Effective Crack Length Research Articles

Combined approach for fatigue crack characterisation in metals

In this work a comprehensive characterisation of the fatigue crack growth of an Al 2024 alloy is presented. A powerful Christopher-James-Patterson (CJP) model is used for multi-parameter characterisation of the crack state at a few different locations through the fatigue crack growth. The CJP model of crack tip displacements and stress fields was proposed in order to better capture the influences on the applied elastic stress field of the plastic enclave that is generated around a growing fatigue crack. The model does this through a set of elastic stresses applied at a notional elastic-plastic boundary, and it has been shown to accurately model plastic zone shape and size, whilst its ability to predict the effective range of stress intensity factor during a fatigue cycle has been verified. Thus, the model can predict the driving force component of the crack and additional components that account for different shielding mechanisms. CJP model is combined with full-field non-contact Digital Image Correlation (DIC) so that the model can be fed at any moment with real experimental information. The results are then correlated with Paris law data for Al 2024 alloy through Scanning Electron Microscopy (SEM) observations of the fracture surface. In this work the effect of crack length and load level are thoroughly studied and validated with fatigue crack growth rate measurements.

Stress intensity factor estimation of cracks originating from square, circular or elliptical hole in a plate subjected to tension

The use of Linear Elastic Fracture Mechanics (LEFM) in the assessment of reliability and performance, with the help of the concepts from Finite Elements Method, provides practical and convenient ways to study the growth of crack and fracture in the materials. While the Boundary Element Method is another tool usually used to deal with elastic fracture problems, the Finite Element Method has many powerful means to simulate and conduct experiments virtually. In this work, the influence of cracks originating from different hole shapes on the mode I Stress Intensity Factor (SIF) is analysed in Abaqus simulation package. To accomplish this, a two-dimensional finite element model of a plate containing cracks originating from square, circular or elliptical hole is created and then subjected to tension. The objective is to investigate the effect of crack length on the mode I SIF for the different shapes of holes. As the crack length is increased by 367% in all the three cases of square, circular and elliptical holes, the SIF increased respectively by 170.7%, 170.6% and 167.3%. These outcomes indicate that the magnitude of SIF increases by increasing the crack length and vice-versa. However, in the case of elliptical hole, the percent increase in SIF, is slightly less than the other two hole shapes.

Three-point bending test and simulation study on pipe with crack repaired by composite material

Objectives In order to study the bearing characteristics and failure modes of the cracked pipe wrapped with fiber reinforced polymer, A three-point bending test was carried out on a cracked aluminum alloy pipe reinforced by carbon fiber reinforced polymer using epoxy resin. Methods The repair effect was evaluated by comparing the load-displacement curves before and after repair, and the effects of crack length, repair widthand thickness on the bearing capacity and failure mode of specimens were further discussed. The three-point bending simulation model of cracked pipe repaired by CFRP was established to simulate the failure of adhesive layer and carbon fiber cloth. The numerical results are compared well with the corresponding experimental results. Results The test and simulation results show that three-layer carbon fiber cloth can effectively inhibit the crack propagation. With the increase of the number and length of reinforcement layer, the ultimate bearing capacity of the specimen increases. The maximum bearing capacity of the specimens repaired with four-layer carbon fiber cloth has greatly exceeded the pipe without crack, but the ductility and shear bearing capacity of the pipe are reduced. For the same repair layer, the ultimate bearing capacity after repair shows a greater downward trend with the increase of the crack length. Conclusions The research results have certain guidance and reference significance for cracked pipe reinforcement in engineering.

Molecular dynamics simulation of edge crack propagation in single crystalline alpha quartz

Edge crack propagation of single-crystalline alpha quartz under mode I loading condition was investigated using a molecular dynamics simulation. Five different crack lengths are used to analyze the effects of crack length on each sample's crack growth behavior. The effect of crack length was studied in terms of the material's stress-strain curve, strain energy, fracture toughness, atomic analysis of crack propagation, and crack opening deformation. The results revealed that during tensile loading, the pre-cracked crystalline quartz samples are fractured in a brittle approach. The fracture stress in the pre-cracked sample (40 Å length) is dropped about 70% compared to pristine quartz. Moreover, the effect of loading velocity on the mechanical properties is investigated. According to the findings, maximum stress rises by enhancing the loading velocity, and fracture toughness improves. The fracture surface energy of the single crystalline alpha quartz is calculated, and based on the results, there is a good agreement with experimental data.

Paintings crack initiation time caused by microclimate

The current paper aims to use an irreversible cohesive zone model to investigate the effects of temperature and relative humidity cycles on multilayer thin-film paintings. The homogenous one-dimensional paint layers composed of alkyd and acrylic gesso over a canvas foundation (support) with known constant thicknesses are considered as the mechanical model of painting. Experimental data was used for mathematical modeling of canvas as a linear elastic material and paint as a viscoelastic material with the Prony series. Growth of crack through the length of the paint layers under the low amplitude cyclic stresses are modeled by cyclic mechanical loadings. The three-dimensional system is modeled using a finite element method. Fatigue damage parameters such as crack initiation time and maximum loads are calculated by an irreversible cohesive zone model used to control the interface separation. In addition, the effects of initial crack length and layers thickness are studied. With the increase of the painting thickness and/or the initial crack length, the value of the maximum force increases. Moreover, by increasing the Relative Humidity (RH) and the temperature difference at loading by one cycle per day, the values of initiation time of delamination decrease. It is shown that the thickness of painting layers is the most important parameter in crack initiation times and crack growth rate in historical paintings in museums and conservation settings.

Atomistic studies of ductile fracture of a single crystalline cantor alloy containing a crack at cryogenic temperatures

In this paper, atomistic studies show that Cantor alloys containing a pre-existing crack under tension are ductile at cryogenic temperatures. Specifically, the effects of crack length on the mechanical properties of single-crystalline Cantor alloys under mode I loading at the temperature of 0.1 K are investigated via molecular dynamics (MD) simulations. For different initial crack lengths ranging from 25 to 45 nm, the J-integral is calculated at the critical point of dislocation emission, and the work-of-fracture is calculated at the fracture strain. The results show that the Young’s modulus and yield stress decrease with the increased crack length. The J-integral is not significantly affected by the crack length, due to the fact it is governed by the length-independent unstable stacking fault energy. However, the work-of-fracture increases with increased crack length. Nucleation and growth of nanosized cavities in front of the crack tip are observed and the crack propagates through coalescence of cavities, which agrees well with previous experimental findings. As the tensile strain increases, there is a transition from cavitation to shear faulting, after which the stress-strain responses are independent of the crack length. The cavitation and shear faulting dissipate a large amount of energy needed for crack propagation, leading to ductile fracture of Cantor alloys at cryogenic temperatures.

A solution method for free vibration of intact and cracked polygonal thin plates using the Ritz method and Jacobi polynomials

A method for solving for the free vibration of intact and straight through-cracked polygonal thin plates with arbitrary boundary conditions is proposed. To obtain the expressions for the energy integral, the polygonal domain of integration is divided into triangular and trapezoidal domains by a set of parallel lines passing through the vertexes. The energy integral can then be calculated analytically in closed form using the properties of Jacobi orthogonal polynomials, which are the admissible functions of the Ritz method in the framework of the Kirchhoff plate theory. The boundary conditions are modeled using linear springs to restrain the plate edges. The model for solving polygonal thin plate vibration for arbitrary boundary conditions is thus obtained. Accordingly, the cracked polygonal plate is decomposed into several polygonal subdomains based on the crack by applying the technique of domain decomposition. Each subdomain is solved as an intact plate. The subdomains are then connected by a set of linear springs with variable stiffness, and the crack or rigid connection is determined by setting the spring stiffness to zero or infinity, respectively. The convergence and accuracy of the proposed method are verified by comparing the numerical examples with results available in the literature. The proposed method is also applied to determine the natural frequencies of a concave pentagonal plate and cracked regular hexagonal plates. The effect of crack length and inclination on the natural frequencies and mode shapes of cracked regular hexagonal plates with several boundary conditions are studied. The natural frequencies of cracked regular hexagonal plates tabulated are the first published vibration data, and can be used as a reference for future studies.

Crack Length Effect on the Fracture Behavior of Single-Crystals and Bi-Crystals of Aluminum.

Molecular dynamics simulations of cracked nanocrystals of aluminum were performed in order to investigate the crack length and grain boundary effects. Atomistic models of single-crystals and bi-crystals were built considering 11 different crack lengths. Novel approaches based on fracture mechanics concepts were proposed to predict the crack length effect on single-crystals and bi-crystals. The results showed that the effect of the grain boundary on the fracture resistance was beneficial increasing the fracture toughness almost four times for bi-crystals.

Initial R-curves for trans-laminar fracture of quasi-isotropic carbon/epoxy laminates from specimens with increasing size

In this paper, a set of initial R-curves were measured for three different in-plane sizes using scaled Over-height Compact Tension (OCT) specimens and two different stacking sequences. The data reduction scheme was based on a Virtual Crack Closure Technique which is informed by the measured failure load and effective crack length. The R-curve effects were studied by using X-ray Computed Tomography to measure the crack length throughout fracture propagation. It was found that the initial R-curves measured from all three specimen sizes follow the same linearly increasing trend, with similar results for both stacking sequences. However, no plateau was seen on any of the measured R-curves, implying that even the largest specimens are not large enough to generate a full R-curve.

Analysis of stress intensity factors in railway wheel under the influence of stress field due to heat treatment and press-fitting process

Railway transportation system is one of the main needs of the population living in industrialized countries. Many studies have been conducted by engineers due to the importance of railway wheels and railways as a major part of the train. But due to progress in railway technology, in recent years a new type of train wheel known as rim-wheels is presented that their fracture is investigated in this study. The goal of the present study is to calculate stress intensity factors numerically using the boundary element method in railway wheels based on experimental data of material behavior. For this purpose, a series of experiments were performed to determine the behavior of the railway wheel material as well as the data required for numerical analysis. The innovation of this research is that the stress intensity factor is calculated resulting from residual stress of press-fit and heat-treatment processes. Then, the stress intensity factors resulting from the two processes are superimposed in pure mode I, mode II, and mode III loading due to the same crack geometries. Also, the study includes a survey on the effect of crack length on crack propagation as one of its main effective factors. Besides, fatigue crack growth path is calculated and its propagation is also estimated and the effect of different parameters is studied on fatigue crack growth and path.

Numerical Simulation and Analysis of Tunnel Failure Mode by Stochastic Fracture Model

The dip angle, length, spacing, and fracture distance of rock fissure affect the morphology of roadway after collapse. The numerical simulation software CDEM is used to simulate the morphology of roadway collapse. The Monte Carlo model is used to simulate different types of crack models in two-dimensional plane and generate different crack models. The effects of crack angle, crack length, fracture distance, and spacing on the deformation of surrounding rock are analyzed. The influence of different rock burst on the failure strap-fall modes of fissure roadway and roadway in different sections is analyzed, and the stability law of roadway is studied. Under the condition of high stress, the roadway shape has little influence on the distribution of the principal stress difference of surrounding rock, but the equivalent excavation radius determines the distribution of the plastic zone of surrounding rock. The larger the ineffective reinforcement zone is, the larger the deformation around the roadway will be. The decrease of the angle between the structural plane and the vertical stress increases the failure range of the roadway under the gravity burst pressure. Under the horizontal tectonic stress type rock burst, when the structural plane inclination angle is 0°, the two-sided caving body fills the roadway and the roof caving range becomes smaller.

Using digital image correlation to automate the measurement of crack length and fracture energy in the mode I testing of structural adhesive joints

In this study, the crack lengths in adhesively bonded double cantilever beam (DCB) test specimens have been determined using the digital image correlation technique in combination with an elastic foundation model. This method facilitates the continuous measurement of the crack length and offers significant advantages over conventional visual observation including improved accuracy and the potential for automation. This method has been applied to three joints bonded with different structural adhesives, and fracture energy Gc values calculated with the effective crack lengths determined by this method have been shown to be accurate by comparison to Jc values. Finally, a new method is proposed to correct the crack lengths that are visually measured and the Gc values determined using the standard analysis. This scheme is shown to improve the accuracy of the Gc values appreciably.

Fracture properties of slag-based alkali-activated seawater coral aggregate concrete

The development of cracks inside concrete is harmful to the structural durability of seawater coral aggregate concrete (CAC) subjected to an aggressive marine environment. Thus, three-point bending (TPB) tests were performed on the notched beams to determine the fracture properties of cement-based CAC and slag-based alkali-activated CAC (AACAC) at different initial crack-depth ratios (a0/H = 0.2, 0.3, 0.4, and 0.5) and alkaline contents (Na2O-to-binder ratios of 3%, 4%, and 6% by mass). The initial fracture toughness (KICini), critical effective crack length (ac), and unstable fracture toughness (KICun) of the CAC and AACAC were calculated and analyzed based on the double-K fracture criterion. Then, the fracture energy (GF) and characteristic length (lch) were introduced to analyze the energy consumption and brittleness of concrete. It was found that increasing the a0/H ratio reduced the initial cracking load (Pini), peak load (Pmax), ac, GF, and lch, but increased the Pini/Pmax ratio, KICini, KICun, and KICini/KICun ratio, implying that a higher a0/H ratio had a detrimental effect on the crack propagation and increased the brittleness of the AACAC. Additionally, a higher alkaline content, i.e., a greater compressive strength of concrete, upgraded the values of Pini, Pmax, KICini, KICun, and GF due to better mechanical interaction at paste-aggregate interfaces. However, the Pini/Pmax ratio, ac, and lch were steadily lowered with increasing concrete strength, justified by an increase in brittleness. Moreover, the notched AACAC beams contained higher ac (approximately 12.2% increase) and lower KICini/KICun (approximately 4.6% decrease) than those of the notched CAC beams, demonstrating that the existence of alkali-activated materials (AAMs) was beneficial to crack propagation due to improved interfacial transition zone (ITZ) between the paste matrix and aggregates.

Effect of PVA fiber on mechanical properties of fly ash-based geopolymer concrete

Abstract The effects of polyvinyl alcohol (PVA) fiber content on mechanical and fracture properties of geopolymer concrete (GPC) were investigated in the present study. Mechanical properties include cubic compressive, prism compressive, tensile and flexural strengths, and elastic modulus. The evaluation indices in fracture properties were measured by using the three-point bending test. Geopolymer was prepared by fly ash, metakaolin, and alkali activator, which was obtained by mixing sodium hydroxide and sodium silicate solutions. The volume fractions of PVA fiber (length 12 mm and diameter 40 μm) were 0, 0.2, 0.4, 0.6, 0.8, and 1.0%. The results indicate that the effects of the PVA fiber on the cubic and prism compressive strengths and elastic modulus are similar. A tendency of first increasing and then decreasing with the increase in the PVA fiber content was observed in these properties. They all reached a maximum at 0.2% PVA fiber content. There was also a similar tendency of first increase and then decrease for tensile and flexural strengths, peak load, critical effective crack lengths, fracture toughness, and fracture energy of GPC, which were significantly improved by the PVA fiber. They reached a maximum at 0.8% PVA fiber content, except the tensile strength whose maximum was at 1.0% PVA fiber volume fraction. Considering the parameters analyzed, it seems that the 0.8% PVA fiber content provides optimal reinforcement of the mechanical properties of GPC.

Investigations of strain rate, size, and crack length effects on the mechanical response of polycaprolactone electrospun membranes

The effects of strain rate, size (height × width), and pre-existing crack length on the mechanical response of polycaprolactone electrospun membranes were investigated by tension tests conducted at room temperature. In particular, tensile tests were performed with three different strain rates for strain rate effect tests, seven different geometries for elucidating the size effect, and three different initial notch lengths for crack growth experiments. The electrospun membranes were produced by the electrospinning technique using a polycaprolactone solution prepared in 1, 1, 1, 3, 3, 3-hexafluoro-2-propanol as the solvent. Scanning electron microscopy was utilized to show the continuous fiber structure without bead formation. The average fiber diameter was calculated as 1.113 ± 0.270 μm by using scanning electron microscopy images of the membranes. The chemical structure of polycaprolactone was analyzed by Fourier transform infrared spectroscopy, and the toxicity and cell viability of the electrospun membranes were shown by CellTiter 96® Aqueous One Solution Cell Proliferation Assay (MTS test). It was observed that the ultimate tensile strength and Young’s modulus decreased, and the elongation at failure value increased as the strain rate decreased from 10−1 to 10−3 s−1. Besides, positive strain rate sensitivity was observed on the mechanical response of electrospun polycaprolactone membranes. Moreover, the dependency of mechanical response on the size geometry has been well studied, and the optimum height and width combinations were specified. Also, crack growth was studied in terms of both macroscopic and microstructural deformation mechanisms and it is observed that individual fiber deformations and interactions are highly effective on the mechanical behavior and also propagation of the crack. Consequently, in this study, the size and strain rate effects and crack growth on the mechanical response of electrospun polycaprolactone membranes have been investigated extensively, and the results presented herein constitute an essential guideline for the usage of polycaprolactone electrospun membranes at different loading scenarios.

Mechanical and fracture properties of steel fiber-reinforced geopolymer concrete

Abstract In this study, the effects of steel fibers on the mechanical properties of the geopolymer concrete – compressive, splitting tensile, and flexural strength; compressive elastic modulus; and fracture properties – were evaluated. Milling steel fibers were incorporated into the geopolymer concrete, and the volume fraction of the steel fibers was varied from 0 to 2.5%. Fly ash and metakaolin were chosen as the geopolymer precursors. Fracture parameters – critical effective crack length, initial fracture toughness, and unstable fracture toughness – were measured by a three-point bending test. The results indicated that all the mechanical properties of the geopolymer concrete are remarkably improved by the steel fibers with the optimum dosage. When the steel fiber content was under 2%, the cubic and axial compressive strength and the compressive elastic modulus increased. The inclusion of 2% steel fibers enhanced the cubic and axial compressive strength and the compressive elastic modulus by 27.6, 23.7, and 47.7%, respectively. When the steel fiber content exceeded 2%, the cubic and axial compressive strength and the compressive elastic modulus decreased, having values still higher than those of the geopolymer concrete without steel fibers. The splitting tensile strength and flexural strength of the concrete were enhanced with increasing steel fiber content. When the steel fiber content was 2.5%, the increment of the splitting tensile strength was 39.8%, whereas that of the flexural strength was 134.6%. The addition of steel fibers effectively improved the fracture toughness of the geopolymer concrete. With 2.5% steel fibers, the initial fracture toughness had an increase of 27.8%, and the unstable fracture toughness increased by 12.74 times compared to that of the geopolymer concrete without the steel fibers.

Experimental study on fracture properties of concrete under cyclic loading using digital image correlation method

Three-point bending tests are performed on notched concrete beams under various cyclic loading regimes. Meanwhile, the digital image correlation (DIC) method is used to monitor the crack propagation. The fatigue fracture life decreases with the loading level increases for constant-amplitude cyclic loading. The residual crack mouth opening displacement (CMOD) accumulates and fracture stiffness degrades with the loading process. The size of fracture process zone (FPZ) can be determined based on the full displacement field monitored by DIC method. The length of FPZ increases linearly with the increasing of effective crack length before the crack tip opening displacement (CTOD) exceeds the critical value. When CTOD exceeds the critical value, a macroscopic crack formed in front of the initial crack tip. For cyclic envelope loading, the length of FPZ increases at beginning and then decreases with the increasing of effective crack length. For constant-amplitude loading, CTOD never reaches the critical value, and the macroscopic crack does not propagate forward. Finally, it is found that both the calculated effective crack lengths of concrete under constant-amplitude loading by two-parameter model (TPM) and DIC methods present three-stage feature, but the values calculated by TPM are smaller than those by DIC method.

New insights into the fracture mechanism of flattened Brazilian disc specimen using digital image correlation

As a simple and convenient testing method, the flattened Brazilian disc (FBD) specimen has been widely used to determine the tensile strength and mode-I fracture toughness of rocks. However, the precision of the mechanical parameters calibrated by FBD testing method needs to be further evaluated. In this paper, digital image correlation (DIC) technique is used to capture the progressive failure process of FBD specimen, and some new insights are provided for further understanding the fracture mechanism of FBD specimens. Firstly, the horizontal tensile strain history in the center region of FBD specimen is obtained via DIC technique, and combined with loading force history, the tensile stress–strain curve of rocks can be determined. Then, by analyzing the horizontal strain and displacement field near the central crack of FBD specimen, the central crack tip positions are identified. The progressive failure process of FBD specimen shows that the micro-crack and fracture process zone (FPZ) has grown at the center of FBD specimen at the moment of first peak force Pmax. After the Pmax, the central crack propagates unsteadily towards the flattened ends of FBD specimen, while is hindered after the loading force declined to the local minimal force Pmin. Therefore, it is not proper to determine the mode-I fracture toughness KIC using the local minimal force Pmin in FBD tests. In this study, a modified calculation method to determine KIC is proposed using the first peak force Pmax and its corresponding central effective crack length observed via DIC technique. In addition, the cracking nature of the secondary crack is identified, and the second rise of the loading force is induced by the compression-shear failure near the flattened ends of FBD specimen. These results are beneficial to better understanding the progressive fracture mechanism of FBD specimen and improving the accuracy of KIC calibrated by FBD testing method.

Uniaxial tearing properties and the tearing residual strength models of PTFE coated fabric

This study presents an experimental and analytical investigation on central crack tearing properties of PTFE coated fabric. Firstly, tearing tests under uniaxial tension load were carried out to investigate the influence of crack length and crack orientation on tearing properties of PTFE coated fabric. Tear failure process was carefully recorded and two types of failure modes can be characterized, i.e. progressive failure and brutal failure. The effect of initial crack length and orientation on tearing residual strength (TRS) can be attributed to the numbers of the cut yarns, which can be represented by the equivalent crack length. Secondly, the available TRS models are summarized and discussed in detail. It is found that these models can be classified into two types, i.e. fracture-mechanic-based models and stress-field-based models. By comparing the prediction results with test data, these models present to be only valid for small crack conditions, and the stress-field-based model shows better accuracy.

Influence of surrounding rock temperature on fracture parameters of concrete for shotcrete use in the hot-dry tunnel environments

The objective of this study was to explore the influence of the surrounding rock temperature on fracture parameters of concrete. Four different surrounding rock temperatures were adopted and the three-point bending test on notched beams was conducted in this paper. Based on this test, the fracture energy, initial fracture toughness, unstable fracture toughness, and crack extension resistance of concrete were calculated via the double-K fracture model the KR curve crack propagation criterion. The results are summarized as follows: (1) The fracture energy of concrete beams increased first then decreased with the increment of the hot-dry environment temperature, and reached the peak at 60 °C. (2) The initial fracture toughness, unstable fracture toughness, and crack extension resistance of concrete decreased with the increment of the hot-dry temperature. (3) The length of the fracture process zone increased first then decreased with the increment of the effective crack length.