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The paper describes analytical and numerical approaches of modelling of an unidirectional lamina. In a frame of the analytical homogenization, Voigt-model, Reuss-model, Halpin-Tsai semi-empirical model and periodic microstructure model are described. In a frame of the numerical homogenization, finite element model with hexagonal and square periodic...
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... ratio for the material of the indenter, respectively. E r is the reduced elastic modulus which is calculated as follows: S is the contact stiffness, β is the correction constant for various shapes of indenters 9 . The indentation modulus is especially important for the evaluation of thin films because it is normally not identical to the values known for bulk materials. During nanoindentation of thin films, a small oscillating load with a frequen- cy of 0.05 200 Hz and amplitude of 60 nN 300 mN was superimposed onto the primary load. The method is called CSM (Continuous Stiffness Measurement) method. The system analysed dynamic response of tested material, measuring the contact stiffness S , and changes in mechanical values during loading as a function of penetration depth. Scratch testing is one of the most widely used testing methods for the investigation of the adhesion and other mechanical properties of thin film-substrate structures. The standard for scratch testing was created for hard thin films like TiN with the thickness of several μ m, where the critical forces are in the order of a few tens of Newton. The principle of the scratch test is a relative motion of the support with the sample against an indenter, which is loaded with a selected normal force 6 . The acting forces, the normal force F N , lateral force F L and friction force F t are shown in Fig. 3. In this work, the tested films were 50 nm thick and were deposited on soft polystyrene foils. The applied constant forces F N were chosen <50 mN based on the previous studies of polymeric substrates. The tests in this force range are called nanoscratch tests. Three different forces, 1 mN, 10 mN and 50 mN, were used for constant force nanoscratch tests and the force from 1 mN to 10 mN was applied during the rising force nanoscratch test. The lengths of scratches of 200 μ m for constant force and 400 μ m for the rising force type of scratches were selected. Scanning electron microscopy (SEM, Quanta 200) was used for scratch morphology visualization 8 immediately after testing in order to eliminate the relaxation which is known to occur in polymeric ...
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... the composite has periodic microstructure, then Fourier series can be used to estimate all the components of the stiffness tensor of the composite. Explicit formulas for a composite reinforced by long circular cylindrical fibres, which are periodically arranged in a square array a 2 = a 3 ( Fig. 3), are written in the following way 3 . Because the microstructure has square symmetry, the stiffness tensor has six unique coefficients given ...
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Citations
... Taking into account the different size scales of mechanical modelling of structure elements composed of fiber reinforced composites, the micro, macro and structural modeling levels must be considered [12][13][14][15][16]. ...
Sandwich panel with laminate faces is used for free vibration analysis. The periodic microstructure and Mori- Tanaka model are used for homogenization of unidirectional fiber reinforced composite. The Shear Deformation Theory is considered for analytical and numerical analysis. FEM in ANSYS is used for numerical analysis. The effect of sandwich design parameters such as panel length, core thickness and fiber reinforced angle on vibration response is investigated. Natural frequencies of sandwich panel versus sandwich design parameters are presented in graphical form. From the results can be concluded that sandwich design parameters affect the natural frequencies of sandwich panels, and this effect is important for designing of sandwich panels under dynamic load.
... The use of fiber-reinforced concrete in the solution of construction problems is very wide and includes foundations, slabs on the ground [38][39][40], beams [41], industrial floors [42], and beams without shear reinforcement [43,44]. Importantly, the design and use of fiber-reinforced concrete needs to be approached qualitatively, because fibers affect basic mechanical properties and fracture properties [34,35], and the residual tensile strength and elastic properties of the material are particularly important [45]. Adequate knowledge of concrete and quasi-brittle materials should not only include information on compressive and tensile strength from the viewpoint of mechanical properties, but should also include details regarding crack initiation [46][47][48][49] and knowledge of the crack propagation process. ...
The current findings on concrete with fibers show that research has focused primarily on individual aspects, especially in terms of mechanical properties and structural uses. However, no broader view of the problems solved has been provided. In this study, we present a conceptual overview of a new, comprehensive experimental program for the assessment of fiber-reinforced concrete, which includes the analysis of microstructural and structural elements, as well as specific features such as shrinkage and resistance to pressurized water. The proposed experimental program included several variants of schemes for the dosing of fibers into concrete, using steel fibers that were short and straight. Fiber dosing was performed up to 110 kg/m3. The basic tests performed included tests of the compressive strength of concrete, and of the split and flexural tensile strength for different dosing amounts. Within the structural tests of reinforced concrete beams without shear reinforcement, two variants of spans with different degrees of reinforcement were implemented. Herein, the test results are evaluated graphically with a detailed analysis of the positive effect of fibers, and we also provide general recommendations for the structural uses of the fibers used and the design of fiber-reinforced concrete structures. Among the important results of this experimental program was the observation of a significant increase (of the order of tens) of the percentage of the split tensile strength and an increase of the overall load-bearing capacity of the reinforced concrete beams without shear reinforcement. Among the important aspects of our findings is the fact that a fine-grained concrete mixture was used, which increased resistance to pressure water seepage, and therefore, the effect of shrinkage can be influenced by the method of production and the treatment of the concrete used. We also provide detailed figures of the microstructure.
... But due to the weak through thickness properties, laminated composites are prone to delamination which is the most common mode of failure for laminated composites. Kormanikova and Kotrasova [4] calculated the longitudinal Young's modulus, transverse Young's modulus, inplane shear modulus and Poison ratio of a unidirectional laminate and reported that in a frame of the analytical homogenization, comparatively better results obtained from the periodic microstructure model. Recently, Kirtania and Chakraborty [5] determined the thermoelastic properties of CNT/epoxy composite by considering a representative volume element. ...
... Various analytical techniques of homogenization such as Reuss model, Voigt model and Periodic microstructure model are available for the evaluation of the elastic properties of the laminated composite. In the present study, the periodic microstructure model [4] has been used for calculation of elastic properties of the laminated composites. Each laminate is composed of four laminas of thickness 0.5 mm as shown in Fig. 1. ...
... These are reflected in the following Eqs. (2)(3)(4). These five independent elastic constants can be determined using the following relations [13]. ...
A comparative study of elastic properties and mode I fracture energy has been presented between conventional carbon fibre (CF)/epoxy and advanced carbon nanotube (CNT)/epoxy laminated composite materials. The volume fraction of CNT fibres has been considered as 15%, 30%, and 60% whereas; the volume fraction of CF has been kept constant at 60%. Three stacking sequences of the laminates viz.[0/0/0/0], [0/90/0/90] and [0/30/–30/90] have been considered in the present analysis. Periodic microstructure model has been used to calculate the elastic properties of the laminated composites. It has been observed analytically that the addition of only 15% CNT in epoxy will give almost the same value of longitudinal Young’s modulus as compared to the addition of 60% CF in epoxy. Finite element (FE) analysis of double cantilever beam specimens made from laminated composite has also been performed. It has been observed from FE analysis that the addition of 15% CNT in epoxy will also give almost the same value of mode I fracture energy as compared to the addition of 60% CF in epoxy. The value of mode I fracture energy for [0/0/0/0] laminated composite is two times higher than the other two types of laminated composites.
... They differ in the basic matrix -concrete and the fibers used (shape, material) [3]. There are a number of recommendations [3][4][5][6], standards [7] or national standards [8] for the design of fibers reinforced concrete structures, but they mainly focus on the testing and determination of mechanical properties [9][10][11][12][13] for analytical or simplified computational models. However, when using advanced numerical simulations [14], [15] there are a number of possibilities to describe the behavior of fiber reinforced concrete, which cannot be interpreted directly from the recommendations and standards. ...
The paper presents research focused on modeling of lightweight concrete beams combining reinforced and fiber concrete. The paper solves the selected case of the RC beam, which was experimentally tested. The advanced numerical model and calculation used for an experiment into account the non-linear behavior and collapse of the beam. For the experiment, a specific cross-section with an opening that relieves the beam is selected. Non-linear analysis in combination with the finite element method is used for numerical modeling. Specifically, 3D calculation model and fracture-plastic material for concrete are used.
... We also distinguish the nature of the behavior of the concrete matrix and fibers in crack propagation, namely, whether the matrix cracks, the fibers break, or the fibers are pulled out of the matrix. For practical reasons, these phenomena are described with the help of the residual tensile strength [16] or elastic properties of the material [17]. For concrete of lower compressive and tensile strengths, steel fibers are typically rapidly activated. ...
Fiber-reinforced concrete has a wide application in practice, and many fields of research are devoted to it. In most cases, this is a specific problem, i.e., the determination of the mechanical properties or the test method. However, wider knowledge of the effect of fiber in concrete is unavailable or insufficient for selected test series that cannot be compared. This article deals with the processing of a comprehensive test study and the impact of two types of fibers on the quantitative and qualitative parameters of concrete. Testing was performed for fiber dosages of 0, 40, 75, and 110 kg/m3. The fibers were hooked and straight. The influence of the fibers on the mechanical properties in fiber-reinforced concrete was analyzed by functional dependence. The selected mechanical properties were compressive strength, splitting tensile strength, bending tensile strength, and fracture energy. The results also include the resulting load–displacement diagrams and summary recommendations for the structural use and design of fiber-reinforced concrete structures. The shear resistance of reinforced concrete beams with hooked fibers was also verified by tests.
... Also, Fidelus et al. [2], Anumandla et al. [3], Shen and Xiang [4] utilized the rule of mixture and extended rule of mixture to find the effective elastic property of the composite structure. [4][5][6][7][8][9][10][11] utilized the Halpin-Tsai approach for the effective elastic properties of the composite material which they used. The explicit formulation for the Mori-Tanaka tensor which was utilized for the unidirectional (UD) FRC in Liu and Huang [12]. ...
Nonlinear flexural analysis of sandwich composite beam with multiwall carbon nanotube (MWCNT) reinforced composite face sheet and bottom sheet under the thermo-mechanically induced loading using finite element method is carried out. Solution of current bending analysis is performed using Newton’s Raphson approach by using higher order shear deformation theory (HSDT) and non-linearity with Von Kármán kinematics. The sandwich laminated composite beam is subjected to uniform, linear and nonlinear varying temperature distribution through thickness of the beam. The sandwich beam with MWCNT reinforced composite facesheet and bottom sheet is subjected to point, uniformly distributed (UDL), hydrostatic and sinusoidal loading. The two phase matrix is utilized with E-Glass fiber to form three phase composite face sheet and bottom sheet by Halpin-Tsai model. The static bending analysis is performed for evaluating the transverse central deflection of three and five layered sandwich composite beam. Transverse central deflection is measured by varying CNT volume fraction, uniformly distributed, linearly and nonlinear varying temperature distribution, thickness ratio, boundary condition, number of walls of carbon nanotube by using interactive MATLAB code.
... The FRC has typically a better tensile strength and toughness. The actual determination of the responsibility and mechanical testing of FRC are dedicated experts in researches and recommendations [14][15][16][17]. In particular, there are a number of approaches that differ in the test configuration to determine the tensile strength. ...
... Fiber reinforced concrete structures are still able to carry external loads even after exceeding the tensile strength. Fracture mechanics or specialized constitutive relations are often used to describe mechanical properties of fiber reinforced concrete (Karihaloo and Wang, 2000, Kormanikova and Kotrasova, 2011, Zaborski, 2016. Inverse analysis also is used to determine the mechanical parameters , Sucharda, 2020. ...
The paper deals with an experimental study of shear resistance of reinforced concrete beams without shear reinforcement. A concrete specimen is reinforced besides the steel reinforcing bars also with straight, short fibers with dosing 40, 75 and 110 kg/m³. The research is focused on determining the effect of fibers dosing on the load capacity of the reinforced concrete beams. The research is complemented with numerical modeling of experiments, where one of the possible approaches to the advanced design of structures respecting the actual behavior and failure of fiber reinforced concrete is illustrated, using non-linear analysis and finite element method. A fracture-plastic material model and 3D computational model are chosen for modeling reinforced concrete beams with fibers. Besides common material testing, fracture mechanical tests are performed within the experimental program, specifically a three-point bending test with a notch. In the paper the results of types of tests and the determined fracture energy are compared.
... There are a number of fibers for reinforcing concrete structures. It is also important to describe and formulate the fiber reinforced concrete (Kormanikova andKotrasova, 2011, Zaborski, 2016). They differ mainly in material, thickness or geometry (Brandt, ...
... There are a number of fibers for reinforcing concrete structures. It is also important to describe and formulate the fiber reinforced concrete (Kormanikova andKotrasova, 2011, Zaborski, 2016). They differ mainly in material, thickness or geometry (Brandt, 2008, Kasagani, andRao, 2016.). ...
The paper deals with approaches to numerical modelling of fiber reinforced concrete in computer simulations of laboratory tests and the choice of input parameters of the used material model. Two types of fibers with 75 kg/m³ dosage are selected for comparison. The fibers used differ mainly in the geometry. The paper evaluates also of laboratory test the basic mechanical properties, which are subsequently used as input parameters in numerical models. The tests include compressive strength, splitting tensile strength and bending tensile strength from the three-point test. The three-point bending test is then used for 3D computer model and fracture-plastic material model. Specifically, it was used to evaluate of numerical simulations of load-displacement diagrams from the three-point test.
... Other benefits of fibre concrete may include limitation of shrinkage cracks [11] and deformations of concrete, increased ductility and fatigue strength, improved consistency (no falling-off at marginal parts of concrete). For the design of structures from fibre concrete, it is important to know in details its properties, which are most frequently defined in laboratories on testing samples [12,13,14]. Fibre concrete itself and its testing are dealt with in the Czech Republic and globally on a long time basis. ...
The study specializes in the area of mechanical properties of select fibre reinforcement concrete. For the research fibre concrete reinforced with short steel fibres was used without bending. Fibre concrete is produced in the dosing 40 and 75 kg/m ³ . Laboratory program includes a complete group of tests, i.e. concrete compressive strength in cubes, three-point bending test, and split tension strength perpendicular and parallel to filling direction. Results are processed in summary, and they also include fracture-mechanical parameters needed for structural modelling. The research carried out found the positive influence of fibre on tensile strength and fracture energy. However, with more fibre, only fracture energy increases. It has also been found that the effect on compressive strength is small. For numerical modelling, the suitability of using a 3D computational model in combination with the fracture-plastic material model for fibre reinforcement concrete was verified.
