A Relationship between Fracture Toughness Kc and Energy Release Rate Gc According to Fracture Morphology Analysis
Abstract
:1. Introduction
2. Methods
2.1. The Test Methods for Fracture Toughness and Related Constraints
2.2. Fractal Dimension Calculation Method
3. Experimental Section
3.1. Materials and Specimen
3.2. Experiment Procedure
4. Results and Discussion
4.1. Experiment Results
4.2. Fractal Dimension Analysis of Fractures
5. Conclusions
- By incorporating the fractal dimension into the calculation of the true fracture surface area, termed the ubiquitiform surface area, the energy release rate GC could be derived from the external work and ubiquitiform surface area. The proposed method, accounting for distinct fractal dimensions in different fracture regions, yielded KC values closer to the experimental data compared to utilizing the nominal fracture area.
- The fractal dimensions of the plane stress and plane strain fracture regions were determined separately using the box-counting method. The plane strain region exhibited a higher fractal dimension, indicating greater roughness and tortuosity compared to the plane stress region.
- The fractal dimension in the plane strain fracture region followed a normal distribution. Consequently, the relationship between fracture toughness KC and its dispersion could be quantified through the distribution of fractal dimensions in this region.
- Further research could focus on refining these methods and exploring their applicability to a broader range of materials and loading conditions to generalize the findings.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
a0 | Initial crack length |
Ab | Plane strain fracture region |
Ap | Area of the nominal region |
At | Total area of As and Ab |
As | Plane stress fracture region |
Aauf | Ubiquitiform surface area |
Atuf | Ubiquitiform surface area of the fracture |
B | Specimen thickness |
ΔB | Interval between each curve |
D | Ubiquitiform complexity |
dF | Fractal dimension |
dFi | Fractal dimension of the ith curve |
E | Young’s modulus |
GC | Energy release rate |
i | ith curve |
KC | Fracture toughness |
KCu | Fracture toughness by integrating the fractal dimension and fracture energy |
KIC | Plane strain fracture toughness |
KQ | Conditional fracture toughness |
l | Nominal straight-line length of the two-dimensional crack growth curve |
lF | Corresponding fractal curve length |
luf | Ubiquitiform length |
n | Number of divided crack propagation regions curves |
N(δ) | Number of squares (in box-counting dimension method) |
Pmax | Maximum load |
Pq | Critical load |
W | Width of the specimen |
Wt | Work performed by an external force |
δ | The side length δ of the squares (in box-counting dimension method) |
δe | Elongation |
Tensile strength | |
σy | Yield strength |
v | Poisson’s ratio |
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Mechanical Property | Young’s Modulus E/GPa | Poisson’s Ratio v | Yield Strength σy/MPa | Tensile Strength σb/MPa | Elongation δe |
---|---|---|---|---|---|
Value | 180.3 | 0.32 | 1152 | 1344 | 15.4% |
No. | B (mm) | Ws (mm) | a (mm) | Ws-a (mm) | 2.5(KQ/σy)2 (mm) | Equation (1) Y/N? | KQ |
---|---|---|---|---|---|---|---|
R-15 | 15.38 | 29.99 | 16.38 | 13.61 | 26.42 | N | 118.42 |
R-20 | 20.48 | 39.99 | 21.11 | 18.88 | 30.80 | N | 127.87 |
R-22.5 | 22.88 | 44.97 | 22.41 | 22.56 | 31.70 | N | 129.71 |
R-25 | 25.45 | 50.01 | 25.93 | 24.08 | 29.10 | N | 124.38 |
No. | dFa | Atuf (mm2) | Aauf (mm2) | W (J) | KCu (MPa·m0.5) | KQ (MPa·m0.5) |
---|---|---|---|---|---|---|
R-15-550 | 1.0892 | 317.93 | 316.4387 | 48.6504 | 175.68 | 118.42 |
R-20-550 | 1.1015 | 658.42 | 642.7561 | 72.9385 | 150.94 | 127.87 |
R-22.5-550 | 1.1235 | 1019.8 | 991.1947 | 84.4629 | 130.79 | 129.71 |
R-25-550 | 1.1249 | 1216.76 | 1194.168 | 102.9412 | 131.55 | 124.38 |
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Liu, H.; Yan, J.; Li, A.; He, Z.; Xie, Y.; Yan, H.; Huang, D. A Relationship between Fracture Toughness Kc and Energy Release Rate Gc According to Fracture Morphology Analysis. Crystals 2024, 14, 740. https://doi.org/10.3390/cryst14080740
Liu H, Yan J, Li A, He Z, Xie Y, Yan H, Huang D. A Relationship between Fracture Toughness Kc and Energy Release Rate Gc According to Fracture Morphology Analysis. Crystals. 2024; 14(8):740. https://doi.org/10.3390/cryst14080740
Chicago/Turabian StyleLiu, Haohao, Jinlun Yan, Aofei Li, Zhenyu He, Yuchen Xie, Han Yan, and Dawei Huang. 2024. "A Relationship between Fracture Toughness Kc and Energy Release Rate Gc According to Fracture Morphology Analysis" Crystals 14, no. 8: 740. https://doi.org/10.3390/cryst14080740