Quasi-brittle Composites Research Articles

On a computational stress-based non-local damage model for quasi-brittle composites

Numerical models for the stress and strain analysis of quasi-brittle composites, such as cement-based ones, supplied by various stiffening particles, under mechanical, thermal, etc. loads should handle i) the creation of certain micro-damaged zones, antecedent to ii) the initiation and propagation of a system of macroscopic cracks. Whereas ii) can be analysed using some extended, generalized or similar finite element technique (XFEM, GFEM, etc. algorithms), i) must rely on a smeared crack formulation, whose regularization properties are derived from a non-local stress evaluation. This paper studies mathematical and computational properties of such model, based on the Eringen's approach, useful in many applications in civil engineering.

English

Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying the dynamical approach using the Kelvin viscoelastic model and cohesive interface properties. The existence and convergence results rely on the semilinear computational scheme coming from the method of discretization in time, using several types of Rothe sequences, coupled with the extended finite element method (XFEM) for practical calculations. Numerical examples refer to cementitious samples reinforced by short steel fibres, with increasing number of applications as constructive parts in civil engineering.

Identifying the Range of Micro-Events Preceding the Critical Point in the Destruction Process in Traditional and Quasi-Brittle Cement Composites with the Use of a Sound Spectrum.

This paper presents the possibilities of determining the range of stresses preceding the critical destruction process in cement composites with the use of micro-events identified by means of a sound spectrum. The presented test results refer to the earlier papers in which micro-events (destruction processes) were identified but without determining the stress level of their occurrence. This paper indicates a correlation of 2/3 of the stress level corresponding to the elastic range with the occurrence of micro-events in traditional and quasi-brittle composites. Tests were carried out on beams (with and without reinforcement) subjected to four-point bending. In summary, it is suggested that the conclusions can be extended to other test cases (e.g., compression strength), which should be confirmed by the appropriate tests. The paper also indicates a need for further research to identify micro-events. The correct recognition of micro-events is important for the safety and durability of traditional and quasi-brittle cement composites.

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

Heterogeneous quasibrittle composites like concrete, ceramics and rocks comprise grains held together by bonds. The question on whether or not the path of the crack that leads to failure can be predicted from known microstructural features, viz. bond connectivity, size, fracture surface energy and strength, remains open. Many fracture criteria exist. The most widely used are based on a postulated stress and/or energy extremal. Since force and energy share common transmission paths, their flow bottleneck may be the precursory failure mechanism to reconcile these optimality criteria in one unified framework. We explore this in the framework of network flow theory, using microstructural data from 3D discrete element models of concrete under uniaxial tension. We find the force and energy bottlenecks emerge in the same path and provide an early and accurate prediction of the ultimate macrocrack path {mathcal {C}}. Relative to all feasible crack paths, the Griffith’s fracture surface energy and the Francfort–Marigo energy functional are minimum in {mathcal {C}}; likewise for the critical strain energy density if bonds are uniformly sized. Redundancies in transmission paths govern prefailure dynamics, and predispose {mathcal {C}} to cascading failure during which the concomitant energy release rate and normal (Rankine) stress become maximum along {mathcal {C}}.

Nonlocal dynamic damage modelling of quasi-brittle composites using the scaled boundary finite element method

In this contribution, a nonlocal approach is proposed to model the dynamic damage of quasi-brittle composites within the framework of the scaled boundary finite element method (SBFEM). The image-based quadtree decomposition is used to automatically achieve multi-level mesh of a domain with geometric as well as material discontinuities. By enforcing a 2:1 balanced condition, only limited types of S-domains are used. Owning to the salient capability of the SBFEM in constructing polygons with arbitrary edges and nodes, there is no extra burden on dealing with hanging nodes between neighbouring S-domains in different sizes. Furthermore, the strain modes and the original stiffness matrix of each S-domain and the weighting matrix for nonlocal formulation are all pre-computed initially and extracted in subsequent time steps. Consequently, the computational efficiency of the proposed approach is considerably accelerated. The mesh dependence is well eliminated by using an integral-type nonlocal model. Several benchmarks are simulated to demonstrate the efficiency, robustness and variability of the proposed approach for macroscale and mesoscale problems. It is found that the proposed method can model multiple crack propagation and crack branching as well. Compared with the case under static load, the failure mode of quasi-brittle materials under dynamic load depends not only on the strength of each component but also on the propagation of stress wave.

A virtual element and interface based concurrent multiscale method for failure analysis of quasi brittle heterogeneous composites

The use of multiscale schemes for computational failure evaluations of quasi-brittle composites, particularly concrete, has become a promising challenge for evaluating the complex degradation mechanisms at different scales of observations. In the framework of standard finite element procedures, both concurrent and semi-concurrent multiscale procedures have so far been considered for analysing failure behaviour of quasi-brittle materials. When it comes to composite materials like concrete with heterogeneous meso-structures due to the presence of highly irregular inclusions regarding both size and geometry, the material meso-structure critically determines the macroscopic mechanical properties and thus the mechanical response to external loading. In this work a concurrent multiscale method is proposed for numerical analysis of the failure behaviour of heterogeneous and quasi-brittle materials like concrete. This is based on combining a discretization based on the Virtual Element Method (VEM) and Interface Elements (IEs) in the framework of the discrete crack approach using a mixed augmented Lagrangian for the interfaces. Mesoscale numerical simulations of 3 point beam specimens are presented to assess the quality of the proposed concurrent multiscale procedure to accurately and effectively capture the relevant features of their failure mechanisms, highlighting the advantages of using the VEM technology.

Assessment of the Mechanical Properties of ESD Pseudoplastic Resins for Joints in Working Elements of Concrete Structures.

Concrete structure joints are filled in mainly in the course of sealing works ensuring protection against the influence of water. This paper presents the methodology of testing the mechanical properties of ESD pseudoplastic resins (E-elastic deformation, S-strengthening control, D-deflection control) recommended for concrete structure joint fillers. The existing standards and papers concerning quasi-brittle cement composites do not provide an adequate point of reference for the tested resins. The lack of a standardised testing method hampers the development of materials universally used in expansion joint fillers in reinforced concrete structures as well as the assessment of their properties and durability. An assessment of the obtained results by reference to the reference sample has been suggested in the article. A test stand and a method of assessing the mechanical properties results (including adhesion to concrete surface) of pseudoplastic resins in the axial tensile test have been presented.

Modeling microfracture evolution in heterogeneous composites: A coupled cohesive phase-field model

Modeling micro-crack evolution in highly heterogeneous solids has been a major challenge in brittle materials owing to their complex microstructures and the complicated interactions between their components. The present work aims to address this challenging task through the development of a novel coupled cohesive phase-field model that can accurately predict the evolution of microfracture and describe interfacial de-bonding in quasi-brittle composites. As a crucial part of our modeling framework, the interface is described by an auxiliary interface variable, thus the interface properties can be regularized. The developed model has the following novelties: (1) the coupled cohesive phase field method is accomplished by implementing a gradient damage formulation to predict crack nucleation and propagation in quasi-brittle solids; (2) the interface properties in complex heterogeneities are regularized by the interaction between matrix and inclusions properties, as well as the width of the interface; and (3) it can precisely predict the crack evolution (crack initiation, propagation, deflection into the matrix) in quasi-brittle heterogeneous solids. Particularly, the proposed model is validated using our implemented experimental results, from which the micro-crack trajectories in fiber-cement composites were observed. The proposed approach shows great potentials in predicting the fiber de-bonding as well as the micro-crack kinking path in complicated quasi-brittle materials.

Identification of the Destruction Process in Quasi Brittle Concrete with Dispersed Fibers Based on Acoustic Emission and Sound Spectrum.

The paper presents the identification of the destruction process in a quasi-brittle composite based on acoustic emission and the sound spectrum. The tests were conducted on a quasi-brittle composite. The sample was made from ordinary concrete with dispersed polypropylene fibers. The possibility of identifying the destruction process based on the acoustic emission and sound spectrum was confirmed and the ability to identify the destruction process was demonstrated. It was noted that in order to recognize the failure mechanisms accurately, it is necessary to first identify them separately. Three- and two-dimensional spectra were used to identify the destruction process. The three-dimensional spectrum provides additional information, enabling a better recognition of changes in the structure of the samples on the basis of the analysis of sound intensity, amplitudes, and frequencies. The paper shows the possibility of constructing quasi-brittle composites to limit the risk of catastrophic destruction processes and the possibility of identifying those processes with the use of acoustic emission at different stages of destruction.

Topology optimization for maximizing the fracture resistance of quasi-brittle composites

In this paper, we propose a numerical framework for optimizing the fracture resistance of quasi-brittle composites through a modification of the topology of the inclusion phase. The phase field method to fracturing is adopted within a regularized description of discontinuities, allowing to take into account cracking in regular meshes, which is highly advantageous for topology optimization purpose. Extended bi-directional evolutionary structural optimization (BESO) method is employed and formulated to find the optimal distribution of inclusion phase, given a target volume fraction of inclusion and seeking a maximal fracture resistance. A computationally efficient adjoint sensitivity formulation is derived to account for the whole fracturing process, involving crack initiation, propagation and complete failure of the specimen. The effectiveness of developed framework is illustrated through a series of 2D and 3D benchmark tests.

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.

Development of two-phase unit cell: for modeling the deformation and failure response of quasi-brittle composites

This paper discusses the conceptual development of unit cell (UC) approach in modeling the total deformation and failure response of quasi-brittle composites. The UCs were modeled with only two distinct phases, namely the volume fractions of the matrix phase and that of the inclusion phase, for the mechanical characterization of the materials under consideration. A study has been carried out to determine the minimum size of the UC, above which the predicted response may be size independent, making it a representative unit of the four quasi-brittle composites considered. The minimum size required was observed to be higher than that of a pure deformation model, and the results varied with the total volume fraction of the constituent phases. The failure strength predicted by the UC of a particular volume fraction was also compared with that of the corresponding experimental results, resulting in a good correlation between the two.

Fracture model of brittle and quasibrittle materials and geomedia

A general model and a unified mathematical formalism are proposed for description of inelastic deformation and fracture of any solids, where brittle or plastic, as their evolution in effective force fields. Loaded solids and media are considered as nonlinear dynamic systems. One of the main tasks of the work is to show that if deformation and fracture of a strong medium is treated as its evolution in effective force fields, numerical solutions of equations of solid mechanics do demonstrate the fundamental properties of nonlinear dynamic systems—self-organized criticality and two-stage evolution (a rather slow quasistationary stage and a superfast catastrophic stage or a blowup mode). The model is tested by simulation of fracture of quasibrittle composites under axial compression. Calculations are also presented for the now developing tectonic flows and seismic processes in Central Asia, including the Baikal rift zone and the Altai-Sayany folded region. It is shown that numerical solutions of all examined problems of inelastic deformation and fracture demonstrate self-organized criticality of loaded media, including peculiarities of slow dynamics and spatial-temporal migration of deformation activity, and as well as two-stage fracture: comparatively slow quasi-equilibrium damage accumulation and superfast catastrophic fracture. The predicted seismic events obey the Gutenberg-Richter law.

Does representative volume element exist for quasi-brittle composites?

Abstract The validity on the use of representative volume element (RVE) to predict the mechanical behavior of quasi-brittle composites is addressed based on studies of porous epoxy under tensile action. For the elastic behavior, the more efficient single particle (SP) RVE approach predicts accurately when the volume fraction is less than a critical value of 15–20% depending on the relative stiffness of the matrix and the inclusion. At higher volume fraction, the multiple particle (MP) RVE provides accurate predictions with less than 6% error, for MP-RVE sizes that are at least 6 times larger than the size of the inclusion. In the inelastic softening regime, the RVE does not exist for the homogenized stress–strain behavior due to the high localization of damage. Instead, the fracture energy or toughness should be used as a size-independent measure in the RVE approach to describe the fracture response in quasi-brittle composites. The fracture toughness predicted with the MP-RVE models shows size invariance and compares well with the experiments for volume fractions of up to 20% with deviations of less than 6%, while the SP-RVE models are only recommended for use at volume fractions of less than 10%.

Determination of the size of the representative volume element for random quasi-brittle composites

A representative volume element (RVE) is related to the domain size of a microstructure providing a “good” statistical representation of typical material properties. The size of an RVE for the class of quasi-brittle random heterogeneous materials under dynamic loading is one of the major questions to be answered in this paper. A new statistical strategy is thus proposed for the RVE size determination. The microstructure illustrating the methodology of the RVE size determination is a metal matrix composite with randomly distributed aligned brittle inclusions: the hydrided Zircaloy constituting nuclear claddings. For a given volume fraction of inclusions, the periodic RVE size is found in the case of overall elastic properties and of overall fracture energy. In the latter case, the term “representative” is discussed since the fracture tends to localize. A correlation factor between the “elastic” RVE and the “fracture” RVE is discussed.

New size number and the fracture state of concrete structure

A new size number describing the fracture state of concrete structures is developed in which the structural size and the main fracture properties of concrete are dealt with. The relation between the fracture state of concrete beams loaded in bending and the newly proposed size number is presented graphically. The shape of the stress - crack curve, which is a typical property of most quasi-brittle composites like concrete, is found to be an important factor in determining the size number together with the fracture energy, the elastic modulus and the ultimate tensile strength of materials. The influence of 'the structural size on the fracture state is also graphically presented.

Numerical simulation of crack propagation from microcracking to fracture

By numerical simulation, damage processes of quasi-brittle composites can be studied. The Bochum Method allows the calculation of all states of cracked material structure during the loading process from microcracking to fracture. Using this method a damage process of tensile loaded material was found which is not identical with assumptions used for determining the G F value of fracture energy. Separating energy in (micro)crack formation from (macro) crack propagation, the authors propose a procedure to evaluate the G F value from tensile or bending tests.