Mechanics in Engineering ›› 2019, Vol. 41 ›› Issue (4): 445-448.doi: 10.6052/1000-0879-18-486

• Research on Education • Previous Articles     Next Articles


HU Hengshan,SONG Yongjia   

  1. Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001,China
  • Received:2018-12-10 Online:2019-08-27 Published:2019-08-26
  • Contact: HU Hengshan


The stress transformation formula, which is also called the Cauchy's formula for stresses on slanted surfaces, is widely used in solid mechanics. No explicit statement has been found on its limitations in application. The stresses at the sharp point of a V-shaped free-surface notch on a bar under axial loading at both ends are examined as an example. With the two intersecting surfaces being free, it is deduced from the transformation equations that the sharp point is stress free. This deduction is however contradictory to the fact that the stress concentrates near the sharp point. Clearly the stress transformation formula leads to incorrect results and thus is not valid at that sharp point. It is known that if the stress transformation formula is valid, the stress components constitute a stress tensor, but the stress at the sharp concave corner is shown to be discontinuous and double-valued. It is further pointed out that stress transformation formula is not applicable to any point where a stress component has discontinuity or lacks of uniqueness at a surface passing through that point. The tip of any crack is the case.

Key words: stress transformation, stress element, V shaped cut, stress tensor, single-valued

CLC Number: 

  • O34