PSI - Issue 68

Morteza Khomami Abadi et al. / Procedia Structural Integrity 68 (2025) 1312–1318 Author name / Structural Integrity Procedia 00 (2025) 000–000

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2. Overview 2.1. Overview of Stress intensity factor (SIF)

The stress intensity factor (KI) predicts the stress field at the crack or notch tip. It is a theoretical construct that is commonly used to a homogenous, linear elastic material and serves as a failure criterion for brittle materials. The magnitude of SIFs is determined based on the specimen geometry, fracture or notch size and placement, boundary and loading conditions, as well as material parameters. Here are some proposed relationships for calculating the stress intensity factor of the beam subjected to the bending moment as shown in Fig. 1:

Fig. 1. Cracked beam under bending moment The stress intensity factor of the beam under bending moment is presented in Eq. 1. ! = ⎪⎨ ⎩ ⎪⎧ 6 ℎ " √ # 3.99 ( ) 0 ≤ ≤ 0.6 ℎ √ℎ8(1− ) $ 0.6 ≤ ≤ 1.0⎭⎪⎬⎪ ⎫ , = ℎ # ( ) = 1.12 − 1.40 + 7.33 " − 13.083 $ + 14 % [ Kumar ] # ( ) = D & " ' tan & " ' × (.*"$+(.,** .,/012. ! # " 33 $ 450. ! # " 3 [ Yokoyama and Chen ] in which is crack length, ℎ is beam height, is beam thickness, and define the bending moment. The stress intensity factors for the single–edge and center cracked plates under tension according to Fig. 2 were presented as follows: (1)

(a) (b) Fig. 2. Cracked plates under tension (a) Single–edge crack (b) Center crack The stress intensity factor of the single–edge and center cracked plates under tension is presented in Eq. 2, 3 respectively. ! = √ ( ) , = 0< <0.6 ( ) = 1.12 − 0.23 + 10.55 " − 21.72 $ + 30.39 % (2) ! = √ ( ) , = 0< <0.7 ( ) = 1.0 + 0.128 − 0.288 " + 1.523 $ (3) in which is crack length, is plate width, and is defined as the tensile stress on the edges of the plates. In the above relationships, parameters such as crack location and material properties were ignored. In addition, the loading and boundary conditions are only limited to the beam under bending moment and plate under tension and do