From the present research, it can be seen that researchers have proposed different methods for calculating cracking moments and bending bearing capacity for RPC structures and composite structures of RPC with other materials [11,12]. Zingaila et al. [13] experimentally investigated the mechanical properties of a combined beam made of ordinary concrete and ultra-high performance concrete and calculated the cracking moment of the combined beam using the layered method. Zhang et al. [14] conducted flexural tests on damaged bridge decks reinforced by ultra-high performance concrete and established analytical equations for the cracking and ultimate flexural bearing capacity of the composite structure. Yang et al. [15] proposed an analytical method for predicting the bending response of ultra-high-performance fiber-reinforced concrete structures, which can accurately predict the bending strength of ultra-high-performance fiber-reinforced concrete beams. Ujike et al. [16] used RPC to strengthen a part of the tensile zone of reinforced concrete beams and used elasticity theory to estimate the cracking moment of this composite material. Turker et al. [17] also researched the bending performance of ultra-high-performance fiber-reinforced concrete beams by four-point bending tests and proposed two numerical methods for predicting the nominal moment bearing capacity of these materials. Sim et al. [18] proposed flexural design guidelines for precast prestressed concrete members and found that the traditional equivalent rectangular stress block in compression can still be used to produce satisfactory results in prestressed concrete members. Prem et al. [19] developed an integrated nonlinear fracture mechanics model to predict the moment carrying capacity of ultra-high performance concrete reinforced damaged reinforcement concrete composite beams. Based on the planar section assumption and specific damage criterion, Guo et al. [20] used the numerical integration method to simulate the full process of flexural behavior of RPC and ordinary concrete composite beams and obtained the full section moment-curvature curves for different design scenarios. Chi et al. [21] investigated the effect of different water-cement ratios and different fiber compositions on the flexural performance of RPC beams using finite element analysis and deduced the formulae for calculating the flexural bearing capacity of RPC beams with different fiber compositions. Similarly, Chen et al. [22] derived an equation for calculating the ultimate flexural bearing capacity of ultra-high performance concrete beams utilizing ANSYS finite element simulation analysis. Qi et al. [23] carried out an experimental and analytical study of steel-ultra-high performance fiber concrete composite beams and calculated the flexural strength of the specimens using a simplified analytical method. Hasgul et al. [24] proved through an experimental study that the simplified numerical method for the flexural design of fiber-reinforced concrete was also applied to ultra-high-performance fiber-reinforced concrete beams. Cao et al. [25] investigated the flexural behavior of prestressed RPC in-situ panels suffering from four-point bending and established a modified formula for the flexural bearing capacity of prestressed RPC in-situ panels, considering the tensile strength of the RPC and prestressing stress. In addition, Cao et al. [26] also analyzed the effect of longitudinal reinforcement ratio and reinforcement diameter on the cracking moment of high-strength reinforcement RPC beams, and established formulas for calculating the resistance coefficient of plasticity in section and the cracking moment of high-strength reinforcement RPC beams.
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The calculated value of cracking moment for all test beams can be obtained by bringing γ and Equation (16) into Equation (3) and comparing it with the test value of cracking moment, as shown in Table 4.
Bonded composite repair has been presented as an effective and efficient technique to increase the service life of cracked components. In early attempts, researchers repaired the cracked plate using different types of composite patches [6,7,8,9,10,11,12]. Rabinovitch et al. [13] found that the composite patches were available in numerous types based on the properties of the materials. Moreover, the effects of several patches, such as single or double varieties, in the reduction of the SIF were analysed [14,15,16]. In addition, the patches were designed with different dimensions and shapes to identify their effects on a damaged structure [17]. The effects of an adhesive bonding between the plate and patch were studied and analysed by Ratwani [6] analytically and numerically to determine the stress transmitted from the adhesive to the cracked structure which leads to a decrease in SIF.
Reddy et al. [34] performed a numerical study of a notch SIF for a centre-cracked plate with a circular hole. They presented a study of the combined behaviours of crack-stop holes and CFRP-reinforced steel plates. Andersson et al. [56] evaluated SIFs by fitting asymptotic displacement functions. Subsequently, the displacements, in general, were more accurately computed than the stresses; this method is, in most situations, preferable compared to stress-based approaches. Talebi et al. [57] investigated the nonlinear fracture mechanics of cracked plates with the effects of adhesive bonding of a composite patch repair. Consequently, the SIF was calculated using the given equation of an infinite plate with a center crack:
Hattori et al. [58] used the extended-boundary element method (XBEM) formulation to calculate the SIF of a cracked plate composed of an anisotropic material. In addition, Xie et al. (2017) calculated the SIF using a dual-boundary integral equation with a mode-I crack-opening displacement of a three-dimensional cracked plate. Oudad et al. [59] analysed the mode-I crack opening of an aircraft structure panel with a bonded composite patch repair. The SIF of an embedded semielliptical crack in a finite plate subjected to a uniaxial tension load was defined by Ivanez and Braun [16] for single- and double-composite patches. Yu et al. [60] focused on the establishment of the interaction integral (I-integral) for decoupling the force SIFs and coupled SIFs of a crack in functionally graded micropolar material (FGMM). They showed the derivation of the I-integral method from the J-integral method by superimposing an auxiliary field on the actual field. Wang et al. [61] studied the SIFs of double-edged cracked steel plates strengthened with fibre-reinforced polymer (FRP) plates, and used the theoretical expression by Tada to determine the SIF of the bonded-composite repair method.
Mohammadi et al. [64] performed three-dimensional FE analyses of the crack growth for a given problem while considering the real crack-front shape of the aluminium centre-cracked plate with the composite patch, and the stress and strain fields of the repaired panels were obtained using the ANSYS FE program. Papadopoulos et al. [65] used the ANSYS 11.0 software to validate their experimental results by using a triangular element, eight-noded SOLID82 element type for a cracked plate, and the same element type was used for an adhesive and composite patch. A plane strain condition was considered in the evaluation of the SIF using the ANSYS FE code. Tsouvalis et al. [66] performed a numerical analysis of a composite patch model using ANSYS 10.0 to validate the experimental results. The SOLID95 element type was used to model the cracked plate, adhesive bond, and carbon/epoxy patch. Oudad et al. [19] used a nonlinear, three-dimensional FE method to compute the contour and the size of the plastic zone ahead of repaired cracks with a bonded composite patch in the ABAQUS FE code.
Albedah et al. [15] used ABAQUS to simulate single- and double-sided composite patches with three subsections to model the cracked plate, the adhesive, and the composite patch. The model contained 32,254 eight-node brick elements with 48,381 nodes and a total number of 103,797 degrees of freedom: 17,195 in the plate, 9406 in the adhesive layer, and 7998 in the patch subsections. It presented variations in the SIF according to the crack length for the single and symmetric double patch. Ergun et al. [68] used special quarter-point elements at the crack tip for the calculation of the SIF using the numerical-solution 2D FE code FRANC2D/L. Djamel et al. [69] used the same code to evaluate the SIF using the MVCCI, in which the singularity at the head of the crack was integrated into the solution by replacing the elements at the top of the crack with particular quarter-point elements.
Lei et al. [70] used the higher-order 3D element, eight-noded isotropic SOLID45 to model the substrate panel and adhesive layer and the eight-node anisotropic layered SOLID46 for the composite patch to establish a three-layer model of the repaired panel using ANSYS code. Srilakshmi et al. [71] used ANSYS 13.0 to capture a high-stress gradient near the crack tip. The 20-noded SOLID186 element was used to model the cracked structure, adhesive, and composite patch, which were simulated using the multipoint constrained algorithm (MPC). In the MPC algorithm, all three degrees of freedom were constrained and involved contact and target surfaces that came into contact with one another. In this study, the SIF was estimated from the energy-release rate using VCCT. Benyahia et al. [17,23] considered the effects of the patch shape, dimensions, patch material, and cross-sectional area essential to repair the cracked plate on the reduction in the SIF using ABAQUS. Mhamdia et al. [24] evaluated the SIF using VCCT of the cracked plate with an adhesively bonded composite patch using ABAQUS software. The main contribution was to identify the effects of thermomechanical loading on the cracked plate at different temperatures and tensile loads. Behnam et al. [72] repaired a cracked aluminium panel using the concept of the cohesive-zone model and extended the finite-element method (XFEM) to model the progressive damage in the adhesive of the composite patch repair using ABAQUS FE code. 2ff7e9595c
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