PSI - Issue 71

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

155

Compression test data

Indentation test data

Failure load Weibull PDF (390, 8.5)

Failure load Weibull PDF

Three point bend test

10

Failure load Weibull PDF (76210, 10.25)

8

6

(1056, 3.45)

8

6

4

6

4

4

Frequency

2

Frequency

Frequency

2

2

0

56000 64000 72000 80000 88000 0

0

500

1000

1500

300

330

360

390

420

450

Failure load (N)

Failure load (N)

Failure load (N)

(a)

(c)

(b)

Fig. 4: Distribution of failure load obtained after testing using (a) cylindrical indenter; (b) three point bend test setup; (c) compression fixtures.

5. Evaluation of tensile stresses in cylindrical indentation using finite element analysis The stresses from the three-point bend and compression tests can be readily obtained. However, to evaluate the failure stresses under indentation tests, finite element analysis was conducted. Details of this analysis are discussed in the following sections. 5.1 Description of finite element model A 3D finite element symmetric model of cylindrical indentation was created, as illustrated in Fig. 5(a). The roller diameter is taken as 4 mm and thickness of the specimen is 4 mm similar to that taken in the experiments. The value of Young ’s modulus is taken as 72 GPa and Poisson’s ratio of 0.23 for modeling the glass specimen. The Indenter is made of tungsten carbide material having Young’s modulus of 700 GPa and Poisson’s ratio of 0.3. Symmetric boundary conditions were applied to the model, while displacement boundary conditions were assigned to the top of the roller surface. The specimen was constrained to move vertically at its bottom surface. Twenty-noded brick elements were utilized, and the meshing is depicted in Fig. 5(b). A mesh convergence study was performed. Contact modeling was established between the roller and the specimen surface, with the contact and target surfaces shown in Fig. 5(c). The augmented Lagrangian method was used as the contact algorithm. The roller penetrated the specimen in numerous substeps, and at each step, the total load acting on the roller was evaluated and corresponding tensile stresses were noted.

(b)

(a)

(c)

Fig. 5: Details of the finite element model (a) 3D model with boundary conditions; (b) Mesh used for study; (c) contact surfaces.

5.2 Quantification of tensile stresses beneath the indenter The roller was pressed onto the specimen to a specific displacement and the tensile stresses beneath the roller in both the depth and longitudinal directions were found out. These stresses plotted for the 1056 N, median load value obtained from indentation experiments for the glass specimen. Fig. 6(a) illustrates the stress contour in the x-direction (perpendicular to the cross-section of the glass specimen). Notably, a localized maximum stress of approximately 160 MPa occurs at the glass surface. While this localized stress does not result in significant deformation, it may lead to the formation of micro-cracks beneath the indenter. At about 0.12 mm beneath the indenter, a tensile stress of around