Macro-mechanical analysis of tensile strength of glass/carbon fiber reinforced plastics hybrid composites under hydrothermal environment

The material properties of composite materials are affected by changes in temperature and moisture. This study used the glass/carbon fiber reinforced plastic hybrid composite (G/CFRPHC) laminate as the research objects. The stiffness and strength of the composite lamina were expressed as a function of hydrothermal parameters. Based on classical lamination theory(CLT) and macro-mechanical analysis, using MATLAB programming, the tensile strength of G/CFRPHC laminates under a hydrothermal environment was studied. In addition, the influence of temperature, ply thickness, ply stacking sequence, and ply angle on the tensile strength of G/CFRPHC laminates under a hydrothermal environment was discussed. The results show that the tensile strength of G/CFRPHC laminates decreases with the increase of temperature and laying angle in the temperature range of 20 °C ∼ 110 °C in the hydrothermal environment (moisture absorption rate C 1 = 0.5%). Furthermore, for the G/CFRPHC laminates with laying modes of (02G/90mC)S, (04G/90mC)S, (06G/90mC)S, as m increases, their tensile strength gradually decreases. The tensile strength of G/CFRPHC laminates with the same ply angle but different ply stacking sequence is also not the same.


Introduction
In recent years, fiber hybrid composite materials have been widely used in aerospace, wind turbine blades, automobiles, civil infrastructure, and other fields due to their high designability. As a result, they have broad application prospects in the future [1][2][3][4]. However, as the composite material will be exposed to the hydrothermal environment for a long time during transportation and use, the mechanical properties of materials will decrease [5]. And then affect the strength of composites [6][7][8].
At present, many scholars at home and abroad have explored and studied the strength of composite materials under hydrothermal environments. Through experiments and finite element analysis, Zhao Y [9] established a prediction model for the tensile strength of resin-based fiber-reinforced composite laminates under hydrothermal conditions but only considered single fiber-reinforced composite materials. Barbero E J [10] established a model to predict the tensile strength of unidirectional e-glass fiber composites in a hydrothermal environment. However, this model is based on the curve fitting of data and is aimed at single fiberreinforced composite materials. Xu H H [11] studied the tensile strength of multi-directional G/CFRPHC through experiments and finite element analysis but did not consider the influence of the hydrothermal environment on its tensile strength. Literature [12][13][14][15][16][17] found through hydrothermal aging experiments that the tensile strength of composite materials Significant declined when exposed to a hydrothermal environment for a long time. Through experiments, Cao S et al [18] studied the tensile strength of carbon fiber reinforced composites, glass/carbon fiber reinforced plastic hybrid composite, and carbon fiber/basalt fiber reinforced plastic hybrid composites at high temperatures. The results show that the tensile strength of different fiberreinforced polymer (FRP) laminates will decrease significantly with increasing temperature. Through experimental research, Naito K et al [19] found that the tensile strength of G/CFRPHC increased with the increase of carbon fiber volume fraction and decreases with temperature rise. The literature [18,19] is based on experimental research, without detailed theoretical analysis, and does not consider the effect of moisture on its tensile strength. Ali J SM et al [20] analyzed the bending strength of composite laminates under thermal and mechanical coupling based on high-order shears deformation theory. Shen H S [21] studied the bending strength of composite laminates under thermal and mechanical coupling and elastic foundation. Although the literature [20,21] analyzed the strength of composite materials based on theory, it only considered the influence of temperature and did not consider the impact of moisture changes.
Through reviewing relevant literature, it is found that many scholars at home and abroad have conducted relevant researches on the tensile strength of composites under hydrothermal environment. But it mainly focuses on experimental research, with relatively little theoretical research. Moreover, the influencing factors considered by various scholars also have their emphasis, and single fiber-reinforced composite materials are mainly studied. However, there are few reports on the effect of the hydrothermal environment on the tensile strength of G/CFRPHC.
The current theoretical research on the strength of composite materials under hydrothermal environment only considers the hydrothermal load caused by the hydrothermal environment while ignoring its impact on the properties of composite materials. This article starts from the perspective of macro-mechanics. For G/CFRPHC laminates, considering the hydrothermal load generated by the hydrothermal environment and the impact on the composite material performance, a prediction model of the tensile strength of G/CFRPHC under the hydrothermal environment is established. It optimizes the strength calculation theory of composite laminates. It discusses the influence of temperature, layer thickness, ply stacking sequence, and laying angle on the tensile strength of G/CFRPHC laminates under a hydrothermal environment. Thus, it has crucial theoretical guiding significance for the structural design, manufacturing, use, and strength prediction of G/CFRPHC laminates in hydrothermal environments.

Theoretical analysis
Assume that the room temperature is 20°C and the working temperature is 20°C∼110°C. This study used the (G/CFRPHC) laminate as the research objects. The laminate thickness is T. The G/CFRPHC laminate is in a hydrothermal environment (the moisture absorption rate of the laminate is C 1 =0.5%), and an in-plane tensile load Nx is applied to it. As shown in figure 1.

Degradation model of a composite lamina under hydrothermal environment
Reference [22], in this study, the lamina elastic parameters (E 11 , E 22 , G 12 , G 23 ), coefficient of damp thermal expansion (β 11 , β 21 , α 11 , α 21 ), in the hydrothermal environment has a linear relationship with the temperature change (T 1 ) and the moisture absorption rate (C 1 ). as follows    According to the positive axis stiffness matrix, the off-axis stiffness matrix of any layer (assuming the kth layer) of the fiber-reinforced composite lamina can be calculated as follows: Calculation of flexibility matrix of G/CFRPHC laminate Since the G/CFRPHC laminates studied in this paper are symmetrical, the coupling stiffness matrix is [B] = 0.
Since the G/CFRPHC laminate is studied in this paper, when k is the glass fiber/epoxy resin layer,Q ij is the offaxis stiffness of the glass fiber/epoxy lamina. When k is the carbon fiber/epoxy resin layer,Q ij is the off-axis stiffness of the carbon fiber/epoxy lamina. Because [B] = 0, the flexibility matrix of the G/CFRPHC laminate is calculated as follows

Calculation of the off-axis hydrothermal expansion coefficient of the lamina of different layers and different materials
In actual engineering, each layer of composite laminates is mostly off-axis. Thus, for any k-layer G/CFRPHC laminates, the off-axis hydrothermal expansion coefficient is:

Calculation of the wet internal force and thermal internal force of G/CFRPHC laminates
The temperature and moisture environment of the G/CFRPHC laminates studied in this paper is uniformly changed, unchanged along the thickness direction, only the last amount of change is considered, and the change process is not considered. Calculate the wet internal force and thermal internal force of the G/CFRPHC laminate as follows Since this paper takes G/CFRPHC laminate as the research object, theQ , k {α} k and {β} k of different material layers are different. First {N T } is the thermal internal force of the G/CFRPHC laminate. The second {N H } is the wet internal force of the G/CFRPHC laminate.

Calculation of the spindle stress of each lamina in the G/CFRPHC laminate
Since the G/CFRPHC laminate studied in this paper only bears the action of the in-plane force {N}, the components of the in-plane moment {M} are zero, and all of the elements of {κ} is also zero. In the state of plane stress, the relationship between wet internal force, thermal internal force and external load and midplane strain can be obtained from the composite material in a hydrothermal environment CLT as follows Where {ε 0 N } is the midplane strain caused by the external load. {ε 0 T } is the midplane strain caused by temperature. {ε 0 H } is the midplane strain caused by moisture.
Since the various components of {κ} are zero, the strain {ε N } caused by the external load at any point in the lamina is equal to the midplane strain {ε 0 N } caused by the external load, that is In the same way, the total hydrothermal strain {ε S } caused by temperature and moisture at coordinate z at any point of each lamina can be calculated as follows The lamina assumed in this paper is unconstrained, and the free wet-heat deformation {ε f } of the lamina of different materials can be calculated as follows The total hydrothermal strain and the free hydrothermal strain of lamina of different materials can be calculated to obtain the residual strain {ε R } at each point in the G/CFRPHC laminate as follows The strain caused by the external load and the residual strain at each point in the laminate can be used to obtain the off-axis strain {ε} k of the lamina in a hydrothermal environment as follows According to the calculated off-axis strain of the lamina under the hydrothermal environment, the principal axis stress {σ} k of the lamina with different material layers can be obtained in the following

Calculation of tensile strength of G/CFRPHC laminate under hydrothermal environment
The strength of the laminated board is related to the strength of the lamina. Therefore, to consider the influence of the hydrothermal environment on the mechanical properties of the lamina, the power function of the dimensionless temperature T * proposed by Tsai [23] can be introduced to modify the strength of the lamina. The expressions are as follows The superscript 0 at formulas (22)∼(28) represents the material's mechanical properties in the dry state at room temperature. X t , X c , Y t , Y c , and S 12 are the longitudinal tensile, compressive strength, transverse tensile, compressive strength, and in-plane shears strength of the lamina in a hydrothermal environment. f∼k is the hydrothermal degradation constant. The glass transition temperature of the material at room temperature is T g 0 . T g is the glass transition temperature of the material at the working temperature.
It is shown in the literature [24] that the Hoffman strength criterion is relatively close to the experimental measurement value. Therefore, the principal axis stress of each lamina obtained by formula (21) is substituted into the Hoffman strength criterion to calculate the strength of the G/CFRPHC laminate.

Stiffness correction of the lamina in a hydrothermal environment
As long as the strength of single or multiple layers in the composite laminates fails, the laminate will have stiffness reduction, and the stress of the single-layer will be redistributed. Therefore, it is necessary to calculate the residual stiffness of the laminate again to determine the internal force of the other lamina. This paper adopts the method of stiffness reduction correction of partial failure assumption. After the stiffness is corrected, continue applying the tensile load at the x-direction, performing stiffness correction, stress redistribution, Hoffman strength criterion checks, judging whether it fails, and iterating until all layers are destroyed. The ultimate strength obtained is the tensile strength of the G/CFRPHC laminate.   The mechanical parameters of carbon fiber/epoxy single-layer board (T700/5528A) and glass fiber/epoxy lamina (QF210/5528A) in literature [11] are input into the strength prediction model of this paper. The hydrothermal conditions are average temperature and dry state. (Moisture absorption rates C 1 =0). Then a tensile load at the x-direction is applied to the laminate, which is compared with the predicted value of tensile strength of the multi-directional hybrid composite material based on the hybrid effect coefficient in the literature [11]. The results are shown in table 1. The solution in this paper is similar to the finite element solution in [11]. Therefore, the accuracy of the model in this paper is verified.

Program design and verification
Verification example 2. Tensile strength of carbon fiber/polyamide resin composite laminate under hydrothermal environment The mechanical parameters of the carbon fiber/polyamide resin lamina (T300/BMP316) in the literature [9] are input into the strength prediction model of this paper. Then compared with the experimental value of the tensile strength of the laminate in the literature [9], the results are shown in table 2. It can be seen that the solution in this paper is the be similar to the experimental value solution in literature [9], which again verifies the effectiveness of the strength prediction model in this paper.
The above two verification examples prove that the program written by Matlab for calculating the tensile strength of G/CFRPHC under a hydrothermal environment is reliable. And the present theoretical model based on CLT, macro-mechanical analysis method, stiffness reduction correction, and Hoffman strength criterion in solving the tensile strength of G/CFRPHC in a hydrothermal environment has high calculation accuracy.   show that the tensile strength of G/CFRPHC laminates decrease with increasing temperature in a hydrothermal environment. For example, in a hydrothermal environment of 20°C∼110°C, the tensile strength of (0 G /90 C ) 4S is better than (45 G /0 C /90 G /−45 C /0 G /90 C /45 G /−45 C ) S . Among them, the tensile strength calculated without considering the influence of hydrothermal environment on the mechanical properties of the lamina at a temperature of 110°C, and the tensile strength calculated by considering the impact of the hydrothermal environment on the mechanical properties of the lamina, differs respectively by 44.78 MPa, 30.00 MPa. Because, in a hydrothermal environment, the diffusion of moisture in the lamina matrix is promoted due to the increase in temperature. The generated osmotic pressure causes micro-cracks inside the matrix, which increases the distance between the macromolecular structures of the matrix and plasticizes the matrix [26]. Therefore, affect the tensile strength of the lamina. It can be seen that in the calculation of tensile strength of G/CFRPHC laminates, the influence of the hydrothermal environment on the mechanical properties of singlelayer laminates cannot be ignored.
In the temperature range of 20°C ∼ 110°C in a hydrothermal environment, from the curve B in figure 3(a), we can see that the (0 G /90 C ) 4S as the temperature increases, its tensile strength is compared with 20°C decreases respectively by 1.00%, 3.71%, and 9.10%. The curve B in figure 3(b) shows that the tensile strength of (45 G /0 C /−45 G /90 C ) 2S compared with that at 20°C decreased by 1.51%, 3.90%, and 9.86%. In a hydrothermal environment, the increase in temperature promotes the diffusion of moisture in the lamina matrix, and the matrix is plasticized, resulting in faster degradation of the matrix performance. At the same time, the mismatch of the hydrothermal expansion coefficient of carbon fiber/epoxy lamina and glass fiber/epoxy lamina under the hydrothermal environment will reduce the interface bonding performance of each lamina. The rate of moisture infiltration into the interface microcracks is accelerated, causing further degradation of the interface performance. Therefore, as the temperature increases, the tensile strength of G/CFHC laminates decreases more and more. Consistent with the conclusion of [27][28][29].

The influence of layer thickness on the tensile strength of G/CFRPHC under hydrothermal environment
Laminate thickness is a critical physical parameter in a hydrothermal environment. Due to the different thicknesses of the laminate, its tensile strength may also be dissimilar. This article uses three types of G/ CFRPHC laminates (0 2G /90 mC ) S , (0 4G /90 mC ) S , (0 6G /90 mC ) S , all of which are 150 mm × 60 mm × a mm in size. According to the different values of m, to explore the tensile strength law of G/CFRPHC laminate in a hydrothermal environment (moisture absorption rates C 1 =0.5%). It can be seen from figures 4(a)-(c) that for three different types of G/CFRPHC laminates in a hydrothermal environment of 20°C∼110°C, the G/CFRPHC laminates increase with the thickness of 90º layup. As a result, its tensile strength gradually decreases. The possible reason is that the local stress concentration near the fiber in the 0°layer becomes more and more severe due to the matrix cracking in the 90°layer as the thickness of the singlelayer increases. Consistent with the conclusion of [30]. Therefore, when designing the G/CFRPHC laminate project in the hydrothermal environment, the number of layers overlapping the same laying angle should be as small as possible. The reason is that this can slow down the tension-shear coupling between the individual layers of the G/CFRPHC laminate, reduce the interlayer stress, and improve the tensile strength of the laminate. Furthermore, it can be seen from figure 4(d) that the tensile strength of the G/CFRPHC laminate also is increased by increasing the number of the 0°main bearing layer of the G/CFRPHC laminate.   laying angle but different ply stacking sequences are (90 G /45 C /−45 G /0 C ) 2S , (0 G /45 C /90 G /−45 C ) 2S , (45 G /0 C /−45 G /90 C ) 2S , (0 G /45 C /−45 G /90 C ) 2S . The size of the laminate is 150 mm × 60 mm × 4.92 mm. Then, calculate the moisture absorption rate C 1 =0(dry state) and C 1 =0.5%(wet condition). In both cases, the tensile strength of laminates with temperature changes is shown in figures 5(a) and (b). Figures 5(a) and (b) show the influence of the ply stacking sequence on the tensile strength of the G/ CFRPHC laminate in the wet state and the dry form, respectively. It can be seen that the tensile strength of G/ CFRPHC laminates with the same laying angle but different ply stacking sequence in a dry and wet environment from 20°C ∼110°C is also dissimilar. Among them, the tensile strength of (0 G /45 C /90 G /−45 C ) 2S and (45 G /0 C /−45 G /90 C ) 2S is better than the other two laminates. The possible reason is that the ±45º two layers in (90 G /45 C /−45 G /0 C ) 2S and (0 G /45 C /−45 G /90 C ) 2S are adjacent. Therefore, it will cause the tension-shear coupling coefficient of G/CFRPHC laminates to be inconsistent and cause interlaminar shear stress, resulting in lower tensile strength. Consistent with the conclusion of [30]. Thus, in the hydrothermal environment, designing the G/CFRPHC laminate structure, the 45°layer and the −45°layer should be laid at intervals to reduce the interlaminar shear stress, thereby increasing the tensile strength of the G/CFRPHC laminate. Consistent with the conclusion of [14]. From figures 6(a)-(d), it can be found that under the high-temperature environment of 80°C and 110°C, when the laying angle of G/CFRPHC laminate is 90°, when the environment transitions from the dry state to the wet form, its tensile strength decreases respectively 19.29% and 23.32%. Thus, it can be seen that in a high-temperature environment, moisture has a more significant impact on the tensile strength of the G/CFRPHC laminate with a 90°laying angle. From figures 6(a)-(d), it can be seen that in a dry and wet environment, when the laying angle of G/CFRPHC laminates increases from 0°to 90°, its tensile strength decreases continuously. Consistent with the conclusion of [31,32]. Therefore, when designing G/ CFRPHC laminates in the hydrothermal environment, the off-axis angle should be strictly controlled to prevent huge deflection angles from causing too low tensile strength of G/CFRPHC laminates.

Conclusions
In this research, the macro-mechanical analysis of the tensile strength of G/CFRPHC under the hydrothermal environment is carried out. Furthermore, the influence of temperature, layer thickness, ply stacking sequence, and layering angle on the tensile strength of G/CFRPHC laminates under a hydrothermal environment was studied. Based on the above research, the following conclusions can be drawn: In the hydrothermal environment, the tensile strength of G/CFRPHC laminates after being subjected to a tensile load at the x-direction decreases more and more as the temperature increases. In the G/CFRPHC engineering design, the number of layers overlapping the same laying direction should be as small as possible. Because this can slow down the tension-shear coupling between the layers of the G/CFRPHC laminate, reduce the interlayer stress, and improve the tensile strength of the laminate. With the increase of the 0°main bearing layer, the tensile strength of G/CFHC laminates also increases. In the hydrothermal environment, in the G/ CFRPHC laminate design, the 45°layer and the −45°layer should be laid apart to reduce the interlayer shear stress and increase the tensile strength of the G/CFRPHC laminate. When the laying angle of G/CFRPHC laminates is from 0°to 90°, as the laying angle increases, its tensile strength decreases continuously. Among them, in a high-temperature environment of 80°C and 110°C, moisture significantly impacts the tensile strength of the G/CFRPHC laminate with a 90°laying angle.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).