PSI - Issue 71

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

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42.4 MPa is present across the full cross-section of the specimen, which primarily contributes to the specimen's fracture into two parts under tensile loads. Fig. 6(b) displays the variation of tensile stress in the longitudinal and depth directions at both the centre and surface of the specimen. Compressive stresses are generated near the contact point, but at a distance of, approximately, 0.15 mm, the maximum tensile stress occurs at both the centre and surface of the specimen. This maximum tensile stress then decreases to constant values of 15 MPa and 6.5 MPa at the surface and centre, respectively. Additionally, the stresses along longitudinal direction peak at 16 MPa at both the centre and surface, subsequently dropping to 7.3 MPa at the surface and 8.4 MPa at the centre. Fig. 6(c) illustrates how tensile stresses vary with indenter displacement into the specimen at different locations along the depth direction. At a depth of 0.1 mm from the top surface, tensile stress develops up to an indenter displacement of 0.0065 mm, contributing to the specimen's fracture. However, with further indentation, these stresses transition to a compressive nature. The maximum tensile stress value shifts deeper beneath the indenter with further indentation. At approximately 0.7 mm away from the roller contact, tensile stresses continue to accumulate, thus, reaching 28 MPa at an indenter displacement of 0.015 mm. These stresses remain similar with further increases in depth from the top surface of the specimen.

Location along depth from contact location (mm) 0.1 0.4 0.2 0.7 0.3 1.5

Along depth (at the surface) Along longitudinal direction (at the surface) Along depth (at the centre) Along longitudinal direction (at the centre)

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Stress (MPa)

Stress (MPa)

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Indenter displacement (mm)

Distance from the contact location (mm)

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(c)

(a)

Fig. 6: (a) Tensile stress contour (S x (MPa)) at median load of 1056 N; (b) Variation of stress (S x ) along longitudinal and depth direction at median load of 1056 N; (c) Stress variation with indenter displacement at different location along depth of specimen. 6. Results and discussions Stresses were assessed for all test configurations, with distributions obtained as outlined in previous sections. Fig. 7(a) presents a comparison of the CDF of failure stresses. It is evident that the median failure stress decreases from 50.5 MPa for the three-point bend test to 42.5 MPa for the indentation method. This has to do with the mechanism of failure in TPB and indentation are different, qualitatively it can be inferred that the TPB specimen is less constrained than the indentation specimen.

Compressive failure stress (MPa)

Compressive failure stress (MPa)

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Cylindrical indenter TPB test

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TPB test data Weibull model Cylindrical indenter data Weibull model

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Compression test

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Frequency

Compression data Weibull model

Reduction in tensile stress at failure

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0.0 Probability of fracture

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Failure stress (MPa)

Failure Stress (MPa)

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Fig. 7: Comparison of distributions in failure stresses for different test configuration (a) CDF; (b) PDF.

Additionally, the median compressive stress for the float glass is measured at 740 MPa. The Weibull CDF function aligns closely with the experimental failure stress data. It was noted that the scatter in failure stresses is greater for the indentation tests compared to the compression tests, likely due to the behavior of flaws under tensile stresses. Fig. 7(b) displays the PDF, illustrating the reduction in tensile stresses required for the failure of the glass specimen in the indentation test case.