PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1212–1225 Auth r name / Structural Integrity Procedia 00 (2019) 0 0–000

1214

3

3 R and 4 R , and length, a . The

is treated as a beam of ring-shaped cross-section of internal and external radiuses,

4 R , varies linearly along the beam length

radius of the beam cross-section,

l R R R R 1 2 1 4   

x

,

(1)

where

x l   0 .

(2) In (1), x is the longitudinal centroidal axis (Fig. 1). The beam is loaded quickly in torsion at the free end of internal crack arm and then held. The strains in the beam do not change with time. The stresses decrease with time (i.e., the beam exhibits stress relaxation behaviour). The angle of twist of the free end of the internal crack is is denoted by  . The external crack arm is free of stresses.

Fig. 1. Geometry of a continuously inhomogeneous viscoelastic beam with a longitudinal crack of length, a . The beam exhibits continuous material inhomogeneity in both radial and length directions. The shear modulus, 0 G , varies exponentially in radial direction