Version 1.0 · Technical note · Self-published · Not peer reviewed (internal review only; see Use of AI tools)

How strong is 3D printed continuous carbon fiber? Bead geometry, same-scale sections and a layered finite element estimate

Nick Sonnentag

Sunnyday Technologies, Wisconsin, USA · ORCID 0009-0002-1897-384X · research@sunn3d.com

1. Introduction

Many polymer parts meet most requirements but fall short on stiffness or strength at one location. A single carbon fiber strand placed along the load path may supply that increment.

This requires the design to place fiber strand by strand along the load path. Each strand is a towpreg: a bundle (tow) of carbon filaments pre-impregnated with a resin that FibreSeek describes as thermoset [1], without giving its chemistry or cure state. Standard-modulus carbon fiber is linear-elastic to failure at about 1.5 to 2% strain, with no yielding [2]. It should be placed only where the load requires it.

The FibreSeeker 3, announced in September 2025 [3], allows this to be tested outside an industrial laboratory. The FibreSeeker 3 (FibreSeek) Kickstarter campaign closed on 1 January 2026 with US$4,698,825 pledged by 1,539 backers against a US$50,000 goal [4], [5]. It was offered to Kickstarter backers at US$2,699 to US$2,999 [3], [5] (vendor list price US$3,499 [6]; about US$5,000 through US resellers as of August 2026 [5]). FibreSeek gives a tensile strength of up to 900 MPa (about 130 ksi, our conversion) [6], [7] without fiber orientation, layup or test method. Comparable published values for printed continuous carbon, such as 905 MPa for Markforged 0° laminates [8], are measured in the fiber direction on unidirectional coupons. Reviewer results summarized in [5] varied by load type; these are not controlled tests.

This note answers four questions. (1) What fraction of a printed bead is carbon? (2) How does the bead compare, at the same scale, with published sections from other continuous-fiber platforms? (3) Where must fiber be placed to raise stiffness and load to first damage in bending? (4) How do published coupon values compare with what a bead laid at nozzle-diameter spacing can reach? Fiber cost, print time and part performance all depend on where, and how much, fiber is laid.

2. Process background

In co-extrusion, the strand passes through a heated composite nozzle together with metered thermoplastic and is pressed onto the previous layer as one bead. Anisoprint [9] and the FibreSeeker 3 [6] co-extrude the strand with thermoplastic. Markforged prints a pre-impregnated fiber filament without added polymer [10]. The FibreSeeker 3 cuts the strand with a built-in cutter [6], so each fiber run has a minimum length set by the cutter-to-tip distance, and the strand cannot follow corners tighter than its minimum bend radius; FibreSeek publishes neither value. On these desktop platforms fiber is laid only in planar layers. In the model of Section 3.3, walls, infill and skins are unreinforced.

For the FibreSeeker 3 this note takes a 0.0094 in (0.24 mm) strand and a 0.028 in (0.70 mm) composite nozzle. The nozzle diameter is published [6]. The strand diameter was measured by the author with a digital caliper at several locations along the X-CCF strand supplied with the FibreSeeker 3 he received as a Kickstarter backer; the readings were consistent at 0.24 mm. This note assumes fiber layers 0.24 mm tall, equal to two 0.0047 in (0.12 mm) polymer layers, and fiber paths 0.70 mm apart, equal to the nozzle diameter. Both are the author's process settings, not published FibreSeeker 3 settings. A 0.24 mm layer gives no compaction of a 0.24 mm strand; bonding and void content at zero compaction are unverified, and any layer-height or overfill error will flatten the strand. The model allows path spacings from 0.35 to 0.70 mm. At 0.35 mm the polymer flow must drop to about a third of the default, leaving about 0.11 mm of polymer between strands. At 0.35 mm the 0.70 mm nozzle face also overlaps the previous strand by half its width, with a risk of dragging or displacing it. Neither spacing below the 0.70 mm nozzle diameter nor zero-compaction 0.24 mm layers has been shown to print on the FibreSeeker 3.

3. Methods

3.1 Bead composition

The strand area and bead area follow from the dimensions above, with the bead idealized as a rectangle of width w and height h:

A_s = π d²/4 = 0.0452 mm²,   A_b = w h = 0.70 × 0.24 = 0.168 mm²,   φ_s = A_s/A_b = 0.269 (1)

FibreSeek's store page lists the X-CCF strand as 1K with approximately 60% fiber by volume, without a method [7]. The default carbon volume fraction within the strand, V_s, takes that value; the model allows 30 to 85%. The listing and the measured diameter do not agree: 1,000 filaments of 7 µm [2] in a 0.24 mm strand would be 85% carbon. At 60%, 1,000 filaments imply filaments of about 5.9 µm, or, at 7 µm, a strand of about 0.29 mm. Either the filament size or the listing differs from the supplied strand, and a caliper may understate the diameter of a compressible strand. The upper bound, 85%, approaches the hexagonal packing limit (90.7%) and exceeds the roughly 70% that impregnated tows achieve in practice [2], so it is a geometric bound only. A 1,000-filament tow of 8.6 µm filaments, as measured in Markforged strand [11], would not fit in 0.24 mm. With fiber paths a distance s apart in a layer of height h, the carbon volume fraction of the fiber layer is

V_c = A_s V_s / (s h) (2)

At the default s = 0.70 mm and V_s = 60%, V_c = 16%. A bead with semicircular ends (stadium, 0.156 mm²) gives φ_s = 0.291. Fig. 1 shows the bead drawn to scale, with 7 µm filaments placed on a randomly jittered hexagonal lattice at V_s.

3.2 Same-scale comparison with published sections

Polished sections of Markforged material [10] and a co-extruded Anisoprint strand [9], both published under CC BY 4.0, were cropped and rescaled to a common scale. Scales were set from scale bars measured in pixels: 40 µm = 29 px (ref. [10], Fig. 4a); 50 µm = 17.5 px (ref. [10], Fig. 6b, consistent with its 125 µm layer spacing; ±0.5 px is ±3% in scale); 1,000 µm = 1,275 px (ref. [9], Fig. 9). Modeled sections were drawn at the same scale.

3.3 Finite element model

A bar 4 in (101.6 mm) between supports, 1/2 in (12.7 mm) wide and about 1/4 in (6.24 mm, 52 layers of 0.12 mm) thick was loaded in three-point bending with 30 lbf (133 N) spread over 5 mm at midspan. The span-to-depth ratio, 16.3, matches ASTM D790. The supports are point constraints at the bar-end nodes, with no overhang. The model is linear-elastic, two-dimensional plane stress, with 120 × 52 four-node bilinear elements (2 × 2 Gauss integration) and layers perfectly bonded. Polymer and PPA-CF elements are isotropic (Poisson's ratio 0.35). Fiber-layer elements are orthotropic: the axial modulus follows Section 3.4, and the transverse modulus (1.1 E_m), shear modulus (E_m/2.6) and Poisson's ratio (0.3) are assumed.

Each face carries two 0.12 mm polymer skin layers, then three 0.24 mm fiber layers separated by 0.12 mm polymer layers, so fiber lies 0.24 to 1.20 mm from each face. Fiber paths fill 10.5 mm of the width, with unreinforced walls about 1.1 mm wide at both edges; at the default 0.70 mm spacing that is 15 straight runs along the full bar per layer, each cut individually. Cut runs were chosen because turns of 0.35 mm radius at 0.70 mm pitch are unlikely to print; the start and end of each run fall at the bar ends. Each fiber layer is homogenized at its carbon volume fraction V_c (Eq. 2). Four bars were solved: no fiber; three fiber layers near each face; three fiber layers near the tension face only; and a solid bar of chopped-carbon PPA-CF with no continuous fiber (Section 3.5).

Damage is assessed per element as the axial stress σ_x divided by an estimated first-damage stress, in tension or compression; other stress components are not checked. In fiber layers the bead stress, σ_x E_b/E_x, is used; it is about 19% above the width average because the walls share the layer. Polymer first damage is checked against yield stress in tension and compression strength in compression; tabulated yield strains are measured values used only for display. In the graphical abstract's strain mode the polymer is therefore closer to first damage than the colors show; the legend tick marks the polymer's tabulated yield strain. Fiber layers are brittle, so yield and ultimate coincide, and their failure strain is lower in compression than in tension. The fiber-layer stress shown there is the width average including the walls. Elements are checked only 6 to 15 mm from midspan, outside the loading-nose contact zone. Because the bending moment varies linearly along the span, each checked element is scaled to the peak midspan moment, by a factor of 1.1 to 1.4. The load to first damage is the load at which the first element reaches 1.0. For the plain PLA bar this is 38 lbf. Local crushing or kinking under the loading nose is not captured.

Verification. Refining the mesh from 60 × 52 to 240 × 104 elements changes stiffness ratios by up to 1.6% and load ratios by up to 2.1%; the plain-bar deflection converges to 0.196 in, against 0.197 in from Euler-Bernoulli theory with Timoshenko shear correction. Moving the check region anywhere between 4 and 25 mm from midspan changes load ratios by less than 1%. A transformed-section beam calculation with shear correction gives stiffness ratios of 4.62 (fiber near both faces), 1.92 (tension face only) and 5.07 (PPA-CF), against the FEA's 4.6, 1.9 and 5.1. A hand calculation gives 37.2 lbf to first damage for the plain PLA bar, against the FEA's 38 lbf, and beam theory gives the PPA-CF load ratio as 168/51 = 3.29, against 3.3. The studies run from code/convergence.js and code/reproduce.js in the repository (Data and code availability). They verify one solver against theory; they do not validate the model against tests.

3.4 Fiber-layer calibration

Each fiber layer's properties are set per unit carbon volume fraction V_c by a rule of mixtures with assumed efficiencies, chosen against peer-reviewed 0° coupon data. With E_m the matrix modulus and c the compression-to-tension strength ratio:

E = 161 GPa · V_c + E_m (1 − V_c),   σ_t = 2,100 MPa · V_c,   σ_c = c σ_t (3)

The coefficients are bracketed by three studies. Iragi et al. [8] tested Markforged [0]₁₆ laminates at 31.4% fiber by volume measured by acid digestion (ASTM D3171): 69.4 GPa and 905 MPa in tension (ASTM D3039) and 426 MPa in compression (ASTM D3410), a compression-to-tension ratio of 0.47. Smojver et al. [12] tested Anisoprint continuous carbon in PA, five specimens, at a fiber fraction of 0.25 measured by computed tomography: 37.8 ± 1.5 GPa and 236 ± 20 MPa in tension; the same group reports 37.84 GPa for that system [13]. Adumitroaie et al. [14] report 60 GPa, 750 MPa and 290 MPa in compression for Anisoprint continuous carbon in PLA at a fiber fraction of 25 to 27%; four of the six authors are affiliated with Anisoprint and no scatter is given, so it is treated as an upper bound. The modulus coefficient, 161 GPa, is 70% of a 230 GPa standard-modulus fiber [2]; the strength coefficient, 2,100 MPa, is 60% of a 3,500 MPa fiber. Eq. (3) is set below the Markforged (Iragi et al.) and Anisoprint (Adumitroaie et al.) data and above Smojver et al., on the upper side of the published strength range; no regression was fitted. At each study's fiber fraction (matrix modulus 1.0 to 3.5 GPa) it lies 24 to 26% below Iragi et al. in modulus and 27% below in tensile strength; 23 to 32% below Adumitroaie et al. in modulus and 24 to 30% below in strength (fiber fraction 25 to 27%); and 8 to 14% above Smojver et al. in modulus, at 2.2 times their tensile strength. Smojver et al. tested thermoset towpreg, the closer analogue to X-CCF. At their strength per unit carbon (236 MPa / 0.25 = 944 MPa · V_c), the load to first damage at otherwise default inputs is 0.9× with fiber on the tension face and 0.3×, 0.4× or 0.6× with fiber near both faces (compression 24%, 33% or 47%); stiffness is unchanged (Section 4.4). The implied tensile failure strain, 2,100/161 = 1.30%, is close to the 1.27% measured by Iragi et al. Because the coefficients rest on mean coupon values, the model's results are mean estimates. No peer-reviewed coupon data on FibreSeek hardware or the X-CCF strand exist as of 4 October 2026.

Printed continuous carbon is much weaker in compression than in tension, and c is the least certain input. FibreSeek's X-CCF data sheet gives 33% for PLA (287/883 MPa) and 24% for PETG (203/859 MPa), with compression to ASTM D6641 [1]. These vendor ratios are the defaults. The data sheet's columns are misaligned (Section 5); read the other way, the two ratios swap, 24% for PLA and 33% for PETG. FibreSeek publishes no value for nylon, so the lower vendor ratio, 24%, is assumed; the only peer-reviewed polyamide-matrix ratio retrieved for this note is 47%, measured by Iragi et al. to ASTM D3410 on Markforged laminates, whose strand is thermoplastic-impregnated [8]; Smojver et al. [12] report compression tests not retrieved here. For Anisoprint's thermoset towpreg, the closer process analogue to X-CCF, Adumitroaie et al. give 39% (290/750 MPa) [14]. Results are reported at 33% and at 47%. The coupon ratio is applied unchanged at lower V_c and in flexure, where the compressed layer is supported laterally by polymer.

3.5 Polymers and the chopped-carbon reference

The default polymer is PLA, from two grades: modulus 2.3 GPa, yield 51 MPa and yield strain 2.9% from Prusament ISO 527 data, and break strain 6.3% from Polymaker PolyLite data [15]; compression strength 78.1 MPa from Amza et al. [16], peer reviewed, on unaged cubes loaded along the build axis. PETG values are from Faidallah et al. [17], peer reviewed, on ASTM D3039 0° coupons, the same standard as FibreSeek's data: 1.62 GPa, 28.3 MPa, 4.2% strain at maximum stress and a nominal 7.5% at break (7.0% strain at break). These are low against vendor data. PETG compression strength is 65.9 MPa [16]. ISO 527 dogbones of the same PETG read 15 to 17% lower than D3039 coupons [17], so every value not on the D3039 basis is flagged in Table 1. Nylon is Polymaker PolyMide CoPA (PA6/66), annealed (80 °C, 6 h) and dry, ISO 527 [15]: 2.7 GPa, 78 MPa and 12.7% at break. Conditioned (wet) values in the same data sheet are 0.72 GPa and 34.3 MPa, so the nylon row is a dry upper bound. Nylon compression strength is not published and is taken equal to tension; its yield strain is not published and is estimated as 78/2,700 = 2.9%.

The fourth bar is solid Bambu Lab PPA-CF, a chopped-carbon-fiber composite with a polyphthalamide (semi-aromatic polyamide) matrix, from the manufacturer's ISO 527 X-Y data, dry and not annealed [18]: 11.8 GPa, 168 MPa and 3.2% at break, brittle. Its safety data sheet lists 12 to 18% carbon fibre by weight [18]; at the published density of 1.25 g/cm³ and about 1.78 g/cm³ for carbon fiber, that is about 8 to 13% carbon by volume. Its compression strength is not published; compression is taken equal to tension, and tension governs first damage in this bar. It is a widely available chopped-carbon filament with a published ISO 527 data sheet, used here as the chopped-fiber reference; it contains no continuous fiber. It prints at high nozzle and chamber temperatures from dry filament [18], and its abrasive fiber calls for a hardened nozzle. Its values are dry and fall as the polyamide absorbs moisture. PPA-CF is not on FibreSeek's list of supported filaments [6], and it may not print on the FibreSeeker 3; the comparison is between materials on their published data, on no particular printer.

4. Results

4.1 Bead composition

The strand occupies 26.9% of the bead and polymer the remaining 73.1%. At the assumed strand carbon fraction, carbon is the following share of the bead:

The polymer added at the nozzle is 0.1228 mm² per unit length, or 0.051 mm of 1.75 mm feedstock filament per mm of strand laid. The polymer flanks the strand on both sides. In the idealized 0.24 mm layer the strand touches the top and bottom of the bead, so cover above and below comes from the adjacent polymer layers. Encapsulation and bonding must be confirmed by sectioning.

4.2 Comparison with published sections

Fig. 2 places the bead next to published sections at one scale. The Markforged strand measures 0.013 to 0.015 in (0.33 to 0.38 mm) [11], [19] and is described as about 1,000 carbon filaments in a polyamide matrix [10]. SEM image analysis gives 23.35% carbon by volume for the strand as supplied on the spool, and 22.6% is reported for spool material by Blok et al.; values of 26.0 and 28.7% are computed in the same study from published images of printed parts [11]. Thermogravimetric analysis (TGA) of the tow gives 47.2% carbon by mass, 37.4% by volume after conversion with the constituent densities; this value applies to the tow only [10]. Acid digestion (ASTM D3171) of printed Markforged laminates gives 31.4% [8]. All but the TGA-derived 37.4% lie below the 34 to 68% that 1,000 filaments of 7 to 8.6 µm would give in that strand (our calculation); 37.4% agrees with Lupone et al.'s count of about 1,000 filaments of 7.1 µm in a 0.38 mm strand (35%) [10]. Papa et al. state V_f = 69% for printed Markforged laminates without giving a method [20]; at the strand values above it cannot be the carbon volume fraction of the laminate, and it may be a mass fraction. These differences in method are not resolved here. Markforged prints the strand without added polymer, and printing flattens it into 0.0049 in (0.125 mm) layers about 0.9 mm wide, with about 11% voids measured by image analysis of polished sections [10]. The strand area, 0.086 to 0.113 mm², is about equal to that bead section, so the Markforged bead is essentially all strand. The Anisoprint CCF strand, a 1.5K tow pre-impregnated with a thermoset (epoxy) resin [9], [14], is 0.36 mm, with about 57% carbon within the as-supplied tow (reseller listing) [21]. It is co-extruded in 0.3 mm layers; one research specimen shows large voids around the strand [9]. The 0.24 mm strand is the smallest of the three (Table 2).

4.3 Deposition rate

Per unit path length, the 0.70 × 0.24 mm bead has 1.49 times the section of the 0.9 × 0.125 mm Markforged bead. The difference is added polymer: the Markforged bead is essentially all strand, and the FibreSeeker 3 bead is 73% polymer. Because a 0.70 mm bead covers less width than a 0.9 mm bead, filling a layer of given width takes 1.29 times the path length. Per unit thickness, the 0.24 mm layer replaces about two 0.125 mm Markforged layers, so the path length per unit volume of fiber layer is about 0.67 times Markforged's.

Carbon per unit path length cannot be ranked from published data. The Markforged strand carries 0.019 to 0.042 mm² of carbon (0.086 to 0.113 mm² at 22.6 to 37.4%), and a 0.24 mm strand carries 0.014 to 0.038 mm² at 30 to 85% (0.027 mm² at 60%). The ranges overlap.

The published rates are 2.39 cm³/h, a print setting on a Markforged X7 [20], and 20 cm³/h in the FibreSeeker 3 specification [6], whose basis (bead volume, strand volume or nozzle capacity) is not stated. At 0.168 mm² the specification implies about 33 mm/s head speed if the rate is bead volume, or about 120 mm/s if it is strand volume. The two values were obtained differently and are not directly comparable; bead size alone accounts for a factor of 1.49.

4.4 Flexural stiffness and first damage

The bar with fiber near both faces is 3.1% carbon by volume; about 19% of the bar volume is fiber bead, placed near the outer surfaces. Results for the four bars are given in Table 3. At 30 lbf the plain PLA bar deflects 0.195 in, and it reaches first damage at 38 lbf.

Fiber near both faces. Stiffness rises 4.6-fold. The top fiber layers are in compression; the model takes fiber compression strength as 33% of tension. In this model those top layers reach their estimated first-damage stress first, at a lower load than the plain bar (0.9×). At the peer-reviewed ratio, 47%, the load to first damage is 1.3× (Table 3, last column). At Smojver et al.'s fiber strength the load to first damage is 0.3× (24%), 0.4× (33%) or 0.6× (47%) (Table 4).

Fiber on the tension face only. With half the fiber, stiffness rises 1.9-fold and the load to first damage 2.0-fold, at both compression ratios. First damage is fiber tension in the outermost fiber layer, so this result does not depend on c. It does depend on the fiber tensile strength: at Smojver et al.'s value it is 0.9× (Table 4). A fourth tension-face layer raises the load to first damage from 2.0× to 2.1×.

Solid PPA-CF bar. The chopped-carbon composite bar, with no continuous fiber, is 5.1 times as stiff as the plain bar and reaches 3.3 times its load to first damage, the ratio of the tensile strengths (168/51). It has the highest load to first damage of the four bars.

Strength range. Stiffness does not depend on fiber strength or compression ratio: 4.6× (both faces) and 1.9× (tension face) at the defaults, and 7.8× at 0.35 mm. It scales with carbon content (both faces 2.8× to 6.0× at 30 to 85% strand carbon; Table 4). Load to first damage depends on fiber quality and compression strength: 0.9× to 2.0× for the tension face and 0.3× to 1.3× for both faces (compression at 24 to 47% of tension), between Smojver et al.'s fiber strength and Eq. (3). With low-strength fiber on the tension face, for example a void-rich strand, the fiber layer reaches its failure strain before the PLA reaches its yield stress: at Smojver et al.'s strength the fiber-layer failure strain is about 0.55% in tension, against about 2.2% for PLA at its 51 MPa yield stress. First damage is then fiber breakage while the PLA still carries load; whether the bar holds that load after the fiber breaks is not modeled. Continuous fiber gives a large stiffness gain, and a load to first damage that may be below or above the plain bar's, depending on fiber placement, fiber quality and compression strength.

The four bars reach first damage by different mechanisms: polymer yield in the plain bar, fiber compression with fiber near both faces, fiber tension on the tension face and tensile fracture of the chopped-carbon composite. Equal ratios therefore do not mean equal ultimate strength, and no strength beyond first damage is computed.

Table 4 gives the sensitivity to the assumed inputs. Each row changes one input from the defaults, except the rows that change spacing or fiber strength together with compression. Stiffness does not depend on the compression ratio in this linear model.

The tension-face load ratio does not change with the compression ratio, but it falls from 2.0× to 0.9× at Smojver et al.'s fiber strength. The both-face load ratio spans 0.3× to 1.3× across fiber strength and compression at 24 to 47%; it is the least certain result in this note. Stiffness does not change with fiber strength or compression ratio; it scales with carbon content. Ratios in the polymer rows are relative to a different plain bar in each row: the weak D3039 PETG makes the fiber ratios larger, and the stronger nylon makes them smaller.

4.5 Vendor coupon values versus fiber content of a 0.70 mm bead

FibreSeek's X-CCF coupons reach 82 to 84 GPa [1]. With standard-modulus fiber (230 GPa) at 100% efficiency, that requires at least 35% carbon by volume in the fiber layer (about 28% with intermediate-modulus fiber of about 290 GPa; FibreSeek does not state the fiber grade); using Eq. (3) it requires about 50 to 52%. Either bound is above the 26.9% a 0.70 mm bead can hold. In a 0.70 × 0.24 mm bead, even a strand of 100% carbon, which is physically impossible because round fibers pack to at most 90.7% [2], gives 26.9% carbon: 45 GPa and 565 MPa with Eq. (3), or 64 GPa and 940 MPa ideal. At 60% strand carbon in 0.24 mm layers, Eq. (2) places the published coupons at fiber paths about 0.22 to 0.32 mm apart (Table 5). The lower end is narrower than the 0.24 mm strand, so the strand must flatten; flattened strands in thinner layers are the other route. The coupons are fiber-dense laminates. At 0.35 mm, the closest spacing the model allows and still below FibreSeek's coupon density, the fiber layer is 32.3% carbon and 53.6 GPa.

5. Discussion

Effect of fiber placement. In this model, continuous fiber raises stiffness wherever it is laid. Load to first damage depends on where the fiber is laid and on its strength. With fiber near both faces, the fiber in compression adds stiffness and print time, and the load to first damage is 0.3× to 1.3× across fiber strength and compression at 24 to 47% (Table 4). Fiber on the tension face gives 0.9× to 2.0× at every compression ratio modeled; the lower value is at Smojver et al.'s fiber strength, where first damage is fiber breakage and the PLA still carries load. The bending results reported in [5] could reflect fiber in compression; the layouts of those parts are not known.

Vendor coupons versus 0.70 mm beads. FibreSeek's X-CCF 1K data sheet (code TDS1219; ASTM D3039, D6641 and D790; typical values) [1] gives, for PLA + X-CCF, 883 MPa tensile strength, 84 GPa, 0.91% strain at break, 287 MPa compression strength and 494 MPa flexural strength, and for PETG + X-CCF 859 MPa, 82 GPa, 1.05%, 203 MPa and 294 MPa. The PDF's columns are misaligned; the matrix assignment here follows the order of the text in the PDF. The data sheet gives no carbon fraction, layup, fiber spacing, print settings or conditioning. With a 0.24 mm strand these values cannot come from 0.70 mm beads (Section 4.5).

Typical values and allowables. FibreSeek publishes typical values and states that they are "not intended for use in design specifications" [1]. Design allowables are statistical: a B-basis value is exceeded by 90% of the population with 95% confidence [22], which for five normally distributed specimens is about the mean minus 3.4 standard deviations. FibreSeek's 883 ± 156 MPa would give about 350 MPa if n = 5 (our calculation); n is not stated [1]. Smojver et al. report 236 ± 20 MPa [12], and Iragi et al. 905 ± 4 MPa [8], a far smaller spread than FibreSeek's. Eq. (3) rests on means, so the model's results are mean estimates, and a part designed to them has no margin for scatter.

Speed versus performance. Denser fiber paths take longer to print. At 0.35 mm spacing, the closest the model allows and still below FibreSeek's coupon density, fiber near both faces gives 7.8× stiffness and 1.8× (33%) or 2.5× (47%) load to first damage at the Eq. (3) strength, against 4.6× and 0.9× or 1.3× at 0.70 mm; fiber on the tension face gives 2.2× stiffness and 2.3× load (Table 4). Each path carries the same strand with about a third of the polymer, and each fiber layer holds twice the fiber. Each fiber layer then needs twice the path length and twice the fiber runs (30 instead of 15 per layer), so twice the cuts and restarts and twice the strand; strand use and fiber print time roughly double for the gain. That spacing has not been shown to print (Section 2).

Continuous against chopped carbon. Continuous fiber at the default spacing reaches 4.6× stiffness with 3.1% carbon in PLA, and 7.8× at 0.35 mm with 6.2%. The PPA-CF bar, a whole bar of a 168 MPa chopped-carbon composite, reaches 5.1× stiffness and has the highest load to first damage of the four bars, 3.3×. Its safety data sheet gives 12 to 18% carbon fibre by weight, about 8 to 13% by volume [18]. Per unit of carbon, the continuous strand adds about 2.5 to 3.5 times as much stiffness: 1.2 stiffness ratio points per percent carbon against 0.3 to 0.5 for PPA-CF. Most of PPA-CF's load to first damage comes from its polyamide matrix rather than its fiber; no data for the unfilled matrix are published to separate the two. Chopped fiber carries its full strength only above a critical length, typically a few hundred micrometres in polyamides, and compounding and extrusion shorten fibers; fiber length is not published for this filament, so the share of its carbon that acts as reinforcement rather than as stiffening filler cannot be stated. A stiffer matrix would raise the absolute stiffness and strength of the continuous-fiber bars; ratios against the plain bar of that polymer would be smaller, as the nylon row of Table 4 shows.

Deposition rate and production value. At a fixed machine-hour rate, halving print time halves the machine share of part cost; fiber, polymer, labor and scrap are not reduced by it. A larger bead lays more volume per unit path length, and in the co-extruded bead the added volume is polymer. Whole-part time also depends on the fiber share of the print, on travel and on cut-and-restart overhead at every fiber run; none of these has been measured here. The figure of merit is whole-part time at equal performance. No published study reports it.

Material efficiency. Infused and autoclave-cured laminates are about 45 to 65% carbon by volume [2] (Fig. 3). The bar in Section 4.4 is 3.1% carbon by volume and gains 4.6 times the stiffness. With fiber on the tension face only, about 1.5% carbon gives 1.9 times the stiffness and 2.0 times the load to first damage at the default inputs, or 0.9 times at Smojver et al.'s fiber strength. No molds, vacuum bagging or curing ovens are used. The comparison is with the unreinforced polymer part, and fiber cost was not assessed.

Dynamic behavior. With uniform full-length fiber, as in the bar of Section 4.4, the mode shapes are unchanged and the natural frequencies scale with the square root of stiffness: about 2.1× for fiber near both faces and about 1.4× for the tension face only (carbon adds about 1.3% to the mass). Local fiber or lattice layouts change the mode shapes as well, so each design must be computed or measured.

6. Limitations

• All results are model estimates. No specimen was printed, sectioned or tested for this note.
• The strand diameter (0.24 mm) is the author's caliper measurement of the supplied strand. The 60% carbon within the strand is FibreSeek's store-page value without a method, and it does not agree with the listed 1K tow at that diameter (Section 3.1). The 0.24 mm fiber layer height and 0.70 mm path spacing are the author's process settings.
• Path spacing below the 0.70 mm nozzle diameter, and 0.24 mm layers that give no compaction of the 0.24 mm strand, have not been shown to print. Bonding and void content at zero compaction are unverified.
• The fiber-layer calibration (Eq. 3) rests on coupons from other platforms (Markforged, Anisoprint) with different matrices and fiber fractions. It lies 24 to 30% below two of them in tensile strength and is 2.2 times the third (Smojver et al.); at that strength the tension-face load to first damage falls from 2.0× to 0.9× and the both-face load is 0.3× to 0.6× (Table 4), with stiffness unchanged (Section 3.4). No peer-reviewed coupon data for FibreSeek hardware or the X-CCF strand exist yet.
• The fiber layer has the same modulus in compression as in tension. FibreSeek's compressive moduli are 62% (PLA) and 40% (PETG) of its tensile moduli [1]. If that holds in the bar, the both-face stiffness ratio is overstated, and the compression-limited both-face load to first damage is understated, because the softer compressed layers would carry less stress. This also holds under a strain criterion, because the coupon compressive failure strain (0.5 ± 0.03% on the data sheet [1]) exceeds the model's 0.40%. FibreSeek does not state the cause of the low compressive moduli [1].
• FibreSeek's values are vendor typical values from one data sheet, with no carbon fraction, layup or conditioning stated [1]. The default compression ratio comes from them, and the both-face strength result depends on the choice (Table 4). The coupon ratio is applied unchanged at lower V_c and in flexure.
• The transverse and shear properties of the fiber layers are assumed (Section 3.3).
• Nylon and PPA-CF values are dry; conditioned values are lower (nylon 0.72 GPa and 34.3 MPa wet [15]). PPA-CF and nylon compression strengths are not published and are taken equal to tension; the nylon yield strain is estimated. Most polymer values are manufacturer ISO 527 data, not on the D3039 basis (flagged in Table 1).
• The FEA is linear-elastic, two-dimensional and plane stress, with perfectly bonded layers. It omits fiber microbuckling, delamination, voids, fiber waviness, transverse strength and interlayer (Z) strength. Only σ_x is checked; there is no interlaminar shear check at the fiber-layer interfaces.
• No strength beyond first damage is computed. First damage is not final failure, and no post-damage (ply-discount) estimate of ultimate load is made.
• The supports are points at the bar ends with no overhang, and fiber anchorage beyond the supports is not modeled. Printed fiber runs end at the part boundary, where load transfer into the fiber is unknown.
• FibreSeek describes the strand as thermoset-impregnated [1]; the polymer then bonds to it by adhesion only, and perfect bonding overstates load transfer and compression support. The strand-to-polymer bond strength is unknown.
• Thermal residual stress from the expansion mismatch between polymer and carbon is not modeled. It places the fiber in compression before load is applied, and the tension-face layout is unsymmetric, so warpage and preload are expected.
• The solver is verified against beam theory and by mesh and check-region studies (Section 3.3), all with one code. A cross-check in a second finite element code has not been made.
• First damage is evaluated 6 to 15 mm from midspan and scaled to the peak moment. Local crushing or fiber kinking under the loading nose is not captured.
• The model is static. Natural frequencies are estimated by scaling only; mode shapes and damping were not computed.
• The deposition rates in Table 2 are one print setting and one specification of unstated basis; they are not a like-for-like comparison.
• Fiber and polymer cost, machine cost and depreciation, labor, scrap and failed prints, cut-and-restart overhead per fiber run, toolpath limits (minimum strand length, minimum bend radius) and machine reliability are not covered. No cost or value conclusion should be drawn from this note.

7. Future work

• Polished sections of printed FibreSeeker 3 bars, to measure strand diameter, flattening, encapsulation and voids against Fig. 1 and Fig. 2.
• Measurement of carbon content within the strand by image analysis of polished sections [11], cross-checked by acid digestion (ASTM D3171) or inert-atmosphere TGA with char correction, and by tow linear density with fiber density (about 1.78 g/cm³ [2]).
• Coupon tests of X-CCF in PLA and PETG at stated path spacing and measured carbon fraction (ASTM D3039 and D6641, at least five specimens), reporting scatter, compressive modulus and minimum values.
• Three-point bend tests of the layouts in Section 3.3, using the ASTM D790 geometry as modeled (specimen length at least 125 mm), with ASTM D7264 in parallel, at least five specimens per layout, to test the predicted stiffness and first-damage ratios.
• Strand-to-polymer interfacial shear (ASTM D2344 short-beam shear or pull-out), to replace the perfect-bond assumption.
• A cross-check of one layered case in a second finite element code; four-point bending (ASTM D6272) to remove the load-introduction exclusion; interlaminar shear, residual stress and post-first-damage estimates.
• Whole-part print time and cost per part at equal performance, against an established platform.
• Modal analysis and vibration measurement of fiber-reinforced parts and lattices.
• Characterization of auxetic continuous-fiber lattices.

8. Conclusions

1. A 0.24 mm strand is 27% of a 0.70 × 0.24 mm bead, and carbon is about 16% of the bead at the assumed strand composition.
2. Per unit path length the 0.70 × 0.24 mm bead has 1.49 times the section of the Markforged bead; the difference is added polymer. Carbon per unit length cannot be ranked from published data.
3. In this model, fiber raises stiffness wherever it is laid: 4.6× with fiber near both faces of a PLA bar and 1.9× on the tension face alone, at 0.70 mm spacing, and 7.8× near both faces at 0.35 mm. Stiffness does not depend on fiber strength or compression ratio and scales with carbon content (both faces 2.8× to 6.0× at 30 to 85% strand carbon). Load to first damage depends on fiber quality and compression strength: 0.9× to 2.0× for the tension face and 0.3× to 1.3× for both faces (compression at 24 to 47% of tension). With low-strength fiber on the tension face, first damage is fiber breakage while the PLA still carries load; whether the bar holds that load after the fiber breaks is not modeled.
4. FibreSeek's vendor typical coupon values (82 to 84 GPa) need at least 35% carbon in the fiber layer with standard-modulus fiber, or about 28% with intermediate-modulus fiber; a 0.70 mm bead cannot exceed 26.9% even with an all-carbon strand. They correspond to fiber paths about 0.22 to 0.32 mm apart at 60% strand carbon in 0.24 mm layers, or to flattened strands. At 0.35 mm the model gives 7.8× stiffness, with the same strand per path and about a third of the polymer; that spacing has not been shown to print.
5. A solid PPA-CF bar gives 5.1× stiffness and 3.3× load to first damage, the highest load of the four bars. It contains about 8 to 13% carbon by volume (safety data sheet, 12 to 18% by weight), three to four times as much as the both-faces bar; per unit of carbon, the continuous strand adds about 2.5 to 3.5 times as much stiffness.

Predict. Print. Test.

9. Collaboration

The invitation at the start of this note applies: corrections, and collaboration with educational institutions and third-party, non-commercial associations. Coupons and custom printing are provided subject to availability and a written agreement covering cost, intellectual property, publication rights and liability.

Coupons are offered in standard geometries: tensile (ASTM D3039 or ISO 527-4/5, tabbed), flexural (ASTM D7264 or ISO 14125 for the composite; ASTM D790 for the polymer), short-beam shear (ASTM D2344), compression (ASTM D6641), in-plane shear (ASTM D3518, ±45°) and 90° tension (ASTM D3039, transverse), at least five per condition. They are printed in-house on the author's FibreSeeker 3 using validated G-code, to prevent machine damage. Its 11.8 × 11.8 × 9.6 in (300 × 300 × 245 mm) build volume [6] fits a 10 in (250 mm) D3039 coupon. Each batch is supplied with its slicer file, layer stack, fiber orientation, print parameters and conditioning record (ASTM D5229 for composite coupons; ASTM D618 for unreinforced polymer coupons), and reports the measured fiber volume fraction (ASTM D3171 or polished-section image analysis), the path spacing, and the printer model and firmware. Contact research@sunn3d.com.