On the overall accuracy of the Modified Wöhler Curve Method in estimating high-cycle multiaxial fatigue strength

The aim of the present paper is to systematically investigate the accuracy of the so-called Modified Wöhler Curve Method (MWCM) in estimating high-cycle fatigue strength of plain and notched engineering materials damaged by in-service multiaxial load histories. In more detail, the MWCM, which is a bi-parametrical critical plane approach, postulates that initiation and Stage I propagation of fatigue cracks occur on those material planes experiencing the maximum shear stress amplitude (this being assumed to be always true independently from the degree of multiaxiality of the applied loading path). Further, the fatigue damage extent is hypothesised to depend also on the maximum stress perpendicular to the critical plane, the mean normal stress being corrected through the so-called mean stress sensitivity index (i.e., a material constant capable of quantifying the sensitivity of the assessed material to the presence of superimposed static stresses). In the present investigation, the overall accuracy of the MWCM in estimating high-cycle fatigue strength was checked through 704 endurance limits taken from the literature and generated, under multiaxial fatigue loading, by testing both plain and notched samples made of 71 different materials. Such a massive validation exercise allowed us to prove that the MWCM is highly accurate, resulting in 95% of the estimates falling within an error interval equal to ±15%

Gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics

According to Gradient Mechanics (GM), stress fields have to be determined by directlyincorporating into the stress analysis a length scale which that takes into account the material microstructuralfeatures. This peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longersingular, even though the assessed material is assumed to obey a linear-elastic constitutive law. Given both thegeometry of the cracked component being assessed and the value of the material length scale, the magnitude ofthe corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by takingfull advantage of those computational methods specifically devised to numerically implement gradient elasticity.In the present investigation, it is first shown that GM’s length scale can directly be estimated from the materialultimate tensile strength and the plane strain fracture toughness through the critical distance value calculatedaccording to the Theory of Critical Distances. Next, by post-processing a large number of experimental resultstaken from the literature and generated by testing cracked ceramics, it is shown that gradient enriched linearelasticcrack tip stresses can successfully be used to model the transition from the short- to the long-crackregime under Mode I static loading

Sulla stima di macro, micro e nano-durezza di materiali metallici mediante analisi elasto-plastiche agli elementi finiti

Il lavoro sintetizzato nel presente articolo si pone come obiettivo primario quello di investigare la possibilità di stimare, mediante un approccio elasto-plastico agli elementi finiti, la durezza dei materiali metallici convenzionali, e questo sia a livello macroscopico, che a livello microscopico, che, infine, a livello nanoscopico. Per verificare validità e accuratezza della metodologia FEM sviluppata, sono state condotte una serie di analisi sperimentali su tre materiali metallici aventi caratteristiche metallurgiche estremamente diverse: una lega d’alluminio (Al 7075-T6), un acciaio a basso tenore di carbonio (BS970-En3B) e, infine, un acciaio austenitico (AISI 316L). L’indentazione Vickers è stata simulata con analisi elasto–plastiche agli elementi finiti considerando carichi di prova nell’intervallo tra 490 N e 490 µN e calibrando le simulazioni numeriche mediante curve monotone tensione–deformazione ottenute da prove di trazione eseguite utilizzando provini sia di dimensione convenzionale che aventi larghezza della zona calibrata dell’ordine dei 100 µm.La sistematica comparazione tra risultati sperimentali e simulazioni numeriche ha posto in evidenza come l’aumentare del valore della durezza misurata al diminuire della dimensione dell’impronta possa essere imputata al ruolo giocato dalla reale morfologia del materiale, ruolo che diventa predominante sulla plasticità convenzionale quando le dimensioni della superficie indentata diventano comparabili con le dimensioni medie della grana cristallina delle leghe esaminate. Tali fenomeni, pertanto, non hanno consentito di estendere l’utilizzo della meccanica del continuo fino ad un livello nanoscopico per determinare correttamente i valori della durezza. Alla luce di questi risultati è stata, però, proposta una semplice metodologia di correzione delle stime eseguite mediante gli elementi finiti che si è dimostrata un valido strumento da utilizzarsi in situazioni di interesse pratico per stimare la durezza dei materiali metallici, indipendentemente dalla dimensione della superficie indentata

On the overall accuracy of the Modified Wöhler Curve Method in estimating high-cycle multiaxial fatigue strength

The aim of the present paper is to systematically investigate the accuracy of the so-called Modified Wöhler Curve Method (MWCM) in estimating high-cycle fatigue strength of plain and notched engineering materials damaged by in-service multiaxial load histories. In more detail, the MWCM, which is a bi-parametrical critical plane approach, postulates that initiation and Stage I propagation of fatigue cracks occur on those material planes experiencing the maximum shear stress amplitude (this being assumed to be always true independently from the degree of multiaxiality of the applied loading path). Further, the fatigue damage extent is hypothesised to depend also on the maximum stress perpendicular to the critical plane, the mean normal stress being corrected through the so-called mean stress sensitivity index (i.e., a material constant capable of quantifying the sensitivity of the assessed material to the presence of superimposed static stresses). In the present investigation, the overall accuracy of the MWCM in estimating high-cycle fatigue strength was checked through 704 endurance limits taken from the literature and generated, under multiaxial fatigue loading, by testing both plain and notched samples made of 71 different materials. Such a massive validation exercise allowed us to prove that the MWCM is highly accurate, resulting in 95% of the estimates falling within an error interval equal to ±15%

The Strain energy density to estimate lifetime of notched components subjected to variable amplitude fatigue loading

In the present paper, the approach based on the strain energy density (SED) averaged over a structural volume is reformulated to estimate the lifetime of notched components subjected to variable amplitude (VA) uniaxial fatigue loading. The accuracy and reliability of the proposed reformulation of the SED approach was checked against a large number of data taken from the literature and generated, under two different load spectra, by testing specimens of carbon steel C40 containing notches of different sharpness. Such a validation exercise allowed us to demonstrate that the extension of the SED approach as proposed in the present paper is capable of accurately estimating fatigue damage in notched components subjected to in-service VA fatigue loading

Evaluation of different techniques in estimating orientation of crack initiation planes and fatigue lifetime under complex multiaxial loading paths

In the present investigation, the accuracy of two methods, i.e., the Shear Strain-Maximum Variance Method (γ-MVM) and the Maximum Damage Method (MDM), in predicting the orientation of the crack initiation planes was checked by considering several results taken from the literature and generated by testing five different metallic materials under complex multiaxial loading. The γ-MVM postulates that the critical plane is that material plane containing the direction experiencing the maximum variance of the resolved shear strain. In contrast, the MDM defines the critical plane as that material plane on which the accumulated damage reaches its maximum value. In the present investigation, the MDM was applied in conjunction with Fatemi-Socie's (FS) multiaxial fatigue criterion, Bannantine-Socie's (BS) cycle counting method, and Miner's linear rule. The validation exercise being performed demonstrated that both the γ-MVM and the MDM were capable of accurately predicting the orientation of the crack initiation planes in the selected metals. Subsequently, the reliability of three different design methodologies suitable for estimating fatigue lifetime of metals subjected to variable amplitude multiaxial loading was assessed quantitatively by using a number of experimental results taken from the literature. In more detail, Methodology A was based on the MDM applied along with the FS criterion, the BS cycle counting method, and Miner's rule. Methodology B made use of the γ-MVM, the FS criterion, the BS cycle counting method, and Miner's linear rule. Finally, Methodology C involved the γ-MVM, the Modified Manson Coffin Curve Method (MMCCM), the classical Rain-Flow cycle counting method, and Miner's linear rule. According to this systematic validation exercise, the usage of these three design procedures was seen to result in satisfactory predictions, with the estimates falling within an error band of three

Crack initiation and propagation paths in small diameter FSW 6082-T6 aluminium tubes under fatigue loading

This paper reports results of fatigue tests of friction stir welded (FSW) aluminium tubes. Relatively small 38 mm diameter tubes were used and hence an automated FSW process using a retracting tool was designed for this project, as the wall thickness of the aluminium tube was similar to the diameter of the FSW tool. This is a more complex joint geometry to weld than the more usual larger diameter tube reported in the literature. S-N fatigue testing was performed using load ratios of R = 0.1 and R = -1. Crack path analysis was performed using both low magnification stereo microscopy and scanning electron microscopy, in order to identify crack initiation sites and to determine the direction of crack propagation. Work is still in progress to follow the crack path through the various microstructural zones associated with the weld. A simple statistical analysis was used to characterize the most typical crack initiation site. This work forms part of a wider project directed at determining multiaxial fatigue design rules for small diameter 6082-T6 aluminium tubes that could be of use in the ground vehicle industry

Fatigue testing and analysis of steel plates manufactured by wire-arc directed energy deposition

Wire-arc directed energy deposition (DED), also known as wire-arc additive manufacturing (WAAM), is a metal 3D printing technique that is recognised for its high efficiency, cost-effectiveness, flexibility in build scales and suitability for the construction sector. However, there remains a lack of fundamental data on the structural performance of WAAM elements, especially regarding their fatigue behaviour. A comprehensive experimental study into the fatigue behaviour of WAAM steel plates has therefore been undertaken and is reported herein. Following geometric, mechanical and microstructural characterisation, a series of WAAM coupons was tested under uniaxial high-cycle fatigue loading. A total of 75 fatigue tests on both as-built and machined coupons, covering various stress ranges and stress ratios (R = 0.1, 0.2, 0.3 and 0.4), have been conducted. The local stress concentrations in the as-built coupons induced by their surface undulations have also been studied by numerical simulations. The fatigue test results were analysed using constant life diagrams (CLDs) and S-N (stress-life) diagrams, based on both nominal and local stresses. The CLDs revealed that the fatigue strength of the as-built WAAM steel was relatively insensitive to the different stress ratios. The S-N diagrams showed that the surface undulations resulted in a reduction of about 35% in the fatigue endurance limit for the as-built WAAM material relative to the machined material, and a reduction of about 60% in fatigue life under the same load level. The as-built and machined WAAM coupons were shown to exhibit similar fatigue behaviour to conventional steel butt welds and S355 structural steel plates, respectively. Preliminary nominal stress-based and local stress-based S-N curves were also proposed for the WAAM steel

Sharp V-notches in viscoplastic solids: strain energy rate density rule and fracture toughness

Different from Neuber’s rule or Glinka’s energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G-NSIF) for sharp V-notch in viscoplastic solids, the concept of SERD for sharp V-notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V-notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V-notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G-NSIF have been discussed. Some typical solutions for SERD and SED for sharp V-notched specimens are investigated