Correlation Between Mechanical Properties and Particle Size of Fiber-Reinforced Selective Laser Sintering

Abstract

When basalt fibers are evenly and layer-wise laid down in the laser sintering area, it can effectively enhance the bending strength and the tensile strength of the precoated sand mold prepared by selective laser sintering (SLS). However, the reinforcing effect of the fibers is influenced by the particle size of the precoated sand. Therefore, in this study, the same sintering parameters were used to prepare specimen of precoated sand with different particle sizes. Then, 0.05−0.20 wt% of basalt fibers was added to the precoated sand mold. The green/dry bending strength and tensile strength of the specimens were tested. And, in combination with the fracture morphology of the specimens, the reinforcing effect of the fibers in different particle sizes of the precoated sand was investigation. The results suggest that, as the precoated sand size decreased, the bending and tensile strengths of the specimens without fibers showed a trend of first decreasing and then increasing. This was influenced by the thickness of the resin layer on the surface of the precoated sand and the number of resin necks. The reinforcing effect of the fibers in the specimens is related to the pore diameter between the precoated sand. After calculation, the optimal amounts of fibers added to the specimen were found to be exponentially correlated with the particle size of the precoated sand, with a correlation coefficient of over 80%. That is, in the preparation of fiber-reinforced SLS-precoated sand molds, the larger the diameter of the precoated sand aggregate, the more fibers are required to be added, providing a certain theoretical basis for the subsequent production process.

Keywords

laser selective sintering particle size fiber reinforcement correlation

Introduction

Selective laser sintering (SLS) technology emerged in the 1990s and has since gained widespread adoption across various industries.^1–4 Particularly in the casting industry, SLS demonstrates remarkable potential due to its rapid prototyping capacity and exceptional design versatility, which effectively overcome multiple limitations associated with conventional casting methodologies.^5–7 However, SLS sand molds have low green strength and need to be dried before they can be used for liquid metal casting.⁸ Although, increasing the wall thickness of the sand molds can improve the strength, but it will bring new problems. Since the precoated sand belongs to resin sand, and the particles are attached with phenolic resin. Gases are generated under the high temperature, and if these gases cannot be discharged from the sand mold in time, the filling capacity of the metal liquid will be affected,^9,10 which, in turn, produces casting defects. Furthermore, increased wall thickness significantly impairs the thermal conductivity of sand molds,¹¹ leading to prolonged solidification times of molten metal. Longer solidification times will promote excessive grain growth and microstructural coarsening, ultimately resulting in deteriorated mechanical properties of cast components. These technical limitations highlight the critical need for developing innovative enhancement methods that can simultaneously optimize the sand mold’s structural integrity while maintaining superior casting quality standards. The fiber-reinforced polymers have been used in various 3D printing not only for enhancing mechanical properties but also to add additional functionality, including electrical properties.¹² Such as the printing preparation of glass fiber reinforced PEEK^13,14(poly(ether-ether-ketone)) and nylon fiber reinforced materials¹⁵, the performance of the matrix has been enhanced by adding fibers. In addition, fibers can also be added to the casting mold to improve its performance, such as carbon fiber-reinforced shell for investment casting.¹⁶ Therefore, this investigation employs basalt fiber-reinforced SLS-coated sand molds. Basalt fibers, renowned for their exceptional mechanical properties, thermal stability, and corrosion resistance, have been extensively utilized as concrete reinforcement materialsm,¹⁷ while preliminary research has demonstrated the feasibility of fiber-reinforced precoated sand molds.¹⁸ However, in this research, the precoated sand was mixed with the fiber alcohol suspension by using the wet-mixing method. During the drying process, since alcohol can dissolve the resin, it results in an uneven distribution of the resin on the surface of the precoated sand. In this study, fibers were selectively laid layer by layer within the laser sintering zone, which prevented the resin from dissolving in alcohol, shortened the preparation process, and evenly dispersed the fibers.

Extensive research in construction materials science has demonstrated that the particle size distribution of concrete aggregates significantly influences the composite’s performance.^19–21 The variation in aggregate particle sizes directly determines the pore structure formation within the concrete matrix, subsequently affecting the material’s overall density. This microstructural characteristic plays a pivotal role in governing both the mechanical properties and long-term durability of concrete composites. To optimize material density and enhance performance, stone powder is commonly incorporated as a supplementary material.²² Experimental investigations have revealed a strong correlation between particle size distribution and optimal stone powder dosage, with raw materials exhibiting higher porosity typically requiring increased stone powder content to effectively fill the void network and achieve desired density parameters. SLS technology similarly encounters the critical influence of powder particle size distribution on final part, where inter-aggregate porosity significantly impacts both dimensional precision and mechanical performance of fabricated components.^23,24 In precoated sand systems, the variation in aggregate grain sizes creates distinct pore structures within the matrix, which may potentially influence the reinforcement efficiency of basalt fibers. To systematically investigate the correlation between fiber reinforcement effectiveness and sand grain size distribution, in this study, five sizes of precoated sand were selected for the experiments. Through controlled fiber weight fraction variations and comprehensive performance evaluation, combined with detailed fracture surface morphology analysis, a mathematical model was developed through experimental data regression to establish the quantitative relationship between optimal fiber content and aggregate particle size distribution for each specimen category.

Materials and Methods

Experimental materials

The experimental materials comprised precoated sand supplied by Lianxin Sand Group, specifically formulated through precise gradation of five distinct grain size distributions designated as D1–D5, arranged in descending order of particle size. The detailed particle size distribution parameters are presented in Figure 1, where the mesh number represents the sieve openings per linear inch, with corresponding average aggregate diameters provided in micrometers. The process of sand preparation maintained consistent resin and hardener proportions relative to sand weight, independent of particle size variations. For reinforcement, basalt fibers manufactured by Que Pananjie were utilized, characterized by 4 mm length, 6–13 µm diameter, and 2.63–2.65 g/cm³ density. The experimental apparatus was the AFS-500 laser selective sintering rapid prototyping machine produced by Beijing Longyuan Company.

FIG. 1.

The size and ratio of the precoated sand for different specimens.

Experimental methods

The precoated sand specimens were fabricated in accordance with the Chinese Machinery Industry Standard JB/T8583-2008, utilizing standardized “8”-shaped tensile specimens and rectangular bending specimens, with detailed dimensions illustrated in Figure 2. The tensile and bending strength were conducted using an intelligent sand universal strength testing machine (SWY-IIIS, Changde Fangzhu Instrument and Equipment Co., Ltd., China). The tensile strength was equipped with a special fixture to record the maximum load at sample fracture. The bending strength was a three-point bending type, with the span of the support point being 60 mm. And the loading rate of the testing machine’s pressure head was 8 mm/s. The green strength and the dry strength of the specimens needed to be tested, and the average value of five valid specimens was taken for each set of data.

FIG. 2.

Specimen size [(A) tensile specimen; (B) bending specimen].

Gas generation and gas generation rate were conducted in strict compliance with the Chinese Machinery Industry Standard JB/T8583-2008. Gas generation refers to the ability of a certain amount of precoated sand to release gas when heated. The gas generation rate refers to the volume of gas produced per unit mass of sand or binder within a unit time at a certain temperature. Raise the gas generation tester to 1,000 ± 5°C. Take 1 ± 0.01 g of the specimen and place it in the steel boat. Quickly use an iron rod to push the steel boat to the red-hot part of the quartz tube and seal the mouth of the quartz tube. The tester will simultaneously record the gas generation and the gas generation rate. Keep this for 3 min, then stop the recording.

The printing parameters were optimized as follows: laser power at 35 W, scanning velocity of 2,400 mm/s, preheating temperature maintained at 70°C, and layer thickness set at 0.2 mm. Post-processing involved a thermal treatment protocol of 220°C for 150 min. For fiber-reinforced specimens, a specialized layer-by-layer laying method was implemented (Fig. 3), where the printing process was paused at predetermined layers to laying fiber. This involved positioning a custom mold above the sintering zone and vibrating screen mesh to achieve uniform fiber distribution across the target layer. The dispersed fibers were systematically collected and relaying to ensure complete coverage. Given the specimen thickness of 11.18 mm, fibers were distributed across four distinct layers to optimize homogeneity and reinforcement effectiveness throughout the cross section.

FIG. 3.

Schematic of fiber layup.

To systematically investigate the correlation between fiber reinforcement efficiency and sand particle size distribution, the experimental protocol was structured into two primary components: 1.

Initial phase: Comprehensive performance evaluation of precoated sand specimens across varying grain size distributions. This involved quantitative characterization of raw sand properties through gas evolution analysis, true density measurement, and bulk density assessment. Subsequently, standardized specimens were fabricated under identical printing parameters (laser power: 35 W, scanning speed: 2,400 mm/s, layer thickness: 0.2 mm) and drying conditions (220°C for 150 min). Mechanical properties were quantitatively assessed through comparative analysis of tensile and bending strength measurements, conducted both green and dry.

Reinforcement phase: Systematic addition of basalt fibers with controlled weight fractions of 0.05 wt%, 0.1 wt%, 0.15 wt%, and 0.2 wt% relative to weight of specimen. This phase encompassed dual comparative analyses: first, evaluating strength variation within each sand group across different fiber contents. And second, comparing mechanical performance across different sand groups at equivalent fiber loading levels. The mechanical characterization was complemented by detailed fractographic analysis using scanning electron microscopy to establish the correlation between fiber reinforcement mechanisms, interfacial bonding characteristics, and sand grain size distribution, thereby elucidating the fundamental structure–property relationships in the composite system.

Results and Discussion

Differences in the performance of each group of precoated sand

The gas evolution of precoated sand primarily originates from the thermal decomposition of drying agents and phenolic resin components²⁵ to be used to determine the resin content of each group of precoated sand. The detailed results are presented in Figure 4. Experimental data revealed consistent gas evolution values across all specimen groups, demonstrating minimal variation (standard deviation <5%) that fell within the measurement error range. This indicates that the gassing properties are independent of the grain size variation, and the resin content of each group of precoated sands is close to each other.

FIG. 4.

Five groups of precoated sand gassing properties.

Comprehensive density characterization, encompassing both true density and bulk density measurements,^26,27 was conducted to evaluate the fundamental packing characteristics of precoated sand specimens. As illustrated in Figure 5, true density values remained consistent across all groups, ranging from 2.41 to 2.46 g/cm³, indicating uniform material composition. However, bulk density exhibited a distinct positive correlation with decreasing particle size, increasing from 1.77 g/cm³ for group D1 (coarsest) to 1.87 g/cm³ for group D5 (finest). This phenomenon can be attributed to particle packing dynamics: finer particles enable more efficient space filling with reduced interparticle voids, resulting in denser packing configurations. Conversely, larger particles create more substantial interstitial spaces, leading to lower overall packing density and increased void fraction within the specimen matrix.

FIG. 5.

Specimen packing density and true density.

The specimens were prepared according to the same parameters for each group of sand, and the green/dry bending strength and tensile strength of the specimens were tested, respectively. The green strength is shown in Figure 6A; the specimen strength shows a trend of decreasing and then increasing with decreasing grain size. After drying the specimen, as shown in Figure 6B, the trend of strength change is the same as that of the green strength.

FIG. 6.

Strength trend with particle size [(A) green strength; (B) dry strength].

The coating process maintains consistent resin application parameters regardless of particle size variations, with fixed resin consumption per unit mass of raw sand. This process characteristic leads to an inverse relationship between particle size and resin layer thickness due to specific surface area effects. As illustrated in Figure 7, larger particles (e.g., D1 group) exhibit reduced specific surface area, resulting in thicker resin coatings that form robust interparticle necks, thereby enhancing mechanical strength. Conversely, finer particles (e.g., D3 group) present increased specific surface area, leading to thinner resin layers and consequently weaker bonding. However, the strength reduction caused by diminished bond strength is counterbalanced when particle size decreases beyond a critical threshold (e.g., D5 group), where the exponential increase in the number of resin necks per unit volume ultimately dominates the mechanical behavior, resulting in net strength enhancement through increased connection density despite reduced individual bond strength.

FIG. 7.

Schematic diagram of particle size variation and microscopic morphology images [(A) D1; (B) D5].

Effect of fiber addition on specimen properties

Systematic fiber reinforcement was implemented across all specimen groups, with Figure 8 illustrating the variation in green strength as a function of basalt fiber addition for different particle size distributions. The strength exhibited distinct trends based on sand gradation: specimens with coarser particles (D1 and D2 groups) demonstrated a monotonic increase in initial strength with higher fiber addition, suggesting effective load-bearing capacity enhancement. The strength curves of groups D3, D4 and D5 are differentfrom those of groups D1 and D2. As the amount of fibers added increases, the strength initially increases and then gradually decreases. This non-monotonic behavior suggests the existence of an optimal fiber addition threshold, beyond which additional fiber incorporation may lead to interfacial stress concentration or fiber agglomeration effects that compromise the composite’s structural integrity.

FIG. 8.

Trend of green strength with fiber addition [(A) D1; (B) D2; (C) D3; (D) D4; (E) D5].

The green specimens undergo limited curing through transient laser heating, where, despite high energy density, the brief exposure duration results in incomplete resin polymerization.²⁸ This partial curing leads to suboptimal interfacial bonding between basalt fibers and precoated sand matrix, with reinforcement primarily achieved through fiber debonding mechanisms. At lower fiber addition, the reinforcement effect remains negligible across all specimen groups. As fiber addition increases, the strength of the specimen is enhanced. However, excessive fiber incorporation induces stress concentration and potential fiber clustering, leading to strength reduction in certain specimen groups.

After drying, as illustrated in Figure 9, it reveals similar strength trends across all groups compared with green specimens but with significantly enhanced mechanical properties. The complete drying process facilitates improved interfacial bonding between basalt fibers and the sand matrix, resulting in more effective stress transfer and composite reinforcement.

FIG. 9.

Trend of cured strength with fiber addition [(A) D1; (B) D2; (C) D3; (D) D4; (E) D5].

Fibers provide three primary reinforcement mechanisms to the precoated sand specimens, as illustrated by the fracture morphology in Figure 9. The first mechanism is fiber debonding, depicted in Figure 10A. When the specimen is subjected to stress, the bonding interface between the fiber and the resin fails, as the fiber–resin bond strength is lower than the fiber’s breaking strength. This process absorbs part of the load, thereby enhancing the specimen’s strength.

FIG. 10.

Fiber reinforcement effects [(A) fiber debonding; (B) fiber deformation and fracture; (C) pull-off of the fibers]

The second mechanism involves fiber deformation and fracture under shear stress, as shown in Figure 10B. When the specimen experiences shear forces, the fibers are broken in the matrix to withstand the external force, thus improving the specimen’s bending capacity.

The most effective reinforcement mechanism is pull-off of the fibers, as shown in Figure 10C. Under tensile stress, the load is transferred to the stronger fibers through the bonding interface between the fibers and the matrix. If the bonding force exceeds the fiber’s breaking strength, the fibers will fracture, thereby sharing a significant portion of the load and enhancing the specimen’s mechanical properties.

These three mechanisms collectively contribute to the improved performance of the precoated sand specimens reinforced with basalt fibers.

Influence of the particle size of the precoated sand on fiber reinforcement

From Figures 8 and 9, it is evident that the optimal fiber addition varies across different groups of specimens. For the specimens in groups D1 and D2, the strength consistently increases with higher fiber addition. In contrast, the optimal fiber addition for group D3 specimens is 0.15 wt%, while for groups D4 and D5, it is 0.10 wt%. To explore the relationship between the fiber reinforcement effect and particle size, the strength growth rates of specimens with fiber additions ranging from 0.05 wt% to 0.20 wt% were analyzed, as illustrated in Figure 11.

FIG. 11.

Trend of growth rate of specimen strength with fiber addition [(A) 0.05 wt%; (B) 0.10 wt%; (C) 0.15 wt%; (D) 0.20 wt%].

When the fiber addition was 0.05 wt%, the strength growth rate of the specimens remained below 8%, indicating that such a low fiber addition had a negligible impact on the specimens’ strength. Due to testing errors, no clear trend related to particle size was observed at this fiber addition level. However, when the fiber addition was increased to 0.10 wt%, the strength growth rate exhibited a noticeable enhancement as the particle size decreased. This fiber addition level proved to be optimal for the specimens in groups D4 and D5, achieving the highest strength growth rate of over 20%.

At a fiber addition of 0.15 wt%, the strength growth rate demonstrated a trend of initially increasing and then decreasing as the particle size decreased. Compared with the 0.05 wt% and 0.10 wt% fiber additions, the strength growth rate for groups D1 and D2 improved significantly at 0.15 wt%, while the growth rate for groups D4 and D5 declined. Notably, the D3 group achieved the highest strength growth rate of 34.9% at this fiber addition level.

When the fiber addition was further increased to 0.20 wt%, the strength growth rate exhibited a clear decreasing trend as the particle size decreased. This suggests that excessive fiber addition may not always be beneficial and can lead to diminishing returns, particularly for specimens with smaller particle sizes.

During the specimen preparation process, when the fiber addition was set to 0.20 wt%, no abnormalities were observed during the powder spreading stage for groups D1 and D2, as illustrated in Figure 12A and B. The dimensional accuracy of these specimens remained largely unaffected, as shown in Figure 13A. However, when preparing specimens for groups D3, D4, and D5, some fibers were pushed away by the powder-spreading roller, leaving visible traces on the surface of the forming cylinder, as depicted in Figure 11C–E.

FIG. 12.

Specimen preparation process [(A) D1; (B) D2; (C) D3; (D) D4; (E) D5].

FIG. 13.

Finished specimens [(A) D1; (B) D5].

In the case of D5 group specimens, the excessive fiber content caused significant friction during the powder spreading process, leading to partial displacement of the specimens and resulting in deformation, as shown in Figure 13B. This highlights the challenges associated with higher fiber additions, particularly for specimens with smaller particle sizes, where fiber dispersion and interaction with the powder spreading process can compromise the structural integrity and dimensional accuracy of the final specimens.

The bulk density of the precoated sand increases as the particle size decreases, indicating that larger particles have more pore volume between them. As shown in Figure 14, calculations reveal that the smallest pore diameter for D1 group particles in a one-dimensional plane is approximately 32 µm, which can ideally accommodate up to three fibers within a single pore. In contrast, the smallest pore diameter for the D5 group is about 10 µm, allowing only one fiber to be effectively combined. Observations of the specimen’s microscopic morphology and measurements of pore diameters align closely with these calculations, as illustrated in Figure 15.

FIG. 14.

Schematic of minimum pore size of particles [(A) D1; (B) D5].

FIG. 15.

Specimen microscopic morphology [(A) D1; (B) D5].

When the precoated sand particle size is larger, the pore volume between the particles is also larger, requiring fibers to fill these cavities before additional fibers can be effectively contact with the matrix. At a fiber addition of 0.20 wt%, more fibers can be accommodated in the pores during the preparation of D1 group specimens; the powder spreading roller does not displace fibers, allowing specimen strength to continue increasing with higher fiber additions. However, as the particle size decreases, the pore volume reduces, and fewer fibers are needed to fill the pores. For example, in the D5 group specimens, pore space cannot accommodate 0.20 wt% of fibers, so the roller pushes away a part of fibers. This explains why the strength improvement for smaller particle sizes does not benefit from higher fiber additions and may even be compromised.

Observe the fracture morphology of the specimen. In the green specimen, the fiber and precoated sand bonding is poor; mainly fiber debonding is dominant. Observation of the cured specimen can be a clearer understanding of the fiber reinforcement mechanism. In order to distinguish between fiber debonding and fiber break, in the figure with dots as well as solid-line circle marking.

Figure 16 illustrates the fracture morphology of specimens with 0.10 wt% fiber addition. In Figure 16A, which depicts the D1 group specimens, the fibers have fewer bonding points with the sand grains. Some fibers fill the pores but fail to establish effective contact with the sand grains, resulting in minimal reinforcement. Figure 16B shows traces of fiber debonding in the D2 group specimens. Although the particle size is slightly smaller than that of D1, increasing the contact area between fibers and sand particles, the reinforcement effect remains dominated by debonding.

FIG. 16.

Fracture morphology with 0.10 wt% fiber addition [(A) D1; (B) D2; (C) D3; (D) D4; (E) D5].

In Figure 16C, clear signs of fiber breakage are visible alongside fiber debonding. As the particle size further decreases, the bonding between fibers and sand grains strengthens, leading to an increase in fiber breakage compared with the D1 and D2 groups. This enhancement in bonding improves the overall reinforcement effect.

For the D4 and D5 group specimens, a fiber addition of 0.10 wt% provided the optimal strength. Microscopic observations revealed numerous broken fibers, indicating the best reinforcement effect for these groups. At this fiber addition level, the effective contact area between the fibers and sand grains increased as the grain size decreased, further enhancing the reinforcement mechanism.

The fracture morphology of specimens with 0.15 wt% fiber addition is shown in Figure 17. In Figure 17A, which depicts the D1 group, a significant amount of fiber debonding and breakage is observed. Due to the larger particle size, fibers must first fill the pores to establish sufficient effective contact with the sand particles. However, this process significantly increases the bonding area between the fibers and the specimen. Notably, instances of a single fiber breaking twice can be observed, indicating strong bonding between the fibers and the matrix, which enhances the reinforcement effect. Figure 17B illustrates the fracture morphology of the D2 group specimen. Numerous traces of fiber debonding and fracture are also visible, and the reinforcement effect is markedly improved compared with specimens with 0.10 wt% fiber addition.

FIG. 17.

Fracture morphology of fiber addition 0.15 wt% [(A) D1; (B) D2; (C) D3; (D) D4; (E) D5].

For the D3 group, a fiber addition of 0.15 wt% proves to be optimal, as shown in Figure 17C. Although the number of fibers is higher, it has minimal impact on the specimen’s structure, and no delamination is observed. Clear evidence of fiber reinforcement can be seen in the image. However, as the grain size of the sand decreases further, the strength of the specimens begins to decline. Figure 17D and E reveals that fibers produce a noticeable cutting effect on the specimens. As the particle size decreases, the pore space shrinks, making it difficult to accommodate an excessive number of fibers. This leads to delamination within the specimens and a subsequent reduction in strength.

Figure 18 illustrates the fracture morphology of specimens with a fiber addition of 0.20 wt%. Figure 18A depicts the D1 group, where no clear delamination is observed. The gap between the fiber diameters and the pores is large, and a significant number of fibers are filled between the particles, as indicated by the dashed circles in the figure. These fibers primarily occupy space, increasing the effective contact area and allowing sufficient fibers to reinforce the specimen. However, the utilization efficiency of the fibers is relatively low. Similarly, Figure 18B shows a large number of fibers within the gaps, but these do not negatively affect the specimen’s structure and still contribute to reinforcement. In contrast, Figure 18C reveals that the fiber layer hinders the bonding between two adjacent layers of precoated sand, weakening the reinforcement effect and causing the strength to begin decreasing.

FIG. 18.

Fracture morphology of fiber addition 0.20 wt% [(A) D1; (B) D2; (C) D3; (D) D4; (E) D5].

Figure 18D and E exhibits similar microscopic morphologies, where an excessive number of fibers leads to interlayer cuts and structural damage. This significantly reduces the specimen’s strength, to the extent that it may even fall below the strength of specimens without any fiber addition.

Correlation analysis of fiber addition and particle size on strength

In this study, it was observed that a greater number of fibers can be incorporated as the grain size of the precoated sand increases. The optimal fiber addition for each group was determined, and a function was fitted to analyze the correlation between the optimal fiber addition and the grain size of the precoated sand. As illustrated in Figure 19, the relationship between the optimal fiber addition and the particle size of the specimen follows an exponential distribution, with a correlation coefficient exceeding 80% after function fitting.

FIG. 19.

Correlation analysis between optimum fiber addition and particle size.

When the precoated sand particle size is small, the diameter of the interparticle pores is also small, allowing a limited number of fibers to effectively combine with the sand particles to achieve the best reinforcement effect. With the particle size increases, the pore diameter expands, requiring more fibers to fill these pores to establish effective contact with the sand particles, thereby increasing the number of fibers needed. However, as the grain size of the precoated sand continues to grow, the optimal fiber addition converges to a fixed value and does not increase further. The reason is the laser sintering area is fixed, and an excessive number of fibers can lead to interlayer splitting of the specimen, damaging its structure and significantly reducing its strength.

It is important to note that this correlation analysis applies specifically to cases where the fiber diameter is comparable to the diameter of the smallest particle gaps. If the fiber diameter changes or if the fibers undergo modifications, the correlation analysis should be adjusted accordingly to reflect these variations.

Conclusion

To investigate the relationship between fiber reinforcement in molds and the particle size of precoated sand aggregates, an experimental study was conducted using five groups of precoated sand. Through property testing, fracture morphology observation, and correlation calculations, the following conclusions were drawn: (1)

The bending and tensile strength of the specimens are influenced by changes in the thickness of the resin film and the number of resin necks in the precoated sand. As the grain size decreases, the strength initially decreases and then increases. Basalt fibers, as a reinforcing phase, significantly enhance the bending and tensile strength by absorbing loads through mechanisms such as fiber debonding, breaking, and pull-off. However, excessive fibers can have a cutting effect on specimens with small aggregate particle sizes, leading to a reduction in strength.

(2)

The optimal fiber addition exhibits an exponential relationship with the aggregate particle size, with a correlation coefficient exceeding 80%. For smaller pore spaces between sand particles, a limited number of fibers can achieve the best reinforcement effect. As the precoated sand particle size increases, the optimal fiber addition should also increase. However, when the particle size continues to grow, the optimal fiber addition converges to a fixed value.

(3)

In practical production, it is advisable to use precoated sand with aggregate particle sizes of less than 75 µm or smaller for manufacturing sand molds. At this particle size, the molds can achieve higher initial strength, require fewer reinforcing phases for effective reinforcement, and produce castings with lower surface roughness due to the finer particle size.

Authors’ Contributions

Conceptualization: K.L.; Methodology: Z.F., Y.S., and L.C.; Formal analysis: L.C. and X.C.; Investigation: L.C., Z.F., and Y.S.; Supervision: Y.S., Z.F., and X.C.; Funding acquisition: K.L.; Resources: K.L.; Visualization: L.C. and Z.F.; Validation: Y.S. and X.C.; Writing—original draft: L.C.; and Writing—review and editing: K.L. and Z.F.. All authors have read and agreed to the published version of the article.

Footnotes

Consent to Participate

All authors consent to participate.

Consent for Publication

All authors consent to publication.

Data Availability

All of the material is owned by the authors, and/or no permissions are required. The results/data/figures in this article have not been published elsewhere, nor are they under consideration by another publisher.

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