PSI - Issue 28

228 Behzad V. Farahani et al. / Procedia Structural Integrity 28 (2020) 226–233 Behzad V. Farahani et al / Structural Integrity Procedia 00 (2020) 000–000 3 considering ��� � ��� � and � � ��� . Then, the model was numerically analysed using Finite Element method (FEM) and Radial Point Interpolation (RPIM) and Natural Neighbour Version (NNRPIM) Meshless formulations. Encouraging SIF results put into evidence that the proposed numerical methodology agreed well with the DIC leading to validate the numerical schemes, see Fig. 1-b). Furthermore, Tavares et al. (Tavares et al. 2015) carried out a DIC study on the SIF determination of CT specimens considering both mode I and II loading conditions for several measured crack lengths. The problem was also computationally solved by the Dual Boundary Element Method (DBEM). The successful acquired results reasonably agreed to DIC outcome leading to verify the proposed approaches. In both mentioned works, a hybrid experimental/numerical analysis was employed in which the SIF was evaluated relying on an overdeterministic algorithm. Overall, amongst other methods used for similar purposes, DIC offers the advantage of allowing for a less complex experimental setup and less controlled experimental conditions. All that is required for a simple 2D/3D DIC test is digital cameras, a light source and a speckle pattern on the investigated surface that can be achieved, for instance, by spray-painting. It is also versatile in the sense that it can be used in combination with a variety of digital image acquisition tools, such as microscopes. The main disadvantage is the lower accuracy of strain measurements when compared to interferometry-based techniques; it is therefore not recommended for small deformations (Pan et al. 2009). In general, DIC is a technique with applicability and potential in structural monitoring: the fact that it is contactless, full field and relatively simple to set up makes it suitable for the detection of damage in engineering structures such as railway infrastructure, c.f. [(Farahani, Barros, et al. 2019; Farahani, Barros, et al. 2020)]. It is also used in experimental measurements in material characterization as presented in (Farahani, Amaral, et al. 2020). Moreover, there are several works dealing with the DIC analysis to study the fracture characterization carried out by Arteiro et al. in composite laminates (Arteiro et al. 2015); Fiber Reinforced Polymers (FRPs) and masonry (Ghiassi et al. 2015); Cement-Based Materials (Dourado et al. 2015); aluminium structures (Zhang and He 2012) and structural steels (Ju, Liu, and Liu 2006; Silva et al. 2017). 3. Thermoelastic Stress Analysis Thermoelastic stress analysis (TSA) classified as a thermography method being an optical technique to evaluate the stress distribution in engineering fields, based on thermal variations. Fundamentally, TSA is implemented to assess the stress field at structural components. Thermoelastic data can be effectively used to evaluate principal stresses on specimen’s surfaces and crack growth rates. Stanley et al. (Stanley and Chan 1985) carried out a research on the stress analysis in relation to thermoelastic effects. They verified the validity of the thermoelastic stress fundamentals with the experimental tests within theoretical formulations, which are considered significantly in this work. Moreover, a proper review of the TSA has been made to compare the obtained stress measurements with other experimental approaches (Everett 1989). In the practical point of view, to prepare the specimen for a TSA test, a black ink with a thermal emissivity ε = 0.97 should be used to provide a surface with deep matt. In theory, the standard relationship between a small temperature change for any material leading to a linear system of equations presented as: �� � � �� � � � � , in which, K is the thermoelastic constant, represented as � � � � , the expression � � � � � is the stress magnitude derived from thermoelastic stress analysis and � , � are the stress components in principal directions (Stanley and Chan 1985). As a widely used application of TSA in LEFM, Farahani et al. (Farahani, Tavares, Moreira, et al. 2017; Farahani, Tavares, and Moreira 2016) carried out a research on the SIF determination where the experimental data acquired by TSA was used to validate the numerical solution obtained by FEM and meshless methods, see Fig. 1-c). They firstly identified the stress function “ stress amplitude” governing the TSA calculations in the Williams’ series expansion as; ��� � � ∑ � �� � � � � � �� ���� � � � � �� � , �� � � � √�� ���� . (1) Where ��� � � � �� � � � � �� �� �� � and � denotes the mode I SIF. Besides � � presents the polar coordinates of the points respecting the crack tip.