Mechanical properties and modeling of licorice root fiber-reinforced eco-friendly polymer composites

Abstract

Licorice root fibers are promising natural reinforcements for polymer composites due to their favorable mechanical properties, rapid growth, and environmental sustainability. This study investigates the influence of fiber morphology and dispersion on the mechanical performance of epoxy-based laminated composites reinforced with licorice root fibers. Two fiber configurations, including bundles and milled fibers sieved to mesh sizes 20, 40, 60, and 80, are evaluated. Composites are fabricated using LY5052 epoxy resin and HY5052 hardener, and tensile properties are measured according to ASTM D3039. Analytical predictions are conducted using Halpin-Tsai and Mori-Tanaka models to assess uniform and clustered fiber distributions. Results show that elastic modulus decreases with decreasing fiber size (bundled fibers > mesh 20 > mesh 40 > mesh 60 > mesh 80), reflecting the importance of fiber aspect ratio and load-transfer efficiency. In contrast, toughness and strain energy increase with finer powders, indicating enhanced energy absorption and fracture resistance. These findings demonstrate that fiber morphology, fineness, and dispersion critically govern stiffness, toughness, and ductility in licorice root fiber composites, providing mechanistic insights and practical guidance for the design and optimization of sustainable biocomposites.

Keywords

eco-friendly fibers licorice root material characterization natural composites mechanical properties

Introduction

Growing global awareness of environmental pollution and the overproduction of nonrenewable petroleum-based products has heightened interest in natural fibers as reinforcements across diverse industries. The use of lightweight structures to reduce production costs is particularly appealing to design engineers.¹ Agro-food processing generates abundant lignocellulosic fibrous waste from a wide range of botanical sources. Recent efforts have explored extracting lignin from this waste to expand its utility beyond energy recovery toward new materials.² Natural-fiber reinforced composites, commonly referred to as green composites, offer environmental advantages over conventional synthetic materials.³ Their benefits include low cost, low density, biodegradability, abundant availability, and potential health advantages, such as reduced respiratory and dermal irritation. Consequently, natural-fiber composites have found applications in automotive components, construction, sports equipment, consumer goods, furniture, piping, tanks, and rotor blades.^4–6

Licorice (Glycyrrhiza glabra) roots and stolons have a long-standing traditional use across regions that include China, Turkey, Israel, and parts of southern Europe (e.g., southern Italy).⁷ In Iran, licorice is widely cultivated in areas such as Lorestan, Azerbaijan, Kermanshah, Bakhtiari, Esfahan (Fereydunshahr, Eqlid, Nahavand), and Karak, where the plant is harvested primarily for medicinal purposes. Historically, licorice has been employed as a medicinal plant and in confectionery; its applications have since expanded to cosmetics. The licorice market was valued at approximately USD 42 million in 2007.⁸

The licorice root is a lignocellulosic material. Analyses reported in the literature show approximate compositions of 3% water-soluble polysaccharides, 30.7% cellulose, and 27.5-25.1% lignin, with a substantial hemicellulose fraction (values vary by method; Komarov’s method vs acid hydrolysis).^9–11 Traditionally, licorice root is used as a sweetener and flavoring agent in the food industry and as a source of saponins and flavonoids, the latter associated with anti-inflammatory effects.^12,13 The principal compound of interest is glycyrrhizin, a saponin formed by glycyrrhetic acid (a triterpenoid aglycone) linked to a glucuronic acid disaccharide. Glycyrrhizin is typically extracted with hot ethanol.¹⁴ Licorice flavonoids contribute to reported activity against Helicobacter pylori and may act as liver protectants.¹⁵ More recently, licorice extracts have been proposed for incorporation into active antioxidant food packaging films based on soy protein.¹⁶

Despite growing interest in sustainable, bio-based composites, the use of agricultural and herbal residues such as licorice root fibers remains poorly understood. Specifically, systematic studies on how fiber size (mesh variation), bundle structure, and interfacial behavior affect mechanical performance, fracture mechanisms, and the validity of micromechanical models are scarce.

In this work, licorice root fibers are randomly oriented within the polymer matrix due to the chosen manufacturing route and the use of short, chopped fibers. This random orientation, common in compression-molded natural-fiber composites, yields quasi-isotropic in-plane behavior and reflects practical, scalable processing. To capture this state in micromechanics, orientation-averaged formulations of Halpin–Tsai and Mori–Tanaka^17–21 are employed, corresponding to a three-dimensionally random fiber distribution. Consequently, the predicted elastic properties reflect realistic load sharing rather than idealized unidirectional reinforcement. Both models are leveraged for their established physical basis in short and natural fiber-reinforced composites. Halpin–Tsai^17,18 offers a simple, first-order estimation of stiffness that incorporates fiber aspect ratio, volume fraction, and geometry, particularly suitable for discontinuous natural fibers with size variability. Mori–Tanaka^19–21 provides a more rigorous mean-field homogenization, accounting for inclusion-matrix interactions, load transfer efficiency, and stress distribution at moderate fiber contents and with improved interfacial bonding. Using both approaches allows a comparative assessment of a semi-empirical model and a micromechanically grounded method, enhancing interpretation and corroborating experimental trends.

The research problem addressed in this study is therefore to establish a clear structure-property relationship for licorice root fiber-reinforced eco-friendly composites by integrating experimental mechanical testing, SEM based fracture analysis, and micromechanical modeling. The composites are fabricated using a conventional molding-based manufacturing process suitable for natural fiber-reinforced polymers. Licorice root fibers, prepared at different mesh sizes (20, 40, 60, and 80) as well as in bundle form, are first dried to minimize moisture-related defects and then mechanically mixed with the polymer matrix to ensure uniform dispersion. Subsequently, the mixture is consolidated under controlled temperature conditions to achieve proper wetting of the fibers and adequate matrix flow. This manufacturing approach is intentionally selected because it is industrially feasible, environmentally compatible, and representative of real applications of eco-friendly composites. Moreover, it allows the investigation of fiber size and morphology effects without introducing additional complexity related to specialized processing routes. The work aims to assess the predictive capability of the Halpin-Tsai and Mori-Tanaka models and to clarify how fiber morphology governs stress transfer and failure mechanisms. This approach provides both scientific insight and practical guidance for the design of sustainable natural fiber composites.

Materials and methods

Residues of licorice root

Licorice root fibers (Figure 1) represent a unique class of functional agro-waste fibers that combine lignocellulosic reinforcement with inherent bioactivity, elevated surface polarity, and enhanced porosity. In contrast to conventional natural fibers such as jute, sisal, and kenaf, which primarily function as passive mechanical reinforcements, licorice root fibers can act as active material constituents. Their comparatively higher content of pectin, extractives, and phenolic compounds increases the density of accessible hydroxyl functional groups, thereby promoting stronger interfacial interactions with polar polymer matrices and potentially reducing the need for chemical surface modification. Furthermore, the presence of bioactive phytochemicals, including glycyrrhizin, flavonoids, and saponins, imparts intrinsic antioxidant and antimicrobial properties, enabling the development of multifunctional composite systems. From a structural perspective, the distinctive microfibrillar architecture and pectin-rich composition may facilitate improved energy dissipation, enhanced toughness, and greater resistance to crack propagation, despite a potentially lower stiffness relative to high-cellulose fibers. From a sustainability standpoint, these fibers are derived from medicinal plant waste, enabling simultaneous material utilization and bioactive compound recovery. This contributes to a reduced agricultural footprint compared with fiber-dedicated crops and enhances the circular-economy value per unit mass. Collectively, these attributes position licorice root fibers as promising alternatives that extend the functional and design capabilities of natural-fiber-reinforced composites beyond those achievable with conventional agro-waste fibers. Table 1 compares the mechanical properties of Licorice fiber with a few conventional natural fibers.^22–24

Figure 1.

Licorice plant and licorice root.

Table 1.

Mechanical performance of licorice root fibers compared to other agro-waste fibers^22–24.

Property	Licorice fiber	Jute	Sisal	Kenaf
Tensile strength	Moderate	High	Very high	High
Elastic modulus	Moderate	High	High	Moderate
Toughness	High	Moderate	Low	Moderate

Licorice root fibers are lignocellulosic and therefore hygroscopic²⁵ and this study characterizes their moisture content (MC). For assessment, two licorice root samples with masses of 0.26 g and 0.243 g were oven-dried at 60°C for 4 h, then immersed in distilled water for 24 h. After immersion, the samples were weighed again, yielding final masses of 0.671 g and 0.681 g, respectively. These results indicate a moderate to high moisture content, which is typical for natural fibers and reflects their porous structure and the microfibrillar morphology of licorice root fibers. Uncontrolled moisture uptake can degrade bonding strength, dimensional stability, and long-term durability of fiber-reinforced composites. Consequently, surface modification and effective moisture management are important strategies to enhance fiber-matrix adhesion. By improving interfacial compatibility and reducing hygroscopic sensitivity, licorice root fibers can be viably employed as reinforcements in bio-based and conventional polymer composites.

To determine the density of licorice root, a 1 cm × 1 cm × 1 cm cube (volume = 1 cm³), as shown in Figure 2, was prepared from dried licorice root material using a precision blade. The cube was weighed on a digital balance with a resolution of 0.01 g. The measured mass was 1.17 g, yielding a bulk density of 1.17 $(\frac{g r}{{c m}^{3}})$ , $(ρ = \frac{m}{V})$ .

Figure 2.

Experimental procedure for measuring the density of licorice root.

In this study, we have performed Fourier Transform Infrared Spectroscopy, also known as FTIR analysis or FTIR Spectroscopy to reach a better understanding about the nature of licorice root residue. The FTIR spectrum of licorice root fibers (Figure 3) reveals the presence of typical functional groups associated with lignocellulosic natural fibers, confirming their complex chemical composition consisting mainly of cellulose, hemicellulose, lignin, and minor extractives. A broad and intense absorption band observed around 3400–3500 cm⁻¹ corresponds to the O-H stretching vibration, which is characteristic of hydroxyl groups present in cellulose and hemicellulose. This broad peak also indicates strong intermolecular hydrogen bonding and the hydrophilic nature of the fibers. The absorption bands appearing near 2920–2850 cm⁻¹ are attributed to C-H stretching vibrations of aliphatic-CH and-CH₂ groups, commonly associated with polysaccharide backbones and waxy components of natural fibers. A noticeable peak around 1730–1650 cm⁻¹ can be assigned to C=O stretching vibrations, which are related to carbonyl groups present in hemicellulose, pectin, and residual lignin. Additionally, the absorption near 1600–1510 cm⁻¹ is associated with the aromatic skeletal vibrations of lignin, confirming its presence in the licorice root fibers. The band observed around 1420–1370 cm⁻¹ corresponds to C-H bending vibrations, while peaks in the range of 1260–1230 cm⁻¹ are attributed to C-O stretching of aryl-alkyl ether linkages, typical of lignin and hemicellulose structures. Strong absorption bands in the region of 1160–1030 cm⁻¹ are related to C-O-C and C-O stretching vibrations, which are characteristic of cellulose and hemicellulose polysaccharides. These peaks confirm the dominance of carbohydrate components in the fiber structure. Finally, the absorption bands below 900 cm⁻¹ are associated with β-glycosidic linkages of cellulose and out-of-plane bending vibrations, further supporting the cellulose-rich nature of licorice root fibers. Overall, the FTIR results confirm that licorice root fibers possess a typical lignocellulosic structure, making them suitable for use as reinforcement in polymer composites and other bio-based materials due to their abundant hydroxyl groups and polysaccharide content.

Figure 3.

FTIR spectra of licorice root.

The X-ray diffraction (XRD) pattern of licorice root fibers that have been examined in this study revealed a typical semi-crystalline structure characteristic of natural lignocellulosic materials (Figure 4). A dominant diffraction peak observed at 2θ ≈ 22°–23° was attributed to the (200) crystalline plane of cellulose I, confirming cellulose I as the main crystalline phase. A broad diffraction region around 2θ ≈ 14°–16° corresponded to the amorphous contribution and overlapping cellulose I planes. The crystallinity index (CrI), calculated using the Segal method, was approximately 55.3%, indicating a moderate degree of crystallinity. This value reflects the coexistence of ordered cellulose microfibrils and amorphous components such as hemicellulose and lignin. The obtained crystallinity level is typical for untreated natural fibers and suggests that licorice root fibers possess a balanced structural organization, making them suitable candidates for reinforcement in bio-based and sustainable composite materials.

Figure 4.

XRD pattern of licorice root.

Preparation of licorice fibers

In this study, to evaluate mechanical performance, the licorice root is prepared as (i) bundled licorice root fibers and (ii) milled fibers ground and sieved to mesh sizes 20, 40, 60, and 80. For preparing the bundling fibers, residues were cut longitudinally and gently widened to facilitate subsequent processing. Each fiber was cut to a length of 35 cm and twisted in a clockwise direction. The midpoint of the twisted bundle was positioned on the rod of a previously constructed stand, the two free ends were joined with an adhesive, and the assembly was twisted clockwise once more to complete the bundle, as shown in Figure 5. The bundles were dried at approximately 30°C until uniform and free of observable distortion. Following drying, bundles were removed from the stand and sectioned into 16 cm lengths for insertion into a standard silicone mold.

Figure 5.

Fabricated stand to prepare bundling licorice root fibers.

Mesh classification is a widely accepted approach for controlling fiber size in natural fiber composites and provides a reproducible method to relate fiber geometry to mechanical and fracture behavior. Therefore, powdered licorice root fibers were prepared from root residues by an initial impact reduction followed by milling to generate fines of decreasing particle size. The crushed material was sequentially milled and sieved to obtain fractions corresponding to mesh sizes 20, 40, 60, and 80. Fraction indices are defined such that mesh-20 denotes the coarsest fraction and mesh-80 the finest. The resulting powders for each mesh fraction are presented in Figure 6.

Figure 6.

Powdered licorice root fibers prepared with different sieve mesh sizes.

Finally, the prepared licorice root fibers were washed repeatedly to remove soluble components. Optional alkaline treatment (5 wt% NaOH, 80°C, 2 h) may be applied to enhance fiber purity by removing hemicellulose, pectin, and surface impurities. Fibers were then rinsed to neutral pH and dried.

In Table 2, the fiber length and diameter distributions were quantitatively evaluated as a function of mesh size (20, 40, 60, and 80) to characterize the geometric variation of licorice root fibers used as reinforcement. The distributions were determined based on representative measurements from each mesh fraction, allowing statistical comparison between different fiber sizes.²⁶ Fiber length and diameter were measured from optical microscopy and SEM images using image analysis software. For each mesh size, a statistically meaningful number of fibers was analyzed to obtain average values and standard deviations. This approach ensures reliable characterization of short natural fibers, which typically exhibit a broad size distribution due to mechanical milling and sieving processes.⁴ Reducing the mesh size leads to a systematic reduction in the length and diameter of the fibers, which is accompanied by a narrower distribution range. This reduction in fiber aspect ratio directly influences stress transfer efficiency, fracture mechanisms, and the applicability of micromechanical models such as Halpin-Tsai and Mori-Tanaka.²⁷

Table 2.

Average fiber length and diameter distributions as a function of mesh size.

Mesh size	Average fiber length (µm)	Average fiber diameter (µm)
Mesh 20	3000 ± 300	57 ± 10
Mesh 40	2200 ± 200	50 ± 8
Mesh 60	1200 ± 150	45 ± 6
Mesh 80	350 ± 100	35 ± 5

Preparation of the composite samples

Araldite LY5052 epoxy system is a low-viscosity resin designed to be used with Aradur 5052, a curing mixture based on polyamines, to form a cold-curing epoxy system. This resin–hardener combination is widely employed in aerospace and industrial composites, tooling, and aircraft repair, and the resin system supplied by Huntsman was used as the matrix for composite development. Key characteristics include a low viscosity that facilitates the impregnation of reinforcement materials, an extended pot life of approximately 2 h for 100 mL at ambient temperature, and an ample processing window that enables the fabrication of comparatively large components. The system cures at ambient temperature with high-temperature resistance after post-curing. Post-curing at 100°C–120°C yields an elevated glass transition temperature and enhanced mechanical properties. Laminates produced with this system exhibit high mechanical strength and favorable dynamic properties. Table 3 summarizes representative properties for the LY5052–Aradur 5052 system, including mixed-system viscosity, cure kinetics, Tg, modulus, and fracture toughness, under clearly defined measurement conditions.

Table 3.

Typical properties of epoxy resin and hardener.

Property	Araldite LY 5052	Aradur 5052	Test method
Density 25°C, g/c $m^{3}$	1.17	0.94	ISO 1675
Viscosity 25°C, cP	1000–1500	40–60	ISO 12058-1

Accurate weighing is essential to prevent deviations in the resin-hardener ratio, which can significantly alter the cured matrix properties. Components were weighed with a validated balance to ensure mass accuracy and reproducibility Thorough mixing was performed to achieve a homogeneous distribution of the resin and hardener, with active inclusion of the vessel walls, bottom, and corners to maximize mixing efficiency and minimize concentration gradients. The resin–hardener ratio used for LY5052-Aradur 5052 is provided in Table 4.

Table 4.

Epoxy system mix ratio: LY 5052 resin to Aradur 5052 hardener.

Product	Parts by weight	Parts by volume
Araldite LY 5052	100	100
Aradur 5052	38	47

Five fiber filler loadings were investigated: mesh 20, mesh 40, mesh 60, mesh 80, and a bundle fiber configuration (Tables 5 and 6). The loadings were defined as fractions of the total reactive system mass (epoxy resin plus hardener). Before incorporating the fibers into the resin, the fillers were dried for 2 days at 35°C under ambient conditions to remove moisture. After drying, the powdered fibers were weighed, and the epoxy resin and hardener were combined in a container and stirred until a homogeneous mixture suitable for molding was achieved. Specimens were fabricated in accordance with ASTM D3039.²⁸ The prepared mixture of powdered fibers with epoxy resin and hardener, together with the silicone mold, is shown in Figure 7.

Table 5.

The weight fraction of all the constituent materials used in the composite samples.

Specimen		$w_{f} (g r) :$ Weight of licorice fiber	$w_{m} (g r) :$ Weight of epoxy resin and hardener	$W_{f} (%) :$ Weight percentage of fibers	$W_{m} (%) :$ Weight percent epoxy adhesive + hardener	$w_{c} (g r) :$ Total specimen weight
Mesh20	Sample 20	2.3	10.36	18	82	12.66
	Sample 21	2.3	9.26	20	80	11.56
	Sample 22	2.3	9.79	19	81	12.09
Mesh40	Sample 40	2.3	8.99	20.5	79.5	11.29
	Sample 41	2.3	9.2	20	80	11.5
	Sample 42	2.3	7.01	25	75	9.31
Mesh60	Sample 60	2.3	9.76	19	81	13.06
	Sample 61	2.3	9.76	19.2	80.8	12
	Sample 62	2.3	10.13	18.2	81.5	12.43
Mesh80	Sample 80	2.3	9.87	18.9	81.1	12.17
	Sample 81	2.3	10.27	18.3	81.7	12.58
	Sample 82	2.3	10.7	17.7	82.3	13
Bundle fibers	Sample 10	2.18	9.9	18	82	12.08
	Sample 11	2.25	9.47	19.2	80.8	11.72
	Sample 12	2.46	9.57	20.5	79.5	12.03

Table 6.

The dimensions of the specimens.

Samples		Gauge length(mm)	Gauge width(mm)	Gauge thickness(mm)	Length of sample pieces(mm)
Mesh20	Sample 20	66.4	13.6	4.3	165
	Sample 21	70.7	13.4	4.24	165
	Sample 22	72.1	13.5	4.17	165
Mesh40	Sample 40	70.5	13.3	3.7	165
	Sample 41	70.5	12.8	3.8	165
	Sample 42	69.7	13.4	3.5	165
Mesh60	Sample 60	67	13.5	4	165
	Sample 61	71.5	13.8	4	165
	Sample 62	63.7	13.4	4.4	165
Mesh80	Sample 80	73.17	13.4	4	165
	Sample 81	66.2	13.5	4.2	165
	Sample 82	67.8	13.6	4.36	165
Bundle fibers	Sample 10	73.17	13.4	4	165
	Sample 11	73.17	13.4	4	165
	Sample 12	73.17	13.4	4	165

Figure 7.

Mixture of powdered fibers with epoxy resin and hardener.

To achieve good dispersion of licorice waste, the epoxy resin and root fibers were mixed at room temperature using a hand mixer for approximately 15 min. For each filler concentration, three specimens were produced and tested, and compared with three specimens of pure epoxy resin (neat epoxy) as a reference. The correct stoichiometric amount of hardener was added and manually mixed, taking care to avoid entrapping air in the blend. The reactive systems were poured into silicone molds and cured. The curing cycle consisted of 12 h at ambient temperature. Specimens for mechanical characterization were thus obtained. The dog-bone test specimens were manufactured in accordance with ASTM D638 (Figure 8). The specification of each sample, including the weight percentage of licorice fiber and epoxy resin, is presented in Table 5. Also, Table 6 provides the corresponding dimensions.

Figure 8.

Prepared samples using a powder processed with mesh sizes 20/40/60/80 and bundled fibers.

The composite samples were fabricated with the total fiber volume fraction held constant across all test conditions to isolate the effects of fiber size (mesh number) and fiber bundling on the composite properties. Maintaining a constant total fiber volume fraction is a standard practice in natural fiber composite studies, as it enables meaningful comparison of mechanical behavior and micromechanical modeling results across different fiber morphologies.²⁶ The volume fraction of all the constituent materials used in the composite samples is given in Table 7.

Table 7.

The volume fraction of all the constituent materials used in the composite samples.

Samples		$v_{f} ({c m}^{3}) :$ Volume of licorice fiber	$v_{m} ({c m}^{3}) :$ Volume of epoxy resin and hardener	$V_{f} (%) :$ Volume percentage of fibers	$V_{m} (%) :$ Volume percent epoxy adhesive + hardener	$v_{c} ({c m}^{3}) :$ Total piece volume
Mesh20	Sample 20	1.9658	8.8547	18	82	10.82
	Sample 21	1.9658	7.9145	20	80	9.88
	Sample 22	1.9658	8.3675	19	81	10.3333
Mesh40	Sample 40	1.9658	7.6837	20.5	79.5	9.4595
	Sample 41	1.9658	7.8632	20	80	9.829
	Sample 42	1.9658	5.9914	25	75	7.9572
Mesh60	Sample 60	1.9658	6.817	19	81	8.7828
	Sample 61	1.9658	8.3418	19.2	80.8	10.3076
	Sample 62	1.9658	8.6581	18.2	81.5	10.6239
Mesh80	Sample 80	1.9658	9.3906	18.9	81.1	11.3564
	Sample 81	1.9658	8.7777	18.3	81.7	10.7435
	Sample 82	1.9658	9.1453	17.7	82.3	11.1111
Bundle fibers	Sample 10	1.8632	8.4615	18	82	10.3247
	Sample 11	1.923	8.094	19.2	80.8	10.017
	Sample 12	2.1025	8.1794	20.5	79.5	10.2819

The mechanical properties of the samples were evaluated using a Santam Company STM-20 universal testing machine (made in Iran). The instrument has a loading capacity of 2 tons and is equipped with auxiliary accessories, movable and wedge jaws, and an extensometer for precise strain measurement.

Theoretical models to predict the mechanical properties of natural composites

Random fiber orientation is commonly observed in natural fiber-reinforced composites manufactured via molding or similar processing techniques. This orientation state leads to quasi-isotropic mechanical behavior and is representative of scalable and industrially relevant processing conditions.

In this work, the assumption of randomly oriented fibers was consistently considered in the mechanical characterization and micromechanical modeling. Orientation-averaged formulations were adopted in the Halpin-Tsai^17,18 and Mori-Tanaka^19–21 models to ensure that the analytical predictions realistically reflect the actual fiber orientation and load-transfer mechanisms within the composite.²⁷

Halpin-Tsai model

For composites reinforced with short and randomly oriented licorice root fibers, the moduli $E_{1}$ and $E_{2}$ are interpreted as effective principal moduli obtained through orientation averaging of the Halpin–Tsai formulation. In this case, the fiber modulus used in the calculations represents an orientation-averaged effective fiber modulus derived from intrinsic fiber properties. This approach is commonly employed for semi-isotropic natural fiber composites and enables meaningful comparison between theoretical predictions and experimental results.²⁹ The composite elastic moduli in the principal material directions are denoted as $E_{1}$ (longitudinal) and $E_{2}$ (transverse).

For the single-layer composite with chopped fibers and random in-plane orientation, Figure 9 depicts a representative configuration in which the material exhibits isotropy in the plane.^30,31 The longitudinal and transverse moduli, $E_{1}$ and $E_{2}$ , are obtained from the same longitudinal transverse relationships employed for a unidirectional chopped-fiber composite, extended to the chopped-fiber case in the Halpin-Tsai framework.^29,32,33 In this context, the effective in-plane stiffnesses correspond to the Halpin-Tsai estimates for isotropic in-plane response, i.e., $E_{r a n d o m}$ and $G_{r a n d o m}$ derived from the underlying unidirectional relations, with the effective Poisson’s ratio $ν_{r a n d o m}$ emerging from the standard connection between axial and transverse strains under uniaxial loading. The descriptions align with the conventional Halpin-Tsai parameterization, including the typical use of the reinforcement geometry factor $ξ$ and the modulus ratio $η$ that captures the influence of fiber geometry and orientation on the composite stiffness.^34,35

E_{r a n d o m} = \frac{3}{8} E_{1} + \frac{5}{8} E_{2}, G_{r a n d o m} = \frac{1}{8} E_{1} + \frac{1}{4} E_{2}

(1)

ν_{r a n d o m} = \frac{E_{r a n d o m}}{2 G_{r a n d o m}} - 1

(2)

where

E_{1}

and

E_{2}

denote the longitudinal and transverse moduli of a single-layer composite with unidirectional discontinuous fibers, respectively. Halpin–Tsai formulations for composites reinforced with unidirectional discontinuous fibers assume circular cross-section fibers arranged on a square lattice, and the equations are aligned with the conventional forms found in the literature.^35,36 The fiber aspect ratio is defined as the ratio of the average fiber length,

l_{f}

, to the fiber diameter,

d_{f}

. This aspect ratio has a significant influence on the longitudinal modulus

E_{1}

of the composite, while the transverse modulus

E_{2}

is largely insensitive to the aspect ratio. Consequently, for a discontinuous-fiber composite,

E_{1}

is smaller than for a corresponding continuous-fiber system.^35,37 Elastic moduli, shear modulus, and Poisson’s ratio according to Halpin–Tsai formulations for a single-layer composite with unidirectional discontinuous fibers are

E_{1} = \frac{1 + 2 (\frac{l_{f}}{d_{f}}) η_{L} ν_{f}}{1 - η_{L} ν_{f}} E_{m}, E_{2} = \frac{1 + 2 η_{T} ν_{f}}{1 - η_{T} ν_{f}} E_{m}, G_{12} = G_{21} = \frac{1 + η_{G} ν_{f}}{1 - η_{G} ν_{f}} G_{m}, ν_{12} = ν_{f} \cdot V_{f} + ν_{m} \cdot V_{m}, ν_{21} = ν_{12} \frac{E_{2}}{E_{1}}

(3)

where

η_{L} = \frac{(\frac{E_{f}}{E_{m}}) - 1}{(\frac{E_{f}}{E_{m}}) + 2 (\frac{l_{f}}{d_{f}})}, η_{T} = \frac{(\frac{E_{f}}{E_{m}}) - 1}{(\frac{E_{f}}{E_{m}}) + 2}, η_{G} = \frac{(\frac{G_{f}}{G_{m}}) - 1}{(\frac{G_{f}}{G_{m}}) + 1}

(4)

and

E_{f}

E_{m}

G_{f}

G_{m}

ν_{f}

ν_{m}

V_{f}

V_{m}

are Young’s modulus, shear modulus, Poisson’s ratio, and volume fractions of fiber and matrix, respectively.

Figure 9.

Single-layer composite with chopped fibers and random orientation.

In the case of long bundle-reinforced composites with all bundles aligned in a single direction (Figure 8, samples 10–12), the material exhibits orthotropic behavior with a principal axis along the bundle direction. The effective elastic properties are therefore evaluated using the Halpin-Tsai model in its formulation for aligned, unidirectional reinforcements.³⁸

Mori-Tanaka model

The Mori-Tanaka method¹⁹ has been widely used by researchers to model the effective behavior of composites. This method enables the determination of the mean field as well as the overall effective stiffness of a composite. The Mori-Tanaka approach can model composites that contain different materials and are composed of multiple phases, even when the particle arrangements are random. In the Mori-Tanaka framework, the concentration tensor is obtained from the following equations.¹⁹

A_{s}^{M T} = A_{s}^{d i l} {[f_{m} I + \sum_{r = 2}^{N} f_{r} A_{r}^{d i l}]}^{- 1}

(5)

where

A_{r}^{d i l}

is given by (6) and

f_{m}

is the volume fraction of the matrix material. If we neglect the interaction between the reinforce particles, we arrive at the dilute saturation approximation. The dilute saturation property tensor is given by the following equation³⁹

A_{r}^{d i l} = {[I + S_{r} C_{1}^{- 1} (C_{r} - C_{1})]}^{- 1}

(6)

where

S_{r}

is the Eshelby tensor of the constituent components. The Eshelby tensor can be determined as a function of the dimensions of the

r^{t h}_(a_{i}^{r})

phase reinforcing factors and the matrix properties³⁹

S_{r} = F (C_{1}, a_{1}^{r}, a_{2}^{r}, a_{3}^{r})

(7)

The Eshelby solves the elastic stress field inside and around an elliptical particle inside an infinite matrix.⁴⁰

If the fibers are distributed randomly in the composite, the overall behavior is isotropic. The distribution of fiber orientations in the composite, described by the probability distribution function P(α, β), must satisfy the following normalization condition²⁰

\int_{0}^{2 π} \int_{0}^{\frac{π}{2}} P (α, β) \sin α d α d β = 1

(8)

If the particles are completely randomly arranged, it will be

(α, β) = \frac{π}{2}

. Based on the Mori-Tanaka model, averaging in different directions, and using the averaging theorem, the following equation is developed for the effective modulus of such a composite²⁰

C = (f_{1} C_{1} + f_{r} 〈 C_{r} : A_{r} 〉) : {(f_{1} I + f_{r} 〈 A_{r} 〉)}^{- 1}

(9)

After simplifying and expanding the equations and using the Hill elastic constants,⁴¹ the bulk modulus and shear modulus of the resulting isotropic composite are calculated as follows²⁰

K = K_{m} + \frac{f_{r} (δ_{r} - 3 k_{m} α_{r})}{3 (f_{m} + f_{r} α_{r})}, G = G_{m} + \frac{f_{r} (η_{r} - 2 G_{m} β_{r})}{3 (f_{m} + f_{r} β_{r})}

(10)

Where the constants mentioned in these equations with index (r) are calculated by equation (13) as follows²⁰

α_{r} = \frac{3 (K_{m} + G_{m}) + k_{r} - l_{r}}{3 (K_{m} + G_{m})}

(11)

β_{r} = \frac{1}{5} {\frac{4 G_{m} + 2 k_{r} + l_{r}}{3 (G_{M} + k_{r})} + \frac{4 G_{m}}{G_{m} + p_{r}} + \frac{2 [G_{m} (3 K_{m} + G_{m}) + G_{m} (3 K_{m} + 7 G_{m})]}{G_{m} (3 K_{m} + G_{m}) + m_{r} (3 K_{m} + 7 G_{m})}}

δ_{r} = \frac{1}{3} [n_{r} + 2 l_{r} + \frac{(2 k_{r} + l_{r}) (3 K_{m} + 2 G_{m} - l_{r})}{G_{m} + k_{r}}]

η_{γ} = \frac{1}{5} [\frac{2}{3} (n_{r} - l_{r}) + \frac{8 G_{m} p_{r}}{G_{m} + P_{r}} + \frac{8 m_{r} G_{m} (3 k_{m} + 4 G_{m})}{3 k_{m} (m_{r} + G_{m}) + G_{m} (7 m_{r} + G_{m})} + \frac{2 (k_{r} - l_{r}) (2 G_{m} + l_{r})}{3 (G_{m} + k_{r})}]

In equation (11),

K_{m}

and

G_{m}

are the shear and bulk modulus of the matrix material, respectively. The Hill constants of the fibers, which are specified with the index (r) in the set of equation (11), are also obtained from the constitutive equation of the fibers with laterally isotropic properties as expressed in equation (12).²⁰

σ_{r} = c_{r} ε_{r}

(12)

C_{r} = [\begin{array}{l} \begin{array}{l} \begin{array}{l} \begin{array}{l} n_{r} \\ l_{r} \end{array} \\ k_{r} - m_{r} \\ \begin{array}{l} 0 \\ 0 \\ 0 \end{array} \end{array} \end{array} & \begin{array}{l} \begin{array}{l}  \end{array} \\ \begin{array}{l} \begin{array}{l} \begin{array}{l} l_{r} \\ k_{r} + m_{r} \end{array} \\ l_{r} \\ \begin{array}{l} 0 \\ 0 \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} k_{r} - m_{r} \\ l_{r} \end{array} \\ k_{r} + m_{r} \\ \begin{array}{l} 0 \\ 0 \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} \begin{array}{l} 0 \\ 0 \end{array} \\ 0 \\ \begin{array}{l} p_{r} \\ 0 \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} 0 \\ 0 \end{array} \\ 0 \\ \begin{array}{l} 0 \\ m_{r} \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} 0 \\ 0 \end{array} \\ 0 \\ \begin{array}{l} 0 \\ 0 \\ p_{r} \end{array} \end{array} \end{array} \end{array} \end{array} \end{array}]

It is worth noting that the stiffness matrix introduced in equation (12) is itself obtained by inverting the compliance matrix of equation (13), which forms the mechanical properties of the developed equivalent single strand.²¹

C_{r} = {[\begin{array}{l} \begin{array}{l} \begin{array}{l} \begin{array}{l} 1 / E_{1}^{f} \\ - ν_{21}^{f} / E_{2}^{f} \end{array} \\ - ν_{31}^{f} / E_{3}^{f} \\ \begin{array}{l} 0 \\ 0 \\ 0 \end{array} \end{array} \end{array} & \begin{array}{l} \begin{array}{l}  \end{array} \\ \begin{array}{l} \begin{array}{l} \begin{array}{l} - ν_{12}^{f} / E_{2}^{f} \\ 1 / E_{2}^{f} \end{array} \\ - ν_{32}^{f} / E_{2}^{f} \\ \begin{array}{l} 0 \\ 0 \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} - ν_{13}^{f} / E_{1}^{f} \\ - ν_{23}^{f} / E_{2}^{f} \end{array} \\ 1 / E_{3}^{f} \\ \begin{array}{l} 0 \\ 0 \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} \begin{array}{l} 0 \\ 0 \end{array} \\ 0 \\ \begin{array}{l} 1 / G_{23}^{f} \\ 0 \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} 0 \\ 0 \end{array} \\ 0 \\ \begin{array}{l} 0 \\ 1 / G_{31}^{f} \\ 0 \end{array} \end{array} & \begin{array}{l} \begin{array}{l} 0 \\ 0 \end{array} \\ 0 \\ \begin{array}{l} 0 \\ 0 \\ 1 / G_{12}^{f} \end{array} \end{array} \end{array} \end{array} \end{array} \end{array}]}^{- 1}

(13)

Therefore, by calculating the equivalent single-strand (or single-fiber) compliance matrix from equation (13) and inverting the relevant functions, the equivalent single-strand Hill constants are determined according to equation (12). By substituting these values into equation (11) and using equation (10), the bulk modulus and shear modulus of the composite reinforced with straight licorice root fibers having random fiber orientation in the matrix material are calculated based on the concept of an equivalent single-strand. Finally, using equation (14), the elastic modulus and Poisson’s ratio of the volume element representing the specific case shown in Figure 9 will also be characterized.³⁹

E = \frac{9 K G}{3 K + G}, ν = \frac{3 K - 2 G}{6 K + 2 G}

(14)

The derivation of equation (14) assumes that, despite local heterogeneities such as fiber curvature or clustering (Figure 10), the composite behaves as an effective isotropic medium at the macroscopic scale due to the overall random fiber orientation. Figure 9 represents the idealized case used in micromechanical modeling, where the spatial averaging over many randomly oriented fibers leads to isotropic elastic behavior. Under this assumption, the classical isotropic elasticity relationships between E, $υ$ , K, and G become valid, resulting in equation (14).⁴²

Figure 10.

Representative volume element containing curved fibers with random orientation and clustering.

The Mori–Tanaka method is also employed to evaluate the effective elastic response of the aligned bundle-reinforced composite by modeling the bundles as equivalent cylindrical inclusions embedded in the matrix. For this state, the Eshelby tensor $S_{r}$ corresponds to a cylindrical inclusion aligned with the reinforcement direction. This formulation yields a transversely isotropic (orthotropic in engineering constants) effective response, consistent with the aligned microstructure.^19–21

Characterization of the properties of composites reinforced with straight licorice root fibers arranged in clustered configurations

In the previous section, the properties of composites reinforced with straight licorice root fibers were calculated under the assumption of random orientation of the powdered fibers and in the absence of clustering. When characterizing the properties of the composite containing straight licorice root fibers, the fibers may accumulate into clusters. Shi et al.²⁰ developed a two-parameter model for this purpose. Their model is based on the initial assumption that the clustered powdered fibers, as depicted in Figure 11, behave as spherical particles embedded in the resin matrix. A schematic representation of the representative volume element (RVE) considered by Shi et al. is shown in Figure 11. The key difference between the volume element in Figure 11 and the more general case in Figure 10 is the absence of curved fibers.

Figure 11.

Representative volume element containing straight fibers with random orientation and clustering.

In the representative volume element considered by Shi et al.,²⁰ the powdered fibers are assumed to be uniformly distributed and fully dispersed within the resin, outside the virtual hypothetical environment. Consequently, the mechanical properties of the spherical particles differ from those of the matrix, which itself contains the powdered fibers in a well-distributed and non-aggregated state. They divided the total volume within the resin environment into two parts: the portion contained inside the spherical particles and the portion in the surrounding matrix.²⁰

V_{f i b e r s} = V_{f i b e r s}^{i n c l u s i o n} + V_{f i b e r s}^{m}

(15)

They introduced two different coefficients that represent the bulk state follows²⁰:

μ = \frac{V_{i n c l u s i o n}}{V}, k = \frac{V_{f i b e r s}^{i n c l u s i o n}}{V_{f i b e r s}}

(16)

Let $V_{i n c l u s i o n}$ denote the volume of spherical particles and $V$ the total volume of the unit cell. The parameter $μ$ represents the fraction of the volumetric element occupied by the spherical particles. Where $μ = 1$ , all fibers are uniformly distributed within the resin environment, corresponding to the special case shown in Figure 9 and indicating a state of maximum homogeneity. Reducing $μ$ increases the degree of inhomogeneity in the material and enlarges the regions containing clustered fibers. The parameter $k$ denotes the ratio of fibers located inside the spherical particles to the total number (or volume) of fibers in the unit cell. When $= 1$ , all fibers lie inside the spherical particles, yielding maximum inhomogeneity. If $μ = k$ , the environment is in a homogeneous distribution of fibers. However, for a fixed $μ$ , increasing $k$ relative to $μ$ enhances inhomogeneity in the material. The volume fraction of fibers in the environment is given by the following equation.

f_{f i b e r s} = \frac{V_{f i b e r s}}{V}

(17)

Using equations (15) to (17), the volume fraction of fibers inside the spherical particle and the matrix environment is obtained as follows, respectively.³⁹

\frac{V_{f i b e r s}^{i n c l u s i o n}}{V_{i n c l u s i o n}} = \frac{f_{f i b e r s} k}{μ}, \frac{V_{f i b e r s}^{m}}{V - V_{i n c l u s i o n}} = \frac{f_{f i b e r s} (1 - k)}{1 - μ}

(18)

Figure 11 plays a critical role in linking the experimental observations to the theoretical framework. This clarification ensures consistency between the microstructural evidence, the experimental results, and the analytical model assumptions.⁴³ Moreover, Figure 11 serves as a microstructural justification for the two-phase volume fraction partitioning approach adopted in equations (15)–(18), where fibers are conceptually divided into those located inside aggregated inclusions and those dispersed within the surrounding matrix. The schematic representation of fiber aggregation supports the assumptions used to define the fiber volume fraction inside the inclusion and the matrix environment, which are subsequently employed in the micromechanical modeling.⁴² Therefore, using the Mori-Tanaka model and volume fractions obtained for the inside of the spherical particle and the matrix environment, the mechanical properties of the spherical particle and the matrix are calculated as follows:

K_{i n} = K_{m} + \frac{(δ_{r} - 3 K_{m} α_{r}) f_{r} k}{3 (μ - k f_{r} + k f_{r} α_{r})}

K_{o u t} = K_{m} + \frac{f_{r} (1 - k) (δ_{r} - 3 k_{m} α_{r})}{3 [1 - μ - f_{r} (1 - k) + f_{r} (1 - k) α_{r}]}

(19)

G_{i n} = G_{m} + \frac{f_{r} k (η_{r} - 2 G_{m} β_{r})}{2 (μ - f_{r} k + f_{r} k β_{r})}

G_{o u t} = G_{m} + \frac{f_{r} (1 - k) (η_{r} - 2 G_{m} β_{r})}{2 [1 - μ - f_{r} (1 - k) + f_{r} (1 - k) β_{r}]}

Where the index

i n

means the inside of the spherical particle and

o u t

represents the environment outside the spherical particle or the matrix material. The Tensor-Eshelby for a spherical member whose

\frac{l}{d}

is equal to the unit radius of the spherical particle and is given as follows⁴⁰:

S_{1111} = S_{2222} = S_{3333} = \frac{7 - 5 ν_{o u t}}{15 (1 - ν_{o u t})}

S_{p (11, 22)} = S_{p (11, 33)} = S_{p (22, 33)} = \frac{5 ν_{o u t} - 1}{15 (1 - ν_{o u t})}

(20)

S_{p (1, 2) p (1, 2)} = S_{p (1, 3) p (1, 3)} = S_{p (2, 3) p (2, 3)} = \frac{4 - 5 ν_{o u t}}{15 (1 - ν_{o u t})}

In this case,

ν_{o u t}

which is the Poisson’s ratio of the matrix, no longer takes the value corresponding to the pure resin, and is calculated by the values calculated for the matrix containing licorice root fibers with appropriate dispersion, using equations (19) and (21).²⁰

ν_{o u t} = \frac{3 K_{o u t} - 2 G_{o u t}}{6 K_{o u t} + 2 G_{o u t}}

(21)

After expanding the equations, the mechanical properties of the unit cell shown in Figure 11 are calculated as follows²⁰:

K = K_{o u t} [1 + \frac{μ (\frac{K_{i n}}{K_{o u t}} - 1)}{1 + α (1 - μ) (\frac{K_{i n}}{K_{o u t}} - 1)}], G = G_{o u t} [1 + \frac{μ (\frac{G_{i n}}{G_{o u t}} - 1)}{1 + α (1 - μ) (\frac{G_{i n}}{G_{o u t}} - 1)}]

(22)

α

and

β

in equation (22) are calculated by the following equation³⁹:

α = \frac{1 + ν_{o u t}}{3 (1 - ν_{o u t})}, β = \frac{2 (4 - 5 ν_{o u t})}{15 (1 - ν_{o u t})}

(23)

Therefore, by specifying the two parameters $k$ and $μ$ the volume fraction of licorice root fibers inside the spherical particle and their surrounding resin is determined using equation (18), while the properties of the spherical particles and surrounding resin are obtained from equation (19). Subsequently, the properties of the unit cell are estimated using equations (21) to (23).

Results and discussion

Licorice root fiber waste was prepared in two forms: (A) bundled fibers, and (B) fibers ground and passed through sieves with mesh sizes of 20, 40, 60, and 80. Bundled and powdered fibers were combined with epoxy resin adhesive and hardener according to the standard density specified in the Huntsman adhesive catalogue, and approximately 20% of the licorice root fibers were hand-processed into sample pieces. After fabricating three samples representing different states, the pieces were subjected to tensile testing to determine their mechanical properties in different conditions. The stress–strain responses of the three samples were averaged and synthesized into a single representative stress–strain curve. Ultimately, five stress–strain curves were assembled for comparative visualization and to conclude.

In addressing the macroscopic behavior, this work adopts a hierarchical perspective, with macro-scale modeling treated as the final scale. At the meso-scale, a volumetric element containing licorice root fiber waste, present in multiple straight configurations, was considered, with fibers distributed and oriented in diverse directions. The micromechanical framework was developed first for a specific case comprising only straight licorice root fibers oriented in various directions. Subsequently, the case in which powdered licorice root fibers are incorporated into a resin matrix as a solid mass was investigated.

It is noteworthy that all micromechanical equations presented employ the properties of the developed equivalent fibers as inputs. The inputs to these models are fibers with transverse-isotropic properties, and the corresponding equations are formulated on that basis.

SEM and optical micrographs of the composite’s fracture surface are shown in Figures 12 and 13(a)–(e). The images of the fracture surface of all samples that show fiber-matrix debonding and fiber pull-out are shown in these figures. The corresponding stress-strain diagrams for all samples prepared with meshes 20/40/60/80 and bundle fiber are shown in Figure 14. And their average curve is presented in Figure 15.

Figure 12.

Optical micrographs of composites^, fracture surface showing fiber-matrix debonding and fiber pull-out, scale bar = 500 µm (70×).

Figure 13.

(a) SEM images of fracture surfaces of mesh 20 licorice root fiber-reinforced composites. (b) SEM images of fracture surfaces of mesh 40 licorice root fiber-reinforced composites. (c) SEM images of fracture surfaces of mesh 60 licorice root fiber-reinforced composites. (d) SEM images of fracture surfaces of mesh 80 licorice root fiber-reinforced composites. (e) SEM images of fracture surfaces of bundled licorice fiber-reinforced composites.

Figure 14.

Stress-strain curves for all composite specimens.

Figure 15.

Average Stress-Strain curves for all composite specimens.

A comparison table of the estimated elastic modulus, yield stress, and ultimate tensile stress for all tested samples is provided in Table 8. Table 9 lists, in its second column, three bundled-fiber samples with specified diameters. In the third column, three samples with pure epoxy resin adhesive, and in the fourth column, three composite specimens reinforced with bundled licorice root fibers. These results are based on tensile tests and include comparisons of the elastic modulus, yield stress, and ultimate stress. Strain energy is obtained as the area under the stress-strain curve and is calculated from the standard integral. The ultimate strain and toughness for samples produced with licorice root fiber waste, as well as the average sample from laboratory tests, are presented in Table 10, with a comparison diagram in Figure 16. The toughness or strain energy is determined from the corresponding equation.

Table 8.

Comparison of the elasticity modulus, yield stress, and ultimate stress for all samples.

	Young modules (GPa)					Yield stress (MPa)					Ultimate stress (MPa)
	Mesh size & bundle					Mesh size & bundle					Mesh size & bundle
	Bundle fibres	Mesh 20	Mesh 40	Mesh 60	Mesh 80	Bundle fibres	Mesh 20	Mesh 40	Mesh 60	Mesh 80	Bundle fibres	Mesh 20	Mesh 40	Mesh 60	Mesh 80
Sample1	2	2.18	1.82	1.67	1.11	32.1345	27.4521	31.926	33.045	32.597	32.135	27.45	31.926	33.04	32.6
Sample2	2.7	2.38	2.63	1.43	1.25	25.2797	28.1787	33.057	34.388	30.684	25.28	28.18	33.057	34.39	30.68
Sample3	2.5	1.96	1.79	1.11	1.3	35.5127	27.5247	29.921	32.212	32.807	35.513	27.52	29.921	32.21	32.81
Mean value	2.4	2.1733	2.08	1.4033	1.22	30.9756	27.7185	31.635	33.215	32.029	30.976	27.72	31.635	33.21	32.03

Table 9.

Modulus of elasticity, yield stress, and ultimate stress for bundled fiber samples, pure epoxy resin samples, and composite samples reinforced with bundled licorice root fibers.

	Bundle fiber			Matrix			Bundle fiber-reinforced matrix
	Young modules (GPa)	Yield stress (MPa)	Ultimate stress (MPa)	Young modules (GPa)	Yield stress (MPa)	Ultimate stress (MPa)	Young modules (GPa)	Yield stress (MPa)	Ultimate stress (MPa)
Sample1	0.5	15.7062	15.7062	3	24.0735	24.0735	2	32.1345	32.1345
Sample2	0.636	16.5723	16.5723	3	24.0735	24.0735	2.7	25.2797	25.2797
Sample3	0.833	26.2109	26.2109	3	24.0735	24.0735	2.5	35.5127	35.5127
Mean value	0.656	19.496	19.496	3	24.0735	24.0735	2.4	30.9756	30.9756

Table 10.

The failure strain, toughness, and their average for all specimens.

	Failure strain ( $ε_{f}$ )					Toughness (MPa)
	Mesh size & bundle					Mesh size & bundle
	Bundle fibers	Mesh 20	Mesh 40	Mesh 60	Mesh 80	Bundle fibers	Mesh 20	Mesh 40	Mesh 60	Mesh 80
Sample1	0.013	0.012	0.015	0.0179	0.0218	0.218	0.215	0.2212	0.275	0.331
Sample2	0.0105	0.0118	0.01362	0.0196	0.022	0.133	0.242	0.211	0.312	0.311
Sample3	0.0122	0.0125	0.0167	0.0245	0.0197	0.215	0.1562	0.229	0.3063	0.295
Mean value	0.0119	0.0121	0.01511	0.02067	0.02117	0.18867	0.2066	0.2204	0.297	0.31233

Figure 16.

Comparison of the strain energy of all composite specimens.

In Table 8, the small difference observed between the yield stress and ultimate tensile stress is an inherent experimental characteristic of the studied composites rather than a measurement artifact. The licorice root fiber reinforced composites exhibit quasi-brittle behavior, which is typical for polymer composites reinforced with short, randomly oriented natural fibers. Once yielding begins, damage mechanisms such as matrix cracking and fiber-matrix interfacial debonding are rapidly activated, resulting in a limited plastic deformation region before final fracture.

Furthermore, the short fiber length associated with different mesh sizes (20-80) restricts effective load transfer after yielding, leading to a rapid transition from elastic deformation to failure. This behavior is more pronounced in composites containing bundled fibers due to local stress concentration and premature crack initiation. Consequently, the yield stress and ultimate stress values appear very close. This trend is physically meaningful and consistent with the experimentally observed fracture mechanisms, confirming the reliability of the tensile test results.

SEM fracture micrograph analysis of composites

Micrographs, particularly SEM and optical microscopy, are powerful qualitative tools for assessing dispersion, revealing fiber distribution patterns, interfacial quality, and agglomeration tendencies without requiring quantitative analysis. Uniform dispersion is indicated by an even spatial distribution of fibers throughout the matrix, the absence of large fiber-rich or matrix-rich domains, and limited fiber agglomeration. In well-dispersed systems, individual fibers or small bundles appear embedded and distinct rather than forming dense clusters. Dispersion uniformity influences load-transfer efficiency, crack propagation, and interfacial stability under stress. Favorable dispersion typically yields fibers well encapsulated by the matrix, reduced interfacial voids, and a gradual transition between fiber surface and matrix. Poor dispersion is evidenced by fiber pull-outs, interfacial gaps, and localized fiber stacking. In micrographs, agglomeration appears as dark, dense fiber regions, overlapping or entangled fibrils, and uneven contrast across the cross-section. Such features disrupt uniform stress transfer and can create microstructural discontinuities.

From a microstructural perspective, licorice root fibers can achieve acceptable to good dispersion uniformity when processing promotes fiber separation and matrix wetting. SEM and optical micrographs (Figures 12 and 13(a)–(e)) typically reveal that licorice root fibers exhibit a heterogeneous morphology with irregular cross-sections, surface roughness, and fibrillar substructures. These inherent features strongly influence dispersion behavior once the fibers are embedded in a polymer or bio-based matrix. Due to their natural origin and fibrillar nature, licorice root fibers may show a tendency to self-associate, particularly if insufficiently separated during processing.

Micrographs frequently indicate random fiber orientation. Random orientation supports isotropic behavior when dispersion is uniform. However, preferential alignment or layered distribution suggests flow-induced segregation, and fiber sedimentation or surface accumulation indicates dispersion instability. Uniform dispersion is inferred when fibers appear consistently distributed across different magnifications and observation zones.

Mesh 20 (coarse fibers, high aspect ratio)

The SEM fracture micrographs of mesh 20 composites (Figure 13(a)) reveal extensive fiber pull-out with long exposed licorice root fibers, indicating that fracture is governed primarily by interfacial debonding rather than fiber rupture. The rough fracture surface and visible gaps between fibers and matrix suggest insufficient interfacial adhesion due to the relatively low specific surface area of coarse fibers. The high aspect ratio enables load transfer along the fiber length. However, once debonding initiates, fibers are easily extracted from the matrix, resulting in pull-out-dominated failure. This mechanism dissipates fracture energy but limits stiffness and strength enhancement.

Mesh 40 (intermediate fiber size)

For mesh 40 composites (Figure 13(b)), the fracture surface exhibits a mixed fracture morphology, combining partial fiber pull-out with noticeable matrix cracking. Compared to mesh 20, fiber dispersion is improved, and the fiber–matrix interface appears more intimate, leading to enhanced stress transfer. Cracks are frequently deflected at fiber–matrix interfaces, indicating a transition from purely interfacial failure toward a more cooperative fiber–matrix fracture process. This balanced behavior reflects a favorable compromise between fiber aspect ratio and interfacial surface area.

Mesh 60 (fine fibers, optimal dispersion)

The SEM micrographs of mesh 60 samples (Figure 13(c)) are characterized by short fiber pull-out, frequent fiber breakage, and pronounced crack deflection and crack pinning mechanisms. The fracture surface is dense and tortuous, with minimal interfacial gaps, indicating strong fiber–matrix bonding. The increased specific surface area of fine licorice root fibers promotes effective stress transfer, forcing cracks to propagate along longer and more complex paths. Consequently, energy dissipation occurs through fiber fracture, microcracking, and crack deflection rather than simple debonding, resulting in the highest fracture resistance and energy absorption among the studied mesh sizes.

Mesh 80 (very fine fibers, low effective aspect ratio)

In mesh 80 composites (Figure 13(d)), the dominant fracture feature is matrix cracking, while fiber pull-out is minimal and fiber fracture is less effective in arresting crack propagation. Excessive size reduction significantly lowers the effective fiber aspect ratio, causing licorice root fibers to behave more like particulate fillers than true reinforcements. As a result, the ability of fibers to bridge cracks and redistribute stresses is reduced, leading to relatively smooth fracture surfaces and a brittle, matrix-dominated failure mode.

Bundle fiber composites

SEM fracture micrographs of bundle fiber composites (Figure 13(e)) show severe interfacial debonding, void formation, and bundle splitting. Poor impregnation of the matrix into fiber bundles creates resin-starved regions and stress concentration sites. Cracks preferentially initiate within the bundles and propagate rapidly along weak inter-bundle interfaces, resulting in premature and catastrophic failure. The non-uniform stress distribution within the bundle structure severely limits effective load transfer and fracture resistance.

Effect of fiber aspect ratio on stress transfer

The fiber aspect ratio (length-to-diameter ratio) plays a critical role in load transfer efficiency from the matrix to the reinforcement. High-aspect-ratio fibers provide a larger embedded length within the matrix, enabling more effective stress transfer through interfacial shear stresses. When the fiber aspect ratio is reduced due to milling, sieving, or processing-induced breakage, the effective load-bearing capability of the fiber decreases. Short fibers may not reach the critical fiber length, which is required for the fiber to develop its maximum tensile stress before interfacial debonding occurs. As a result, stress transfer becomes incomplete, leading to premature fiber pull-out rather than fiber fracture. This mechanism directly contributes to the overestimation of stiffness by micromechanical models, which typically assume ideal fiber geometry and sufficient aspect ratio.

Influence of interfacial area and fiber size reduction

Reducing fiber size (or mesh size) increases the specific interfacial surface area between the fibers and the matrix. While a larger interfacial area can enhance stress transfer in theory, this benefit strongly depends on the quality of interfacial bonding. In natural fiber composites, increased interfacial area may also intensify stress concentrations at fiber ends, promote interfacial debonding due to weak chemical compatibility, increase sensitivity to moisture absorption, and microvoid formation. Therefore, when the fiber aspect ratio decreases simultaneously with an increase in interfacial area, the net effect can be deterioration of stress transfer efficiency, particularly if interfacial adhesion is not sufficiently strong.

Crack propagation mechanisms

Fiber aspect ratio and interfacial characteristics significantly influence crack initiation and propagation paths. High aspect ratio fibers tend to bridge cracks effectively, forcing crack deflection and increasing crack tortuosity. These delay crack growth and improve damage tolerance. Low aspect ratio fibers provide limited crack-bridging capability, allowing cracks to propagate more directly through the matrix or along weak interfaces. Increased interfacial area with weak bonding promotes interfacial crack propagation, where cracks preferentially grow along the fiber–matrix interface rather than being deflected or arrested. Consequently, composites reinforced with finer fibers often exhibit a transition from fiber-dominated fracture to matrix- or interface-dominated fracture mechanisms.

Energy absorption and toughening mechanisms

Energy absorption during fracture is governed by mechanisms such as fiber pull-out, debonding, crack deflection, and plastic deformation of the matrix. The balance between these mechanisms changes with fiber aspect ratio. Long fibers enhance energy absorption through extensive crack bridging and frictional pull-out over longer embedded lengths. Short fibers dissipate less energy during pull-out due to reduced frictional sliding distance. Increased interfacial area may increase the number of debonding sites, but each event absorbs less energy when fibers are short. As a result, although finer fibers increase the number of fiber-matrix interfaces, the total absorbed fracture energy may decrease, leading to reduced toughness and impact resistance.

Halpin–Tsai and Mori–Tanaka predictions for uniformly powdered licorice root fibers in a polymer matrix

In this section, the mechanical properties obtained for various sample pieces are compared with the analytical predictions from the Halpin-Tsai and Mori-Tanaka micromechanics models, assuming a uniform fiber distribution. The comparisons are presented in Figure 17. Table 11 summarizes the calculations of the Halpin-Tsai and Mori-Tanaka moduli for uniformly powdered licorice root fibers, derived from the experimental results across all samples.

Figure 17.

The obtained results for the elastic modulus of different specimens are compared with the obtained analytical results using Halpin-Tsai and Mori-Tanaka models in the case of uniform fiber distribution.

Table 11.

Comparison of the experimental results with those obtained by the Halpin-Tsai and Mori-Tanaka models for uniformly powdered licorice root fibers.

Experimental
	E(MPa)	$E_{f}$	$E_{m}$	$ρ_{f}$	$ρ_{m}$	$V_{f}$	$V_{m}$	$v_{12}$	$G_{f}$	$G_{m}$
Mesh 20	2300	419	3120	1.17	1.17	0.18	0.82	0.3	160	1200
Mesh 40	2120	419	3120	1.17	1.17	0.2	0.8	0.3	160	1200
Mesh 60	1760	419	3120	1.17	1.17	0.19	0.81	0.3	160	1200
Mesh 80	1500	419	3120	1.17	1.17	0.19	0.81	0.3	160	1200
Bundle fiber	2000	419	3120	1.17	1.17	0.18	0.82	0.3	160	1200

Halpin-Tsai
	$η_{L}$	$η_{T}$	$η_{G}$	$E_{1}$	$E_{2}$	$G_{12}$	$G_{21}$	$E_{ran}$	$G_{ran}$	$v_{ran}$
Mesh 20	−0.0082	−0.4056	−0.9819	2576	2417.6	671.7	671.7	2477	926.4	0.337
Mesh 40	−0.0112	−0.4056	−0.7225	2485	2400	890	890	2431.8	910.6	0.3352
Mesh 60	−0.0112	−0.4056	−0.763	2735	2400	896	896	2526	941.9	0.34
Mesh 80	−0.406	−0.406	−0.7484	2450	2450	841.1	841.1	2450	918.7	0.333
Bundle fiber	−0.0043	−0.4056	−0.763	2700	3110	910	910	-	-	-

Mori-Tanaka
	$E_{1}^{f}$	$E_{2}^{f}$	$K_{m}$	$α_{r}$	$δ_{r}$	$η_{r}$	$β_{r}$	$K$	$G$	$E$
Mesh 20	2580	1.36	2600	0.999	4.332	1.446	1.362	2.39	1046	2738
Mesh 40	2566.3	1344	2600	1.041	5.161	1.623	1.412	2400	1085	2830
Mesh 60	2607	1402.4	2600	1.043	5.18	1.672	1.328	2414	1063	2780
Mesh 80	2607	1402	2600	1.042	5.246	1.585	1.387	2420	985	2602

The Halpin-Tsai model predicts longitudinal and transverse modules in the range of 2450–2735 MPa, showing good agreement with experimental trends but with a moderate overestimation, particularly for mesh 60. The Mori-Tanaka approach yields Young’s modulus values between 2602 and 2830 MPa, consistently higher than both experimental and Halpin-Tsai. This behavior is attributed to the assumption of ideal load transfer and uniform stress distribution within the composite. Figure 17 demonstrates that Halpin-Tsai provides closer agreement with experimental data, while Mori-Tanaka represents an upper-bound estimation.

Mechanical properties in licorice root fiber–reinforced composites with clustered fiber distributions

In Figure 18(a)–(e), variations in the elastic modulus of licorice-reinforced composites are presented as functions of the agglomeration indices μ and k. Table 12 reports the Young’s modulus calculations obtained via the Mori-Tanaka method for the non-uniform distribution of licorice root fibers, derived from experimental results and parameterized by μ and k for mesh 20.

Figure 18.

(a) Young’s modulus of a composite containing licorice root fibers in a clustering state for mesh 20. (b) Young’s modulus of a composite containing licorice root fibers in a clustering state for mesh 40. (c) Young’s modulus of a composite containing licorice root fibers in a clustering state for mesh 60. (d) Young’s modulus of a composite containing licorice root fibers in a clustering state for mesh 80.

Table 12.

Calculated Young’s modulus using the Mori-Tanaka method for the non-uniform distribution of licorice root fibers (mesh 20) and different clustering indices.

Mesh 20	Agglomeration index (μ)
	0.1	0.2	0.3	0.4	0.5	0.6	0.8	0.9	1
	Young’s modulus (MPa)
k = 0.5	1551.4	2238.2	2506.7	2649.8	2738.8	2799.5	2876.8	2903	2924.1
k = 0.6	1317.3	2087.5	2396.5	2563.2	2667.4	2738.8	2830.2	2861.2	2886.2
k = 0.7	1102.1	1943.9	2290.1	2478.8	2597.6	2679.2	2784.2	2819.9	2848.8
k = 0.8	903.4	1807	2187.1	2396.5	2529.2	2620.7	2738.8	2779.1	2811.7
k = 0.9	719.3	1676.3	2087.5	2316.3	2462.2	2563.2	2694	2738.8	2775.1
k = 1	547.6	1551.4	1991	2238.2	2396.5	2506.7	2649.8	2699	2750
Resin	547.6	547.6	547.6	547.6	547.6	547.6	547.6	547.6	547.6
Fully-dispersed	2924.1	2924.1	2924.1	2924.1	2924.1	2924.1	2924.1	2924.1	2924.1

As illustrated in Figure 18 (a)–(d), when the indices μ and k are equal, the material properties converge toward a completely homogeneous state. Increasing μ drives the material toward homogeneity, while decreasing μ enhances inhomogeneity, reducing the strengthening effect and steering the behavior toward that of the pure resin. Conversely, decreasing k, which represents the degree of fiber aggregation within the spherical particles, increases the strengthening effect as the material trends toward homogenization. When k approaches unity, a completely agglomerated state emerges, with all powdered fibers concentrating within the spherical particles. These observations indicate that greater inhomogeneity exerts a pronounced negative impact on the modulus of the surrounding environment. By promoting a more uniform distribution of fibers and achieving a homogeneous environment, the strengthening effect rises, and the mechanical properties exhibit more pronounced enhancement. In fact, with increasing mass (or content), the system experiences greater inhomogeneity, and the heightened fiber-fiber interactions reduce the net contribution of fiber environment interactions, leading to a deterioration of mechanical properties.

Figure 19 illustrates the influence of the clustering phenomenon, as described by the Mori-Tanaka model, on Poisson’s ratio. Unlike the behavior observed for Young’s modulus, Poisson’s ratio decreases with increasing dispersion of the uniformly powdered licorice root fibers. Given that the Poisson’s ratio of the developed equivalent fibers is lower than that of the matrix material (approximately 0.3 vs 0.34), the strengthening effect produced by a more homogeneous environment leads to a more pronounced reduction in Poisson’s ratio as the reinforcement intensity increases. Conversely, a reduction in the reinforcing effect, potentially due to fiber clustering, diminishes the impact of the powdered fibers on the matrix, causing the Poisson’s ratio to approach that of the resin.

Figure 19.

Poisson’s ratio of a composite containing powdered licorice root fibers in a clustering state.

From another perspective, as the filling fraction of powdered licorice root fibers and their diffusion within the resin environment increase, the material tends toward a more homogeneous state, accompanied by an increase in the elastic modulus. Under a constant load in one direction, the corresponding elongation along the length increases, while the lateral deformation decreases, resulting in a lower Poisson’s ratio as defined by the ratio of transverse to longitudinal strains. Table 13 reports the Poisson’s ratio calculations within the Mori-Tanaka framework for the non-uniform state of powdered licorice root fibers, derived from experimental results and the parameters μ and k for mesh 20.

Table 13.

Calculated Poisson’s ratio using the Mori-Tanaka model for agglomerated licorice fiber-reinforced composite (mesh 20) and different agglomeration parameters μ and k.

Mesh 20	Agglomeration index (μ)
	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	Poisson’s ratio
k = 0.5	0.3302	0.3217	0.3156	0.3119	0.3092	0.3078	0.3067	0.3059	0.3053	0.3048
k = 0.6	0.3327	0.3238	0.3176	0.3136	0.3109	0.3092	0.308	0.307	0.3063	0.3057
k = 0.7	0.3343	0.326	0.3196	0.3153	0.3125	0.3106	0.3092	0.3081	0.3073	0.3066
k = 0.8	0.3363	0.3282	0.3218	0.3172	0.3141	0.312	0.3104	0.3092	0.3082	0.3075
k = 0.9	0.3378	0.3302	0.324	0.319	0.3157	0.3133	0.3116	0.3103	0.3092	0.3083
k = 1	0.3392	0.3324	0.326	0.3207	0.3172	0.3146	0.3128	0.3113	0.3101	0.3089
Fully-dispersed	0.3045	0.3045	0.3045	0.3045	0.3045	0.3045	0.3045	0.3045	0.3045	0.3045
Resin	0.3392	0.3392	0.3392	0.3392	0.3392	0.3392	0.3392	0.3392	0.3392	0.3392

Accuracy of theoretical models

The combined effects of reduced fiber aspect ratio and increased interfacial area elucidate why micromechanical models such as Halpin-Tsai and Mori-Tanaka tend to overpredict the elastic properties at smaller fiber sizes. Both models assume near-ideal conditions, including perfect interfacial bonding, uniform stress transfer, and regularized fiber geometry. As the fiber aspect ratio decreases and interfacial damage mechanisms become more influential, these assumptions become progressively less tenable, leading to deviations from measured responses. To assess the predictive capability of the Halpin-Tsai and Mori-Tanaka formulations, a quantitative error analysis was conducted by comparing the predicted Young’s modulus with the experimentally measured modulus across all mesh sizes and the bundled-fiber sample, as illustrated in Figures 20 and 21. The analysis reveals that both models systematically overestimate the elastic modulus, with the magnitude of overprediction increasing for finer mesh sizes. This trend reflects the diminishing load-transfer efficiency and the growing influence of interfacial defects and dispersion quality at low aspect ratios. Notably, the Mori-Tanaka model, when extended to include clustering effects, exhibits a lower mean error and stronger correlation with the experimental data (higher R²) than Halpin–Tsai. At Mesh 60 and Mesh 80, the observed increases in error are attributed to factors such as fiber breakage, further reductions in effective aspect ratio, non-uniform dispersion, and particle agglomeration phenomena not captured by the Halpin-Tsai framework. These findings underscore the importance of accounting for microstructural realism, including dispersion state and interfacial integrity, in predicting the elastic response of natural-fiber composites.

Figure 20.

Comparison of the Halpin-Tsai model and experimental results with the coefficient of linear determination $R^{2}$ .

Figure 21.

Comparison of the Mori-Tanaka model and experimental results with the coefficient of linear determination $R^{2}$ .

Conclusions

This study evaluated the mechanical properties and modulus predictions of licorice root fiber waste-reinforced composites, comparing two fiber morphologies, bundled fibers and powders produced by sieving into mesh sizes 20, 40, 60, and 80, and assessing the influence of powder fineness and packing on stiffness, toughness, and ductility. The predictive performance of two homogenization models for natural-fiber systems was also examined. Powder fineness increases with decreasing mesh size, and the measured modulus of elasticity exhibits a decreasing trend in the order: bundled fibers > mesh 20 > mesh 40 > mesh 60 > mesh 80. The bundled-fiber composite demonstrates the highest stiffness, reflecting superior resistance to elastic deformation, whereas the finest powder (mesh 80) yields the lowest stiffness. This trend underscores the crucial role of fiber form and dispersion state in load-transfer efficiency. Across the sieving sizes, finer powders enhance toughness, with mesh 80 displaying the greatest energy absorption. The observed increase in toughness with powder fineness indicates improved impact resistance and a reduced propensity for abrupt failure, likely arising from more distributed deformation and altered crack pathways. The finest powder (mesh 80) leads to higher average ultimate strain for both bundled- and powdered-fiber composites, suggesting an expanded regime of plastic deformation prior to catastrophic failure. This enhancement in ductility accompanies a trade-off with stiffness, illustrating the balancing act between stiffness and deformability in natural-fiber composites. The results highlight how fiber morphology and the corresponding dispersion state modulate the mechanical response of the composite. A reduction in fiber aspect ratio diminishes effective stress transfer and crack-bridging capability, while an increased interfacial area promotes debonding and matrix-dominated fracture. These combined effects accelerate crack propagation and reduce energy absorption, partly explaining deviations between micromechanical predictions and experimental observations for finely sized natural fibers. The findings emphasize the sensitivity of predictive accuracy to particle size and dispersion quality. Extending from mesh 20 to mesh 60, improvements in fiber dispersion and interfacial bonding favor a transition from pull-out-dominated fracture to mechanisms dominated by fiber fracture and crack deflection, thereby enhancing energy absorption and fracture toughness. Further refinement to mesh 80 reduces the effective fiber aspect ratio, promoting matrix-controlled brittle fracture and diminishing toughness. Bundled fibers exhibit comparatively poorer fracture behavior due to limited matrix penetration and stress localization. Both micromechanical models yielded reasonable upper-bound predictions for the studied systems. However, the Mori-Tanaka model demonstrates superior agreement with experimental data for uniformly powdered licorice root fiber composites. Deviations at the smallest particle sizes reveal intrinsic limitations of continuum-based homogenization when applied to natural, heterogeneous reinforcements, signaling a need for model refinements or alternative approaches to capture size- and morphology-dependent effects. The results delineate general trends in stiffness, toughness, and ductility as functions of fiber form and powder fineness, and they provide a comparative assessment of homogenization models for licorice root fiber-reinforced composites. Practical implications include guidance for processing parameters aimed at optimizing dispersion and interfacial bonding to tailor performance for targeted applications. Future work should explore a broader range of fiber contents, processing strategies to improve separation and wetting, and the development or calibration of models that better accommodate the heterogeneity of natural fibers across length scales.

Footnotes

ORCID iD

Mohammad Hossein Yas

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

Plocher

Panesar

. Review on design and structural optimisation in additive manufacturing: towards next-generation lightweight structures. Mater Des 2019; 183: 108164. https://doi.org/10.1016/j.matdes.2019.108164

Collins

Nechifor

Tanasă

, et al. Valorization of lignin in polymer and composite systems for advanced engineering applications–a review. Int J Biol Macromol 2019; 131: 828–849. https://doi.org/10.1016/j.ijbiomac.2019.03.069

Fiore

Di Bella

Valenza

. The effect of alkaline treatment on mechanical properties of kenaf fibers and their epoxy composites. Compos B Eng 2015; 68: 14–21. https://doi.org/10.1016/j.compositesb.2014.08.025

Bledzki

Gassan

. Composites reinforced with cellulose based fibres. Prog Polym Sci 1999; 24: 221–274. https://doi.org/10.1016/s0079-6700(98)00018-5

Pickering

. Properties and performance of natural-fibre composites. Elsevier, 2008.

Puttegowda

Rangappa

Jawaid

, et al. Potential of natural/synthetic hybrid composites for aerospace applications. Sustainable composites for aerospace applications. Elsevier, 2018, pp. 315–351.

Housemna

Lacey

. The licorice root in industry. Ind Eng Chem 1929; 21: 915–917. https://doi.org/10.1021/ie50238a008

Hayashi

Sudo

. Economic importance of licorice. Plant Biotechnol 2009; 26: 101–104. https://doi.org/10.5511/plantbiotechnology.26.101

Edwards

. Determination of lignin and cellulose in forages by extraction with triethylene glycol. J Sci Food Agric 1973; 24: 381–388. https://doi.org/10.1002/jsfa.2740240405

10.

Komarov

. Handbook for Laboratory Work on the Chemistry of Wood and Cellulose. Gostekhlesizdat, 1934, 55.

11.

Sdykov

Abduazimov

. Lignins of Allochruza paniculata and Glycyrrhiza glabra. Chem Nat Compd 2002; 38: 288–290. https://doi.org/10.1023/a:1020496414684

12.

Bai

Yao

G-D

Ren

, et al. Triterpenoid saponins and flavonoids from licorice residues with anti-inflammatory activity. Ind Crop Prod 2018; 125: 50–58. https://doi.org/10.1016/j.indcrop.2018.08.075

13.

Schmid

Dawid

Peters

, et al. Saponins from European licorice roots (Glycyrrhiza glabra). J Nat Prod 2018; 81: 1734–1744. https://doi.org/10.1021/acs.jnatprod.8b00022

14.

Kim

H-S

Lee

S-Y

Kim

B-Y

, et al. Effects of modifiers on the supercritical CO2 extraction of glycyrrhizin from licorice and the morphology of licorice tissue after extraction. Biotechnol Bioproc Eng 2004; 9: 447–453. https://doi.org/10.1007/bf02933484

15.

Fukai

Marumo

Kaitou

, et al. Anti-Helicobacter pylori flavonoids from licorice extract. Life Sci 2002; 71: 1449–1463. https://doi.org/10.1016/s0024-3205(02)01864-7

16.

Han

Wang

. Preparation and characterization of antioxidant soy protein isolate films incorporating licorice residue extract. Food Hydrocoll 2018; 75: 13–21. https://doi.org/10.1016/j.foodhyd.2017.09.020

17.

Ashton

Halpin

Petit

. Primer on composite materials: analysis, 1969. (No Title).

18.

Halpin

. Stiffness and expansion estimates for oriented short fiber composites. J Compos Mater 1969; 3: 732–734. https://doi.org/10.1177/002199836900300419

19.

Mori

Tanaka

. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 1973; 21: 571–574. https://doi.org/10.1016/0001-6160(73)90064-3

20.

Shi

D-L

Feng

X-Q

Huang

, et al. The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. J Eng Mater Technol 2004; 126: 250–257. https://doi.org/10.1115/1.1751182

21.

Yas

Heshmati

. Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load. Appl Math Model 2012; 36: 1371–1394. https://doi.org/10.1016/j.apm.2011.08.037

22.

Mwaikambo

Ansell

. Chemical modification of hemp, sisal, jute, and kapok fibers by alkalization. J Appl Polym Sci 2002; 84: 2222–2234. https://doi.org/10.1002/app.10460

23.

Pastorino

Cornara

Soares

, et al. Liquorice (Glycyrrhiza glabra): a phytochemical and pharmacological review. Phytother Res 2018; 32: 2323–2339. https://doi.org/10.1002/ptr.6178

24.

Sisti

Totaro

Vannini

, et al. Retting process as a pretreatment of natural fibers for the development of polymer composites. Lignocellulosic composite materials. Springer, 2017, pp. 97–135.

25.

Akhil

Radhika

Saleh

, et al. A comprehensive review on plant‐based natural fiber reinforced polymer composites: fabrication, properties, and applications. Polym Compos 2023; 44: 2598–2633. https://doi.org/10.1002/pc.27274

26.

Pickering

Efendy

MGA

. A review of recent developments in natural fibre composites and their mechanical performance. Compos Part A-Appl Sci Manuf 2016; 83: 98–112. https://doi.org/10.1016/j.compositesa.2015.08.038

27.

Thomason

. The influence of fibre length and concentration on the properties of glass fibre reinforced polypropylene: 5. Injection moulded long and short fibre PP. Compos Part A-Appl Sci Manuf 2002; 33: 1641–1652. https://doi.org/10.1016/s1359-835x(02)00179-3

28.

Plangpleng

Charoenphun

Polpanich

, et al. Flexible gamma ray shielding based on natural Rubber/BaSO4 nanocomposites. Radiat Phys Chem 2022; 199: 110311. https://doi.org/10.1016/j.radphyschem.2022.110311

29.

S-Y

Lauke

Mäder

, et al. Tensile properties of short-glass-fiber-and short-carbon-fiber-reinforced polypropylene composites. Compos Appl Sci Manuf 2000; 31: 1117–1125. https://doi.org/10.1016/s1359-835x(00)00068-3

30.

Affdl

JCH

Kardos

. The Halpin‐Tsai equations: a review. Polym Eng Sci 1976; 16: 344–352. https://doi.org/10.1002/pen.760160512

31.

Gay

. Composite materials: design and applications. CRC Press, 2022.

32.

Cox

. The elasticity and strength of paper and other fibrous materials. Br J Appl Phys 1952; 3: 72–79. https://doi.org/10.1088/0508-3443/3/3/302

33.

Deoray

Kandasubramanian

. Review on three-dimensionally emulated fiber-embedded lactic acid polymer composites: opportunities in engineering sector. Polym-Plast Technol Eng 2018; 57: 860–874. https://doi.org/10.1080/03602559.2017.1354226

34.

Advani

Tucker

III . The use of tensors to describe and predict fiber orientation in short fiber composites. J Rheol 1987; 31: 751–784. https://doi.org/10.1122/1.549945

35.

Landel

Nielsen

. Mechanical properties of polymers and composites. CRC Press, 1993.

36.

Halpin

. Effects of environmental factors on composite materials, 1969.

37.

Gibson

. Principles of composite material mechanics. CRC Press, 2007.

38.

Kaw

. Mechanics of composite materials. Taylor & Francis, 2005.

39.

Rafiee

Ghorbanhosseini

. Stochastic multi-scale modeling of randomly grown CNTs on carbon fiber. Mech Mater 2017; 106: 1–7. https://doi.org/10.1016/j.mechmat.2017.01.001

40.

Eshelby

. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the royal society of London Series A Mathematical and physical sciences 1957; 241: 376–396. https://doi.org/10.1098/rspa.1957.0133

41.

Hill

. A self-consistent mechanics of composite materials. J Mech Phys Solid 1965; 13: 213–222. https://doi.org/10.1016/0022-5096(65)90010-4

42.

Benveniste

. A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech Mater 1987; 6: 147–157. https://doi.org/10.1016/0167-6636(87)90005-6

43.

Christensen

. Mechanics of composite materials. Dover Publications, 2005.