PSI - Issue 54

588 Francisco Q. de Melo et al. / Procedia Structural Integrity 54 (2024) 585–592 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 Factors ( , = or for tension or bending) were calculated by (Rice and Levy 1972) grounding the expressions on former studies by (Gross and Srawley 1965): = 2 ∑ ( ) 8 =0 ; , = , (6) Where is the local crack depth at current coordinate over the crack line, ( ) vs the plate thickness , = ( )/ , and stand for bending and tension, respectively factors ( ) ( = ,.., ) were calculated by (Rice and Levy 1972). In next section, an alternative solution based on simple concepts and solutions is proposed. The solution for factors as in matrix (2) does not involve series forms as in (6) and leads to quite simple expressions. This solution is based on the classical Mohr’s method of Moment Areas in the determination of displacements/rotations in trussed or beam structures. 2.2. Evaluation of the concept of SDZ - Stress Dead Zones: Procedure A classical method for displacements and rotations of structural components subjected to joint tension/bending diagrams is reviewed. Considering a thin flat plate with a side edge straight crack, it is supposed that this structural element has shell displacement/forces capability, resisting in-plane membrane forces and out-of-plane transverse forces or bending moments. Under such a described force system, it is possible to identify the plate volume, zones where the stress field resulting from the external force system is practically meaningless and will be neglected in the foregoing model development. Such zones will be named as Stress Dead Zones (SDZ): • The specimen is subjected to remote tension and/or bending, then SDZ zones at the crack vicinity will be considered to have an irrelevant stress field compared with other areas of the specimen. • It is important to delimit such zones where stress can be neglected. The use of such a procedure allows the computation of flexibility factors of matrix (2) in a simple and practical way. Each line-spring element is subjected to tension or bending unitary forces, leading to relative extensional displacements and rotations at the crack faces. The accurate delimitation of the SDZ is fundamental to set up a precise model equivalent to the edge cracked plate, where now this element has no crack. However, its flexibility should be the same as the previously cracked element, thanks to the removal of structurally non-relevant material enclosed in the SDZ area. The identification of the SDZ areas can be carried out by two techniques: a) Use a finite element discretization of the structural model, a side edge cracked plate, subjected to an in-plane tensile force or pure bending moment. The post-processing reveals the existence of an approximately doubly triangular zone where the equivalent stress field is much smaller than the one in other zones. In Figure 2, it is possible to identify such triangular zones close to the crack line, darker than the remaining filling pattern. b) Experimental investigation in the characterization of the deformation field in a thin plate having a side edge crack. The main objective of this step is the identification of zones where the stress field much less relevant than the remaining in the whole volume of the component. The more important characteristic of the SDZ area is the triangular geometry approach, namely the proportion between both rectangular sides of the triangle identified above. To confirm the geometry of such an area, the optical technique Digital Image Correlation (DIC) techniques was the selected tool. Figure 2 shows the triangular zone where the deformation field can be associated with a low intensity stress, given it refers to a rigid body displacement. It can also be assumed, as an approach, that the vertical side of both triangles defining the SDZ are approximately larger than the crack length in a scale factor of about 1,25 . Then the proportion factor used in next formulations is =1,25 , then for methodology, it is reminded that if a is the crack length, then is the vertical side of SDZ-triangles. 4