PSI - Issue 60

A.B. Penurkar et al. / Procedia Structural Integrity 60 (2024) 355–363 A. B. Penurkar/ StructuralIntegrity Procedia 00 (2023) 000 – 000

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(a) (b) Fig. 6: Box plot showing outliers obtained after testing specimen of thickness (a) 4 mm (b) 8 mm.

4. Evaluation of Weibull distribution parameters for different thickness of glass After obtaining the fracture stress in bending from all the tests for different thickness of glass specimen, histogram plots of fracture stress in bending were plotted as shown in Fig. 7. This was done to evaluate the distribution of failure stresses for different thickness of glass. Different distributions were fitted, however, Weibull type of distribution matches well with the failure stress data. The two parameter Weibull curve matches well with that of the failure data for 4 mm thickness (Fig. 7a) and 8 mm thickness (Fig. 7b). General equation of failure probability for the cumulative distribution function (CDF) of the Weibull distribution as shown in Eq. (4). = 1 − exp [−( ) ] (4) where β is the Weibull exponent or shape parameter, θ is the Weibull scale parameter, σ f is the equivalent fracture stress. The shape parameter, β, indicates the variability of the data and thus, higher values of β lead to a steeper CDF and represent a smaller scatter of strength in the data. The size parameter, θ, represents the stress level, below which 63.2% of the specimens fail and together with the shape parameter dictates the position of the CDF along the horizontal axis. These parameters were obtained for both the thickness of specimen. It was observed that there is substantial change in the value of size parameter with increase in thickness from 4 mm to 8 mm. However, there is not much change in shape parameter observed. Value of shape parameter is around 9, however, it changes from 46.24 to 40.24 MPa with increase in thickness from 4 mm to 8 mm respectively. This indicates that lower stresses are required for the fracture to occur for higher thickness of glass. This is due to the increase in probability of finding a defect for higher specimen thickness as compared to lesser thickness of glass. Comparison of the Weibull model for 4 mm and 8 mm thickness of glass is shown in Fig. 8. It was observed that there is a shift in representative fracture stress from 46.24 MPa to 40.24 MPa with the increase in thickness from 4 mm to 8 mm respectively. As discussed previously, the increase in thickness will lead to more zone where minor crack/defects might be present. Under external loading condition, these crack shall get activated due to high stress concentration near to its crack tip. Since glass is brittle in nature, these crack will get propagated rapidly leading to its fracture. Hence, with increase in thickness, probability of finding defects increases leading to reduction in fracture stress required for the glass to break.