INVESTIGATION ON FATIGUE DAMAGE MECHANISM OF MODERN CONCRETE MICROSTRUCTURE BY LATTICE MODEL

Transcription

1 INVESTIGATION ON FATIGUE DAMAGE MECHANISM OF MODERN CONCRETE MICROSTRUCTURE BY LATTICE MODEL L.P. Guo (1, ), W. Sun (1,), An. Carpinteri (3), A. Spagnoli (3) and W.Ch. Qin (4) (1) Jiangsu Key Laboratory of Construction Materials, Nanjing 11189, China () College of Materials Science & Engineering, Southeast University, Nanjing 11189, China (3) Department of Civil Engineering, University of Parma, Parma 43100, Italy (4) YXLON International X-Ray GmbH Shanghai Rep. Office, Shanghai 00041, China Abstract The effect of microstructure property on fatigue damage mechanism of modern concrete has been paid much more interest in the last decade. The fatigue damage mechanisms of modern concrete are mainly controlled by the volume fraction and distribution of coarse aggregates as well as the mechanical behaviors of matrix and matrix-aggregate interfacial zone. In order to discover the effect of microstructure on mechanical performance of cementitious composites, the lattice model has been put forward by some experts in Delft (J.G.M. van Mier, E. Schlangen, etc.) one decade ago. However, the most of previous lattice model were established based on the artificial microstructure and the research work mainly focused on the static mechanical behavior of cementitious composites like concrete. In present work, the effects of microstructure properties on damage mechanism of concrete under 4-points bending cyclic loads with constant stress amplitude are investigated by an improved D lattice model and micro-focus computer tomography (micro-ct) images of concrete microstructures. The maximum strain and displacement of beam elements in different microstructures are compared with each other. The modeling results of main crack paths in concrete microstructures and the fatigue lives of concretes are consistent with the experimental results. In addition, the numerical results show that the improved lattice model is effective for the investigation of fatigue damage mechanism of concrete under cyclic loading and for the fatigue-life prediction of concrete with different microstructures. 1. INTRODUCTION The effect of microstructure property on fatigue damage mechanism of modern concrete has been paid much more interest in the last decade. With the admixtures of reactive mineral powders and high performance superplasticizer in fresh paste of modern concrete, the morphological and mechanical properties of modern concrete microstructure are greatly 1179

2 different with before. Because the amounts and characteristics of main reaction products (i.e. C-S-H gel, calcium hydroxide) in the concrete microstructure change with the type and dosage of reactive admixtures and with the decrease of water-to-cement ratio. Although the fatigue damage mechanisms of concrete are mainly controlled by the volume fraction and distribution of coarse aggregates, the developments in the components of modern concrete surely have positive contributions on the nucleation and growth of fatigue cracks in matrix and matrixaggregate interfacial zone during the cyclic loading. The size of fracture process zone at the crack tip is also changed correspondingly [1]. Therefore, the fatigue damage mechanism of modern concrete is obviously different with that of normal concrete used in many decades ago. In recent decade, with the construction of modern concrete infrastructures in developing countries, the effects of reactive admixtures on the complicated degradation mechanism of their microstructures under cyclic loading are paid more and more attention. Their fatigue lives are also need to be accurately predicted as well. In order to discover the effect of microstructure on mechanical performance of cementitious composites, the lattice model has been put forward by some experts in Delft (J.G.M. van Mier, E. Schlangen, etc.) one decade ago [-4]. By defining the elastic beam element or truss element as the different constituents of concrete, the concrete microstructure is represented by a lattice mesh composed of D or 3D elements with different mechanical and materials properties. In past one decade, the lattice model was very useful to clarify the material degradation process of concrete microstructure exposed to monotonic loading. Lilliu and coworkers [5] discussed the simulation results of D and 3D lattice model in these loading conditions. They found that the D lattice model is more economical than 3D lattice model. The D lattice model is reliable for simulating the fracture processes in concrete [5]. Unfortunately, the lattice model is not used until now to simulate the damage process of modern concrete under cyclic loading. The research purpose of present project is to resolve this problem through improving the classic D lattice model by introduction of fatigue damage law and fatigue failure criterion for the lattice element. In order to conduct the numerical simulation of modern concrete under cyclic loading with the lattice model, the concrete sample was scanned by an X-ray microfocus computer tomography (micro-ct) to obtain the actual microstructure images of concrete before the fatigue test. The simulation and experimental results of the same concrete sample under constant amplitude cyclic load are compared and discussed. Based on the simulation results of fatigue damage process in concrete with the improved lattice model, the effect of reactive mineral admixture on the fatigue damage mechanism of modern concrete would be explained as well.. ESTABLISHMENT OF IMPROVED LATTICE MODEL The modeling process, run using the commercial code ABAQUS, consists of five steps: (a) Obtaining the micro-ct images of the tested concrete sample with high resolution (Section.1); (b) Establishing a regular geometric lattice mesh based on micro-ct images of the actual concrete microstructure (Section.); (c) Establishing a complex model for concrete prism (Section.3); (d) Determination of geometric and material parameters for model elements (Section.4); (e) Introduction of fatigue damage and failure criterion (Section.5). 1180

3 .1 Acquisition of micro-ct image The quality of concrete microstructure image is the first critical factor for the accuracy of lattice model. Since the gray level is the only criterion to distinguish the different concrete phases (i.e. aggregate, voids, matrix, aggregate-matrix interfacial zone) from the images of concrete microstructure with image process software, the contrast and resolution of these images should be high enough in order to guarantee the accuracy of image process results. In order to compare the modeling results and experimental results of concrete fatigue damage under 4-point bending cyclic loads, the tested concrete sample is non-destructively scanned by an X-ray micro-ct system before the fatigue test to obtain the original image of concrete microstructure for the modeling. A concrete sample with bending strength of 9.3 MPa are chosen for modeling and discussion in this study. This concrete sample is a prism with size of 100 mm 100 mm 400 mm and the effective span of it is 300mm. The middle section of it with size of 100mm x 100mm x 100mm is scanned by a micro-ct system. The settings of micro-ct system for this study are: 180kV, 0.4mA (X-ray tube current), 3D cone-beam radiation source with a circular source trajectory, high-resolution planar equispaced detector with a number of elements, and reconstructed 3D image of pixels in X-,Y- and Z-axis respectively. Two projections of concrete microstructure are selected for modeling and discussions (see Fig. 1). In Fig.1, the aggregate is shown in white and light gray, the mortar matrix is shown in dark gray, the void and micro-crack are shown in black. The area ratio of aggregates and concrete cross-section is 38%. (a) Image A for lattice model (b) Image B for lattice model Figure1: Two micro-ct images of concrete microstructure selected for lattice model. Establishment of regular geometric lattice mesh Based on the captured micro-ct image of concrete microstructure, a lattice mesh with regular geometry is established. The lattice elements describing the different phases in the concrete microstructure are recognized by the statistic gray value of each phase shown in the digital images. As present in Fig.1, the gray value of voids and micro-cracks is obviously higher than those of mortar matrix and aggregate. After calculating the mean gray level of different density aggregates, the boundaries of coarse and fine aggregates are filtered from the mortar matrix. A commercial code MATLAB is employed to process the micro-ct images and to establish the regular triangular lattice mesh on these images. The length of the lattice 1181

4 element is chosen according to the principle mentioned in Ref. [6], that is: l d a,min /3, where d a,min is the minimum diameter of interest for the study in the aggregates. When the element length is higher than this critical value, the lattice element mesh would be too coarse to accurately distinguish each concrete constituent. Because the minimum diameter of the interested aggregates is 3mm, the lattice element 1mm long is selected for this study. If the two ends of a lattice element located in a zone with similar gray level, this lattice element is correspondingly defined as one of the main concrete phases (i.e. aggregate, void, matrix). If a lattice element encompasses two zones with large difference of gray level, it is assumed that the element lies on an Interfacial Transition Zone (ITZ). With a self-compiled MATLAB subroutine, four interfacial transition zones can be recognized: void-matrix ITZ, void-aggregate ITZ, matrix-aggregate ITZ and aggregate-aggregate ITZ. The mechanical properties of void-matrix and void-aggregate ITZs are assumed to be the same as the void properties, whereas the aggregate-aggregate ITZ is assumed to have the same mechanical properties as those of the matrix-aggregate ITZ. Therefore, the lattice elements are separated into four groups (i.e. voids, matrix, matrix-aggregate ITZ, aggregates) and respectively labeled with four group numbers. The lattice meshes with lattice element 1mm long established on Image A are shown in Fig. as an example, where the elements of the different groups are displayed in different colors. The red color is for aggregate, the pink color is for mortar matrix, the yellow color is for voids and the light blue color is for matrix-aggregate ITZ. With the selfcompiled MATLAB subroutine, the spatial coordinate values and the group number of each lattice element are recorded in a text file for the following modeling. Figure : Lattice mesh established on Fig.1a (l =1mm).3 Establishment of complex model for concrete prism In order to simulate the fatigue damage process of concrete prism under 4-point cyclic bending load, the lattice mesh has been combined with two ends of concrete blocks through a self-compiled VISUAL FORTRAN subroutine to establish a complex model for this study. The two bottom end nodes (located at a relative distance along the 1-axis equal to 300 mm) of this complex model are simply supported, and two point loads acting downwards along the - axis are applied to the two top nodes at the lattice-homogeneous block interfaces (located at a relative distance along the 1-axis equal to 100 mm). The obtained complex model of the simple supported concrete prism based on Image A is shown in Fig.3. The aggregates in the middle section of concrete prism are highlighted in red color. Figure 3: Complex model of simple supported concrete prism established on Image A 118

5 The fatigue loading tests are conducted via a cycle block approach, that is, each cycle in the model is assumed to represent a block of a certain number of loading cycles. Such a number of cycles depend on the considered fatigue stress level..4 Determination of geometric and material parameters for model elements Since the simulation of concrete fatigue damage is conducted with the complex model above established, the geometric and material parameters of lattice element and concrete block element need to be determined based on some recommended principles and related experimental results. In the present study, the cross-sectional area of the concrete blocks and the thickness of lattice element are assumed to be equal to unity. The lattice element type is a -node linear Timoshenko beam with a rectangular cross-section. The cross-sectional area of the lattice element is chosen according to the Poisson s ratio of its corresponding concrete continent (like were reported in Refs [, 7]) and described as below. h l = * 1 3v * v + 1 Where v* is the Poisson s ratio of each concrete constituent (mortar matrix, matrix-aggregate ITZ, aggregate). h and l is the height and length of lattice element, respectively. The test result of Poisson s ratio is 0. and 0.1 for matrix and aggregate, respectively. Since the Poisson s ratio of matrix-aggregate ITZ is impossible tested in lab, it is assumed to be equal to the test result of matrix. After the geometric parameters of lattice elements are fixed, the material parameters of them have to be carefully determined for the following modeling. The five necessary material parameters for the Timoshenko lattice element are the initial elastic modulus E 0, initial shear modulus G 0, Poisson's ratio v, tensile strength f t and ultimate tensile strain t. Note that the material parameters of the lattice element are determined by the mechanical properties of its corresponding concrete constituent according to the following relations: h * 3 + E l E 0 = () 3 h 1 + l E G 0 0 = (3) (1 + v ) l * ft = f t (4) 3 h l l h f t * 1 + f t = = 3 h f t = 3 h l 3 l (5) ε t = ε * t E 0 h E h h h l 1 l l E 3 h 3 h l l (1) 1183

6 Where, E*, f t * and t * is the initial elastic modulus, tensile strength and ultimate tensile strain of concrete continent, respectively..5 Fatigue damage definition and failure criterion The macroscopic behaviour of concrete under cyclic loading is typically characterized by a progressive degradation of the material stiffness. This softening phenomenon is not only connected with the fatigue loading cycles but it is also related to the tensile stress/strain level. It is well-known that the mesoscopic softening behavior of concrete under cyclic loading is caused by the growth and coalescence of micro-cracks in the concrete microstructure. That means that the mechanical properties of concrete are gradually and locally degraded under cyclic loading. In the present model, we assume that the aggregate would not rupture during cyclic loads because of their very high Young modulus. The matrix and the matrix-aggregate ITZ are the possible locations where micro-cracks can initiate. Further, we assume that the Young modulus and the shear modulus of lattice elements representing the matrix and matrixaggregate ITZ are constant and equal to their initial values (E 0 and G 0 ) when the axial stress of these lattice elements are not positive value. That means the degradation of the lattice element stiffness can only occur under tensile condition. Therefore, a fatigue damage function D f is proposed based on above assumptions. Such a function is composed of two parts: the first part D 1 is defined as a linear/nonlinear function of fatigue loading cycles for high/low stress level; the second part D is established as a function of the maximum tensile strain i at a number n i of loading cycles. Therefore, the fatigue damage function D f is defined as: D f ni = D1 D ( εi ) (6) N c n i i for S 0.75 n i = N (7) D1 N n for S > 0.75 N D ( ε ) ε i i = α (8) εt where n i is the number of fatigue loading cycles at the i th time instant, and N is the total fatigue life; c i is a constant related to stress level and material type, which can be deduced from the experimental curves of loading cycles versus maximum displacement; S is the fatigue stress level (i.e. the ratio of the maximum applied bending stress in the cycles and the bending strength of concrete); α is a model constant which is related to the type of lattice element and the geometric and mechanical properties of the concrete microstructure. Therefore, the stiffness degradation of matrix and matrix-aggregate ITZ elements can be expressed as follows: Ei = ( 1 D f ) E0, Gi = ( 1 D f ) G0 (9) 1184

7 where 0 D f 0.99, E i and G i is respectively the Young modulus and shear modulus of the damaged lattice element at the i th time instant. Now a failure criterion for matrix and matrix-aggregate ITZ is proposed. Since the fatigue stress level is always lower than 1.0 (i.e. the applied maximum cyclic stress is lower than the tensile strength of concrete), the tensile stress in lattice element of concrete is always lower than its ultimate tensile strength. Therefore, the final failure of the lattice element should be described by its ultimate tensile strain (see Eq.(5)). If the axial strain at i th time instant is larger than the ultimate tensile strain (i.e. ε i > εt ), the lattice element is assumed to fail. Then, the element failure is represented by setting the Young modulus E i equal to 10% of E 0. The failed element would be obviously elongated with a large tensile strain to represent the initiation of a new fatigue crack. The axial stress in the failed element is redistributed to other neighbor elements through the lattice node. When these neighbor elements are subsequently failed and elongated with a large tensile strain, it would represent the propagation of this crack. The fatigue damage definition and failure criterion above mentioned are implemented in a FORTRAN user subroutine (named UMAT) which is linked to the ABAQUS code. The fatigue damage process of concrete microstructure under cyclic loading is automatically analyzed by importing the UMAT subroutine to ABAQUS software. 3. RESULTS AND DISCUSSIONS For casting the modern concrete shown in Fig.1, a P.II 4.5 Portland cement with specific surface area of 309 m / kg is used as the main cementitious material. A ground granulated blast-furnace slag with specific surface area of 37 m / kg was mixed into concrete as 30% mass fraction of total cementitious materials. Crushed basalt aggregates and natural sand are used as coarse and fine aggregates, respectively. The size range of natural sand is 0.15 mm to 4.75 mm. That of crushed basalt aggregate is 5mm to 0mm. The water-to-cement ratio is equal to 0.35 for concrete and 0.3 for matrix. The slumps of fresh concrete were controlled to be in the range of 8 cm to 1 cm by adjusting the dosage of the super-plasticizer. The hydration age of the tested specimens are 90-days in the standard curing conditions (0 ± C and 90% relative humidity). The loading speed is 0.06MPa/s for tensile strength test. The Young modulus and Poisson ratio of concrete and microstructure constituents are tested according to the Chinese standard (GB/T ). The test results of Young modulus and Poisson ratio of concrete are equal to 48.7 GPa and 0., respectively. The test results of mechanical properties of aggregate ( a ), matrix ( m ) and matrix-aggregate ITZ ( ITZ ) are: tensile strength f t, a / f t, m modulus 0.1/0., v ITZ = 30MPa / 14MPa, f t, ITZ / f t, m =.MPa / 14MPa; Young E a / E m = 160GPa / 7GPa, E ITZ / E m =9GPa / 7GPa; Poisson ratio v a / v m = / v m = 0./0.. The test results of mean ultimate tensile strain ε t of matrix and matrix-aggregate ITZ is equal to 00 µε and 50 µε, respectively. The Young modulus of matrix-aggregate ITZ is deduced from the initial tangent slope of the tensile stress and strain curve. Since the Poisson s ratio of matrix-aggregate ITZ is impossible achieved through the mechanical test, it is assumed to be equal to the test result of matrix. After the mechanical properties of each concrete constituent were tested in the lab, the geometrical and mechanical 1185

8 properties (h, E 0, G 0, and i ) to be assigned to the lattice elements of three concrete phases could be calculated based on Eqs(1) to (5). The lattice elements are assigned to be 1 mm long. All elements are assumed to have a thickness equal to unity. The height of the lattice elements is determined by Eq. (1), that is, h=0.8 mm is assumed for the aggregate elements and h=0.58 mm is assumed for the other elements. E 0, a / E 0, m = 118GPa / 60GPa, E 0, ITZ / E 0, m = 7.5GPa / 60GPa, E 0, void = 10-9 GPa, G, ITZ 0 / G, m 0 = 3.1 GPa / 5GPa, v a / v m = 0.1/0., v ITZ strain ε t assigned to the lattice elements of matrix and matrix-aggregate ITZ is 40 µε and 300 µε, respectively. Here we only investigate the fatigue damage mechanism of concrete under fatigue stress level of 0.70 (i.e. the applied maximum cyclic load is 70% of the concrete bending strength). The loading frequency is 10Hz. The mean test result of concrete fatigue life at this stress level is 187,490 cycle numbers. The fatigue damage cumulating in concrete microstructure and other predicted parameters are present and discussed as follows. / v m = 0./0.. The ultimate tensile 3.1 Fatigue damage propagation and fatigue life prediction The mechanical properties of lattice elements under cyclic tensile stress are degraded with the increase of cycle numbers. When the fatigue failure criterion holds, some lattice elements which represent the fatigue micro-cracks are obviously elongated in Fig.4. When a long fatigue crack presents in the lattice model, the cycle numbers at this step time are assumed to be the fatigue life of HPC. The predicted fatigue life of HPC is 190,000 cycles for Fig.1a and 186,000 cycles for Fig.1b, respectively. The fatigue life of HPC predicted by beam lattice model is consistent with the experimental results. Since the axial strains of failed elements are higher than those of other elements, they were shown in red and purple color. Some damaged elements were present in blue color. More than one micro-crack initiate from the bottom section of concrete microstructure, but only one of them propagates with a long path and leads the concrete fracture happened. This predicted result about the main fatigue crack is consistent with the experimental result. Based on the color difference between failed and damaged elements, it is easy to find the initiation site and propagation path of the main fatigue cracks from Fig.4. After comparing Fig.4 and Fig.1, we found that most of predicted micro-cracks initiate from the weakest position (i.e. the matrix-aggregate ITZs) in the concrete microstructure. Furthermore, the zigzag path of the micro-cracks is influenced by the diameter and spatial distribution of aggregates around the crack tip. These mechanisms of HPC fatigue damage concluded from the simulation results can be supported by the experimental results reported in Ref. [8, 9]. 3. Main mechanical parameters Based on the modeling output results, some important mechanical parameters of lattice elements at different cycles are abstracted and compared with the test results. The predicted maximum displacement and mean value of maximum tensile strain at the middle bottom of HPC is presented in Fig.5 and Fig.6, respectively. Note that the first data shown in these figures is collected at the first loading cycle. It is clear that these parameters and cycle numbers curves are composed of three stages: before 10% of fatigue life, the maximum displacement and tensile strain fast increases to a stable value with 1186

9 the increase of loading cycles; from 10% to 90% of fatigue life, the maximum displacement and tensile strain slowly increases with cycles; after 90% of fatigue life, the maximum displacement and tensile strain suddenly increases to the final value corresponding to concrete collapse. These three stages quantitatively reflect the strain softening effect of lattice elements during the cyclic loading. (a) Predicted fatigue cracks base on Fig.1a (b) Predicted fatigue cracks base on Fig.1b Figure 4: Predicted fatigue cracks in HPC microstructures at the final failure Figure 5 : Maximum displacement of HPC Figure 6: Mean value of maximum tensile strain in lattice elements located along the middle bottom line of HPC model Except the mechanical parameters of whole HPC model, those of failed lattice elements along the main crack (as were shown in Fig.4) are also meaningful for the investigation on the concrete fatigue damage. The axial stress and strain of failed elements predicted on Fig.1a are as follows: σ beam, S =0. 70 = 0.39MPa, ε beam, S=0. 70 = Based on Eq(9), the critical damage of failed lattice elements along the main crack shown in Fig.1a is for stress 1187

10 level of Those of failed elements predicted on Fig.1b are beam, S =0. 70 = 0.4MPa and ε beam, S=0.70 = The critical damage of failed lattice elements along the main crack shown in Fig.1b is for the same stress level. It is obvious that the critical damage of failed elements predicted on Fig.1a and Fig.1b are nearly equal to each other. 4. CONCLUSIONS The results show that the established lattice model is effective and stable for fatigue damage simulation and fatigue life prediction of heterogeneous materials like HPC. After comparing the predicted parameters with test results, it could be found that the predicted mechanical parameters of HPC model and lattice elements are not greatly affected by the difference of HPC microstructure geometry. Because of the lower mechanical properties of matrix-aggregate ITZ than those of matrix, the fatigue micro-cracks almost initiate and propagate in this weak area under cyclic loading. The zigzag path of them is closely related to the diameter and spatial distribution of aggregates around the crack tip. ACKNOWLEDGEMENTS This research was sponsored by Education Ministry of China for furthering research work abroad (No ), and was supported by the Excellent Doctoral Dissertation Foundation of Southeast University of China (Grant No. YBTJ-051). REFERENCES [1] Guo, L.P., Sun, W., Carpinteri, An., Chen, B., He, X.Y. Real-time detection and analysis of damage in high-performance concrete under cyclic bending. Exp. Mech. Accepted in March 008. [] Schlangen, E. and Garboczi, E.J. Fracture simulations of concrete using lattice models: computational aspects. Eng. Frac. Mech. 57(/3)(1997): [3] Chiaia, B., Vervuurt, A. and Van Mier, J.G.M. Lattice model evaluation of progressive failure in disordered particle composites. Eng. Frac. Mech. 57(/3)(1997): [4] Van Mier, J.G.M., and Van Vliet, M.R.A. Experimentation, numerical simulation and the role of engineering judgment in the fracture mechanics of concrete and concrete structures. Cons. Building Mate. (13)(1999): 3-14 [5] Lilliu, G. and Van Mier, J.G.M. 3D lattice type fracture model for concrete. Eng. Frac. Mech. (70)(003): [6] Leite, J.P.B., Slowik, V., Mihashi, H. Computer simulation of fracture processes of concrete using mesolevel models of lattice structures. Cem. Concre. Res. (34)(004): [7] Lilliu, G. 3D analysis of fracture processes in concrete. Ph.D. thesis. Delft University of Technology, (007): 151 [8] Guo, L.P., Sun, W., Zheng, K.R., Chen, H.J., Liu, B. Study on the Flexural Fatigue Performance and Fractal Mechanism of Concrete with High Proportions of Ground Granulated Blast-furnace Slag. Cem. Concre. Res. 37()(007): 4-50 [9] Zheng, K.R., Sun, W., Miao, C.W., Guo, L.P., Zhou, W.L. and Chen, H.J. Effects of Mineral Admixtures on Fatigue Behavior of Concrete. J. Building Mate. 10(4)(007): σ 1188