CHEN Changrong. Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1172-1179. doi: 10.21656/1000-0887.380191
Citation: CHEN Changrong. Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1172-1179. doi: 10.21656/1000-0887.380191

Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack

doi: 10.21656/1000-0887.380191
Funds:  The National Natural Science Foundation of China(51175321)
  • Received Date: 2017-07-05
  • Rev Recd Date: 2018-03-07
  • Publish Date: 2018-10-01
  • The difference between the J-integrals with and without a crack along a far-field contour was considered to analyze the energy release rate of the crack extension in an infinite plane. Two material cases were studied: a homogeneous material and a layered material. The constant displacement load was applied far from the crack, the crack was assumed to be perpendicular to the load, and the interfaces of the layered material were parallel to the load. The difference between the J-integrals with and without a crack represents the change of the far-field J-integral when a crack is introduced into the loaded material. For the central crack in a homogeneous infinite plane with a unit thickness, the energy release rate is the integral of the released strain energy density along the symmetry axis, and equals the product of the strain energy density without a crack and the perimeter of a circle, where the diameter of the circle is the crack length. For the central crack in an infinite plane of the layered material with a unit thickness, the energy release rate of crack extension equals the integral of the released strain energy density along the symmetry axis minus the change of the interface J-integral.
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