Lucie Malíková

Crack Path Investigation Using the Generalized Maximum Tangential Stress Criterion: Antisymmetrical Four-Point Bending Specimen

A mixed-mode geometry has been chosen in order to investigate crack propagation through the specimen. There exist several criteria for estimation of the crack path, and this work enriches the concept by application of multi-parameter fracture mechanics. Particularly, the classical MTS criterion is presented in its generalized form when several initial terms of the so-called Williams series expansion are used for the tangential stress approximation. The results obtained show that the generalized approach can be important in some special cases, when the criterion shall be applied in a larger distance from the crack tip.

Comparison of Calibration Functions for Short Edge Cracks under Selected Loads

Attention to the fatigue cracks in steel structures and bridges has been paid for long time. In spite to efforts to eliminate the creation and propagation of fatigue cracks throughout the designed service life, cracks are still revealed during inspections. Note, that depending on location of initial crack, the crack may propagate from the edge or from the surface. The theoretical model of fatigue crack progression is based on linear fracture mechanics. Steel specimens are subjected to various load (tension, three-and four-point bending, pure bending etc.). The calibration functions for short edge cracks are compared for various load and the discrepancies are discussed.

Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms

A study on the accuracy of the values of Williams’ expansion terms influenced by rounding numbers is presented. The results are presented taking into account a three-point bend single edge notched beam. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams’ power series (WPS). Determination of the coefficients of the terms of this series is performed using the least squaresbased regression technique known as the over-deterministic method (ODM), for which displacements data obtained numerically in software ANSYS are taken as inputs. The values of Williams’ expansion terms based on the displacement data obtained are calculated by using various levels of rounding numbers and the results are compared and discussed.

Application of the Williams Expansion near a Bi-Material Interface

A simplified model of a crack approaching a bi-material interface is modelled by means of the finite element method in order to investigate the significance of the higher-order terms of the Williams expansion for the proper approximation of the opening crack-tip stress near the bi-material interface. The discussion on results is presented and the importance of the higher-order terms proved.

Modelling of interfacial transition zone effect on resistance to crack propagation in fine-grained cement-based composites

In this paper, the attention is paid to investigation of the importance of the interfacial transition zone (ITZ) in selected fine-grained cement-based composites for the global fracture behaviour. This is a region of cement paste around the aggregate particles which specific features could have significant impact on the final behaviour of cement composites with a crack tip nearby this interface under applied tension. The aim of this work is to show the basic interface microstructure by scanning electron microscopy (SEM) done by MIRA3 TESCAN and to analyse the behaviour of such composite by numerical modelling. Numerical studies assume two different ITZ thicknesses taken from SEM analysis. A simplified cracked geometry (consisting of three phases – matrix, ITZ, and aggregate) is modelled by means of the finite element method with a crack terminating at the matrix–ITZ interface. ITZ’s modulus of elasticity is taken from generalized self-consistent scheme. A few conclusions are discussed based on comparison of the average values of the opening stress ahead of the crack tip with their critical values. The analyses dealing with the effect of ITZ’s properties on the stress distribution should contribute to better description of toughening mechanisms in silicate-based composites.

Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria

The presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric fourpoint bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semianalytically using both the maximum tangential stress criterion and the strain energy density criterion (implemented as a procedure within the used finite element computational code) as well as numerically (from verification reasons). Multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series. Recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. It appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.).

Crack Propagation in Various Double Cantilever Beam Geometric Configurations

A multi-parameter form of the well-known Maximum Tangential Stress criterion is applied on a series of Double Cantilever Beam configurations in order to investigate the initial crack propagation direction. A comparison with results obtained by means of the classical one-parameter fracture criterion is performed. The main idea was to find out if the generalized form of the fracture criterion is able to describe the crack deflection that was observed experimentally for several geometric configurations although the crack was loaded under pure mode I. Numerical analyses by means of finite elements were carried out and obtained results discussed.

Impact of specific fracture energy investigated in front of the crack tip of three-point bending specimen

Presented study is focused on the analysis of the dependence of the specific fracture energy value on the assumed work of fracture in threepoint bending tests. Specimens of different sizes and relative notch lengths are assumed in this study, in order to take into account the size effect. The three-point bending test of cracked specimens is simulated numerically by means of commercial software based on the finite element method with implemented cohesive crack model. Three levels of the specific fracture energy are considered.

Williams expansion-based approximation of the stress field in an Al 2024 body with a crack from optical measurements

A study on the approximation of the stress field in the vicinity of crack tip in a compact tension specimen made from Al 2024-T351 is presented. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (ODM) for which displacements data obtained experimentally via optical measurements are taken as inputs. The stress fields reconstructed based on the displacement data obtained experimentally by means of optical measurements are verified by means of the stress field approximations derived for the normalized CT specimen via hybrid elements.

Particulate Composite Damage: The Influence of Particle Shape on Crack Path

Using stiff particles mixed into polymer matrix may significantly improve global mechanical response of the composite. Unfortunately, this process leads to other side effects, for example, presence of stress concentration at the particle-matrix interface or negative influence on the fracture toughness. The paper presents an approach to estimate the influence of particles on the micro-crack propagation. Material properties of matrix and particles were estimated experimentally. A two-dimensional computational model was proposed and all calculations were done in software ANSYS. On the base of linear elastic fracture mechanics, the influence of the particle shape on the micro-crack propagation paths was analyzed via numerical studies. The results of numerical simulations show that the shape of the particles can significantly influence the micro-crack path as well as the stress intensity factor on the crack tip, which corresponds to fracture toughness of polymer composite filled with rigid particles. The conclusions of this paper could contribute to better understanding of the behavior of the polymer composites.