1 Introduction

In today's manufacturing industries, producing failure-resistant composites for various automotive and aircraft parts is a major challenge. It is important to analyze the performance of parts to prevent unexpected failures and ensure the safety of both humans and machines. Composite materials could serve as an ideal substitute for conventional materials when it pertains to achieving lightweight and better mechanical properties [1]. Polymeric composites are known for their improved fatigue resistance, higher stiffness and toughness, lightweight nature, and versatility in terms of size and geometry [2, 3]. Consequently, there has been a significant increase in the use of this material in many applications [4,5,6,7,8]. This is because composites can offer superior properties like enhanced strength, lightweight, corrosion resistance, increased natural frequencies, and longer lifespan [9, 10].

Polymeric composites are created by combining fibers and a matrix [11]. Fibers, such as E-glass fiber, are widely used in industries like automotive, aerospace, marine, and military due to their strength [12, 13]. They are also increasingly employed in gas industries, construction, and home appliances [2]. E-glass fiber is commercially accessible and provides low cost and high tensile strength, making it suitable for various fiber composites [14,15,16]. Glass fibers have advantages such as affordability, high tensile strength, chemical resistance, insulation properties, lightweight, and versatility in industrial products [17, 18]. Researching the fiber and matrix content of E-glass reinforced composites can enhance the mechanical properties of machine components, including automotive and aircraft parts. Polyester resin, on the other hand, offers benefits such as strong adhesion, easy availability, and compatibility with different reinforcement forms during the composite-forming process.

When materials are loaded over a prolonged time, creep behaviors dictate the structural stabilities of the composites [19, 20]. Laminating fibers and matrices in different weight ratios is an approach to creating a unique composite structure [21,22,23,24,25]. Yet, there is a paucity of studies assessing the influence of fiber and matrix concentration on the creep behavior of E-glass/Polyester composite. Understanding creep behavior is necessary when designing parts for long-term use [4, 26]. Creep testing helps determine a material's resistance to deformation. It provides data on how much strain a material exhibits under specific load and temperature conditions, enabling engineers to select materials with appropriate creep resistance for applications where long-term stability is crucial [27]. In addition, creep testing is significant in evaluating a material's resistance to time-dependent deformation, predicting its service life, aiding material selection and design, ensuring safety and reliability, and complying with industry standards. It plays a crucial role in industries such as aerospace, power generation, oil and gas, and any field where materials are subjected to prolonged stress or high temperatures.

To this end, this study aims to examine the creep behavior of E-glass/polyester composite with different loading conditions. The influence of the quantity of fiber and matrix in a composite is investigated by simulating the creep sample with various weight concentrations. Several studies have investigated the impact of fiber and matrix contents on the mechanical properties of composite structures [28]. Brauner et al. [29] analyzed the creep behavior of glass fiber/polypropylene using various loading conditions. The outcome demonstrates that having creep throughout the play range aids in achieving the best potential performance. However, the disadvantage of this approach is its difficulty to apply in sophisticated composite layers. On the other hand, Hossein Darban et al. [30] Formulates a novel buckling model for a Bernoulli–Euler Nano beam resting on a Pasternak elastic foundation. The model incorporates the local-nonlocal stress-driven gradient elasticity theory to account for size-dependency and it provides insightful evidence about microstructural analysis. Similarly, Julia R. Greer et al. [31] Reports about the classical laws of mechanics and states that mechanical properties are independent of sample size. However, experiments and molecular dynamics simulations have shown that crystals exhibit size effects at the sub-micron scale. These size effects can be explained by strain gradients and also by the dependence of yield strength on sample size. Further F. Cornacchia et al. [32] investigate nanostructures within classical continuum theory by incorporating a second-order strain gradient nonlocal theory. It explores different Nano plate configurations, materials, aspect ratios, and nonlocal ratios, providing dimensionless results for transverse displacements, normal stresses, and shear stresses by comparing them with the classical theory. Moreover, Wenxian et al., Lai and Liu [33, 34] conduct elastic and elastic–plastic studies, different kinds of stress assessment using FEA, and reports that along the stress classification line, the average of all the component stresses of the cylindrical shell under internal pressure is determined and the membrane stress is referred to as the mean value of the stresses.

To generalize, the previous research has extensively examined the creep behavior of composite materials, considering various factors such as temperature, fiber volume ratio [26], loading condition [20, 28], fiber orientation, and creep rupture characteristics [35, 36]. Although significant progress has been made in these investigations, none of them have provided conclusive evidence regarding the optimal quantities of fiber and matrix for develo** composites with superior creep strength. Therefore, it is essential to design and construct a new experimental setup that can achieve a balanced weight composition of the composite, which has not been explored in previous studies. Additionally, the specific configuration of composite laminate susceptible to creep loading, used in this research, has not been previously investigated. Moreover, studying the fiber weight ratio of composite materials is of significant importance for several reasons. The fiber weight ratio directly influences the mechanical properties of composites. As the fiber volume fraction increases, the stiffness, strength, and load-bearing capacity of the composite material generally improve [37]. Composite materials are valued for their high strength-to-weight ratio. By studying the fiber weight ratio, researchers and engineers can determine the optimal balance between the weight of the fibers and the matrix material. Increasing the fiber weight ratio allows for a reduction in the amount of matrix material, resulting in lighter composites without compromising strength. This is particularly important in industries such as aerospace, automotive, and sports equipment manufacturing, where weight reduction is a primary consideration. Higher fiber weight ratios lead to enhanced tensile strength, compressive strength, flexural strength, and impact resistance. As such, studying the fiber weight ratio helps optimize composite materials for specific applications [38]. Therefore, by studying the fiber weight ratio, researchers can determine the minimum fiber content required to achieve the desired mechanical properties. This helps in optimizing the composite's cost-effectiveness by minimizing the use of costly fibers while still meeting performance requirements [39]. The primary challenge in creating the composite structure lies in determining the appropriate ratio of composite components, namely the reinforcement (fiber) and the matrix [40, 41]. Consequently, conducting a study on E-glass/polyester composites while considering variable fiber-matrix weight ratios is of great significance, and by examining the impact of different fiber and matrix weight ratios on the creep behavior of E-glass/polyester composites, it can reduce material fracture caused by layer delamination [42]. While enhancing the bonding strength within the laminate. Typically, delamination happens concurrently at the interface between various layers and it is a distinct and localized damaging event [43]. Therefore, by understanding the optimal weight ratio between the fiber and matrix in the composite and by properly determining the weight concentration of fiber and matrices, it could optimize mechanical properties, achieving weight reduction, cost optimization, and ensuring durability which enables researchers and engineers to design and develop composites tailored for specific applications in various industries, ranging from aerospace and automotive to home and sporting goods. The remaining part of the study is organized as follows. Section 2 presents the material and method followed by presenting and discussing the results in Sect. 3 and Sect. 4 concludes.

2 Material and methods

2.1 Materials

Polyester resin is utilized in this investigation as the matrix. It is made by dissolving vinyl monomers with linear long-chain polymers. Strong mechanical properties, resistance to corrosion, lightweight, and affordability are some of its major attributes. It has densities between 1.1 and 1.43 g/cm3 and a glass transition temperature between 70 and 120 °C. As reinforcement E-glass fibers were used. The fibers were obtained from World Glass Fiber Private Limited Company. While selecting E-glass fiber among various fiber types, different factors are taken into account. For instance, in contrast to other materials, it is available in a wide range of forms, has excellent strength characteristics, is inexpensive, and offers remarkable performance for structural application. Similarly, Trimethyl hexamethylene diamine was also used as a hardener to accelerate the formation of the composite. Further, to ease the removal of the formed composite from the mold, a wax (Miracle Gloss V3) mold-releasing agent was used.

2.2 Methods

For the test sample preparation 65/35, 55/45, and 35/65 fiber-to-matrix concentrations are utilized. This is because using these compositions helps to create strongly tightened and highly bonded laminate. Further, by pelleting the content of composite constituents, lightweight could be developed without affecting the load resistance capacity. Moreover, it enables the reduction of the cost of constituent materials (resin, fiber, and hardener) of the composite. The method of impregnation used was the hand lay-up technique due to ease of operation. To start with, wax was applied to the bottom of a mold, the shape of which is easy to separate the object from the mold. Over the wax, a layer of a premix of the polyester and hardener in the ratio of 10:1 was applied. Then, the fiber matrix weight ratio was maintained at 65/35, 55/45, and 35/65. A portion of the fibers was laid on top of the matrix layer. Thereafter, a layer of the matrix was laid on top of the fibers. Further, on top of that, the fibers were sprinkled again and the process continued till the required size of the composite was obtained as demonstrated in Fig. 1 of the methodological framework. Finally, the composite inside the mold was cured for the desired period of 2 and a half days at room temperature. Then, the final composite product was obtained as shown in Fig. 2.

Fig. 1
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The framework of the study methodology

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Fig. 2
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Finished structure of E-glass/polyester composite

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2.3 Creep experiment

To conduct the creep experiment, the WP600 creep machine was used. Originally the American Society for Testing and Materials, created ASTM D2990, a standard test technique, to determine the fiber-reinforced composites' tensile, compressive, and creep properties [44]. Therefore, the dimension and geometry of test samples were prepared to meet the requirement of ASTM D2990 in desired sizes for each composition of fiber-matrix weight ratio as shown in Fig. 3. Two specimens were prepared for each fiber-matrix composition and a total of six specimens were tested using creep loads at room temperature. The test specimen is clamped in the sample holder to protect it from stress. The deformation or extension of the test specimen during loading was measured with a dial gauge. The gauge was connected with the upper movable sample holder and the tensile force was generated by weight load and transferred to the specimen via the transmission lever which the weight load has been hanged. Then, the test was done by mounting the specimen in the sample holder and applying a constant tensile creep load. The deformation value of the specimen was displayed in the dial gauge and each value was recorded. Finally, the creep response of different fiber-to-matrix weight ratios has been determined until the test samples are broken.

Fig. 3
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Illustrative visualization of the overall process of composite formation and experimentation

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2.4 Micrograph analysis of creep surface.

The following figures display photos of creep fractures on the E-glass composite surface. The evidence for a well-trapped fiber and matrix is shown in Fig. 4. The fiber pulls out in place of fiber fracture demonstrating the absence of void and porous nature, and fibers are consistently spread over the matrix. This suggests that there has been an improvement in their interfacial adhesion. The shattered matrix and fiber in Fig. 5 illustrate how the sharing of particles and fiber and the small voids are evidence for the absence of fiber. This is because the matrix is unable to cover the fiber mate sufficiently and precipitate non-uniform adhesion force between the laminate. Following this many voids developed in the surface of the composite and stress concentration was increased. Thus, the load-transferring capacity through the fiber–matrix interface was decreased. The micrograph image of the composite shown in Fig. 6 reveals that some areas of the surface are covered with air-bubbled matrix and coagulated resin. These manufacturing defects result the weak interfacial bonding among the fibers and the polymer.

Fig. 4
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Micrograph of 65% fiber creep surface

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Fig. 5
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Micrograph of 55% fiber creep surface

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Fig. 6
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Micrograph of 35% fiber creep surface

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2.5 Theoretical analysis

To represent the creep model in the finite element analysis (FEA), the Maxwell model was applied. To use the Maxwell model k1, k2, and k3 (material constant) must be determined first. The general creep equation to represent the Maxwell model is given as [26],

$${\text{Creep strain}}\left( {{}_{{\text{c}}} } \right) = {\text{k}}1*{\upsigma }^{{{\text{k}}2}}* {\text{t}}^{{{\text{k}}3}}* {\text{Exp}}.*\left( { - \frac{{\text{Q}}}{{{\text{RT}}}}} \right)$$
(1)

where σ is the applied stress, t is the time of creep testing, Q is the activation energy, R is the Boltzmann’s constant and T is the absolute temperature. In this study, the test was conducted at room temperature and constant for all creep tests. Hence the Q/RT term has been taken to be zero and according to [26] (1) becomes,

$${\text{Creep strain}}\left( {{}_{{\text{c}}} } \right) = {\text{k}}1*{\upsigma }^{{{\text{k}}2}}* {\text{t}}^{{{\text{k}}3}}$$
(2)

For the FEA using ansys, the constant k1,k2, and k3 are determined as an input. k3 was determined by taking the slope of log strain versus log time plot for each weight concentration and load as presented in Fig. 7a. Similarly, k2 was found from the log strain versus log stress graph in slope bases as shown in Fig. 7b. Finally, by putting the values of k2 and k3 in the general creep equation, k1 can be obtained. The material constant for each weight of composite at different loads is summarised in Table 1.

Fig. 7
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a log strain versus log time and b log strain versus log stress for 65% fiber

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Table 1 Creep constant for each weight ratio used in FEA
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2.6 Finite element modeling for creep analysis

For the finite element analysis (FEA) ansys16 software package has been employed. Since it comprises various features and tools which are more convenient for numerical investigation. The three-dimensional composite test specimen was modeled using Ansys composite pre-post (ACP Pre) as shown in Fig. 8a and the quarter symmetric portion of the creep specimen has been taken from the overall specimen structure to minimize the computational cost and time. Various parameters are needed as input to conduct the FEA. These input parameters are obtained from the experiment. To conduct the analysis, primarily the structure of the test specimen could be discretized to be appropriate for the computational tool. There are various settings for the generation of mesh. To robust and realistic results, the distribution of mesh elements is tactically controlled [45]. Following this, the mesh independence (grid independence) test was done first. It was conducted by customizing different mesh sizes to the mesh setting until getting an acceptable number of elements and nods in the manner the best analysis solution could be achieved with the available computational resources.

Fig. 8
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a 3D Composite model and b Loading, boundary condition, and Finite element mesh of creep specimen

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Table 2. Summarizes grid independence tests. The various mesh sizes result in the different number of nodes and elements. At 0.03 mm mesh size 774,016, the number of elements and 110, 8919 nodes are computed, and after 0.03 mm, similar elements and similar nodes are obtained and further proceeding has no effect on the result rather than consuming computational time and cost. Consequently, using 774,016 triangular elements with 110, 8919 nodes, the finite element analysis has been done. Figure 8b presents the finite element mesh of the test model and for the analysis, the appropriate boundary condition was applied to the creep specimen. The bottom area of the specimen is supported fixed and the tensile force was applied over the top area of the specimen in the manner the tool holder of the creep testing machine was fixed at the lower end and loaded with tensile force on top of it which are similar with used in the experimental test as shown in Fig. 8b with red circles.

Table 2 Grid independence test
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3 Results and discussion

The comparison between the experimental (EXP) and the finite element analysis (FEA) results is illustrated in the following figures. Each figure shows the creep behavior of the composite material under various loads at a constant time. For the experimental and finite element analysis, three different weight ratios were used. For each weight ratio, three creep loads (20, 30, and 40 N) are applied. As the load is applied, the specimen is initially deformed at a manner of quick rate, but as time exceeds the rate of deformation slowly decreases and becomes constant. When the time increases further from the previous, the rate of strain becomes constant for a long time and the secondary stage, which is the most important part of the creep curve has occurred. The minimal creep rate of the three compositions of composite materials has occurred at the secondary state.

Figure 9 presents the result of 65% weight composition. Based on the information provided, it appears that the experiment involved applying loads of 20 N, 30 N, and 40 N individually to a test specimen. From the figure, it is mentioned that the load was progressively raised over time, and the deformation of the specimen increased along with the load. Deformation refers to the change in shape or size of an object under the action of external forces and the term strain is also mentioned in relation to the experiment. Strain is a measure of the deformation experienced by a material relative to its original size or shape. In this case, as the load increased, the strain of the test specimen also increased. This suggests that the material underwent greater deformation as the load was increased. Fracture refers to the separation or breaking of a material into two or more pieces. The result further states that the test specimen was fractured completely. In this context, it suggests that the applied load eventually exceeded the strength of the specimen, leading to its failure and complete fracture.

Fig. 9
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A comparison of experimental and FEA results of Strain versus time for 65% weight at different loads

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Figure 10 shows the weight composition of 55% with 20, 30, and 40 N loads to examine the creep resistance capability. The experiment involves subjecting the sample to different loads 20 N, 30 N, and 40 N. These loads are applied to examine the creep resistance capability of the material. Creep refers to the tendency of a material to deform or undergo plastic flow under the influence of a constant load over an extended period. It is an important property to consider for materials that will be subjected to long-term stress or load-bearing applications. Based on the information provided, it is stated that as the load increased from 20 to 40 N, both in the experimental and finite element analysis, the developed strain was increased. This means that as the load increased, the material experienced greater deformation or elongation. This suggests that the material tested in weight percentages of 55% exhibited a higher degree of deformation or strain under the applied loads compared to the material tested with 65% weight. This indicates a lower resistance to creep for the material in Fig. 10.

Fig. 10
figure 10

A comparison of experimental and FEA results of Strain versus time for 55% weight at different loads

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Likewise, as Fig. 11 illustrates, time-dependent strain was developed with three distinct loads and a weight concentration of 35%. In this case, the highest strain and lowest creep resistance were observed. This implies that the material exhibited a large amount of deformation under load and had poor resistance to long-term deformation at elevated temperatures. From the data, it can be inferred that there were similarities in the way the strain increased for each weight ratio tested. This suggests that the weight ratio of the components had a consistent influence on the deformation behavior of the material. Therefore, the composite with a weight percentage of 65% exhibited good creep strain compared to the weight percentages of 55% and 35%. This suggests that the composite with a higher weight percentage of the specific component had better resistance to long-term deformation under load at elevated temperatures. The addition of fiber percentage in the composite is believed to contribute to the increased deformation resistance of the material. Fiber reinforcement can enhance the load-bearing capacity and stiffness of composite materials, making them more resistant to deformation. Since, the fibers act as reinforcements, distributing applied loads and impeding the movement of dislocations within the material. As a result, the composite with a higher fiber percentage exhibited improved resistance to deformation, as demonstrated by its lower strain values.

Fig. 11
figure 11

A comparison of experimental and FEA results of Strain versus time for 45% weight at different loads

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This data set shows a close relation between the experimental and numerical results with minimal difference. The environment is one of the main causes of this difference and one of the key variables in the analysis is humidity, which varies throughout time [26]. The experiment treated the humidity as constant whereas, in the numerical simulation, the change was ignored. Another factor is the way the specimen was fixed. The specimen slipped negligibly during the experiment, and in the simulation, this issue did not occur.

Figure 12 shows the modulus of elasticity for experimental and finite element results of the three composite weight percentages regarding cree** time. Creep testing is therefore a time-dependent process, with the test specimen gradually deforming throughout the test period until creep rapture occurs. Subsequently, the modulus of elasticity of each composition was dropped as the loading period rose. This is a result of the test specimen experiencing increasing deformation upon tensile loading at each time interval and Elasticity decreases as a result of greater deformation. Figure 9 demonstrates that the experimental and finite element results for the composite with a weight percentage of 65% have a greater elasticity value than the other. This demonstrates that increasing the fiber concentration in the composite can enhance the strength properties. The modulus of elasticity of the composites was shown to rise as fiber content increased and these materials are appropriate for structural applications because of their high stiffness [14]. Moreover, the presence of a high elasticity indicates high stiffness and this relationship provided a clear and certain indication of the ability of this type of reinforcement to reduce the formation of gaps and voids within the matrix during the molding process [26]. However, simply adding more fiber to a composite does not necessarily result in improved mechanical properties, as uneven fiber results in weak bonding between the lamina and micro cracking developed in the composite [46].

Fig. 12
figure 12

A comparison of experimental and FEA results of Modulus of elasticity for different weight ratios at 40 N load

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With finite element analysis, mechanical parameters like as strength, bending, temperature distribution, and stress throughout the whole component can be evaluated [47]. It could be possible to look at creep behavior using isotropic composite properties [48]. In this analysis, we evaluated the stress in the entire structure of the specimen as one value to differentiate the strength between each composition.

Figure 13 shows the finite element result of E-glass/polyester composite material with 65% weight. As depicted in Fig. 13a the maximum total deformation displayed in the red color of the test specimen was 7.59 mm and the transferred stresses through the available matrix as shown in Fig. 13b are 62.4 Mpa. The equivalent strain developed when it was gradually loaded is 2.6 as seen in Fig. 13c. This outcome confirms that the composite has an adequate fiber and matrix concentration and that the numerical and experimental findings correlate satisfactorily.

Fig. 13
figure 13

a Total deformation, b equivalent stress, and c equivalent strain of 65% weight ratio

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Figure 14 presents the composite result with 55% fiber and 45% matrix concentration. In this concentration the fiber content was reduced to 55% however, the content of the matrix increased to 45%. As a result, total deformation, equivalent stress, and creep strain values are 9.25 mm, 0.76 Mpa, and 3.51, respectively. This is not only the effect of fiber but including the matrix, which increased from 35 to 45%. It may be noted that the specimens are completely delaminated and the layer of the composite has been separated as soon as the load is applied [49]. Figure 15 presents the results of the composite specimen with 35% fiber and 65% matrix concentration. It reveals that 10.03 mm deformation is shown in Fig. 15a. Hence, the fiber content dropped to 35% while the matrix concentration increased to 65%. This shows that the excessive content of the matrix material can result in the formation of bubbles during the preparation of a composite. Following this, surface voids and uneven surface structures occurred in the composite during curing time. Therefore, the constituent of the composite could be balanced to increase creep strength [50].

Fig. 14
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Total deformation a equivalent stress b and equivalent strain c of 55% weight ratio

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Fig. 15
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Total deformation a equivalent stress b and equivalent strain c of 35% weight ratio

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Moreover, the values of equivalent stress for this concentration are 80.27 Mpa as shown in Fig. 15b. This is due to the contents of the fiber and matrix the composite comprised. Hence, the amount of fiber was reduced to 35% but the main load-carrying element in a composite structure is the reinforced fiber, and the strength of the composite increases as the fiber concentration increases [51]. As such, the resistance capacity of the composite was decreased accordingly. Therefore, the fiber and matrix content utilized in a composite is technically balanced and the layers are bonded in a compatible manner. On the other hand, when fewer matrixes are utilized, it is difficult to impregnate the fiber sufficiently which results in inadequate load transmission between the resin and fiber.

4 Conclusion

In this study, an investigation of the influence of fiber-matrix concentration on the creep strength of E-glass/polyester composite was presented and the main findings are summarized below.

  1. 1.

    The results indicated that the stress transferred increased with a higher percentage of matrix content. Specifically, stress values of 62.43, 70.76, and 80.27 MPa were obtained with matrix contents of 35%, 45%, and 65%, respectively. This implies that for better load resistance, the matrix quantity should be appropriately proportioned with the reinforced fiber.

  2. 2.

    The study highlighted the effect of matrix concentration on the total deformation of the structure. As the matrix content increased, the composite structure exhibited higher creep deformation and this emphasized the importance of the fiber-matrix relationship in determining the creep characteristics of the composite.

  3. 3.

    The study found that an imbalance in fiber content within the composite led to manufacturing flaws and weakened creep strength.

  4. 4.

    Insufficient impregnation of the fiber occurred when fewer matrixes were used, resulting in inadequate load transmission between the resin and fiber.

  5. 5.

    Among the investigated weight concentrations, the composite with 65% fiber weight demonstrated the most favorable creep behavior. This suggested that beyond this value, the weight ratio of the reinforcement could enhance creep characteristics.

  6. 6.

    Increasing reinforcement extends the secondary stage in the creep curve which improves breakage time, and stress distribution, reducing stress levels and increasing the modulus of elasticity and stiffness.

  7. 7.

    Finite element results show a close correlation between experimental and numerical findings, supporting the idea that E-glass/polyester composites in vehicle body components offer several benefits. Such as improved failure resistance, lightweight design, lower fuel consumption, and environmental sustainability.