The Mathematical Thsory of Equilibrium Cracks in Brittle Fracture BY G . I . BARENBLATT Institute of Geology and Development of Combustible Minerals of the U.S.S.R. Academy of Sciences. Moscow. U.S.S.R.' Page I . Introduction ............................ 56 62 89 69 73 74 I1 . The Development of the Equilibrium Crack Theory .......... I11 . The Structure of the Edge of an Equilibrium Crack in a Brittle Body . . 1 . Stresses and Strains Near the Edge of an Arbitrary Surface of Dis- continuity of Normal Displacement ................. 2 . Stresses and Strains Near the Edge of an Equilibrium Crack ..... 3 . Determination of the Boundaries of Equilibrium Cracks ....... IV . Basic Hypotheses and General Statement of the Problem of Equilibrium Cracks ............................... 1 . Forces of Cohesion; Inner and Edge Regions; Basic Hypotheses ... 2 . Modulus of Cohesion ....................... 3 . The Boundary Condition at the Contour of an Equilibrium Crack . . 5 . Derivation of the Boundary Condition at the Contour of an Equilibrium Crack by Energy Considerations .................. 8 . Experimental Confirmation of the Theory of Brittle Fracture; Quasi-Brittle Fracture ........................... 7 . Cracks in thin Plates ....................... 4 . Basic Problems in the Theory of Equilibrium Cracks ........ 76 76 80 81 82 84 85 89 V . Special Problems in the Theory of Equilibrium Cracks ......... 90 1 . Isolated Straight Cracks ...................... 90 2 . Plane Axisymmetrical Cracks ................... 98 3 . The Extension of Isolated Cracks Under Proportional Loading; Stability of Isolated Cracks ........................ 97 4 . Cracks Extending to the Surface of the Body ........... 103 5 . Cracks Near Boundaries of a Body; Systems of Cracks ....... 107 8 . Cracks in Rocks ......................... 112 ......... 114 1 . Wedging of an Infinite Body ................... 114 2 . Wedging of a Strip ........................ 119 3 . Dynamic Problems in the Theory of Cracks ............ 121 References ................................ 125 VI . Wedging; Dynamic Problems in the Theory of Cracks * Present address: Institute of Mechanics. Moscow State University. Moscow. USSR . 56
The Mathematical Thsory of Equilibrium Cracks in Brittle Fracture
May 20, 2023
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