Microstructural analysis to uniaxial low cyclic compression of high-strength concrete after high temperature

Abstract

The uniaxial compressive cycling tests of high-strength concrete after high temperature under different stress were carried out using the electrohydraulic servo-controlled fatigue testing system. The investigation focused on low-cycle fatigue to figure out the relationship between microstructural development and number of cycles. The variation in microstructure during uniaxial compressive fatigue process was systematically analyzed and compared using ultrasonic, micro-hardness test, mercury intrusion porosimetry, and scanning electron microscopy. It is found that at the same life ratio, the cumulative fatigue damage caused by the lower stress is greater than that caused by the higher stress, and the four kinds of test methods used to measure the microstructure are consistent, interrelated, and confirmed with each other well. Through the nonlinear regression analysis of fatigue residual strain and microstructural parameters, the relationship models between them were established. Furthermore, the fatigue damage models based on microstructural parameters were established. On this basis, both the dynamic evolution process and damage mechanism of microstructure during uniaxial compressive fatigue were further revealed.

Keywords

high-strength concrete high temperature microstructure uniaxial compression fatigue

Introduction

In recent years, high-strength concrete (HSC) is widely used in the world. However, it might suffer from high-temperature processes caused by fire or other factors, as well as cyclic loading such as earthquakes, vehicles, and wind waves so that HSC tends to be damaged in different degrees. In order to meet the requirements of seismic fortification of HSC structures after fire, it is necessary to take full account of the damage caused by the comprehensive conditions of temperature processes and fatigue to HSC structures. Furthermore, the damage is not only at the macroscopic but also at the microstructure and microstructural damage is the root cause of macroscopic damage. Therefore, it is very important to understand the developments of microstructure of HSC under high temperature and uniaxial compressive fatigue.

In the past few decades, many research works have been carried out to investigate the fatigue properties and microstructure of HSC after high temperature. The research focused on the compressive fatigue properties of plain concrete at 100°C–300°C and pointed out that micro-cracks formed on the interface of aggregate gradually develop with the increasing temperature. Under the cyclic loading, these micro-cracks were further expanded, which greatly reduced the uniaxial compressive fatigue behavior of ordinary-strength concrete (Zhou and Zhang, 2001). In comparison with ordinary-strength concrete, the mechanical properties and fatigue damage of HSC after high temperature were investigated and found that fatigue deformation modulus and fatigue longitudinal total strain were in accordance with the three-stage development. The regression analysis of fatigue life (the number of cycles to failure) was carried out in order to establish the damage model between high-temperature process and compressive fatigue damage (Gao, 2017).

The microstructure of HSC will gradually deteriorate with the temperature increasing and will burst at high temperatures (Li et al., 2008). Differential thermal analysis (DTA), thermo gravimetric analysis (TGA), scanning electron microscopy (SEM), and mercury intrusion porosimetry (MIP) were used to test the changes of microstructure of high-performance concrete after high temperatures (Liu et al., 2008). In order to establish the mathematical model between high temperature and residual strength, the microstructural evolution mechanism of HSC under the effect of high temperature was investigated by ultrasonic, micro-hardness test, X-ray diffraction (XRD), SEM, and MIP (Liu, 2016; Zhao and Liu, 2015). A number of experimental studies have reported the effects of high temperature on pore structure and micro-cracks of HSC using SEM, XRD, and MIP and correlation between macroscopic physical properties and microstructure (Georgali and Tsakiridis, 2005; Henry et al., 2014; Rossino et al., 2015; Saridemir et al., 2016).

In terms of material behavior, the development of fatigue damage in microstructure was rarely investigated. Several investigations used the multi-scale method to analyze the fatigue crack propagation in concrete. The crack propagation was described using stress intensity factor (SIF), which also predicted the process of micro-crack propagation. It pointed out that the sample size played an important role in the process of micro-crack propagation. Finally, fatigue crack growth model was established (Gaedicke et al., 2009; Shah et al., 2014; Simon and Chandra Kishen, 2017).

At present, these research works mostly focus on the single effect of high temperature or fatigue damage. However, few studies on the microstructural properties of HSC after high temperature and fatigue loading were done. Therefore, the microstructural behavior of HSC after high temperature and uniaxial compressive fatigue was investigated intensively within the scope of a research focusing on low-cycle fatigue. The microstructure of HSC after high-temperature and uniaxial compressive fatigue was analyzed and compared using ultrasonic, micro-hardness test, MIP, and SEM. Based on the nonlinear regression analysis of fatigue residual strain and the microstructural parameters, the relationship models between them were established. Furthermore, the fatigue damage models based on microstructural parameters were established. On this basis, both the dynamic evolution process and damage mechanism of microstructure were further revealed, which could be used as a reference for nondestructive testing, fatigue damage analysis, and structural assessment of HSC suffering from fire or other high-temperature process.

Experimental program

The uniaxial compressive fatigue test of HSC after high temperature

The 100 mm × 100 mm × 100 mm cube specimens were produced with the material of C60, whose mixture proportion is shown in Table 1. The heating of specimens carried out by exposing them to 100°C, 300°C, 500°C, 700°C, and 900°C each target temperatures. The specimens were, respectively, exposed to target temperature for 1 h in steady-state condition. The thermocouples were put at 30 mm of the three adjacent surfaces of HSC in order to measure the temperature field. At the end of heating process, the specimens were exposed to slow cooling in the air (Liu, 2016; Zhao and Liu, 2015).

Table 1.

Mixture composition of HSC (kg/m³).

Cement	Sand	Coarse aggregate	Water	Water-reducingagent	Water/binder
510	720	1040	144	11.0	0.32

HSC: high-strength concrete.

The static load test was carried out with the electrohydraulic servo pressure machine. The axis of specimen was coincident with the axis of the machine panel before test, then repeatedly preloading and unloading the specimen three times with 20% of the upper limit load; then, pressure was applied at a rate of 0.3–0.8 MPa/s on the specimen until failure, and the compressive strength of the specimen was obtained (Gao, 2017).

The uniaxial compressive fatigue tests were performed in the PA-500 electrohydraulic servo-controlled fatigue testing system. The tests were carried out under load control with a sinusoidal waveform of 10 Hz. Three different stress were considered. Those maximum stress were 0.80, 0.85, and 0.90, respectively. The minimum stress was 0.10 (Gao, 2017).

The microstructural tests of HSC during uniaxial compressive fatigue process after high temperature

In this study, microstructural analyses during uniaxial compressive fatigue process of HSC exposed to elevated temperature were performed using NM-4B nonmetal ultrasonic testing analyzer, FM-800 micro-hardness test, Autopore IV9500 MIP, and HITACHI S-4300 SEM. The ultrasonic analyses were performed on the two surfaces unexposed to elevated temperature. The specimens completed by ultrasonic testing were cut parallel to the surface without elevated temperature along the center line into 10-mm slices, which were used for the micro-hardness analyses. The MIP analyses and the SEM analyses were performed at 30 mm of the three adjacent surfaces of the small pieces. For the SEM analyses, the small pieces were mounted on the brass stubs using carbon tapes and covered with gold (Liu, 2016; Zhao and Liu, 2015). Test equipment are shown in Figures 1 to 3.

Figure 1.

FM-800 micro-hardness test.

Figure 2.

Autopore IV9500 pressure mercury test.

Figure 3.

HITACHI S-4300 scanning electron microscope.

Test results of fatigue

Heating system

The heating rate was set according to the ISO834 fire standard temperature–time curve (Liu, 2016; Zhao and Liu, 2015), as shown in Figure 4. Previous related research has measured the change of temperature field of 30 mm from the adjacent three surfaces of test blocks (Liu, 2016; Zhao and Liu, 2015). The temperature field is shown in Figure 4. In the heating stage, the temperature increased in different degrees inside the test block, temperature near the fire surface rose faster, but at the central part rose relatively slowly. When the heating temperature reached the specified temperature, with the increase in holding time, the temperature near the four surfaces gradually remained stable. However, the temperature at the measured points was still slowly rising and the heating rate was low. The main reason is that concrete is a thermal inert material, which has a large temperature gradient inside concrete. Although the initial temperature of the external surface was very high, the heat conduction was getting less and less at the measured points, so the temperature rose slowly. When the temperature was constant, the temperature near the surface quickly reached the target temperature and remained stable, but concrete continued to absorb energy and transfer it to the inside, the internal temperature gradually increased (PX-X: Heating temperature-holding time; P1-1: heating temperature is 100°C, holding time is 1 h).

Figure 4.

The internal temperature field of 30 mm from the adjacent three surfaces of test block.

Fatigue life of HSC after high temperature

Fatigue life of HSC after high temperature is shown in Table 2. It is generally believed that the fatigue life of concrete is subject to the lognormal distribution. Therefore, the logarithm of the mean value of the fatigue life obtained under the same stress is used as the average fatigue life (Gao, 2017). The compressive strength of HSC after high temperature is measured under the condition of antifriction.

Table 2.

Fatigue life of HSC after high temperature.

Specimen number	$f_{c}^{T}$ (MPa)	Fatigue life (Ni) $0.9 f_{c}^{T} 0.85 f_{c}^{T} 0.8 f_{c}^{T}$			Fatigue life (ln Ni) $0.9 f_{c}^{T} 0.85 f_{c}^{T} 0.8 f_{c}^{T}$			$Y_{1} = ϕ^{- 1} (F (\ln N_{i}))$
RT	49.6	15,488	67,608	194,984	9.65	11.12	12.18	0.257	0.366	0.844
P1-1	34.6	177	32,359	141,253	5.18	10.38	11.86	−0.49	0.23	0.78
P3-1	39.4	199	16,218	64,565	5.29	9.69	11.08	−0.169	0.284	0.825
P5-1	38.8	363	109,647	141,253	5.89	11.61	11.86	−0.055	0.3	0.765
P7-1	19.3	2137	20,892	67,608	7.67	9.95	11.12	0.119	0.261	0.533
P9-1	10.0	891	3630	17,378	6.79	8.2	9.76	−0.185	−0.167	0.36

RT: room temperature; HSC: high-strength concrete;.

The lognormal distribution of the linear regression analysis is shown in Figure 5. It can be seen that the correlation coefficient (R²) is high and the linear relationship between ln Ni and Y₁ is better, which indicates that fatigue life of HSC under uniaxial compression fatigue after high temperature is subject to a lognormal distribution.

Figure 5.

Linear regression analysis of lognormal distribution of fatigue life for HSC after high temperature.

Test results and analyses of microstructure

Ultrasonic testing results and analyses

The sonic time was used to characterize the fatigue damage of HSC subjected to uniaxial compressive fatigue after high temperature. The sonic time of a certain number of cycles was measured at different stress. The test results are shown in Figure 6. The test block would be destroyed when loaded to 100% of the fatigue life, so the corresponding sonic time cannot be measured.

Figure 6.

Relationship between sonic time and relative number of cycles of HSC after high temperature: (a) RT, (b) P1-1, (c) P3-1, (d) P5-1, (e) P7-1, and (f) P9-1.

The effects of the relative number of cycles and the maximum stress on sonic time values of HSC after high temperature are shown in Figure 6(a) to (f) in three-dimensional (3D) graphs. These figures show that the sonic time values noticeably increase with the increase in the number of cycles. The sonic time values increase between 12.74 and 30.1 μs at 75% of the fatigue life. Furthermore, the sonic time values increase between 7.55 and 16.99 μs at the stage from before loading to 25% of the fatigue life. It was concluded that the sonic time increases with the increase in the number of cycles and its growth rate is generally fast–slow, which shows that the fatigue damage of HSC after high temperature increases rapidly at the beginning, while in the second stage of fatigue damage development it grows slowly.

On the other hand, the effect of different stress on the sonic time at the same temperature was compared and analyzed. At the same life ratio, HSC has higher sonic time values caused by low stress than that caused by higher stress, which also indicated that fatigue damage of HSC caused by low stress was higher at the same life ratio. Similar observations have been reported by the compressive fatigue damage of concrete under lateral pressure (Zhu and Song, 2004).

The variation of sonic time with the increase in the number of cycles was consistent with the development of the total strain and the residual strain of HSC after high temperature (Gao, 2017). The increase in sonic time and strain all indicated the accumulation of fatigue damage of HSC after high temperature.

Micro-hardness test results and analyses

The interfacial transition zone (ITZ) is the weakest area in HSC and the pores and micro-cracks usually develop from the interfacial zones between aggregate particles and cementitious matrix. The micro-hardness of the ITZ is a comprehensive reflection of the performance. So micro-hardness analyses were performed on ITZ at the 30 mm position of the adjacent three surfaces of HSC. The test results are shown in Figure 7.

Figure 7.

Relationship between micro-hardness and relative number of cycles of HSC after high temperature: (a) RT, (b) P1-1,(c) P3-1, (d) P5-1, (e) P7-1, and (f) P9-1.

The effects of the relative number of cycles and the maximum stress on micro-hardness (HV) of ITZ are shown in Figure 7(a) to (f) in 3D graphs. On the one hand, these figures show that the HV values of ITZ obviously decrease with the increase in the number of cycles. The HV values decrease between 13.88 and 23.99 GPa at 75% of the fatigue life. Furthermore, the HV values decrease obviously about 6.13–17.28 GPa from before loading to 25% of the fatigue life. It was concluded that the micro-hardness of ITZ is decreasing with the increase in the number of cycles and the decrease rate is generally fast–slow. On the other hand, the effect of different stress on the micro-hardness of ITZ at the same temperature was compared and analyzed. The range of reduction in the micro-hardness of ITZ at the low stress is greater than that at higher stress at the same life ratio, which is consistent with the results of ultrasonic.

Furthermore, it is observed that the higher temperature, the less the reduction in the HV values at the point of 75% of the fatigue life, especially when it is exposed to 500°C, 700°C, and 900°C. This indicates that fatigue process has a greater impact on micro-hardness at lower temperature, while the effect of temperature on the reduction in micro-hardness is more obvious after higher temperature.

MIP test results and analyses

The MIP test was carried out at the 30 mm position of the three adjacent surfaces of HSC. The pore characteristics of the samples were quantitatively analyzed. The test results are shown in Table 3 and Figures 8 to 10. In this study, the pores were divided into the harmless pores (pore diameter <50 nm), the harmful pores (50 nm < pore diameter < 200 nm) and the more harmful pores (pore diameter >200 nm) based on the pore size distribution principles (Wu and Lian, 1999) and the pore characteristics of HSC (PX-X-X-X: heating temperature–holding time–maximum stress–relative number of cycles).

Table 3.

Test result of MIP.

Serialnumber	Code	The most probablepore size (nm)	The total porevolume (mL/g)	<50 nm (%)	50–200 nm (%)	>200 nm (%)
1	RT	32.4	0.0531	57.6	24.3	18.1
	RT-0.9-25%	50.3	0.0577	44.4	34.5	21.1
	RT-0.9-50%	40.3	0.0558	53.6	28	18.4
	RT-0.9-75%	62.5	0.0590	37.1	38.8	24.1
	RT-0.9-100%	77.1	0.0624	32.2	42.3	25.5
2	P1-1	40.3	0.0565	53.5	29.2	17.3
	P1-1-0.9-25%	62.5	0.0604	37.9	43	19.1
	P1-1-0.9-50%	66.3	0.0628	29.5	47.5	23
	P1-1-0.9-75%	70.5	0.0641	30.4	43.7	25.9
	P1-1-0.9-100%	77.1	0.0663	22.8	47.5	29.7
3	P3-1	50.3	0.0625	48.2	33.6	18.2
	P3-1-0.85-25%	62.5	0.0658	34.5	42.4	23.1
	P3-1-0.85-50%	77.1	0.0633	27.8	46.8	25.4
	P3-1-0.85-75%	70.4	0.0659	27.7	44.5	27.8
	P3-1-0.85-100%	88.6	0.0694	22.2	45.7	32.1
4	P5-1	77.1	0.0694	26.8	41.4	31.8
	P5-1-0.85-25%	95.3	0.0718	21.4	47.9	30.7
	P5-1-0.85-50%	85.1	0.0711	21.9	44.9	33.2
	P5-1-0.85-75%	95.4	0.0723	18.5	45.9	35.5
	P5-1-0.85-100%	106.4	0.0765	15.9	47.8	36.2
5	P7-1	86.2	0.0702	22.5	43.2	34.3
	P7-1-0.8-25%	95.6	0.0767	20.5	48.1	31.4
	P7-1-0.8-50%	101.2	0.0806	21.7	40.2	38.1
	P7-1-0.8-75%	98.5	0.0789	22.8	46.1	31.1
	P7-1-0.8-100%	105.1	0.0820	20.7	50.2	29.1
6	P9-1	120.5	0.0835	17.5	42.2	40.3
	P9-1-0.8-25%	125.7	0.0882	16.1	42.4	41.5
	P9-1-0.8-50%	128.7	0.0904	16.7	38.8	44.5
	P9-1-0.8-75%	123.6	0.0933	14.8	39	46.2
	P9-1-0.8-100%	125.4	0.1000	13.6	38.2	48.2

RT: room temperature; MIP: mercury intrusion porosimetry.

Figure 8.

Relationship between the total pore volume and relative number of cycles of HSC after high temperature.

Figure 9.

Relationship between the most probable pore size and relative number of cycles of HSC after high temperature.

Figure 10.

Relationship between the pores volume of 50–200 nm and relative number of cycles of HSC after high temperature.

The pore characteristics during fatigue process of HSC after high temperature are shown in Table 3 and Figures 8 to 10. When loaded to fatigue failure, a considerable increase in the total pore volume is observed by 0.0069–0.0165 mL/g. The main difference in the pore size distribution between before loading and fatigue failure is found in the pores of 4.9–44.7 nm. It can be seen that the total pore volume and the most probable pore size tend to increase significantly, with the increase in the number of cycles. The incremental rates of the total pore volume and the most probable pore size develop rapidly at the stage from before loading to 25% of the fatigue life. However, the incremental rates of the parameters tend to flatten at the stage of 25% to 75% of the fatigue life and become faster at the stage from 75% of the fatigue life to fatigue failure. The variation of the parameters shows the three-stage rule of fast–slow–fast, which is also consistent with the development of the total strain and the residual strain of HSC after high temperature (Gao, 2017).

It can be seen from Table 3 and Figure 10. The harmful pores of 50–200 nm increase obviously by 6.4%–18.3%. The number of harmless pores (pore diameter <50 nm) reduces to a certain extent. At the stage from before loading to 25% of the fatigue life, the pore characteristics are mainly manifested in that some harmless pores developed into the harmful pores so that the variation of porosity is significant. At the stage of 25% to 50% of the fatigue life, the main manifestation is that the harmful pores develop into the more harmful pores, leading to the reduction in harmful pores at this stage. The growth of the harmful holes slows down from 50% of fatigue life to fatigue failure. This is consistent with the pore characteristics (Han et al., 2017).

SEM observation and image analysis

Microstructural analyses during fatigue process of HSC after high temperature were carried out by SEM. The microstructure and interface between the aggregate particles and cementitious materials were examined on the crushed sample surfaces. As can be seen in Figures 11 to 13, the changes emerged in pore structure, micro-crack, and interface with the increase in the number of cycles. At lower temperatures, the ITZ between the aggregate particles and cementitious materials is compact and the cementitious materials is dense, continuous, and intact without obvious defects, as is shown in Figure 11(a) and Figure 12(a). When the elevated temperature was 700°C, the cementitious materials is crisp and the micro-cracks turn to criss-cross compared to 300°C and room temperature with obvious initial defects, as seen in Figure 13(a). As shown in Figures 11(b) to 13(b), when loaded to 50% of the fatigue life, the ITZ becomes looser and the number of pores increases dramatically. A large number of micro-cracks appear on the interface of aggregate and then expand from the edge of aggregate to cementitious materials. At this time, fatigue damage is mainly the accumulation of new micro-cracks in cementitious materials and the stable expansion of the original micro-cracks. The SEM images at fatigue failure are shown in Figures 11(c) to 13(c). It is clear that obvious stratification, stripping, and dislocation appear in the ITZ between the aggregate particles and cementitious materials, and a lot of communication gaps and voids emerge as well. On the other hand, the length and width of micro-cracks in cementitious materials grow rapidly, and the micro-cracks keep merging with the bond cracks and the leading cracks come into being. Then leading cracks continue to expand along the depth direction, forming a macroscopic fracture, which eventually leads to fatigue failure.

Figure 11.

SEM images during fatigue process at RT-0.9: (a) RT, (b) RT-0.9-50%, and (c) RT-0.9-100%.

Figure 12.

SEM images during fatigue process at P3-1-0.85: (a) P3-1, (b) P3-1-0.85-50%, and (c) P3-1-0.85-100%.

Figure 13.

SEM images during fatigue process at P7-1-0.8: (a) P7-1, (b) P7-1-0.8-50%, and (c) 7-1-0.8-100%.

The ITZ is the weakest area in HSC, in which the pores and micro-cracks development usually appear. The growth in the number of pores and cracks is consistent with the increase in the number of cycles, which caused the decrease in the bonding strength. It is concluded that the reduction in the bonding strength is a natural result of large pores and cracks due to the increase in the number of cycles. These cracks caused considerable reduction in the fatigue properties of HSC after high temperature. So the fatigue failure of HSC after high temperature occurs first in the ITZ. Similar conclusions and reports are revealed in the literature (Gaedicke et al., 2009; Simon and Chandra Kishen, 2017; Zhou and Zhang, 2001).

The relationship models of microstructural parameters and fatigue residual strain

The cumulative fatigue damage of HSC after high temperature is mainly manifested by the change of fatigue residual strain on the macroscopic and the change of the parameters on microstructure. Therefore, the fatigue residual strain and the change of the microstructural parameters both reflect the accumulation process of fatigue damage in a certain quantitative relationship.

As can be seen in Figure 14, the fatigue residual strain of HSC after high temperature shows three-stages rules, just as the total strain of fatigue (Gao, 2017). In order to obtain the relationships between the microstructural parameters (y) and the fatigue residual strain (ε_r,T) at different stress, the nonlinear regression of the microstructural parameters (y), the fatigue residual strain (ε_r,T), and the relative number of cycles (N/N_f) were formed, as shown in equation (1) (Table 4)

y = a ε_{r, T} + b {(\frac{N}{N_{f}})}^{3} + c {(\frac{N}{N_{f}})}^{2} + d (\frac{N}{N_{f}}) + eT + ft + g

(1)

where y is microstructural parameters; a, b, c, d, e, f, and g are coefficients.

Figure 14.

Relationship between fatigue residual strain and relative number of cycles of HSC after high temperature.

Table 4.

Expressions for coefficients of formula (1).

Microstructuralparameters	S _max	Coefficients							Correlation coefficient
Microstructuralparameters	S _max	a	b	c	d	e	f	g	Correlation coefficient
T_s	0.8	0.09	−89.69	142.17	−93.31	0.048	6.3	72.8	0.8321
	0.85	0.14	−84.48	126.32	−90.28	0.052	7.98	50.78	0.8479
	0.9	0.085	−42.24	54.46	−59.6	0.06	7.5	57.23	0.8242
HV	0.8	−0.04	40.44	−59.82	32.6	−0.045	−5.62	72.67	0.8137
	0.85	−0.074	44.34	−70.43	58.8	−0.039	−4.52	60.45	0.8241
	0.9	−0.046	22.13	−24.69	27.7	−0.04	−7.82	68.24	0.8046
V	0.8	0.89 × 10⁻⁵	−0.0088	0.013	−0.0045	1.1 × 10⁻⁵	0.0012	0.073	0.8282
	0.85	1.25 × 10⁻⁵	−0.0075	0.012	−0.0093	0.8 × 10⁻⁵	0.0025	0.0683	0.7942
	0.9	0.093 × 10⁻⁵	−0.0045	0.005	−0.0064	0.9 × 10⁻⁵	0.0016	0.0124	0.8013

Fatigue damage models based on the microstructural parameters

The cumulative fatigue damage of HSC at the microstructure is manifested by the continuous expansion of internal micro-pores and micro-cracks, so the fatigue damage model can be established based on the microstructural parameters. According to the basic concepts of damage mechanics (Miner, 1945) and the development laws of sonic time, micro-hardness, and the total pore volume on HSC after high temperature and uniaxial compressive fatigue, the fatigue damage D is defined based on the microstructural parameters:

The fatigue damage D_m based on T_S is defined. The damage equation is given as follows

D_{m} = \frac{T_{s} - T_{S}^{0}}{T_{S}^{0.75 Nf} - T_{S}^{0}}, D_{m} \in (0, 1)

(2)

where $T_{S}^{0}$ is the sonic time of HSC after high temperature, T_S is the sonic time during fatigue process of HSC after high temperature, and $T_{S}^{0.75 Nf}$ is the sonic time at 75% of fatigue life of HSC after high temperature. The relationships between the fatigue damage D_m and relative number of cycles of HSC after high temperature are shown in Figure 15.

2. The fatigue damage D_n based on HV is defined. The damage equation is given as follows

D_{n} = \frac{HV - H V^{0}}{H V^{0.75 Nf} - H V^{0}}, D_{n} \in (0, 1)

(3)

where HV⁰ is the micro-hardness of HSC after high temperature, HV is the micro-hardness during fatigue process of HSC after high temperature, and $H V^{0.75 Nf}$ is the micro-hardness at 75% of fatigue life of HSC after high temperature. The relationships between the fatigue damage D_n and relative number of cycles of HSC after high temperature are shown in Figure 16.

3. The fatigue damage D₀ based on V is defined. The damage equation is given as follows

D_{o} = \frac{V - V^{0}}{V^{Nf} - V^{0}}, D_{o} \in (0, 1)

(4)

where V⁰ is the total pore volume of HSC after high temperature, V is the total pore volume during fatigue process of HSC after high temperature, and $V^{Nf}$ is the total pore volume at fatigue failure of HSC after high temperature. The relationships between the fatigue damage D₀ and relative number of cycles of HSC after high temperature are shown in Figure 17.

Figure 15.

Relationship between fatigue damage D_m and relative number of cycles of HSC after high temperature: (a) S_max = 0.90, (b) S_max = 0.85, and (c) S_max = 0.80.

Figure 16.

Relationship between fatigue damage D_n and relative number of cycles of HSC after high temperature: (a) S_max = 0.90, (b) S_max = 0.85, and (c) S_max = 0.80.

Figure 17.

Relationship between fatigue damage D₀ and relative number of cycles of HSC after high temperature.

Above all, the proposed fatigue damage models can be used for multistage fatigue cumulative damage analysis of HSC after high temperature, which is achieved agreeable to the results of Gao (2017). This analysis can also be used to predict remaining fatigue life of the sample.

Discussion

This work focuses on the microstructure during uniaxial compressive fatigue process of HSC after high temperature. Both the dynamic evolution process and damage mechanism of microstructure were further revealed.

The changes of microstructural parameters such as sonic time, micro-hardness, pore size distribution, and accumulated mercury content show a fast–slow–fast trend as three-stage rules. This indicates that the internal micro-crack development can be divided into three stages, which is consistent with the three-stage rules of the longitudinal total strain and residual strain of HSC after high temperature subjected to uniaxial compressive fatigue (Gao, 2017).

Before fatigue loading, a lot of micro-voids and micro-cracks have existed in HSC after high temperature. The formation of these defects is related to the process of coagulation, hardening, and high temperatures. The first stage (the rapid micro-cracks development stage) is from before loading to 25% of the fatigue life. In this stage, micro-voids quickly absorb the energy in ITZ so that the pore diameter and the porosity increase sharply and the micro-cracks are formed, which causes a significant increase in sonic time and considerable decrease in micro-hardness. At this time, the micro-cracks extend substantially along the boundaries of aggregate.

The second stage (the micro-cracks linear development stage) is from 25% to 75% of the fatigue life. During this process, the micro-cracks will expand. The area adjacent to the tip of micro-cracks has not been destroyed, but the material can be considered to have been destroyed at the tip micro-crack area. Due to the large reduction in the modulus of elasticity of material destruction area, the ability to resist deformation is weak and the stiffness at both ends is relatively high so that the micro-crack tip has produced a relatively strong stress concentration. After the micro-cracks are gradually away from aggregate, the direction of expansion is essentially constant. In this stage, development of micro-cracks enters into a stable stage and amplitude of the measured parameters tends to be gentle.

The third stage is from 75% of fatigue life to fatigue failure. The change of pore size and accumulated mercury in this stage is faster and micro-crack width is increasing. The formed micro-cracks expand with others in cementitious materials, which gradually form macro-cracks. These macroscopic cracks extend unsteadily in the depth direction under the action of fatigue loading, which eventually leads to failure, so amplitude of the parameters change fast in this stage. The whole process can be confirmed by the consistency of the parameters such as sonic time, micro-hardness, pore size distribution, and cumulative mercury content as well as the images during fatigue process by SEM.

Conclusion

The following conclusions were drawn from the experimental results described in this article:

With the increase in the number of cycles, the sonic time tends to increase, while the micro-hardness decreases. The number of the most probable pore size, the total pore volume, and the harmful pores tend to increase significantly and the number of the harmless pores reduces to a certain extent in ITZ. The variations of the parameters show almost fast–slow–fast trend and obvious three-stage rules. The changes of pores and micro-cracks during fatigue process are analyzed and compared qualitatively by SEM images.

At the same life ratio, the cumulative fatigue damage caused by the lower stress is greater than that caused by the higher stress during uniaxial compressive fatigue of HSC after high temperature.

The four kinds of test methods used to measure the microstructure are consistent, interrelated, and confirmed with each other well. The relationship models between the fatigue residual strain and the microstructural parameters are established. Furthermore, the fatigue damage models based on microstructural parameters were established. On this basis, both the dynamic evolution process and damage mechanism of microstructure of HSC during fatigue process after high temperature are deeply revealed, which could be used as a reference for nondestructive testing, fatigue damage analysis, and structure assessment of HSC suffering from fire or other high-temperature processes.

Footnotes

Appendix 1 Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research described in this paper was financially supported by the National Natural Science Foundation of China (Grant No. 51378045). The authors express their gratitude for this financial support. This work was supported by Beijing Higher Institution Engineering Research Center of Civil Engineering Structure and Renewable Material (Beijing University of Civil Engineering and Architecture), Beijing Collaborative Innovation Center of Energy Conservation and Emission Reduction Technology and Beijing Advanced Innovation Center for Future Urban Design. The authors acknowledge the mentioned support gratefully.

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