A THEORY FOR THE FRACTURE OF THIN PLATES SUBJECTED TO BENDING AND TWISTING MOMENTS

Stress fields near the tip of a through crack in an elastic plate unde r bending and twisting moments are reviewed assuming both Kirchhoff an d Reissner plate theories. The crack tip displacement and rotation fie lds based on the Reissner theory are calculated here for the first tim e. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmond s and Duva's [16] result that the value of the J-integral based on eit her theory is the same for thin plates, a universal relationship betwe en the Kirchhoff theory stress intensity factors and the Reissner theo ry stress intensity factors is obtained for thin plates. Calculation o f Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. A small scale yielding like mo del of the crack tip fields is discussed, where the Kirchhoff theory f ields are considered to be the far field conditions for the Reissner t heory fields. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.