Stress Crack Opening Research Articles

Combining artificial intelligence with different plasticity induced crack closure criteria to determine opening and closing loads on a three-dimensional centre cracked specimen

Fracture due to fatigue crack growth remains a significant failure mode in both brittle and ductile materials. When dealing with crack tip plasticity induced phenomena, characterized by high strain and stress field gradients, only highly refined meshes around the crack tip can produce accurate results. Therefore, optimized mesh parameters must be used, in order to achieve high quality models with low computational costs. In this study, artificial intelligence models and a numerical three-dimensional model for a middle tension specimen were combined to enhance crack closure and opening loads assessment. The numerical accuracy was analysed based on the estimated stress and strain fields, plastic zone shape and size and crack closure and opening load values. Two artificial neural networks were trained using four different crack lengths, mesh sizes and simulated plastic wakes. The networks were capable of stress and strain field predictions and crack opening and closure load determination. It was verified that the crack stress criterion is strongly correlated with the principal strain field and the displacement field around the crack tip, providing a viable way to analyse plasticity induced crack closure.

Tensile constitutive relationship of UHPFRC from crack hinge based inverse analysis of notched beams

The structural applications of ultra-high performance fiber reinforced concrete (UHPFRC) in the construction industry can be promoted if proper constitutive models can be established for design. The various tension test methods for UHPFRC are being adopted to develop a complete stress-crack width or strain response for design. This study aims to understand the fracture behavior of UHPFRC by testing notched beams under a three-point bending configuration. This testing method helps in quality control checks and obtaining complete tension stress-crack opening behavior that can be used for design. The tensile stress-crack width response of UHPFRC is obtained using the load-CMOD response. The variables considered in this study are the volume fraction of fibers (1 % and 2 %), types of steel fibers (straight, combination of straight and hooked ended), and different cross-section dimensions (100×100×500 mm and 75×75×500 mm). A crack hinge-based inverse analysis method is used for UHPFRC to obtain the complete tensile stress-crack opening response. Stress-strain relations from inverse analysis and direct tension stress-crack opening results are compared and found to be similar. A data-driven tension stress-crack opening response UHPFRC is verified by simulating the girder's response using nonlinear finite element analysis (NFEA). Thus, the proposed inverse analysis can be used to obtain the multi-linear tensile stress-crack opening response which is adequate for capturing the structural response.

CDPM2F: A damage-plasticity approach for modelling the failure of strain hardening cementitious composites

For the use of micro-mechanics based constitutive models for fibre reinforced strain hardening cementitious composites in finite element simulations of structural components, it is required to link the crack opening at the scale of fibres to the cracking strain at the scale of structural components. We aim to establish this link by incorporating a micro-mechanics based fibre bridging stress crack opening law into a macroscopic damage-plasticity approach, which we call CDPM2F. The model is implemented in the open-source finite element program OOFEM. The model produces mesh-insensitive results and its response agrees well with experimental results for failure in tension, shear and compression reported in the literature.

Analytical solution of two non‐identical edge cracks in an infinite strip under anti‐plane shear wave

AbstractThis article presents an extensive analytical solution addressing the interaction between two non‐identical edge cracks in an infinite orthotropic strip under anti‐plane shear waves. Most studies assume identical cracks or single edge crack in a strip, but this research breaks new ground by considering cracks of different sizes. By incorporating mixed‐type boundary conditions, the study derives dual integral equations. These equations are then transformed into a singular integral equation of Cauchy type with the aid of a trial solution and contour integration technique. The singular integral equation is further converted into a system of integral equations, which are solved numerically utilizing Jacobi polynomials. The obtained solutions are utilized to derive expressions for the stress intensity factor (SIF) and crack opening displacement (COD) at the crack tip using Krenk's interpolation formulae. The derived results are presented graphically and compared against existing solutions for single edge crack and symmetric edge cracks in static scenario.

Effectiveness of the Concrete Equivalent Mortar Method for the Prediction of Fresh and Hardened Properties of Concrete

Modern concrete mix design is a complex process involving superplasticisers, fine powders, and fibres, requiring time and energy due to the high number of trial tests needed to achieve rheological properties in the fresh state. Concrete batching involves the extensive use of materials, time, and the testing of chemical admixtures, with various methodologies proposed. Therefore, in some instances, the required design properties (physical and mechanical) are not achieved, leading to the loss of resources. The concrete equivalent mortar (CEM) method was introduced to anticipate concrete behaviour at fresh and hardened states. Moreover, the CEM method saves time and costs by replacing coarse aggregates with an equivalent sand mass, resulting in an equivalent specific surface area at the mortar scale. This study aims to evaluate the performance of fibre in CEM and concrete and determine the relationships between the CEM and the concrete in fresh and hardened states. Steel and polypropylene fibres were used to design three series of mixtures (CEM and concrete): normal-strength concrete (NSC), high-strength concrete (HSC), high-strength concrete with fly ash (HSCFA), and equivalent normal-strength mortar (NSM), high-strength mortar (HSM), and high-strength mortar with fly ash (HSMFA). This study used three-point bending tests and digital image correlation to evaluate load and crack mouth opening displacement (CMOD) curves. An analytical mode I crack propagation model was developed using a tri-linear stress–crack opening relationship. Post-cracking parameters were optimised using inverse analysis and compared to actual MC2010 characteristic values. The concrete slump is approximately half of the CEM flow; its compressive strength ranges between 78% and 82% of CEM strength, while its flexural strength is 60% of CEM strength. The post-cracking behaviour showed a significant difference attributed to the presence of aggregates in concrete. The fracture energy of concrete is 28.6% of the CEM fracture energy, while the critical crack opening of the concrete is 60% of that of the CEM.

Analytical modelling of the orientation dependency of 3D printed SHCC at increasing levels of scale

3D printable strain hardening cementitious composites (3DP-SHCC) stand out for their high ductility and increase in tensile strength after initial cracking. Due to the printing process, which includes the pumping and extruding of the material, the fibres are not uniformly orientated in the material but have an orientation dependency due to the specific printing process applied. Three different cases for the fibre orientation distribution functions are presented with increasing levels of relation to the printing process. These three cases have been used in a micro-mechanical model to verify with experimental stress-crack opening results (single crack). Furthermore, a spring model is used to give insight into the potential to develop pseudo strain hardening behaviour (multiple cracking) in various printing directions. The method is also used to model the experimentally obtained spread in uni-axial tensile dogbone test results. From these experimental dogbone tests, average stress-strain relations are determined in two directions. Finally, a multi-layer method is used on the component level to validate the use of these average stress-strain relations for modelling the bending behaviour of printed elements in multiple directions.

Elastic fields of double branched and Kalthoff–Winkler cracks in a half-plane

We demonstrate in this paper a combination of the Schwarz–Christoffel mapping and Muskhelishvili’s approach with fractional function series in solving the elastic fields of a cracked half-plane, and zoom in on two typical problems, a double branched crack with two rays emanating from one point on the edge and two edge cracks spaced by a certain distance. Typical loading conditions are considered, including far-field uniform tensile stress and concentrated loads along either the tangential or the normal direction of the free surface. We supply a semi-analytic solution to those boundary-value problems in the cracked half-plane, and validate the theory by comparing the theoretical results in terms of stress fields, stress intensity factors (SIFs) and crack opening displacement (COD) with those from finite-element simulations. The theoretical approach shows how two edge cracks may shield the stress intensity factors of each other in a quantitative manner. For the typical Kalthoff–Winkler cracks of length a and being spaced by a distance d, their SIFs KI decay with decreasing d, and KI=KI0−KI1[1−exp(−a/d)]. It converges to KI0—the SIF of a single edge crack when d approaches to infinity. Those observations and the theory approach itself provide a general way to analyze the mechanical consequence of edge cracks in engineering practice.

Analytical and numerical modeling of plain concrete’s post-cracking behavior using a trilinear softening curve

The aim of the present work is to investigate the softening behavior of a notched concrete beam under a three-point bending test analytically, experimentally, and numerically using XFEM in Abaqus. This study presented a trilinear stress-strain softening curve-based analytical model to describe the complete flexural behavior of plain concrete beams. The article also provides the mathematical equations necessary for calculating the force-crack opening displacement during all cracking phases until failure. An inverse analysis of the force-CMOD curves obtained experimentally has optimized the parameters required for the identification of the tensile stress-crack opening relationship. The ABAQUS environment was used for numerical modeling using the extended finite element method (XFEM), and a good agreement between the experimental and numerical results has been noticed.

On the dynamic mode-III crack in the elastic continuum consisting of sandy properties

The aim of the present investigation is to come up with a mathematical model for the dynamic mode III crack in an elastic continuum consisting of dry sandy properties. For the analysis of the propagating mode-III crack due to the propagating Love-type wave in an elastic continuum consisting of dry sandy properties, the results for the stress intensity factor (SIF) and crack opening displacement (COD) have been developed in closed form. The complex variable integral transform mathematical methods consisting of the two-sided Fourier integral transform, along with the Weiner-Hopf technique, serve as a salient feature of the adopted mathematical treatment for determining the SIF and COD in the closed form. Moreover, the expressions for the SIF and COD for the limiting static mode-III crack have also been obtained and deduced for special cases of elastic medium. The effects of existing parameters, viz. dry sandiness parameter, depth of crack, crack velocity on the SIF and COD . The effect of physical materials parameters has been shown numerically as well as graphically.

Asymptotic solutions for large fractures growing parallel to a free plane

Straight 2D and disc-like cracks situated close to a parallel free plane are considered and asymptotic solutions for the stress intensity factors (SIFs) and crack opening are developed. Two asymptotic terms with respect to the small ratio of distance from the surface to the crack length/radius are derived. The derivation is based on considering the material between the crack and the free surface as an elastically supported beam or circular plate. The crack is considered to be opened either by uniform tensile stress or a pair of concentrated forces or moments representing the action of central defects (these represent for instance the crack growth from initial inclined crack or pore under compression acting parallel to the free surface). A crack with non-interacting surfaces (the conventional crack) and a crack with linear links between the surfaces are considered. Interaction with the free surface is shown to considerably increase the crack opening and SIFs, while the presence of the elastic links can reduce these crack parameters. In particular, the opening and SIFs of a crack with linear links under a pair of concentrated forces/moments exponentially vanish with the crack dimensions tending to infinity. The obtained asymptotic solutions provide a simple and accurate tool for investigating mechanisms of surface delamination and spallation (including thermal spallation and strain rockbursts).

Predicting the moment resistance and localization strain of reinforced UHPFRC cross-sections subjected to bending

The determination of the ultimate moment resistance of UHPFRC sections additionally reinforced with reinforcing steel or prestressing requires addressing the failure mode “crack localization”. At this failure mode, the growth of a single localized crack initiates the failure of the structural member. The onset of crack localization generally coincides with the decrease of fiber contribution in the flexural crack. In order to predict both the ultimate moment resistance and the localization strain, a verification method is derived based on mechanical principles. The contribution of UHPFRC in tension to the moment resistance is estimated by a stress block which is calibrated by means of experimental stress-crack opening relations. The stress block is applied to the tension zone of the section and is limited to a specific crack width being correlated with the beginning decrease of the fiber contribution in the flexural crack. To convert the crack width into strain a structural characteristic length is defined accounting for both the size effect and the reinforcement configuration. The proposed method is checked against experimental results and by parameter studies. The comparison with the results obtained by applying the stress–strain relation defined in NF P18-710 shows differences in the predicted localization strain which are predominantly attributed to the fact that the structural characteristic length defined in NF P18-710 does not account for the reinforcement configuration.

Shear transfer in fly ash concrete with electric arc furnace aggregates

The friction shear behaviour of concrete containing electric arc furnace (EAF) slag (hereafter called EAFC) was experimentally evaluated and compared with a reference counterpart made with only natural aggregates. Two concrete mixes were cast, both containing a cement blended with 30% fly ash to improve their sustainability. For each mix, other than analysing the main mechanical properties (compressive strength, tensile strength and elastic modulus), push-off specimens were tested to determine the shear strength, failure modes, stress–slip and stress–crack opening curves. There was a clearly enhancement in the shear strength of EAFC compared with the reference concrete, even though the relations between shear strength and tensile strength were similar for the two concretes. The results were also compared with data from the literature pertaining to ordinary concrete and recycled aggregate concrete. Existing models from both design codes and the literature were applied to the experimental results and conservative predictions were obtained in all cases. The safety margin for the EAFC was found to be higher than that for the reference concrete.

A Simplified Inverse Analysis Procedure for the Stress-Crack Opening Relationship of Fiber-Reinforced Concrete

The direct tensile test (DTT) is the most recommended test to determine the tensile behavior of fiber-reinforced concrete (FRC). However, this test is challenging to perform. Several studies have investigated inverse analysis to determine this behavior through simplified tests, such as the bending test. This study deals with developing a new approach to perform an inverse analysis for the three-point bending test (3PBT) involving FRC. A new proposed methodology concerns carrying out the inverse analysis procedure by parts. Initially, the parameters that influence the initial part of the stress–crack opening curve are adjusted. Progressively, the other parameters are adjusted considering the increment of the curve section. This procedure provides an implemented algorithm with more efficiency. A new strategy that deals with the establishment of criteria for parameters is proposed. Its results are compared with experimental data from other literature, whose steel fiber-reinforced concrete (SFRC) tested characteristics present different attributes such as fibers, shape, and length. The proposed methodology obtained the stress–crack opening curves in direct tension with reasonable accuracy, indicating that this methodology can be helpful in the characterization of the post-cracking FRC behavior.

Uniaxial tensile response and tensile constitutive model of ultra-high performance concrete containing coarse aggregate (CA-UHPC)

To establish the tensile constitutive model of ultra-high performance concrete containing coarse aggregate (CA-UHPC), monotonic and cyclic uniaxial tensile tests for CA-UHPC with fiber volume fractions of 2.5% and 2.0% were conducted. Test results showed that CA-UHPC exhibits approximately linear stress-strain relation up to the tensile strength, and tensile softening response composed of the smeared- and localized-cracking stages, regardless of the tested fiber contents. Based on the monotonic test data, the tensile stress-crack opening model of CA-UHPC was established, and the model was further simplified into tri-linear relation. Based on the cyclic test results, tensile damage evolution laws according to the strain equivalence principle and the energy equivalence principle were developed, respectively. Finally, the proposed tensile constitutive model and the calibrated tensile damage evolution laws were demonstrated to effectively predict the mechanical response of CA-UHPC members under both monotonic tension and cyclic tension through numerical simulations.

Experimental verification of indirect tests for stress-crack opening curve of concrete in tension from a round robin test: application to railway sleeper elements

This paper presents experimental verification of indirect tests for the determination of the stress-crack opening curve of concrete, based on the method described in the RILEM TC 187-SOC report and submitted to ACI Committee 446 for Fracture Toughness Testing of Concrete, which relies on the standard cohesive model. In such method, a bilinear approximation of the softening curve is determined from three-point bending tests of notched specimens under crack-mouth-opening-displacement control and from tensile splitting tests, which produces good predictions of the complete crack evolution. The current work focusses on the brittleness length, which is directly related to the parameters of the linear curve defined by the first branch of the bilinear curve, and is one of the main fracture parameters of concrete, since it controls the behaviour of thin cracks. This length can be obtained from a simple version of experiments conducted up to peak load, thus, favouring its application in the industry. In particular, this work presents the results of a round-robin test carried out in collaboration with the Spanish Association of Railway Sleeper Element Manufacturers to determine the brittleness length of concrete. A specific implementation of the method has been proposed in order to perform the tests by using the facilities available in all the factories. The results of the round-robin test have been satisfactory, thus, supporting the viability of the RILEM and ACI proposals. Moreover, a method has been developed which allows the brittleness length of concrete to be determined easily in railway sleeper element factories.

Analytical fracture parameters of two unequal collinear interface cracks in an orthotropic bimaterial

This paper presents an analytical solution for the fracture parameters of two unequal collinear interface cracks (UCIC) in an infinite orthotropic or isotropic bimaterial subject to in-plane loading. The analytical expressions for the stress intensity factors (SIF), Jk-integrals and crack opening displacements of two UCIC in an infinite orthotropic bimaterial plate are derived using the complex variable method and evaluated in conjunction with the Jacobian elliptic functions and elliptic integrals. The presented theory is verified using the boundary element method. The results show that the fracture parameters are greatly influenced by mismatch of the engineering constants and proximity of the cracks. The inner tip of the longer crack always experiences the maximum SIFs and Jk values. These fracture parameters will increase exponentially when the distance between the cracks inner tips decreases. This study provides a baseline for the verification of future numerical and experimental studies of two UCIC which is not currently available in the SIFs handbooks.

Moving semi-infinite crack between dissimilarorthotropic strips

In this paper, we conceive a semi-infinite moving crack between two bonded dissimilar orthotropic strips. Fourier transform has been adopted to reduce the mixed boundary value problem to a standard Wiener–Hopf equation. To determine the stress intensity factor (SIF) and crack opening displacement (COD), the Wiener–Hopf equation is solved in asymptotic sense for stress free boundary. Finally, the variation of SIF and COD is demonstrated graphically with respect to several orthotropic material parameters.

PVA fiber reinforced cement composites with calcined cutter soil mixing residue as a partial cement replacement

In this paper, a cutter soil mixing residue (CSMR), which is a soil–cement solid waste, was calcined and then used as a partial cement replacement in polyvinyl alcohol fiber reinforced cement composites (PVA-FRCCs). The binder chemistry was characterized using XRD, TGA and FTIR. The fiber–matrix interfacial properties were examined with SEM. The composite mechanical properties, including compressive strength, flexural properties and tensile behaviors and fiber bridging stress-crack opening relationships, were investigated. Results showed that the calcined CSMR can produce additional hydrates to aid the strength gain and densify the fiber–matrix interface. With a cement replacement level up to 40%, the tensile strength was not compromised, while the tensile strain capacity significantly increased to a maximum value of 3.2%. The micromechanical analysis revealed that the improved strain capacity is mainly attributed to the optimized fiber–matrix interface yielding enhanced pseudo strain-hardening indices. The results obtained in this study indicate that calcined CSMR is an attractive novel supplementary cementitious material for developing greener strain-hardening cementitious composites.

Mathematical modelling for multiple straight cracks with coalesced yield zones

Solution for a normally loaded infinite isotropic plate containing five cracks with coalesced yield zones is obtained using a complex variable method. Influence of coalesced yield zones on the load bearing capability of the infinite plate is analyzed. Analytical expressions for stress intensity factors, displacement components and crack opening displacement (COD) are obtained. Numerical study is carried out to determine the yield zone length, applied load ratio and COD. The numerical results are reported graphically between some important parameters.

An inverse analysis method for multi-linear tensile stress-crack opening relationship of 3D/4D/5D steel fiber reinforced concrete

The tensile stress-crack opening (σ-w) relationship of steel fiber reinforced concrete (SFRC) is of much importance for calculating the resistance of structures at serviceability and ultimate limit state. In this paper, the analytical solutions for the flexural response of SFRC beams were firstly developed by considering the multi-linear σ-w relationship of SFRC. Then, the parameters of the multi-linear σ-w relationship were obtained by using an inverse analysis method based on the analytical solutions and the experimental results of ten groups of notched concrete beams with 3D, 4D and 5D steel fibers. Results showed that the σ-w relationship of SFRC are changed from strain softening to strain hardening with increasing fiber volume fraction and number of fiber end hooks. The concrete beams with 4D and 5D steel fibers possess the higher flexural properties than the concrete beams with 3D steel fibers. In addition, the proposed analytical solutions and inverse analysis method could be applied to notched and unnotched SFRC beams with 3D, 4D and 5D steel fiber.