Terms Of Stress Intensity Factor Research Articles

Experimental and FEM Analysis for Fracture Performance Evaluation of Concrete Made with Recycled Construction and Demolition Waste Aggregates

Paper presents experimental and Finite Element Method (FEM) analysis of fracture behavior of concrete made using Recycled Aggregate (RA). Concrete mixes were prepared using Construction and Demolition Waste (CDW) as replacement of natural coarse aggregates. To study fracture performance, concrete mixes were prepared with water to cementitious content (w/b) ratios between 0.4 and 0.5. Beam specimens of size 100 mm x 100 mm x 500 mm were cast and tested as per method of Three-point bend test on notched beam proposed by RILEM. Fracture parameters like fracture energy, stress intensity factor, energy release rate and characteristic length were evaluated using Load-CMOD (Crack Mouth Opening Displacement) and load deformation curves. Mechanical properties of concrete such as compressive and flexural strength, modulus of elasticity and split tensile strength were also evaluated. The performance of concrete using RA has been compared with concrete using Natural Aggregate (NA) from literature. Results suggest slightly better fracture performance in case of concrete made using RA in comparison to conventional concrete in spite of having similar strength and w/b ratio. Fracture energy parameter in terms of stress intensity factor obtained from FEM analysis were similar to experimental results wherein no significant variation in stress intensity factor for concrete mixes with recycled and natural aggregate were observed. However, it can be stated that values of stress intensity factor of 0.47_NA was lowest and 0.5_RA was highest. There was no significant difference in average fracture energy of mixes and it lies in range of 180 N/m to 300 N/m.

Experimental data-driven uncertainty quantification for the dynamic fracture toughness of particulate polymer composites

This paper presents an experimental investigation supported by data-driven approaches concerning the influence of critical stochastic effects on the dynamic fracture toughness of glass-filled epoxy composites using a computationally efficient framework of uncertainty quantification. Three different shapes of glass particles are considered including rod, spherical and flaky shapes with coupled stochastic variations in aspect ratio, dynamic elastic modulus and volume fraction. An artificial neural network based surrogate assisted Monte Carlo simulation is carried out here in conjunction with advanced experimental techniques like digital image correlation and scanning electron microscopy to quantify the uncertainty and sensitivity associated with the dynamic fracture toughness of composites in terms of stress intensity factor under dynamic impact. The study reveals that the pre-crack initiation time regime shows the most prominent effect of uncertainty. Additionally, rod shape and the aspect ratio are the most sensitive filler type and input parameter respectively for characterizing dynamic fracture toughness. Here the quantitative results based on large-scale data-driven approaches convincingly demonstrate using a computational mapping between the stochastic input and output parameter spaces that the effect of uncertainty gets pronounced significantly while propagating from the compound source level to the impact responses. Such outcomes based on experimental data essentially bring us to the realization that quantification of uncertainty is of utmost importance for developing a reliable and practically relevant inclusive analysis and design framework for the dynamic fracture of particulate composites. With limited literature available on the determination of fracture toughness considering inertial effects, the present work demonstrates a novel and insightful experimental approach for uncertainty quantification and sensitivity analysis of dynamic fracture toughness of particulate polymer composites based on surrogate modeling.

A Study On Effects of Flaw Shape Idealization On the Interaction of Co-Planar Surface Flaws Subjected to Tension Load

Abstract Engineering Critical Assessment (ECA) guidelines contain rules to assess flaw interaction. Major flaw dimensions (depth or height and length) are typically characterized assuming the flaws to be contained entirely within a bounding rectangle through a procedure known as flaw idealization. In fracture mechanics based calculations, flaws are often assumed to be (semi-)elliptical when evaluating possible interaction. This paper investigates the implication of this simplification for the specific case of two identical co-planar surface breaking flaws. Two flaw shapes are considered and compared: semi-elliptical and canoe-shaped (quarter-circular ends with constant depth elsewhere). Especially for long and shallow flaws, the canoe-shaped configuration best approximates the bounding rectangle, whereas the semi-elliptical shape only touches the bounding rectangle at three points (deepest point and two points at the surface). Several flaw dimensions and spacing distances are studied through an extensive parametric study comprising both linear elastic and elastic-plastic finite element simulations. The results, evaluated in terms of stress intensity factor (SIF) and J-integral, show that the flaw shape idealization, particularly for long and shallow flaws, can significantly affect the degree of interaction between identical co-planar flaws. The inconsistency between semi-elliptical and canoe-shaped flaw shapes is observed in a linear elastic analysis and becomes more pronounced at higher loading levels evaluated in elastic-plastic analyses

XFEM Simulation of Tensile and Fracture Behavior of Ultrafine-Grained Al 6061 Alloy

In the present work, the tensile and fracture behavior of ultra-fine grained (UFG) Al 6061 alloy was simulated using extended finite element method (XFEM). UFG Al 6061 alloy processed by cryorolling (CR) and accumulative roll bonding (ARB) was investigated in this work. Numerical simulations of two-dimensional and three-dimensional models were performed in “Abaqus 6.14” software using an elastic-plastic approach, and the results obtained were validated with the experimental results. The specimens corresponding to the three-point bend test, compact tension test with center crack, and double edge cracks were analyzed using XFEM (eXtended Finite Element Method) approach. In XFEM, the partition of unity (PU) was used to model a crack in the standard finite element mesh. The tensile and fracture properties obtained from the simulation were in tandem with the experimental data. UFG Al alloy showed higher tensile strength and fracture toughness compared to their bulk solution treated counterparts. Fracture toughness was measured in terms of stress intensity factor and J integral. In CR Al alloys, with increasing thickness reduction, an increase in stress intensity factor and a decrease in the J integral was observed. This behavior is attributed to the increase in strength and decrease in ductility of CR samples with increasing thickness reduction. In ARB Al alloys, the strength and ductility have increased with an increase in number of cycles. It also revealed an increase in both the stress intensity factor and J integral in ARB processed Al alloys with increase in number of cycles, as evident from XFEM simulation results.

Size effect in creep–fatigue crack growth interaction in P2M steel

AbstractAn investigation of the crack propagation under the creep–fatigue interaction in C(T) specimens of P2M steel was carried out. Numerical calculations included the determination of the stress–strain state fields for the viscoelastic material, as well as the distributions of stress triaxiality, nonlinear stress intensity factors, and the C‐integral along the crack front in specimen with different thickness. The interpretation of the experimental results under fatigue–creep interaction is given by the elastic and nonlinear stress intensity factors in terms of the traditional and new normalized cyclic fracture diagrams. Considering the size effects through the creep‐dominated stress intensity factors caused differences in the crack growth behavior. In specimens with the same geometry, the crack growth rate under the creep–fatigue interaction increased monotonically compared with harmonic fatigue, and the superposition of fatigue and creep contributions shows an order of magnitude increase in the total crack growth rate with respect to the pure creep.

A Numerical Investigation of an Abnormal Phenomenon of Stress Intensity Factor (SIF) in a Cracked T-Butt Joint Accounting for Welding Effect

Industry design standards such as BS 7910 deployed some empirical formulas for the prediction of stress intensity factor (SIF) based on simulation results from traditional finite element method (FEM). However, such FEM simulation occasionally failed to convince people due to the large discrepancies compared with engineering practice. As a consequence, inaccuracy predictions via such formulas in engineering standards inevitably occur, which will compromise the safety of structures. In our previous research work, an abnormal phenomenon of SIF in a cracked T-butt joint accounting for welding effect has been observed. Compared with BS 7910, the calculation results of SIF at the surface points of welded specimens cannot be well predicted, with a large discrepancy appearing. In order to explore such problem with an abnormal increase at the surface points of cracked welded specimens, a numerical investigation in terms of SIF among BS 7910, XFEM, and FEM is performed in this paper. Numerical models on both a simple cracked plate without welding effect and a cracked T-butt joint with welding effect are developed through ABAQUS. Parametric studies in terms of the effects of varied crack depth to thickness ratio (a/T) and the effects of crack depth to crack half-length ratio (a/c) are carried out. Empirical solutions from BS 7910 are used for comparison. It is found that the XFEM can provide predictions of SIF at both the crack deepest point and crack surface point of a simple cracked plate as accurate as FEM. For a T-butt joint with a transverse stiffener, a large discrepancy in terms of the weld magnification factors (Mk) occurs at the crack surface point compared with empirical predictions. An exceptional increase of von Mises stress gradient in regions close to the weld-toe is found through the simulation of FEM, whereas a constant stress gradient is obtained through XFEM. The comparison results indicate an inappropriate prediction of SIF by the utilization of the empirical formulas in BS 7910. A more reasonable prediction of the SIF at the surface point of a crack is obtained by the XFEM. Therefore, further updating of the empirical solutions in BS 7910 for SIF accounting for welding effect is recommended.

Analytical solution of T-stresses for an inclined crack in compression

It is widely accepted that T-stress near crack tip has a considerably effect on crack behavior. In the classic fracture mechanics, only Tx (T-stress component in x-direction) was addressed, and recently one researcher pointed out that both Tx and Ty exist for a crack in compression. In order to theoretically study the T-stress for an inclined crack under compression, analytical solution of stresses near crack tip was derived from the complex stress functions which were obtained according to the crack surfaces stress conditions and boundary conditions. The analytical solution of stresses consists of two parts: one is singular term which is the same as the classical stress expressed in terms of stress intensity factor, and the other is non-singularity term which can be expressed in terms of three components of T-stress, i.e. Tx, Ty and Txy, which indicates that the T-stress should have three components. In order to validate the result of T-stress, the crack initiation angle was calculated by the MTS criterion for four cases: (1) without T-stress, (2) Tx only, (3) Tx and Ty, and (4) Tx, Ty and Txy. The prediction results of the crack initiation angles by MTS criterion were compared to the previous test results of PMMA and the test results conducted in this study by using sandstone specimens with an inclined crack under uniaxial compression. The results show that the prediction results by considering the three components Tx, Ty and Txy can better fit both test results of PMMA and sandstone, which indicates that the T-stress near crack tip should have three components Tx, Ty and Txy, and all of them have effect on crack initiation behavior.

New formulation for fracture toughness characterization using four-point bend specimens

The present work aims to present a new complete procedure to characterize fracture toughness in terms of stress intensity factor K or the J−integral for Mode I of loading using four-point bend specimens. Four-Point Bend (4PB) specimens are shown to be valid configurations for fracture toughness characterization tests with certain advantages when compared to traditional three-point bend geometries and single edge notch tension SE(T) specimens under clamped conditions. Fracture toughness is a key parameter in defining critical flaw sizes in a fitness-for-service (FFS) procedure based upon fracture mechanics principles. Accurate estimation of fracture toughness is therefore necessary to assess the integrity of critical engineering structures by following the failure assessment diagram concept. Extensive 3D finite element analyses were performed to obtain the analytical relationships necessary to calculate the fracture toughness parameters. New formulas are provided for the elastic compliance, stress intensity factor, and eta factor for calculating fracture toughness valid for four-point bend specimens. Using the distance between inner and outer roller supports as a normalization parameter, the stress intensity factor and the normalized elastic compliance equations are shown to be independent of the specimen supporting configuration. The eta factor based upon the CMOD is dependent on the distance between external and internal roller supports as well as a∕W. Experimental fracture tests were carried out to check the practicality of the methodology. J-R curves obtained by four-point bend specimens were compared to resistance curves derived from three-point SE(B) specimens and clamped SE(T) samples which are standardized specimens. The results show that the four-point bend specimens provide reliable fracture toughness values somewhat higher than three-point bend geometries.

Determination of fracture toughness of polymer coating using micro-scale digital image correlation technique

This paper presents a comprehensive study on determining the interface adhesive strength of the polymer coating/substrate system to improve its durability. Interfacial stress intensity factors based on the crack tip opening displacement (CTOD) method were theoretically analysed and verified by the finite element simulation. Thereafter, an experimental setup was established with the micro-scale digital image correlation (DIC) method to measure the CTODs and the designed loading fixture for multi-angle loading. The apparent specimen rotation and out-of-plane displacement were significantly restrained in the test, and the measured displacement accuracy of the micro-scale DIC method was approximately 1/10 of the minimum CTOD value. Mixed-mode stress intensity factors and an interfacial failure criterion curve in terms of stress intensity factors were obtained. Furthermore, the test method was applied to evaluate the interfacial fracture toughness of nanoparticle-reinforced epoxy coatings. The experimental results demonstrate that determining the stress intensity factors on the interface of the polymer coating/substrate system based on the CTODs is an effective and reliable approach.

Modeling of crack repair using piezoelectric material: XFEM approach

PurposeThe purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.Design/methodology/approachThe extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.FindingsThe effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.Originality/valueThe presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

Modelling the criticality of silicon nitride surface imperfections under rolling and sliding contact

Ceramic rolling elements of hybrid bearings may initially include surface imperfections. In order to provide reliable operation of a bearing, the criticality of such imperfections under rolling contact fatigue is examined by defining them as Star features: intersecting semi-elliptical surface cracks. Parametric study is conducted using Finite Element Method and discussed with help of previously published experimental observations. The effects of the Star feature morphology and configuration, contact pressure and crack face friction are investigated in terms of stress intensity factors. Possible crack propagation scenarios are explained in the present study.

Fractal scaling and crack-size effects on creep crack growth

Scaling effects on the creep crack growth behaviour are investigated by analyzing the results of compact tension (CT) tests on different-sized notched steel specimens appearing in the literature. Creep crack growth rate data are correlated to the elastic stress-intensity factor in terms of a Paris-type law, da∕dt = C0Kq, where C0 turns out to be a crack-size dependent coefficient of proportionality. Considering specimens with the same loading configuration (CT) and the same thickness, the observed crack-size effect on the creep crack growth rate is discussed on the basis of self-similarity considerations, and geometrically interpreted in terms of fractal tortuosity of the crack profile. A size-independent formulation of the creep crack growth law correlating renormalized quantities is finally deduced and confirmed by the experimental results.

Fracture analysis of cracked thin-walled structures using a high-order XFEM and Irwin’s integral

We develop a novel fracture mechanics framework for cracked thin-walled structures based on the Mindlin-Reissner plate theory. The mixed interpolation of tensorial components (MITC) plate element within the extended finite element method (XFEM) is used for the discretization. High-order crack-tip enrichment functions are employed to resolve the linear elastic near field solutions and the stress intensity factors (SIFs) are extracted by using an analytical derivation of Irwin’s crack closure integral.The closed-form formulation of Irwin’s integral, given in terms of enriched degrees of freedom (DOFs), is shown to be valid for both structured and unstructured meshes. The SIFs of through-the-thickness cracks in thin-walled structures can thus be directly obtained upon the solution of the XFEM discrete system, without the need of constructing auxiliary fields for mode separation.The performance of the proposed approach is studied on several benchmark examples consisting of cracked plates and shells. We first consider plate examples with an inclined crack and two cracks approaching each other. Excellent accuracy in terms of SIFs, on structured and unstructured meshes is reported, even on rather coarse meshes. In particular, the case of two approaching cracks showcases the potential of Irwin’s integral in addressing crack coalescence problems. Finally, we demonstrate the accuracy of the proposed method on cylindrical-shell type problems with a crack subjected to either tension, torsion, or internal pressure.

Modeling of Capillary Shrinkage and Cracking in Early-Age Concrete

. Scientific hypothesis on moistening shrinkage mechanism for cement stone and concrete has been assumed as a basis for the present paper. Physical ideas on a mechanism for cracks volume increment in a concrete model presented as two-level structure have been accepted as a theoretical basis for a calculation method of crack resistance during capillary shrinkage. These ideas are the following: a matrix of hardening cement stone with inclusions and emptiness of various forms (cracks) as result of influences that change an intense deformed state in a point and a volume. The following assumptions have been accepted while making a theoretical justification for a calculation method of shrinkable concrete crack resistance. Following this methodology approaches of fracture mechanics according to a generalized criterion have been applied in the paper. Concrete is considered as an elastic quasi-homogeneous two-component medium which consists of the following parts:a) constructive part: a matrix – a cement stone with structural elements of crushed stone, sand; b) destructive part: emptiness – capillaries cracks and pores (cavities with initial cracks in walls). Emptiness in a matrix and contact zones are presented by a coordinated five-level system in the form and sizes which are multiple to a diameter due to impacts while reaching critical sizes. These critical sizes make it possible to pass from one level into another one according to the following scheme: size stabilization – accumulation delocalization – critical concentration in single volume – transition to the following level. Process of cracks formation and their growth are considered as a result of non-power influences on the basis of crack theory principles from a condition that fields of deformation and tension creating schemes of a normal separation and shift occur in the top part of each crack at its level in the initial concrete volume. Ксij(t) parameter as algebraic amount of critical values Kij in the whole system of all levels of cracks filling canonical volume up to critical concentration has been accepted as a generalized constant of property for concrete crack resistance in time, its resistance to formation, accumulation in volumes of micro-cracks and formation of trunk cracks with critical values. External temperature, moistening long influences create fields of tension in the top parts of cracks. Concrete destruction processes due to cracks are considered as generalized deformedintensed state in some initial volume having physical features which are inherent to a composite with strength and deformative properties. It is possible to realize analytical calculations for assessment of tension and crack resistance of concrete at early age on the basis of a generalized criterion in terms of stress intensity factor due to modern experimental data on capillary pressure value (70 kPa in 180 min after concrete placing). The developed algorithm of calculation allows to consider factors influencing on capillary pressure: type of cement, modifiers and mineral additives, concrete curing conditions.

An arc-length method for controlled cohesive crack propagation using high-order XFEM and Irwin’s crack closure integral

Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure.To address these challenges, we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle.Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.

Dual boundary element method and finite element method for mixed‐mode crack propagation simulations in a cracked hollow shaft

AbstractThree‐dimensional mixed‐mode crack propagation simulations were performed by means of the dual boundary element method code BEASY and 2 finite element method‐based crack propagation codes: ZENCRACK (ZC) and CRACKTRACER3D (CT3D). The stress intensity factors (SIFs) along the front of an initial semielliptical crack, initiated from the external surface of a shaft, were calculated for 4 different load cases: bending, press fit, shear, and torsion. The methods used for the SIF assessment along the crack front were the J‐integral for BEASY and ZC and the quarter point element stress method for CT3D. Subsequently, crack propagation simulations were performed, with the crack growth rate evaluated by using Paris' law, calibrated for the material at stake (American Society for Testing and Materials A469 steel). The kink angles were evaluated by using the minimum strain energy density and maximum tangential stress criteria for BEASY, the maximum energy release rate and maximum tangential stress for ZC, and the maximum principal asymptotic stress for CT3D. The results obtained in terms of SIFs and crack propagation life show very good agreement among the 3 codes. Also, the shape of the propagated crack, which is significantly out‐of‐plane for the shear and torsion loading, matched very well.

3D simulation of hydride-assisted crack propagation in zircaloy-4 using XFEM

Influence of hydride precipitated at the tip of the crack on crack propagation in zircaloy-4 is numerically investigated using the extended finite element method (XFEM). Numerical simulation is performed on compact tension specimen to understand the effects of crack and hydride lengths on crack propagation in terms of stress intensity factor and J-integral. The values of stress intensity factor and J-integral indicate that hydride induces the crack instability. The stress intensity factor decreases with the precipitation of brittle hydride phase at the crack tip, resulting in hydride-assisted crack propagation. A comparison of crack propagation behaviour with different hydride lengths is also presented. The crack remains stable in the absence of the hydride while it propagates when hydride is considered at its tip for the same applied load. The crack arrests only after reaching to the zircaloy metal matrix causing complete fracture of hydride.

Effect of Residual Stresses on Safe Life Prediction of Railway Axles

Residual stresses play an important role in fatigue crack growth in railway axles. Due to crack closure, they affect not only the stress ratio R but add directly to the effective range of the cyclic crack load in terms of stress intensity factor. In order to account for this effect in a safe life analysis, the stress intensity factor KIrs due to the residual stress is required. The cut-compliance method is a suitable means to determine KIrs. The method is described briefly, and by an example it is shown how it can be applied to railway axles. The obtained residual stresses turned out to be compressive in the vicinity of the surface, which is beneficial for the fatigue performance of the axle. If these stresses are accounted for in the crack growth law, the calculated safe life in case of a pre-existing crack-like defect is increased dramatically. Furthermore, the effect of the press-fit of the wheels is investigated. The corresponding stresses were calculated by FEM. Actually, these stresses represent another type of residual stresses and can be superimposed to the measured residual stresses in the analysis. They also affect the crack growth rate significantly.

Evaluation of crack-tip fields from DIC data: A parametric study

In the past two decades, crack-tip mechanics has been studied increasingly using full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), crack opening displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, the position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF by using Williams’ model. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation around the crack-tip has been examined. The comparison between nominal and experimental values of KI showed that the effect of subset size on the measured KI is negligible compared to the effect of the field of view and the position of the area of interest.

Multiple and non-planar crack propagation analyses in thin structures using FCPAS

In this study, multiple and non-planar crack propagation analyses are performed using Fracture and Crack Propagation Analysis System (FCPAS). In an effort to apply and validate FCPAS procedures for multiple and non-planar crack propagation analyses, various problems are solved and the results are compared with data available in the literature. The method makes use of finite elements, specifically three-dimensional enriched elements to compute stress intensity factors (SIFs) without special meshing requirements. A fatigue crack propagation criterion, such as Paris-Erdo?an equation, is also used along with stress intensity factors to conduct the simulation. Finite element models are generated within ANSYS™ software, converted into and solved in FRAC3D program, which employs enriched crack tip elements. Having computed the SIFs for a given crack growth increment and using a growth criterion, the next incremental crack path is predicted and the fracture model is updated to reflect the non-planar crack growth. This procedure is repeated until cracks reach a desired length or when SIFs exceed the fracture toughness of the material. It is shown that FCPAS results are in good agreement with literature data in terms of SIFs, crack paths and crack growth life of the structure. Thus, accuracy and reliability of FCPAS software for multiple and non-planar crack propagation in thin structures is proven.