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This Ph.D. thesis was written under the supervision of Assoc. prof. Pavel Hutař, Ph.D., and Assoc. prof. Luboš Náhlík, Ph.D. The thesis is focused on the effect of plasticity induced crack closure, its characteristic and ways of numerical modelling. Premature fatigue crack closure has a significant effect on the fatigue crack propagation rate and therefore on the residual lifetime of a structure. A three-dimensional numerical model allows a detailed look at the stress and strain distribution along the crack front, and particularly it allows a local description of parameters along the crack front which governs the fatigue crack propagation rate. In the first part of the thesis, the study is focused on the influence of a singular stress field at the vicinity of the free surface on the crack front curvature without crack closure being involved. In the second part, a numerical model in 2D of plasticity induced crack closure was created and verified by experimental results. In the final part, a 3D numerical model is used to describe the influence of the crack closure on its fatigue propagation rate and explains typical crack front curvature. The suggested technique allows quantitative accuracy improvement of numerical simulation of the fatigue crack propagation and therefore, more reliable estimation of the residual lifetime of the cracked structure.

In the past, the disagreement of near-threshold fatigue-crack growth (FCG) rate data generated from constant Kmax tests, high load ratio (minimum to maximum load) constant R tests, and ΔKeff based data was a mysterious issue. Because of the disagreement, a variety of test or analysis methods were created to correlate FCG rate data. It was suspected that the ASTM threshold test method using load reduction was inducing remote crack closure due to plastically deformed material, which caused elevated thresholds and slower rates than steady-state behavior. The first goal of this study was the development of a test method to eliminate remote closure during threshold testing. In order to avoid/minimize remote closure effect, compression-precracking methods were used to initiate a crack from a starter notch on compact specimens. Two materials with different fatigue crack surface profiles (flat or very rough) were tested and the results generated from the conventional ASTM precracking method and the compression-precracking test method were compared. In order to understand the disagreement of near-threshold data, crack-opening load measurements were performed from locally (near crack tip) installed strain gages instead of the remote gage (i.e., back face gage). Some careful specimen preparations were performed to avoid out-of-plane bending, to maintain straight crack fronts, and to ensure testing system linearity. It was known that remote gages, such as crack-mouth- opening-displacement-gages were insensitive to measuring load-strain records near threshold. By using local gages, the crack closure effects were clearly observed even in high load ratio (R) tests, like or higher than R = 0.7, and constant Kmax tests, which were believed to be crack closure free. By measuring load-reduced-strain records from local gages, crack-opening loads were able to correlate FCG rate data and showed that ΔKeff-rate data was unique for a wide variety of materials. By comparing (ΔKeff)th values, it may provide reasonable guidance for the material resistance against FCG. Because of “high R crack closure”, some theories considered in the past may need to be reconsidered. First, constant Kmax tests are not entirely crack-closure free. Second, there is no critical load ratio, Rc, to indicate the transition from crack-closure affected to crack-closure free data, and Kmax effects that appear in ΔKth-Kmax relations. Research has shown that the three dominate crack-closure mechanisms (plasticity-, roughness- and debris-induced crack closure) FCG rate behavior in the threshold regime from low to high load ratios.

Fretting fatigue is a damage process that may arise in engineering applications where small cyclic relative displacements develop inside contacts leading to detrimental effects on the material fatigue properties. Fretting is located in regions not easily accessible, which makes it a dangerous phenomenon. It is therefore important to be able to make reliable predictions of the fretting fatigue lives. The work presented in this thesis has its focus on different aspects related to fretting fatigue in the titanium alloy Ti-17. A fretting experiment was developed which allowed for separate control of the three main fretting loads. Initially, the evolution of the coefficient of friction inside the slip region was investigated experimentally and analytically. Subsequently, 28 fretting tests were performed in which large fatigue cracks developed. The fretting tests were firstly evaluated with respect to fatigue crack initiation through five multiaxial fatigue criteria. The criteria predicted a too high fretting fatigue limit. A possible clue to the discrepancy was found in the fretting induced surface roughness with the asperity-pit interactions. The fatigue growth of the large fretting cracks was numerically modelled through a parametric crack growth procedure. The predicted lives were compared to the experimental outcome. The numerical simulations showed that linear elastic fracture mechanics was an appropriate tool for the prediction of fretting fatigue propagation lives in the long crack regime. Fatigue cracks spend most of their propagation life in the small crack regime. The possibility of modelling the small crack behaviour is therefore very important from the engineering point of view. The fatigue growth of through thickness short cracks was studied experimentally and numerically in the four-point bend configuration. It was found that linear elastic fracture mechanics and closure-free material growth data furnished conservative estimates for cracks longer than 50 μm. One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental results on fretting life with or without shot peening were simulated. The fatigue life enhancement in shot peened specimens could be explained by slower crack growth in the surface material layer with residual compressive stresses. / QC 20100827

Τα δομικά στοιχεία των μηχανολογικών κατασκευών υπόκεινται σε επαναλαμβανόμενες κυκλικές καταπονήσεις, από τις οποίες δημιουργούνται και διαδίδονται ρωγμές. Οι καταπονήσεις αυτές, οι οποίες προκαλούν κόπωση στις κατασκευές, μπορεί να είναι είτε καθαρά μηχανικές είτε θερμικές ή να προκύπτουν σα συνδυασμός θερμικής και μηχανικής φόρτισης. Τυπικές περιπτώσεις θερμικών και θερμομηχανικών φορτίσεων εμφανίζονται σε κατασκευές, όπως σωλήνες κυκλωμάτων ψύξης, πιεστικά δοχεία, συνιστώσες ηλεκτρικών κυκλωμάτων, θάλαμοι μηχανών εσωτερικής καύσης και πτερύγια στροβιλοκινητήρων. Η κυκλική μεταβολή του θερμικού φορτίου στις προαναφερθείσες περιπτώσεις, συνιστά συνθήκες θερμικής κόπωσης. Επίσης, λόγω της σχετικά υψηλής συχνότητας του φορτίου η θερμοκρασία παρουσιάζει έντονη μεταβολή στο χώρο και στο χρόνο. Ο προσδιορισμός της διάρκειας ζωής ενός δομικού στοιχείου κατά τη φάση του σχεδιασμού μπορεί να γίνει με τη βοήθεια πειραματικών διαδικασιών. Τα πειράματα όμως κόπωσης είναι δαπανηρά και χρονοβόρα και προφανώς απαιτούνται περισσότερες από μια πειραματικές δοκιμές. Οπότε, είναι εύλογο να υπάρχουν υπολογιστικά εργαλεία που να δίνουν τη δυνατότητα στο μηχανικό να εκτιμήσει την διάρκεια ζωής ή τη σοβαρότητα της βλάβης ενός εξαρτήματος. Τα περισσότερα υπολογιστικά μοντέλα αναφέρονται σε καθαρά μηχανικές καταπονήσεις. Έτσι υπάρχει πρόσφορο έδαφος για την ανάπτυξη υπολογιστικών εργαλείων για την ανάλυση προβλημάτων θερμικής και θερμομηχανικής κόπωσης. Τέτοιου είδους εργαλεία θα πρέπει να λαμβάνουν υπόψη το κλείσιμο των ρωγμών, που συμβαίνει λόγω των θερμικών παραμορφώσεων, διότι είναι δυνατόν να επηρεάζεται τοπικά το θερμοκρασιακό πεδίο. Επομένως, χρειάζεται επαναληπτική διαδικασία για τον προσδιορισμό του θερμικού και τασικού πεδίου που αλληλεπιδρούν. Είναι προφανές ότι η ανάλυση της θερμικής κόπωσης εξελίσσεται σε συνθέτη διαδικασία, που θα πρέπει να συμπεριλαμβάνει τον υπολογισμό της κατανομής της θερμοκρασίας, την τοπική επίδραση του άκρου της ρωγμής στο τασικό πεδίο καθώς και την επαφή των επιφανειών της ρωγμής. Η μέθοδος των συνοριακών στοιχείων είναι ικανή να αντιμετωπίζει τέτοιου είδους τοπικές επιδράσεις. Η παρούσα διατριβή επικεντρώνεται στην ανάπτυξη υπολογιστικού εργαλείου βασισμένου στα συνοριακά στοιχεία, για την πρόβλεψη της διάδοσης ρωγμών και την εκτίμηση της διάρκειας ζωής, εξαρτημάτων υπό θερμική και θερμομηχανική κόπωση. Έμφαση δίνεται σε περιπτώσεις που το θερμικό φορτίο προκαλεί κλείσιμο της ρωγμής και σε περιπτώσεις διεπιφανειακών ρωγμών, όπου το θερμοκρασιακό πεδίο επηρεάζεται από την θερμική αντίσταση ανάμεσα στις επιφάνειες της ρωγμής. Στο πρώτο κεφάλαιο γίνεται βιβλιογραφική ανασκόπηση σε εργασίες που εστιάζουν σε φαινόμενα κόπωσης και διάδοσης ρωγμών, καθώς και στην ανάπτυξη υπολογιστικών μοντέλων για την πρόβλεψη της διάδοσης ρωγμών. Επιπλέον, προσδιορίζεται λεπτομερώς το αντικείμενο της παρούσας διατριβής και εξηγείται η συνεισφορά της και τα καινοτόμα σημεία της. Στο δεύτερο κεφάλαιο περιγράφεται η ιδιόμορφη συμπεριφορά του άκρου της ρωγμής, δίνονται οι διατυπώσεις των μεγεθών θραύσης που χρησιμοποιούνται στην ανάλυση της κόπωσης και αναφέρονται τρόποι με τους οποίους μελετάται η διάδοση ρωγμών. Στο τρίτο κεφάλαιο περιγράφονται λεπτομερώς οι ολοκληρωτικές συνοριακές διατυπώσεις για την επίλυση προβλημάτων θερμοελαστικότητας. Στο τέταρτο κεφάλαιο περιγράφονται οι υπολογιστικές διαδικασίες που ακολουθούνται στην παρούσα εργασία για τον προσδιορισμό του πεδίου θερμοκρασιών και μετατοπίσεων, καθώς και ο τρόπος που προσομοιώνεται η διάδοση ρωγμής. Στο πέμπτο κεφάλαιο παρατίθενται τα αποτελέσματα που προέκυψαν από τις αναλύσεις για διάφορες περιπτώσεις, ενώ στο έκτο κεφάλαιο εξάγονται συμπεράσματα και διατυπώνονται προτάσεις για μελλοντική έρευνα. / The prediction of fatigue life is essential for the integrity and reliability of a structure when designing engineering components that undergo cyclic loading. In most cases, the mechanical cyclic loads are taken into account in order to evaluate the life and damage tolerance of structures with existing cracks. However, there exists a category of structures that experience severe thermal cycling that acts alongside the mechanical loads. Such structures include cooling system pipes, pressure vessels, pistons and combustion chambers of internal combustion engines, gas turbine blades and components of electrical circuits. Interfacial crack growth is of paramount importance when designing components that are protected by thermal barrier coatings in order to increase their endurance and efficiency. These types of structures are exposed to very intense thermo-mechanical cycling, which gradually causes delamination and eventually leads to spallation of the coating Numerical simulations, via the finite element method, are a common trend, when analysing the endurance of coated components. However, important aspects such as the heat exchange between the contacting faces and friction are not taken into account in fracture assessments of these components. The boundary element method is very attractive for crack-growth analyses because only the boundary is meshed, rather than the whole domain of the problem. In the present thesis, the boundary integral equations of uncoupled, time-dependent thermo-elasticity are employed to account for the time-varying nature of the thermal load. Our study discusses the influence of crack closure on quasi-static, sub-critical crack extension in the presence of thermo-mechanical cyclic loading. Appropriate thermal and mechanical boundary conditions are imposed on the numerical model to account for the contact state. The validity of the code to compute the temperature distribution under thermal cycling is checked through analytical solutions. Afterwards, a pure mode-I and mixed mode fracture problems in homogeneous material are analysed and the results are compared to other boundary element solutions. The singularity resulting from tractions and heat flux around the crack tip is effectively captured by singular quarter-point elements, while the fracture magnitudes can be computed using appropriate traction formulas. In these problems, the fatigue life is evaluated in terms of load cycle when the crack closure is considered. The number of cycles required for an existing crack to grow a certain length can be empirically predicted using the Paris’ law. The crack extension angle is evaluated by means of the maximum circumferential stress. The results are discussed, clearly indicating the impact of crack closure on fatigue life evaluation. The main conclusion is that crack closure should be incorporated into the analysis whenever the contact effect is inevitable. Otherwise, the fatigue life may be underestimated, leading to a conservative design. Finally, the sub-domain boundary element procedure is applied to interfacial cracks where the crack closure is more pronounced. Specifically, a case of a thermal barrier coating system is investigated. The thermal resistance between the contacting crack faces is incorporated into the procedure and it is assumed to be dependent on the contact pressure. If crack closure due to thermal distortion takes place, then the displacement and traction field may affect the heat flux between the crack faces, and the thermal and mechanical parts of the problem will need to be solved repeatedly until thermo-mechanical convergence is achieved. The results suggest that there are significant effects on the behaviour of stably growing cracks and the evaluation of failure capacity, emanating from crack closure, the amount of thermal resistance and the phase angle between the mechanical and thermal loads.

[pt] Após identificar que uma trinca de fadiga permanecia fechada durante parte do ciclo, Elber assumiu que o dano era induzido apenas pela fração do carregamento acima da carga necessária para abrir a trinca. Diversos modelos foram propostos utilizando o Delta Keff como força motriz da propagação, como os modelos da faixa plástica (strip-yield), que são amplamente utilizados para prever vida residual de componentes trincados. Embora o fenômeno do fechamento da trinca esteja provado, sua real importância na propagação da trinca de fadiga ainda é controversa. Outros mecanismos, além do fechamento da trinca, foram utilizados na tentativa de explicar os efeitos de sequência do carregamento na propagação em amplitude variável como o campo de tensão residual à frente da trinca. Mesmo após mais de 50 anos de pesquisas desde a proposição da primeira regra de propagação por Paris ainda não há consenso nem sobre o mecanismo nem sobre a modelagem. Esse trabalho tem como objetivo apresentar uma modelagem para prever propagação da trinca de fadiga com base na hipótese de que o dano acumulado por deformação plástica seria a força motriz para propagação. A modelagem proposta se diferença de outros modelos de acúmulo de dano por permitir que o contato existente entre as superfícies da trinca exerça influência sobre as deformações plástica à frente de sua ponta. Os resultados mostram que a modelagem proposta possui capacidade de reproduzir curvas de propagação semelhante ao modelo strip-yield. / [en] After identify that a fatigue crack remains closed during part of the load cycle, Elber assumed the damage was induced only by the cycle part over the load required to open the crack. Several models were developed based on Delta Keff as the strip-yield ones, which are widely used to predict residual lives of cracked components. Although the crack closure phenomenon is well proven its actual significance for the propagation is still controversial. Others mechanisms, beyond the crack closure, were used in trying to explain the sequence effects on variable amplitude crack propagation like the residual stress field ahead of the crack tip. However even after more than 50 years of research since the first propagation rule proposed by Paris there is no neither about the mechanism neither about modelling. This work has the aim of present a modelling to predict fatigue crack growth based on the hypothesis that the damage accumulated by cyclic plastic strain would be propagation the drive force. The modelling proposed differs from others damage accumulation models by allowing the existed contact between the crack surfaces to exercise its influence on plastic strain ahead of the crack tip. The results show that the proposed model is able to reproduce propagation curves similar to the model strip-yield.

Finite element analyses are frequently used to model growing fatigue cracks and the associated plasticity-induced crack closure. Two-dimensional, elastic-perfectly plastic finite element analyses of middle-crack tension (M(T)), bend (SEB), and compact tension (C(T)) geometries were conducted to study fatigue crack closure and to calculate the crack opening values under plane-strain and plane-stress conditions. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus similar initial forward plastic zone sizes. Mesh refinement studies were performed on all geometries with various element types. For the C(T) geometry, negligible crack opening loads under plane-strain conditions were observed. In contrast, for the M(T) specimen, the plane-strain crack opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for the C(T), SEB, and M(T) specimens. Next, the crack opening values of the C(T), SEB and M(T) specimens were compared under various stress levels and load ratios. The effect of a highly refined mesh on crack opening values was noted and significantly lower crack opening values than those reported in literature were found. A new methodology is presented to calculate crack opening values in planar geometries using the crack surface nodal force distribution under minimum loading as determined from finite element analyses. The calculated crack opening values are compared with values obtained using finite element analysis and more conventional crack opening assessment methodologies. It is shown that the new method is independent of loading increment, integration method (normal and reduced integration), and crack opening assessment location. The compared opening values were in good agreement with strip-yield models.

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Due to the increasing use of cyclically loaded cast aluminum components in automotive and aerospace applications, fatigue and fatigue crack growth characteristics of aluminum castings are of great interest. Despite the extensive research efforts dedicated to this topic, a fundamental, mechanistic understanding of these alloys' behavior when subjected to dynamic loading is still lacking. This fundamental research investigated the mechanisms active at the microstructure level during dynamic loading and failure of conventionally cast and SSM Al-Si-Mg alloys. Five model alloys were cast to isolate the individual contribution of constituent phases on fatigue resistance. The major constituent phases, alpha-Al dendrites, Al/Si eutectic phase, and Mg-Si strengthening precipitates were mechanistically investigated to relate microstructure to near-threshold crack growth (Delta Kth) and crack propagation regimes (Regions II and III) for alloys of different Si composition/morphology, grain size, secondary dendrite arm spacing, heat treatment. A procedure to evaluate the actual fracture toughness from fatigue crack growth data was successfully developed based on a complex Elastic-Plastic-Fracture-Mechanics (EPFM/J-integral) approach. Residual stress-microstructure interactions, commonly overlooked by researches in the field, were also comprehensively defined and accounted for both experimentally and mathematically, and future revisions of ASTM E647 are expected.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.