Sabrina Vantadori

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.

Expected position of the fatigue fracture plane by using the weighted mean principal Euler angles

The expected principal stress axes under multiaxial fatigue loading are determined by averaging the instantaneous Euler angles through suitable weight functions. Then, the fracture plane position is derived from such expected principal stress directions. Three weight functions based on stress parameters are discussed by comparing theoretical predictions with available test results related to six metallic materials under proportional and non-proportional loading. The fatigue fracture plane position under multiaxial loading may be established on the basis of the averaged direction of the maximum principal stress, with such a direction deduced by employing proper weight functions.

Critical Plane Orientation Influence on Multiaxial High-Cycle Fatigue Assessment

In the present paper, the multiaxial fatigue lifetime of structural components failing in the high-cycle fatigue regime is evaluated by employing the modified Carpinteri-Spagnoli (C-S) multiaxial fatigue criterion based on the critical plane approach. In the above criterion, the critical plane position is linked to averaged principal stress directions through an off-angle 8. Then, the fatigue damage parameter used is determined by a nonlinear combination of an equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane. In the present paper, some modifications of the original expression for the off-angle 8 are implemented in the modified Carpinteri-Spagnoli criterion. In particular, modified expressions recently proposed by Lagoda et al. are in accordance with the assumption originally developed by Carpinteri and co-workers, that is, the off-angle is a function of the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress. Such expressions can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical estimations and, only for materials with hard and very hard fatigue behaviour, the modified 8 relationships are shown to yield fatigue lifetime results slightly better than those determined through the original 8 expression.

Analysis of Cracked and Notched Round Bars Under Rotary Bending

The fatigue growth of surface flaws in both smooth and notched round bars subjected to rotary bending was numerically simulated by means of a two-parameter theoretical model proposed by the first author. The stress intensity factor distribution along the crack front was needed in order to apply the model. Therefore, finite element analyses and the superposition principle were used to determine such a distribution for a wide range of crack configurations and any position of the flaw with respect to the bending moment axis. The results related to rotary bending are compared to those related to pulsating cyclic bending, and a qualitative comparison is made with some data reported in the literature.

Life estimation by varying the critical plane orientation in the modified Carpinteri-Spagnoli criterion

The modified Carpinteri-Spagnoli (C-S) criterion is a multiaxial high-cycle fatigue criterion based on the critical plane approach. According to such a criterion, the orientation of the critical plane is linked to both the averaged directions of the principal stress axes and the fatigue properties of the material. The latter dependence is taken into account through a rotational angle, ?. Then, the multiaxial fatigue strength estimation is performed by computing an equivalent stress amplitude on the critical plane. In the present paper, some modifications of the original ? expression are implemented in the modified C-S criterion. More precisely, such modified expressions of ? depend on the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress (in accordance with the original expression), and can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical results in order to verify if the modified ?expressions are able to improve the fatigue strength estimation capability of the modified C-S criterion.

Influence of Residual Stresses on Fatigue Crack Propagation in Pearlitic Cold-Drawn Steel Wires

The aim of the present paper is to evaluate the effect of residual stresses, due to cold-drawing process, on the fatigue crack propagation in a pearlitic steel wire with a V-shaped circumferential notch. In order to analyse the effect of the notch severity on the residual stress distribution, three different values of the notch root radius are examined. The residual stress distributions in the reduced cross-section of such wires are numerically evaluated through FE analyses which simulate the material removing operation in the notched region. The stress-intensity factors (SIFs) related to tension loading and residual stresses are computed. Then, the crack propagation under cyclic tension combined with the residual stresses is analysed by taking into account the above SIF values and the actual stress ratio, which is different from that due to cyclic tension only.

Joined application of a multiaxial critical plane criterion and a strain energy density criterion in low-cycle fatigue

In the present paper, the multiaxial fatigue life assessment of notched structural components is performed by employing a strain-based multiaxial fatigue criterion. Such a criterion, depending on the critical plane concept, is extended by implementing the control volume concept reated to the Strain Energy Density (SED) approach: a material point located at a certain distance from the notch tip is assumed to be the verification point where to perform the above assessment. Such a distance, measured along the notch bisector, is a function of both the biaxiality ratio (defined as the ratio between the applied shear stress amplitude and the normal stress amplitude) and the control volume radii under Mode I and Mode III. Once the position of the verification point is determined, the fatigue lifetime is assessed through an equivalent strain amplitude, acting on the critical plane, together with a unique material reference curve (i.e. the Manson-Coffin curve). Some uniaxial and multiaxial fatigue data related to V-notched round bars made of titanium grade 5 alloy (Ti-6Al-4V) are examined to validate the present criterion.

Review of the Influence of non-singular higher order terms on the stress field of thin welded lap joints and small inclined cracks in plates

In stress analysis of cracked plates, alongside the stress intensity factor which quantifies the singular stress component perpendicular to the crack plane, the role played in crack growth by the constant term parallel to the crack plane, called the T-stress, has been widely investigated by many researchers. There are, however, cases of practical interest where the influence on the stress field of the higher order terms in the series expansion for the crack tip stress field, is not negligible. The main aim of the present investigation is to present and apply a set of equations able to describe more accurately the stress components for those cases where the mode I and mode II stress intensity factors used in combination with the T-stress are unable to characterise with sufficient precision the complete stress field ahead the crack tip. The starting point is represented by the Williams’ solution (Williams, 1957) where stresses as expressed in terms of a power series. An example is investigated of a thin-thickness welded lap joint characterized by various joint width to thickness ratios, in the range of d/t ranging from 0.5 to 5. The present paper indicates that the local stresses as well as the strain energy averaged over a control volume which embraces the slip tip, can be evaluated with satisfactory precision only by taking into account a further four terms besides KI, KII and T-stress.

Fretting High-Cycle Fatigue Assessment through a Multiaxial Critical Plane-Based Criterion in Conjunction with the Taylor’s Point Method

The critical plane-based multiaxial criterion originally proposed by the authors for plain fatigue is here applied to estimate the crack initiation life of fretting high-cycle fatigued structural components. Although fretting fatigue can be regarded as a case of multiaxial fatigue, the common multiaxial fatigue criteria have to be modified to account for the severe stress gradients in the contact zone. Therefore, the above criterion is used in conjunction with the Taylor’s point method to numerically estimate the fatigue life of Ti-6Al-4V and Al-4Cu specimens under cylindrical contacts.

Estimation of fatigue life of selected construction materials under cyclic loading

In the literature, there are many criteria of multiaxial fatigue. They are based on various assumptions and parameters describing the process of fatigue. Among them, there is a special group of criteria based on the concept of critical plane. Some of them in their equations take into account the ratio of normal and shear stresses. Macha has formulated the criterion of maximum normal and shear stress in fracture plane which can be generalised for the scope of random loading of numerous criteria. In the present study authors estimated the fatigue life of several construction materials. For the purposes of the analysis, the authors proposed modified Carpinteri et al. method to find orientation of critical plane, which is used in multiaxial fatigue criterion defined in critical plane. This plane is turned through the angle of ? in relation to the plane defined by maximum normal stresses. In this study authors analyzed the variability calculation of fatigue life, depending on the angle ?. Simulation studies were conducted in which it was assumed that ? ? . For each of the 46 angles, we calculated parameters B and K appearing in the formula defining equivalent stress. Then we calculated fatigue life according to the proposed model for each of the obtained angles ?. Fatigue life analysis was carried out in order to verify which angle ? gives the most similar results.