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1

Fracture interference and propagation geometry of hydraulic fractures based on XFEM in an unconventional oil reservoir

Liang Shuang, Wang Di, Liu Dan, Tian Yang, Wang Haibo, Li Fengxia, Dong Gang, Yin Chengfeng, Yang Yi

Archives of Mining Sciences

|

2023

|

Vol. 68, no. 2

301--318

EN

Unconventional oil and gas reservoirs are characterised by low porosity, low permeability and low natural deliverability. At present, horizontal wells staged fracturing is an effective development method. However, in the case of staged hydraulic fracturing in horizontal wells, stress interference occurs between multiple fractures, leading to fracture deformation and even inhibiting the formation of fractures, thereby affecting reservoir production. In this paper, based on the extended finite element method (XFEM), considering the fluid flow in the fracture and fracturing fluid filtration, we analyse the effects of fracturing fluid pumping rate, fracture spacing and elastic modulus on horizontal in-situ stress, fracture parameters and fracture extension pattern during different fracturing initiation processes. The results show that the induced stress generated by the action of fracturing fluid changes the direction of horizontal in-situ stress in the elliptical region around the fracture. In the mode of simultaneous fracture initiation (TFIS), the extension of two symmetrical fractures is “repulsive”; in the mode of two fractures initiated at different times (TFIDT), the extension direction is “mutual attraction”. A large pumping rate and small elastic modulus are conducive to fracture propagation. In the TFIS mode, two fractures alternately expand, while in the TFIDT mode, the impact of rock mechanical properties and construction parameters on fracture propagation will be amplified. The extension of subsequent fractures will be restrained, especially when the fracture spacing is less than 10 m. The width of the previously created fracture will be severely affected, even causing a partial closure and becoming elongated fractures.

2

Numerical and Experimental Study of Crack Propagation in the Tensile Composite Plate with the Open Hole

Wysmulski Paweł

Advances in Science and Technology. Research Journal

|

2023

|

Vol. 17, no 4

249--261

EN

In this study, the thin-walled plate with the central open hole made of carbon-epoxy composite was investigated. The plate was tested in tension to investigate the mechanism of crack formation in the composite structure. The studies were carried out using two individual methods: experimental and numerical. In the experiment test, load was measured as the function of plate elongation. The Plate elongation was analysed using the Aramis optical non-contact measurement system. In the numerical study, the FEM model reproducing the experimental conditions was developed in the Abaqus software. The cracking process was modelled using the XFEM method (extended finite element method). This procedure allowed the of the composite to be examined over the full range of the tensile load. The behaviour of the plate with a circular open hole was investigated before damage symptoms and the damage initiation load was determined. The study continued to analyse the initial cracking and delamination of the laminate layers, together with crack propagation leading to cracking of all the laminate layers (complete failure of the composite structure). The novelty of this study is that it uses the popular XFEM method to describe the cracking and failure of the composite structure. In addition, the study proposes the novel method for determining the crack initiation and failure loads of the composite plate under tension, and the results obtained thereby are verified numerically.

3

Experimental and numerical study of the effect of the presence of a geometric discontinuity of variable shape on the tensile strength of an epoxy polymer

Saada Khalissa, Amroune Salah, Zaoui Moussa, Houari Amin, Madani Kouider, Hachaichi Amina

Acta Mechanica et Automatica

|

2023

|

Vol. 17, no. 2

192--199

EN

The presence of geometric discontinuity in a material reduces considerably its resistance to mechanical stresses, therefore reducing the service life of materials. The analysis of structural behaviour in the presence of geometric discontinuities is important to ensure the proper use, especially if it is regarding a material of weak mechanical properties such as a polymer. The objective of the present work is to analyse the effect of the notch presence of variable geometric shapes on the tensile strength of epoxy-type polymer specimens. A series of tensile tests were carried out on standardised specimens, taking into account the presence or absence of a notch. Each series of tests contains five specimens. Two notch shapes were considered: circular (hole) and elliptical. The experimental results in terms of stress–strain clearly show that the presence of notches reduces considerably the resistance of the material, where the maximum stress for the undamaged specimen was 41.22 MPa and the lowest stress for the elliptical-notched specimen was 11.21 MPa. A numerical analysis by the extended finite element method (XFEM) was undertaken on the same geometric models; in addition, the results in stress–strain form were validated with the experimental results. A remarkable improvement was obtained (generally an error within 0.06%) for strain, maximum stress, Young’s modulus and elongation values. An exponential decrease was noted in the stress, strain, and Young’s modulus in the presence of a notch in the material.

4

Study of calculation method of pure mode II stress intensity factor of fine-grained concrete using different numerical models

Zhou Changlin, Peng Bo, Deng An, Gao Xiaofeng, Li Yaojia, Zhou Lei, Zhu Zheming

Journal of Theoretical and Applied Mechanics

|

2021

|

Vol. 59 nr 2

251--264

EN

Measuring and calculating methods of critical stress intensity factors (SIFs) have become hot topics which attracted large attention recently. In this work, anti-symmetrical four-point bending tests of cracked fine-grained concrete specimens were conducted experimentally and numerically by using a computer-controlled universal testing machine and ABAQUS code. A comparative study of the calculation method of pure mode II stress intensity factor of a fine-grained concrete was performed by utilizing the conventional finite element method (FEM) in two and three dimensions as well as the extended finite element method (XFEM) in three dimensions. The results show that in three-dimensional models, the crack mode is closest to the pure mode II at the center of specimen thickness. Pure mode II stress intensity factors obtained by SEAM2D and XFEM3D are 1.013 and 1.0617 times that by SEAM3D, respectively. Pure mode II stress intensity factors of the fine-grained concrete obtained by the conventional FEM are more stable than that by XFEM. The number of mesh circles has slight influence on the calculation results of pure mode II stress intensity factor.

5

Crack propagation analysis in selected railway bogie components

Mysłek Adam

Technical Transactions

|

2020

|

Vol. 117, iss. 1

art. no. e2020017

EN

This paper presents the practical application of fracture mechanics in investigating the possibility of crack propagation in a brake calliper bracket mounted in a vehicle bogie. The extended finite element method available in the Abaqus software was used. This method allows the modelling of material damage and its propagation independently of the finite element mesh. Damage can arise in any area of finite elements without changing the mesh. Numerical simulation of crack propagation was performed in order to analyse how crack changes as a result of the location change of damage initiation.

PL

W artykule przedstawiono praktyczne zastosowanie mechaniki pękania w badaniu możliwości propagacji pęknięć w wsporniku zacisku hamulca zamontowanym w wózku pojazdu. Zastosowano rozszerzoną metodę elementów skończonych dostępną w oprogramowaniu Abaqus. Ta metoda umożliwia modelowanie uszkodzeń materiału i jego rozprzestrzenianie się niezależnie od siatki elementów skończonych. Uszkodzenie może powstać w dowolnym obszarze elementów skończonych bez zmiany siatki. Przeprowadzono numeryczną symulację propagacji pęknięć w celu analizy zmian propagacji w wyniku zmiany lokalizacji inicjacji uszkodzeń.

6

On some problems in determining tensile parameters of concrete model from size effect tests

Marzec Ireneusz, Bobiński Jerzy

Polish Maritime Research

|

2019

|

nr 2

115--125

EN

The paper presents results of numerical simulations of size effect phenomenon in concrete specimens. The behaviour of in-plane geometrically similar notched and unnotched beams under three-point bending is investigated. In total 18 beams are analysed. Concrete beams of four different sizes and five different notch to depth ratios are simulated. Two methods are applied to describe cracks. First, an elasto-plastic constitutive law with a Rankine criterion and an associated flow rule is defined. In order to obtain mesh independent results, an integral non-local theory is used as a regularisation method in the softening regime. Alternatively, cracks are described in a discrete way within Extended Finite Element Method (XFEM). Two softening relationships in the softening regime are studied: a bilinear and an exponential curve. Obtained numerical results are compared with experimental outcomes recently reported in literature. Calculated maximum forces (nominal strengths) are quantitatively verified against experimental values, but the force – displacement curves are also examined. It is shown that both approaches give results consistent with experiments. Moreover, both softening curves with different initial fracture energies can produce similar force-displacement curves.

7

An enhanced XFEM for the discontinuous Poisson problem

Stąpór Paweł

Archive of Mechanical Engineering

|

2019

|

Vol. LXVI, nr 1

25--37

EN

In the paper, the extended finite element method (XFEM) is combined with a recovery procedure in the analysis of the discontinuous Poisson problem. The model considers the weak as well as the strong discontinuity. Computationally efficient low-order finite elements provided good convergence are used. The combination of the XFEM with a recovery procedure allows for optimal convergence rates in the gradient i.e. as the same order as the primary solution. The discontinuity is modelled independently of the finite element mesh using a step-enrichment and level set approach. The results show improved gradient prediction locally for the interface element and globally for the entire domain.

8

XFEM simulation of the influence of cracking introduced by pre-loading on the strengthening of a cement treated mixture

Brzeziński K.

Journal of Theoretical and Applied Mechanics

|

2018

|

Vol. 56 nr 4

927—938

EN

The paper attempts to explain the phenomenon of a static strength increase due to the previous cyclic loading. Finite Element Method simulation of the potential strengthening mechanism is presented. The crack growth is controlled by the energy criterion used in the linear fracture theory. A wedge splitting test has been performed in order to determine the critical energy release rate of the tested mixture GIC . It was observed that the appearance of additional cracks in the material may lead to an increase of its strength. Analysis of the tensile stress distribution allows for a qualitative explanation of the observed phenomenon.

9

Fem analysis of pressure vessel with an investigation of crack growth on cylindrical surface

Balac M., Grbovic A., Petrovic A., Popovic V.

Eksploatacja i Niezawodność

|

2018

|

Vol. 20, no. 3

378--386

EN

To ensure reliability of pressure vessels during service it is necessary to (1) know properties of materials used in their design and (2) evaluate vessels’ behaviour under different working conditions with satisfying accuracy. Due to various technical and/or technological requirements, nozzles are usually welded on vessel’s shell producing geometrical discontinuities that reduce the safety factor. To evaluate their influence, vessels with two different nozzles were experimentally studied and critical areas for crack initiation have been identified by 3D Digital Image Correlation (DIC) method. After that, the numerical analysis of equivalent 3D finite element model was performed and obtained results were compared with experimental values. In the most critical area, next to the one of the nozzles, crack was initiated and then growth of the damage was simulated using extended finite element method (XFEM). In this paper evaluation of stress intensity factors (SIFs) along crack path is presented, as well as the most probable direction of the crack propagation on the shell. Based on SIFs values, critical length of the crack and number of pressure cycles to the final failure were estimated.

PL

Aby zapewnić niezawodność zbiorników ciśnieniowych podczas pracy, konieczna jest (1) znajomość właściwości materiałów zastosowanych do ich konstrukcji oraz (2) wystarczająco dokładna ocena zachowania zbiornika w różnych warunkach pracy. Ze względu na różne wymagania techniczne i/lub technologiczne, króćce zwykle spawa się do płaszcza zbiornika, w wyniku czego powstają geometryczne nieciągłości, które zmniejszają współczynnik bezpieczeństwa. Aby ocenić ich wpływ, przeprowadzono eksperymentalne badania zbiorników z dwoma różnymi króćcami i określono obszary krytyczne dla inicjacji pęknięć wykorzystując metodę trójwymiarowej cyfrowej korelacji obrazu (DIC). Następnie przeprowadzono analizę numeryczną równoważnego modelu elementów skończonych 3D, a uzyskane wyniki porównano z wartościami eksperymentalnymi. W najbardziej krytycznym obszarze, w pobliżu jednego z króćców, inicjowano pęknięcie, a następnie symulowano rozwój uszkodzenia przy użyciu rozszerzonej metody elementów skończonych (XFEM). W artykule przedstawiono ocenę współczynników intensyfikacji naprężeń (SIF) wzdłuż ścieżki pękania oraz najbardziej prawdopodobnego kierunku propagacji pęknięć na płaszczu zbiornika. Na podstawie wartości SIF, oszacowano krytyczną długość pęknięcia i liczbę cykli ciśnieniowych do ostatecznego uszkodzenia.

10

Numerical analysis of damage in silica filled epoxy products using XFEM and its verifications

Płatek R., Malinowski Ł., Zwoliński P.

Technical Transactions

|

2017

|

Vol. 7(114)

199--207

EN

The paper summarizes the study of cracking phenomena in silica filled epoxy material. Numerical analyses of cracking phenomena were performed using Extended Finite Element Method (XFEM) for a full scale element as well as in a microscale, for the Representative Volume Element (RVE). Experimental verification consists of both C2 tests for real products and in-situ tensile tests and microstructural observations with the Scanning Electron Microscope (SEM). At the end, a summary with conclusions related to the prepared numerical analyses and experiments is included.

PL

W artykule przedstawiono wyniki analiz pękania izolacji żywicznej wypełnionej kwarcem. Analizy numeryczne przeprowadzone były dla obiektu w pełnej skali, jak i dla próbki reprezentatywnej (RVE) w mikroskali. Weryfikacja eksperymentalna zawierała obserwacje produktów po testach C2, testy in-situ oraz obserwacje pod mikroskopem zniszczonej struktury. Podsumowanie wraz z wnioskami z badań zawarto na końcu artykułu.

11

Numerical modelling of hydraulically bonded mixture with rubber admixture due to applied mechanical loadings

Pietras D., Sadowski T.

Budownictwo i Architektura

|

2017

|

Vol. 16, nr 3

95--102

EN

Abstract: In this paper the application of the Extended Finite Element Method (XFEM) to anticipate change of the behaviour of composite with complex internal structure after use of the admixtures was presented. The response to mechanical loadings of bent beams made of hydraulically bonded mixture with rubber admixture was considered. The impact of the rubber granulate on the value of fracture energy was analysed. Moreover, the influence of an interfacial transmission zone quality on the achieved effect was assessed. Calculations were conducted by means of the muli-scale numerical model which was built in ABAQUS finite element method environment. The results derived indicate beneficial effect of rubber granulate on fracture energy of hydraulically bonded mixture.

12

An Improved XFEM for the Poisson Equation with Discontinuous Coefficients

Stąpór P.

Archive of Mechanical Engineering

|

2017

|

Vol. LXIV, nr 1

123--144

EN

Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.

13

Numeryczny model pękania dla stali dwufazowych

Perzyński K., Madej Ł.

Hutnik, Wiadomości Hutnicze

|

2016

|

Vol. 83, nr 4

141--146

PL

Celem badań jest opracowanie modeli numerycznych odzwierciedlających mechanizmy pękania w stali dwufazowej Dual Phase (DP), bazujących na koncepcji cyfrowej reprezentacji materiału. Zaproponowane w pracy rozwiązanie wykorzystuje sprzęgnięcie dwóch podejść numerycznych szeroko stosowanych w symulacjach o charakterze komercyjnym: metody elementów skończonych i rozszerzonej metody elementów skończonych. Podejście takie umożliwia stosunkowo łatwe wykorzystanie modeli pękania kruchego oraz ciągliwego w praktycznych zastosowaniach ze względu na użycie standardowych rozwiązań stosowanych w aplikacjach numerycznych. Nowatorskie jest zastosowanie cyfrowej reprezentacji materiału i koncepcji modelowania wieloskalowego do opisu zachowania się materiału w niższych skalach wymiarowych. Opracowany model został zweryfikowany z wynikami pomiarów zrealizowanych podczas testu wywijania otworu (HE – Hole Expansion).

EN

Development of a robust model of failure for Dual Phase (DP) steels based on modern numerical approaches that take microstructure explicitly into account during simulation is the main aim of the paper. Modeling procedure is based on conventional numerical damage models, however combined with the DMR (Digital Material Representation) approach. As a result, a combined model of ductile and brittle fractures which occur in ferrite and martensite, respectively, was established. Ductile fracture is modelled by the Ductile Fracture criterion implemented within conventional FE model, while brittle one is predicted by more sophisticated eXtended Finite Element Method (XFEM). Proper data transfer protocols between these two methods were also proposed to create a hybrid numerical model. Developed solution was validated with experimental data from the hole expansion (HE) test.

14

Extended finite element numerical analysis of scale effect in notched glass fiber reinforced epoxy composite

Abdellah M. Y., Alsoufi M. S., Hassan M. K., Ghulman H. A., Mohamed A. F.

Archive of Mechanical Engineering

|

2015

|

Vol. LXII, nr 2

217--236

EN

Nominal strength reduction in cross ply laminates of [0/90]2s is observed in tensile tests of glass fiber composite laminates having central open hole of diameters varying from 2 to 10 mm. This is well known as the size effect. The extended finite element method (XFEM) is implemented to simulate the fracture process and size effect (scale effect) in the glass fiber reinforced polymer laminates weakened by holes or notches. The analysis shows that XFEM results are in good agreement with the experimental results specifying nominal strength and in good agreement with the analytical results based on the cohesive zone model specifying crack opening displacement and the fracture process zone length.

PL

Zmniejszenie nominalnej wytrzymałości laminatu warstwowego z poprzecznym ułożeniem włókien typu [0/90]2s jest obserwowane dla naprężeń rozciągających w laminatach kompozytowych z włóknem szklanym mających centralny otwór o średnicy od 2 do 10 mm. Jest to dobrze znany efekt rozmiaru (efekt skali). Rozszerzona analiza metodą elementów skończonych (XFEM) została zastosowana w celu symulacji procesu pękania i efektu skali w polimerowych laminatach z włóknem szklanym osłabionych obecnością karbu lub otworu. W pracy wykazano, że wyniki metody XFEM dotyczące wytrzymałości nominalnej są zgodne z danymi eksperymentalnymi, dobrze zgadzają sią z wynikami analitycznymi opartymi na modelu strefy spójnej i pozwalają określić przemieszczenie otworu szczeliny i długość strefy procesu pęknięcia.

15

Modeling of fracture propagation in concrete structures using a constitutive relation with embedded discontinuity

Pietruszczak S., Haghighat E.

Studia Geotechnica et Mechanica

|

2014

|

Vol. 36, nr 4

27--32

EN

In this paper, the problem of modeling of mixed mode cracking in concrete structures is addressed within the context of a constitutive law with embedded discontinuity (CLED). This approach, which was originally developed for describing the propagation of localized deformation in a “smeared” sense, is enhanced here to model a discrete nature of crack propagation. The latter is achieved by coupling the CLED approach with the level-set method, which is commonly used within the framework of Extended Finite Element (XFEM). Numerical simulations of experimental tests conducted at Delft University, which involve four-point bending of a notched concrete beam under the action of two independent actuators, are presented. The results based on enhanced CLED approach are directly compared with XFEM simulations. The predictions from both these methodologies are quite consistent with the experimental data, thereby giving advantage to CLED scheme in view of its simplicity in the numerical implementation.

16

Lemaitre's damage nonlocal model performance under crack initiation and propagation

Seabra M., Cesar de Sa J.

Computer Methods in Materials Science

|

2013

|

Vol. 13, No. 1

30--35

EN

Modelling of ductile fracture is a rather challenging task due to the complexity of the physical phenomena involved. In ductile metals, material progressive degradation, which is strongly associated with large plastic straining, may be captured using the Lemaitre damage model. Nevertheless, to model the propagation of macro-cracks, the use of a discontinuous approach is in general imperative. Therefore, in this work, the Lemaitre Damage model is combined with the XFEM for a complete description of ductile failure. In addition, as in general continuous softening models suffer from pathological mesh dependence, a non-local formulation is implemented and its effects on crack initiation and propagation are evaluated.

PL

Modelowanie pęknięć plastycznych jest zagadnieniem trudnym ze względu na złożoność występujących zjawisk fizycznych. W metalach plastycznych postępujące zniszczenie materiału, związane ściśle z dużymi odkształceniami plastycznymi, może być opisane modelem opracowanym przez Lemaitre’a. Niemniej jednak model propagacji makro uszkodzeń wymaga uwzględnienia nieciągłości tych zjawisk. Dlatego w niniejszej pracy model uszkodzeń Lemaitre’a został połączony z modelem XMES, co pozwoliło na kompletny opis zjawiska pęknięcia plastycznego. Ponadto, ponieważ modele ciągłe stosowane do opisu mięknięcia materiału są uzależnione od siatki elementów skończonych, zastosowano sformułowanie nielokalne, co umożliwiło modelowanie zarówno inicjacji jak i rozprzestrzeniania się pęknięć.

17

Numerical modeling of fracture during nanoindentation of the TiN coatings obtained with the PLD process

Perzyński K., Madej Ł.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2013

|

Vol. 61, nr 4

973--978

EN

In order to improve mechanical, frictional or biocompatibility behavior of well know materials like titanium (Ti) or titanium nitride (TiN) scientists are trying to develop new manufacturing and processing operations. One of those methods, that provide interesting results, is called deposition process. During deposition a material is upgraded with new surface layers that are characterized by specific required properties. These layers have usually different mechanical properties in comparison with a substrate material. A combination of different properties of the deposited layers can significantly change behavior of the structure under an exploitation condition. However, layers have usually nanometer scale, which causes problems with performing standard plastometric tests. One of the possibilities to solve this issue is an application of specially designed tests like nanoindentation. Nanoindentation can provide valuable information regarding mechanical and strength behavior of nanostructure components. These investigations are of importance to properly identify and design properties of the mentioned deposited materials. Unfortunately, experimental analyses at these scales are usually very expensive. That is why Authors decided to develop a numerical model of the nanoindentation test to investigate material behavior under loading conditions that can support experimental research. The overall aim of this research is development of a failure model, which can take into account morphology of microstructure of ceramic TiN layer deposited on the silicon substrate. Modeling of crack behavior was realized on the basis of the extended finite element method (XFEM).

18

Numerical simulation of temperature field in heterogeneous material with the XFEM

Yu T. T., Gong Z. W.

Archives of Civil and Mechanical Engineering

|

2013

|

Vol. 13, no. 2

199--208

EN

The purpose of this paper is to focus on modeling temperature field in heterogeneous materials. The heat conductivity is adopted as the basic parameter for calculation. The extended finite element method (XFEM) is applied for simulation of temperature field. For one element that contains no material interface, the temperature function will be degenerated into that of the conventional finite element. For the element containing material interfaces, the standard temperature based approximation is enriched by incorporating level-set-based enrichment functions which model the interfaces. For unsteady temperature field, the improved precise integration method is adopted for the solution of the ordinary differential equations. The mesh generation can be considerably simplified and high-quality meshes are obtained; meanwhile the solution of good precision and stability can be achieved.

19

Simulations of fracture in concrete elements using continuous and discontinuous models

Bobiński J., Tejchman J.

Mechanics and Control

|

2011

|

Vol. 30, no. 4

183-193

EN

The paper presents results of numerical simulations of fracture in concrete using two different approaches. First, fracture was modelled in a smeared way by an elasto-plastic and a damage continuum model. In elasto-plasticity, a Rankine criterion was used. The degradation of the stiffness in the damage model was described as a scalar variable of an equivalent strain measure. To ensure mesh-independent results, a non-local theory was used. Second, fracture was simulated as discontinuities with the aid of cohesive elements and Extended Finite Element Method (XFEM). The experimental benchmark test for concrete by Nooru-Mohamed under mixed mode conditions was modelled. The obtained numerical results were compared with the corresponding experimental ones.

PL

W pracy przedstawiono wyniki symulacji numerycznych MES pękania w betonie z wykorzystaniem dwóch różnych podejść. Po pierwsze, zastosowano ciągły (przesmarowany) opis rys w teorii plastyczności oraz model degradacji modułu sprężystości z różnymi opisami odkształcenia zastępczego w ramach kontynualnej mechaniki uszkodzeń. Oba prawa rozszerzono o długość charakterystyczną mikrostruktury w ramach teorii nielokalnej w celu uzyskania wyników niezależnych od siatki MES. Po drugie, jako alternatywę do symulacji propagacji rys zastosowano nieciągły opis pola przemieszczeń, wykorzystując elementy kohezyjne oraz rozszerzoną metodę elementów skończonych XFEM. Przeprowadzono symulacje numeryczne testu Nooru-Mohamada z jednoczesnym rozciąganiem i ścinaniem betonu. Uzyskane wyniki numeryczne porównano z wynikami doświadczalnymi.

20

Analysis of the stress concentration in the nanomultilayer coatings based on digital representation of the structure

Perzyński K., Major Ł., Madej Ł., Pietrzyk M.

Archives of Metallurgy and Materials

|

2011

|

Vol. 56, iss. 2

393-399

EN

Investigation of the stress concentration in the nanomultilayer materials under exploitation conditions is the main objective of the work. During loading a failure can initiate and propagate, which have important impact on material strength and reliability. This is of importance when materials for biological applications are considered. Special features of the investigated material, including irregular shape of the boundaries and columnar structure of these layers lead to growth of local stresses in the material and may be responsible for mentioned instabilities. To capture this behavior during numerical modeling an innovative solutions are required. Authors propose numerical simulation, which combines algorithms of the deposition process for realistic digital material representation of coatings and finite element (FE) approach for modeling of material behavior under loading. Algorithm of the deposition process is implemented using the cellular automata (CA) approach. Based on the developed model, a simple plastometric compression tests are simulated to analyze stress distribution in the material and possibility of failure initiation. These results are compared qualitatively with experimental data, including ball-on-test and transmission electron microscope (TEM) observation. Obtained results are the basis for development of a numerical model for fracture propagation with adopted extended finite element method (XFEM).

PL

Głównym celem pracy jest zaproponowanie podejścia numerycznego umożliwiającego analizę koncentracji naprężeń w materiałach o strukturze nanowarstwowej przeznaczonych dla bioinżynierii. Jest to szczególnie istotne w przypadku prowadzenia analizy zachowania się materiałów w warunkach eksploatacji ponieważ umożliwia zlokalizowanie miejsc szczególnie narażonych na uszkodzenia. Do przeprowadzenia szczegółowej analizy numerycznej konieczne jest uwzględnienie typowych cech nanowarstwowego materiału np. nieregularnego kształtu granicy pomiędzy warstwami. W tym celu Autorzy zastosowali model MES sprzężony z jawną reprezentacją mikrostruktury i automatami komórkowym (CA). Model na bazie CA uwzględnia wspomniane specyficzne cechy analizowanych materiałów. W pracy przedstawiono algorytm generowania cyfrowej reprezentacji nanowarstw oraz wyniki symulacji z wykorzystaniem opracowanego modelu numerycznego dla warstw bez uwzględnienia chropowatości granicy międzywarstwowej, jak i z jej uwzględnieniem. Uzyskane wyniki w formie rozkładów naprężeń stały się podstawą do opracowania modelu procesu pękania w analizowanych materiałach z wykorzystaniem metody eXtended Finite Element Method (XFEM). Przykłady uzyskanych wyników również zamieszczono w niniejszej pracy.