Issue 41

V.Shlyannikov et alii, Frattura ed Integrità Strutturale, 41 (2017) 285-292; DOI: 10.3221/IGF-ESIS.41.38 286 M ULTI - AXIAL RUPTURE BEHAVIOR he many experimental results of uniaxial tension creep rupture tests of structural materials different properties show that the stress rupture time behavior can be accurately described by power-law equation     t A (1) where A and  are constants independent of stress for a given material. Values of  for a variety of materials tested at different temperatures described by an approximate relationship with the Norton equation exponent  = 0.7 n . It has been shown by Hayhurst [1] that under multi-axial loading conditions the constant A should be a function of the stress invariants            1 2 mp t A J J (2) where  mp is the maximum principal tensile stress, J 1 is the first stress invariant,  2 J is the second deviatoric stress invariant,  ,  and  are constants (  +  +  = 1). In terms of principal stresses J 1 and  2 J are given by       1 1 2 3 J ,                        2 2 2 2 1 2 2 3 3 1 1 6 J (3) The most general multi-axial creep rupture criterion is obtained by Pisarenko-Lebedev [2], which unites the limiting state theories in the form of the maximum principal tensile stress and the von Mises condition           2 1 eff mp J (4) in which  is the experimental material constant that is determined as the ratio of uniaxial tensile to compression strength  =  t /  c . For brittle fracture  =0, while for ductile fracture  =1. Hayhurst [1] have mentioned that a general representation of multi-axial creep rupture behavior must exhibit the sensitivity of micro-structural changes to the maximum principal tensile stress and express the stress sensitivity of different materials to final collapse or failure mechanism. The preceding review of creep rupture equations indicates that a general formulation of stress function which satisfies these requirements can be consists two parts:  in the tension-tension quadrant the behavior can be approximated by combination of the maximum hydrostatic stress and an octahedral shear stress criteria                  1 2 1 2 1 1 f D J J fJ f J (5)  in the tension-compression quadrant the behavior can be approximated by combination of the maximum principal tensile stress and an octahedral shear stress criteria in the form of the Pisarenko-Lebedev limiting state theory [2]                    2 2 1 1 mp mp f D J f f J (6) where      1 f ,      1 f (7) By substituting Eq.(3) into (4) and (5) and writing     2 1 , the stress function can be represented in the normalized form:  plane stress                         2 1 1 1 mp f D (8)                      2 1 1 mp f D (9) T