PSI - Issue 54

Francisco Q. de Melo et al. / Procedia Structural Integrity 54 (2024) 585–592

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Author name / Structural Integrity Procedia 00 (2019) 000 – 000

a)

b)

c)

Figure 2: a)2D detailed schematic of the experimental specimen and DIC speckle for DIC, b) DIC experimental strain field contour for load stage for 3,9 c) DIC experimental strain field contour for load stage for 4,2 2.3. The line spring constitutive formulas by the Moment Area Method We can obtain the displacement or rotation at a point of a beam as follows: a) Bending moment diagram due to a system of forces, multiplied by a bending moment diagram due to a unitary force at a point: A displacement is obtained at that point; b) Bending moment diagram due to a system of forces, multiplied by the bending moment due to a unitary moment at a point, gives a rotation at that point; c) Bending moment due to externally applied bending moments along the beam, multiplied by the bending moment due to a unitary force at a point: Gives a displacement at that point that is equal to value obtained in b) (its value is the reflected value obtained in b); d) Bending moment diagram due to a set of moments multiplied by a bending moment diagram due to a unitary moment at a point gives a rotation at that point. From these procedures, is clear how to evaluate flexibility factors to establish a Line-Spring compliance matrix as matrix (2) , where unitary forces and moments generate moment diagrams to be multiplied as described above, leading to the flexibility matrix factors. However, such calculations will work only with each side edge cracked plate, as shown in Figure 1 modified after removing the SDZ material. Extensional force, or stress, extends and bends the cracked thin plate (line spring). When this side edge cracked plate is modified under the concept of stress dead zones removal, the equivalent structure is the trapezoidal variable section beam O E E’A’ a s depicted in Figure 3-a) . The area of a generic section at level from the crack line, with − of the crack plane reference basis, is given by: ( ) = [ℎ − ( − / )] , (7) where Î(0, ) and is the edge cracked plate thickness. Considering third order bending moment of inertia: 3 ( )= [ℎ−( − / )] 3 12 , (8) Given the eccentricity of the resulting force ℎ (at application point 2 ), related to point 1 : The maximum intensity of the bending moment is (around point 1 ). = ℎ × /2 , (9) this moment decreases with progress of variable z as follows: