A plane elastic–plastic problem of stress distribution in a circular hole thin plate involving initiation and propagation of cracks in an elastic zone, is considered. It is assumed that the stress level is such that the circular hole is entirely enclosed by the plastic deformations zone. The plate material satisfies the Tresca–Saint Venant plasticity condition. It is supposed that cracks initiation and fracture of the plate material occur in the loading process in the elastic zone. Location and size of prefracture zone in the plate material are unknown in advance and are to be determined. The methods of theory of perturbations and theory of singular integral equations are used. As a crack appearance condition, we use the criterion of critical opening of prefracture zone faces. The interface of elastic and plastic deformations and also the location and sizes of crack initiation zones are found.

考虑了圆孔薄板中应力分布的平面弹塑性问题，该问题涉及弹性区域中裂纹的产生和扩展。假定应力水平使得圆形孔被塑性变形区完全包围。板材满足Tresca-Saint Venant可塑性条件。可以认为，在弹性区域的加载过程中，发生了板材的裂纹产生和断裂。板材料中预裂区的位置和大小事先未知，需要确定。使用摄动理论和奇异积分方程的方法。作为裂缝出现条件，我们使用预裂缝区面的临界开口标准。