Analysis Of Stresses And Strains Near The End Of A Crack Traversing A Plate Irwinl [Updated]

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By George R Irwin Introduction When a notched beam end is subjected to a vertical load and can be considered as an infinite plate, the following equation is valid: (1) Eq. 1 where is the applied vertical load, is the applied vertical axial stress, is the second normal stress component, is the third normal stress component, is the transverse strain, is the displacement along the crack, is the distance from the crack tip to the neutral plane, is the displacement of the neutral plane, is the first transverse normal stress component, is the first transverse normal stress component, is the second transverse normal stress component, is the first transverse normal stress component, is the second transverse normal stress component, is the second transverse normal stress component, and is the first normal stress component. Equation 1 where the above values and quantities are taken at the crack tip. The effect of the second normal stress component on the crack propagation is the object of the present investigation. The following assumptions are made in carrying out this investigation: (1) the neutral plane of the crack remains in the plane of the original surface of the specimen (for notched specimens only), (2) the shear stresses in the neutral plane are zero, and (3) the first normal stress component is zero. The results given in the present paper are all valid for this particular case only. The following procedures are used to determine the effect of the second normal stress component on the crack tip. One can define a new coordinate system by placing the crack tip in the center of the coordinate system and the crack axis at an angle. The angle must be such that this new coordinate system is orthogonal to the original coordinate system. The following equations of motion for the new coordinate system are valid: (2) Eq. 2 where is the applied vertical axial stress. The expressions for the shear stress in the original and in the new coordinate systems are: (3) Eq. 3 (4) Eq. 4 In the expression for is the area moment of inertia, and in the expression for is the transverse displacement of the crack tip. If one defines: (5) Eq. 5 (6) Eq. 6 then (7) Eq

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