Three-dimensional fatigue crack propagation by means of first order SIF approximation

In this paper we make use of a closed-form solution for mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on homotopy transformations of a disc. The utilised equations are very accurate when the flaw is a small deviation from a circle. Under the hypothesis of an isolated crack, the SIF at each point of the crack border is calculated to assess the crack shape after propagation. The solution is proposed in terms of the Fourier series and the crack growth rate equation is taken according to Paris' low. Many examples are proposed with the aim of predicting the final shape of different types of embedded planar flaws in butt welded joints under fatigue tensile loading

Stress intensity factor for small embedded cracks in weldments

In the present work, the stress intensity factor (SIF) of embedded small cracks placed at the weld toe is calculated by means of two procedures based on the Oore-Burns integral. In the first approach, the defect is considered as a circular disk and the SIF is evaluated by means of the Oore- Burns weight function. By taking advantage of a suitable change of variable, the singularity of the weight function on the crack border can be removed. In this way, the numerical evaluation of the SIF is possible without the use of specific integration algorithms, although the nominal stress field becomes singular when the crack approaches a V-sharpe notch. As an example, the obtained equations are applied to a defect located in the neighbourhood of a weld toe with an opening angle of 135 degrees under mode I loading. Subsequently, for a crack similar to a star domain with a border expressed by means of the Fourier series, the SIF is given by means of an explicit equation based on the Oore-Burns weight function

Il gradiente implicito nella verifica a fatica di giunzioni saldate sollecitate a fatica

L’incremento delle potenzialità di strumenti per la progettazione assistita (come modellatori solidi e strumenti per FEA in grado di gestire modelli molto complessi) permette di ipotizzare lo sviluppo di strumenti numerici specifici per la previsione della resistenza a fatica delle giunzioni saldate. Tali strumenti potrebbero essere in grado di valutare l’influenza di geometria e carichi senza la necessità di elaborazioni successive, e spesso, del progettista (come nelle tensioni di Hot Spot). Il presente lavoro propone una metodologia di calcolo adatta alla previsione della vita a fatica di giunzioni saldate complesse. Un indice di resistenza è ottenuto innanzitutto risolvendo il problema tensionale completamente in modo numerico (agli elementi finiti) . La previsione della resistenza a fatica, è calcolata facendo uso di un modello analitico basato sul gradiente implicito che assume come tensione efficace la tensione equivalente non locale derivante dalla tensione principale. Dapprima verrà tarato il metodo su prove sperimentali eseguite su giunzioni saldate a croce, successivamente il metodo verrà utilizzato per la verifica a fatica di giunzioni saldate più complesse a sviluppo tridimensionale

On the notch sensitivity of cast iron under multi-axial fatigue loading

This work deals with the notch sensitivity of sharp notches under multi-axial fatigue loading. The main discussion concerns the differences in notch sensitivity at high cycle fatigue regime, between tensile, torsional and combined loading. For this comparison, this paper considers a large set of fatigue experimental tests and several computing simulations analyzed with several notch theories for predicting fatigue life of a component. The considered experimental data, taken from literature, deal with the fatigue behavior of cast iron circumferentially V-notched specimens under tension, torsion, and combined loading mode. This paper tries toapply several techniques for theoretical strength assessment and to compare different procedures. The examined procedures need the computation of many parameters, focusing on the importance of using the tensile resistance to set these parameters or using both tensile and torsion resistances. However, the improvements obtained by means of the more complex procedures are not noteworthy, compared to the overall scatter. In author's opinion, the differences in notch sensitivity under tensile and torsional loading remain questionable

A brittle fracture criterion for PMMA V-notches tensile specimens based on a length-enriched eXtended Finite Element approach

A criterion for the prediction of the static failure loads in tensile PMMA specimens with sharp notches is presented. The proposed criterion is based on a regularized version of the eXtended Finite Element Method (XFEM), which has been previously applied to concrete-like materials. The main feature of the proposed approach is that the cracking process is not treated as a local process, but it is modeled by assuming that macro-cracks stem from the interaction of micro-cracks within a finite width process zone. The case of a brittle materials with thin process zone is tackled by assuming one layer of enriched finite elements. Preliminary results concerning PMMA specimens subjected to mode-one loading are presented

Previsione della resistenza a fatica in saldature per punti attraverso modellazione solida

Nel presente lavoro vengono messi a confronto due metodi idonei per la verifica di giunzionisaldate per punti: il metodo del raggio di raccordo fittizio ed il metodo del gradiente implicito. Il primo imponeun raggio di raccordo diverso da zero al piede o alla radice del cordone di saldatura, il secondo, invece,considera più semplicemente la saldatura come un intaglio acuto. Il confronto è fatto sulla capacità di prevederel’affidabilità di giunti saldati per punti in acciaio aventi spessore variabile da 0.8 a 1.5 mm. Tali giunti sonosollecitati a taglio (giunti a semplice sovrapposizione) o a trazione (giunti a tazza). Infine, è discussa lacondizione di convergenza delle analisi numeriche necessarie, in entrambi i metodi, per il calcolo di una tensioneequivalente da porre a confronto direttamente con la di resistenza a fatica del materiale

a preliminary investigation of strength models for degenerate graphite clusters in grey cast iron

Abstract Defects morphology primarily affects the mechanical properties of grey cast iron. In large castings, porosity and clusters of degenerate graphite are heterogeneously dispersed into the ferrous matrix and serve as initiation sites for fatigue and fracture processes. Strength and toughness of nodular cast iron compare to many grades of steel but experiments show that nodular cast iron also exhibits some specific effects, different from those typical of steels and due to cast iron microstructural inhomogeneity. In the present communication, we report on a preliminary investigation aimed at correlating the effect of the graphite microstructure to the mechanical properties of the material via a simplified geometrical description of the defects

Il gradiente implicito nella verifica a fatica di giunzioni saldate sollecitate a fatica

L’incremento delle potenzialità di strumenti per la progettazione assistita (come modellatori solidi e strumenti per FEA in grado di gestire modelli molto complessi) permette di ipotizzare lo sviluppo di strumenti numerici specifici per la previsione della resistenza a fatica delle giunzioni saldate. Tali strumenti potrebbero essere in grado di valutare l’influenza di geometria e carichi senza la necessità di elaborazioni successive, e spesso, del progettista (come nelle tensioni di Hot Spot). Il presente lavoro propone una metodologia di calcolo adatta alla previsione della vita a fatica di giunzioni saldate complesse. Un indice di resistenza è ottenuto innanzitutto risolvendo il problema tensionale completamente in modo numerico (agli elementi finiti) . La previsione della resistenza a fatica, è calcolata facendo uso di un modello analitico basato sul gradiente implicito che assume come tensione efficace la tensione equivalente non locale derivante dalla tensione principale. Dapprima verrà tarato il metodo su prove sperimentali eseguite su giunzioni saldate a croce, successivamente il metodo verrà utilizzato per la verifica a fatica di giunzioni saldate più complesse a sviluppo tridimensionale

Mode I Stress Intensity Factors for triangular corner crack nearby intersecting of cylindrical holes

The paper deals with the Stress Intensity Factor assessment of cracks at the intersection of holes loaded by internal pressure. Triangular flaws are considered at the intersection of two holes inside a specific specimen. The research examines the influence of hole diameter ratio D1/D2 and the angle between their axes ?. Numerical analysis is performed to determine the Stress Intensity Factors (SIF) of mode I in many different geometric configurations.The actual shape of a real crack nucleated at the intersection of two cylindrical holes is subject to variableinternal pressure and is usually geometrically complex. The Stress Intensity Factor changes along the crackcontour and the crack shape development is controlled by its local value, e.g. during a fatigue loading. Ingeneral, the estimation of the Stress Intensity Factors of cracks with a complex shape is made by means ofnumerical methods since closed form solutions in literature are limited. However, in order to solve the problemof crack propagation more quickly, in the case of a crack corner at the intersection between two cylindricalholes, we can assume, in agreement with scientific literature, a symmetrical triangular crack shape and the Stress Intensity Factor are only calculated at the middle of the crack. Obviously, this is a strong approximation, but this allows a reduction in the computation effort for crack growth rate assessments and safety evaluation.In this paper, the weight function technique is used by integrating the actual stress field evaluated in the uncracked model. The method of the weight function is of general validity and the weight function is related to the displacement components close to the crack front, as proposed by Bueckner and Rice. From a computational point of view, the use of the three-dimensional weight function is complex and in scientific literature a weight function of general validity is not available. Nevertheless, thanks to the work conducted by Petroski and Achenbach, Shen and Glinka, an efficient generalised weight function has been adopted and then developed by Sha and Yang [9], which considers a series expansion of non-singular terms. In this way, the integration of the weight function, multiplied by a nominal stress, is made along a line and not in a two-dimensional domain. In this preliminary work, according to Herz et al., we consider a weight function with three terms by assuming a priori the coefficients of the second and third non-singular terms. This contribution is essentially an extension of a previous paper by Herz et al. They only considered the case of D1/D2=1 and ?=90° (Di are the diameters of the two cylindrical holes and a is the angle between their axis). Here, we extend the analysis to D1/D2 equal to 2, 4 and 8 with an ? of 60 and 45 degrees.  With the aid of three-dimensional modelling, an accurate FE model of a triangular corner crack at differentcrack depths has been made. Subsequently, by using ANSYS finite element software, it is possible to employ thecommand KCAL that evaluates the Stress Intensity Factors in the middle of the crack. Subsequently, acomparison between numerical FE results and the analytical results, giving the values of the unknowncoefficients of the weight function (the unknown coefficient is indicated in the paper as M1).As reported in the tables, the accuracy of the weight functions in SIF predictions is about 5% despite the strongsimplification previously introduced in the model. This result is considerable because it is possible to determinethe Stress Intensity Factor of a triangular shaped crack by a line integral of a stress profile in a model withoutconsidering the crack

Previsione della resistenza a fatica in saldature per punti attraverso modellazione solida

Nel presente lavoro vengono messi a confronto due metodi idonei per la verifica di giunzionisaldate per punti: il metodo del raggio di raccordo fittizio ed il metodo del gradiente implicito. Il primo imponeun raggio di raccordo diverso da zero al piede o alla radice del cordone di saldatura, il secondo, invece,considera più semplicemente la saldatura come un intaglio acuto. Il confronto è fatto sulla capacità di prevederel’affidabilità di giunti saldati per punti in acciaio aventi spessore variabile da 0.8 a 1.5 mm. Tali giunti sonosollecitati a taglio (giunti a semplice sovrapposizione) o a trazione (giunti a tazza). Infine, è discussa lacondizione di convergenza delle analisi numeriche necessarie, in entrambi i metodi, per il calcolo di una tensioneequivalente da porre a confronto direttamente con la di resistenza a fatica del materiale