In this paper, woven fabrics of glass fiber/carbon fiber intra-hybrid in plain structure were used to fabricate fiber reinforced plastic (FRP) composite by hand lay-up method. The investigation on tensile property was carried out on specimens in 7 orientations including 0 °/5 °/15 °/75 °/85 °/90 ° in previous works. With the specimen parameters and experimental data, FEM model was built by the software of Marc. By combining the experimental results and finite element analysis, the modulus was simulated and calculated at the first stage. Then interfacial stress of the 0 degree and 90 degree was also calculated. By the initial fracture stress data from experiment as well as the simulation value of interfacial strength of 0 and 90 degree, the initial fracture stress of the off-axial specimens was calculated and predicted. The result shows that the interfacial strength of the glass fiber bundle is higher than that of the carbon fiber bundle in transverse direction. By using the interfacial strength and according to the Von Mises yielding criterion, the initial fracture stress was predicted, which can be a contribution to the design or predict of the material properties.
Textile fabric is one of the important reinforcements widely used in manufacturing composites in variety of fields, such as automobile, construction and basic facilities. Among them, woven fabrics are probably the most commonly used form of textile composites in structural applications by far [
Currently, most of the pure and hybrid woven fabrics used in textile composites are simple 2D fundamental weaves, i.e., plain, twill and satin weaves [
Due to the complicated microstructure of woven fabric, understanding of mechanical properties of textile fabric reinforced composite materials is of importance [
For these reasons, there are a lot of papers on the research by numerical analysis method to understand the woven fabric reinforced composite [
As stated above, understanding of mechanical properties of textile fabric reinforced composite materials is of great importance for the complicated microstructure of woven fabric. And due to the reason that it is difficult to observe and obtain the interfacial property of the transverse fiber bundle from experimental data, which plays an important role of the initial fracture property, numerical analysis method is considered to be adopted to understand the initial fracture behavior of woven fabric reinforced composite.
In this paper, composites fabricated with woven fabric of glass/carbon intra-hybrid in plain structure by hand lay-up method were adopted. Investigation on the tensile property was carried out on specimens in 7 orientations including 0˚/5˚/15˚/75˚/85˚/90˚ in previous works. With the specimen parameters and experimental data, FEM model was built by software Marc. At the first stage, tensile moduli were calculated and compared with experimental results. On the premise of the validity of the simulation value of tensile modulus, interfacial stresses of the transverse elements in 0 degree and 90 degree models were also calculated. Among those, the maximum was regarded as the interfacial strength of the transverse fiber bundles. By the experimental data of initial fracture stress as well as the simulation value of interfacial strength of 0 and 90 degree, the initial fracture stress as well as the distribution of interface elements of the off-axial specimens were calculated and predicted.
In previous work [
Tensile test was carried out on an Instron universal testing machine at the speed of 1 mm/min and the test room temperature is 22˚C. Strain gauges were used to measure the tensile strain. 3 specimens have been repeated for each type. Max stress, modulus and the stress-strain curves of 7 types of specimens were
Tensile strength (MPa) | Elastic modulus (GPa) | Elongation (%) | Density (g/cm3) | |
---|---|---|---|---|
Glass | 2300 - 2400 | 70 - 76 | 3 - 3.2 | 2.55 - 2.62 |
Carbon | 4900 | 230 | 2.1 | 1.8 |
Vinyl Ester | 69-89 | 3 | 6.0 - 8.0 | 1.2(25˚C) |
obtained and analyzed. Knee point stress was obtained by AE device during the tensile test. In order to investigate the initial fracture behavior of the intra CF/GF woven composite, especially for the difference between the GF and CF, video was shot during the tensile test.
The detail of the result of the tensile test in previous work is summarized and shown in
Besides, in previous work [
Tensile modulus (GPa) | Tensile Strength (MPa) | Initial fracture stress (MPa) | Initial fracture strain Rate (%) | |
---|---|---|---|---|
0 | 23.2 | 351.4 | 32.9 | 3.7 |
5 | 21.1 | 278.5 | 39.3 | 3.2 |
15 | 18.5 | 157.4 | 38.1 | 4.3 |
45 | 12.0 | 112.6 | 32.6 | 5.5 |
75 | 40.5 | 225.2 | 87.9 | 5.0 |
85 | 49.2 | 494.1 | 198.3 | 4.3 |
90 | 50.5 | 780.6 | 184.2 | 4.8 |
stage. More transverse crack appeared with the increase of the tensile load. And in previous work [
In previous works [
To build up the model by Marc, parameters of the weft and warp yearns are necessary. Specimen was cut and buried in resin to obtain the exact dimension of the weft fiber bundle and warp fiber bundle. After polishing, optical observation was carried out to get the geometric parameters.
Four types of parameters including the major axis, minor axis, distance between fiber bundles (d0) as well as the fiber bundle area as
Major axis (mm) | Minor axis (mm) | Area (mm2) | Distance between fiber bundle (mm) | |
---|---|---|---|---|
Warp | 4.170 | 0.237 | 0.608 | 4.259 |
Weft | 4.056 | 0.256 | 0.747 | 4.244 |
After the model was built, mechanical properties of the weft and warp yeans were identified. For mechanical parameters, Vf (volume fraction of reinforce fiber), modulus, of glass fiber bundle and carbon fiber bundle are necessary. Since the elastic modulus of a fiber bundle in matrix is different with its catalogue elastic modulus value, it need to be recalculated Here, the Vf of the fiber bundle is calculated by the number and the area of the filaments and the cross section area of the fiber bundle by Equation (1) as follows:
V f = A N S (1)
Here A is the area of the fiber bundle cross-section; N is the number of filaments in one fibber bundle; S is the sum of the fibers in cross section area.
These three values are measured and obtained by the optical observation of the fiber bundle cross-section. After the Vf is obtained, with the elastic modulus of the fiber and the resin, the modulus of the fiber bundle is calculated by the composite rule. Young’s modulus and the Poisson ratio are two necessary parameters for the mechanical property of fiber bundles.
Models are controlled by displacement in this study. For on-axis model of 0 degree and 90 degree, unit displacement 1 mm was applied to the model along the load direction x and y axial direction separately. However, there is difference between the axis and off axis models, for the boundary conditions. Take the 5 degree for examples, for on-axis model of 0 degree, unit displacement 1mm was applied to the model along the load direction. While for off-axis model of 5 degree model, it was considered to apply the displacement in 5 degree orientation, instead of build a model with off-axis fiber bundles. Then the displacement along 5 degree was divided into x and y two directions as it is shown in
Based on the results of the geometric parameter and mechanical property, model of both 0 degree and 90 degree were built at first, elastic modulus and the max interfacial fracture stress was calculated and compared.
In order to analysis the mechanism of the initial fracture stage, the simulation was carried out within the elastic area. For on-axis model of 0 degree and 90 degree, unit displacement 1 mm was applied to the model along the load direction
Degree | Experimental tensile modulus (GPa) | Simulation tensile modulus (GPa) | Error (%) |
---|---|---|---|
0 | 23.2 | 22.3 | 4% |
90 | 50.5 | 48.8 | 3% |
Degree | Experimental tensile modulus (GPa) | Simulation tensile modulus (GPa) | Error (%) |
---|---|---|---|
5 | 21.1 | 22.2 | 5% |
85 | 49.2 | 48.3 | 2% |
x and y axial direction separately. The simulation modulus was calculated by summarizing the total stress of all the nodes along the applied force direction first and then dividing by the corresponding cross-section area. The analysis result of modulus by FEM model and compared with the result from experiment as shown in
Tensile modulus was also calculated for off-axis cases. The analysis result of tensile modulus by FEM model and compared with the result from experiment as shown in
As load increased during the experiment, initial fracture happened within the transverse fiber bundle of the specimen. It is known from the previous work that
initial fracture in plain woven fabric composite was confirmed as transverse crack in weft fiber bundle. For the 0 degree and 90 degree, the axial tensile stress was clarified as the dominate stress, which suggest that the tensile force is the main fracture reason for the interfacial element. In order to get the interfacial strength in transverse fiber bundle, the principal stress of the interfacial elements was calculated by dividing the axial force of the interphase element by the cross section area because the shear stress. Combining with the initial fracture stress from the experiment and the initial fracture from the model, interfacial strength of the glass fiber bundle and carbon fiber bundle as transverse direction was calculated by the Equation (2).
σ interfacial = σ i n i t i a l σ ′ ⋅ σ ′ interfacial (2)
Here σ i n i t i a l is initial fracture stress from experimental data; σ ′ i n i t i a l is calculated value of initial fracture stress from model; σ interfacial is the simulation value of interfacial strength in transverse fiber bundle; σ ′ interfacial is calculated value of interfacial strength from on axis models.
As it is known, the yield point stress can be usually measured by tensile test of the unidirectional composite. For axial reinforcement like woven fabric, due to the complex load situation, it is difficult to judge the yield point because the shear stress might be involved in the meantime. The von Mises yield criterion is used to solve the yield point problem of multi-axial stress situation involved with more than one stress component. The von Mises yield criterion suggests that the yielding of material begins when the second deviatoric stress invariant reaches a critical value. Among the interfacial elements, not only the tensile stress along the elements’ axial direction, but also the shear stress along the vertical direction were clarified.
The Von Mises stress of the interfacial elements was calculated according to Equation (3):
σ i,interfacial = { ( σ x x − σ y y ) 2 + ( σ y y − σ z z ) 2 + ( σ z z − σ x x ) 2 + 3 ( σ x y 2 + σ x z 2 + σ y x 2 + σ y z 2 + σ z x 2 + σ z y 2 ) } 2 (3)
Here σ x x , σ y y and
The result of both max principal stress and the Von Mises stress of the interfacial elements is shown in
And for glass/carbon hybrid, the transverse fiber bundles’ interfacial strength of the 90 degree (transverse fiber bundle is glass fiber) is much higher than that of the 0 degree (transverse fiber bundle is glass fiber), which shows that the interfacial strength property of glass fiber bundle is better than the carbon fiber bundle in transvers direction. According to previous works, if one is to calculate
Degree | Initial fracture stress (MPa) | Max axial stress (MPa) | Von Mises (MPa) | Simulation interfacial Strength (MPa) | Simulation initial fracture (MPa) | Error (%) |
---|---|---|---|---|---|---|
0 | 32.9 | 356.4 | 357.6 | 11.0 (carbon) | - | - |
90 | 184.2 | 438.9 | 440.5 | 28.1 (glass) | - | - |
5 | 39.3 | 354.6 | 355.9 | - | 40.4 | 3% |
85 | 198.3 | 420.2 | 421.5 | - | 189.9 | 4% |
the interfacial fracture stress, the stress distribution at a fiber-matrix interface subjected to loading must be known. Thus, in order to find out where the max interfacial stress happened, interfacial stress value of every transverse fiber bundles were collect from both the principal stress and Von Mises stress. And the results show that for both the principal stress and Von Mises stress, the max value happened at the same position.
Where the max value of the Von Mises stress of 0/5/85/90 degree happened is shown in
With the interfacial strength from the on-axial models and the Von Mises stress from the off-axial, the initial fracture value can be predicted by Equation (4) as follows:
Here
The analysis result of interfacial strength and the initial fracture stress by FEM model and compared with the result from experiment is also shown in
In this study, 3D solid beam element was adopted. As it is referred to the local coordinate of the beam element, x direction and y direction is perpendicular in cross section plane and z direction is along the beam longitude axial direction as illustrating in
Max axial stress (MPa) | Shear stress (MPa) | Von Mises equivalent stress (MPa) | Max Principal stress (MPa) | |
---|---|---|---|---|
0 | 270.4(−) | 33.8(−) | 271.4(−) | 282.0(−) |
5 | 266.5(−1%) | 38.6(14%) | 266.9(−2%) | 283.0(−0%) |
85 | 138.8(−1%) | 33.0(4%) | 140.9(−3%) | 149.3(−3%) |
90 | 143.5(−) | 31.9(−) | 145.5(−) | 154.6(−) |
values in local coordinate of the beam elements are showing a waveform changes with relatively high values between two warp fiber bundles and low value in the cross area of warp and weft fiber bundles. Besides, according to
In order to get a good knowledge of the mechanical properties of woven fabric reinforced composites, numerical analysis method is considered to be a valid method to understand the initial fracture behavior for the complicated microstructure of woven fabric reinforced composite. In this paper, FEM model of woven structure was built up, then tensile modulus and the interfacial properties of the transverse fiber bundle were simulated and compared. From on-axial models, the interfacial strength of the glass fiber bundle and carbon fiber bundle was calculated. The results show that the interfacial strength of the glass fiber bundle is higher than that of the carbon fiber bundle in transverse direction. By using the interfacial strength, the initial fracture stress of off-axis cases was predicted. And the distribution of the axial stress, shear stress, Von Mises equivalent stress and principal stress was calculated and illustrated. It is clarified that in off-axis cases, shear stress in interphase elements is higher than on-axis cases, which showed that the transverse fiber bundles were subjected to higher shear stress. Through model built by Marc and analysis by FEM, the modulus and the initial fracture stress simulation can be achieved, which can be a contribution to the design or predict of the material properties.
Xu, Z.L., Nakai, A., Yang, Y.Q. and Hiroyuki, H. (2018) A Study on the Initial Fracture Behavior of CF/GF Intra-Hybrid Woven Fabric Reinforced Composites. Open Journal of Composite Materials, 8, 11-27. https://doi.org/10.4236/ojcm.2018.81002