Jakub Sobek

Multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite WST specimens

For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in larger distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. The stress intensity factor K, T-stress and even higher-order terms of William series were determined and subsequently utilized for analytical approximation of the stress field. A good fit between the analytical and numerical solution in dependence on the distance from the crack tip was shown, compared and discussed. Presented approach is considered as suitable for estimation of the fracture process zone extent in silicate composite materials.

Accurate Description of Near-Crack-Tip Fields for the Estimation of Inelastic Zone Extent in Quasi-Brittle Materials

A description of stress and displacement fields by means of the Williams power series using also higher-order terms is the focus of this paper. Coefficients of this series are determined via the over-deterministic method from the results of conventional finite element (FE) analysis. A study is conducted into the selection of the FE node set whose results are processed in this regression technique. Coefficients up to the twelfth term were determined with high precision. The effect of the position of the FE node set on the accuracy of the values of the higher-order term coefficients is reported.

NUMERICAL STUDY OF FAILURE OF CEMENTITIOUS COMPOSITE SPECIMENS IN MODIFIED COMPACT TENSION FRACTURE TEST

Abstract The paper introduces a numerical analysis of failure process in specimens loaded in modified Compact Tension (CT) test configuration which are intended to be used for estimation of fracture parameters of quasi-brittle cement-based materials, including the extent of the fracture process zone. Specimen set (consisting of three sizes), designated to future testing in lab by X-ray imaging, was modelled in ATENA 2D finite element method software. Several variants of the tensile load eccentricity, the way of the load application and the initial crack length were considered in order to optimize the range of demanding experiments.

Selecting a Suitable Specimen Shape with Low Constraint Value for Determination of Fracture Parameters of Cementitious Composites

The stress intensity factor and the T-stress describing the near-crack-tip fields for selected specimen shapes of a test geometry based on wedge splitting and three point bending tests with several variants of boundary conditions are computed using finite element software ANSYS. The test configuration in question is expected to be a convenient alternative to classical fracture tests (especially the tensile ones) for investigation of the quasi-brittle fracture of building materials, when low constraint is requested. These specimens are investigated within the framework of two-parameter fracture mechanics; near-crack-tip stress field parameters are determined and compared with those of the wedge splitting test due to their shape similarity. The sensitivity of the values of these parameters to the boundary conditions is also shown. Suitable choice of the shape of the specimens is discussed.

Acoustic Emission from Quasi-Brittle Failure of Cementitious Composites - Experimental Measurements and Cohesive Crack Model Simulations

Conducted loading tests of plain concrete specimens are briefly introduced in the paper together with description of the performed numerical simulations of these tests in ATENA 3D software. The simulation results of concrete failure are analysed in detail and compared with the experimental results recording failure processes with the help of acoustic emission. The simulation results are in good agreement with the recorded data.

Numerical Modelling of a Chevron Notched Bend Specimen - Plane Model

The paper focuses on a numerical modelling of the initial chevron notch in test specimens subjected to the three-point bending test geometry configuration. The plane model is used with variable thicknesses of the layers with plane stress condition. The number of layers is being investigated and the influence of some input parameters like relative crack length, breadth of initial notch, etc. is evaluated by value of the stress intensity factor for tension loading mode.

Analytical Approximation of Crack-Tip Stress Field: Study on Efficient Determination of Coefficients of Higher Order Terms of Williams Power Expansion

The paper presents a study on accuracy of the multi-parameter approximation of the stress field in a cracked body using Williams power series calibrated according to results of FEM computation. Main attention is paid to a detailed analysis of suitable selection of FE nodes, whose results serve as inputs to the over-deterministic method (ODM) employed for determination of the coefficients of terms of the Williams expansion describing the crack-tip field. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity versus nodes selected from a specific part of the test specimen body in a specific way. Comparison is made with the usage of the authors’ own developed procedures enabling both the determination of the coefficients of the analytical approximation of stress field based on the FE results and the backward reconstruction of the field from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study.

Work of Fracture due to Compressive Component of Loading in Wedge Splitting Test on Quasi-Brittle Cementitious Specimens

The paper presents an analysis of the influence of the compressive (vertical) component of the loading force in the wedge splitting test on the values of fracture characteristics determined using standard procedures where this component is ignored. Particularly, a portion of work of fracture due to this compressive component of loading working on vertical displacements is investigated and given into relation with the common part of work of fracture calculated in the horizontal direction only. The results show that, based on the angle and width of the wedge used in the particular WST configuration, the portion of the work of fracture due to compressive loading can be considerable and should not be neglected.

Estimation of the Zone of Failure Extent in Quasi-Brittle Specimens with Different Crack-Tip Constraint Conditions from Stress Field

A multi-parameter fracture mechanics concept based on the Williams power series is applied on novel cracked specimen geometries utilizing combined boundary conditions of the wedge splitting and the three-point bending test. Crack tip stress fields for various configurations (causing different constraint conditions at the crack tip and thus also different fracture process zone extents) are numerically investigated and subsequently analytically reconstructed using developed procedure. An importance of using higher order terms of the Williams series is demonstrated.

Comparison of Fracture Tests Numerical Models Created with Real Material Properties

This contribution discusses numerical models of three different fracture tests – three-point bending (3PB), modified compact tension (modCT) and wedge-splitting test (WST). The aim is to compare loading diagrams (loading force vs. crack mouth opening displacement) obtained from these numerical models, created with real material properties. These properties were acquired from experimental data measurement. To assemble the numerical models, ATENA Science FEM software was used. In this software, damaging of the structure/specimen occurred by cracks can be modelled, their initiation and progressive propagation can be seen throughout the loading process.