Influence of the selection of different construction materials on the stress–strain state of the track

2.1 Analysis of the stress–strain relationship of carbon fiber composites

Carbon fiber composite materials are favored in the field of rail transit research because of their lightweight structure. Different from common metal materials, the material has anisotropy. It is made of polymer matrix and carbon fiber dual materials. The advantages of material properties are obvious, and therefore, more complex expressions have been obtained in macroscopic mechanical analysis. For a continuous elastic solid that can still maintain a state of equilibrium when the external load is applied, the stress corresponding to its internal point in a three-dimensional coordinate system σ can be decomposed into nine stress components, which are three normal stresses, denoted as σ x , σ y , and σ z , and six shear stresses, denoted as τ x y , τ x z , τ y x , τ y z , τ z x , and τ z y , whose matrix form can be expressed by the following formula:

It should be pointed out that, restricted by the law of mutual equality of shear stress, τ x y = τ y x , τ x z = τ z x , and τ y z = τ z y , there are only six independent stress components after three-dimensional decomposition, which are taken as σ x , σ y , σ z , τ x y , τ y z , and τ z x . Similarly, the strain tensor corresponding to any internal point can also be expressed in the matrix form:

where ε x , ε y , and ε z represent the line strain, and ε x y , ε y z , and ε z x represent the tensor shear strain. Considering that in practical engineering applications, engineering shear strain is often used to represent, so it is necessary to convert the quantitative relationship between the two according to the following formula:

where γ x y , γ y z , and γ z x represent the engineering shear strain. For anisotropic materials such as carbon fiber composites, the stress component has a consistent correspondence with its strain component. In the case of linear elasticity and small deformation, this relationship can be expressed by the elastic constant matrix:

where D 11 to D 66 is an elastic constant introduced for anisotropic materials, and 36 elastic constants are obtained through arrangement and combination. However, according to the existing energy experiments, 15 of the 36 elastic constants are independent, and only 21 independent elastic constants exist. Figure 1 is a schematic diagram of orthotropic materials in a rectangular coordinate system.

Figure 1

Schematic diagram of orthotropic materials in a rectangular coordinate system.

Coordinate systems 1, 2, and 3 in Figure 1 refer to the main axis coordinate system of the orthotropic material, wherein the coordinate system is used to indicate the fiber direction; the coordinate system 2 is used to indicate the direction of the vertical fiber; and the coordinate system 3 is used to indicate the thickness direction. The carbon fiber composite material can be regarded as an orthotropic material because it has two or more elastic symmetry axes and symmetry planes at 90°C with each other. And under the decomposition of the main axis coordinate system, the material tension and shear effect are also decomposed, so that the shear stress and shear strain are only related in the own plane, so the elastic constant can be reduced to 9. Combined with engineering practice, carbon fiber composite materials are often used in the form of laminated sheets. At the same time, because the dimensions of the fiber direction and the vertical fiber direction are far larger than the thickness direction, the stress value in this direction can be ignored, so there is σ 3 = τ 23 = τ 31 = 0 . Based on the aforementioned analysis, it can be seen that the expressions of the stress–strain relationship of the carbon fiber composite sheet are given by:

where P i j and Y i j represent the kneading degree and stiffness index, respectively. The stress–strain relationship of each layer of the carbon fiber composite material used as a laminate according to the sheet theory can be expressed by the following formula:

where Y ¯ k represents the k layer stiffness transformation matrix; Z k represents the k layer distance; ε x 0 , ε y 0 , and γ x y 0 represent the laminate surface strain; and K x , K y , and K x y represent the laminate surface curvature. Define the finite element of the composite internal force along the width direction of the laminated plate as N , and the resultant internal force moment along the width direction as M , the mathematical relationship between the two is obtained by the following formula:

where h represents the thickness of the laminate, and A, B, and D jointly form the stiffness matrix of the laminated plate, which is a third-order symmetric square matrix. When the laminated plate is a symmetric laminated plate, B is a third-order zero square matrix. It can be seen from Eq. (8) that the resultant internal force is obtained by integrating the internal moment along the thickness direction.

2.2 Analysis of on-orbit stress–strain relationship of epoxy asphalt material

For epoxy asphalt materials, the temperature change will have a great impact on their mechanical properties, but most material performance tests only consider the changes brought by −20 and 23℃ on the mechanical properties of the material and do not expand the effect of going to other temperature regions on the damage of asphalt materials. The study of mechanical properties of materials includes viscoelasticity, stretchability, and interfacial adhesion. In the viscoelastic analysis of epoxy asphalt materials, there are two kinds of tests: static test and dynamic test. The static test tends to investigate the creep and relaxation dimensions of the material, that is, the mechanical test is only carried out under the condition that the stress remains unchanged, but in practical engineering, there are many alternating stresses, so it is more appropriate to use dynamic mechanical tests that consider alternating stresses. The expression of stress–strain hysteresis relationship in dynamic analysis is given by the following formula:

where σ and γ represent the stress value and strain value at a certain time, respectively; σ 0 and γ 0 represent the stress–strain amplitude, respectively; and w , t , and δ represent the angular velocity, time, and phase angle, respectively. It can be seen from formula (9) that the dynamic mechanical analysis monitors the corresponding strain changes by applying a sinusoidal alternating stress. Under the influence of dynamic applied load, the ratio of stress to strain is negative, and its ratio is shown in the following formula:

where G ⁎ represents the shear stiffness modulus, which is presented in a complex number, G ̇ represents the shear modulus of the material stored, and G ̈ represents the shear modulus of the material loss. Tensile performance experiments often use multi-position-enhanced loading, operate on the fixture, and stop loading after the sample is completely broken, so as to obtain the relationship between the tensile stress value and the strain value of the corresponding material. The tensile strength calculation formula is expressed as:

where σ s is the tensile strength and its unit is MPa; P max indicates the maximum applied load before the specimen breaks and damages, in N; and b and d represent the width and thickness of the working section of the sample, respectively, in mm. The elongation at break is expressed as:

where ε m represents the elongation at break of the material, Δ L b represents the corresponding gauge length elongation when the material is fractured and damaged, and L 0 represents the length of the gauge length section, and the unit is mm. When the strain value is between 0.001 and 0.003, the elastic modulus is expressed by the following formula:

E represents the elastic modulus of the material, and E is measured in MPa. P 1 and P 2 represent the load magnitude of ε x 1 and ε x 2 , respectively, and their units are Newton; and ε x 1 and ε x 2 represent the actual strain values around 0.001 and 0.003, respectively. Figure 2 reflects the relationship between the epoxy asphalt material and the binder.

Figure 2

Relationship between epoxy asphalt material and binder.

As can be seen from Figure 2, wetting will occur between the bituminous material and the binder. This is because there will be many voids on the surface of the asphalt material, and after the binder is fully combined with it, the latter will penetrate as strongly as the former, forming mechanical interlocking, thereby generating bond strength. As shown in Figure 2, F 1 represents the surface tension of the asphalt material and F 2 the surface tension of the binder itself, and the angle between the two reflects the quality of the bonding effect.

3.1 Experimental results of mechanical properties of carbon fiber composites based on temperature changes

The carbon fiber composite material used in the research experiment is composed of EN199 resin matrix in the matrix phase and carbon fiber in the reinforcing phase, and the glass transition temperature of the resin matrix material is 120°C; there is no difference from test piece 1 to test piece 5. The reason for setting 5 is that it reflects repeated tests and avoids the contingency of single test piece experiment. Since the glass transition temperature of general resin-based materials is around 300°C, when the material is in a non-standard environment, especially in high-temperature humid heat and low-temperature dry–cooling conditions, the bearing capacity of the material will be significantly reduced. In this part, the stress–strain state of the material in various environments is monitored experimentally. The high temperature test is realized by UTM51 series electronic universal machine. For the high temperature and humidity test, let the samples stand for more than 24 h in an environment with a relative humidity of 70 ± 3.5℃ and 85 ± 4.5℃ and then use them for the standard test. The low-temperature experiment was realized by magnetic torquing system tension-twisting machine. Figure 3 is a graph showing the results of tensile properties in a high-temperature and wet-state experiment.

Figure 3

Tensile property curve of high-temperature wet test: (a) high-temperature wet tensile force–displacement curve and (b) high-temperature wet tensile stress–strain curve.

From the curve of tensile force and specimen displacement in Figure 3(a), it can be seen that with the increase in tensile force from specimen 1 to specimen 5, the deformation and displacement of specimen itself increase linearly. For example, for specimen 1, the tensile external force corresponding to the linear increasing stage ranges from 0 to 19.8 kN, and the maximum displacement is 2.87 mm. Then, specimen 1 breaks instantaneously, and the curve drops sharply. The curve changes of the rest of the specimens are not different from this; only the displacement point at the maximum tensile force value is different: 2.34 and 25.8 kN − 2.43 mm. From Figure 3(b), it can be seen that the stress–strain relationship in the tensile state presents a linear positive proportional relationship, and the linearly increasing nodes from specimen 1 to specimen 5 are 526.1 MPa – 0.0092 and 575.2 MPa – 0.0094, 575.1 MPa – 0.0089, 576.1 MPa – 0.0095 and 610.3 MPa – 0.0079. Figure 4 is a graph showing the results of shear performance in a high-temperature and wet-state experiment.

Figure 4

Curve of shear performance results of high-temperature wet test: (a) high-temperature wet shear force–displacement curve and (b) high-temperature wet shear stress–strain curve.

From Figure 4(a) and (b), it can be seen that the relationship between shear force and displacement or shear stress–strain relationship of carbon fiber composite specimens in the early high-temperature and humid environment shows a nonlinear increasing relationship. In the relationship between force and displacement, the curve first shows a trend of rapid increase and then slow increase. The inflection point of the speed change from specimen 1 to specimen 5 is about 1.5 mm, and the corresponding maximum shear force is 5.4 kN – 13.9 mm, respectively, 5.6 kN – 13.7 mm, 5.5 kN – 14.1 mm, 5.05 kN – 12 mm, and 5.5 kN – 14.0 mm. In the shear stress–strain relationship, the maximum stress corresponding to displacements of specimen 1 to specimen 5 is 0.0649, 0.0620, 0.0660, 0.0590, and 0.0587 mm. Figure 5 is a graph showing the results of tensile properties in a low-temperature dry-state experiment.

Figure 5

Curve of tensile property results of low-temperature dry test: (a) low-temperature dry tensile force–displacement curve and (b) low-temperature dry tensile stress–strain curve.

It can be seen from Figure 5 that the variation trend of the tensile curve in the dry state at low temperature is similar to that in the wet state at high temperature. The tensile force and displacement and tensile stress–strain show a linear increasing relationship, while the shear force and displacement and shearing stress–strain show a nonlinear increasing relationship. The displacement and strain corresponding to the maximum tensile force of specimen 1 to specimen 5 are 3.78, 3.51, 3.99, 2.90, and 2.72 mm and 0.0080, 0.0081, 0.0072, 0.0068, and 0.0066, respectively. Figure 6 is a graph showing the results of shear performance in a low-temperature dry-state experiment.

Figure 6

Curve of shear performance results of low-temperature dry test: (a) low-temperature dry shear force–displacement curve and (b) low-temperature dry shear stress–strain curve.

It can be seen from Figure 6 that the displacement and strain corresponding to the maximum shear force of specimen 1 to specimen 5 are 9.40, 10.05, 10.10, 9.80, and 10.20 mm, and 0.058, 0.042, 0.051, 0.041, and 0.046, respectively. Table 1 is a comparison table of strength parameters in different environments after calculation.

From Table 1, it can be seen that in terms of tensile strength, the tensile strength parameters, shear modulus size, and compressive strength parameters obtained from standard environmental experiments are 771.83, 94.24, and 830.93, respectively. The strength parameters corresponding to the high-temperature wet state and low-temperature dry state are lower than the standard values, indicating that the material exhibits varying degrees of performance degradation in abnormal environments. Among them, for the tensile strength parameter, the maximum degradation occurs in the low-temperature dry condition, the tensile strength of the material is 534.2 MPa, and the degradation rate is 30.8%. For the shear modulus, the maximum degradation occurs in the high-temperature wet state. Under the state condition, the corresponding value is 51.4 MPa and the degradation rate is 45.5%. In terms of compressive strength, the maximum degradation rate also appeared in the high-temperature and wet state, the corresponding value was 648.47 MPa, and the degradation rate was 21.9%.

3.2 Experimental results of mechanical properties of epoxy asphalt materials based on temperature changes

The research uses dynamic mechanical analysis instruments made in the United States to carry out temperature tests on epoxy asphalt materials, including viscoelasticity tests, tensile performance tests, and interfacial bonding performance tests. Figure 5 is the change curve of material viscoelasticity under each test temperature experiment.

On the basis of change curve in Figure 7, the storage modulus of epoxy asphalt material increases as the temperature decreases from +80°C to −80°C. When the temperature is lower than −50°C, the storage modulus of the material is as high as 2698.79 MPa, and when the temperature is higher than 50℃, the storage modulus of the material can be lower than 0.25 MPa. According to these two nodes, epoxy asphalt materials can be divided into low-temperature glass state, medium-temperature transition state, and high-temperature rubber state. At the same time, in line with loss modulus curve in Figure 5, the highest value of the modulus is 394.69 MPa near the temperature of −42°C. The high loss modulus only occurs in the glass transition process. In this process, high energy loss is achieved because the molecular motion of the material lags behind the stress change level. Therefore, −42°C can be regarded as the glass transition temperature of the epoxy asphalt material. The phase angle curve has two peaks and one peak-to-peak value. The first peak of the phase angle is 0.619 at −16.9°C, followed by a secondary peak of 0.638 at 18.8°C, and the peak-to-peak valley appears at −6.3°C. The phase angle is 0.604. The reason for the double peak phenomenon is that the epoxy bitumen material is a multi-component material, and there is intra-group repulsion between the modified bitumen and the curing agent, which makes the phase appear double peak. At the same time, the temperature zone corresponding to the phase angle tangent value higher than 0.3 is −40 to 67°C, which includes the working temperature range of epoxy asphalt material, that is, between −20 and 60°C. The storage modulus, loss modulus, and phase angle reflect the elastic properties, viscous properties, and viscoelastic ratio of the material, respectively. Therefore, in the working temperature range, even if the material encounters instantaneous shocks such as train starting or parking, it can rely on its elastic properties. Good viscoelasticity buffers the dynamic load, resists the deformation caused by the external force, and returns to the stable state under the fast response. Figure 8 is a graph showing the results of tensile mechanical properties test.

Figure 7

Viscoelastic change curve of materials under various test temperatures.

Figure 8

Curve chart of tensile mechanical property test results: (a) tensile stress–strain curve and (b) tensile strength and elongation at break curve.

On the basis of Figure 8(a), the relationship between tensile stress and strain of epoxy asphalt material is divided into two categories within its working temperature range. The first type is the curve from −20 to 0°C. This type of curve reflects the characteristics of elastic deformation and is divided into two stages of change. The first stage is between 0 and 71% of the strain, which is called the elastic deformation zone. At this time, the tensile stress and strain approximately show a positive proportional linear increase relationship, and the maximum stress value is reached at the strain of 71%, which is 0.62, 0.41, and 0.33 MPa. The strain between 71 and 375% is the second stage, which is called the post-yielding stress softening zone. At this time, the increase of strain will reduce the tensile stress of the material, the material will shrink, and the tensile interface will decrease until the material breaks. The second type is the curve from 0 to 60°C. Compared with the first type of curve, there is no post-yielding stress softening zone. The epoxy asphalt material as a whole exhibits linear elastic characteristics, that is, the curve before and after the temperature increase can keep the same slope, and the stress and strain always show a positive correlation. In line with Figure 8(b), the increase in temperature reduces the tensile strength of the epoxy asphalt material. In the entire working temperature range, the tensile strength value of the material decreases from 0.629 to 0.258 MPa, and the curvature also shows a downward trend. The minimum tensile strength is 0.258 MPa. The elongation at break of the material had a tendency of raising before reducing, increasing from 311.78 to 354.55% in the entire working temperature zone and then decreasing to 228.89%. Figure 9 is a graph showing the results of the interfacial adhesion test.

Figure 9

Curve of interface adhesion test results: (a) stress–strain curve of interfacial adhesion, (b) bond strength change curve, and (c) change curve of bond elongation.

The interfacial adhesion mainly occurs between the contact between epoxy asphalt and concrete; especially, the working temperature of the material is higher than the glass transition temperature, so the material will show significant adhesion performance under variable temperature conditions. On the basis of Figure 9(a), when the test temperature is set between −20 and 0°C, the interface bond of the material will be damaged, corresponding to three processes, namely, the rising section where the stress increases linearly with the strain; after reaching the maximum compressive stress of the interface, the stress decreases with the strain and the failure section where the material is gradually and completely separated from the concrete. When the test temperature is set from 0 to 60°C, the failure process of the material will be divided into two stages. The first stage is an approximate linear region where the stress increases with the strain, and the second stage is that the strain further increases but the stress rapidly follows. Destruction segment reduces and eventually separates from the concrete. On the basis of Figure 9(b), the bond strength of epoxy asphalt material decreases continuously with the increase in temperature, and the decreasing speed shows a trend of first fast and then slow. In the whole working temperature area of the material, the bond strength decreases from 0.568 to 0.0331 MPa. Among them, in the temperature zone −20 to 0°C, 0 to 40°C, and 40 to 60°C, the decrease rates of adhesion degree are 65.1, 75, and 26.7%, respectively. On the basis of Figure 9(c), the bond elongation shows a trend of first increase and then decrease, and taking 0°C as the dividing point, in the temperature range below 0°C, the bond elongation increases from −20°C to 85.7% increased to 256.7% at 0°C, while the bond elongation of the material decreased from 256.7% at 0°C to 80.6% in the temperature region above 0°C. Therefore, the results show that epoxy asphalt materials exhibit different mechanical properties before and after the demarcation point at 0°C.