1 Theoretical background

Concrete has been used widely and it has been modified according to the requirement such as High performance concrete (HPC), Ultra high performance concrete (UHPC), Self-compacting concrete (SCC), etc. due to its many advantages such as durability, low cost, greater strength etc. [8]. [37] mentioned about the use of SCC is designed for high formwork filling capacity, for good stability etc. [41] mentioned about the usage of cement leads to have adverse impact on environment in terms of emission of CO2, the cement produces around 7% greenhouse gases. The SCC has been introduced as environmental friendly material, which can be mold into any shape, with improved durability, with remarkable improved fresh properties [30]. The recycled aggregate concrete (RAC) has created interest due to its economic and environmental aspects, the RCA absorbs more water and increases its shrinkage, the use of steel fibers in RCA concrete improves the mechanical properties of concrete [9].

[20] stated that, the fracture energy will get affected by w/c ratio of the mix, it is decreased with increase in w/c ratio. [5] used w/c ratio in SCC from 0.35 to 0.7, the fracture toughness of w/c ratio 0.7 observed highest and fracture energy observed maximum at w/c ratio 0.4. [6, 7] mentioned about the fracture parameters for SCC and effect of maximum size of aggregate on it and it has been observed that as aggregate size increases the fracture properties of SCC improved significant. [6, 7] investigated the fracture parameters for SCC with volume and size of coarse aggregate, the results are in line with work done by [2, 6, 7, 19, 29] regarding the increase in volume of coarse aggregate leads to increase in fracture energy of concrete. [14] investigated fracture properties of SCC by SEM and work of fracture method (WFM) on notched beams. The WFM shows the correlation of compressive strength and fracture energy, the fracture energy increases with increase in compressive strength while in SEM fracture energy slightly decreases with increase in compressive strength. [23] stated that the due to higher w/c the concrete is identified as a brittle material when tested under three point bend test and concluded that three point bend test and wedge splitting test (WPT) are influenced by strength of cement paste and amount of coarse aggregate used respectively.

[38] mentioned the mechanical and fracture parameters are strongly affected by amount fibers used and type of fiber used in concrete, same is the case observed by [1, 4, 13, 16, 24, 28] and [22]. [31, 36] has used fly ash based geo polymer concrete (GPC) for study and concluded that fracture energy observed with GPC found similar to Ordinary Portland cement (OPC), the compressive strength is directly proportional to fracture energy. [21, 27] observed, generally Nano material are having issue related to dispersion in concrete, many Nano material required ultra-sonication treatment for effective dispersion of particles. TiO2 particles are adhering to self-assembled monolayer due to which the ultra-sonication can be eliminated and effective dispersion of particles can takes place easily.

DIC technique has increasing the attention of researchers as it provides the information about the crack opening displacement (COD) [42]. [10, 12] used DIC for mortar in which the OPC is partially replaced with limestone/metakaoline, the results obtained through DIC are very well matching with results obtained through experiment. [43] and [11, 25] used DIC and acoustic emission (AE) technique for examination of fracture in concrete and concluded that the AE technique is suitable to identification of fracture growth which was happened due to macro crack and DIC will useful for opening of cracks at various locations. [40] used DIC in concrete using multi wall carbon Nano tubes (MWCNT), Nano silica, Nano alumina etc. and concluded that DIC technique is effective while conducting fracture test for determination of crack length. [35] mentioned that, the use of higher amount of FA used in concrete leads to have many voids in concrete and they will be different from dense structure. [26] served the water to binder ratio has a significant effect, the concrete with low water to binder ratio the peak load increases and increase in volume of fibers also increases the peak load.

2 Preparation of specimens and experimental setup

The three point bend test (TPB) was performed confirming to [32]. The concrete beams were prepared according to mix design shown in Table 1. Nano TiO2 was used along with F class fly ash. Ordinary Portland cement (OPC) 53 grade was used for the all mixes confirming to IS 12269-2013 (IS 12269-2013). For dispersion of Nano TiO2 particles, polycarboxylate based superplasticizer was used. [15, 41] reported the use of polycarboxylate based superplasticizer showed great effect on dispersion properties of Nano particles. Also ultra-sonication was adopted to avoid the accumulation of Nano particles. The coarse aggregate was used with fineness modulus of 2.65, a specific gravity of 2.85 and water absorption 1.4%. The maximum size of coarse aggregate (da) is 20 mm having specific gravity 2.7 and absorption of water 0.85%. The 1, 2, 3 and 4% of NT used along with constant 30 percentage of FA with constant w/c ratio 0.38.

Table 1 Mix proportions
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To evaluate the fracture properties of concrete, the geometrical similar beams of size 74.90 × 74.90 × 200 mm, 74.90 × 149.80 × 400 mm, 74.90 × 299.60 × 600 mm (Width × Depth × Length) (Figs. 1, 2) were prepared by Size effect method (SEM) confirming to [33] recommendations. The length to depth (l/d) ratio was kept 2.67 and notch is provided at center of beam with the beam depth ratio of 0.25. A 2 mm thick notch having 25 mm depth was prepared while casting the specimens; the steel plate was inserted in the mold and the same has been removed after 24 h. The demolded specimens were kept for curing in curing tank till the date of testing. A closed loop servo control machine with the capacity of 50kN (Fig. 3) with CMOD opening of 0.03 mm/min. In addition to that the 150 × 150 × 700 mm beams, 150 × 150 × 150 mm cubes and 150 mm diameter and 300 mm height cylinder were casted with reference to ASTM C 78 (ASTM Standard C78), IS 516-1959 (IS 516-1959) and ASTM C 469 [3] to understand the flexure, compressive and split tensile strength of concrete respectively.

Fig. 1
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Beam specimens

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Fig. 2
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Molds of specimens for concrete

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Fig. 3
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Experimental set up for fracture test

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3 Digital image correlation technique and evaluation of opening displacement

DIC useful for measurement of displacement of spackles in a digital image. Which is noncontact measurement technique which helps to get the data related displacement of the surface of specimen. The specimens were painted by black and white paint to improve the correlation of image. The images were captured before and after at various stages of loading and unloading with the help of digital camera. The images were captured at rate of 5 s per image at far distance from testing setup using remote to avoid the vibrations and disturbance. The distance between camera lens and specimen kept constant throughout the experiment as shown in Fig. 4. The intensity and positions of lights are kept constant throughout the experiment. In DIC technique, the correlation between the deformed and undeformed images is measured to study the displacement fields. A point in (x, y) in the undeformed (original) image is correlated with a point (x*, y*) in the deformed image as mentioned in Eq. 1 and Fig. 5. A suitable region of interest is chosen as shown in Fig. 6 and with help of VIC 2D software displacement fields are measured.

Fig. 4
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Experimental setup for DIC

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Fig. 5
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Deformed and undeform pattern of image

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Fig. 6
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Region of interest for DIC study

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$${x}^{*}=x+ \mu (x,y)$$
$${y}^{*}=y+ v (x,y)$$
(1)

The μ and \(\text{v}\) represents horizontal and vertical displacement respectively, these displacement fields are measured by minimization of the correlation coefficient (C), which can be states as,

$$\text{C}=\frac{\sum [\text{G}\left(\text{x},\text{y}\right)-\text{H }({\text{x}}^{*}{\text{y}}^{* }){]}^{2}}{\sum [{\text{G}}^{2 }\left(\text{x},\text{y}\right)]}$$
(2)

where, G and H are grey scale light intensity with respect to point, the crack opening displacement and the crack extension can be determined from the u-displacement field findings.

4 Results and discussion

4.1 Mechanical and fracture properties

Table 2 and Figs. 7, 8 shows the detailed results of compressive strength, flexure strength, split tensile strength and fracture energy. The compressive strength of control concrete (CC) was observed 52.21 N/mm2, the NT3FA30 observed high compressive strength (56.02 N/mm2) compared with all the mixes and NT1FA30 found low (50.20 N/mm2) in all the mixes. Which indicates compressive strength increases from 1% NT to 3% NT and declines after 3% NT. The same is the case for flexural strength and split tensile strength, the NT3FA30 found high 8.87 N/mm2 and 4.25 N/mm2 respectively which indicates the 3% NT observed to be an optimum dose for as far as mechanical properties of concrete. Figure 8 shows the fracture energy details, which clearly states that the fracture energy increases with increase in NT 1% to 3% and after 3% it declines, which may happen due to leaching out of excess amount of Nano particles as observed by [18]. The NT3FA30 observed highest fracture energy which is improved about 10.93% compared with CC. Regarding fracture toughness, it has been observed that the fracture toughness increases with increase in NT percent from 1 to 4 and 4%, which is improved around 31.49% compared with CC. As per [17] the most favorable fracture toughness was observed at 20% of FA. The [39] observed the use of FA showed better performance in fracture and mechanical properties of concrete. The NT gives better results in fracture and mechanical properties this will have great impact of dispersion of Nano particles mentioned by [34], the has been observed in present study.

Table 2 Details of mechanical and fracture properties
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Fig. 7
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Results a Compressive strength, b Tensile strength and flexural strength

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Fig. 8
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Results of fracture energy and fracture toughness

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The plot of Load Vs CMOD graphs is shown in Fig. 9. NT4FA30 mix shows the highest peak load and lower that CC, which indicates the use of FA and NT as replacement to OPC improves the peak load conditions.

Fig. 9
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Plot of load vs CMOD

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4.2 Digital image correlation

The load vs crack opening displacement responses are shown in Fig. 10, on the curve P1–P4 points represents the displacement at different stages, the changes happening in crack extension can be observed. The first image represents pre-cracking phase.

Fig. 10
figure 10

Load vs CMOD of notched beam specimen

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Displacement of concrete beams are shown in Fig. 11, the first point P1 represents point at before cracking. The crack extension and crack opening is zero which indicates the uniform horizontal displacement near notch. Second point P2 represents point represents crack propagation the crack is visible at this stage which is stable. Third point P3 represents extension of crack which is in unstable. Fourth image P4 represents unstable extension of crack at crack tip of the specimen. The sharp transformation of crack extension is observed from P2 to P3 and P3 to P4 and that is clearly visible. The vertical displacement at notch point of specimen is measured by using LVDT and DIC (Fig. 12). It has been seen very good relation has been observed between displacement measured using DIC techniques and by using LVDT. Which indicated the effective usefulness of DIC technique.

Fig. 11
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Horizontal displacements at various stages of loading

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Fig. 12
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Displacement vs Image number

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5 Conclusion

The conclusion made from the work is as follows:

  1. 1.

    The results obtained from experiment shows that, the 3% NT has a great influence on fracture energy which is improved by 10.93% compared with control concrete.

  2. 2.

    The fracture energy increased from 1 to 3% NT and after 3% NT it declines, which indicate the excess amount of NT may have adverse impact on fracture energy.

  3. 3.

    The compressive strength, split tensile strength and flexural strength increases from 1 to 3% NT and after 3% NT it declines.

  4. 4.

    The fracture toughness increases with increase in NT from 1 to 4% and NT 4% has shown high fracture toughness, which is significantly improved by 31.49% compared with control concrete.

  5. 5.

    The peak load is increased with increase in size of specimen in all mixes.

  6. 6.

    DIC is an efficient approach for measuring fracture lengths and crack opening.

  7. 7.

    A good acceptable relation is observed in crack opening displacement and displacement measured by DIC and using clip gauge.

  8. 8.

    It can be summarizes that, the substitute for traditional way of measurement by using clip gauges and LVDTs is simple DIC technique can be very much useful.