Finite Fracture Mechanics and Cohesive Crack Model: Size effects through a unified formulation

Finite Fracture Mechanics and Cohesive Crack Model can effectively predict the strength of plain, cracked or notched structural components, overcoming the classical drawbacks of Linear Elastic Fracture Mechanics. Aim of the present work is to investigate size effects by expressing each model as a unified system of two equations, describing a stress requirement and the energy balance, respectively. Brittle crack onset in two different structural configurations is considered: (i) a circular hole in a tensile slab; (ii) an un-notched beam under pure bending. The study is performed through a semi-analytical parametric approach. Finally, theoretical strength predictions are validated with experimental results available in the literature for both geometries, and with estimations by the point criterion in the framework of Theory of Critical Distances

Finite Fracture Mechanics: Size effects on spheroidal voids and corrosion pits

The present work aims at investigating the size effect of a spheroidal cavity in an infinite linear elastic continuum under remote tension, by means of the coupled Finite Fracture Mechanics (FFM) [1] approach. FFM is a coupled fracture criterion which allows to provide strength predictions based on the simultaneous fulfilment of a stress condition and the energy balance. Although initially proposed and applied only to static problems, FFM was later extended to assess the fatigue limit of structural components [2]. Whereas the static formulation requires the knowledge of the material ultimate tensile strength and of the fracture toughness, both the plain fatigue limit and the threshold value of the stress intensity factor range are needed in the fatigue regime. To implement the FFM, the longitudinal stress field and the Stress Intensity Factor (SIF) related to an annular crack surrounding the spheroidal void, are obtained numerically through a parametric axisymmetric Finite Element Analysis (FEAs). In these analysis, to evaluate the effect of the void geometry, the void axis ratio is varied between 0.1 and 10. Furthermore, to encompass also the influence of the material, different Poisson’s ratios are considered ranging between 0.1 and 0.5. Semi-analytical approximating functions providing the stress concentration factor Kt and the SIF itself are put forward. In the framework of fatigue failure, one of the most important issues is that related to corrosion pitting, a very localized and critical form of damage. Studies focused on this topic have been proposed since the middle of the last century, by approximating the pit shape as in between hemispherical and hemispheroidal. In particular, different works focused on the estimation of Kt, through three-dimensional (3D) FEAs. On the down side, precise 3D FEAs are computationally expensive and thus not adequate for preliminary sizing of structural components. Furthermore, Kt based studies are not able to catch any size-effect according to classical linear elasticity. For these reasons, Härkegård (2015) [3] approximated the fatigue behaviour of a hemispherical pit by that of a spherical cavity in an infinite tensile body. Following this idea, in the present study, the strength estimations, obtained for a spheroidal void in an infinite linear elastic continuum under remote tension, are compared with experimental fatigue data related to corrosion pitting on two different material: (i) 12% Cr martensitic [4] and (ii) 17-4PH turbine-grade steels [5]. References [1] Leguillon D. Strength or toughness? A criterion for crack onset at a notch. Eur J Mech - A/Solids. 2002;21: 61–72. [2] Sapora A, Cornetti P, Campagnolo A, Meneghetti G. Fatigue limit: Crack and notch sensitivity by Finite Fracture Mechanics. Theor Appl Fract Mech. 2020;105: 102407. [3] Härkegård G. Short-crack modelling of the effect of corrosion pits on the fatigue limit of 12% Cr steel. Fatigue Fract Eng Mater Struct. 2015;38: 1009–1016. [4] Salzman R, Gandy D, Rieger N, et al. Corrosion-Fatigue Prediction Methodology for 12% Cr Steam Turbine Blades. In: Volume 1: Fuels and Combustion, Material Handling, Emissions; Steam Generators; Heat Exchangers and Cooling Systems; Turbines, Generators and Auxiliaries; Plant Operations and Maintenance. American Society of Mechanical Engineers; 2013. [5] Schönbauer BM, Stanzl-Tschegg SE, Perlega A, et al. The influence of corrosion pits on the fatigue life of 17-4PH steam turbine blade steel. Eng Fract Mech. 2015;147: 158–175

Finite Fracture Mechanics and Cohesive Crack Model: Size effects through a unified formulation

Finite Fracture Mechanics and Cohesive Crack Model can effectively predict the strength of plain, cracked or notched structural components, overcoming the classical drawbacks of Linear Elastic Fracture Mechanics. Aim of the present work is to investigate size effects by expressing each model as a unified system of two equations, describing a stress requirement and the energy balance, respectively. Brittle crack onset in two different structural configurations is considered: (i) a circular hole in a tensile slab; (ii) an un-notched beam under pure bending. The study is performed through a semi-analytical parametric approach. Finally, theoretical strength predictions are validated with experimental results available in the literature for both geometries, and with estimations by the point criterion in the framework of Theory of Critical Distances