Václav Veselý

Parallelization of lattice modelling for estimation of fracture process zone extent in cementitious composites

This paper is focused on the verification and validation of the developing technique for estimation of the extent (the size and shape) of the fracture process zone (FPZ) in quasi-brittle silicate-based specimens/structures during failure process (termed the ReFraPro -Reconstruction of Fracture Process - technique). Most experimental data published in the literature are incomplete for its sound validation; therefore, numerical simulations by means of physical discretization of continuum are used for supplementing the verification of the technique. A discrete spring network/lattice particle-type model formulated as a nonlinear dynamical system is utilized. Parallelized implementation within the CUDA environment helps to decrease the computational cost of the simulations to an admissible level. The conducted analysis demonstrates satisfactory agreement of the size and shape of the FPZ reconstructed by the ReFraPro technique with both the data of the performed simulations and selected experimental data from literature.

An application for the fracture characterisation of quasi-brittle materials taking into account fracture process zone influence

Abstract The paper introduces a Java application programmed for the advanced determination of the fracture characteristics of silicate-based materials failing in a quasi-brittle manner. The tool reconstructs the progress of a quasi-brittle fracture from the measured load–displacement curve and the knowledge of basic mechanical properties of the material. The main contribution of the proposed approach is that it takes the characteristics of the Fracture Process Zone (FPZ, particularly its extent, i.e. its size and shape) evolving at the tip of the propagating crack during the failure process into account and incorporates them into the fracture-mechanical parameter evaluation procedure(s). This approach is expected to substantially diminish the influence of the test specimen’s size/shape and the test geometry on the values of the parameters of nonlinear fracture models determined from the records of fracture tests on laboratory specimens. The application implements a developed technique for estimation of the size and shape of the FPZ. The technique is based on an amalgamation of several modelling concepts dealing with the failure of structural materials, i.e. multi-parameter linear elastic fracture mechanics, classical nonlinear fracture models for concrete (equivalent elastic crack and cohesive crack models), and the plasticity approach. The knowledge of the FPZ’s extent is employed for the relation of a part of the entire work of fracture to its characteristics within the presented approach. The verification and validation of the developed technique is performed via numerical simulations using the authors’ own computational code based on physical discretization of continuum and selected sets of experimental evidence published in the literature. Reasonable agreement is observed between the outputs of the presented semi-analytical technique and both the simulation results and the experimental data.

Convergence Study on Application of the Over-Deterministic Method for Determination of Near-Tip Fields in a Cracked Plate Loaded in Mixed-Mode

Multi-parameter description of crack behavior in quasi-brittle materials offers still enough space for investigations. Several studies have been carried out by the authors in this field [1-3]. One part of the publications by the authors (this work included) contain analyses of the accuracy, convergence and/or tuning of the over-deterministic method that enables determination of the coefficients of the higher-order terms in Williams expansion approximating the stress and displacement fields in a cracked body without any complicated FE formulations. These intermediate studies should bring together a list of recommendations how to use the ODM as effectively as possible and obtain reliable enough values of coefficients of the higher-order terms. Thus, the stress/displacement field can be determined precisely even in a larger distance from the crack tip, which is crucial for assessment of the fracture occurring in quasi-brittle materials.

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.

Influence of Boundary Conditions on Higher Order Terms of Near-Crack-Tip Stress Field in a WST Specimen

A precise description of the stress and deformation fields in a cracked body is provided using multi-parameter fracture mechanics based on the approximation of the fields by means of the Williams’ power series. This paper presents a detailed analysis of the stress field in a wedge-splitting test geometry specimen aimed at the calculation of coefficients of the higher order terms (up to 14) of the Williams’ expansion. The numerical study is conducted with the use of a conventional finite element package; however, for processing of the results an over-deterministic method is employed. Special attention is paid to the influence of boundary conditions of the test geometry on the values of the coefficients of the higher order terms of the Williams’ series. The results are compared to data from the literature; a strong effect of the boundary conditions is observed.

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.

Effect of the Load Eccentricity on Fracture Behaviour of Cementitious Materials Subjected to the Modified Compact Tension Test

Fracture properties of quasi-brittle cementitious composites are typically determined from the load–displacement response recorded during a fracture test by using the work-of-fracture method or possibly other relevant fracture models. Our contribution is focused on a set of experimental tests which are used to study the fracture behaviour on notched dog-bone-shaped specimens made of cementitious materials. These specimens are subjected to modified compact tension (ModCT) test under a specific range of eccentricity of the tensile load. This type of test generates a stress state in the specimen ligament which combines a direct tension with a defined level of bending due to eccentricity of the tensile load. Several values of relative notch length are also considered. While the crack propagates, a variety of stress states, resulting in variations in the crack-tip stress and deformation constraint, appears in the ligament zone because of the changes in the eccentricity of the applied load, which influences the fracture behaviour of the investigated specimens. The K-calibration, T-stress, CMOD and COD curves for ModCT specimens are introduced and variations of these curves with varying load eccentricity are discussed.

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.

Investigation of Fracture and Electrical Resistivity Parameters of Cementitious Composite for their Utilization in Deterioration Models

The paper is focusing on the investigation of the effective crack length obtained from bending test on concrete notched beams with the complementary measurements of electrical resistivity of the tested concrete. The electrical resistivity measurements are performed on several stages of the fracture process along the specimen ligament for each tested notched beam. Gained results of the concrete resistivity during the fracture process, i.e. its dependence on the crack length or opening, provide information which should be taken into account in structural durability analyses. The fracture tests are conducted for a set of specimens differing in the notch length. Changes of the concrete resistivity with increasing effective crack length are observed and discussed.