Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches
Abstract
:1. Introduction
2. Materials and Methods
2.1. Material, Tests and Experimental Results
2.2. Analytical Approach: Mixed-Mode Fracture Criterion
3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
d | Notch length in SVNBD specimens |
D | Diameter of the circular specimens |
ft | Tensile strength |
KIc | Fracture toughness |
KISV, KIISV | Sharp V-notch stress intensity factor under mode I and mode II |
KIfSV, KIIfSV | Critical values of KISV and KIISV, respectively |
KI* | Dimensionless parameters for stress terms in cracked conditions |
P | Applied load |
Pf | Fracture load |
rc,V | Critical distance for sharp V-notch |
t | Specimen thickness |
YIV, YIIV | Dimensionless parameters for stress terms in notched conditions |
α | Half of the notch opening angle |
β | Loading angle for Brazilian disk specimen |
βII | Loading angle corresponding to pure mode II loading |
λi | Eigenvalues |
σrθ | In-plane shear stress |
σθθ | Tangential stress |
σθθc | Critical value of σθθ |
θ0 | Notch bifurcation angle |
θ0I | Notch bifurcation angle for pure mode I |
θ0II | Notch bifurcation angle for pure mode II |
ω | Notch solid angle |
BD | Brazilian disk |
CBD | Cracked Brazilian disk specimen |
MTS | Maximum tangential stress criterion |
MTS-FEM | Modified MTS criterion based on the finite element method |
SVNBD | Sharp V-notched Brazilian disk |
SV-MTS | MTS criterion for sharp V-notch |
References
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D (mm) | t (mm) | d (mm) | 2α (°) | β (°) | Pf Avg. (N) | Standard Deviation SD (N) |
---|---|---|---|---|---|---|
150 | 29.4 | 75 | 30 | 0 | 6335.7 | 646.9 |
150 | 32 | 75 | 30 | 8 | 8081.3 | 1725.0 |
150 | 27.7 | 75 | 30 | 16 | 8572.4 | 1692.7 |
150 | 30.4 | 75 | 30 | 25 | 7263.7 | 1307.7 |
150 | 31.4 | 75 | 60 | 0 | 6599.7 | 857.7 |
150 | 33.3 | 75 | 60 | 9 | 7096.3 | 1228.3 |
150 | 35.5 | 75 | 60 | 18 | 5732.4 | 1307.0 |
150 | 34.4 | 75 | 60 | 28 | 5743.8 | 2612.6 |
150 | 33.9 | 75 | 90 | 0 | 2903.5 | 274.7 |
150 | 34.5 | 75 | 90 | 11 | 3421.2 | 706.3 |
150 | 32.8 | 75 | 90 | 22 | 5283.6 | 638.7 |
150 | 34.6 | 75 | 90 | 34 | 7396.1 | 813.4 |
Avg. (N) | ||||||||
---|---|---|---|---|---|---|---|---|
30 | 0 | 6335.7 | 0.5014 | 0.5982 | 1.27 | 0 | 0.502 (MPa·m0.4986) | 0 (MPa·m0.4018) |
8 | 8081.3 | 0.5014 | 0.5982 | 0.97 | 3.65 | 0.447 (MPa·m0.4986) | 2.163 (MPa·m0.4018) | |
16 | 8572.4 | 0.5014 | 0.5982 | 0.53 | 6.13 | 0.298 (MPa·m0.4986) | 4.436 (MPa·m0.4018) | |
25 | 7263.7 | 0.5014 | 0.5982 | 0 | 7.85 | 0 (MPa·m0.4986) | 4.44 (MPa·m0.4018) | |
60 | 0 | 6599.7 | 0.5122 | 0.7309 | 1.94 | 0 | 0.765 (MPa·m0.4878) | 0 (MPa·m0.2691) |
9 | 7096.3 | 0.5122 | 0.7309 | 1.65 | 5.43 | 0.672 (MPa·m0.4878) | 3.895 (MPa·m0.2691) | |
18 | 5732.4 | 0.5122 | 0.7309 | 1 | 8.21 | 0.302 (MPa·m0.4878) | 4.374 (MPa·m0.2691) | |
28 | 5743.8 | 0.5122 | 0.7309 | 0 | 9.75 | 0 (MPa·m0.4878) | 5.391 (MPa·m0.2691) | |
90 | 0 | 2903.5 | 0.5448 | 0.9085 | 3.87 | 0 | 0.677 (MPa·m0.4552) | 0 (MPa·m0.0915) |
11 | 3421.2 | 0.5448 | 0.9085 | 3.26 | 8.65 | 0.652 (MPa·m0.4552) | 4.436 (MPa·m0.0915) | |
22 | 5283.6 | 0.5448 | 0.9085 | 1.86 | 12.21 | 0.615 (MPa·m0.4552) | 10.365 (MPa·m0.0915) | |
34 | 7396.1 | 0.5448 | 0.9085 | 0 | 14.56 | 0 (MPa·m0.4552) | 16.402 (MPa·m0.0915) |
Pf (N) | Dicrepancy (%) | |||||
---|---|---|---|---|---|---|
Experiment | SV-MTS | MTS-FEM | SV-MTS | MTS-FEM | ||
30° | 0 | 6335.7 | 6335.7 | 7103.3 | 0.0 | 12.1 |
8 | 8081.3 | 3311.1 | 7566.9 | 59.0 | 6.4 | |
16 | 8572.4 | 1401.7 | 7847.2 | 83.6 | 8.5 | |
25 | 7263.7 | 1117.8 | 6532.1 | 84.6 | 10.1 | |
Mean discrepancy (%) | 56.3 | 9.25 | ||||
60 | 0 | 6599.7 | 6599.7 | 5879.6 | 0.0 | 10.9 |
9 | 7096.3 | 3668.5 | 6557.8 | 48.3 | 7.5 | |
18 | 5732.4 | 2325 | 5858.8 | 59.4 | 2.2 | |
28 | 5743.8 | 1813.1 | 5271.3 | 68.4 | 8.2 | |
Mean discrepancy (%) | 45.2 | 7.2 | ||||
90 | 0 | 2903.5 | 2903.5 | 3243.9 | 0.0 | 11.7 |
11 | 3421.2 | 2023.3 | 3787.2 | 40.9 | 10.7 | |
22 | 5283.6 | 1378 | 4624.2 | 73.9 | 12.5 | |
34 | 7396.1 | 1266.2 | 6645.7 | 82.9 | 10.2 | |
Mean discrepancy (%) | 49.4 | 11.2 |
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Arabnia, A.; Akbardoost, J.; Cicero, S.; Torabi, A.R. Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches. Materials 2022, 15, 8779. https://doi.org/10.3390/ma15248779
Arabnia A, Akbardoost J, Cicero S, Torabi AR. Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches. Materials. 2022; 15(24):8779. https://doi.org/10.3390/ma15248779
Chicago/Turabian StyleArabnia, Ali, Javad Akbardoost, Sergio Cicero, and Ali Reza Torabi. 2022. "Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches" Materials 15, no. 24: 8779. https://doi.org/10.3390/ma15248779