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Effect of wetting–drying cycles on mode I and mode II fracture toughness of cement mortar and concrete
Journal Pre-proofs Effect of Wetting–Drying Cycles on Mode I and Mode II Fracture Toughness of Cement Mortar and Concrete Arash Dehestani, Mehdi Hosseini, Alireza Taleb Beydokhti PII: DOI: Reference:
S0167-8442(19)30370-2 https://doi.org/10.1016/j.tafmec.2019.102448 TAFMEC 102448
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
9 July 2019 14 December 2019 18 December 2019
Please cite this article as: A. Dehestani, M. Hosseini, A. Taleb Beydokhti, Effect of Wetting–Drying Cycles on Mode I and Mode II Fracture Toughness of Cement Mortar and Concrete, Theoretical and Applied Fracture Mechanics (2019), doi: https://doi.org/10.1016/j.tafmec.2019.102448
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Effect of Wetting–Drying Cycles on Mode I and Mode II Fracture Toughness of Cement Mortar and Concrete Arash Dehestani1, Mehdi Hosseini2, Alireza Taleb Beydokhti3 1- M. Sc. student, Imam Khomeini international university, Qazvin, Iran 2- Associate professor, Imam Khomeini international university, Qazvin, Iran 3- Assistant professor, Imam Khomeini international university, Qazvin, Iran
Abstract Cement mortar and concrete are affected by wetting–drying cycles due to variable precipitation and evaporation rates and changes in the level of water reservoirs in most development projects such as dam construction projects. The alternating interaction of water with cement mortar and concrete affects mode I and mode II fracture toughness and accelerates their erosion rate. Hence, it is necessary to evaluate the effect of wetting–drying cycles on mode I and mode II fracture toughness. Cement mortar and concrete specimens were prepared for this purpose. The mode I and mode II fracture toughness were determined by conducting tests on centrally cracked Brazilian disc (CCBD) specimens. A chevron notch and a straight-through crack were created respectively in cement mortar and concrete specimens. The specimens were loaded after 0 (the specimen subject to no wetting-drying cycles), 1, 4, 8, 16 and 20 wetting–drying cycles. The mode I and mode II fracture toughness of cement mortar and concrete decreased with increasing the number of wetting–drying cycles. Porosity and paste volume (cement and water volume) were identified as the main factors reducing fracture toughness and fracture toughness reduction rate. Keywords: Wetting–drying cycles, mode I and mode II fracture toughness, cement mortar, concrete, chevron notch. 1. Introduction Fracture mechanics concerns crack formation and propagation in solids and structures and their impacts on structural deformation and deterioration (Anderson, 2017). Stress intensity factor is an index representing stress magnitude at the crack tip. Critical stress intensity factor, also known as fracture toughness, is an important material property. A crack starts to propagate when stress intensity coefficient reaches a critical value during loading (Brock, 1989). Generally, cracks are exposed to stress in three ways and, accordingly, three fracture modes can be considered for cracks, namely tensile, shear and combined fracture (Aliha and Ayatollahi, 2011). Mode I, mode II and combined fracture toughness can be determined through are various experimental methods such as three–point bending on semi–circular specimens (Aliha and Ayatollahi, 2011), four–point bending (Margevicius et al., 1999) and centrally cracked Brazilian disc (CSCBD) and cracked chevron notch Brazilian disc (CCNBD) testing under compression (Atkinson et al., 1982, Fowell et al., 1995, Hua et al., 2017, Hua et al., 2016, Hua et al., 2015). CSCBD and CCNBD specimens were used in this study due to ease of preparation, simple geometry and testing, available loading equipment and the ability for determining mode I, mode II
and combined fracture toughness by changing loading angle (Dong et al., 2004, Atkinson et al., 1982). Concrete is used for various purposes in most engineering projects. Accordingly, interaction of water with cement mortar and concrete is inevitable, which consequently increases the porosity and propagation of microcracks and reduces the fracture toughness. Cement mortar is extensively used in bridges, water reservoirs and silos, filling and repairing cracks in old concretes and injection in rocks (Ohama and Ramachandran, 1996). Various types of concrete are also extensively used in development projects. Wetting–drying cycles strongly affect cement mortar and concrete in engineering structures so that they may experience deterioration due to the successive interactions of water with cement mortar and concrete. Few studies are available on the effect of wetting–drying cycles on fracture toughness of cement mortar and concrete, while most studies in the literature have focused on strength parameters and physical and mechanical properties other than fracture toughness. Soroushian et al. (1994) studied the effect of wetting–drying and freeze–thaw cycles on cement composites reinforced with wood fibers. The 280×400×10 mm specimens were saturated in water for 1.2 h and then dried for 5.5 h at 82 ̊C. The flexural toughness of unreinforced and fiber-reinforced specimens was found to decrease after experiencing wetting–drying cycles. The flexural toughness of fiberreinforced composites was considerably higher than that of unreinforced specimens. Hua et al. (2015, 2016 and 2017) investigated the effect of wetting–drying cycles on the mode I, mode II and combined fracture toughness of CCBD sandstone specimens. The specimens were first saturated in water for 48 h and then dried for 24 h at 105 ̊C. Their results showed a decrease in the mode I, mode II and combined fracture toughness of sandstone with increasing the number of wetting–drying cycles. Polder and Peelen (2002) studied chloride transfer and steel corrosion in cubic concrete specimens (100 mm3) with different compositions under wetting (saline solutions)–drying cycles. Concrete strength was measured after 1, 2, 4, 5, 6, 8, 12, 16, 20, 24, 30 and 52 cycles. According to their results, chloride diffusion and steel corrosion increased with increasing the number of cycles and water/cement ratio. Chloride diffusion was initially increased and then increased by approaching towards the depth of specimens. Mohr et al. (2005) evaluated durability of 2.54×2.54×30.5 cm cement paste composites under wetting–drying cycles. The specimens were first saturated in water for 23.5 h at 20 ̊C and then dried for 0.5 h in air at 22 ̊C with a relative humidity of 60%. The specimens were dried in an oven at 65 ̊C and a relative humidity of 20% for 23.5 h and then cooled in air at 22 ̊C with a relative humidity of 60%. The saturated specimens were tested after 0, 1, 2, 5, 10, 15 and 25 cycles. Concrete strength decreased with increasing the number of wetting–drying cycles. Wu et al. (2017) studied concrete, mortar and paste (a mixture of 1462.8 kg type I cement and 512 kg water) prepared with different water/cement ratios and coarse particles under different drying and wetting regimes. Oxygen diffusivity, permeability, electrical conductivity, the density of microcracks and porosity were measured to investigate the effect of drying–induced shrinkage and damage on transport properties. According to the results, wetting and drying regimes had destructive impacts on specimens. In a study by Mirsayar and Park, traditional strain-, stress- and strain energy-based fracture criteria for prediction of crack propagation angle in cracked chevron notched Brazilian disc (CCNBD) were compared with experimental data in the literature. Experiments were conducted on cement mortar specimens. The maximum tensile stress (MTS) was used for the stress-based criterion. Moreover, the maximum energy release rate (G) and minimum strain energy density (SED) were considered for the strain energy-based criteria, whereas the
strain-based criteria included the extend maximum tangential strain-based criterion (EMTSN) and maximum tangential strain (MTSN). Hence, these criteria were compared with experimental data for high-strength cement mortar (HSCM) provided by Atahan et al. (2005). Comparisons showed the poor performance of traditional criteria in predicting crack propagation angle in CCNBD specimens. Among the tested criteria, EMSTN managed to properly predict crack propagation direction and onset of fracture because it considers the effect of the first non-singular strain term in addition to the singular strain term (Mirsayar and Park, 2016). In another study, Mirsayar et al. examined the mixed-mode fracture behavior of cement concrete both experimentally and theoretically using semicircular bend (SCB) specimens. The employed cement mix design was composed of 350 kg/m3 cement, a water/cement ratio of 0.46, 862 kg/m3 coarse-grained materials, 972 kg/m3 fine-grained materials and 1.5 kg/m3 super plasticizer. The mixed-mode fracture of cement concrete was evaluated and compared with experimental data by MTSN, MTS and strain energy density (SED) and EMTSN. Based on the comparison results, the traditional fracture criteria (MTS, SED and MTSN), which only consider singular terms of the crack tip field equations, are not able to predict experimental results. However, EMTSN provides a more accurate forecast of experimental results than the traditional fracture criteria. They came to this conclusion that strain-based criteria can be considered as a proper fracture model due to simplicity and taking into account material properties (Mirsayar et al., 2018). Ghomian and Dehestani (2019) studied mode I and mode II fracture energy of self-consolidating concrete (SCC) specimens. They used two specimen configurations for analyzing mode II fracture of SCC with different water/cement ratios. To compare mode I and mode II fracture, beam specimens with one notch at the bottom were used to calculate mode I fracture toughness. Coarse-grained Type II Portland cement of naturally crushed rocks was used with a maximum size of 12.5 mm and 9.5 mm for gravel and sand, respectively. The specimens were treated for 28 days at 20 ̊C. They obtained a good approximate estimate for mode II fracture energy and ratio of mode II to mode I fracture energy (GII/GI) using compressive strength and tensile stress of crack. They also concluded crack propagation and an increase in the mode II fracture energy with decreasing w/c and increasing compressive strength. The concrete also showed a brittle behavior with increasing specimen size and compressive strength. Razmi and Mirsayar (2017) investigated the mixedmode fracture properties of jute fiber-reinforced concrete. They studied the effect of jute fiber level on mixed-mode fracture toughness, uniaxial compressive strength, tensile strength and flexibility strength. The materials used in the concrete include normal Portland cement, coarse-grained rock materials with a maximum size of 19 mm, fine-grained materials with a fineness modulus of 3.4 and 110M carboxylic. The strength tests were conducted on 7- and 28-day concrete specimens. Cracked semi-circular bend specimens were used to determine the mixed-mode fracture toughness. 100-mm3 specimens were used for uniaxial compressive strength, whereas cylindrical specimens with a diameter of 100 mm and height of 200 mm were used for tensile strength measurements. Their results showed an increase in the mixedmode fracture toughness, uniaxial compressive strength and tensile strength of 7- and 28-day
specimens with increasing jute fiber content. Kumar and Rao (2015) presented an empirical relation for mode II fracture energy of concrete. The concrete specimens were prepared using normal Portland cement, natural fineand coarse-grained river materials, ground granulated blast furnace slag (GGBS) and various levels of super plasticizer and water/cement ratios. To reach their ultimate strength, all specimens were cured in water for 28 days. The study results showed that an increase in the grade of concrete increases the brittleness of the member and fracture energy. Stress–based fracture criteria are simpler than energy–based ones and demonstrate the role of each parameter in estimating fracture initiation. In contrast, energy–based criteria predict fracture initiation more accurately. Strain–based criteria combine the characteristics of both the aforementioned criteria (Mirsayar, 2015). Wu (1974) proposed a dual fracture criterion for plain concrete. Accordingly, a material may fail due to shear or tension depending on the stress or strain mode. This criterion is able to predict experimental results with a reasonable accuracy. Chang modified the maximum principal strain theory, also known as the Saint-Venant’s theory (Timoshenko, 1953), and proposed the modified maximum strain criterion using the elliptic crack and slit crack models. This criterion is dependent on Poisson’s ratio. Mirsayar (2015) presented the extended maximum tangential strain based criterion (EMTSN) or modified MTSN by taking into account the T–Strain as well as the singular strain field using poly methyl methacrylate (PMMA) specimens. Accordingly, the modified criterion overestimates the fracture initiation angle. Although both T–Strain and Poisson’s ratio significantly affect the fracture initiation angle in pure mode II, no effect is observed in pure mode I. In other studies, the traditional fracture criteria have been compared with the EMTSN criterion. Experiments were conducted on various materials such as graphite (Mirsayar et al., 2016), dental restorative materials (Mirsayar, 2018) and marble rock (Mirsayar et al., 2018) under different loading conditions (mode I, mode II and mixed) using various methods in order to determine the fracture toughness. In all of these studies, the EMSTN criterion predicts the experimental data more accurately compared to the traditional fracture criteria. Aliha et al. (2018) studied the effect of synthetic forta–ferro (SFF) fibers on fracture load, fracture toughness and work of fracture of concrete under pure mode I and pure mode III. Edge notched disk bend (ENBD) specimens were used for this purpose. The concrete composites reinforced with SFF fibers showed a higher fracture load, fracture toughness and work of fracture than plain concrete. In both cases, the highest KIC and KIIIC were obtained for the concrete reinforced with 0.3% SFF fibers. Mirsayar et al. (2017) investigated the interfacial bond strength of Portland cement concrete (PCC) and asphalt concrete (AC) using bi–material semi–circular bending specimens (SCB). Accordingly, a novel test called biomaterial semi–circular bend (BSCB) was proposed for mixed mode tests. The stress intensity factors KI and KII for the BSCB specimens are dependent on crack length, crack inclination angle, location of supports, loading, and elastic
properties of both bonded materials. Fakhri et al. (2017) experimentally analyzed the behavior of crack in roller compacted concrete (RCC) with reclaimed asphalt pavement (RAP) and crumb rubber under pure mode I and mode II using semi–circular bending (SCB) and four–point bending (4PB) specimens. They aimed at finding a suitable geometry for fracture specimens and investigating the effect of RCC specifications including aggregate gradation, cement content and waste materials on pure mode I and mode II fracture toughness of RCC mixtures. The results indicated the higher KI/KII of SCB specimens than 4PB specimens. This difference originates from the geometric factors that reduce the load–bearing capacity and directly affect the fracture toughness. Aliha et al. (2012) prepared cracked and un–cracked SCB specimens, respectively, for determining mode I fracture toughness and tensile strength of polymer concrete (PC) and compared the results with those of plain concrete. The mode I fracture toughness and tensile strength of PC were 3.31 and 4.47 times of plain concrete. Heidari–Rarani et al. (2014) studied the mechanical durability of an optimized epoxy PC under freeze–thaw cycles by considering fracture toughness and tensile strength. Un–cracked Brazilian disc (BD) and single edge notch bending (SENB) specimens were, respectively, used in tensile strength and fracture toughness tests. Three thermal cycles, namely 25 to –30 ̊C (Cycle A), 25 to 70 ̊C (Cycle B) and –30 to 70 ̊C (Cycle C), were applied to the specimens. The results indicated the significant impact of the thermal cycle B on the fracture toughness and tensile strength. The results were compared with those under environmental conditions. Using SCB specimens, Shi et al. (2019) proposed a new method for critical stress intensity factor and critical crack tip opening displacement (CTOD_C). They compared fracture properties and flexibility of Portland cement containing reclaimed asphalt pavement (RAP– PCC) with Portland cement concrete (PCC). According to their results, RAP–PCC showed a higher CTOD_C than plain concrete with the same critical stress factor. Moreover, RAP–PCC was more flexible than PCC. The results showed a decrease in the peak point and slope (gradient) with increasing the number of wetting–drying cycles and weakening of the cement mortar and concrete.
Although mode III fracture toughness rarely occurs in concrete, there are studies on this mode in the literature. Golewski (2017) experimentally studied the effect of fly ash (FA) penetration on the fracture toughness of plane concrete. Golewski proposed a new test method for estimating mode III fracture toughness of concretes with 0, 20 and 30% FA. The concrete was prepared from normal Portland cement, 8 mm gravel, sand, silica, FA and plasticizer. The effect of FA on the mode III fracture toughness of concrete was systematically studied. He found that adding 20% FA to the concrete caused an increase in the mode III fracture toughness while 30% FA reduced the mode III fracture toughness. The mode III to mode II fracture toughness ratio of 0.59 indicated a larger mode II fracture toughness than mode III fracture toughness.
Golewski and Sadowski (2016) measured the mode III fracture toughness and uniaxial compressive strength of three types of concrete with different fly ash contents. The concrete was prepared from normal Portland cement, natural gravel aggregates, sand, fly ash and plasticizer. The same water/cement ratio was used in all specimens (w/c=0.4). Concretes with 0, 20 and 30% FA were tested. Young (concrete younger than 7 days) and mature (more than 7 days) concrete composites were subjected to mode III loading after 3, 7, 28, 90, 180 and 365 days. Their results showed a decrease in the mode III fracture toughness of young concrete by adding 20 and 30% FA as compared to the concrete with 0% FA. The mode III fracture toughness of the concrete containing 20% FA increased after 28 days. However, the mode III fracture toughness of the concrete containing 30% FA was less than that of concrete with 0% FA. The mode III fracture toughness of the concrete containing 20% FA increased by 4.4% after a long curing period while that of the concrete with 30% FA decreased by 14.1%. The increase in the fracture toughness of the concrete containing 30% FA was only observed for a half-year period. These results were consistent with those of uniaxial compressive strength tests (Golewski and Sadowski, 2016). In another study, Golewski (2017) examined the effect of FA on the mode III fracture toughness of concretes containing 0, 20 and 30% FA. A flat fractured cross-section was observed by scanning electron microscopy (SEM). According to SEM micrographs, semi-circular multi-faceted cracks were formed on the fractured cross-section. The fracture toughness of the three modes were compared and a KIIIc/KIc of 2.35, 2.3 and 2.39 was, respectively, obtained for FA-00, FA-20 and FA-30. A similar KIIIc/KIc of 0.59 was, however, obtained for all concrete series. The highly similar results, especially the same KIIIc/KIc values, may represent a very accurate test for all fracture modes. In addition, the results of mode III fracture toughness were less scattered than mode I and mode II fracture toughness.
According to the literature, few articles have been conducted on the effect of number of wetting– drying cycles on fracture toughness of concrete. However, Brazilian discs were not used in this article. As innovative aspects of this study compared with Soroushian et al. (1994), CCNBD and CCDB specimens were used to investigate the effect of wetting–drying cycles on the fracture toughness of cement mortar and concrete specimens. Before fracture toughness testing, the specimens were saturated in 20 ̊C water for 48 h and then dried at 105 ̊C for 24 h. The mode I and mode II fracture toughness were determined by testing CCBD specimens. A chevron notch and a straight-through notch were created respectively in cement mortar and concrete specimens. The specimens were loaded after 1, 4, 8, 16 and 20 wetting– drying cycles.
2. Materials specifications 2.1. Cement mortar and concrete mix designs
Two mix designs were used in these experiments. The cement mortar consisted of water, cement and fine–grained beach sand. Concrete was made of water, cement, fine–grained beach sand and gravel. Figure 1 shows the mix designs for cement mortar and concrete specimens.
Figure 1: Mix designs for cement mortar and concrete specimens
2.2. Physical and mechanical properties of cement mortar and concrete Table 1 lists some physical and mechanical properties of cement mortar and concrete. All experiments were performed based on ISRM standards (Ulusay and Hudson, 2007). Table 1: Physical and mechanical properties of concrete specimens specimens Cement mortar Concrete
dry unit weight (kN/m3) 19.09 18.48
uniaxial compressive strength (MPa) 26 23
tensile strength (MPa) 3.73 3.1
effective porosity (%) 17.03 17.01
3. Specimen preparation 3.3. Cement mortar specimens A total of eight cylindrical molds with a length of 200 mm and an inner diameter of 71.14 mm were used for preparation of cement mortar specimens. The cylindrical cement mortar specimens were cured in water for 28 days to reach their ultimate strength. The specimens were then cut into discs with an approximate thickness of 24 mm. Figure 2 shows the preparation stages. After cutting cylindrical concrete specimens, the center point and crack direction for all specimens were determined by a center finder to create a chevron notch at the center of the disc. To prepare the CCNBD specimens, two notches were cut at the center on both sides of specimens by a small cutterhead with a disc diameter of 40 mm and a thickness of 1 mm. The crack depth (hc) from each side was about 13 mm. The cutterhead blade was cooled with water during the cutting of the chevron notch. Figure 3 schematically shows the chevron notching process in circular disc specimens. The notch created in the Brazilian disc should satisfy some standards that are specified by α1=a1/R and αB=B/R, where R represents disc radius, B disc thickness and a1 is half-length of the crack. As shown in Fig. 4, the standards have been met in preparation of specimens (Aliha and
Ayatolahi, 2014).
Figure 2: Preparation of cement mortar specimens
Figure 3: Chevron notching in CCNBD specimen
Figure 4: Geometric characteristics required for the CCNBD specimen in cement mortar 3.2. Concrete specimens Straight-through cracks were decided to be created in the concrete specimens since the gravel in the concrete could have caused damage to the cutterhead. Concrete was poured into special molds with a metal blade in the center. The straight-through crack was created by the central metal blade (Fig. 5). The thickness, diameter and crack length of concrete specimens were close together due to the use of a mold for preparation of concrete discs.
Figure 5: A metal mold for preparation of concrete specimens with a straight through crack 4. Experiments 4.1. Wetting–drying cycles The prepared specimens should undergo wetting–drying cycles. The experimental method proposed by Hua et al. (2015, 2016 and 2017) was used for this purpose. In each cycle, the specimens were cured in water for 48 h to be completely saturated (Figure 6) and then dried in an oven at 105 ᵒC for
24 h. Fracture toughness test on concrete and cement mortar specimens was performed after 0, 1, 4, 8, 16 and 20 cycles. The 0th cycle refers to the dry specimens not undergoing any wetting–drying cycle. These specimens are considered as the reference for measuring the fracture toughness of other specimens exposed to different number of wetting–drying cycles. Accordingly, each cycle lasted 3 days and thus all 20 cycles lasted 60 days.
Figure 6: Saturation of specimens in water
4.2. Experiments on concrete specimens 4.2.1. Cement mortar specimens A chevron notch was created in the cement mortar specimens. A loading rate of 0.2 kN/s was used in the experiments. The mode I fracture toughness (KIC) of CCNBD specimens is obtained from Eq. 1: 𝑃𝑚𝑎𝑥
∗ 𝐾𝐼𝐶 = 𝐵 𝐷𝑌𝑚𝑖𝑛
(1)
where 𝑃𝑚𝑎𝑥 is the fracture force, B disc thickness, D disc diameter. The critical stress intensity ∗ factor (𝑌𝑚𝑖𝑛 ) is obtained from Eq. 2: ∗ (2) = 𝑢𝑒𝑣𝛼1 𝑌𝑚𝑖𝑛 where u and v are constant parameters obtained from 𝛼0 and 𝛼𝐵 in Table 2 (Fowell et al., 1995).
Parameters α1 and αB are, respectively, defined as a1/R and B/R where R represents disc radius, B disc thickness and a1 is the half-length of the outer crack in Fig. 7 (Aliha and Ayatolahi, 2014). The loading direction is aligned with the crack direction to determine mode I fracture toughness of all specimens (α=0)
Table 2: 𝒖 and 𝒗 obtained from α0 and αB (Fowell et al., 1995) α0
0.200
0.250
0.275
0.300
0.325
0.350
0.375
0.400
0.680
0.2667
0.2704
0.2718
0.2744
0.2774
0.2807
0.2848
0.2888
0.720
0.2650
0.2683
0.2705
0.2727
0.2763
0.2794
0.2831
0.2871
0.760
0.2637
0.2668
0.2693
0.2719
0.2744
0.2781
0.2819
0.2860
0.800
0.2625
0.2657
0.2680
0.2706
0.2736
0.2772
0.2811
0.2845
0.840
0.2612
0.2649
0.2672
0.2699
0.2727
0.2763
0.2801
0.2831
0.880
0.2602
0.2642
0.2668
0.2691
0.2723
0.2754
0.2793
0.2816
0.920
0.2598
0.2634
0.2658
0.2684
0.2716
0.2747
0.2782
0.2811
0.960
0.2593
0.2633
0.2655
0.2685
0.2710
0.2746
0.2767
0.2799
1.000
0.2591
0.2630
0.2653
0.2679
0.2709
0.2738
0.2768
0.2786
0.680
1.7676
1.7711
1.7757
1.7759
1.7754
1.7741
1.7700
1.7666
0.720
1.7647
1.7698
1.7708
1.7722
1.7693
1.7683
1.7652
1.7617
0.760
1.7600
1.7656
1.7649
1.7652
1.7662
1.7624
1.7593
1.7554
0.800
1.7557
1.7611
1.7613
1.7603
1.7596
1.7561
1.7525
1.7512
0.840
1.7522
1.7547
1.7551
1.7548
1.7535
1.7499
1.7469
1.7473
0.880
1.7487
1.7492
1.7478
1.7487
1.7463
1.7452
1.7403
1.7434
0.920
1.7423
1.7446
1.7443
1.7432
1.7411
1.7389
1.7360
1.7363
0.960
1.7370
1.7373
1.7372
1.7346
1.7344
1.7309
1.7343
1.7331
1.000
1.7308
1.7307
1.7306
1.7297
1.7273
1.7270
1.7258
1.7302
αB
𝑢
𝑣
Pure mode II fracture toughness (KIIC) is obtained from Eq. 3 (Aliha and Ayatolahi, 2014): 𝐾𝐼𝐼𝐶 =
𝑃𝑚𝑎𝑥
𝛼
𝛼1 ― 𝛼0
𝛼 ― 𝛼0 𝑌𝐼𝐼
𝜋𝑅𝐵 𝑅
(3)
where 𝑌𝐼𝐼 is the geometric factor for pure mode II, which is dependent on the crack length to disc radius ratio (a/R) of the CCNBD specimens. This geometric factor can be obtained both theoretically and numerically by finite element method (FEM) with the parameters given in Eq. 4. This equation was first presented by Atkinson et al. (1982): 𝑛
𝐿
𝑌𝐼𝐼 = 2𝑠𝑖𝑛2 𝜑∑𝑖 = 1𝑆𝑖(𝑎)2𝑖 ― 2𝐵𝑖(𝜑)
(4)
Figure 7 shows variations of YII with respect to the a/R ratio for CCNBD specimens. To determine the mode II fracture toughness, the average angle between the crack and loading directions was 26.5 for the CCNBD specimens as obtained from Fig. 8.
Figure 7: Variations of geometric factor of mode II with respect to a/R ratio for CCNBD specimens (Aliha and Ayatollahi, 2014)
Figure 8: Variations of pure mode II crack inclination angel with respect to the a/R ratio (Aliha and Ayatollahi, 2014) Figure 9 schematically shows the geometry and mode II loading of a CCNBD specimen.
Figure 9: The geometry and loading of a CCNBD specimen (Aliha and Ayatolahi, 2014) 4.4.2. Concrete specimens Straight-through cracks were created in the concrete specimens. A disc with a central straight crack was used for determining the fracture toughness. Atkinson et al. (1982) proposed Eqs. 5 and 6 for calculating mode I and mode II fracture toughness: 𝐾𝐼𝐶 = 𝐾𝐼𝐼𝐶 =
𝑃 𝑎 𝜋 𝑅𝐵 𝑃 𝑎
𝑁𝐼
(5)
𝑁𝐼𝐼
(6)
𝜋 𝑅𝐵
where KIC represents mode I fracture toughness, KIIC mode II fracture toughness, R Brazilian disc radius, B disc thickness, P fracture force, and a half-length of the crack. Moreover, NI and NII respectively show mode I and mode II normalized stress intensity factors, which are dependent on the a/R ratio and crack–loading direction angle (β). Loading direction is aligned with the central crack direction in the mode I fracture toughness test (β=0). Parameters NI and NII are respectively obtained from Eqs. 7 and 8 for a/R ≥ 0.3 (Atkinson et al., 1982): 𝑎 2
𝑁𝐼 = 1 ― 4 𝑆𝑖𝑛2𝛽 + 4 𝑆𝑖𝑛2𝛽( 1 ― 4𝑐𝑜𝑠2𝛽) (𝑅) 𝑁𝐼𝐼 =
[2 + (8 𝐶𝑂𝑆 𝛽 ― 2
)]𝑆𝑖𝑛2𝛽
𝑎 2 5(𝑅)
(7) (8)
where β represents the angle between the crack and loading directions. By equating NI to zero to determine mode II fracture toughness, the average value for β is obtained as 28.8 ̊. Figure 10 schematically shows the geometry and mode II loading of a CCBD specimen.
Figure 10: A centrally cracked Brazilian disc (CCBD) specimen under compression (Hua et al., 2015) 5. Results The results on the mode I and mode II fracture toughness and porosity of cement mortar and cement after different wetting–drying cycles are presented in this section. 5.1. Fracture toughness of cement mortar specimens The mode I and mode II fracture toughness of cemnet mortar specimens decreased with increasing the number of wetting–drying cycles. The effect of 20 wetting–drying cycles on the mode II fracture toughness was greater than mode I fratcure toughness by 1.55 (i.e. reduction of mode II fracture toughness relative to mode I fracture toughness). The average mode I fracture toughness of cement mortar specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.3, 0.28, 0.27, 0.26, 0.25 and 0.24 MPa 𝑚, respectively. The mode I fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 6.66, 10, 13.33, 16.66 and 20% relative to the specimen subject to no wettingdrying cycles, respectively. The average mode II fracture toughness of cement mortar specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.77, 0.68, 0.65, 0.62, 0.59 and 0.53 MPa 𝑚, respectively. The mode II fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 11.68, 15.58, 19.48, 23.37 and 31.16% relative to the specimen subject to no wetting-drying cycles, respectively. Figure 11 shows the cement mortar specimens after fracture in the mode I and mode II fracture toughness tests. The results are shown in Table 3 and Fig. 12.
b a Figure 11: Cement mortar specimens after fracture, (a) mode I and (b) mode II fracture toughness
Table 3: Mode I and mode II fracture toughness of cement mortar Specimen
Number of cycle
fracture mode
fracture load )KN(
mode I fracture toughness (MPa m)
mode II fracture toughness (MPa m)
C-1-1
0
I
3.1
0.33
C-1-2
0
I
3.1
0.32
C-1-6 C-1-3
0 0
I II
2.6 3.9
0.27
C-1-4
0
II
3.7
C-1-5 C-9-5
0 1
II I
3.8 2.7
0.28
C-9-7
1
I
2.6
0.28
C-9-1
1
II
3.3
0.73
C-9-3
1
II
3.1
0.64
C-4-6
4
I
2.5
0.27
C-8-7
4
I
2.7
0.3
C-7-4
4
I
2.4
0.25
C-6-4
4
I
2.5
0.26
C-2-3
4
II
3.1
0.65
C-2-4
4
II
3.2
0.66
C-2-7
4
II
3.3
0.68
C-2-5 C-6-1
4 8
II I
3.1 2.4
0.25
C-4-4
8
I
2.7
0.28
C-6-7 C-3-1
8 8
I I
2.6 2.4
0.26 0.25
C-9-6
8
I
2.5
0.26
C-6-6
8
II
2.9
0.59
C-8-1
8
II
3.1
0.63
C-7-6
8
II
3
0.63
C-7-7
8
II
3
C-4-2
16
I
2.6
0.26
C-7-1
16
I
2.5
0.25
C-3-3
16
I
2.3
0.23
C-8-2
16
I
2.5
0.26
C-3-5
16
II
2.7
0.6
C-8-6
16
II
2.8
0.59
C-4-3
16
II
2.9
0.59
C-6-2
16
II
2.8
0.58
C-4-7
20
I
2.4
0.24
C-5-1
20
I
2.4
0.24
C-3-2
20
I
2.3
0.23
C-9-4
20
II
2.6
0.55
C-4-1
20
II
2.7
0.54
C-8-4 C-5-6
20 20
II II
2.5 2.6
0.51 0.54
0.81
average mode I or II fracture toughness (MPa m) 0.3
decrease fracture toughness (%)
0.77
-
0.28
6.66
0.68
11.68
0.27
10
0.65
15.58
0.26
13.33
0.62
19.48
0.25
16.66
0.59
23.37
0.24
20
0.53
31.16
-
0.74 0.76
0.61
0.63
0.9
Fracture Toughness(MPa√m)
0.8 Mode I Average
0.7 0.6 0.5
Mode II Average
0.4 0.3
Linear (Mode I Average)
0.2 0.1
Linear (Mode II Average)
0 0
4
8
12
16
20
24
Number of Wetting - Drying Cycles
Figure 12: The relationship between the number of wetting–drying cycles and mode I and mode II fracture toughness of cement mortar specimens 5.2. Fracture toughness of concrete specimens The mode I and mode II fracture toughness of concrete specimens decreased with increasing the number of wetting–drying cycles. The effect of 20 wetting–drying cycles on the mode II fracture toughness was greater than mode I fratcure toughness by 0.69 (i.e. reduction of mode II fracture toughness relative to mode I fracture toughness). The average mode I fracture toughness of concrete specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.157, 0.151, 0.148, 0.136, 0.131 and 0.129 MPa 𝑚, respectively. The mode I fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 3.82, 5.73, 13.37, 16.56 and 17.83% relative to the specimen subject to no wettingdrying cycles, respectively. The average mode II fracture toughness of concrete specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.365, 0.356, 0.353, 0.336, 0.328 and 0.32 MPa 𝑚, respectively. The mode II fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 2.46, 3.28, 7.94, 10.13 and 12.32% relative to the specimen subject to no wetting-drying cycles, respectively. Figure 13 shows the concrete specimens after fracture in the mode I and mode II fracture toughness tests. The results are shown in Table 4 and Fig. 14.
a b Figure 13: Concrete specimens after fracture, (a) mode I and (b) mode II fracture toughness
Loading on the specimen for determining mode I fracture toughness and the load-displacement curves were shown in Figs. 15 and 16 respectively. The Fig 16 showed a decrease in the peak point and slope of curves with increasing the number of wetting–drying cycles and weakening of the cement mortar and concrete.
Table 4: Mode I and mode II fracture toughness of concrete specimens Specimen
Number of cycle
fracture mode
fracture load )KN(
mode I fracture
0
I
3
0.158
ć-5-3
0
I
3.1
0.156
ć-5-1
0
II
3.3
0.356
ć-1-1
0
II
3.5
0.375
c-4-5
1
I
2.8
0.145
c-4-2
1
I
3
0.155
c-4-4
1
I
2.9
0.153
c-4-3
1
II
3.3
0.348
c-4-1
1
II
3.4
0.365
c-5-1
4
I
2.8
0.146
c-6-1
4
I
2.9
0.153
c-5-2
4
I
2.8
0.146
c-5-4
4
II
3.3
0.35
c-5-3
4
II
3.2
0.356
C-6-2
8
I
2.6
0.136
C-3-3
8
I
2.7
0.137
c-6-4
8
II
3.2
0.346
C-6-3
8
II
3.1
0.327
C-3-6
16
I
2.6
0.134
C-3-5
16
I
2.5
0.129
C-3-1
16
II
3
0.319
C-2-2
16
II
3.2
0.337
c-2-4
20
I
2.6
0.131
C-1-2
20
I
2.5
0.127
C-2-3
20
II
3
0.311
C-2-1
20
II
3
0.329
toughness (MPa m )
mode II fracture toughness (MPa m)
ć-5-4
average mode I or II fracture toughness (MPa m)
decrease fracture toughness (%)
0.157 0.365 0.151
3.82
0.356
2.46
0.148
5.73
0.353
3.28
0.136
13.37
0.336
7.94
0.131
16.56
0.328
10.13
0.129
17.83
0.32
12.32
0.45
Fracture Toughness (MPa√m)
0.4
Mode I Average
0.35 0.3
Mode II Average
0.25 0.2
Linear (Mode I Average)
0.15 0.1
Linear (Mode II Average)
0.05 0 0
4
8
12
16
20
24
Number of Wetting - Drying Cycles
Figure 14: The relationship between the number of wetting–drying cycles and mode I and mode II fracture toughness of concrete specimens
Figure 15: Loading on the specimen for determining mode I fracture toughness
Figure16: The load-displacement curves were shown in Figs. 15 and 16 respectively.
5.3. Effective porosity of cement mortar and concrete specimens As clearly seen in Fig. 17, effective porosity increases with increasing the number of wetting– drying cycles. Several specimens were used in each cycle to calculate an accurate value for average effective porosity. After 0 (the specimen subject to no wetting-drying cycles), 1, 4, 8, 16 and 20 cycles, the specimens were saturated by a vacuum pump, after which the saturated and immersion weights were measured. The specimens were then dried in an oven and their dry mass was calculated. An effective porosity of 17.03, 17.5, 17.8, 18.05, 18.15 and 18.35% was obtained for cement mortar specimens after 1, 4, 8, 10, 16 and 20 cycles, respectively. The corresponding value for concrete specimens was 17.01, 17.65, 18, 18.3, 19.1 and 19.7%, respectively. The porosity of cement mortar and concrete specimens increased by 1.32 and 2.69% after 20 cycles, respectively.
Figure 17: Variations of porosity with respect to the number of wetting–drying cycles
6. Discussion The mode I and mode II fracture toughness of concrete were less than those of cement mortar. The reduction in mode I and mode II fracture toughness reduction of concrete was also less than that of cement mortar. This can be related to crack formation during drying, mix design and paste volume of cement mortar and concrete specimens. Cement paste is a key component in the concrete structure. Cement paste contains hydration products, unhydrated particles, cavities and pore water. Hydration products are generated by reacting water with cement components. The majority of hydration products are produced from reaction of C3S and C2S with water. These reactions produce hydrated calcium silicate (C-S-H) and calcium hydroxide (Mehta and Monterio, 2001). Ettringite is also formed during hydration. The formation of ettringite begins as soon as cement is combined with water (Barnes et al., 1992). This type of ettringite called early ettringite grows homogenously. The concrete volume increases as a result of ettringite formation. The resulting swelling, however, is harmless (Collepardi, 2003) and fills the pores in the cement (Macledo and Hall, 1991). The specimen size does not change when cement paste is saturated. However, the specimen is deformed and shrunk during drying when C-S-H gel loses some of its adsorbed water. Drying–induced shrinkage of concrete is usually affected by gravel volume and hardness, water and cement volume, relative humidity and the time the concrete is exposed to environmental humidity. Concrete cracking usually occurs as a result of shrinkage–induced tensile fracture (Mehta and Monterio, 2017). Starting their propagation through cement paste from the cement paste-grain boundary, the microcracks are stopped when they collide with the grains (Wu et al., 2015). Delayed ettringite is formed when dried concrete is exposed to moisture again. Delayed ettringite is in fact heterogeneous formation of ettringite crystals in the cement after complete drying during which sulfate compounds are supplied by cement. These crystals are called secondary or delayed ettringite (Collepardi, 2003). Two types of ettringite are formed depending on the sulfate source including internal and external sulfate sources. The key factors affecting formation of delayed ettringite include (1) overheating (60-70 ̊C) while concreting, which prevents formation of nonexpansive early ettringite and (2) the presence of sulfates mainly in cement and to a lower extent in water and coarse-grained materials. These sulfates may react with aluminates in the cement in the presence of water to form secondary ettringite. A wet environment also affects formation of delayed ettringite so that all damages caused by secondary ettringite appear at regions exposed to water (Leklou et al., 2012). The water filling concrete pores is necessary for migration of reacting ions 𝑆𝑂24 ― , 𝐴𝑙(𝑂𝐻)4― and 𝐶𝑎2 + in order for the ettringite to deposit in the microcracks (Collepardi et al., 2003). Concretes undergoing alternating wetting-drying cycles are more susceptible to damage than those exposed to permanent wetting (Thaulow et al., 1996, Collpardi, 2001) due to formation of delayed ettringite after drying of concrete and onset of re-wetting. This can be related to the key role of saturation in ettringite deposition. Water causes migration of ions in the cement matrix to microcrack and the subsequent deposition of ettringite crystals and opening of cracks. Consequently, successive wetting-drying cycles lead to formation of microcracks and increased porosity. Due to heterogeneous expansion in the concrete, delayed ettringite formation causes
tensile stress and crack formation in the concrete (Leklou et al., 2012, Diamond, 1996). Ettringite shrinks due to water loss during drying (Diamond, 1996). Strength and fracture toughness decrease with increasing porosity (Kearsley and Wainwright, 2002). Hydration and the subsequent formation of delayed ettringite deposits occur more intensely in cement mortar due to the higher cement volume, consequently leading to a lower rate of growth for porosity in cement mortar than concrete. The water–cement ratio (w/c) in the cement mortar equals 0.5 with a paste volume (water and cement volume) of 60% (relative to total volume). The corresponding w/c in concrete equals 0.75 with a paste volume of 28%. Unlike paste, gravels and sand in cement mortar and concrete specimens are not affected by saturation during wetting–drying cycles. Due to the lower paste volume and higher w/c of concrete compared to cement mortar, the adhesive force between concrete components is less than that of cement mortar, which consequently leads to the lower fracture toughness of concrete. According to the results of the fracture toughness tests, cement mortar is more sensitive to wetting– drying cycles. The mode I and mode II fracture toughness of cement mortar decreased by 20 and 31.16% after 20 cycles relative to the specimen subject to no wetting-drying cycles, respectively. The corresponding values for concrete were 17.83 and 12.32%, respectively. Due to its higher paste volume, cement mortar is affected by the water volume to a greater extent, consequently resulting in the higher sensitivity of the fracture toughness of cement mortar compared to concrete. Comparison of the mode I and mode II fracture toughness of cement mortar and concrete showed that despite higher homogeneity of cement mortar compared to concrete, cement mortar results are more scattered than those obtained for concrete. This can be related to the preparation method. As discussed in the specimen preparation section, the diameter, thickness and length of crack in all concrete specimens prepared in the prefabricated molds are almost the same, which leads to less scattered data. In contrast, the cement mortar specimens were prepared by an operator using a cutterhead blade. Despite compliance with relevant standards, the specimen and crack sizes of the cement mortar specimens are slightly different, leading to more scattered data than concrete. 7. Conclusion The effect of wetting–drying cycles on the mode I and mode II fracture toughness of cement mortar and concrete was investigated. The cement mortar and concrete specimens were loaded after 0 (the specimen subject to no wetting-drying cycles), 1, 4, 8, 16, 20 cycles. The results are summarized as follows: The mode I and mode II fracture toughness of cement mortar and concrete decreased with increasing the number of wetting–drying cycles. The lower volume of cement paste in the concrete causes lower adhesion than concrete, leading to the lower fracture toughness than cement mortar. The mode I and mode II fracture toughness of cement mortar linearly decreased by 20 and 31.16% after 20 cycles, respectively. The correlation coefficient between the mode I and mode II fracture toughness and the number of cycles was 0.86 and 0.83, respectively. The mode I and mode II fracture toughness of concrete linearly decreased by 17.83 and 12.32% after 20 cycles, respectively. The correlation coefficient between the mode I and mode II fracture toughness and the number of cycles was 0.9 and 0.94, respectively.
The mode I and mode II fracture toughness of cement mortar specimens were more affected by wetting–drying cycles as compared with concrete specimens. The mode I and mode II fracture toughness of cement mortar and concrete decreased with increasing porosity. Shrinkage during drying and formation of delayed ettringite during re-wetting deteriorate cement mortar and concrete, leading to reduced fracture toughness. Cement mortar is more sensitive to wetting–drying cycles than concrete due to its higher paste volume.
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Highlights:
Investigating the effect of the number of wetting- drying the mode I and mode II fracture toughness of concrete and cement mortar by the CCNBD test.
Presenting the relationship between the mode I and mode II fracture toughness and the number of wetting- drying for concrete and cement mortar.
Presenting the relationship between effective porosity and the number of wetting- drying for concrete and cement mortar.
S0167-8442(19)30370-2 https://doi.org/10.1016/j.tafmec.2019.102448 TAFMEC 102448
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
9 July 2019 14 December 2019 18 December 2019
Please cite this article as: A. Dehestani, M. Hosseini, A. Taleb Beydokhti, Effect of Wetting–Drying Cycles on Mode I and Mode II Fracture Toughness of Cement Mortar and Concrete, Theoretical and Applied Fracture Mechanics (2019), doi: https://doi.org/10.1016/j.tafmec.2019.102448
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Effect of Wetting–Drying Cycles on Mode I and Mode II Fracture Toughness of Cement Mortar and Concrete Arash Dehestani1, Mehdi Hosseini2, Alireza Taleb Beydokhti3 1- M. Sc. student, Imam Khomeini international university, Qazvin, Iran 2- Associate professor, Imam Khomeini international university, Qazvin, Iran 3- Assistant professor, Imam Khomeini international university, Qazvin, Iran
Abstract Cement mortar and concrete are affected by wetting–drying cycles due to variable precipitation and evaporation rates and changes in the level of water reservoirs in most development projects such as dam construction projects. The alternating interaction of water with cement mortar and concrete affects mode I and mode II fracture toughness and accelerates their erosion rate. Hence, it is necessary to evaluate the effect of wetting–drying cycles on mode I and mode II fracture toughness. Cement mortar and concrete specimens were prepared for this purpose. The mode I and mode II fracture toughness were determined by conducting tests on centrally cracked Brazilian disc (CCBD) specimens. A chevron notch and a straight-through crack were created respectively in cement mortar and concrete specimens. The specimens were loaded after 0 (the specimen subject to no wetting-drying cycles), 1, 4, 8, 16 and 20 wetting–drying cycles. The mode I and mode II fracture toughness of cement mortar and concrete decreased with increasing the number of wetting–drying cycles. Porosity and paste volume (cement and water volume) were identified as the main factors reducing fracture toughness and fracture toughness reduction rate. Keywords: Wetting–drying cycles, mode I and mode II fracture toughness, cement mortar, concrete, chevron notch. 1. Introduction Fracture mechanics concerns crack formation and propagation in solids and structures and their impacts on structural deformation and deterioration (Anderson, 2017). Stress intensity factor is an index representing stress magnitude at the crack tip. Critical stress intensity factor, also known as fracture toughness, is an important material property. A crack starts to propagate when stress intensity coefficient reaches a critical value during loading (Brock, 1989). Generally, cracks are exposed to stress in three ways and, accordingly, three fracture modes can be considered for cracks, namely tensile, shear and combined fracture (Aliha and Ayatollahi, 2011). Mode I, mode II and combined fracture toughness can be determined through are various experimental methods such as three–point bending on semi–circular specimens (Aliha and Ayatollahi, 2011), four–point bending (Margevicius et al., 1999) and centrally cracked Brazilian disc (CSCBD) and cracked chevron notch Brazilian disc (CCNBD) testing under compression (Atkinson et al., 1982, Fowell et al., 1995, Hua et al., 2017, Hua et al., 2016, Hua et al., 2015). CSCBD and CCNBD specimens were used in this study due to ease of preparation, simple geometry and testing, available loading equipment and the ability for determining mode I, mode II
and combined fracture toughness by changing loading angle (Dong et al., 2004, Atkinson et al., 1982). Concrete is used for various purposes in most engineering projects. Accordingly, interaction of water with cement mortar and concrete is inevitable, which consequently increases the porosity and propagation of microcracks and reduces the fracture toughness. Cement mortar is extensively used in bridges, water reservoirs and silos, filling and repairing cracks in old concretes and injection in rocks (Ohama and Ramachandran, 1996). Various types of concrete are also extensively used in development projects. Wetting–drying cycles strongly affect cement mortar and concrete in engineering structures so that they may experience deterioration due to the successive interactions of water with cement mortar and concrete. Few studies are available on the effect of wetting–drying cycles on fracture toughness of cement mortar and concrete, while most studies in the literature have focused on strength parameters and physical and mechanical properties other than fracture toughness. Soroushian et al. (1994) studied the effect of wetting–drying and freeze–thaw cycles on cement composites reinforced with wood fibers. The 280×400×10 mm specimens were saturated in water for 1.2 h and then dried for 5.5 h at 82 ̊C. The flexural toughness of unreinforced and fiber-reinforced specimens was found to decrease after experiencing wetting–drying cycles. The flexural toughness of fiberreinforced composites was considerably higher than that of unreinforced specimens. Hua et al. (2015, 2016 and 2017) investigated the effect of wetting–drying cycles on the mode I, mode II and combined fracture toughness of CCBD sandstone specimens. The specimens were first saturated in water for 48 h and then dried for 24 h at 105 ̊C. Their results showed a decrease in the mode I, mode II and combined fracture toughness of sandstone with increasing the number of wetting–drying cycles. Polder and Peelen (2002) studied chloride transfer and steel corrosion in cubic concrete specimens (100 mm3) with different compositions under wetting (saline solutions)–drying cycles. Concrete strength was measured after 1, 2, 4, 5, 6, 8, 12, 16, 20, 24, 30 and 52 cycles. According to their results, chloride diffusion and steel corrosion increased with increasing the number of cycles and water/cement ratio. Chloride diffusion was initially increased and then increased by approaching towards the depth of specimens. Mohr et al. (2005) evaluated durability of 2.54×2.54×30.5 cm cement paste composites under wetting–drying cycles. The specimens were first saturated in water for 23.5 h at 20 ̊C and then dried for 0.5 h in air at 22 ̊C with a relative humidity of 60%. The specimens were dried in an oven at 65 ̊C and a relative humidity of 20% for 23.5 h and then cooled in air at 22 ̊C with a relative humidity of 60%. The saturated specimens were tested after 0, 1, 2, 5, 10, 15 and 25 cycles. Concrete strength decreased with increasing the number of wetting–drying cycles. Wu et al. (2017) studied concrete, mortar and paste (a mixture of 1462.8 kg type I cement and 512 kg water) prepared with different water/cement ratios and coarse particles under different drying and wetting regimes. Oxygen diffusivity, permeability, electrical conductivity, the density of microcracks and porosity were measured to investigate the effect of drying–induced shrinkage and damage on transport properties. According to the results, wetting and drying regimes had destructive impacts on specimens. In a study by Mirsayar and Park, traditional strain-, stress- and strain energy-based fracture criteria for prediction of crack propagation angle in cracked chevron notched Brazilian disc (CCNBD) were compared with experimental data in the literature. Experiments were conducted on cement mortar specimens. The maximum tensile stress (MTS) was used for the stress-based criterion. Moreover, the maximum energy release rate (G) and minimum strain energy density (SED) were considered for the strain energy-based criteria, whereas the
strain-based criteria included the extend maximum tangential strain-based criterion (EMTSN) and maximum tangential strain (MTSN). Hence, these criteria were compared with experimental data for high-strength cement mortar (HSCM) provided by Atahan et al. (2005). Comparisons showed the poor performance of traditional criteria in predicting crack propagation angle in CCNBD specimens. Among the tested criteria, EMSTN managed to properly predict crack propagation direction and onset of fracture because it considers the effect of the first non-singular strain term in addition to the singular strain term (Mirsayar and Park, 2016). In another study, Mirsayar et al. examined the mixed-mode fracture behavior of cement concrete both experimentally and theoretically using semicircular bend (SCB) specimens. The employed cement mix design was composed of 350 kg/m3 cement, a water/cement ratio of 0.46, 862 kg/m3 coarse-grained materials, 972 kg/m3 fine-grained materials and 1.5 kg/m3 super plasticizer. The mixed-mode fracture of cement concrete was evaluated and compared with experimental data by MTSN, MTS and strain energy density (SED) and EMTSN. Based on the comparison results, the traditional fracture criteria (MTS, SED and MTSN), which only consider singular terms of the crack tip field equations, are not able to predict experimental results. However, EMTSN provides a more accurate forecast of experimental results than the traditional fracture criteria. They came to this conclusion that strain-based criteria can be considered as a proper fracture model due to simplicity and taking into account material properties (Mirsayar et al., 2018). Ghomian and Dehestani (2019) studied mode I and mode II fracture energy of self-consolidating concrete (SCC) specimens. They used two specimen configurations for analyzing mode II fracture of SCC with different water/cement ratios. To compare mode I and mode II fracture, beam specimens with one notch at the bottom were used to calculate mode I fracture toughness. Coarse-grained Type II Portland cement of naturally crushed rocks was used with a maximum size of 12.5 mm and 9.5 mm for gravel and sand, respectively. The specimens were treated for 28 days at 20 ̊C. They obtained a good approximate estimate for mode II fracture energy and ratio of mode II to mode I fracture energy (GII/GI) using compressive strength and tensile stress of crack. They also concluded crack propagation and an increase in the mode II fracture energy with decreasing w/c and increasing compressive strength. The concrete also showed a brittle behavior with increasing specimen size and compressive strength. Razmi and Mirsayar (2017) investigated the mixedmode fracture properties of jute fiber-reinforced concrete. They studied the effect of jute fiber level on mixed-mode fracture toughness, uniaxial compressive strength, tensile strength and flexibility strength. The materials used in the concrete include normal Portland cement, coarse-grained rock materials with a maximum size of 19 mm, fine-grained materials with a fineness modulus of 3.4 and 110M carboxylic. The strength tests were conducted on 7- and 28-day concrete specimens. Cracked semi-circular bend specimens were used to determine the mixed-mode fracture toughness. 100-mm3 specimens were used for uniaxial compressive strength, whereas cylindrical specimens with a diameter of 100 mm and height of 200 mm were used for tensile strength measurements. Their results showed an increase in the mixedmode fracture toughness, uniaxial compressive strength and tensile strength of 7- and 28-day
specimens with increasing jute fiber content. Kumar and Rao (2015) presented an empirical relation for mode II fracture energy of concrete. The concrete specimens were prepared using normal Portland cement, natural fineand coarse-grained river materials, ground granulated blast furnace slag (GGBS) and various levels of super plasticizer and water/cement ratios. To reach their ultimate strength, all specimens were cured in water for 28 days. The study results showed that an increase in the grade of concrete increases the brittleness of the member and fracture energy. Stress–based fracture criteria are simpler than energy–based ones and demonstrate the role of each parameter in estimating fracture initiation. In contrast, energy–based criteria predict fracture initiation more accurately. Strain–based criteria combine the characteristics of both the aforementioned criteria (Mirsayar, 2015). Wu (1974) proposed a dual fracture criterion for plain concrete. Accordingly, a material may fail due to shear or tension depending on the stress or strain mode. This criterion is able to predict experimental results with a reasonable accuracy. Chang modified the maximum principal strain theory, also known as the Saint-Venant’s theory (Timoshenko, 1953), and proposed the modified maximum strain criterion using the elliptic crack and slit crack models. This criterion is dependent on Poisson’s ratio. Mirsayar (2015) presented the extended maximum tangential strain based criterion (EMTSN) or modified MTSN by taking into account the T–Strain as well as the singular strain field using poly methyl methacrylate (PMMA) specimens. Accordingly, the modified criterion overestimates the fracture initiation angle. Although both T–Strain and Poisson’s ratio significantly affect the fracture initiation angle in pure mode II, no effect is observed in pure mode I. In other studies, the traditional fracture criteria have been compared with the EMTSN criterion. Experiments were conducted on various materials such as graphite (Mirsayar et al., 2016), dental restorative materials (Mirsayar, 2018) and marble rock (Mirsayar et al., 2018) under different loading conditions (mode I, mode II and mixed) using various methods in order to determine the fracture toughness. In all of these studies, the EMSTN criterion predicts the experimental data more accurately compared to the traditional fracture criteria. Aliha et al. (2018) studied the effect of synthetic forta–ferro (SFF) fibers on fracture load, fracture toughness and work of fracture of concrete under pure mode I and pure mode III. Edge notched disk bend (ENBD) specimens were used for this purpose. The concrete composites reinforced with SFF fibers showed a higher fracture load, fracture toughness and work of fracture than plain concrete. In both cases, the highest KIC and KIIIC were obtained for the concrete reinforced with 0.3% SFF fibers. Mirsayar et al. (2017) investigated the interfacial bond strength of Portland cement concrete (PCC) and asphalt concrete (AC) using bi–material semi–circular bending specimens (SCB). Accordingly, a novel test called biomaterial semi–circular bend (BSCB) was proposed for mixed mode tests. The stress intensity factors KI and KII for the BSCB specimens are dependent on crack length, crack inclination angle, location of supports, loading, and elastic
properties of both bonded materials. Fakhri et al. (2017) experimentally analyzed the behavior of crack in roller compacted concrete (RCC) with reclaimed asphalt pavement (RAP) and crumb rubber under pure mode I and mode II using semi–circular bending (SCB) and four–point bending (4PB) specimens. They aimed at finding a suitable geometry for fracture specimens and investigating the effect of RCC specifications including aggregate gradation, cement content and waste materials on pure mode I and mode II fracture toughness of RCC mixtures. The results indicated the higher KI/KII of SCB specimens than 4PB specimens. This difference originates from the geometric factors that reduce the load–bearing capacity and directly affect the fracture toughness. Aliha et al. (2012) prepared cracked and un–cracked SCB specimens, respectively, for determining mode I fracture toughness and tensile strength of polymer concrete (PC) and compared the results with those of plain concrete. The mode I fracture toughness and tensile strength of PC were 3.31 and 4.47 times of plain concrete. Heidari–Rarani et al. (2014) studied the mechanical durability of an optimized epoxy PC under freeze–thaw cycles by considering fracture toughness and tensile strength. Un–cracked Brazilian disc (BD) and single edge notch bending (SENB) specimens were, respectively, used in tensile strength and fracture toughness tests. Three thermal cycles, namely 25 to –30 ̊C (Cycle A), 25 to 70 ̊C (Cycle B) and –30 to 70 ̊C (Cycle C), were applied to the specimens. The results indicated the significant impact of the thermal cycle B on the fracture toughness and tensile strength. The results were compared with those under environmental conditions. Using SCB specimens, Shi et al. (2019) proposed a new method for critical stress intensity factor and critical crack tip opening displacement (CTOD_C). They compared fracture properties and flexibility of Portland cement containing reclaimed asphalt pavement (RAP– PCC) with Portland cement concrete (PCC). According to their results, RAP–PCC showed a higher CTOD_C than plain concrete with the same critical stress factor. Moreover, RAP–PCC was more flexible than PCC. The results showed a decrease in the peak point and slope (gradient) with increasing the number of wetting–drying cycles and weakening of the cement mortar and concrete.
Although mode III fracture toughness rarely occurs in concrete, there are studies on this mode in the literature. Golewski (2017) experimentally studied the effect of fly ash (FA) penetration on the fracture toughness of plane concrete. Golewski proposed a new test method for estimating mode III fracture toughness of concretes with 0, 20 and 30% FA. The concrete was prepared from normal Portland cement, 8 mm gravel, sand, silica, FA and plasticizer. The effect of FA on the mode III fracture toughness of concrete was systematically studied. He found that adding 20% FA to the concrete caused an increase in the mode III fracture toughness while 30% FA reduced the mode III fracture toughness. The mode III to mode II fracture toughness ratio of 0.59 indicated a larger mode II fracture toughness than mode III fracture toughness.
Golewski and Sadowski (2016) measured the mode III fracture toughness and uniaxial compressive strength of three types of concrete with different fly ash contents. The concrete was prepared from normal Portland cement, natural gravel aggregates, sand, fly ash and plasticizer. The same water/cement ratio was used in all specimens (w/c=0.4). Concretes with 0, 20 and 30% FA were tested. Young (concrete younger than 7 days) and mature (more than 7 days) concrete composites were subjected to mode III loading after 3, 7, 28, 90, 180 and 365 days. Their results showed a decrease in the mode III fracture toughness of young concrete by adding 20 and 30% FA as compared to the concrete with 0% FA. The mode III fracture toughness of the concrete containing 20% FA increased after 28 days. However, the mode III fracture toughness of the concrete containing 30% FA was less than that of concrete with 0% FA. The mode III fracture toughness of the concrete containing 20% FA increased by 4.4% after a long curing period while that of the concrete with 30% FA decreased by 14.1%. The increase in the fracture toughness of the concrete containing 30% FA was only observed for a half-year period. These results were consistent with those of uniaxial compressive strength tests (Golewski and Sadowski, 2016). In another study, Golewski (2017) examined the effect of FA on the mode III fracture toughness of concretes containing 0, 20 and 30% FA. A flat fractured cross-section was observed by scanning electron microscopy (SEM). According to SEM micrographs, semi-circular multi-faceted cracks were formed on the fractured cross-section. The fracture toughness of the three modes were compared and a KIIIc/KIc of 2.35, 2.3 and 2.39 was, respectively, obtained for FA-00, FA-20 and FA-30. A similar KIIIc/KIc of 0.59 was, however, obtained for all concrete series. The highly similar results, especially the same KIIIc/KIc values, may represent a very accurate test for all fracture modes. In addition, the results of mode III fracture toughness were less scattered than mode I and mode II fracture toughness.
According to the literature, few articles have been conducted on the effect of number of wetting– drying cycles on fracture toughness of concrete. However, Brazilian discs were not used in this article. As innovative aspects of this study compared with Soroushian et al. (1994), CCNBD and CCDB specimens were used to investigate the effect of wetting–drying cycles on the fracture toughness of cement mortar and concrete specimens. Before fracture toughness testing, the specimens were saturated in 20 ̊C water for 48 h and then dried at 105 ̊C for 24 h. The mode I and mode II fracture toughness were determined by testing CCBD specimens. A chevron notch and a straight-through notch were created respectively in cement mortar and concrete specimens. The specimens were loaded after 1, 4, 8, 16 and 20 wetting– drying cycles.
2. Materials specifications 2.1. Cement mortar and concrete mix designs
Two mix designs were used in these experiments. The cement mortar consisted of water, cement and fine–grained beach sand. Concrete was made of water, cement, fine–grained beach sand and gravel. Figure 1 shows the mix designs for cement mortar and concrete specimens.
Figure 1: Mix designs for cement mortar and concrete specimens
2.2. Physical and mechanical properties of cement mortar and concrete Table 1 lists some physical and mechanical properties of cement mortar and concrete. All experiments were performed based on ISRM standards (Ulusay and Hudson, 2007). Table 1: Physical and mechanical properties of concrete specimens specimens Cement mortar Concrete
dry unit weight (kN/m3) 19.09 18.48
uniaxial compressive strength (MPa) 26 23
tensile strength (MPa) 3.73 3.1
effective porosity (%) 17.03 17.01
3. Specimen preparation 3.3. Cement mortar specimens A total of eight cylindrical molds with a length of 200 mm and an inner diameter of 71.14 mm were used for preparation of cement mortar specimens. The cylindrical cement mortar specimens were cured in water for 28 days to reach their ultimate strength. The specimens were then cut into discs with an approximate thickness of 24 mm. Figure 2 shows the preparation stages. After cutting cylindrical concrete specimens, the center point and crack direction for all specimens were determined by a center finder to create a chevron notch at the center of the disc. To prepare the CCNBD specimens, two notches were cut at the center on both sides of specimens by a small cutterhead with a disc diameter of 40 mm and a thickness of 1 mm. The crack depth (hc) from each side was about 13 mm. The cutterhead blade was cooled with water during the cutting of the chevron notch. Figure 3 schematically shows the chevron notching process in circular disc specimens. The notch created in the Brazilian disc should satisfy some standards that are specified by α1=a1/R and αB=B/R, where R represents disc radius, B disc thickness and a1 is half-length of the crack. As shown in Fig. 4, the standards have been met in preparation of specimens (Aliha and
Ayatolahi, 2014).
Figure 2: Preparation of cement mortar specimens
Figure 3: Chevron notching in CCNBD specimen
Figure 4: Geometric characteristics required for the CCNBD specimen in cement mortar 3.2. Concrete specimens Straight-through cracks were decided to be created in the concrete specimens since the gravel in the concrete could have caused damage to the cutterhead. Concrete was poured into special molds with a metal blade in the center. The straight-through crack was created by the central metal blade (Fig. 5). The thickness, diameter and crack length of concrete specimens were close together due to the use of a mold for preparation of concrete discs.
Figure 5: A metal mold for preparation of concrete specimens with a straight through crack 4. Experiments 4.1. Wetting–drying cycles The prepared specimens should undergo wetting–drying cycles. The experimental method proposed by Hua et al. (2015, 2016 and 2017) was used for this purpose. In each cycle, the specimens were cured in water for 48 h to be completely saturated (Figure 6) and then dried in an oven at 105 ᵒC for
24 h. Fracture toughness test on concrete and cement mortar specimens was performed after 0, 1, 4, 8, 16 and 20 cycles. The 0th cycle refers to the dry specimens not undergoing any wetting–drying cycle. These specimens are considered as the reference for measuring the fracture toughness of other specimens exposed to different number of wetting–drying cycles. Accordingly, each cycle lasted 3 days and thus all 20 cycles lasted 60 days.
Figure 6: Saturation of specimens in water
4.2. Experiments on concrete specimens 4.2.1. Cement mortar specimens A chevron notch was created in the cement mortar specimens. A loading rate of 0.2 kN/s was used in the experiments. The mode I fracture toughness (KIC) of CCNBD specimens is obtained from Eq. 1: 𝑃𝑚𝑎𝑥
∗ 𝐾𝐼𝐶 = 𝐵 𝐷𝑌𝑚𝑖𝑛
(1)
where 𝑃𝑚𝑎𝑥 is the fracture force, B disc thickness, D disc diameter. The critical stress intensity ∗ factor (𝑌𝑚𝑖𝑛 ) is obtained from Eq. 2: ∗ (2) = 𝑢𝑒𝑣𝛼1 𝑌𝑚𝑖𝑛 where u and v are constant parameters obtained from 𝛼0 and 𝛼𝐵 in Table 2 (Fowell et al., 1995).
Parameters α1 and αB are, respectively, defined as a1/R and B/R where R represents disc radius, B disc thickness and a1 is the half-length of the outer crack in Fig. 7 (Aliha and Ayatolahi, 2014). The loading direction is aligned with the crack direction to determine mode I fracture toughness of all specimens (α=0)
Table 2: 𝒖 and 𝒗 obtained from α0 and αB (Fowell et al., 1995) α0
0.200
0.250
0.275
0.300
0.325
0.350
0.375
0.400
0.680
0.2667
0.2704
0.2718
0.2744
0.2774
0.2807
0.2848
0.2888
0.720
0.2650
0.2683
0.2705
0.2727
0.2763
0.2794
0.2831
0.2871
0.760
0.2637
0.2668
0.2693
0.2719
0.2744
0.2781
0.2819
0.2860
0.800
0.2625
0.2657
0.2680
0.2706
0.2736
0.2772
0.2811
0.2845
0.840
0.2612
0.2649
0.2672
0.2699
0.2727
0.2763
0.2801
0.2831
0.880
0.2602
0.2642
0.2668
0.2691
0.2723
0.2754
0.2793
0.2816
0.920
0.2598
0.2634
0.2658
0.2684
0.2716
0.2747
0.2782
0.2811
0.960
0.2593
0.2633
0.2655
0.2685
0.2710
0.2746
0.2767
0.2799
1.000
0.2591
0.2630
0.2653
0.2679
0.2709
0.2738
0.2768
0.2786
0.680
1.7676
1.7711
1.7757
1.7759
1.7754
1.7741
1.7700
1.7666
0.720
1.7647
1.7698
1.7708
1.7722
1.7693
1.7683
1.7652
1.7617
0.760
1.7600
1.7656
1.7649
1.7652
1.7662
1.7624
1.7593
1.7554
0.800
1.7557
1.7611
1.7613
1.7603
1.7596
1.7561
1.7525
1.7512
0.840
1.7522
1.7547
1.7551
1.7548
1.7535
1.7499
1.7469
1.7473
0.880
1.7487
1.7492
1.7478
1.7487
1.7463
1.7452
1.7403
1.7434
0.920
1.7423
1.7446
1.7443
1.7432
1.7411
1.7389
1.7360
1.7363
0.960
1.7370
1.7373
1.7372
1.7346
1.7344
1.7309
1.7343
1.7331
1.000
1.7308
1.7307
1.7306
1.7297
1.7273
1.7270
1.7258
1.7302
αB
𝑢
𝑣
Pure mode II fracture toughness (KIIC) is obtained from Eq. 3 (Aliha and Ayatolahi, 2014): 𝐾𝐼𝐼𝐶 =
𝑃𝑚𝑎𝑥
𝛼
𝛼1 ― 𝛼0
𝛼 ― 𝛼0 𝑌𝐼𝐼
𝜋𝑅𝐵 𝑅
(3)
where 𝑌𝐼𝐼 is the geometric factor for pure mode II, which is dependent on the crack length to disc radius ratio (a/R) of the CCNBD specimens. This geometric factor can be obtained both theoretically and numerically by finite element method (FEM) with the parameters given in Eq. 4. This equation was first presented by Atkinson et al. (1982): 𝑛
𝐿
𝑌𝐼𝐼 = 2𝑠𝑖𝑛2 𝜑∑𝑖 = 1𝑆𝑖(𝑎)2𝑖 ― 2𝐵𝑖(𝜑)
(4)
Figure 7 shows variations of YII with respect to the a/R ratio for CCNBD specimens. To determine the mode II fracture toughness, the average angle between the crack and loading directions was 26.5 for the CCNBD specimens as obtained from Fig. 8.
Figure 7: Variations of geometric factor of mode II with respect to a/R ratio for CCNBD specimens (Aliha and Ayatollahi, 2014)
Figure 8: Variations of pure mode II crack inclination angel with respect to the a/R ratio (Aliha and Ayatollahi, 2014) Figure 9 schematically shows the geometry and mode II loading of a CCNBD specimen.
Figure 9: The geometry and loading of a CCNBD specimen (Aliha and Ayatolahi, 2014) 4.4.2. Concrete specimens Straight-through cracks were created in the concrete specimens. A disc with a central straight crack was used for determining the fracture toughness. Atkinson et al. (1982) proposed Eqs. 5 and 6 for calculating mode I and mode II fracture toughness: 𝐾𝐼𝐶 = 𝐾𝐼𝐼𝐶 =
𝑃 𝑎 𝜋 𝑅𝐵 𝑃 𝑎
𝑁𝐼
(5)
𝑁𝐼𝐼
(6)
𝜋 𝑅𝐵
where KIC represents mode I fracture toughness, KIIC mode II fracture toughness, R Brazilian disc radius, B disc thickness, P fracture force, and a half-length of the crack. Moreover, NI and NII respectively show mode I and mode II normalized stress intensity factors, which are dependent on the a/R ratio and crack–loading direction angle (β). Loading direction is aligned with the central crack direction in the mode I fracture toughness test (β=0). Parameters NI and NII are respectively obtained from Eqs. 7 and 8 for a/R ≥ 0.3 (Atkinson et al., 1982): 𝑎 2
𝑁𝐼 = 1 ― 4 𝑆𝑖𝑛2𝛽 + 4 𝑆𝑖𝑛2𝛽( 1 ― 4𝑐𝑜𝑠2𝛽) (𝑅) 𝑁𝐼𝐼 =
[2 + (8 𝐶𝑂𝑆 𝛽 ― 2
)]𝑆𝑖𝑛2𝛽
𝑎 2 5(𝑅)
(7) (8)
where β represents the angle between the crack and loading directions. By equating NI to zero to determine mode II fracture toughness, the average value for β is obtained as 28.8 ̊. Figure 10 schematically shows the geometry and mode II loading of a CCBD specimen.
Figure 10: A centrally cracked Brazilian disc (CCBD) specimen under compression (Hua et al., 2015) 5. Results The results on the mode I and mode II fracture toughness and porosity of cement mortar and cement after different wetting–drying cycles are presented in this section. 5.1. Fracture toughness of cement mortar specimens The mode I and mode II fracture toughness of cemnet mortar specimens decreased with increasing the number of wetting–drying cycles. The effect of 20 wetting–drying cycles on the mode II fracture toughness was greater than mode I fratcure toughness by 1.55 (i.e. reduction of mode II fracture toughness relative to mode I fracture toughness). The average mode I fracture toughness of cement mortar specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.3, 0.28, 0.27, 0.26, 0.25 and 0.24 MPa 𝑚, respectively. The mode I fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 6.66, 10, 13.33, 16.66 and 20% relative to the specimen subject to no wettingdrying cycles, respectively. The average mode II fracture toughness of cement mortar specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.77, 0.68, 0.65, 0.62, 0.59 and 0.53 MPa 𝑚, respectively. The mode II fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 11.68, 15.58, 19.48, 23.37 and 31.16% relative to the specimen subject to no wetting-drying cycles, respectively. Figure 11 shows the cement mortar specimens after fracture in the mode I and mode II fracture toughness tests. The results are shown in Table 3 and Fig. 12.
b a Figure 11: Cement mortar specimens after fracture, (a) mode I and (b) mode II fracture toughness
Table 3: Mode I and mode II fracture toughness of cement mortar Specimen
Number of cycle
fracture mode
fracture load )KN(
mode I fracture toughness (MPa m)
mode II fracture toughness (MPa m)
C-1-1
0
I
3.1
0.33
C-1-2
0
I
3.1
0.32
C-1-6 C-1-3
0 0
I II
2.6 3.9
0.27
C-1-4
0
II
3.7
C-1-5 C-9-5
0 1
II I
3.8 2.7
0.28
C-9-7
1
I
2.6
0.28
C-9-1
1
II
3.3
0.73
C-9-3
1
II
3.1
0.64
C-4-6
4
I
2.5
0.27
C-8-7
4
I
2.7
0.3
C-7-4
4
I
2.4
0.25
C-6-4
4
I
2.5
0.26
C-2-3
4
II
3.1
0.65
C-2-4
4
II
3.2
0.66
C-2-7
4
II
3.3
0.68
C-2-5 C-6-1
4 8
II I
3.1 2.4
0.25
C-4-4
8
I
2.7
0.28
C-6-7 C-3-1
8 8
I I
2.6 2.4
0.26 0.25
C-9-6
8
I
2.5
0.26
C-6-6
8
II
2.9
0.59
C-8-1
8
II
3.1
0.63
C-7-6
8
II
3
0.63
C-7-7
8
II
3
C-4-2
16
I
2.6
0.26
C-7-1
16
I
2.5
0.25
C-3-3
16
I
2.3
0.23
C-8-2
16
I
2.5
0.26
C-3-5
16
II
2.7
0.6
C-8-6
16
II
2.8
0.59
C-4-3
16
II
2.9
0.59
C-6-2
16
II
2.8
0.58
C-4-7
20
I
2.4
0.24
C-5-1
20
I
2.4
0.24
C-3-2
20
I
2.3
0.23
C-9-4
20
II
2.6
0.55
C-4-1
20
II
2.7
0.54
C-8-4 C-5-6
20 20
II II
2.5 2.6
0.51 0.54
0.81
average mode I or II fracture toughness (MPa m) 0.3
decrease fracture toughness (%)
0.77
-
0.28
6.66
0.68
11.68
0.27
10
0.65
15.58
0.26
13.33
0.62
19.48
0.25
16.66
0.59
23.37
0.24
20
0.53
31.16
-
0.74 0.76
0.61
0.63
0.9
Fracture Toughness(MPa√m)
0.8 Mode I Average
0.7 0.6 0.5
Mode II Average
0.4 0.3
Linear (Mode I Average)
0.2 0.1
Linear (Mode II Average)
0 0
4
8
12
16
20
24
Number of Wetting - Drying Cycles
Figure 12: The relationship between the number of wetting–drying cycles and mode I and mode II fracture toughness of cement mortar specimens 5.2. Fracture toughness of concrete specimens The mode I and mode II fracture toughness of concrete specimens decreased with increasing the number of wetting–drying cycles. The effect of 20 wetting–drying cycles on the mode II fracture toughness was greater than mode I fratcure toughness by 0.69 (i.e. reduction of mode II fracture toughness relative to mode I fracture toughness). The average mode I fracture toughness of concrete specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.157, 0.151, 0.148, 0.136, 0.131 and 0.129 MPa 𝑚, respectively. The mode I fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 3.82, 5.73, 13.37, 16.56 and 17.83% relative to the specimen subject to no wettingdrying cycles, respectively. The average mode II fracture toughness of concrete specimens after 0, 1, 4, 8, 16 and 20 cycles was 0.365, 0.356, 0.353, 0.336, 0.328 and 0.32 MPa 𝑚, respectively. The mode II fracture toughness of specimens undergoing 1, 4, 8, 16 and 20 cycles decreased by 2.46, 3.28, 7.94, 10.13 and 12.32% relative to the specimen subject to no wetting-drying cycles, respectively. Figure 13 shows the concrete specimens after fracture in the mode I and mode II fracture toughness tests. The results are shown in Table 4 and Fig. 14.
a b Figure 13: Concrete specimens after fracture, (a) mode I and (b) mode II fracture toughness
Loading on the specimen for determining mode I fracture toughness and the load-displacement curves were shown in Figs. 15 and 16 respectively. The Fig 16 showed a decrease in the peak point and slope of curves with increasing the number of wetting–drying cycles and weakening of the cement mortar and concrete.
Table 4: Mode I and mode II fracture toughness of concrete specimens Specimen
Number of cycle
fracture mode
fracture load )KN(
mode I fracture
0
I
3
0.158
ć-5-3
0
I
3.1
0.156
ć-5-1
0
II
3.3
0.356
ć-1-1
0
II
3.5
0.375
c-4-5
1
I
2.8
0.145
c-4-2
1
I
3
0.155
c-4-4
1
I
2.9
0.153
c-4-3
1
II
3.3
0.348
c-4-1
1
II
3.4
0.365
c-5-1
4
I
2.8
0.146
c-6-1
4
I
2.9
0.153
c-5-2
4
I
2.8
0.146
c-5-4
4
II
3.3
0.35
c-5-3
4
II
3.2
0.356
C-6-2
8
I
2.6
0.136
C-3-3
8
I
2.7
0.137
c-6-4
8
II
3.2
0.346
C-6-3
8
II
3.1
0.327
C-3-6
16
I
2.6
0.134
C-3-5
16
I
2.5
0.129
C-3-1
16
II
3
0.319
C-2-2
16
II
3.2
0.337
c-2-4
20
I
2.6
0.131
C-1-2
20
I
2.5
0.127
C-2-3
20
II
3
0.311
C-2-1
20
II
3
0.329
toughness (MPa m )
mode II fracture toughness (MPa m)
ć-5-4
average mode I or II fracture toughness (MPa m)
decrease fracture toughness (%)
0.157 0.365 0.151
3.82
0.356
2.46
0.148
5.73
0.353
3.28
0.136
13.37
0.336
7.94
0.131
16.56
0.328
10.13
0.129
17.83
0.32
12.32
0.45
Fracture Toughness (MPa√m)
0.4
Mode I Average
0.35 0.3
Mode II Average
0.25 0.2
Linear (Mode I Average)
0.15 0.1
Linear (Mode II Average)
0.05 0 0
4
8
12
16
20
24
Number of Wetting - Drying Cycles
Figure 14: The relationship between the number of wetting–drying cycles and mode I and mode II fracture toughness of concrete specimens
Figure 15: Loading on the specimen for determining mode I fracture toughness
Figure16: The load-displacement curves were shown in Figs. 15 and 16 respectively.
5.3. Effective porosity of cement mortar and concrete specimens As clearly seen in Fig. 17, effective porosity increases with increasing the number of wetting– drying cycles. Several specimens were used in each cycle to calculate an accurate value for average effective porosity. After 0 (the specimen subject to no wetting-drying cycles), 1, 4, 8, 16 and 20 cycles, the specimens were saturated by a vacuum pump, after which the saturated and immersion weights were measured. The specimens were then dried in an oven and their dry mass was calculated. An effective porosity of 17.03, 17.5, 17.8, 18.05, 18.15 and 18.35% was obtained for cement mortar specimens after 1, 4, 8, 10, 16 and 20 cycles, respectively. The corresponding value for concrete specimens was 17.01, 17.65, 18, 18.3, 19.1 and 19.7%, respectively. The porosity of cement mortar and concrete specimens increased by 1.32 and 2.69% after 20 cycles, respectively.
Figure 17: Variations of porosity with respect to the number of wetting–drying cycles
6. Discussion The mode I and mode II fracture toughness of concrete were less than those of cement mortar. The reduction in mode I and mode II fracture toughness reduction of concrete was also less than that of cement mortar. This can be related to crack formation during drying, mix design and paste volume of cement mortar and concrete specimens. Cement paste is a key component in the concrete structure. Cement paste contains hydration products, unhydrated particles, cavities and pore water. Hydration products are generated by reacting water with cement components. The majority of hydration products are produced from reaction of C3S and C2S with water. These reactions produce hydrated calcium silicate (C-S-H) and calcium hydroxide (Mehta and Monterio, 2001). Ettringite is also formed during hydration. The formation of ettringite begins as soon as cement is combined with water (Barnes et al., 1992). This type of ettringite called early ettringite grows homogenously. The concrete volume increases as a result of ettringite formation. The resulting swelling, however, is harmless (Collepardi, 2003) and fills the pores in the cement (Macledo and Hall, 1991). The specimen size does not change when cement paste is saturated. However, the specimen is deformed and shrunk during drying when C-S-H gel loses some of its adsorbed water. Drying–induced shrinkage of concrete is usually affected by gravel volume and hardness, water and cement volume, relative humidity and the time the concrete is exposed to environmental humidity. Concrete cracking usually occurs as a result of shrinkage–induced tensile fracture (Mehta and Monterio, 2017). Starting their propagation through cement paste from the cement paste-grain boundary, the microcracks are stopped when they collide with the grains (Wu et al., 2015). Delayed ettringite is formed when dried concrete is exposed to moisture again. Delayed ettringite is in fact heterogeneous formation of ettringite crystals in the cement after complete drying during which sulfate compounds are supplied by cement. These crystals are called secondary or delayed ettringite (Collepardi, 2003). Two types of ettringite are formed depending on the sulfate source including internal and external sulfate sources. The key factors affecting formation of delayed ettringite include (1) overheating (60-70 ̊C) while concreting, which prevents formation of nonexpansive early ettringite and (2) the presence of sulfates mainly in cement and to a lower extent in water and coarse-grained materials. These sulfates may react with aluminates in the cement in the presence of water to form secondary ettringite. A wet environment also affects formation of delayed ettringite so that all damages caused by secondary ettringite appear at regions exposed to water (Leklou et al., 2012). The water filling concrete pores is necessary for migration of reacting ions 𝑆𝑂24 ― , 𝐴𝑙(𝑂𝐻)4― and 𝐶𝑎2 + in order for the ettringite to deposit in the microcracks (Collepardi et al., 2003). Concretes undergoing alternating wetting-drying cycles are more susceptible to damage than those exposed to permanent wetting (Thaulow et al., 1996, Collpardi, 2001) due to formation of delayed ettringite after drying of concrete and onset of re-wetting. This can be related to the key role of saturation in ettringite deposition. Water causes migration of ions in the cement matrix to microcrack and the subsequent deposition of ettringite crystals and opening of cracks. Consequently, successive wetting-drying cycles lead to formation of microcracks and increased porosity. Due to heterogeneous expansion in the concrete, delayed ettringite formation causes
tensile stress and crack formation in the concrete (Leklou et al., 2012, Diamond, 1996). Ettringite shrinks due to water loss during drying (Diamond, 1996). Strength and fracture toughness decrease with increasing porosity (Kearsley and Wainwright, 2002). Hydration and the subsequent formation of delayed ettringite deposits occur more intensely in cement mortar due to the higher cement volume, consequently leading to a lower rate of growth for porosity in cement mortar than concrete. The water–cement ratio (w/c) in the cement mortar equals 0.5 with a paste volume (water and cement volume) of 60% (relative to total volume). The corresponding w/c in concrete equals 0.75 with a paste volume of 28%. Unlike paste, gravels and sand in cement mortar and concrete specimens are not affected by saturation during wetting–drying cycles. Due to the lower paste volume and higher w/c of concrete compared to cement mortar, the adhesive force between concrete components is less than that of cement mortar, which consequently leads to the lower fracture toughness of concrete. According to the results of the fracture toughness tests, cement mortar is more sensitive to wetting– drying cycles. The mode I and mode II fracture toughness of cement mortar decreased by 20 and 31.16% after 20 cycles relative to the specimen subject to no wetting-drying cycles, respectively. The corresponding values for concrete were 17.83 and 12.32%, respectively. Due to its higher paste volume, cement mortar is affected by the water volume to a greater extent, consequently resulting in the higher sensitivity of the fracture toughness of cement mortar compared to concrete. Comparison of the mode I and mode II fracture toughness of cement mortar and concrete showed that despite higher homogeneity of cement mortar compared to concrete, cement mortar results are more scattered than those obtained for concrete. This can be related to the preparation method. As discussed in the specimen preparation section, the diameter, thickness and length of crack in all concrete specimens prepared in the prefabricated molds are almost the same, which leads to less scattered data. In contrast, the cement mortar specimens were prepared by an operator using a cutterhead blade. Despite compliance with relevant standards, the specimen and crack sizes of the cement mortar specimens are slightly different, leading to more scattered data than concrete. 7. Conclusion The effect of wetting–drying cycles on the mode I and mode II fracture toughness of cement mortar and concrete was investigated. The cement mortar and concrete specimens were loaded after 0 (the specimen subject to no wetting-drying cycles), 1, 4, 8, 16, 20 cycles. The results are summarized as follows: The mode I and mode II fracture toughness of cement mortar and concrete decreased with increasing the number of wetting–drying cycles. The lower volume of cement paste in the concrete causes lower adhesion than concrete, leading to the lower fracture toughness than cement mortar. The mode I and mode II fracture toughness of cement mortar linearly decreased by 20 and 31.16% after 20 cycles, respectively. The correlation coefficient between the mode I and mode II fracture toughness and the number of cycles was 0.86 and 0.83, respectively. The mode I and mode II fracture toughness of concrete linearly decreased by 17.83 and 12.32% after 20 cycles, respectively. The correlation coefficient between the mode I and mode II fracture toughness and the number of cycles was 0.9 and 0.94, respectively.
The mode I and mode II fracture toughness of cement mortar specimens were more affected by wetting–drying cycles as compared with concrete specimens. The mode I and mode II fracture toughness of cement mortar and concrete decreased with increasing porosity. Shrinkage during drying and formation of delayed ettringite during re-wetting deteriorate cement mortar and concrete, leading to reduced fracture toughness. Cement mortar is more sensitive to wetting–drying cycles than concrete due to its higher paste volume.
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Highlights:
Investigating the effect of the number of wetting- drying the mode I and mode II fracture toughness of concrete and cement mortar by the CCNBD test.
Presenting the relationship between the mode I and mode II fracture toughness and the number of wetting- drying for concrete and cement mortar.
Presenting the relationship between effective porosity and the number of wetting- drying for concrete and cement mortar.