Influence of construction-induced damage on the degradation of freeze–thawed lightweight cellular concrete

Abstract

During the construction of lightweight cellular concrete (LCC), material damage frequently occurs, causing the degradation and deterioration of the mechanical performance, durability, and subgrade quality of LCC. The construction-induced damage can be more significant than those from the service environment of LCC, such as freeze–thaw (F–T) action in cold regions. However, the effect of construction-induced damage on LCC during F–T cycles is often ignored and the deterioration mechanisms are not yet clarified. In this study, we investigated the factors causing damage during construction using a sample preparation method established to simulate the damage in the laboratory setting. We conducted F–T cycle tests and microstructural characterization to study the effect of microstructural damage on the overall strength of LCC with different water contents under F–T actions. We established the relationship between the pore-area ratio and F–T cycle times, pore-area ratio, and strength, as well as the F–T cycle times and strength under different damage forms. The damage evolution is provided with the rationality of the damage equation, verified by comparing the measured and predicted damage variables. This study would serve as a guide for the construction and performance of LCC in cold regions.

Graphical abstract

Keywords

lightweight cellular concrete / construction-induced damage / freeze-thaw action / microstructure / degradation mechanism

1 Introduction

Lightweight cellular concrete (LCC) is defined by the American Concrete Institute as a mixture of cement, water, and prefabricated foam. As a new type of civil engineering material, LCC has several advantages, including lightweight, self-compacting, high workability, high thermal insulation, and low aggregate consumption [1,2], compared with conventional concrete. Owing to its numerous advantages, LCC has been used in subgrade filling, bridgehead jumping, thermal insulation, among others [3–6].

The mechanical performance and durability of LCC are critical for its applications in civil and construction engineering [7–10]. In a cold environment, freeze–thawing (F–T) action is the leading cause of microstructural damage and deterioration of mechanical properties. Recently, efforts have been made to strengthen LCC with additives [11]; yet, there are only a few studies on the durability of LCC, although there are studies on the microstructural damage and durability of other concrete materials. Luo et al. [12] conducted a quantitative analysis of the microstructural evolution of concrete materials under F–T actions by three-dimensional X-ray computed tomography (CT). They studied the damage characteristics and pore network (porosity, pore size, and pore distribution). Dong et al. [13] combined X-ray nano-CT and a microscale cohesive-zone model to quantitatively investigate the microstructural damage evolution and its effect on fracture behavior of F–T concrete structures. These studies on microscopic mechanisms help understand the essential causes of material failure and improve the properties of materials. However, studies have shown that the F–T failure mechanisms of LCC may be different from that of concrete [14,15]. The presence of water in the large air pores could be the leading cause of LCC failure, whereas the leading cause of F–T failure in concrete is the freezing of water in capillary pores. Therefore, the fundamental investigation of LCC degradation and deterioration in F–T environments cannot directly refer to conventional concrete materials.

Considering the time, the durability of LCC is affected in two stages. In the initial stage (prior to service and operation), the damage may be associated with the quality of the ingredient materials, such as the strength grade of cement, mix ratio, foaming and pouring equipment, and construction and maintenance conditions, which affect the quality of LCC [16,17]. On the other hand, in the service and operation stage, the damage can be affected by the environment and loading, causing the degradation of durability [18–20]. Currently, most studies focus on the impact of environmental and loading factors during the service and operation stage, whereas only a few studies on construction-induced damage during the initial stage have been reported. The damage caused by materials and mixing ratio in the design stage can be reduced through comparison and optimization [21–25]. The damage caused by foaming and pouring equipment can be overcome by employing standardized operations. However, it is difficult to effectively control the pouring uniformity and thickness by construction and specifications in the construction stage. The pouring process inevitably results in pouring intervals and boundaries. Therefore, these four aspects are the key factors affecting the construction-induced damage in LCC.

In this study, we investigated the LCC used in subgrade filling. We simulated the construction-induced damage in laboratory tests. F–T cycle tests and microstructural observations were conducted to examine the mechanisms of strength deterioration in LCC with different water contents. The damage variables were defined in terms of the compressive strength, and the evolution equations of pore-area ratio, F–T cycle times, and damage variables were established with their verified rationality. This study provides a reference and guide for LCC construction in F–T environments to improve the durability of LCC materials.

2 Materials and methods

2.1 Materials

Conch brand 42.5R ordinary Portland cement, produced by Zhonglian Cement Factory, Nanjing, China, was used to prepare the LCC samples. The specific gravity and surface area of the cement were 3.12 kg/m³ and 256.0 m²/kg, respectively. Other basic physical and mechanical properties are listed in Table 1 and the main compound contents in Table 2. The foaming agent was selected from the compound protein bubble liquid produced by Henan Huatai engineering Co., Ltd. with a pH value of 7.0 and density of 1.2 t/m³.

2.2 Sample preparation

Factors causing damage during construction were obtained by analyzing the full life cycle stages. The full life cycle can be divided into the project decision, project implementation, and operation stages. As shown in Fig. 1, the initial stage of LCC includes the design, construction, and preparation stages before usage.

In the construction stage, pouring uniformity, thickness, interval, and boundary setting are the key factors causing damage in LCC. The pouring interval and boundary setting are called “interface technology (IT)”, and they affect the surface strength and durability of samples. Pouring uniformity and thickness are termed “filling technology (FT)”, which mainly affect the internal density uniformity and strength of LCC.

According to the pouring condition of LCC, the similitude theory was employed to determine the pouring parameters of LCC in the laboratory tests. The construction-induced damage was analyzed using two samples already used to simulate the damage, as shown in Fig. 2.

2.2.1 Pouring parameters

According to the specifications [24], LCC thickness should not exceed 80 cm in a single pouring. Samples were prepared using a mold of height 10 cm. During the laboratory simulation of on-site pouring, each physical parameter was determined according to the similarity ratio theory as follows:

In on-site constructions, the thickness of a single pouring is 80 cm. The scale ratio of 1:8 was adopted here, and the geometric similarity ratio was C_{\mathrm{L}}={\displaystyle \frac{\mathrm{Model\; size}}{\mathrm{Prototype\; size}}}=\lambda ={\displaystyle \frac{\mathrm{1}}{\mathrm{8}}}. The pouring parameters are listed in Table 3.

The equation for the pouring parameters is as follows:

(1)f(T,h,P,\gamma ,\sigma ,E,\upsilon )=\mathrm{0},

where T, h, and P are the basic physical parameters, and the other four parameters are defined thus:

(2){\pi }_{\mathrm{1}}={\displaystyle \frac{\gamma }{P{h}^{-\mathrm{3}}}},{\pi }_{\mathrm{2}}={\displaystyle \frac{\sigma }{P{h}^{-\mathrm{2}}}},{\pi }_{\mathrm{3}}={\displaystyle \frac{E}{P{h}^{-\mathrm{2}}}},{\pi }_{\mathrm{4}}=\upsilon \mathrm{.}

The subscript of the scale model is denoted as m. The similarity between the prototype and model is expressed as follows:

(3){\pi }_{\mathrm{1}}={\pi }_{\mathrm{1m}},{\pi }_{\mathrm{2}}={\pi }_{\mathrm{2m}},{\pi }_{\mathrm{3}}={\pi }_{\mathrm{3m}},{\pi }_{\mathrm{4}}={\pi }_{\mathrm{4m}}\mathrm{.}

The time interval of the laboratory pouring was consistent with that of the on-site, thus, C_{\mathrm{T}}={\displaystyle \frac{T_{\mathrm{m}}}{T}}=\mathrm{1}, and C_{\mathrm{P}}={\displaystyle \frac{P_{\mathrm{m}}}{P}}={\lambda }^{\mathrm{2}}={\displaystyle \frac{\mathrm{1}}{\mathrm{64}}}. The materials used in the laboratory test were the same as those used in the field. Other physical parameters were similar after dimensional analyses, as shown in Table 4.

Yu [25] reported that the optimal pouring thickness of LCC should be controlled around 50 cm. Therefore, in the layered pouring simulation, two layers are poured, with each layer having a thickness of 5 cm.

2.2.2 Sample preparation methods

In the construction stage, IT and FT may cause the LCC to develop two types of damage. The following two methods were used to simulate the two possible damages.

a) Sample preparation method for simulating interface technology

Two factors affect IT: pouring interval and boundary. The effect of these factors on the damage formation in LCC was analyzed. Specifically, for pouring intervals, two sets of factors affect the damage in LCC. First, the LCC slurry weight, construction personnel, machinery, and other loads on the lower LCC during the construction of the upper part. Second, the construction joints in layered pouring affect the damage as well as the integrity of the LCC subgrade filling.

Further, because of pouring boundaries, it is necessary to consider the acid and base permeation of rainwater, the effect of ambient temperature, and the concentration of boundary stress, which may damage the durability in the operation stage. To simulate the transverse crack between the pouring layers, the mold was first filled to half (5 cm) and sealed to cure. When the designed pouring interval reached, the mold was completely filled to form the complete sample. After pouring, a plastic wrap was used to cover the cast, and it was maintained for 48 h. The pouring interval was 4, 8, and 16 h, respectively. The sample is shown in Fig. 3.

b) Sample preparation method for simulating filling technology

Two factors affect FT: pouring uniformity and thickness. The effect of these factors on the damage in LCC was analyzed as follows. For the pouring uniformity, during single-layer pouring, the cement slurry density is higher than that of the bubbles. Under the action of gravity, the cement is deposited downward and the bubbles are moved upward when squeezed, resulting in the increased strength of LCC from top to bottom.

For the pouring thickness, layered pouring is sometimes required considering the effects of the heat of hydration and dry shrinkage. The pouring thickness affects the generation of microcracks in LCC. On the other hand, in single-layered pouring, pouring is completed from the bottom and layer by layer, because the slurry is not independent. Therefore, the layer by layer thickness should also be considered in single-layered pouring, and the size also affects the uniformity of pouring.

To simulate the change in density with the depth of the sample, the degree of defoaming was controlled with the time of layered stirring during pouring to control the slurry density. The pouring was performed three times with two pouring intervals. First, the LCC slurry was poured into the mold to 1/3 of the height, and the remaining slurry was stirred according to the designed stirring time. Then, the mold was filled to 2/3 of its height. The remaining slurry was continuously stirred for a designed stirring time and then poured to fill the mold. The stirring time intervals were 1, 3, and 5 min. The sample is shown in Fig. 4.

2.3 Experimental design

2.3.1 Experimental parameters

Unconfined compressive strength is selected as a strength parameter, and the damage variable and pore-area ratio are defined as micro-test parameters.

a) Unconfined compressive strength q_u: Three parallel tests were conducted for each group of two damaged samples. The unconfined compressive strength test was performed after each F–T cycle. The test was conducted according to the highway and geotechnical test regulations [26], and the arithmetic mean value of the three tests was recorded as the compressive strength:

(4)q_{\mathrm{u}}={\displaystyle \frac{F}{A}}\times {\mathrm{10}}^{-3},

where q_u (MPa) is the compressive strength of the LCC, F (kN) the ultimate failure load, and A (m²) the bearing area.

b) Water content {{\displaystyle \omega }}_{\mathrm{R}}: The standard 28-day cured samples were weighed and recorded as M₀. Three sets of parallel samples were subjected to 7-day indoor, standard, and water-immersion curing. The weight was recorded as M₁, and the water content was determined as

(5){\omega }_{\mathrm{R}}={\displaystyle \frac{M_{\mathrm{0}}-M_{\mathrm{1}}}{M_{\mathrm{1}}}}\times \mathrm{100}\%\mathrm{.}

c) Damage variable D: In continuum damage mechanics, the damage variable is often expressed by the attenuation degree of the elastic modulus of materials. The elastic modulus does regularly decreases with the evolution of damage. It is, therefore, assumed that the internal strength of an undamaged sample does not change during unconfined compression tests. When the degree of internal damage increases, the ultimate strength of the sample decreases, and the corresponding failure strain also decreases. In the case of one-dimensional unconfined compression, the LCC damage variable is defined as:

(6)D=\mathrm{1}-{\displaystyle \frac{f_{\mathrm{c}}}{f_{\mathrm{c0}}}},

where f_c0 is the unconfined compressive strength of the initial LCC sample and f_c is the unconfined compressive strength of the damaged sample. When the sample is not damaged, D is 0, and D is 1 when the sample is fully damaged.

d) Pore–area ratio H_S: The pore-area ratio was introduced as the characteristic parameter to describe the damage morphology and evolution process inside the sample, and the effect of the pore-area ratio on the damage was considered. The effect of damage on the performance of LCC after the F–T cycle was studied using microscopy-based phenomenological theory.

2.3.2 Freeze–thawing cycle test

According to specifications [27,28], undamaged samples with a water–gel ratio of 0.58 and bubble content of 700 L/m³ were set as the control for IT and FT, and the F–T cycle test was conducted under the same conditions as the IT and FT damage considering the curing condition, three water content levels were set according to different curing conditions after 28 d, including 7 d of indoor, standard, water-immersion curing, respectively. The water content order was .

During the F–T cycle test, the undamaged samples were labeled D, the IT samples DJ, and the FT samples CD. Three parallel samples were prepared for each group of horizontal samples, as shown in Fig. 5. The F–T cycle test was conducted according to ASTM D560/D560M-16 standard [29] and related studies [30,31], as shown in Fig. 6. Since the simulated temperature of the test is much lower than the temperature in the actual environment and the LCC surface does not directly contact the external environment, the number of F–T cycles that the LCC can withstand in the actual environment is more than that in the test.

2.3.3 Microstructural characterization

As shown in Fig. 7, the image data acquisition system is mainly composed of a long-distance microscope, a CCD camera, a light source, and an image capture card. The optical test system is used to obtain the microparameters and can enlarge the sample surface by 150.

The image data acquisition system imports the microstructure photos into the computer, and the image is analyzed and processed using a self-developed GeoImage program. The image segmentation method is used to binarize the mesoscopic image. Quantitative data on the microstructure of LCC, such as pore-area ratio, pore number, and particle orientation, can be obtained from statistical calculations. Figure 8 shows the microstructure of the LCC and its binary image. The black region shows the pore, and the white region is the skeleton structure of the cement hydration.

3 Results and discussion

3.1 Strength degradation mechanism

Based on the obtained sample strength, microstructural characterization was conducted to analyze the degradation mechanism of LCC strength under F–T action and study the variation law of the F–T cycle times, pore-area ratio, and LCC strength.

The middle part of each sample was selected for the undamaged sample. The middle parts of the upper and lower layers were chosen for the IT sample, and the average value was obtained. The middle part of the layer was directly selected for the FT sample. Each sample was tested three times and the results were averaged. The serial number represents the maintenance mode: serial numbers 1, 2, and 3 for standard, water-immersion, and indoor curing, respectively.

3.1.1 Strength degradation mechanism of undamaged samples

Figure 9 shows the change in the microstructure of the D-2 samples with F–T cycles, and Fig. 10 shows the fitting curve of the pore-area ratio of the undamaged samples with the number of F–T cycles. Figure 11 shows the fitting curve of the sample strength with the pore-area ratio.

For D-2 samples, the pores gradually increased with an increase in the F–T cycles (Fig. 9). Some pores broke up and coalesced with other pores, resulting in a larger pore-area ratio. The microstructural changes indicate that the destruction of the pore structure was the main cause of the decrease in the compressive strength of the LCC under F–T cycles. D-1 and D-3 samples with water content also exhibited a similar trend. Figure 10 quantitatively depicts the relationship between the pore-area ratio and the number of F–T cycles, and it is consistent with the microstructural observation results. For the three curing water contents, the correlation coefficient (R2) of the pore-area ratio and number of F–T cycles fitting curve was greater than 0.95, indicating a profitable linear growth. For the same number of F–T cycles, the pore-area ratios of the three groups of samples were in the order D-2>D-3>D-1, indicating that the pore-area ratio increases with an increase in the water content in the F–T cycle test. Furthermore, as shown in Fig. 11, there is an excellent exponential function relationship between the pore-area ratio and the compressive strength of the sample. As the pore-area ratio increased, the compressive strength of the samples declined linearly. At pore-area ratios greater than 47%, the strength decreased faster with an increase in the pore-area ratio.

3.1.2 Strength degradation mechanism of Interface Technology samples

Figure 12 shows the change in the microstructure of DJ-2 samples with the F–T cycle. Figure 13 shows the fitting curve of the pore-area ratio of the IT samples changing with the number of F–T cycles, and Fig. 14 shows the fitting curve of the sample strength with the pore-area ratio.

As shown in Fig. 12, the pores in DJ-2 samples gradually coalesced as the number of F–T cycles increased, and the pore-area ratio gradually increased. Figure 13 shows that for the three curing water contents, the correlation coefficient of the pore-area ratio and number of F–T cycles fitting curve was greater than 0.9, and the variation trend is similar to that of the undamaged samples. However, with an increase in the F–T cycle, due to the difference in the curing water content, the pore-area ratio of the three sample groups gradually opened a gap, which is different from that of the undamaged samples. The change in the pore-area ratio from the beginning to the end of F–T cycles was in the order DJ-2 (10.5%)>DJ-1 (10.2%)>DJ-3 (10.1%).

Only the data with a pore-area ratio of less than 54% in the IT samples are fitted, as shown in Fig. 14, and they show an excellent exponential relationship. However, the function model is different from that of the undamaged samples. At pore-area ratios less than 47%, the sample strength decreased rapidly with the pore-area ratio. When the pore-area ratio was more than 47%, the rate of decrease in the strength gradually declined, contrary to that of the undamaged samples. The main reason is that the interfacial bond strength of IT samples is destroyed first. Then, the strength of the sample decreases rapidly under the action of F–T cycles. Further, under moderate F–T cycles, the strength of the noninterface part of the samples gradually decreases so that the curve appears as a flat portion. When the durability limit state is reached, the noninterface part of the samples is destroyed, and the curve suddenly decreases again.

By fitting the experimental data, the effect of micropores and F–T cycle on the compressive strength of the IT samples were quantitatively analyzed. Considering that the pore-area ratio is nonlinear with the increase in the number of F–T cycles, and the strength is nonlinear with the increase in the pore-area ratio, the following relation is adopted for fitting:

(7)f_{\mathrm{c}}=f_{\mathrm{c0}}(\mathrm{1}-\gamma \cdot {\displaystyle \frac{b}{\alpha N_{\mathrm{J}}+c}}\cdot \ln (\beta \cdot H_{\mathrm{S}}+\mathrm{1})),

where f_c0 is the unconfined compressive strength of LCC in the initial state (f_c0 = 3.361MPa), N_J is the number of F–T cycles, and H_S is the pore-area ratio. The fitting parameter values are \alpha = -0.09432, b = 1.597, c = 1.709, \beta = 0.3089, \gamma = 0.0704. The correlation coefficient is 0.928.

3.1.3 Strength degradation mechanism of Filling Technology samples

Figures 15–17 show the change in the microstructure of the CD-2 samples with F–T cycles and the fitting curves of the pore-are ratio and change in strength with the number of F–T cycles. As shown in Fig. 15, as the F–T cycle progresses, the pore structure of CD-2 samples changes similar to that of the other two groups of samples. For the three curing water contents, the correlation coefficient of the pore-area ratio and number of F–T cycles fitting curve was greater than 0.9, and the variation trend is similar to that of the undamaged and IT samples (Fig. 16). Without considering the water content, the change in pore-area in the FT samples under F–T cycles was the smallest (9.240%). Figure 17 further shows that with an increase in the pore-area ratio, the fitting curve of the compressive strength and pore-area ratio of the F–T samples conformed to the same exponential function model as that of the undamaged samples. When the pore-area ratio was less than 56%, under the same pore-area ratio, the compressive strength of the immersion cured sample was the minimum, with little difference between the standard cured sample and the indoor cured samples. This indicates that the strength of the water-immersion cured sample in F–T was more affected by the F–T cycle.

By fitting the experimental data, we quantitatively analyzed the effect of micropores and F–T cycles on the compressive strength of the FT samples. The following relation was adopted for fitting:

(8)f_{\mathrm{c}}=f_{\mathrm{c0}}(\mathrm{1}-(\alpha \cdot N_{\mathrm{J}}+\mathrm{1})\cdot \ln (\beta \cdot H_{\mathrm{S}}+\mathrm{1})),

where f_c0 is the unconfined compressive strength of LCC in the initial state, f_c0 = 3.582 MPa, N_J is the number of F–T cycles, and H_S is pore-area ratio. The fitting parameters are \alpha = 0.002388, \beta = 87700, and the correlation coefficient is 0.973.

3.2 Relationship between the strength and damage under F–T cycles

The damage processes and the F–T cycle test are summarized to establish the quantitative relationship between the damage under F–T cycles and the strength of the sample, as follows:

(a) The relationship between the strength and the IT damage under F–T cycles is expressed as follows:

(9)f_{\mathrm{c}}=f_{\mathrm{c0}}[\mathrm{1}-\mathrm{0.0704}\cdot {\displaystyle \frac{\mathrm{1.597}}{\mathrm{1.709}-\mathrm{0.09432}\cdot N_{\mathrm{J}}}}\cdot \ln (\mathrm{0.3089}\cdot H_{\mathrm{S}}+\mathrm{1})],

with a fitting correlation coefficient of 0.928.

(b) The relationship between the strength and the FT damage under F–T cycles is expressed thus:

(10)f_{\mathrm{c}}=f_{\mathrm{c0}}(\mathrm{1}-(\mathrm{0.002388}\cdot N_{\mathrm{J}}+\mathrm{1})\cdot \ln (\mathrm{87700}\cdot H_{\mathrm{S}}+\mathrm{1})),

with a fitting correlation coefficient of 0.973.

3.3 Damage evolution and verification

Based on the above studies, the relations (Eqs. (7) and (8)) can be substituted into Eq. (6) to obtain the damage variable evolution relation under each damage condition. Prior to the F–T cycle test, the pore-area ratio had effects on the damage in the LCC. Hence, when the boundary is set to 0, the damage equation is not 0. However, when the pore-area ratio of LCC is 0 in the extreme state, the F–T cycle has no effect on the strength of LCC, and D is 0 in this case.

3.3.1 Damage variable evolution relation of IT damage under F–T cycles

Equation (11) shows that as H_S and N_J increase, the deterioration degree of the damage increases.

(11)D=\mathrm{1}-{\displaystyle \frac{f_{\mathrm{c}}}{f_{\mathrm{c0}}}}=\mathrm{0.0704}\cdot {\displaystyle \frac{\mathrm{1.597}}{\mathrm{1.709}-\mathrm{0.09432}\cdot N_{\mathrm{J}}}}\cdot \ln (\mathrm{0.3089}\cdot H_{\mathrm{S}}+\mathrm{1})\mathrm{.}

Figure 18 compares the measured and the predicted damage variables. The damage variables increase with the increase in the number of F–T cycles. In general, the error between the measured and the predicted values is small, with the predicted values slightly larger than the measured ones. From the prediction perspective, the relation tends to be more conservative. The maximum error of 0.02 occurred on the 6th attempt, indicating that the established damage variable evolution relation is reasonable.

3.3.2 Damage evolution relation of FT damage under F–T cycles

Equation (12) shows that with an increase in H_S and N_J, the damage deterioration degree increases.

(12)D=\mathrm{1}-{\displaystyle \frac{f_{\mathrm{c}}}{f_{\mathrm{c0}}}}=(\mathrm{0.002388}\cdot N_{\mathrm{J}}+\mathrm{1})\cdot \ln (\mathrm{87700}\cdot H_{\mathrm{S}}+\mathrm{1})\mathrm{.}

Figure 19 compares the measured and the predicted damage variable. In general, the error between the measured and predicted value is small, and the maximum error of 0.009 occurs in the 8th time, indicating that the established damage variable evolution relation is reasonable.

4 Conclusions

In this study, we investigated the effect of construction-induced damage on the strength degradation mechanism of LCC during subgrade filling. The whole life cycle of the LCC was divided into different stages, and the damage was evaluated in each stage. We established a method for simulating the damage based on the similarity theory. Microstructural characterization was conducted to examine the mechanism of degradation of the LCC strength under F–T cycles. The following conclusions are drawn.

1) The fitting curves of the pore-area ratio and the number of F–T cycles of the undamaged, IT, and FT samples all follow the linear growth model. However, the fitting curves of the strength and porosity area ratio of the three samples all conform to the exponential model. As the porosity area ratio increases, the strength of the samples decreases nonlinearly. The undamaged and FT samples conform to the same exponential function model. For the same cycle times, the pore-area ratio is in the order: water-immersion curing sample>standard curing sample>indoor curing sample

2) The fitting relation between the strength of two damaged samples with the change in pore-area ratio and cycle times was obtained. The relationship between the strength of LCC under F–T cycles and the pore-area ratio is quantitatively described, which unifies the macroscopic manifestation of the strength deterioration with the damage in the microstructure.

3) The effect of damage on the strength of LCC was established, and it indicates that the damage becomes more significant with an increase in pore-area ratio and number of F–T cycles. The rationality of the damage evolution relation was verified.

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