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Outline
In the phase field fracture method, the crack is represented by defining an order parameter, and the governing equation describing the crack development is obtained by using the minimum energy variational principle for the system. In this paper, the framework of phase field theory was established through the derivation of governing equations, including the establishment of phase field fracture damage evolution equation and boundary conditions based on the energy principle. Tensile and shear simulations were carried out on a plate with a notch, and the fracture path and support reaction were in good agreement with the results reported in the literature. The crack propagation of lithium-ion batteries with different diameters of silicon anode during charging was simulated using the phase field method. Results show that the large-diameter (400 nm) silicon particles quickly exhibit crack during charging due to the large tensile stress on their surfaces, and the crack propagates inwards. The fracture energy release rate has a great influence on the crack propagation, and a small energy release rate results in more crack initiation points and a high crack density. In comparison, internal fracture appears in small-diameter (100 nm) silicon particles during charging, and the fracture time is earlier than that of large-sized silicon particles.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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