Cracking Localization Research Articles

Probabilistic model for cracking localization in reinforced fibrous concrete beams

This paper proposes a probabilistic model that explains the phenomenon of cracking localization (CL) in RC beams with addition of steel fibers. Quantification of the CL is defined as the ratio between the total number of cracks and the number of significantly wide cracks. The model considers both the fibers and conventional reinforcement ratios, as well as the steel stress hardening and the location of the rebars in the cross-section. The fiber distribution in the concrete mix is considered random while the conventional reinforcement—as deterministic. A cumulative function of the total steel distribution, and a binomial probability function are proposed for a newly defined variable that represents the distribution of the fibers effectiveness along the beam. The model was validated with available data from flexural experiments showing good agreement of the model’s prediction with the reported results. The model shows that the cracking localization level in beams is more pronounced in beams with low reinforcement ratios and relatively large fibers content and enables its quantification.

Quantification of Desiccation Cracking and Strain Localization in Lime-Treated Compacted Expansive Soils Using DIA and DIC

Quantification of Desiccation Cracking and Strain Localization in Lime-Treated Compacted Expansive Soils Using DIA and DIC

Fracture behavior and size effect of UHPFRC: Experimental and meso-scale numerical investigation

In this research, the fracture characteristics and size effect of ultra-high performance fiber reinforced concrete (UHPFRC) are investigated by notched three-point bending beam test and meso-scale numerical simulation. Four series of geometrically similar UHPFRC notched-beams with different sizes were tested at quasi-static condition. Crack patterns during the fracture process were obtained by digital image correlation and the phenomenon of crack initiation, multiple cracking and crack localization were well captured. The macro-scale fracture properties are analyzed by double-K fracture model (DKFM) from the perspective of composite toughening. Results show that the initial fracture toughness evaluates the toughness of matrix and the increment from initial fracture toughness to unstable fracture toughness evaluates the toughening due to fiber bridging. The initial fracture toughness and unstable fracture toughness have no size effect and can be treated as material inherent. Experimental results also show a slight decreasing tendency of strength with the increasing of specimen size, which can be approximately fitted by size effect law (SEL). Then a meso-scale numerical model was developed by explicit representation of fibers and directly considering bond-slip relationship of fiber–matrix. Simulation results show that the meso-scale numerical model developed in this research can well simulate the fracture of UHPFRC in terms of crack patterns, fracture process zone, mechanical response and size effect. Parametric study was also conducted based on the meso-scale numerical model and the effects of fiber content, fiber orientation and interfacial bond strength on fracture performance and size effect are analyzed.

Experimental investigation of cracking localization in RC beams with steel fibers

AbstractThis article presents an experimental study aimed to identify and quantify the cracking localization (CL) phenomenon in under‐reinforced R/SFRC beams. Results of current experiments together with those of previous tests published by the authors were used for quantification of the cracking localization level (CLL) considering the effect of fiber content, Vf, and of longitudinal reinforcement ratio, ρs, over a wide range of ρs and the effect of rebar yield and ultimate strengths. The experimental program consisted of four‐point bending tests of normal strength R/SFRC beam specimens with 400 and 500‐MPa steel and fiber volumetric contents Vf of 0.5 and 0.76%. A new definition is introduced for “significantly wide cracks” that yields a unique definition of the CLL when this phenomenon diminishes. Moreover, it is now proposed to change the definition of CLL. The study identified the existence of a transition point (TP), beyond which addition of fibers to the concrete mix do not affect CLL anymore. Observations from the experimental results prove the consistency of the newly proposed CLL definitions as well as the dependency of CL on both the amount and stress hardening of the tension steel. Their use enables a clear delineation of the CL phenomenon in R/SFRC beams. The importance of this finding refers to the reported decrease of flexural ductility in R/SFRC beams due to high CLL. Hence, the importance of the ability, achieved in the current findings, to quantify the conditions for TPs in various cases.

Modular implementation framework of partitioned path-following strategies: Formulation, algorithms and application to the finite element software Cast3M

Damage, cracking, and strain localization mechanisms often lead to unstable structural responses characterized by snap-backs (i.e., force and displacement decrease simultaneously). Standard nonlinear Newton-based solution algorithms with displacement/force control cannot capture the equilibrium curve in its entirety. This can be overcome using path-following formulations. A general (i.e., valid for any finite element code) implementation framework can be designed and applied to the Cast3M software by collecting the essential concepts and the formalism of partitioned path-following arc-length algorithms. Thanks to these developments, Cast3M is now capable of processing path-following equations without any major modifications. Three path-following constraints were selected to demonstrate the applicability of this framework: a first one on the combination of the displacement increment at a given set of nodes, a second one on the maximum strain increment over the computational domain, and a third one on the maximum elastic predictor of the damage/plastic criterion function over the computational domain. Two- and three-dimensional strain localization simulations show that the proposed framework behaves in a stable and convergent manner, even when multiple severe snap-back instabilities are present. Users of Cast3M shall find the proposed study helpful in that it allows them to focus on developing new path-following equations for the software. Cast3M is developed by the French Alternative Energies and Atomic Energy Commission (CEA) and freely available for research purposes. The developments discussed in this paper have been made available to the user/developer community along with Cast3M 2021 (release date: June 2021).

Probabilistic Finite Element Modeling of Textile Reinforced SHCC Subjected to Uniaxial Tension.

The paper presents a finite element investigation of the effect of material composition and the constituents’ interaction on the tensile behavior of strain-hardening cement-based composites (SHCC) both with and without textile reinforcement. The input material parameters for the SHCC and continuous reinforcement models, as well for their bond, were adopted from reference experimental investigations. The textile reinforcement was discretized by truss elements in the loaded direction only, with the constitutive relationships simulating a carbon and a polymer textile, respectively. For realistic simulation of macroscopic tensile response and multiple cracking patterns in hybrid fiber-reinforced composites subjected to tension, a multi-scale and probabilistic approach was adopted. SHCC was simulated using the smeared crack model, and the input constitutive law reflected the single-crack opening behavior. The probabilistic definition and spatial fluctuation of matrix strength and tensile strength of the SHCC enabled realistic multiple cracking and fracture localization within the loaded model specimens. Two-dimensional (2D) simulations enabled a detailed material assessment with reasonable computational effort and showed adequate accuracy in predicting the experimental findings in terms of macroscopic stress–strain properties, extent of multiple cracking, and average crack width. Besides material optimization, the model is suitable for assessing the strengthening performance of hybrid fiber-reinforced composites on structural elements.

Effect of a High Mg Solute Content on the Hot Workability of Al-Mg Alloys.

The workability of Al-xMg alloys with a high Mg content (Al-6Mg, Al-8Mg, Al-9Mg) was evaluated by investigating the microstructure and processing map. Hot torsion tests were conducted in the range of 350-500 °C between 0.1 and 1 s-1. Constitutive equations were derived from various effective stress-strain curves, and the thermal activation energies for deformation obtained were 171 kJ/mol at Al-6Mg, 195 kJ/mol at Al-8Mg, and 220 kJ/mol at Al-9Mg. In the case of the processing map, the instability region, which widened with increasing Mg content, was due mainly to the influence of the Mg solute, which activated grain boundary cracking and flow localization.

Multiphysics Lattice Discrete Particle Model for the simulation of concrete thermal spalling

Explosive thermal spalling behavior during fire exposure is one of the major issues in the design of modern reinforced concrete structures. Previous experience on fire disasters indicates that spalling of concrete can have serious structural and economic consequences and must be taken into account in the design for fire. However, spalling mechanisms and their interaction still remain in dispute in the scientific community. In order to shed some light on this phenomenon, a discrete hygro-thermal model of concrete at high temperature called DTemPor3 is proposed and a full coupling scheme between DTemPor3 and the Lattice Discrete Particle Model (LDPM) is performed. The proposed multi-physical coupled model features the effect of pore pressure and temperature on the mechanical response as well as the impact of cracking on moisture mass transport and heat transfer. Simulations of typical spalling experiments show good agreements with data gathered from the literature for both high-performance concrete and ordinary concrete, demonstrating the accuracy of the proposed approach. Cracking localization is found to significantly impede the local pore pressure build-up due to the increase of pore or crack volume. The numerical simulations demonstrate that the spalling phenomenon can be successfully reproduced, only when the effect of thermal stresses is taken in account along with the effect of pore pressure on crack initiation.

Flexural and shear behaviour of high-strength SFRC beams without stirrups

This study investigates the effects of steel fibre content and reinforcement ratio on the flexural and shear behaviours of sustainable high-strength concrete (HSC) beams without stirrups. Five different volume fractions of hooked steel fibres, Vf, 0, 0·25, 0·5, 0·75, and 1%, and two different reinforcement ratios, ρ, 0·72 and 2·93%, were considered. Test results indicated that the minimum shear reinforcement of HSC beams was effectively eliminated by adding only a small amount of steel fibres (≥ 0·25 vol%). This amount was much smaller than the minimum requirement of the ACI 318 code. For the lightly reinforced HSC beams, the load-carrying capacity and post-cracking stiffness were improved by adding steel fibres and increasing their amount, whereas the ultimate deflection decreased with the addition of fibres because of the cracking localization phenomenon. For the heavily reinforced HSC beams, the first-cracking load, load-carrying capacity, and deflection capacity all increased with the addition of steel fibres and increasing their amount up to 0·75%. Finally, based on the comparison of experimental and predictive results, Craig's model and Narayanan's and Kwak's models were determined as the best predictive models for the factored flexural and shear strengths of reinforced HSC and steel-fibre-reinforced concrete beams without stirrups, respectively.

Effect of cracking localization on the structural ductility of normal strength and high strength reinforced concrete beams with steel fibers

This article presents a study of cracking localization in normal and high strength concrete beams that include steel fibers and the influence of this localization on their structural ductility. It is shown that for a given fiber type and content, as the reinforcement ratio ρ decreases, the cracking localization level increases. The effect of ρ on the level of cracking localization is more pronounced for low amounts of conventional reinforcement. This range of conventional reinforcement ratio is typical of slabs and especially for the commonly thicker protective slabs. Examination of the effect of the reinforcement ratio on the flexural ductility shows that there exists a transition point below which the ductility ratio decreases with ρ. This transition point is well above the minimum reinforcement ratio, which is required in design codes for plain reinforced concrete elements. Empirical analysis of the relation between cracking localization and ductility ratio shows that up to the same transition point, as cracking localization increases, the flexural ductility decreases. Findings of this study show that the positive effect of adding fibers on enhancing the impact resistance of slabs and beams is conflicted by their negative influence on reducing the structural ductility for low reinforcement ratios, which are typical of protective slabs.

Characterization of Hot Deformation Behavior and Processing Maps of Ti–19Al–22Mo Alloy

The isothermal compression tests were carried out to study the hot deformation behavior and microstructure evolution of Ti–19Al–22Mo alloy. The samples were deformed in the temperature range from 1100 to 1250 °C with an interval of 50 °C, strain rate ranging from 0.01 to 1 s−1 and the height reduction of 50% using Gleeble-3800 thermal–mechanical simulator. By using this experimental data an artificial neural network (ANN) model was developed and evaluated with unseen data. Further, the developed ANN model was used to predict flow stress correction from adiabatic heating at finer intervals of strain rates and temperatures. The predicted isothermal flow stress values were utilized to construct processing maps for Ti–19Al–22Mo alloy at true strain of 0.4 and 0.6. The maximum efficiency was noticed at 1100 °C with the strain rate of 0.01 s−1 associated with dynamic recrystallization and dynamic recovery. The deformation conditions of the instability domains in processing map showed wedge cracking and flow localization. Using the processing maps safe working parameters for hot deformation of Ti–19Al–22Mo alloy was identified.

Quantification of cracking localization in fibre-reinforced concrete beams

The paper presents an analysis of cracking localization in beams made of fibre-reinforced concrete with conventional reinforcement. This phenomenon has been quantified by the ratio m/n between the number of the significantly wide cracks and the total number of flexural cracks that developed within the constant moment zone of the beams. It is shown that beams with larger reinforcement ratio had larger values of m/n, that is, lower cracking localization. For the given concrete mix, when the reinforcement ratios ρ were larger than ∼2% cracking localization was diminished. Furthermore, for low values of ρ, m/n ratios of the specimens with lower fibre contents are somewhat larger than those of the specimens with larger content. It is also shown that as the reinforcement ratio decreases below ∼0.5% the normalized mid-span ultimate deflections decreases as well, which corresponds with the observation of the cracking localization phenomenon for low reinforcement ratios. For larger reinforcement ratio, when m/n increases above ∼0.6, there is no effect of cracking localization on the ultimate deflection. Moreover, in this range of r the values of d are ≳ 1.0, as commonly expected for RFC structural elements. It is noted that the ultimate deflection of the beams corresponds to their flexural ductility.

Cracking localization in tensile conventionally reinforced fibrous concrete bars

This paper presents an experimental verification and quantification of the cracking localization phenomenon in reinforced concrete (RC) tensile prismatic bars with steel fibers. The phenomenon is characterized by significant widening of single or few cracks out of the total number of cracks that develop under tension (as opposed to nearly uniform widening in plain RC members). The experimental program included specimens with two contents of hooked-end fibers (30 and 60kg/m3 that correspond to 0.38 and 0.76% in volume), as well as control specimens without fibers. For each type of mixture, the conventional reinforcement consisted of centrally located deformed rebars at reinforcement ratios of 0.79–4.91%. Results of the tests further support the existence of the cracking localization phenomenon and the trend of its decrease with increasing reinforcement ratio. A quantitative measure of this phenomenon is represented by a ratio between the number of the significantly wide cracks and the total number of cracks in the specimen. Furthermore, the results show that for a given conventional reinforcement ratio, cracking localization is more pronounced for larger amounts of fiber content (and vice versa). A previously developed and presently enhanced theoretical model has been calibrated and it shows good agreement with the experimental results.

Hot Deformation and Processing Maps of Al-15%B4C Composites Containing Sc and Zr

Hot deformation behavior and processing maps of three Al-15%B4C composites denoted as the base composite (Al-15vol.%B4C), S40 (Al-15vol.%B4C-0.4wt.%Sc) and SZ40 (Al-15 vol.%B4C-0.4wt.%Sc-0.24wt.%Zr) were studied by uniaxial compression tests performed at various deformation temperatures and strain rates. The constitutive equations of the three composites were established to describe the effect of the temperature and strain rate on hot deformation behavior. Using the established constitutive equations, the predicted flow stresses on various deformation conditions agreed well with the experimental data. The peak flow stress of the composites increased with the addition of Sc and Zr, attributing to the synthetic effect of solute atoms and dynamic precipitation. The addition of Sc and Zr increased the activation energy for hot deformation of Al-B4C composites. The processing maps of the three composites were constructed to evaluate the hot workability of the composites. The safe domains with optimal deformation conditions were identified for all three composites. In the safe domains, dynamic recovery and dynamic recrystallization were involved as softening mechanisms. The addition of Sc and Zr limited the dynamic softening process, especially for dynamic recrystallization. The microstructure analysis revealed that the flow instability was attributed to the void formation, cracking and flow localization during hot deformation of the composites.

Adaptive technique for discrete models of fracture

Static discrete models are advantageously used for the simulation of fracture in quasibrittle heterogeneous materials. In order to correctly capture strain localization during the fracture process, it is often necessary to represent material heterogeneity in the model directly via its discrete geometry. Depending on the specimen size and the size of the heterogeneities, these simulations are typically extremely computationally demanding. The contribution aims to reduce this computational cost via the implementation of adaptivity in the construction of the discrete model geometry. The simulation starts with coarse discretization, which provides correct elastic behavior and is then adaptively refined during the simulation in regions that suffer high stresses that induce cracking and strain localization. The technique is applied in deterministic and probabilistic simulations and demonstrated on several examples.

Cracking localization and reduced ductility in fiber-reinforced concrete beams with low reinforcement ratios

The effect of adding steel fibers to concrete mixes on the flexural behavior of reinforced concrete (RC) beams was studied experimentally. Tests were conducted on conventionally reinforced beams with different reinforcement ratios, with and without fibers. Results show that the application of steel fibers leads to a pronounced reduction in flexural ductility of beams with low conventional reinforcement ratios (ρ<∼0.5%). Ductility ratios of fibrous RC beam specimens were reduced by 50–80% compared with corresponding ratios measured on control specimens with the same reinforcement ratios but without fibers. The effects of added fibers on the flexural behavior of RC beams were examined and three aspects were reported: ductility ratio (based on deflection), distribution of curvature, and load-carrying capacity.

On Temperature and Strain Rate Dependent Strain Localization Behavior in Ti–6.5Al–3.5Mo–1.5Zr–0.3Si Alloy

Deformation behaviors of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloys with α/β lamellar structure were investigated systematically at different temperatures from room temperature to 950 °C and different strain rates. Results reveal that when the deformation temperature is higher than a critical temperature of 600 °C, an evident transition of deformation behavior from localized shear banding to α/β lamella kinking, flow softening and temperature/strain rate-dependent peak flow stress occurred in the alloy. The critical conditions for the occurrence of internal cracking and strain localization behavior associated with temperature and strain rate were determined.

Flexural behaviour of RC beams in fibre reinforced concrete

Even though a number of research studies have demonstrated the effectiveness of Fibre Reinforced Concrete (FRC) in improving the structural response of RC members under different loading conditions, some concerns recently arose on the sectional ductility under flexure which can be reduced under specific conditions. In fact, fibres do not significantly increase the ultimate moment of RC members and, with rather tough FRC and low strain-hardening ratio of the longitudinal rebars, the rotation capacity can substantially decrease owing to a cracking localization at ultimate limit state.This paper focuses on this topic with a number of experimental results on full-scale FRC beams tested under flexure.Experimental results evidence that fibres, when provided in sufficient amount, are able to move the beam failure from concrete crushing to steel rupture. Under certain circumstances, the overall ductility, measured in terms of displacements, may decrease.On the other hand, in all cases the addition of fibres determines a stiffer and in general enhanced post-cracking behaviour in service conditions.

Hot deformation behavior of a Nb-containing 316LN stainless steel

A Nb-containing 316LN stainless steel was compressed in the temperature range 900–1200 °C and strain rate range 0.01–10 s −1. The mechanical behavior has been characterized using stress–strain curve analysis, kinetic analysis, processing maps, etc. The microstructural evolution was observed and the mechanism of flow instability was discussed. It was found that the work hardening rate and flow stress decreased with increasing deformation temperature and decreasing strain rate. On the contrary, the efficiency of power dissipation increased with them; Flow instability was manifested as cracking and flow localization; The hot deformation equation and the relationships between deformation condition and dynamic recrystallization grain size and fraction were obtained; For Nb-containing 316LN stainless steel, the favorite nucleation sites for dynamic recrystallization are in sequence of triple point, grain boundary, twin boundary and intragranular deformation band; The suggested processing window is given.

Experimental studies of the change of spatial correlation length of acoustic emission events during rock fracture process

Changes in spatial correlation length of acoustic emission (AE) events during fracture process of granite and marble specimens under uniaxial compression are acquired with the single-link cluster (SLC) method. The results show that the 3-D location of AE events directly reflects the process of initiation, propagation and evolution of micro-cracks and the stress re-distribution in the specimens. Two factors may influence the change in spatial correlation length: stress release, which leads to decrease in correlation length, and stress re-distribution, which leads to increase in correlation length. Three types of changes of spatial correlation length of AE events are identified. For those specimens show no significant plastic deformation before failure, the spatial correlation length shows a sharp decrease at the early stage of loading, followed by a continuous increase until reaches its peak value at failure in a power-law relation. However, for specimens that show marked plastic phase before failure, their spatial correlation length can either increase or decrease depending on the combination of the above-mentioned two factors. In one case the specimens show clear cracking localization, which leads to clustering of events, hence reduction in spatial correlation length in zones of cracks localization. However, spatial correlation length shows an increasing trend in the whole process of failure. This increase reflects stress re-distribution and transfer in the specimens. The different characteristics of spatial correlation length during elastic and plastic phases may be used as an indicator for predicting failure of rock.