Finite element procedures for crack path prediction in multi-axial fatigue

Rolling Contact Fatigue (RCF) cracks in rails are among the most detrimental railway track defects regarding reliability and cost. The cracks typically grow in shear mode up to a certain length at which they might arrest or kink into a more tensile-driven growth. This growth scheme appears as a result of non-proportional loading, large plastic deformations at the rail surface and primary compression with crack-face friction. In contrast, most existing crack growth criteria in the literature feature quantities that are susceptible to the limitations of small-scale yielding, e.g. Stress Intensity Factors (SIFs),tensile-mode growth and unloaded crack-faces. Consequently, the range of validity of the existing criteria may be questioned in the non-linear crack growth setting of RCF.In a study of the role of inelastic deformation on the crack loading, elastic–plastic simulations are carried out in pre-cracked tubular specimens subjected to mixed-mode cyclic loading. The crack loading is quantified via the Crack-Tip Displacements (CTDs) in modes I and II. Shakedown and ratcheting effects in the ranges of the CTDs are compared to trends of crack growth curves from experiments in the literature. It is concluded that the ranges of the CTDs can be used for qualitative crack growth assessment in the examined load cases. In addition, a gradient-enhanced mixed variational formulation isdeveloped for overcoming the numerical difficulties associated with the computation of Configurational Forces (CFs) for inelasticity. The mesh sensitivity of the CFs acting on an embedded discrete singularity is investigated. Results highlight that the proposed formulation provides sufficient regularity for the computation of CFs, which may then be used in the formulation of criteria for RCF crack propagation.Predictions of the multi-axial fatigue crack path are performed based on instantaneous crack growth direction criteria. To this end, a generic model for load cycle evaluation is proposed and implemented on criteria based on CFs and CTDs. The predicted directions are compared towards mixed-mode fatigue crack growth experiments from the literature. Of the evaluated criteria, the ones based on CFs and CTDs accurately predict the tensile-mode growth. Classical SIF-based criteria seem to handle tensile-mode growth under moderate shear-mode loading. Moreover, the criterion based on CTDs captures the shear-mode growth and the tensile-mode growth as well as the transition between them. The latter growth schemes essentially resemble the RCF crack growth.In an investigation of the influence of various railway operational parameters on predicted RCF crack growth directions, the coefficient of friction at the wheel–rail interface was found the most influential as compared to the wheel tonnage and crack-face friction. The latter had no effect on predicted directions, due to crack-tip opening at the instances of maximum shear CTDs

Numerical predictions of crack growth direction in a railhead under contact, bending and thermal loads

The effect of different operational loading scenarios on predicted crack growth direction for a propagating inclined railhead crack is assessed by 2D finite element simulations. Studied load scenarios include a moving Hertzian contact load, a temperature drop, rail bending due to a passing wheelset, and combinations thereof. The direction of the unbiased crack propagation is predicted using an accumulative vector crack tip displacement criterion. The numerical model is validated for the individual load scenarios. Restraints due to crack face locking are imposed by a threshold parameter, whose influence is also assessed. For combinations of thermal and contact loads, the predicted crack path is found to diverge gradually from transverse growth, corresponding to pure thermal loading, to shallow growth, corresponding to a pure contact load. For combined bending and contact loading, there is a discrete jump in the predicted crack direction as the contact load increased while the bending load is kept constant. These results are well aligned with empirical experience

The effect of inelastic deformation on crack loading

Rolling contact fatigue (RCF) cracks in rails are among the most detrimental railway track defects, in relation to reliability and cost. The cracks grow in a mixed mode II & III, which in combination with the rotating stress field in the neighborhood of the crack-tip, large plastic deformations on the rail surface, crack face friction due to the compressive stresses from the wheel load and anisotropic crack growth resistance, add to the complexity related to the study of RCF cracks. In contrast, most existing criteria for RCF crack propagation in the literature feature quantities that are susceptible to limitations, such as small scale yielding (see e.g. stress intensity factors), pure mode I growth, unloaded crack faces. Consequently, the range of validity (and precision) of existing criteria may be questioned.The current work focuses on one of the complicating factors: the role of inelastic deformation on the crack loading. At the first part, a qualitative assessment is performed of the mechanisms that accompany elastoplastic deformations of multi-axially loaded cracks. For this purpose, numerical simulations are carried out in pre-cracked tubular specimens subjected to torsional and axial loading in various load configurations. Elastoplastic deformations are quantified here via the relative deformation of initially aligned crack faces, here denoted as crack face displacement. The range of the crack face displacement over each load cycle accounts for the severity of the crack situation (in a manner analogous to the range of the stress intensity factor). Results are identified as shakedown and ratcheting effects and compared to experimental trends in literature.The work continues with the study of configurational (or material) forces for gradient-enhanced inelasticity. The severity of the crack loading is here measured via energy release rates (a generalization of the J-integral for inelasticity with material dissipation), which stem from the computed material forces. The mesh sensitivity of the energy release rates is investigated for the cases of a smooth interface and an embedded discrete singularity. Results highlight that the proposed gradient-regularized scheme provides sufficient regularity for the computation of material forces. Obtaining a rather mesh insensitive material force field for inelasticity, is considered a necessary step towards the development of a criterion for RCF crack propagation based on material forces

The effect of inelastic deformation on crack loading

Rolling contact fatigue (RCF) cracks in rails are among the most detrimental railway track defects, in relation to reliability and cost. The cracks grow in a mixed mode II & III, which in combination with the rotating stress field in the neighborhood of the crack-tip, large plastic deformations on the rail surface, crack face friction due to the compressive stresses from the wheel load and anisotropic crack growth resistance, add to the complexity related to the study of RCF cracks. In contrast, most existing criteria for RCF crack propagation in the literature feature quantities that are susceptible to limitations, such as small scale yielding (see e.g. stress intensity factors), pure mode I growth, unloaded crack faces. Consequently, the range of validity (and precision) of existing criteria may be questioned.The current work focuses on one of the complicating factors: the role of inelastic deformation on the crack loading. At the first part, a qualitative assessment is performed of the mechanisms that accompany elastoplastic deformations of multi-axially loaded cracks. For this purpose, numerical simulations are carried out in pre-cracked tubular specimens subjected to torsional and axial loading in various load configurations. Elastoplastic deformations are quantified here via the relative deformation of initially aligned crack faces, here denoted as crack face displacement. The range of the crack face displacement over each load cycle accounts for the severity of the crack situation (in a manner analogous to the range of the stress intensity factor). Results are identified as shakedown and ratcheting effects and compared to experimental trends in literature.The work continues with the study of configurational (or material) forces for gradient-enhanced inelasticity. The severity of the crack loading is here measured via energy release rates (a generalization of the J-integral for inelasticity with material dissipation), which stem from the computed material forces. The mesh sensitivity of the energy release rates is investigated for the cases of a smooth interface and an embedded discrete singularity. Results highlight that the proposed gradient-regularized scheme provides sufficient regularity for the computation of material forces. Obtaining a rather mesh insensitive material force field for inelasticity, is considered a necessary step towards the development of a criterion for RCF crack propagation based on material forces

Air conditioning using ice-banks

108 σ.Στη σύγχρονη εποχή όπου η θερμοκρασία του περιβάλλοντος έχει αυξηθεί αρκετά, κρίνεται απαραίτητος ο κλιματισμός του χώρου εργασίας, έτσι ώστε να υπάρχει καλύτερη απόδοση του εργατικού δυναμικού. Η χρήση των κλιματιστικών μηχανημάτων όμως, είναι αρκετά ενεργοβόρα και απαιτεί μεγάλη ποσότητα ηλεκτρικής ενέργειας. Εκτός των μεγάλων βιομηχανιών και των εμπορικών κέντρων όπου υπάρχουν μεγάλες κλιματιστικές μονάδες, άρα και πολύ ενεργοβόρες, τα τελευταία χρόνια παρατηρούμε μεγάλη αύξηση των κλιματιστικών που χρησιμοποιούνται σε οικιακούς χώρους. Έτσι τους καλοκαιρινούς μήνες όπου η χρήση των κλιματιστικών αυξάνει, η ΔΕΗ έχει πρόβλημα στο να ανταπεξέρθει. Ειδικότερα τις μεσημεριανές ώρες όπου η ζήτηση φτάνει στο μέγιστο (peak). Τότε η ΔΕΗ αναγκάζεται να διακόψει την παροχή ρεύματος για λίγες ώρες σε κάποιες περιοχές, έτσι ώστε να μην υπερφορτωθεί το σύστημα παροχής ενέργειας. Επίσης για την κάλυψη των αναγκών η ΔΕΗ πρέπει να κατασκευάζει νέες μονάδες παραγωγής ενέργειας, οι οποίες έχουν μεγάλο κόστος κατασκευής. Η χρήση παγολεκάνων όμως μπορεί να βοηθήσει σε αυτό το πρόβλημα. Με την χρήση παγολεκάνων γίνεται μετατόπιση των ψυκτικών φορτίων από ώρες υψηλής ζήτησης, σε ώρες χαμηλής ζήτησης. Με αυτό το τρόπο μειώνεται αισθητά το μέγιστο της ζήτησης της ηλεκτρικής ενέργειας στις ώρες αιχμής. Όμως η αγορά των παγολεκάνων έχει μεγάλο κόστος και για να πειστεί ο ιδιώτης και οι βιομηχανίες να τις εγκαταστήσουν πρέπει να υπάρχουν κάποια κίνητρα από την εταιρεία παροχής ηλεκτρικού ρεύματος. Το πιο σημαντικό από όλα τα κίνητρα είναι η προσφορά μειωμένου τιμολογίου κατά τις βραδυνές ώρες λειτουργίας των παγολεκάνων. Θέμα της διπλωματικής είναι η μελέτη περίπτωσης εφαρμογής συστήματος κλιματισμού με παγολεκάνες σε κτίριο γραφείων. Αρχικά περιγράφεται η αρχή λειτουργίας των συστημάτων αποθήκευσης ψύξης και παρουσιάζονται οι διάφοροι τρόποι και οι στρατηγικές αποθήκευσης. . Στη συνέχεια παρουσιάζεται η μελέτη εφαρμογής, όπου εφαρμόζονται διάφορα σενάρια χρήσης των παγολεκάνων, ξεκινώντας από την πλήρη αποθήκευση πάγου και καταλήγοντας σε διάφορες περιπτώσεις μερικής αποθήκευσης πάγου. Στο τέλος παραθέτονται τα οικονομικά στοιχεία για κάθε περίπτωση καθώς και τα έτη που απαιτούνται για την αποπληρωμή της δαπάνης. Γίνεται σύγκριση των αποτελεσμάτων σε σχέση με την συμβατική περίπτωση κλιματισμού (χωρίς τη χρήση παγολεκάνων). Το συμπέρασμα το οποίο καταλήγουμε είναι ότι η χρήση παγολεκάνων συμφέρει κυρίως στην περίπτωση της πλήρους αποθήκευσης πάγου (24ωρης αδιάκοπης λειτουργίας). Ο χρόνος αποπληρωμής της δαπάνης είναι ελάχιστος και η συνεχής λειτουργία του ψύκτη μειώνει το κόστος συντήρησης, αφού ο ψύκτης λειτουργεί αδιάκοπτα σε σταθερή ισχύς. Όμως για να κριθεί η όλη επένδυση συμφέρουσα πρέπει από την εταιρεία παροχής ηλεκτρικής ενέργειας να υπάρχει συμφωνία για οικονομικό τιμολόγιο.In the modern years where the temperature of environment has been increased , it is essential the air conditioning of working place, so as to have better working and living conditions for people.In the modern years where the temperature of environment has been increased , it is essential the air conditioning of working place, so as to have better working and living conditions for people. The use of air-conditionning however requires big quantity of electric energy. Except the big industries and commercial centres where big air-conditionning units exist, hence there is need for much energy , in recent years we observe big increase of airconditioners in domestic spaces. Thus the summer months where the use of airconditioners increases, National Electrical Company has problem to comply with the demand. More specifically at lunch time hours where the demand reaches its peak, the NATIONAL ELECTRICAL COMPANY is forced to interrupt the benefit of current for few hours in certain regions. So to cover the needs, the NATIONAL ELECTRICAL COMPANY has to manufacture new units of production of energy, but they are very expensive to manufacture. The use of ice banks however can help in this problem. With the use of ice banks we can shift cooling charges from hours of high demand, in hours of low demand. With this way we can decrease considerably the demand of electric energy in the hours of big demand. However ice banks are very expensive and in order to convince the private individual and the industries to install them, certain motives should be given . Most important from all motives is the offer of decreased (economic) tariff for energy consumption. Subject of diplomatic is the study of case of application of system of air conditioning with ice banks in a building of offices. Initially we describe the operation of systems of cooling storage and presente the various ways of use of cooling storage. Afterwards we presente the study of application, where we apply various scripts of use of ice banks, beginning from the full cooling storage and leading to various cases of partial cooling storage. In the end we discuss the economic elements for each case as well as the years that are required for the settlement of expense. We compare the results with the conventional case of air conditioning (without the use ice banks). The conclusion is that the use of ice banks is energy efficient mainly in the case of full cooling storage (24 hours continuous operation). The time of settlement of expense is most minimum and the continuous operation decreases the cost of maintainance. However for this it is required,an agreement with decreased (economic) tariff to exist from the company of electric energy.Δημοσθένης Ι. Φλώρο

Computation of material forces based on a gradient-enhanced mixed variational formulation

Configurational (or material) forces are computed based on a previously derived thermodynamically consistent definition of material forces, in conjunction with a gradient-enhanced constitutive theory. The primary problem solved for is based on a mixed variational formulation. Under the proposed mixed formulation, no nodal smoothing of internal variables for the computation of material forces is required at the post-processing. Results are shown in terms of energetic quantities which stem from the computed material forces. The mesh sensitivity of the latter quantities is examined and compared to respective results based on local constitutive theory in a "standard"displacements-based variational formulation

Evaluation of mixed-mode crack growth criteria under rolling contact conditions

Fatigue crack growth direction criteria are evaluated towards a twin-disc experiment from the literature. The experiment is modelled numerically at different crack lengths. Based on numerically evaluated stresses, strains and displacements, a range of crack growth direction criteria from the literature are evaluated and compared to the experimentally found crack growth direction. In the considered experiment, the growth is essentially shear driven. Of the evaluated criteria employed to a linear elastic analysis, the Maximum Shear Stress (MSS) and Vector Crack-Tip Displacement (VCTD) criteria are found to be able to capture the experimentally found crack growth direction throughout the fatigue life

On configurational forces for gradient-enhanced inelasticity

In this paper we discuss how configurational forces can be computed in an efficient and robust manner when a constitutive continuum model of gradient-enhanced viscoplasticity is adopted, whereby a suitably tailored mixed variational formulation in terms of displacements and micro-stresses is used. It is demonstrated that such a formulation produces sufficient regularity to overcome numerical diffi- culties that are notorious for a local constitutive model. In particular, no nodal smoothing of the internal variable fields is required. Moreover, the pathological mesh sensitivity that has been reported in the literature for a standard local model is no longer present. Numerical results in terms of config- urational forces are shown for (1) a smooth interface and (2) a discrete edge crack. The corresponding configurational forces are computed for different values of the intrinsic length parameter. It is concluded that the convergence of the com- puted configurational forces with mesh refinement depends strongly on this parameter value. Moreover, the convergence behavior for the limit situation of rate-independent plasticity is unaffected by the relaxation time paramete