PSI - Issue 71

A.B. Penurkar et al. / Procedia Structural Integrity 71 (2025) 150–157

154

mm/min until the specimen failed. The compressive load at failure was recorded, and the stress was calculated based on the area under compression. Upon failure, the specimen disintegrated into powder form. Figure 3(d) illustrates the variability in failure load, which ranged from 60 kN to 90 kN, with an average failure load of 73 kN. It was noted that glass exhibits very high strength under compressive loading, in contrast to its brittle behavior under tensile loads. It can also be observed from Fig. 3(a) that the specimen undergoes higher displacement at fracture as compared to indentation and TPB test.

2000

1500

80000

Cylindrical indentation Three point bend test

Failure load Minimum Value Mean Value Maximum Value

Compression test

1200

1500

60000

900

1000

40000

600

Load (N)

500

20000

Failure load (N)

300

Compressive load (N) 0 0

0

0

5

10

15

20

25

30

0.00

0.01

0.02

0.03

0.04

Test number

Displacement (mm)

(b)

(a)

Failure load Minimum Value Mean Value Maximum Value

Failure Load Mimimum value Mean value Maximum value

105

500

90

400

75

300 Failure load (N)

60

Failure Load (kN)

0 2 4 6 8 101214161820222426

45

0

5

10

15

20

Test number

Test number Fig. 3: (a) Typical load-displacement response for different types of tests; (b) Scatter in failure load for cylindrical indentation test (c) Scatter in failure load for three point bend test. (d) Scatter in failure load for compression test. 4. Evaluation of Weibull distribution parameters using failure load To estimate the distribution of scatter in failure load, various types of distributions were fitted to the data. The two parameter Weibull distribution provided the best fit for the failure load across all specimens. A histogram of failure load was created for all test configurations, along with a plotted probability density function (PDF). The PDF is characterized by two parameters: the shape parameter (β) and the scale parameter (θ). The general equation for the cumulative density function (CDF) is given by Eq. (4). = 1 − [− ( ) ] (4) The shape parameter, β, indicates the variability of the data; higher values of β result in a steeper CDF, reflecting less scatter in the strength data. The scale parameter, θ, represents the stress level below which 63.2% of the specimens fail, and, together with the shape parameter, determines the position of the CDF along the horizontal axis. These parameters were calculated for all configurations. Fig. 4 shows that the Weibull distribution aligns well with the failure load data. The scale parameter values were found to be 1056 N for the indentation test, 390 N for the three-point bend test, and 76 kN for the compression tests. Additionally, it was observed that there is greater scatter in the indentation and three-point bend test data compared to the compression test data. This difference is attributed to the presence of flaws that propagate rapidly under tensile stresses, while their impact is minimal during compression testing. (c) (d)