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1

Simulation of the Griffith's Crack Using Own Method of Predicting the Crack Propagation

Podgórski Jerzy, Gontarz Jakub

Advances in Science and Technology. Research Journal

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2021

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Vol. 15, no 4

1--13

EN

The paper presents the results of numerical simulation of brittle material fracture initiated by Griffith's crack situated at any angle with respect to the load direction. The simulations were performed with the Simulia Abaqus FEA system using the X-FEM method. The direction of the crack propagation was determined using the user's subroutine written in Fortran, implemented in the Abaqus system. The authors programmed several conditions for the direction of the fracture propagation: maximum principal stress criterion, Ottosen-Podgórski criterion, three criteria based on displacements around the crack tip, and the MTS criterion, which is based on stress intensity factors. For the purposes of this study, two shapes of the crack tip were analyzed - sharp and blunted. The relationship between the direction of the initial fracture and the direction of crack propagation was found. The simulations were carried out for the angles of the initial crack from 0° to 90°, every 10°. A theoretical analysis of the implemented criteria was also carried out and compared to numerical results. The influence of the shape of the crack tip on the simulation result was analyzed. It was shown that the simulation results closest to the theoretical results were obtained for the own implementation of the stress-based criteria. It has also been proven that the shape of the crack tip has little effect on the result if the finite element mesh is properly densified. However, the sharp crack has a disadvantage for small initial crack angles. The Author’s method of predicting the crack propagation has been proven correct and effective. This work is also the basis for the further development of the described method.

2

Differences between DIN EN 1992-1-1/NA2011 guidelines and EN-1992-1-1:2004 standard with respect to the design of the minimum reinforcement and crack width from imposed deformation

Zych Mariusz, Jaromska Ewa

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 3

627--638

EN

The paper provides a commentary on the differences in the approach to the mechanics of cracking, concerning cracks from imposed deformations and external loads, as defined in DIN EN 1992-1-1/NA (2011) compared with the EN-1992-1-1 (2004) guidelines. Theoretical assumptions of a detailed method of calculating crack width are presented, the assumptions resulting in, inter alia, a different way of determination of cracks maximum spacing in structural elements, satisfying or not satisfying the condition of the minimum degree of reinforcement. For certain cases, in the condition checking allowable cracks width, the necessity of taking account of cumulative action of imposed deformations and external loads is highlighted, while in EN-1992-1-1 (2004) guidelines imposed deformations and external loads are always treated as non-additive actions. Moreover, more detailed regula-tions for minimum reinforcement specification after DIN EN 1992-1-1/NA (2011), which are an inseparable element of cracking checking in the simplified method are also commented on. The paper identifies critical knowledge gaps and thus motivates researchers to close them. Moreover, the discrepancies between what we know and what we need to know are highlighted. This alerts other scholars to the opportunities for a key contribution. Finally, the conclusions for designers and researchers are presented.

3

Deterministyczne i stochastyczne sformułowanie perturbacyjne zagadnień układów belkowych ze szczelinami

Drewko J.

Prace Naukowe Politechniki Szczecińskiej. Wydział Techniki Morskiej

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2008

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Nr 606 (3)

3-118

EN

The study concerns the beams with slots. The conditions of propagation of slots in bent beams are presented here, basing on the Griffith's proposed criterion of the released energy of distortion. There has been introduced a model of substitute joint of the section of slot affected beam, analysis of propagation of slot arrangement has been presented with the application of the adequate variation theorems. The spring issues as well as spring-plastic issues have been considered including the models of plastic zone in front of the top of the slot, as proposed by Irwin and Dugdale, quasi-static and dynamic questions have been discussed. A comparative analysis of the results based on the method proposed by this study has been conducted by use of finite element method (by means of commercial programmes MSC NASTRAN, ABAQUS, ANSYS) and the experimental research works. The substitute stiffness of the section of slot-affected beam has been determined by use of technical bending theory and cracking mechanics, the equivalence conditions of both models have been analysed. The experimental method has been proposed to determine this stiffness, verified for rectangular section steel beam. There is also presented perturbation stochastic formulation of own [specific] issue. All formulations have been conducted within systems with parameters defined both in the deterministic as well as the stochastic manner. In case of random systems a non-static methodology has been elaborated, basing on the linear analysis of the first two probabilistic moments of the values described in the perturbation form. The length and location of slots have been adopted as random variables. The results of the calculations such as the effect of the size and location of slots on the specific frequencies and forms, based on own programmes, have been presented in graphic form, in the two- and three-dimensional drawings.

4

The influence of material properties on the Q-stress value near the crack tip for elastic-plastic materials

Graba M.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 2

269-190

EN

In the paper, the values of the Q-stress determined for various elastic-plastic materials for single edge notched specimens in bending (SEN(B)) are presented. The influence of the yield strength, the work-hardening exponent and the crack length on the Q-parameter is tested. The numerical results are approximated by closed form formulas.

PL

W pracy przedstawione zostaną wartości naprężeń Q wyznaczone dla szeregu materiałów sprężysto-plastycznych dla próbek trójpunktowo zginanych (SEN(B)), które powszechnie wykorzystuje się do wyznaczania odporności na pękanie w warunkach laboratoryjnych. Omówiony zostanie wpływ granicy plastyczności i wykładnika umocnienia na wartość naprężeń Q, a także wpływ długości pęknięcia. Wyniki obliczeń numerycznych aproksymowano formułami analitycznymi. Rezultaty pracy stanowią podręczny katalog krzywych J-Q, możliwy do wykorzystania w praktyce inżynierskiej.

5

Algorithm for determination of ... functions in Hutchinson Rice Rosengren solution and its 3D generalization

Gałkiewicz J., Graba M.

Journal of Theoretical and Applied Mechanics

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2006

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Vol. 44 nr 1

19-30

EN

In the paper the algorithm to determine ... functions that are necessary to obtain values of stresses, strains and displacements in the crack tip neighborhood according to the Hutchinson, Rice and Rosengren solutions is presented. The algorithm can also be used to determine ... functions for a 3D approximate solution of the stress field in front of the crack introduced by Guo Wanlin, where constraint due to the thickness effect is introduced through the Tz function.

PL

W artykule zaprezentowano algorytm pozwalający na określenie funkcji... niezbędnych do opisu pola naprężeń, odkształceń i przemieszczeń w materiałach nieliniowych według prawa Ramberga-Osgooda. Algorytm pozwala uzyskać również wartości funkcji ... dla próbek trójwymiarowych przy wykorzystaniu parametru Tz, który zależy od grubości próbki i może być wyznaczony numerycznie.

6

On frictionally constrained wing-cracks

Selvadurai A. P. S., Willner K., Gaul L.

Archives of Mechanics

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2005

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Vol. 57, nr 2-3

189-207

EN

This paper examines the mechanics of wing-cracks that are located at its extremities of an interface region with Coulomb friction. The region containing the interface and the wing-cracks is first subjected to an isotropic compression, which induces closure of the interface region. The region is then subjected to a uniaxial compression in an incremental fashion. Since the frictional effects are restricted to pre-defined surfaces, the boundary element technique can be applied quite successfully to determine the influence of Coulomb friction on the development of stress intensity factors at the tips of the wing-cracks.