The formula to calculate the critical stress for crack propagation is:
\[ \sigma_c = \sqrt{\frac{2 E \gamma_s}{\pi a}} \]
Where:
Critical stress is the stress required for crack propagation in a brittle material.
Young's Modulus is a mechanical property that describes the relationship between longitudinal stress and longitudinal strain in a material.
Specific surface energy is the energy needed to create a new surface during crack propagation in a brittle material.
Crack length represents the length of a surface crack or half of the length of an internal crack.
Let's assume the following values:
Using the formula:
\[ \sigma_c = \sqrt{\frac{2 \cdot 15 \cdot 0.3}{\pi \cdot 1E-05}} \approx 535.237234845831 \, \text{Pa} \]
The critical stress is approximately 535.237234845831 Pa.
| Young's Modulus (N/m) | Specific Surface Energy (N/m) | Crack Length (m) | Critical Stress (Pa) |
|---|---|---|---|
| 10 | 0.1 | 1.0E-6 | 797.884560802865 |
| 10 | 0.1 | 1.0E-5 | 252.313252202016 |
| 10 | 0.1 | 0.0001 | 79.788456080287 |
| 10 | 0.2 | 1.0E-6 | 1,128.379167095513 |
| 10 | 0.2 | 1.0E-5 | 356.824823230554 |
| 10 | 0.2 | 0.0001 | 112.837916709551 |
| 10 | 0.3 | 1.0E-6 | 1,381.976597885342 |
| 10 | 0.3 | 1.0E-5 | 437.019372236832 |
| 10 | 0.3 | 0.0001 | 138.197659788534 |
| 10 | 0.4 | 1.0E-6 | 1,595.769121605731 |
| 10 | 0.4 | 1.0E-5 | 504.626504404032 |
| 10 | 0.4 | 0.0001 | 159.576912160573 |
| 10 | 0.5 | 1.0E-6 | 1,784.124116152771 |
| 10 | 0.5 | 1.0E-5 | 564.189583547756 |
| 10 | 0.5 | 0.0001 | 178.412411615277 |
| 12 | 0.1 | 1.0E-6 | 874.038744473663 |
| 12 | 0.1 | 1.0E-5 | 276.395319577068 |
| 12 | 0.1 | 0.0001 | 87.403874447366 |
| 12 | 0.2 | 1.0E-6 | 1,236.077446474207 |
| 12 | 0.2 | 1.0E-5 | 390.882009522336 |
| 12 | 0.2 | 0.0001 | 123.607744647421 |
| 12 | 0.3 | 1.0E-6 | 1,513.879513212096 |
| 12 | 0.3 | 1.0E-5 | 478.730736481719 |
| 12 | 0.3 | 0.0001 | 151.387951321210 |
| 12 | 0.4 | 1.0E-6 | 1,748.077488947327 |
| 12 | 0.4 | 1.0E-5 | 552.790639154137 |
| 12 | 0.4 | 0.0001 | 174.807748894733 |
| 12 | 0.5 | 1.0E-6 | 1,954.410047611680 |
| 12 | 0.5 | 1.0E-5 | 618.038723237103 |
| 12 | 0.5 | 0.0001 | 195.441004761168 |
| 14 | 0.1 | 1.0E-6 | 944.069743882630 |
| 14 | 0.1 | 1.0E-5 | 298.541066072092 |
| 14 | 0.1 | 0.0001 | 94.406974388263 |
| 14 | 0.2 | 1.0E-6 | 1,335.116235624909 |
| 14 | 0.2 | 1.0E-5 | 422.200824564475 |
| 14 | 0.2 | 0.0001 | 133.511623562491 |
| 14 | 0.3 | 1.0E-6 | 1,635.176762293252 |
| 14 | 0.3 | 1.0E-5 | 517.088294582641 |
| 14 | 0.3 | 0.0001 | 163.517676229325 |
| 14 | 0.4 | 1.0E-6 | 1,888.139487765259 |
| 14 | 0.4 | 1.0E-5 | 597.082132144185 |
| 14 | 0.4 | 0.0001 | 188.813948776526 |
| 14 | 0.5 | 1.0E-6 | 2,111.004122822376 |
| 14 | 0.5 | 1.0E-5 | 667.558117812455 |
| 14 | 0.5 | 0.0001 | 211.100412282238 |
| 16 | 0.1 | 1.0E-6 | 1,009.253008808064 |
| 16 | 0.1 | 1.0E-5 | 319.153824321146 |
| 16 | 0.1 | 0.0001 | 100.925300880806 |
| 16 | 0.2 | 1.0E-6 | 1,427.299292922217 |
| 16 | 0.2 | 1.0E-5 | 451.351666838205 |
| 16 | 0.2 | 0.0001 | 142.729929292222 |
| 16 | 0.3 | 1.0E-6 | 1,748.077488947327 |
| 16 | 0.3 | 1.0E-5 | 552.790639154137 |
| 16 | 0.3 | 0.0001 | 174.807748894733 |
| 16 | 0.4 | 1.0E-6 | 2,018.506017616128 |
| 16 | 0.4 | 1.0E-5 | 638.307648642292 |
| 16 | 0.4 | 0.0001 | 201.850601761613 |
| 16 | 0.5 | 1.0E-6 | 2,256.758334191025 |
| 16 | 0.5 | 1.0E-5 | 713.649646461109 |
| 16 | 0.5 | 0.0001 | 225.675833419103 |
| 18 | 0.1 | 1.0E-6 | 1,070.474469691663 |
| 18 | 0.1 | 1.0E-5 | 338.513750128654 |
| 18 | 0.1 | 0.0001 | 107.047446969166 |
| 18 | 0.2 | 1.0E-6 | 1,513.879513212096 |
| 18 | 0.2 | 1.0E-5 | 478.730736481719 |
| 18 | 0.2 | 0.0001 | 151.387951321210 |
| 18 | 0.3 | 1.0E-6 | 1,854.116169711310 |
| 18 | 0.3 | 1.0E-5 | 586.323014283504 |
| 18 | 0.3 | 0.0001 | 185.411616971131 |
| 18 | 0.4 | 1.0E-6 | 2,140.948939383326 |
| 18 | 0.4 | 1.0E-5 | 677.027500257308 |
| 18 | 0.4 | 0.0001 | 214.094893938333 |
| 18 | 0.5 | 1.0E-6 | 2,393.653682408596 |
| 18 | 0.5 | 1.0E-5 | 756.939756606048 |
| 18 | 0.5 | 0.0001 | 239.365368240860 |
| 20 | 0.1 | 1.0E-6 | 1,128.379167095513 |
| 20 | 0.1 | 1.0E-5 | 356.824823230554 |
| 20 | 0.1 | 0.0001 | 112.837916709551 |
| 20 | 0.2 | 1.0E-6 | 1,595.769121605731 |
| 20 | 0.2 | 1.0E-5 | 504.626504404032 |
| 20 | 0.2 | 0.0001 | 159.576912160573 |
| 20 | 0.3 | 1.0E-6 | 1,954.410047611680 |
| 20 | 0.3 | 1.0E-5 | 618.038723237104 |
| 20 | 0.3 | 0.0001 | 195.441004761168 |
| 20 | 0.4 | 1.0E-6 | 2,256.758334191025 |
| 20 | 0.4 | 1.0E-5 | 713.649646461109 |
| 20 | 0.4 | 0.0001 | 225.675833419103 |
| 20 | 0.5 | 1.0E-6 | 2,523.132522020160 |
| 20 | 0.5 | 1.0E-5 | 797.884560802865 |
| 20 | 0.5 | 0.0001 | 252.313252202016 |