PSI - Issue 83

Ritesh M. Patel et al. / Procedia Structural Integrity 83 (2026) 41–46

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The semi-circular bend (SCB) specimen under three-point bending is a trustworthy method for determining the mixed-mode - (I/II) fracture toughness of PLA. Chong et al. (1984) and Lim et al. (1994) have promoted the SCB technique as a prospective standard test method. Its main benefits are its basic geometry, ease of manufacture, and the ability to easily create test specimens using the fused deposition modeling method without requiring post-machining processes Aliha (2010), Chong (1984), Lim (1993), (1994). In case of pure mode-II conditions, randomly figuring out crack angle in SCB specimen for experimental work is not feasible. These demand that the SCB specimen undergo numerical analysis prior to the experiment. T -stress and the stress intensity factor have been determined by computer modeling and testing on a range of materials with different span lengths by Ayatollahi et al. (2006), (2007), (2010), (2011) and Fayed (2018). At different span lengths and fracture angles, the mixed mode stress intensity factor (SIF) is computed using an internal finite element code Ameria et al. (2012) and Fayed (2018). Using numerical calculations, the effects of specimen thickness and Poisson’s ratio are examined. The results demonstrated that when Poisson’s ratio goes up, the T -stress and the stress intensity variables (K I , K II ) rise.

Nomenclature K I

Mode I stress intensity factor Mode II stress intensity factor

K II

a α β

Crack length

Crack inclination angle

Bi-axiality ratio

2. Materials and methods A semi-circular bend (SCB) specimen with a radius of 40 mm , 50 mm and 60 mm built and PLA material properties are taken into consideration for the finite element analysis in this study. The ratio of a/R = 0.5 and S/R = 0.5 are the values chosen for the simulation. The SCB specimen is analyzed using the fracture mechanics technique to ascertain the fracture parameters under mixed mode loading conditions. The geometrical constant for the SCB specimen is determined using the analytical method which is described below. The elastic stress field surrounding the crack tip can be described as a collection of infinite series expansions, according to Williams (1957). ఏఏ ൌ √21 2 ൤ ூ ଶ 2 െ 32 ூூ ൨ ൅ܶ ݅݊ ଶ ൅ ൬ ଵ ଶ ൰ ሺ1ሻ Where the crack tip affects the polar coordinates r and θ . The stress intensity factor for mode-I and mode-II are denoted by K I and K II respectively. The first term in Eq. (1) is singular. In addition to being a geometrical constant, the second component of T -stress also has the impact of a higher order value. In this instance, O (r 1/2 ) is essentially insignificant. The stress intensity parameters K I and K II cooperate with T-stress to predict brittle fracture in mixed mode loading. This method uses the path independent J -integral features to extract the mixed mode loading stress intensity factors. Ideally, the SCB specimen's crack tip parameters should be shown in dimensionless forms as follows: These data are used to calculate geometrical constants according to Eq. (2) and (3). Ayatollahi et al. (2006) and Fayed (2018). ூ ൌ ௉ ೎ೝ ଶோ் √ ூ ቀ ோ ௔ , ோ ௌ , ቁ (2) ூூ ൌ ௉ ೎ೝ ଶோ் √ ூூ ቀ ோ ௔ , ோ ௌ , ቁ (3) The specimen thickness is denoted by t , whereas the reference load P cr , is taken from the literature Ayatollahi et al. (2006), (2007), (2010). According to Fig.1. The symbols a , S , and R stand for crack length, span length between two rollers and specimen radius respectively. Both Y I and Y II are non-dimensional factors which are the function of crack inclination angle (α) , a/R , and S/R . The analytical techniques for calculating the T -stress are extremely limited. Because of that particular work uses a simple and universal method to determine the T -stress for mixed mode I/II