Crack patterns in heterogenous rocks using a combined phase field-cohesive interface modeling approach: A numerical study

Rock fracture in geo-materials is a complex phenomenon due to its intrinsic characteristics and the potential external loading conditions. As a result, these materials can experience intricate fracture patterns endowing various cracking phenomena such as: Branching, coalescence, shielding, and amplification, among many others. In this article, we present a numerical investigation concerning the applicability of an original bulk-interface fracture simulation technique to trigger such phenomena within the context of the phase field approach for fracture. In particular, the prediction of failure patterns in heterogenous rock masses with brittle response is accomplished through the current methodology by combining the phase field approach for intact rock failure and the cohesive interface-like modeling approach for its application in joint fracture. Predictions from the present technique are first validated against Brazilian test results, which were developed using alternative phase field methods, and with respect to specimens subjected to different loading case and whose corresponding definitions are characterized by the presence of single and multiple flaws. Subsequently, the numerical study is extended to the analysis of heterogeneous rock masses including joints that separate different potential lithologies, leading to tortuous crack paths, which are observed in many practical situations.Ministerio de Economía y Competitividad MAT2015-71036-

Revisiting the problem of a crack impinging on an interface: A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In the current investigation, this problem is revisited in view of the recent progresses on the phase field approach of brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model, implemented within the finite element method framework using a monolithic fully implicit solution strategy, is applied to provide a further insight into the understanding of the role of model parameters on the above competition. In particular, in this study, the role of the fracture toughness ratio between the interface and the adjoining bulks and of the characteristic fracture-length scales of the dissipative models is analyzed. In the case of a brittle interface, the asymptotic predictions based on linear elastic fracture mechanics criteria for crack penetration, single deflection or double deflection are fully captured by the present method. Moreover, by increasing the size of the process zone along the interface, or by varying the internal length scale of the phase field model, new complex phenomena are emerging, such as simultaneous crack penetration and deflection and the transition from single crack penetration to deflection and penetration with subsequent branching into the bulk. The obtained computational trends are in very good agreement with previous experimental observations and the theoretical considerations on the competition and interplay between both fracture mechanics models open new research perspectives for the simulation and understanding of complex fracture patterns.Unión Europea FP/2007-2013/ERC 306622Ministerio de Economía y Competitividad DPI2012-37187, MAT2015-71036-P y MAT2015-71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP- 105

Voronoi cell finite element modelling of the intergranular fracture mechanism in polycrystalline alumina

The mechanisms of fracture in polycrystalline alumina were investigated at the grain level using both the micromechanical tests and finite element (FE) model. First, the bending experiments were performed on the alumina microcantilever beams with a controlled displacement rate of 10 nm s–1 at the free end; it was observed that the intergranular fracture dominates the failure process. The full scale 3D Voronoi cell FE model of the microcantilever bending tests was then developed and experimentally validated to provide the insight into the cracking mechanisms in the intergranular fracture. It was found that the crystalline morphology and orientation of grains have a significant impact on the localised stress in polycrystalline alumina. The interaction of adjacent grains as well as their different orientations determines the localised tensile and shear stress state in grain boundaries. In the intergranular fracture process, the crack formation and propagation are predominantly governed by tensile opening (mode I) and shear sliding (mode II) along grain boundaries. Additionally, the parametric FE predictions reveal that the bulk failure load of the alumina microcantilever increases with the cohesive strength and total fracture energy of grain boundaries

Micromechanical fracture analysis of high strength steel weldments

Industrijska primena celika povišene cvrstoce u elementima zavarenih konstrukcija cini neophodnim poznavanje ponašanja spojeva ovih materijala pri žilavom lomu. Stoga, procena integriteta zavarenih struktura je potrebna da bi se obezbedio potrebni nivo sigurnsti i pouzdanosti, imajuci u vidu uticaj ogranicenog deformisanja i heterogenosti na ponašanje pri lomu kriticnih zona spoja: zone uticaja toplote (ZUT) i metala šava (MŠ), koji cesto imaju nižu žilavost i višu prelaznu temperaturu. Takode, veoma je važno da procena integriteta bude uradena realno i da ne bude previše konzervativna, kako bi se sprecilo povecanje mase strukture i obezbedilo ekonomicno korišcenje materijala. U ovoj disertaciji, mikromehanicki pristup je korišcen za analizu uticaja mehanicke heterogenosti i ogranicenog deformisanja na žilav lom zavarenih spojeva celika povišene cvrstoce. Ovaj pristup je korišcen kao rešenje za problem prenosivosti parametara klasicne mehanike loma. Takode, motiv za njegovu primenu je i to što standardni parametri mehanike loma: faktor intenziteta napona, otvaranje prsline i konturni Jintegral, ne mogu na odgovarajuci nacin opisati odgovor materijala sa prslinom na dejstvo spoljnog opterecenja u svim uslovima, kao što su izraženo plasticno tecenje (large scale yielding), razliciti uticaji heterogenosti, obika i geometrije zavarenih konstrukcija u eksploataciji. Parametri mehanike loma, odredeni laboratorijskim ispitivanjem epruveta, nisu direktno prenosivi na komponente i stoga se moraju uzeti u obzir dodatni faktori (kao što je uticaj ogranicenog deformisanja). Takode, cilj ove disertacije je odredivanje mehanickih osobina zona zavarenog spoja korišcenjem kombinovanog eksperimentalnonumerickog postupka, što je narocito važno kod zona male širine u okviru ZUT koje su izložene opterecenju u transverzalnom pravcu. Rad na disertaciji je podrazumevao primenu metode konacnih elemenata i eksperimentalna ispitivanja. Eksperimentalna ispitivanja su uradena na zavarenim glatkim epruvetama (uz korišcenje ARAMIS stereometrijskog mernog sistema) za odredivanje mehanickih osobina, kao i epruvetama za savijanje u tri tacke i epruvetama za zatezanje sa pocetnom prslinom u metalu šava i zoni uticaja toplote za analizu ponašanja pri lomu. J-R krive i vrednosti parametra mehanike loma koje odgovaraju pocetku rasta prsline odredene su eksperimentalno i numericki na epruvetama sa pocetnom prslinom u ZUT i MŠ. Numericka analiza elasto-plasticnih modela konacnih elemenata (2D i 3D) je uradena u programskom paketu Abaqus, a mikromehanicki kompletni Gursonov model (CGM) je primenjen preko korisnickog potprograma UMAT (autor Z.L. Zhang). Ograniceno deformisanje oko vrha prsline i promena troosnosti u ligamentu su numericki analizirani na epruvetama za savijanje u tri tacke i onim za zatezanje, da bi se analizirala prenosivost mikromehanickih parametara oštecenja sa jedne epruvete na drugu. Takode, mikromehanickim pristupom je odreden uticaj geometrije i rezultati su uporedeni sa eksperimentalnim podacima. Najveci deo numerickih rezultata dobijenih korišcenjem CGM modela pokazuje dobro slaganje sa eksperimentalnim rezultatima...The industrial application of high strength steel in structural welded components has increased the demand for understanding the ductile failure behavior of this type of welded materials. Therefore, integrity assessment of those welded structures is required in order to ensure a certain level of safety and reliability, having in mind the effects of constraints and heterogeneity on fracture behavior of crucial regions such as: heat affected zone (HAZ) and weld metal (WM) which usually have low toughness and higher transition temperature. It is also essential that the assessment is done in a realistic and not too conservative way in order not to increase the mass of the structure or impair the economic efficiency too much. In this thesis, micromechanical approach has been used to study the effect of mechanical heterogeneity and constraints on ductile fracture of high strength steel weldments. This approach has been used as a solution for the transferability problem of conventional fracture mechanics parameters. It has also been used on basis of that fracture mechanics parameters recommended by standard, such as: stress intensity factor, crack opening displacement and contour J-integral, cannot reliably describe the reaction of a pre-cracked material to the effects of external loading under all conditions such as: large scale yielding, various effects of heterogeneity, shape and geometry of real welded structures. The fracture mechanics parameters, determined from laboratory scale experiments are not also directly transferable to components and hence additional considerations (like constraint effects etc.) need to be taken care of. In addition, the aim of the thesis was to estimate precise mechanical properties using a combined experimental and numerical procedure for various welded joint regions, especially for narrow HAZ regions, when they are subjected to transversally applied load. The study was carried out using finite element method and experiments. Experimental analysis was carried out on: welded smooth tensile specimen with ARAMIS measuring system for estimation mechanical properties, welded single-edge notched bend and flat tensile specimens with pre-cracks in weld metal (WM) and heat-affected zone (HAZ) for studying the ductile fracture behavior. J-R curves and crack growth initiation iii values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in HAZ and WM. Numerical analysis of elastic-plastic finite element models (2D and 3D) was performed in software package Abaqus, with micromechanical complete Gurson model (CGM) applied through user subroutine, UMAT (author: Z.L. Zhang). The crack tip constraint and variation of stress triaxiality in ligament were numerically analyzed on single-edge notched bend and tensile specimens to analyze the transferability of micromechanical damage parameters from one specimen to another. In addition, the geometry effects were also studied by the micromechanical approach and the results were compared with those of the experiments. Most of numerical results obtained with CGM model are in good agreement with the experimental results..

Creep crack-growth: A new path-independent T sub o and computational studies

Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects and large deformations. Two principal conclusions are that delta T sub c is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations