Andrea Carpinteri

Multiaxial high-cycle fatigue criterion for hard metals

Abstract Some multiaxial high-cycle fatigue criteria based on the so-called plane approach are reviewed. According to such an approach, the critical plane where the fatigue life assessment should be performed can be determined by maximising the amplitudes and/or values of some stress components. In the present paper, the critical plane orientation is correlated with the averaged principal stress directions deduced through the weight function method, and new fatigue failure criterion is proposed. The results derived by applying the present criterion and the other critical plane criteria analysed are compared with experimental data related to different brittle (hard) metals under in-phase or out-of-phase sinusoidal biaxial normal and shear stress states.

Shape change of surface cracks in round bars under cyclic axial loading

Abstract An elliptical-arc surface crack in a round bar under cyclic axial loading with constant amplitude is considered. The stress-intensity factor along the crack front is calculated through a finite-element analysis by employing isoparametric solid elements. Then the fatigue crack propagation is examined by means of the Paris-Erdogan law. The aspect ratio a/b of the initial flaw is made to vary from 0.0 (straight crack front) to 1.0 (circular-arc crack front). Moreover, different material properties and loading parameters are considered. For each case being analysed, it is shown that the surface cracks tend to follow preferred propagation paths, with the flaw aspect ratio converging to a value in the range 0.6–0.7.

A fractal analysis of size effect on fatigue crack growth

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structural size, and some theoretical arguments have been proposed to interpret such a phenomenon. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature. In the present paper, by exploiting some concepts of fractal geometry, new definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. Then, a size-dependent crack growth law (expressing crack growth rate against stress intensity factor range) is proposed. Finally, such a law is herein used to interpret relevant experimental data related to concrete.

Expected principal stress directions under multiaxial random loading. Part I: theoretical aspects of the weight function method

As has been observed experimentally by many authors, the position of the fatigue fracture plane appears to strongly depend on the directions of the principal stresses or strains. In Part I of the present work the expected principal stress directions under multiaxial random loading are theoretically obtained by averaging the instantaneous values of the three Euler angles through some suitable weight functions which are assumed to take into account the main factors influencing fatigue behaviour. Then, in Part II, it is examined how such theoretical principal directions determined by applying the proposed procedure are correlated to the position of the experimental fracture plane for some fatigue tests reported in the literature.

Part-through cracks in round bars under cyclic combined axial and bending loading

Abstract Fatigue fracture mechanics concepts can usefully be applied to analyse the propagation of surface cracks in metallic round bars under cyclic combined axial and bending loading. A finite element analysis is carried out to determine the stress field in the case of an elliptical-arc part-through flaw, the aspect ratio, α = a b , of which ranges from 0.0 to 1.2 (α = 0.0 corresponds to the straight front, while α = 1.0 represents the circular-arc front). The fatigue crack growth is numerically examined by means of a two-parameter model based on the Paris-Erdogan law. The propagation paths for different material properties and loading conditions converge to an inclined asymptote in the diagram of α against ξ, where ξ is the relative crack depth of the deepest point on the crack front. Experimental data and theoretical fracture energy considerations reported in the literature validate the results obtained through the above model.

Expected principal stress directions under multiaxial random loading. Part II: numerical simulation and experimental assessment through the weight function method

In Part I of the present work, the theoretical aspects of a proposed procedure to determine the expected principal stress directions under multiaxial random loading have been discussed. This procedure consists of averaging the instantaneous values of the three Euler angles through weight functions. In Part II here, a numerical simulation is presented to illustrate the above theoretical method. As an example, the algorithm proposed is applied to some experimental biaxial in- and out-of-phase stress states to assess the correlation between the expected principal stress directions and the position of the experimental fatigue fracture plane for such tests.

Circumferential surface flaws in pipes under cyclic axial loading

Abstract The behaviour of a circumferential external surface flaw in a metallic round pipe under cyclic axial loading is examined. The defect is assumed to present an elliptical-arc shape with aspect ratio α=a / b ( a , b are the ellipse semi-axes), whereas the relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a , and the pipe wall thickness, t . Thick- and thin-walled pipes are considered. The propagation path of the surface flaw is obtained in the diagram of α against ξ through a two-parameter theoretical model. A simplified model (iso-K criterion) is also applied to predict the stable crack growth. Finally the unstable crack growth process is analysed.

A numerical analysis on the interaction of twin coplanar flaws

In several practical situations, structural components present more than one crack. Such multiple cracks should be considered simultaneously since the interaction phenomenon could produce higher stress-intensity factor (SIF) values with respect to the case of a single crack. In the present paper, the influence of two identical coplanar semi-elliptical surface flaws in a plate with finite width and thickness under various stress distributions perpendicular to the crack faces is numerically analysed. Then the results for such elementary stresses are used to obtain the SIFs for real load cases. Due to the interaction effect, the SIF distribution along the crack front is asymmetric and dependent on the distance δ between the two surface cracks. The distance of non-interaction is evaluated as a function of the crack shape and the crack depth.

Stress intensity factors for straight-fronted edge cracks in round bars

Abstract The stress intensity factors along the crack front are calculated for straight-fronted edge cracks in bars with circular cross-section subjected to tension or bending loading. The results are deduced by means of a three-dimensional finite element analysis and the stress field singular behaviour in the vicinity of the flaw is obtained by shifting the finite element midside nodes near the crack front to quarter-point positions. Different crack depths are examined and the stress intensity factors determined by the present study are compared with those deduced by other investigators.

Part-through cracks in pipes under cyclic bending

Abstract The propagation of a circumferential external surface crack in a metallic round pipe under cyclic bending loading is examined through a two-parameter theoretical model. A finite element analysis is carried out to determine the stress-intensity factor distribution along the front of the flaw, which is assumed to present an elliptical-arc shape with aspect ratio α = a el / b el ( a el , b el =ellipse semi-axes). The relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a , and the pipe wall thickness, t . The parameter R / t , with R =internal radius of the pipe, is made to vary from 1 to 10. The fatigue growth of the surface flaw occurs according to preferred paths in the diagram of α against ξ .