Mechanical Properties and Energy Characteristics of Flawed Samples with Two Non-Parallel Flaws under Uniaxial Compression
Abstract
:1. Introduction
2. Establishment of the Calculation Model
2.1. Parallel Bond Model (PBM)
2.2. Numerical Model Description and Calibration of the PBM
3. Numerical Experiment Results
3.1. Stress–Strain Curve Characteristics
3.2. Strength and Crack Characteristics
4. Energy Characteristic Analysis
4.1. Energy Analysis Principle
4.2. Evolution Process of Energy
- (1)
- The initial compression stage (OA). From the beginning of the loading to point A, there is no crack in the sample. The boundary energy U, strain energy Ue, and dissipated energy Ud increase with the increase in axial strain, and the curves of U and Ue have a larger rate. At point A, the strain energy of samples with flaws of equal length and flaws of unequal length account for 97.66% and 97.58% of the boundary energy, respectively. The boundary energy is completely transformed into the strain energy of the sample. There is basically no energy dissipation. The dissipated energy and friction energy are almost zero.
- (2)
- The linear development stage of dissipated energy (AB). The cracks begin to develop gradually after point A, but the growth rate is quite slow. In this stage, both the dissipated energy and friction energy increase linearly at a low rate. The curves of the boundary energy and strain energy grow approximately linearly. At point B, the strain energy Ue of samples E and F account for 96.45% and 95.82% of the boundary energy U, respectively. Most of the energy is stored in the form of strain energy, which is energy accumulation.
- (3)
- The unstable development stage of dissipated energy (BC). With the increase in axial stress, the cracks continue to develop and propagate, causing part of the strain energy to be released. The curve of the dissipated energy increases in a downward convex form, and the growth rate gradually becomes larger. Both the boundary energy and strain energy are increasing, but the slopes of the energy curves show a downward tendency. The two energy curves are clearly separated. At point C, the strain energy Ue reaches its maximum value, which is referred to as the energy storage limit of the sample.
- (4)
- The post-peak acceleration stage (CD). At point C, the cracks propagate and coalesce into macroscopic cracks, and the strain energy curve begins to drop. The friction energy increases with the degree of friction slip of the cracks. It increases sharply at point C due to the penetration of macroscopic cracks. In the post-peak stage, the growth rate of boundary energy U shows a decreasing state. The strain energy Ue stored in the sample is gradually released and converted into dissipated energy such as friction energy. The dissipated energy of the sample increases exponentially. The proportion of the dissipated energy to the total energy gradually increases until the sample is destroyed.
4.3. Effect of Flaw Angle and Type on Energy Dissipation
5. Discussion
6. Conclusions
- (1)
- The crack-initiation strength and peak strength of the sample increase with the increase in the flaw angle. When the flaw angle is small, the sample shows plastic deformation during uniaxial compression. For larger flaw angles, the sample shows elastic-brittle properties, whose storage energy is larger.
- (2)
- The existence of flaws of unequal length in the sample reduces the stability of the sample. The crack-initiation strength and peak strength of the sample with flaws of unequal length were 18.76% and 6.15% smaller than those of the sample with flaws of equal length, respectively.
- (3)
- The energy-storage limit of the samples with flaws of unequal length is reduced to a certain extent. The strain energy reaches an extreme value at the peak strength, whose growth rate first increases with the strain and then gradually decreases. The strain energy is accumulated in the pre-peak region and released in the post-peak region. The dissipated energy is concave upward with the strain, and the growth rate increases gradually.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Microparameter | Value |
---|---|
Minimum grain diameter, dmin(mm) | 0.55 |
Maximum to minimum grain diameter ratio, dmax/dmin | 1.45 |
Installation gap, ggap | 0.53 × 10−4 |
(GPa) | 4.7 |
1.5 | |
Radius multiplier parameter, λ | 1.0 |
(MPa) | 23.0 |
(MPa) | 32.5 |
Type | Density/(kg/m3) | Young Modulus/GPa | UCS/MPa |
---|---|---|---|
Experimental data | 2200 | 7.50 | 46.35 |
Simulated data | 2200 | 7.54 | 46.10 |
Flaw Angle θ/(°) | Schematic Diagram of Experimental Crack Propagation | Simulated Diagram |
---|---|---|
30 | ||
45 | ||
60 |
Flaw Angle/(°) | Sample E (Equal Length Flaws) | Sample F (Flaws of Unequal Length) | ||
---|---|---|---|---|
Crack Initiation Strength /MPa | Peak Strength/MPa | Crack Initiation Strength/MPa | Peak Strength/MPa | |
30 | 18.55 | 39.37 | 15.31 | 35.27 |
45 | 22.15 | 39.98 | 18.02 | 39.03 |
60 | 27.22 | 45.35 | 21.73 | 42.78 |
Flaw Type | Sample No. | Flaw Angle/(°) | Crack Initiation Strength Point | Peak Strength Point | ||||||
---|---|---|---|---|---|---|---|---|---|---|
U/J | Ue/J | Ud/J | U/J | Ue/J | Ud/J | pe/(%) | ||||
Equal length flaws (E) | E30 | 30 | 273.75 | 266.83 | 6.93 | 97.47 | 1259.45 | 1187.86 | 71.59 | 94.32 |
E45 | 45 | 382.90 | 373.63 | 9.27 | 97.58 | 1401.88 | 1251.78 | 150.10 | 89.29 | |
E60 | 60 | 573.03 | 559.63 | 13.40 | 97.66 | 1690.57 | 1556.44 | 134.13 | 92.07 | |
Flaws of unequal length (F) | F30 | 30 | 190.91 | 186.06 | 4.85 | 97.46 | 1123.51 | 1003.29 | 120.23 | 89.30 |
F45 | 45 | 261.29 | 254.31 | 6.98 | 97.33 | 1256.99 | 1176.69 | 80.30 | 93.61 | |
F60 | 60 | 370.73 | 361.74 | 8.99 | 97.58 | 1567.06 | 1418.39 | 148.67 | 90.51 |
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Li, Q.; Huang, C.; Zhang, Y.; Liang, P.; Yao, X.; Yu, G. Mechanical Properties and Energy Characteristics of Flawed Samples with Two Non-Parallel Flaws under Uniaxial Compression. Sustainability 2023, 15, 459. https://doi.org/10.3390/su15010459
Li Q, Huang C, Zhang Y, Liang P, Yao X, Yu G. Mechanical Properties and Energy Characteristics of Flawed Samples with Two Non-Parallel Flaws under Uniaxial Compression. Sustainability. 2023; 15(1):459. https://doi.org/10.3390/su15010459
Chicago/Turabian StyleLi, Qun, Changfu Huang, Yanbo Zhang, Peng Liang, Xulong Yao, and Guangyuan Yu. 2023. "Mechanical Properties and Energy Characteristics of Flawed Samples with Two Non-Parallel Flaws under Uniaxial Compression" Sustainability 15, no. 1: 459. https://doi.org/10.3390/su15010459