Initial Crack Length Research Articles

Dynamic Fracture Analysis of Natural Gas Pipelines Based on a Cohesive Zone Model

Fracture research of natural gas pipelines with cracks is an important part of pipeline integrity evaluation. Based on the cohesive zone model (CZM), a numerical analysis is conducted of the dynamic fracture of X80 steel pipelines under explosion load. The factors considered include the crack propagation length, crack propagation velocity, dynamic crack tip opening angle (CTOA) and gas pressure. The results show that the whole cracking process can be divided into three stages: rapid cracking, stable propagation, and deceleration and stop cracking. When in the rapid cracking stage, the axial cracking of the pipeline is dominant. However, in the stable propagation stage, lateral expansion plays a more significant role. Besides, there exist upper limits on the length and velocity of crack propagation. In addition, it is also found that the time for the inflection point of rapid cracking and stable propagation is later than that to reach the velocity peak. The dynamic CTOA decreases with axial crack propagation, and the steady-state value of the CTOA is positively correlated with the load. The high-pressure gas escapes from the pipeline along the crack, resulting in the increase of air pressure outside the pipeline. Moreover, the peak pressure outside the pipeline is approximately linear its the initial crack length. The present research on the dynamic fracture mechanics behavior of the pipeline provides a necessary supplement for the test.

Prediction of initiation and total life in fretting fatigue considering kinked cracks

This work proposes a methodology to compute fretting fatigue crack initiation and total life by iterative models calibrated with fatigue stress–strain-life curves. One of the main novelty of such models is the assumption that the crack initiation length is determined by the size of the critical distance. To separate initiation and propagation lives, a numerical approach with finite elements is used. The methodology incorporates not only the multiaxial non-proportional characteristic of the stress field in fretting problems, but also the stress gradient effect. Crack initiation path is obtained by means of the SWT parameter, and to validate it, the analysed results are compared with tests considering a cylindrical-flat configuration (Aluminium 7075-T651 alloy). Most of the life initiation estimates, as well as the total life ones, are within a scatter band of 3.

Effect of water contents and initial crack lengths on mechanical properties and failure modes of pre-cracked compacted clay under uniaxial compression

This study investigated the effect of different water contents (w) and initial crack lengths on the mechanical properties (i.e., the unconfined compressive strength (UCS), deformation modulus, and mode II fracture toughness (KIIC)) and failure modes of pre-cracked compacted clay under uniaxial compression. In this study, 44 intact specimens and 72 pre-cracked specimens with different water contents (18%, 23%, and 28%) and initial crack lengths (0, 15 and 20 mm at 45°, i.e., the angle at which the maximum shear stress acts on the initial crack surface). The results showed that the UCS decreased with a long initial crack or high-water content. In contrast, the deformation modulus depends on water contents, but not on the initial crack length. KIIC was calculated. It was found to depend on the water content. Empirical correlation formulas between KIIC vs. w and KIIC vs. UCS were obtained. Furthermore, the failure modes of the compacted clay were classified into five types. In some specimens, wing cracks propagating from the initial crack disappeared due to contact and gliding of the crack surface by the shear stress, and only secondary cracks were observed at failure.

A two-dimensional ordinary state-based peridynamic model for surface fatigue crack propagation in railheads

Based on ordinary state-based peridynamic theory, a 2D peridynamic model has been established to investigate fatigue crack propagation in railheads. The proposed model is verified in terms of rail deformation under a quasi-static load and the ductile material-related fatigue failure model. Good agreements have been achieved between a finite element model and the experimental results. With the proposed model, the effects of the initial crack angle, initial crack length and wheel-rail friction coefficient on crack propagation in railheads are studied. This research provides a new method for studying crack propagation in railheads.

On mode I/II interlaminar fracture toughness of double-sided-loop 2D woven laminated composites

Two-dimensional (2D) plain fabric is prone to delamination when subjected to bending, shear, impact loads. To enhance the interlayer properties of 2D plain fabrics, standing up loops is added. In this paper, specimens of the double-sided-loop 2D woven laminated composites (DWLC) and general 2D woven laminated composites (GWLC) are made for double cantilever beam (DCB) tests and end-notch flexure (ENF) tests to study their toughening mechanism. Test results show that the values of model I and mode II interlaminar fracture toughness are increased by 870% and 250% for the DWLC compared with the GWLC. Based on the three-linear cohesive zone model (CZM), finite element (FE) models of composite laminates specimens of DCB and ENF considering the phenomenon of interlaminar bridging are established, and numerical results are in good agreement with the experimental data, that verifies the accuracy of the FE models. Using the verified FE models, model I and mode II fracture properties of the DWLC specimens of DCB and ENF with different initial crack lengths are investigated, and the results show that the stress is redistributed and the load gradually decreases as the length of the prefabricated cracks increases. The obtained fracture toughness of the DWLC provides a reference for the toughening methods and the engineering applications of DWLC.

Fault analysis of spur gear using XFEM

Spur gears are the most common and simplest in the geometric visualization, and are used to transmit motion and torque from the engine to the desired locations at different transmission ratios. Since the gears work in high loading conditions over a long period, the study of the gear faults due to the high stresses becomes important. In this study, the stresses generated at the root of the gear teeth due to bending is determined using finite element method (FEM) and validated analytically using Lewis theory. Further a detailed crack propagation analysis has been conducted with two intermediate backup ratios of 0.8 and 1.5 and allowing the initial crack length to vary as 0.125, 0.4, 0.7 and 1 mm and check the behavior of the crack propagation paths in static as well as dynamic loading conditions. Also the crack propagation path of the initial crack is observed at the orientations of 180° and 225° from the positive x-axis. The analysis shows that as the initial crack length increases there is increase in the stresses been generated. Further for both backup ratios of 0.8 and 1.5 it has been observed that the crack propagation paths shows variation as the initial crack length increases for both static and dynamic loadings and causes a shift from propagating through the rim to propagation into the width of the rim and showing vertical as well as horizontal propagation in higher initial crack lengths.

J integral and local strain energy density approach to characterize the cracks in anisotropic hyperelastic skin type composite materials

It has been proposed that the response of soft tissues and skin type materials critically depends on the orientation and re-orientation of reinforcing fiber. Here, we quantify the effect of fiber orientation on the mechanical and fracture properties of anisotropic hyperelastic glass fiber (GF)/polydimethylsiloxane (PDMS) composites through a unified experimental and computational analysis. Experimental results show that the tensile strength and fracture toughness of skin type materials depends on the initial orientation of fiber families and is maximum for 0–90 fiber orientation. The re-orientation of fibers under tensile loading is experimentally demonstrated. The experimental findings are well complimented by the finite element (FE) simulations performed using bilinear strain stiffening fiber and matrix (BLFM) material model for soft tissues. The material model parameters are obtained by fitting the experimental data for a meaningful comparison. It is observed that fiber rotation along the loading direction indeed enhances the resistance to crack growth in skin type materials. The size of process zone (RC) ahead of the crack tip and relative contribution of anisotropic energy is characterized using J integral and average strain energy density (ASED) criteria. The RC and anisotropic energy contribution (ϕaniso-avg/ ϕavg) depends on the fiber orientation with higher values for 0–90 fiber orientation. The larger process zone enhances the fracture toughness for 0–90 orientation in comparison to other orientations. Moreover, RC and ϕaniso-avg/ ϕavg are found to be independent of initial crack length and therefore, they can be considered as material parameters for a given fiber orientation. The findings of the present investigations may be used to explore GF/PDMS composite as a possible candidate for soft actuator and bio-medical applications with enhanced toughness.

Mode II cohesive law of adhesive joints

A novel method is presented for the determination of mode II cohesive law for the characterization of delamination in thin adhesive joints The proposed method is based on the three point end notched flexure test. The data reduction method used is the Beam Theory including Bending Rotation effects method (BTBR), which includes the effect of local deformations, shear and bending rotations. By this method, the initial crack length, the apparent crack length during the crack advance, and the mode II resistance curve are determined. The relative shear displacement at the crack tip is determined as a function of the apparent crack advance that occurs when the generation of the fracture zone progresses. In order to determine the shear displacement an analytical analytical model based on the classical theory of beams is used. Finally, the fracture toughness versus the shear relative displacement is represented and the cohesive law is determined by numerical derivation.

Experimental study on the mechanism of wheel-rail steels crack initiation and wear growth under rolling contact fatigue

A twin-roller fatigue test rig was used to reproduce the process of the coexistence of fatigue crack initiation and wear growth in the specimens from rail specimens. Based on the test rig situation, a prediction model was established according to the prediction method for coexistence of crack initiation and wear growth in rail. Both the results, including wear, crack initiation position and crack length in the specimens by the test and simulation were analyzed for verifying prediction model. The results show that there are many states such as micro-pores and micro-cracks on the contact surface at the same time. The crack initiation position is about 0.031mm from the worn contact surface, which is basically consistent with the experimental observation results. The surface crack length distribution is basically the same, distribution in 0.10~0.35mm. The predicted method of the coexistence of the crack initiation and wear growth is feasible.

Simplified equations for determining double-k fracture parameters of concrete for compact tension test

Polynomial equations in non-dimensional form for various fracture parameters of double-K fracture model for compact tension specimen have been derived and presented in this paper. These equations can be used for computing different double-K fracture parameters of concrete for known material properties and specimen size having relative size of initial crack length of 0.3 without involving much complexity in numerical computations. Values of peak load and corresponding crack opening displacement as necessary to compute the double-K fracture parameters of concrete have been derived from the established fictitious crack model in the present study. A simplified equation in non-dimensional form between peak load and critical crack opening displacement as obtained from a fictitious crack model has also been presented.

Study on fracture evaluation in hydrogen environment in 316L stainless steel used in high pressure hydrogen tank

In today’s growing pollution, hydrogen fuel vehicles are an important alternative to electric vehicles. For Type-4 Hydrogen Tank, a steel boss is normally used for valve mounting. The process of hydrogen embrittlement on steel plays a detrimental role. So, studies on the effect of hydrogen embrittlement on the threaded part of 316L stainless steel boss required for fastening of the valve for the 70 MPa compressed H2 tank have been carried out. For analysis, HEDE mechanism and Paris-Erdogan Law are used. For different values of initial crack length, the critical crack lengths are obtained for a particular loading cycle. The same calculation is repeated for different loading cycles. The analysis result shows that the critical crack length increases with the number of loading cycles. The critical crack length is higher 2% to 4% if the effect of hydrogen embrittlement is taken into account. So, for high pressure hydrogen tanks it is essential to consider the effect of hydrogen embrittlement.

Assessment of fiber factor for the fracture toughness of polyethylene fiber reinforced geopolymer

The influence of polyethylene fiber and water-binder ratio on the fracture properties of high toughness geopolymer is studied in this paper. Polyethylene fibers with 6 vol fractions (0, 0.25%, 0.45%, 0.65%, 0.85%, 1.05% and 1.25%) and different lengths (6 mm and 12 mm) were mixed into geopolymers having various water-binder ratios (0.35 and 0.38). A total of 26 experimental groups of polyethylene fiber reinforced geopolymer (PFRG) for notched beams were set up to observe the development process of displacement and deformation field during the three-point bending test by digital image correlation (DIC). The length, width, and height of the specimen were 160 mm, 40 mm, and 40 mm, respectively, with the initial crack length of 10 mm. The fracture test loading was displacement control, and the loading rate was 0.5 mm/min. The results indicated that the fiber factor (product of fiber length-diameter ratio and volume fraction) for PFRG can describe the comprehensive effect of fiber length and content. The literature shows that the fiber factor effectively improves the fracture performance of concrete materials, but the fracture toughness does not monotonously increase with the increase of the fiber factor. The fracture toughness of PFRG increased first and then decreased with the increase of fiber factor. The gain ratio of initial cracking toughness and unstable fracture toughness was reached to 4.395 and 6.332, respectively. Particularly, the optimum fiber factor can be set as 580.65. The fracture toughness of PFRG with a water-binder ratio of 0.35 was generally greater than that of 0.38. The gain ratio of unstable fracture toughness was greater than that of initial cracking toughness. This increased gain ratio indicates that the polyethylene fiber fully exerts its crack resistance effect only after the cracks appear in the specimen. By comparing the fracture toughness gain ratio of this paper with other literature, it is found that polyethylene fiber has a good toughening effect on geopolymer. Additionally, a fracture toughness prediction model was established via regression analysis, considering fiber factor and water-binder ratio as independent variables. The dense fiber factor Fd of polyethylene in this paper can be set as 600, which is higher than that of the other fibers due to its greater stiffness.

Low-cycle fatigue life prediction assessment of notched aluminum 2024-T3 under cyclic axial loading

ABSTRACT This paper investigates the fatigue behavior of notched 2024-T3 aluminum alloy under axial cyclic loading considering the combination of initiation and propagation phases. Several models based on the critical plane concept are used to predict the fatigue life in the initiation phase. A new method is presented to predict the initial crack length of the hole-type notch and edge-cut type notch specimens. Comparison of the experimental and estimated fatigue lives revealed that there is an acceptable agreement between these two results in the low-cycle fatigue life ranges.

Fracture toughness of single layer boronitrene sheet using MD simulations

In linear elastic fracture mechanics, the critical stress intensity factor (CSIF) is related to the surface energy calculated from the bond energy in the reference configuration. For nanomaterials, the difference between the thus computed CSIF and that found from other methods is attributed to lattice trapping. We show here that the energy release rate (and hence the CSIF) determined from the energy of bonds on the crack surface in the current configuration agrees with that estimated by the traditional methods employing the fracture stress and the initial crack length. We demonstrate this by using molecular dynamics simulations with the Tersoff potential by studying crack propagation in a pre-cracked monolayer boronitrene.

Subcritical Crack Growth Parameters for Glass under Different Environmental Conditions

In the present work, subcritical crack growth in soda‐lime silicate glass is investigated under different environmental conditions. Crack growth parameters as a function of temperature and humidity were determined by dynamic fatigue tests. The specimens were pre‐damaged for constant initial crack lengths in all specimens using the Vickers indenter. The initial flaw size induced by the Vickers indenter was obtained by a scanning electron microscope picture of the fracture surface, which could also show the initial flaw geometry. Furthermore, the influence of humidity and temperature on the failure stress of specimens with a constant initial crack length was simulated and the deviations are shown. A comprehensive version of this investigation is currently (16.03.2021) under review in the Journal for Glass Structures and Engineering.

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 fretting fatigue model based on self-steered cracks

In this article a new fretting fatigue life prediction model is presented. The model can be classified as a variable crack initiation length: the crack initiation and crack propagation phases are calculated as a function of the crack initiation length, and among all the feasible crack initiation lengths and orientations, that producing the minimum fatigue life is considered. In this new proposal the crack direction is automatically determined as a function of fatigue parameters in both phases: initiation and propagation. The model is applied to a wide experimental campaign of fretting fatigue tests, and excellent correlation is obtained between experimental and predicted fretting fatigue lives and crack paths.

Influence of specimen geometry on fracture toughnesses of concrete based on boundary effect model

This paper presents the effect of specimen geometry on fracture characteristics of concrete in terms of fracture toughness KIc and initial fracture toughness KIcini. Three commonly used specimen geometries in laboratory were adopted in the study, that is, three-point bending (TPB), compact tension (CT) and four-point bending (FPB) specimens. The Boundary Effect Model (BEM) was used to determine these two fracture parameters, where a new approach was proposed to derive KIcini. To do this, only the maximum aggregate size dmax, the maximum load Pmax and the initial crack length relative to the specimen depth α0 were required. Previous experiments from TPB, CT and FPB specimens were reutilized to acquire KIc and KIcini, and then the geometry influence on these two fracture toughnesses were investigated. The results show that the gained values of KIc and KIcini from TPB, CT, FPB separately or combined TPB + CT + FPB were rather close, meaning little influence from specimen geometry on fracture toughness. Additionally, the ratio of KIcini/KIc was almost the same regardless of specimen geometry shape and α0 when 0.2 ≤ α0 ≤ 0.8.

Asymptotic analysis of pore crack initiation near a free edge

The matched asymptotic (MA) approach of the coupled criterion (CC) enables studying crack initiation at a pore located near a free edge, which leads to a competition between three possible crack initiation mechanisms, namely crack initiation in the ligament, at the pore side opposite to the free edge or simultaneously at both pore sides. The mechanism that is the most likely to occur depends on both the pore-to-free edge ligament size and the material characteristic length to pore diameter ratio. Simultaneous crack initiations at both pore sides occur for large enough ligament size. For smaller ligament sizes, unilateral pore crack initiation is more likely to occur, within the ligament for small characteristic length to pore diameter ratios and at the pore side opposite to the free edge otherwise. The CC MA approach enables estimating the initiation remote imposed stress as well as the initiation crack length.