Description of concrete fracture at meso-level using Finite Element Method based on X-ray micro-ct images

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1 Description of concrete fracture at meso-level using Finite Element Method based on X-ray micro-ct images Ł. Skarżyński 1, J. Tejchman 1 1 Gdansk University of Technology, Narutowicza 11/12, Gdańsk, Poland Aims The main objective of this study is to experimentally and numerically investigate fracture in concrete under quasi-static bending and fatigue compression. Theoretically concrete was modelled as a random 4-phase material composed of aggregate, cement matrix, interfacial transition zones (ITZs) and air voids. The concrete micro-structure in calculations was directly taken from real concrete specimens based on 3D X-ray microct images. Attention was paid to the shape of cracks between aggregate grains. In addition, the effect of ITZs on fracture was studied. Fracture is a fundamental phenomenon in concrete materials. It is very complex since it consists of main cracks with various branches, secondary cracks and micro-cracks [1]. During fracture, micro-cracks first arise in a hardening region on the stress-strain curve which change gradually during material softening into dominant distinct macroscopic cracks up to damage. Thus, a mechanical fracture process is generally subdivided into two main stages: 1) the appearance of narrow regions of intense deformation (equivalent to the region of intense micro-cracking called fracture process zones (FPZs)) ahead of macro-cracks and 2) the occurrence of discrete macro-cracks [2]. Recently, the application of the high-resolution x-ray micro-ct significantly increased. The image analysis offers the possibility to study in detail the size and shape of individual particles in granular and cementitious materials. The experiments were conducted in order to better understand a fracture process in quasi-brittle materials and to calibrate our mesoscopic continuum and discrete models for its description [3-6]. Next, some numerical 2D calculations at the aggregate level were carried out with the measured micro-structure. At the meso-scale, concrete was reproduced by distinguishing 4 different phases: aggregate, cement matrix, interfacial transition zones ITZs (contact zones between the cement matrix and aggregate) and macro voids [7-9]. In particular, the presence of aggregate particles and ITZs is important since the volume fraction of aggregate can be as high as 70-75% in concrete and the ITZs with the thickness of about µm which are always the weakest region in usual concretes (wherein cracking starts because of their higher porosity) [4]. For concrete, strain localization and cracks are two key parameters needed to estimate the permeability, strength and durability of structural concrete components [1]. Method The concrete was prepared from an ordinary Portland cement (CEM I 32.5 R), aggregate and water. The mean aggregate diameter was d 50=2 mm, maximum aggregate diameter d max=16 mm (Fig. 1) and aggregate volume V agg=75%. The water to cement ratio was 0.42 (Table 1).

2 Figure 1: Grain size distribution curve of concrete (mean aggregate size d 50=2 mm, maximum aggregate diameter d max=16 mm Table 1: Concrete mix used in beam and cubes experiments Components Amount (kg/m 3 ) Cement 810 Sand (0-2 mm) 650 Gravel aggregate (2-8 mm 580 Gravel aggregate (8-16 mm) 580 Water 340 The quasi-static bending tests were carried out on 2 free-supported rectangular notched concrete beams (height H=80 mm, depth B=40 mm and length L=320 mm). The notch of the height of D/10=8 mm and width of 3 mm was located at the mid-span (Fig. 2). The tests were performed with a controlled notch opening displacement rate (crack mouth opening displacement (CMOD)) of mm/min. This type of control allowed for obtaining a gradual increase in the crack opening and a steady strength decrease in a post-peak regime. A CMOD gauge with the length of 5 mm was located in the notch at the beam bottom. The gauge precision was mm at the maximum permissible axial displacement of 2 mm. The uniaxial fatigue compression tests were carried out on concrete cubes mm 3. The tests were carried out with the frequency 2 Hz in the range of load kn (25%-70% of the static failure force). The concrete cuboids with the dimensions of 80 mm (height), 50 mm (width) and 40 mm (depth) were cut out from each beam after each test for scanning by the x-ray microtomograph in order to obtain the 3D images of micro-structure (Fig. 3). The concrete cubes under compression were scanned before loading, after 10'000 cycles, after 40'000 cycles and after 70'000 cycles. The x-ray source voltage of the micro-ct scanner was set to 130 kev, the current was 61 µa and exposure time was equal 2400 ms. The 0.25 mm brass filter was used. The pixel size was µm. The x-ray projections were recorded with the rotation increment of within In order to reduce the noise in the X-ray projections, the frame averaging option was 6 and random movement option was 50. The scanning time was approximately 9 hours. The Bruker-Skyscan sotware (NRecon, CTan, DataViewer and CTvox) were used to reconstruct and process images.

3 Figure 2: General view in experimental set-up with concrete notched beam under quasi-static three-point bending in Instron 5569 Experimental results Figure 3 demonstrates the 3D image of the cracked cubical concrete specimens after the test. The specimen of Fig. 5a was cut out from the beam '1' when the beam was totally cracked along the height. The specimen of Fig. 5b was cut out from the beam '2'. The heterogeneous concrete micro-structure is well visible and the 3 phases (aggregate particles, cement matrix and air voids) can be distinguished (Figs. 6 and 7). Figure 3: Images of cubical specimens mm 3 by 3D micro-ct (SkyScan 1173): a) beam '1' and b) beam '2' The crack width was automatically measured using the CT Analyser Software of SkyScan Figure 4 shows the 3D visualisation of the crack in the specimen '2' (region mm 3 ). In the automatic procedure, the air voids were also treated as the crack. It is

4 visible that the crack area was strongly curved along the beam depth and its height was nonuniform. The crack height was the smallest in the beam mid-depth. The change of the crack width in concrete is presented in Figure 5. The crack width non-linearly changed along the specimen depth and height (between mm) due to a random distribution of aggregate and air voids. The areas marked in blue represent the crack wider than 0.3 mm (it is the width of the crack and macro-void that was crossed by crack). The crack width was the largest just above the notch ( 0.3 mm) and the smallest in the upper specimen region. Figure 4: Concrete specimen: a) three-dimensional crack along cuboid depth and b) 3D visualisation of crack in 3D specimen (h' - height above the notch, b' - cuboid depth and d - cuboid width) Figure 5: Crack width distribution in concrete specimen by micro-computed tomography

5 The crack mainly propagated through ITZs (which were the weakest phase in concrete) and sometimes through air voids. It might very rarely propagate through a single weak aggregate particle (Fig. 6a). The branching phenomenon also occurred (Fig. 6b). Figure 6: Crack width distribution in concrete specimen by micro-computed tomography Figure 7 shows the distribution of macro-voids in the cracked concrete specimen which were divided into the so-called open pores (marked in green) and closed pores (marked in red). The closed pore was defined as the void that did not cross the border of the volume of interest. Other voids that crossed the VOI border were defined as the open pores and cracks. The total void volume was mm 3 where the volume of the open pores was mm 3 and of the closed pores mm 3. The total void volume in the non-cracked specimen was mm 3 where the volume of the open pores was mm 3 and of the closed pores was mm 3. c) Figure 7: 3D images of cracked cubical concrete specimen porosity by 3D micro-ct: a) total porosity, b) open pores representing including crack and c) closed pores

6 Figure 8 presents the cracked concrete cube after different cycles of loading in compression. With increasing number of cycles the specimen became more cracked and existing cracks became wider. The change of the cracking surface width in the concrete cube after cycles of loading is presented in Figure 9. The crack width non-linearly changes along the depth and height of the specimen (between mm) due to a random distribution of aggregate grains and air voids. Figure 8: 3D images of cracked concrete cubes under compression by 3D micro-ct: a) after 40'000 cycles and b) after 70'000 cycles Figure 9: Crack width distribution in concrete cube under compression measured after 70'000 load cycles by micro-computed tomography

7 Numerical finite element results The numerical finite element (FE) simulations of beams under bending were carried out with a simple isotropic continuum constitutive damage and for cubes under fatigue compression with a coupled elasto-plastic damage formulation. The both models were enhanced by a characteristic length of micro-structure by means of a non-local theory. Concrete was assumed at meso-scale as a random heterogeneous material composed of 4 phases: aggregate, cement matrix, interfacial transition zones (ITZs) and macro-voids. ITZs were assumed to be the weakest phase. The real aggregate and air void distributions in the notch area were introduced on the basis of micro-ct scans. The shape, height and location of the localized zone from the FE computations (Fig.9) were in satisfactory agreement with the experimental outcomes (Fig. 6). The effect of the ITZ stiffness on the numerical results is described in Figure 9. The stiffness E ITZ was assumed to be equal to 50%-75% of the cement matrix stiffness. The ultimate beam strength increased with its increasing stiffness. The stiffness of ITZs strongly affected both the load-cmod response and shape of the localized zone (Fig. 9). c) Figure 9: Effect of different elastic modulus of ITZs E ITZ on force-cmod diagram and localized zone (in red) in FE analyses: a) E ITZ =14.6 GPa, b) E ITZ =21.9 GPa and c) experiment (characteristic length of micro-structure l c m =1.5 mm and crack initiation strain κ 0 ITZ = )

8 The coupled elasto-plastic damage model enhanced by a characteristic length of microstructure by means of a non-local theory was also able to capture the crack distribution changes in vertical cross-sections under fatigue compression (Fig. 9). Figure 9: Distribution of 2D calculated localized zones during fatigue compression of concrete: a) after 30'000 load cycles and b) after 70'000 cycles with concrete micro-structure from micro- CT Conclusions The following conclusions can be drawn from experiments on concrete: X-ray micro-ct is a powerful tool for the visualization of concrete micro-structure (aggregate, cement matrix, voids) and crack propagation. It allows for analyzing the 3D crack width distribution. The continuum models enhanced by a characteristic length of micro-structure properly captured the evolution of localized zones where concrete was treated as a heterogeneous four-phase material. Acknowledgements The research work has been carried out within the project: Innovative ways and effective methods of safety improvement and durability of buildings and transport infrastructure in the sustainable development financed by the European Union (POIG /09-01) and the project "Experimental and numerical analysis of coupled deterministic-statistical size effect in brittle materials" financed by the National Science Centre NCN (UMO- 2013/09/B/ST8/03598). References: 1. Bažant, Z. and Planas, J. Fracture and size effect in concrete and other quasi-brittle materials. CRC Press LLC, Boca Raton, Lilliu, G and van Mier, J.G.M. 3D lattice type fracture model for concrete, Engineering Fracture Mechanics 70, , Skarżyński, Ł., Nitka, M. and Tejchman, J. Modelling of concrete fracture at aggregate level using FEM and DEM based on X-ray μct images of internal structure, Engineering Fracture Mechanics 147, 13-35, Marzec, I., Skarżyński, Ł., Bobiński, J. and Tejchman, J. Modelling reinforced concrete beams under mixed shear-tension failure with different continuous approaches, Computers and Concrete 12, , 2013.

9 5. Kozicki, J. and Tejchman, J. Modelling of fracture processes in concrete using a novel lattice model. Granular Matter 10, , Nitka, M. and J. Tejchman, J. Modelling of concrete behaviour in uniaxial compression and tension with DEM. Granular Matter 17, , Sengul, O., Tasdemir, C. and Tasdemir, M. A. Influence of aggregate type on mechanical behaviour of normal- and high-strength concretes, ACI Materials Journal 99, , Kozicki, J. and Tejchman, J. Modelling of fracture processes in concrete using a novel lattice model. Granular Matter 10, , Scrivener, K.L., Crumbie, A.K. and Laugesen, P. The interfacial transition zone in concrete, Nanotechnology in the Construction Industry, 3, , 2009.