Issue 41

S. E. Ferreira et alii, Frattura ed Integrità Strutturale, 41 (2017) 129-138; DOI: 10.3221/IGF-ESIS.41.18 132 Another less arbitrary and probably more reasonable way to estimate the X displacement of the HRR field origin (needed to remove the strain singularity at the crack tip) uses the strains induced by K max at the crack tip predicted by a suitable strain concentration rule, as described in [19]. In any way, the whole da/dN  K curve can be estimated using only well- defined materials properties, without the need for any data-fitting parameter. Such equations describe the simplest formulation of this CDM, since they apply only to constant SIF range conditions, but this model can be further developed to describe FCG under VAL as well, see [20]. Strip-yield models, on the other hand, numerically estimate the K op needed to find  K eff using the classic Dugdale- Barenblatt's idea [25-26], modified to leave a wake of plastically deformed material around the faces of the advancing fatigue crack. Dugdale's model estimates the plastic zone size in a Griffith plate of an elastic perfectly plastic material under plane stress ( pl-  ) conditions, assuming the pz formed ahead of both crack tips under a given K max work under a fixed tensile stress equal to the material yield strength S Y (neglecting strain-hardening and stress gradients inside the pz ). There are several algorithms based on these ideas [5-9]. The SYM algorithm implemented in this work is based in Newman’s original work [6], but it uses the FCG rule and material parameters specified as in the NASGRO code [27]. The validation of this home-made algorithm was performed by comparing its opening stress predictions under several load conditions with results from the literature [28-29]. Newman’s original SYM calculates pz sizes and surface displacements by superposition of two LE problems: (i) a cracked plate loaded by a remote uniform nominal tensile stress and, (ii) a uniform stresses distributed over surface segments near the crack tip. Fig 2 schematizes the crack surface displacements and the stress distributions around the crack tip at the maximum and minimum loads  max and  min . The plastic zones and the crack wakes left by previous cycles are discretized in a series of rigid-perfectly-plastic 1D bar elements, which are assumed to yield at the flow strength of the material, S FL = ( S Y + S U )/ 2 , to somehow account for the otherwise neglected strain-hardening effects – a first order approximation. These elements are either intact at the plastic zone or broken at the crack wake, keeping residual plastic deformations. If they are in contact, the broken bar elements can carry compressive stresses, and they can yield in compression when their stresses reach  S FL . The elements along the crack face that are not in contact do not affect the crack surface displacements, neither carry stresses. Figure 2 : Crack surface displacements and stress distribution along the crack line according to the SYM [6]. It is important to somehow consider the effects of the actually 3D stresses around the crack tip, caused by transversal plastic restrictions induced by the high strain gradients that act there when the plate is thick and cannot be assumed to work under limiting pl-  conditions. To do so in the 1D SYM, it uses a thickness-dependent constraint factor  to