Some implications of corner point singularities

Finite element modelling and analysis of crack shape evolution in mode-I fatigue Middle Cracked Tension specimens

“…If m = 0, the singularity will also be r À0.5 for all b. For mode-I loading, the increase of m reduces the critical angle, b c [27], which is according the results of Fig. 10b.…”

“…Bazant and Estenssoro [26] determined a crack/surface angle that deviates from perpendicular in a manner consistent with subsurface crack advance and which strengthens the vertex singularity to 0.5. This critical angle (b c ) depends on loading mode and on m. For m = 0.3, b c is 79.6°f or mode-I and 113.0°for mixed mode II + III [27]. If m = 0, the singularity will also be r À0.5 for all b.…”

The Effect of the Free Surface on the Singular Stress Field at the Fatigue Crack Front

“…Averages of measured angles of both materials lie in a range between Pook's [7] and Heyder's curve [10]. Fig.…”

“…Once the critical angle between the free surface and the crack front is reached, the process of fatigue crack shaping is finished and the FCPR is constant along the whole crack front. Critical angle is a function of Poisson's ratio and can be estimated by simple Pook's expression [7].…”

“…Also the square-root singularity is ensured along whole crack front, including the vicinity of vertex point. Characteristic angle can be determined by the Pook's empirical expression [7] = 90°− arctan ( 2− ). Same technique was used for the angle determination for both specimens.…”