11.48% d, e = 11.53%e, and e = 11.58% f. The local region where fracture initiates is marked by the black circle ina. Each atom is colored based on the local atomic stress averaged over neighboring atoms located within a cutoff distance of 7 A˚ .

Figure 4 Snapshots of atomic configurations of the core–skin CNF shown for different values of tensile strain: e = 12.84%a, e = 12.89%b, e = 12.94% c, e = 12.98% d, e = 13.03% e, and e = 13.08%f. The middle and outer monolayers of the skin layer

The onset of fracture of the skin in the case of core– skin CNF can be explained by the chemical interac-tion (cross-links) between the core and the skin, leading to nonhomogeneous stress distribution in the skin monolayers. Overall, the analysis of fracture

process in the skinless CNF and core–skin CNF sys-tems suggests that the presence of a skin layer sup-presses the crack nucleation and increases the total strength of the fiber.

Figure 5 Snapshots of atomic configurations of the core–skin CNF illustrating the fracture of the middlea-c and outer d-f skin monolayers. The snapshots are shown for strain values of e = 13.33% a, e = 13.38% b, e = 13.43% c, e = 13.5% d, e = 13.6% e, and e = 13.7% f. Atoms belonging to the carbon

fiber core, inner, middle, and outer skin monolayers are colored green, blue, yellow, and red, respectively. The atoms of the outer skin monolayer are blanked ina-c, while all atoms are shown in d-f.

Figure 6 a Schematic illustration of the cross section of the core– skin carbon fiber structure used in the analysis of the Young’s modulus. The core and skin regions are colored blue and red, respectively. The radii of the core and the whole fiber are denoted as r and R, respectively. b The dependence of the Young’s modulus on the radial fraction of the core region,r/R, predicted by Eq. (2) for two sets of parameters (EI

c,EIs) and (EIIc,EIIs) listed in

The processes defining the fracture strength of the core–skin CNF discussed above are rather complex and are not easily amenable for a formulation in terms of a predictive analytical model. The effective elastic modulus of a core–skin fiber, however, can be described in terms of a simple continuum-level model, similar to that considered in Ref. [9]. Within this model, a core–skin fiber is represented by mechanically uniform core and skin parts deforming independently from each other. The cross section of the core–skin system, with radii of the core and the whole fiber denoted as r and R, respectively, is shown in Fig.6a. During the deformation, the force applied to the whole cross-sectional area, S, should equal to the sum of forces applied to the cross-sectional areas of the core, Sc, and the skin, Ss, i.e., Sr ¼ Scrcþ Ssrs,

where r, rc, and rs are the average normal stresses acting on the whole system, the core, and the skin region, respectively. Using S ¼ pR2_{, S}

c¼ pr2, and

Ss¼ p R 2 r2, we can rewrite the force balance

equation as r¼ r 2 R2rcþ 1  r2 R2   r_s ð1Þ

For the elastic deformation, the normal stresses can be expressed through the Young’s moduli of the core–skin fiber, E, core region, Ec, and skin region, Es, as r = Ee, rc= Ece, and rs = Ese, where e is the axial strain common for the two components of the fiber. The Young’s modulus of the core–skin structure can then be expressed from Eq. (1) as

E ¼ r 2 R2Ecþ 1  r2 R2   Es ð2Þ

This equation can be verified against the results of MD simulations of the core–skin CNF. Using the two sets of values of Ecand Eslisted in Table1for stage I and stage II deformation of the skinless CNF and the 3-monolayer-thick idealized skin, the Young’s mod-ulus of the core–skin CNF predicted by Eq. (2) is plotted in Fig.6b as a function of the radial fraction of the core, r/R. The values of the Young’s modulus obtained in the MD simulation of the core–skin CNF are also shown in Fig.6b by open diamond and circle symbols for r/R equal to about 0.94 and 0.93 during the stages I and II of the elastic deformation, respectively. There is a very good agreement between the Young’s moduli predicted by Eq. (2) and obtained in the MD simulation for stage I

deformation, while a slightly higher value of the Young’s modulus calculated from the MD results for stage II deformation can be attributed to the load redistribution between the core and the skin at large strains, breaking the assumption of the independent deformation of the two components of the fiber used in the derivation of Eq. (2).

While the prediction of the extremely high values of Young’s modulus approaching that of multi-wal-led carbon nanotubes at vanishing r/R is the reflec-tion of idealized structure of the skin region used in the MD simulations, the general trend of the increase in the Young’s modulus with the formation and growth of a skin region with enhanced stiffness and structural ordering is consistent with experimental observations [11,13]. Since the thickness of the skin layer is usually kinetically limited by diffusional processes at the stabilization stage of fiber manufac-turing [61] and cannot be easily increased beyond a certain limit, decreasing the diameter of the fibers down to the levels comparable to the thickness of the skin layer [19–23] may lead to a significant improvement of the mechanical properties.

Conclusions

The effect of the core–skin structure on the mechan-ical properties of carbon nanofibers is investigated in large-scale MD simulations of a core–skin CNF, a CNF with homogeneous structure, and a hollow cylindrical system representing the skin layer alone. The Young’s modulus, tensile strength, and fracture strain are evaluated based on analysis of the stress– strain curves obtained in simulations of tensile test-ing of the computational samples. Based on the results of the simulations, a simple continuum-level model quantifying the effect of the core-to-skin frac-tion on the Young’s modulus is designed and verified.

enhancement of the mechanical properties, i.e., strength and ductility, can be achieved through the elimination of structural imperfections, such as pores, cracks, foreign inclusions, and surface defects.

The incorporation of an idealized skin layer into the computational sample is found to increase both the Young’s modulus and tensile strength of the core–skin CNF. Given a higher stiffness of the skin structure as compared to the core, the increase in the elastic modulus of the composite structure is expec-ted and agrees with experimental observations. The observation of the enhanced tensile strength of the core–skin system, however, contradicts an estab-lished notion of the deleterious effect of the skin layer on the strength of conventional and nanoscale carbon fibers. A detailed analysis of the fracture process in the model core–skin CNF system reveals that the skin layer participates in the local load redistribution at the core–skin interface, inhibits the crack nucleation at the interface, and increases the total strength of the fiber.

The direct mapping of the computational predic-tions to experimental core–skin carbon fibers featur-ing skin layers with a more complex patchy structure consisting of graphitic crystallites of various sizes instead of the defect-free continuous graphene layers wrapped into a cylindrical shell is not possible at the quantitative level. Nevertheless, the results of the simulations demonstrate that the formation of a high-quality skin layer or a gradient microstructure sup-pressing the crack nucleation at the core–skin inter-face may produce a simultaneous increase of stiffness and strength of the carbon fibers. The decrease in strength due to the appearance of the skin layer, commonly observed in experiments, can be attrib-uted to the generation of microcracks and other stress-raising defects at the core–skin interface in the course of the carbon fiber manufacturing involving high-temperature processing and leading to the buildup of residual stresses upon cooling. The appearance of microcracks, however, is not inherent to the formation of the skin layer, which can be cre-ated in a controlled manner through post-processing by mechanical, thermal, chemical, plasma, or laser irradiation treatment. The computational prediction of the enhanced strength of the core–skin CNFs suggests that the design of new carbon fiber manu-facturing or processing methods leading to the gen-eration of a high-quality skin layer, while avoiding the introduction of micropores and other structural

defects at the core–skin interface, may yield the new type of carbon fibers with advanced mechanical properties.

Acknowledgements

Financial support for this word was provided by the U.S. Department of Energy’s Office of Energy Effi-ciency and Renewable Energy (EERE) under the Vehicle Technologies Office Award Number DE-EE0008195. Computational support is provided by the National Science Foundation through the Extreme Science and Engineering Discovery Environment (Project MSS180008).

Declarations

Conflict of interest The authors declare no conflict of interest.

Supplementary Information: The online version contains supplementary material available at http

s://doi.org/10.1007/s10853-021-06221-5.

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