Crack Growth Speed Research Articles

Experimental and analytical characterizations of finite interlaminar crack growth of 2D woven textile composites

Abstract Due to the weave structure of woven textile composites , unstably finite crack growths are observed in the quasi-static interlaminar fracture tests for unidirectional woven textile composites. The unstable crack growth speed and finite crack growth length are up to 60 m/s and 24 mm, respectively. A double compliances method is used to measure the fracture toughnesses for the static and dynamic crack growths. It is found that the double compliances method is very accurate and much simpler than the ASTM standard methods for determining the static fracture toughness . With the help of a high speed camera and the double compliances method, the fracture toughness of the unstable crack is given in this paper.

Cohesive zone model for crack propagation in crystalline silicon nanowires

A fracture of the active particle such as silicon anode results in a potential degradation in lithium-ion batteries with charge/discharge cycle. The massive volume expansion during the lithiation generates large stress which induces the cracking on its surface. We propose the finite element model to have a deep insight into the diffusion-induced stress with fracture process for crystalline silicon nanowires. This model is constructed based on the large deformation theory and cohesive zone model that can describe the failure of Si nanowires. At the beginning of lithiation, high compressive hoop stress is generated on its surface. However, further lithiation, the hoop stress near the surface become less compressive and tensile, which is associated with the “push out effect” as a result of the volume expansion of lithiated material near the phase boundary. When the diffusion induced tensile stress exceeds the fracture threshold, a crack is initiated on the surface and propagates continuously to the center of the silicon nanowire. This crack follows the phase boundary rapidly, but the crack growth speed decreases due to the neighboring compressive hoop stress generated near the phase boundary. From the observation of failure mechanism in Si, we characterize a critical size of Si nanowire, below which fracture can be averted, and we suggest a safe state of charge (safe SOC) depending on its radial size during lithiation.

A micro-macro dynamic compressive-shear fracture model under static confining pressure in brittle rocks

A new dynamic compressive-shear fracture model under static confining pressure is proposed in brittle rocks containing numerous initial microcracks. The formulation of this model is based on the wing crack model, the Mohr-Coulomb failure criterion, the crack-strain relation, and the established dynamic fracture toughness relating axial strain rate. The crack-strain relation is obtained by correlating the micro- and macro damages. The dynamic fracture toughness relating axial strain rate is established by combining the crack-strain relation and dynamic fracture toughness relating crack growth speed. The intact dynamic stress-strain constitutive relationship describing pre-peak hardening phase and post-peak softening phase is presented. The effects of strain rate on dynamic stress-strain relationship, compressive strength, shear strength, cohesion and internal friction are predicted. A novel critical strain rate making the dynamic crack initiation stress equal dynamic compressive strength is found. Exceeding this critical strain rate, the dynamic compressive strength, shear strength, cohesion and internal friction angle have a larger change. The sensitivities of confining pressure, crack size, crack friction, crack inclination angle on dynamic stress-strain relationship, compressive strength, shear strength, cohesion and internal friction angle under high strain rate are also discussed. Rationality of this proposed compressive-shear fracture model is verified by comparing the experimental data.

ACCURATE COMPUTATION ON DYNAMIC SIFS USING IMPROVED XFEM

Compared to the standard extended finite element method (XFEM), the improved XFEM overcomes, in theory, the linear dependence and the ill-conditioning issues, and improves in magnitude of orders the efficiency of linear system solve. In particular, in dynamic crack propagation problems, thanks to the exclusion of the extra dofs on crack tip enriched nodes, the new method eliminates the issue of energy inconsistency or the inconservitive energy transfer caused by dof dynamics, and provides more accurate dynamic stress intensity factors (DSIFs) with much less numerical oscillation. To the best of our knowledge, numerical solution on DSIFs for crack propagation under dynamic loading remains engineeringly unsatisfied. In this paper, the extra-dof free XFEM is extended to implicitly dynamic crack propagation problems-still a remaining difficulty for the current XFEMs. The implicit Newmark algorithm is used for time discretization. A dynamic interaction integral method is employed for DSIFs for both stationary and moving cracks under dynamic loading. Compared with the interaction integral method for static cracks, the dynamic method considers the effects of crack growth speed and inertia terms. The paper investigates in detail the influences of element size, mass matrix formulation, time step size, crack tip enriched zone size, inertia term, crack growth speed, and J-domain mesh/cell sizes of the interaction integral. Numerical tests show satisified accuracy and efficiency of the new method for dynamic crack problems. In particular on the challenging benchmark problem Mode I semi-infinite stationary and then moving crack, the new improved XFEM provides the best DSIFs up to the time of publication.

Analysis of the mechanism of fatigue crack arrest in a cylindrical notched specimen

The phenomenon of fatigue crack arrest in surface-hardened cylindrical specimens with stress concentrators is examined from the perspective of linear fracture mechanics. The stress intensity coefficient (SIC) is considered as the criterion, its scope determines the speed of fatigue crack growth in the case of cyclic loading. The calculations of the study were carried out by the Finite Elements Modeling method using the calculation complex ANSYS. The calculation complex ANSYS that uses the Finite Elements Modeling method in the form of displacements was applied to determine the stress intensity coefficient under bending of cylindrical surface-hardened and non- hardened specimens with the diameter of 10 mm with a semicircular notch with the radius of 0,5 mm. It is established that the stress intensity coefficient has two extremes in the initial area of the fatigue crack development: the minimum and maximum values. The results of the calculation indicate that the minimum value of SIC is lower than its threshold value below which the crack does not develop in the case of a cylindrical surface-hardened notched specimen. This fact is in good agreement with the results of tests of these specimens as non-propagating fatigue cracks were revealed in these specimens only. It is also established that the depth of a crack is approximately 0,02 of the minimum size of the section of a cylindrical specimen for the maximum value of the stress intensity coefficient. The study carried out validates the use of the criterion of average integral residual stresses to calculate the increase of the endurance limit of surface-hardened specimens and parts with stress concentrators due to compressive residual stresses.

Finite Element Simulations of Dynamic Fracture of Full-Scale Gas Transmission Pipelines

The dynamic crack growth in a full-scale gas pipeline of API X80 steel is analyzed using the finite element method with the cohesive zone model. Based on the simulation, it is revealed that for the moderate steady-state crack growth, the crack-tip-opening angle strongly depends on the crack growth speed. In addition, the threshold initial crack sizes under different internal pressures are analyzed, which show a significant three-dimensional effect due to the wall thickness of the pipeline. The presented model offers a feasible way to study some details of the dynamic fracture of full-scale pipelines when tests are difficult or expensive.

Prediction of the Cyclic Life of Pieces with Macrocracks by Thermographic Method

To improve the accuracy for prediction of cyclic life of pieces with macrocracks we propose to use a new thermographic method. Traditionally this question is solved on the basis Paris formula which connects the speed of crack growth (SCG) with Stress intensity factor K. However parameter K is not identical to the SCG because K doesn’t consider non-linear processes at the top of crack (TC). That is why the using K gives the considerable error. For overcoming this problem we proposed instead of K to connect SCG with another diagnostic parameter, such as ΔS(1c)—increment of specific entropy for cycle (ISE) at the TC, which can be calculated with sufficient accuracy through passive temperature field on the surface of tested object. Parameter ISE can be obtained both simultaneously with building of a kinetic fatigue diagram and on the basis of measuring of temperature under exploitation of piece. In both cases the prediction of cyclic lifetime is much higher than with the help parameter K. Besides parameter ISE allows to follow the crack development inside tested object. This means that suggested parameter ISE is more universal and convenient than traditional parameter K.

Study of crack propagation behavior in single crystalline tetragonal zirconia with the phase field method

The tetragonal to monoclinic phase transformation and its toughening effect on the Mode I crack propagation in single crystalline zirconia is investigated by a coupled phase field model. The developed phase field model can simulate the evolution of the tetragonal to monoclinic phase transformation and crack propagation simultaneously. Two tetragonal lattice orientations: 0° and 90°, are studied and compared with the case that the material is untransformable. The numerical results show that the phase transformation always initiates from the crack tip. The phase transformation dramatically reduces the normal stress near the crack tip and slows down the crack growth speed for both orientation angles. A closure of the crack tip may even be observed shortly after the phase transformation, which is caused by the transformation stain and the stress re-distribution at the junction of the monoclinic phase and the crack phase. The lattice orientations have great influences on the final monoclinic microstructure and the transformation toughening effect. This work shows the validity of the phase field method to simulate the microstructure evolution during the crack propagation and it can serve as a robust tool to investigate the transformation toughening behavior of Zirconia ceramics.

Working Life of the I-beam with a Crack

The I-beam containing a crack, loaded by the bending moment and the axial force is considered in this paper. The Mode I stress intensity factor for the beam is determined based on classical expressions with taking into account the cross-section warping by the reduced force and moment, which are valid for the thin-walled beams. On diagrams representing the Mode I stress intensity factor variation with normalized crack length, in intersections of curves for various values of loads and fracture toughness of the beam material, one obtains values of the crack length for which the fracture of the particular beam would occur. The adopted beam material is steel Č.0562 (St 52-3). The Paris law was used for determination of the average crack growth speed. From the diagram of the ΔK (difference between the stress intensity maximum minus and minimum values) variation in terms of the crack length, one can notice that at the beginning, it increases linearly with the crack length, and then, after a certain value of the crack length was reached, it increases abruptly. This could be explained by the fact that the crack length begins to increase suddenly after certain number of load cycles was reached.

3D-kinetic characteristics of slow fatigue crack growth in the aluminum alloy D16T

It is presented the technique based on macro structural analysis of a typical fatigue fracture of a cylindrical specimen of alloy D16T with an annular notch in bending of constructing the diagram of stress intensity coefficient defined the period growth of fatigue crack. Analytical calculation of the change in the exponent m in Peris formula for calculating the speed of fatigue crack growth with respect to depth a in a system with consideration of the increase in the number of cycles N of high-cycle fatigue has be established using experimental data of fatigue fractures of the aluminum alloy D16T. This made it possible to draw the kinematic diagram of a slow fatigue crack growth of D16T in a 3-dimensional coordinate system. Analyzed and numerically determine volumes are formed with the space curve the kinetic diagram of a slow fatigue crack growth. Installed a new kinetic characteristic of fatigue crack growth; i.e. the amount of work of the stress intensity coefficient used to connect parameters of low-cycle fatigue and high-cycle fatigue.

Continuum shape sensitivity analysis and what-if study for two-dimensional multi-scale crack propagation problems using bridging scale decomposition

This paper presents a shape sensitivity analysis and what-if study for two-dimensional multi-scale crack propagation problems using bridging scale decomposition. The sensitivity equations are derived in a continuum setting using direct differentiation method based on a continuum variational formulation of the bridging scale. Due to the fact that the crack propagation speed in an atomistic simulation is discrete in design, and cannot be formulated as a continuous function of shape design variables, we propose a hybrid method that combines analytical sensitivity analysis with finite difference approach. The finite difference part of the sensitivity analysis is only intended for calculating the sensitivity of crack growth speed based on the analytically obtained sensitivity coefficients of structural responses. The theoretical development on sensitivity formulation in this paper extends the application of the method to irregular-shaped finite elements and general design velocity fields. Furthermore, we evaluate and compare several performance measures that quantify crack propagation speed based on crack tip locations for sensitivity analysis and ultimately for structural optimization. A two-dimensional beam example is used to verify the accuracy of the proposed sensitivity approach. It is also demonstrated through a what-if study that with an adequate performance measure, the impact of macroscopic shape changes on microscopic crack propagation speed can be accurately predicted.

Effect of mono and composite coating on dynamic fracture toughness of metals at different temperatures

It is well known that during the operating condition of any metallic structural system the dynamic crack growth speed is in the order of 1–2km/s. Industrial finishes like coating which form the integral part of manufacturing is adopted to improve fracture toughness of metals. These coated samples coated with thin films are mechanically tested by Charpy V-notch impact tester for estimating dynamic fracture toughness. Coatings improve the wear and corrosion resistance of materials; they tend to reduce the strength of materials, because of the increased residual stresses due to the coating process. Defects cannot be precluded from these coated and treated components; strength of those components in the presence of these defects can be analyzed by fracture mechanics approach. An attempt has been made to analyze the effectiveness of coating methods like electroplating, PVD (Physical Vapour Deposition), coating thickness and the service temperature on the fracture behaviour of metals. Experiments have been carried out on EN8 steel and aluminium for different temperatures and the later samples were corroded for 2400h and tested for corrosion resistance. The specimen preparation and experimentations were carried out according to the ASTM standard E-23. Finite element analysis was done by FRANC 2D (Fracture Analysis Code) for estimating the stress intensity factor at different crack lengths along with influence of temperature and corrosion. PVD coated samples of Al–N (aluminium nitride) and nano-crystalline layer of Ti–Al–N (titanium aluminium nitride) showed improved dynamic fracture toughness properties. The same set of samples showed decrease in stress intensity factors and excellent corrosion resistance compared to conventional Ni (nickel) and Cr (chromium) coated samples. Mechanical behaviour of selected metals under heat affected zone is of also discussed in this paper, the study aims at both coated and uncoated cases. Performances of metals in cryogenic condition are also paid attention in this paper.

A New Method on Low-Cycle Corrosion Fatigue of Pipelines Taking Strain as Parameter

As for the more and more severe corrosion fatigue of pipelines in service and the results of the former analyzing means and tests, a new method was brought forward to study the low-cycle corrosion fatigue by using a large pure-bended sample (480 mm×38 mm×12 mm). The experimental samples were obtained from the gas-transmission spiral welded pipe (X65) used in the west-east gas transport project of China. The experiential formula about crack growth speed, , is established via the experimental results under two different environments of air and 3% NaCl solution, and the two constants of a and b were identified.

The dynamic strength of an ordinary chondrite

Abstract– Dynamic and quasistatic unconfined compression experiments were performed on samples of the L5 ordinary chondrite MacAlpine Hills (MAC) 88118. The dynamic compressive strength measurements are the first of its kind for a stony meteorite, and indicate that the material tested here exhibits significant increase in compressive strength with increasing strain rate. This increase in compressive strength is larger than the increases typically observed in terrestrial rock specimens compressed over a similar range of strain rates. The details of the failure process are investigated by recording images of the experiments in real time. Specifically, the crack growth speeds in the dynamic compression experiments are measured from ultrahigh‐speed images. These speeds are significantly lower than the speeds observed in terrestrial analogs that are typically used in numerical investigations of large‐scale impacts. The implications of these measurements of strength and failure process are explored in the contexts of atmospheric disruption of meteors and impact cratering/disruption of asteroids.

판재 Al 2024-T3 합금재료에서 나타나는 두께별 피로균열진전지연거동에 관한 ΔK환산법의 정량적분

Sheet aluminum alloys used in manufacturing of machine structures for transportation show the difference of crack growth speed depending on thickness under the constant fatigue stress condition. The referred thickness effect is a major fatigue failure property of sheet aluminum alloys. In this work, we identified the thickness effect in fatigue test of thick plate and thin plate of Al 2024-T3 alloy under the constant fatigue stress condition, and presented the thickness effect to a correlative equation, which is determined by the shape factor, thickness ratio, and the loading factor, equivalent effective stress intensity ratio depending on thickness, . And we analyzed quantitatively the crack growth retardation behavior in thin plate compared to thick plate by the thickness effect using conversion method. We obtained such values as decrement of thickness(DoT), decrement of stress intensity factor range, (DoS) and identified the relation between them to present the nature of thickness effect in this work.

Statistical Analysis of Fatigue Crack Growth Threshold Based on Test Data

Statistical analyses on fatigue crack growth threshold under three different stress ratios have been done. By the stratified random sampling theory and the weighted least square fitting method, the test data were analyzed based on Paris crack growth rate formulation. The statistical results of the fatigue crack growth threshold under different stress ratios were obtained by linear fitting method. The results show that the fatigue crack growth threshold is influenced by stress ratio R significantly. In the slow crack growth area near the threshold, the increase of stress ratio leads to the decrease of threshold and the increase of crack growth speed. The threshold results under different stress ratios satisfy the normal distribution.

A model for turbulent hydraulic fracture and application to crack propagation at glacier beds

Glaciological observations of under‐flooding suggest that fluid‐induced hydraulic fracture of an ice sheet from its bed sometimes occurs quickly, possibly driven by turbulently flowing water in a broad sheet flow. Taking the approximation of a fully turbulent flow into an elastic ice medium with small fracture toughness, we derive an approximate expression for the crack‐tip speed, opening displacement and pressure profile. We accomplish this by first showing that a Manning‐Strickler channel model for resistance to turbulent flow leads to a mathematical structure somewhat similar to that for resistance to laminar flow of a power law viscous fluid. We then adapt the plane‐strain asymptotic crack solution of Desroches et al. (1994) and the power law self‐similar solution of Adachi and Detournay (2002) for that case to calculate the desired quantities. The speed of crack growth is shown to scale as the overpressure (in excess of ice overburden) to the power 7/6, inversely as ice elastic modulus to the power 2/3, and as the ratio of crack length to wall roughness scale to the power 1/6. We tentatively apply our model by choosing parameter values thought appropriate for a basal crack driven by the rapid drainage of a surface meltwater lake near the margin of the Greenland Ice Sheet. Making various approximations perhaps relevant to this setting, we estimate fluid inflow rate to the basal fracture and vertical and horizontal surface displacements and find order‐of‐magnitude agreement with observations by Das et al. (2008) associated with lake drainage. Finally, we discuss how these preliminary estimates could be improved.

Fatigue Life Evaluation of Unstiffined Aluminum Panels with Multiple Site Damage

Fatigue test were performed on 2024-T62 aluminum panels with MSD cracks, and the fatigue behavior of panels with MSD was analyzed. By the experiment results, the speed of crack growth increased stably in most time of life span, and crack growth rate curves were plotted. Then a rough method was presented to evaluate fatigue life of aluminum panels based a constant geometric factor from the curves and the evaluation is useful in engeering.

Hydrogen concentration behavior around a crack tip under the constant wind rate condition simulated to a moving crack with constant rate

Clarification of the hydrogen diffusion behavior in the metal is important for prevention of hydrogen embrittlement fracture. Previously, some numerical analysis has been performed about hydrogen diffusion behavior under local stress fields by using Finite Element Method or finite difference method. On the other hand, the fatigue crack growth in air, that is, in inert atmosphere, has original speed. However, there is few analysis of hydrogen diffusion behavior including original fatigue crack growth speed. In this research, the effect of crack growth rate on hydrogen diffusion behavior around a crack tip under fatigue condition was clarified based on the numerical analysis and these analyses were conducted under various yield stress. The crack growth speed was modeled by giving uniform flow velocity to the hydrogen distribution in the whole analytical area. The upwind difference method was used for uniform flow velocity. The analytic results were compared between upwind difference and central difference.

Fracture in Composite/Aluminium Joints of Variable Adhesive Properties

A strain gauge technique recently developed with the wedge test, for estimating crack length and, thus, the fracture energy of structural adhesive bonding, has been employed on a system in which one adherend had two types of surface treatment. Simple polishing and polishing with subsequent sandblasting were the treatments used, with a distinct straight line, perpendicular to the sample edges, separating the two. Despite the clear-cut difference in surface treatment, smooth transitions in crack growth speed were noted. This can be explained by the existence of a curved crack front, encroaching gradually on one surface-treated zone, whilst remaining partially on the other. Crack length, a, vs. time, t, curves were exploited to obtain fracture energy vs. crack speed. The multi-valued nature of the relation can also be explained by a non-rectilinear fracture front. The method is proposed as a method for reproducible comparison of surface treatments.