Crack Length Increment Research Articles

Revealing the accelerated crack prolongation behavior under chemical ionomer degradation within the catalyst layer

As a critical electrochemical reaction region of the proton exchange membrane fuel cell (PEMFC), the cracking issue of the catalyst layer (CL) considerably affects the performance and durability of the PEMFC. However, the impact of chemical ionomer degradation on CL cracking has not been comprehensively revealed. This study investigates the effect of chemical ionomer degradation on CL cracking through accelerated stress tests, characterization, and theoretical analysis. The results indicate that the increasing chemical degradation degree facilitates CL cracking. The CL with the most severe chemical degradation has a single total crack length increment of 1.97 times for the novel CL under the same degree of mechanical degradation. CL fracture resistance analyses reveal that the decrease in interface fracture resistance is the predominant impulse in accelerating CL cracking. Furthermore, the cell voltage reduction of the CL with the most severe chemical degradation during mechanical degradation is 34.22 mV at the current density of 1800 mA cm−2, which is 1.82 times for the fresh CL. The increment of activation resistance and mass transfer resistance are the main causes of the larger cell performance loss. The above findings emphasize the significance of high interface fracture resistance in inhibiting CL cracking and offer theoretical support for analyzing post-operational CL cracking.

Fracture response of mitred X70 pipeline with crack defect in butt weld: Experimental and numerical investigation

Crack defects in mitred bends seriously affect the structural safety of steel pipelines. Therefore, particular attention should be paid to fracture failure of mitred bends due to stress concentration and formation of defects. In this paper, the fracture response of mitred butt girth weld pipeline with crack defect was investigated by conducting full-scale experiments on failure pressure of mitred bend with crack in girth weld. The experimental results estimated the failure pressure of cracked mitred pipes with different mitre angles of 0° and 5° to 11.85 MPa and 11.38 MPa, respectively. At constant mitre angle, circumferential burst failure appeared for defect-free mitred bend, while longitudinal leakage failure occurred on cracked mitred pipe. A refined finite element model of mitre pipe with crack defect was then established based on the experimental results. Also, parametric numerical simulation analyses were carried out to study the effects of defect location, soil spring stiffness, as well as geometric parameters of pipes and crack like mitre angle, mitre length, pipe diameter, wall thickness, crack length, and crack depth on crack driving force of mitred bend. The data revealed unsafe service of mitred pipe for defects located on the internal angle and outer wall of mitred pipe. The crack driving force increased with the increment in mitre angle, wall thickness, crack length, and crack depth. A negative correlation was observed between crack driving force and other factors, such as mitre length and soil spring stiffness. Based on the 6800 numerical results derived from parametric numerical model realized by python and ABAQUS, a hybrid prediction model employing support vector regression (SVR) and particle swarm optimization (PSO) was established to predict the pipe’s crack driving force at the weld. A relative error of 13.3% was obtained between the numerical and established driven model results. In sum, the proposed method looks useful for integrity assessment of mitred X70 pipes. It can also be referenced for fitness for service assessment of energy pipes. Finally, some suggestions about maximum allowable mitre angle for mitred bends with various mitre lengths are given.

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.

Blade Crack Detection using Blade Tip Timing

The harsh working environment of compressor threats the integrality of bladed disk. Crack is one of the most fatal faults of rotating blades. Detecting the crack of blades at early stage could ensure the safe operation of gas turbine and save economic costs. Blade tip timing (BTT) is a noncontact blade vibration measurement technique, which is widely used in recent years. In this article, a procedure of crack detection using BTT data is proposed. First, some typical parameters are taken into consideration, including resonance frequency, amplitude change of natural frequency, amplitude of blade tip, phase, and interblade spacing. It has been found that the frequency of the blade will decrease with the increment of crack length and reduction of crack height. In addition, the resonance frequency of the bladed disk will split when the blade cracks. The amplitude of different orders of resonance frequency varies with cracks. The amplitude of the first order changes very slightly, whereas the second and third orders are relatively obvious. The blade tip vibration amplitude and phase change with cracks without obvious regularity. The interblade distance will change due to the appearance of cracks. According to the above rules, the frequency and the interblade distance are adopted as crack diagnosis indicators. First, we use the Lomb-Scargle periodogram to quickly determine whether the crack appears and then use the blade frequency and interblade distance to locate the number of the blade having crack. In the experimental test, BTT data measured on a titanium bladed disk is used to verify the effectiveness of our method.

A tutorial on solving ordinary differential equations using Python and hybrid physics-informed neural network

We present a tutorial on how to directly implement integration of ordinary differential equations through recurrent neural networks using Python. In order to simplify the implementation, we leveraged modern machine learning frameworks such as TensorFlow and Keras. Besides, offering implementation of basic models (such as multilayer perceptrons and recurrent neural networks) and optimization methods, these frameworks offer powerful automatic differentiation. With all that, the main advantage of our approach is that one can implement hybrid models combining physics-informed and data-driven kernels, where data-driven kernels are used to reduce the gap between predictions and observations. Alternatively, we can also perform model parameter identification. In order to illustrate our approach, we used two case studies. The first one consisted of performing fatigue crack growth integration through Euler’s forward method using a hybrid model combining a data-driven stress intensity range model with a physics-based crack length increment model. The second case study consisted of performing model parameter identification of a dynamic two-degree-of-freedom system through Runge–Kutta integration. The examples presented here as well as source codes are all open-source under the GitHub repository https://github.com/PML-UCF/pinn_code_tutorial.

Numerical model of fracture growth in hydraulic re-fracturing

Simulation of fracture propagation with FEM method generates the need of re-meshing to provide more accurate results. This raises a question of determining the direction and criterion of mesh modification. In the case of general-purpose CAE-packages, we deal with a stationary mesh, and the fracture path is usually represented as a chain of elements with degraded properties. The algorithm proposed in this paper is based on the ANSYS Mechanical APDL language for stepwise geometry reconstruction and mesh modification in accordance with the current configuration of a growing fracture and provides a more accurate description of its shape. The fracture propagation process is divided into stages. Each subsequent stage differs from the previous one by the fracture shape modified due to the crack length increment in the calculated direction. To check the adequacy of the model, an experiment on fracture propagation in glass specimens with an initial notching under uniaxial compression was performed. The laboratory experiments were carried out to determine the fracture toughness of rocks. The developed numerical model has been used to solve the problem of re-fracturing for different stress anisotropy in the oil-bearing rock formation.

The effect of creep damage model formulation on crack path prediction

The stress, strain rate and process zone with respect to the creep-crack growth are analyzed by employing damage-evolution equations. The damage models for the fracture of the process zone are represented using a stress and ductility based formulation. Special attention has been addressed in the present study to the influence of the creep damage model formulation on the on crack path prediction. To evaluate the significance of dominating fracture mechanism a comparison of the cases for pure mode II is considered. It was observed that in the case of stress based model one side of the notch, dominated by tensile stresses, blunts, while the other side, dominated by shear strains, sharpens. In the case of ductility based model, there is a tendency for creep damage to localize only at the blunted part of the notch. This because the highest tensile hydrostatic stress and crack-tip constraint always occur near the blunted part of the notch. In this region, the crack growth direction and general creep damage zone deviate from the initial crack plane. As a result of numerical calculations the consequence of the crack deviation angle values, crack length increments and finally crack path were determined.

Mechanics of fatigue crack growth under large-scale plasticity: A direct physical approach for single-valued correlation of fatigue crack growth data

The major challenge in the mechanics of elastic-plastic fatigue crack growth is to find a physically based driving force parameter to correlate the crack growth rates under different loading conditions. Specifically, a parameter that can provide single-valued correlation of crack growth rates, in stress-controlled and strain-controlled fatigue, is needed. Approaches of the past used either cyclic strain (strain intensity factor) or nonlinear-fracture-mechanics based (cyclic J-integral, ΔJ) parameter, to correlate fatigue crack growth. The validity of these approaches, however, has not been established. Further, the J-integral based approach requires experimental load-deflection curves, recorded after every crack length increment, and geometry-correction factors, which are numerically determined and complicated. In the present work, a physically based approach, based on thecumulative change in the cyclic strain energy of the net-section, is used to develop new parameters that can successfully correlate fatigue crack growth behavior in a variety of loading situations. The driving force parameter, capturing the change in the net-section cyclic strain energy, is determined analytically from elastic-plastic behavior of material and from the relative sizes of cracked and uncracked sections in the crack plane. Load-deflection measurements, geometric correction factors, or numerical methods are not needed in the present approach. Remarkably, excellent correlations of fatigue crack growth, in a variety of specimen geometries and for various stress/strain levels, have been found in both stress- or strain-controlled fatigue conditions. This work, extending the author’s earlier works for elastic fatigue crack growth, validates that the change in net-section strain energy is a fundamental quantity in the mechanics of fatigue crack growth.

An experimental-finite element method based on beach marks to determine fatigue crack growth rate in thick plates with varying stress states

The relation between the fatigue crack growth rate and stress state is significant for fatigue life estimation, especially for thick-welded structures with complex stress states. This paper proposes a hybrid Experimental-Finite Element Method aimed to obtain the fatigue crack growth rate corresponding to plane stress and plane strain states. A static load marking method is proposed to mark a series of crack fronts in a single edge notched bending specimen at known numbers of cycles, which is analysed by nonlinear finite element method to evaluate the stress state by a local constraint factor. Stress intensity factor at the center of the thickness and the surface position where plane strain and plane stress states approximately exist and remain unchanged with crack propagation, is calculated by the 1/4-node displacement method with consideration of non-orthogonal mesh influence. The J-integral method and the virtual crack closure technique are also applied to check the performance of the methods in dealing with the actual cracked body problem. Crack length increments are determined based on the crack front profiles. The da/dN-ΔK curves of plane strain and plane stress states are determined and compared with the results from normal fatigue crack growth rate tests according to Chinese standard: GB/T 6398-2000. The fatigue crack growth behavior of a semi-elliptical surface crack located at the weld toe of a T-plate welded joint subjected to cyclic tension loading is assessed based on the curves and the analytical results are compared with the experimental results. The asymptotic crack shape observed in experiments is successfully predicted by using the curves determined by the hybrid method.

Effect of Low-Cycle Fatigue on Fracture Mechanics Parameters According to Speckle Interferometry

Evolution of parameters of fracture mechanics at various stages of low-cycle damage is studied. The developed approach is based on elaboration of optical interference measurements of the deformation response to a small crack length increment. Three sequential symmetrical notches simulate the fatigue crack growth process across the cumulative fatigue damage zone caused by low-cycle fatigue. The values of tangential components of displacement that are measured at several points on cut edges by electronic speckle interferometry are initial experimental information. The coefficients of stress intensity (SIC) and T strains are determined on the basis of the Williams solution. Values of opening and coefficients of stress intensity (SIC) and T strains for cracks of different length with fixed values of preloading cycles Nc equal 0, 100, 1000, 1800, 2500, and 3300 are obtained. The dependences of the parameters of fracture mechanics for cracks of the fixed length on Nc are constructed.

Combining the crack compliance method and speckle interferometry data for determination of stress intensity factors and T-stresses

An advanced experimental technique for determination of the stress intensity factor (SIF) and the T-stress is developed and carefully verified. The approach employs optical interferometric measurements of local deformation response to small crack length increment. Narrow notches are used for crack modeling. Initial experimental data represent in-plane displacement component values measured by electronic speckle-pattern interferometry in the vicinity of the crack tip. Determination of the first four coefficients of Williams’ series is the main feature of the developed technique. Relationships for transition from measured in-plane displacement components to required fracture mechanics parameters are presented. Availability of high-quality interference fringe patterns, which are free from rigid-body motion, serves as a reliable indicator of real strain state near the crack tip. Experimental verification of the proposed method is performed for non-symmetrical and symmetrical crack in thin rectangular plates subjected to uniaxial tension. The distributions of SIF and T-stress values for cracks of different length in residual stress fields near electronically welded joints of thin plates are presented as an example of practical implementing.

Effects of oxygen-related damage on dwell-fatigue crack propagation in a P/M Ni-based superalloy: From 2D to 3D assessment

Effects of oxygen-related damage (i.e. oxidation and dynamic embrittlement) on fatigue crack propagation behavior in an advanced disc alloy have been assessed in air and vacuum under dwell-fatigue conditions at 725°C. The enhanced fatigue crack propagation is closely related to oxygen-related damage at/ahead of the crack tip, which is determined by the testing environment, the dwell period and the crack propagation rate itself based on two dimensional (2D) observation of the crack tip in an optical microscope and scanning electron microscope. X-ray computed tomography has also been employed to examine the differences between three dimension (3D) crack morphology in air and vacuum conditions, and the crack features have been quantified in terms of crack opening displacements, secondary cracks and uncracked bridging ligaments. The results show that the fatigue crack propagation rate is related to the amount of secondary cracks, and the crack length increment in a loading cycle is related to the breaking/cracking of the uncracked bridging ligaments within the discontinuous cracking zone ahead of the crack tip as oxygen-related damage preferentially occurs in these highly deformed regions. By combination of 3D X-ray computed tomography and traditional 2D observation, a deeper understanding is provided of the mechanisms of oxygen-enhanced fatigue crack propagation behavior.

Mode I and mode II fatigue crack growth resistance characteristics of high tempered 65G steel

Purpose: To investigate the fatigue crack growth at normal tension and transverse shear of 65G steel with the high tempered martensite microstructure and to build an appropriate fatigue crack growth rate curves. To determine the main and auxiliary fatigue crack growth resistance characteristics, which are necessary for machine parts life-time estimation at rolling contact fatigue conditions. Design/methodology/approach: For determination of fatigue crack growth resistance at normal tension a standard compact specimens with edge crack were tested using a hydraulic testing machine and fatigue testing at transverse shear were performed on the I-beam specimens with the edge longitudinal crack using the original testing setup. For crack growth measurement an optical cathetometer B-630 was used. The crack growth rate V was calculated as crack length increment during loading cycles. The stress intensity factor range K was determined by dependence "K = (1 – R)Kmax accordingly to the standard test methods. To establish crack faces friction factor at transverse shear fragments of fractured beam specimen containing crack faces were cut out and tested as a friction pair according to Amontons Coulomb's law. On the base of test results the fatigue crack growth rate curves in logarithmic coordinates "K vs. V were built. These graphical dependencies for normal tension and transverse shear were used for determination of fatigue crack growth resistance characteristics: fatigue threshold "Kth, fracture toughness "Kfc, "K1-2 and "K2-3 which indicates the beginning and the end of middle-amplitude region of curve, "K*, parameters C and n of Paris’s equation. Metallographic and fractographic analyses were performed on the scanning electronic microscope Zeiss EVO 40XVP. Findings: Empirical dependences of the stress intensity factor range on fatigue crack growth rate at normal tension and transverse shear of 65G steel with the high tempered martensite microstructure are obtained. Based on these graphical dependencies the fatigue thresholds and fracture toughness as well as the parameters of Paris’s equation are determined. Research limitations/implications: The fatigue crack growth on 65G steel under low-, medium- and high-amplitude cyclic loading at normal tension and transverse shear was investigated. The fatigue crack growth rate values for a wide range of stress intensity factor are estimated. On the base of fractographical analysis the features of fracture of high tempered martensite in 65G steel at transverse shear are studied. It is shown that the transverse shear crack faces friction factor for high tempered martensite structure is less than for low tempered martensite. Practical implications: Using the fatigue crack growth resistance characteristics of 65G steel at normal tension and transverse shear and related fatigue crack growth rate curves it is possible to predict the life-time of machine parts made of steels with high tempered martensite structure, working at rolling contact fatigue conditions. Originality/value: Complete fatigue crack growth rate curves of 65G steel with tempered martensite structure at normal tension and transverse shear are built and the fatigue crack growth resistance characteristics for both modes of fracture are determined for the first time.

Surface Crack Growth Rate under Tension and Bending in Aluminum Alloys and Steel

Fatigue surface crack growth is studied using FE-analysis and experiments for aluminum alloy D16 and low carbon steel under tension and bending. The subject for the study is central notched specimens with external semi-elliptical surface crack.Crack growth rate was determined on precracked specimens under tension and three point bend loadings. As experimental result the crack length increment on the specimen surface and crack edges opening displacement were obtained. A relationship between the crack form geometry and a number of loading cycles was obtained during tests by beach marks produced on each specimen.For the experimental surface crack paths in tested specimens the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of In-integral was calculated by finite element analysis along semi-elliptical crack front. The governing parameter of the elastic-plastic stress fields In-integral was used as the foundation of the elastic-plastic stress intensity factor. The plastic stress intensity factor approach was applied to the fatigue crack growth on the free surface of the specimens and in the deepest point of the semi-elliptical surface crack front.A significant influence of material properties and loading type on crack growth rate characteristics was established in the present study.The experimental and numerical results of the present study shows that the elastic-plastic stress intensity factor, which is sensitive to elastic-plastic material properties, is attractive for fatigue crack growth rate characterization.

Influence of crack propagation on electrical resistivity and ultrasonic characteristics of normal concrete assessed by sequential TPB fracture test

The paper is focused on the investigation of the effect of tensile failure propagation on the change in values of electrical resistivity and ultrasound pulse passing time within the central section of beam bend specimens made of normal concrete. These two physical characteristics may be employed as a quality indicator of the concrete cover within the procedures of the assessment of the structural durability. The three-point bending test configuration was utilised to drive the crack propagation process through several loading–unloading cycles, between which, the electrical resistivity and ultrasonic measurements over the fractured region were performed. Equivalent elastic crack model was used for estimation of the fracture progression (described via the effective crack length increment) at those loading stages. The relationships between changes of the non-destructively determined parameters, the effective crack length and the distance from crack tip are discussed with respect to two variants of treatment of the test specimens’ surface: the pre-dried surface and the wet surface. A difference between the ultrasonic and electrical resistivity measurements ability with respect to crack width is found in the case of wet samples.

Application of Diffraction-Amalgamated Grain Boundary Tracking to Fatigue Crack Propagation Behavior in High Strength Aluminum Alloy

The fatigue crack propagation behavior in an Al-Zn-Mg-Cu alloy was investigated by amalgamating X-ray diffraction (XRD) with grain boundary tracking (GBT). The integrated technique, Diffraction-Amalgamated Grain Boundary Tracking (DAGT), provides new possibilities for mapping grain morphologies and crystallographic orientations in three-dimension (3D). 3D crack morphologies at different propagation stages in the bulk of metallic materials were successfully obtained by using Synchrotron Radiation X-ray Microtomography (SRCT). Using 2D slices of the 3D crack, the crack length increment was measured to calculate the crack growth rate which varies significantly. Typical crack morphology, such as crack tilt, is detected by the observation of 2D tomographic slice image. The observed interaction between fatigue crack and polycrystalline microstructures can be analyzed in 3D. Through this synthesis of techniques, DAGT, a detailed direct assessment of microstructure and crack propagation behaviors has been achieved.

Numerical model of crack growth in hydraulic re-fracturing

Crack propagation simulations with FEM employ remeshing to provide more accurate results. This raises a question about the direction and criterion of mesh modification. In the case of general-purpose CAE-packages, we have to deal with a stationary mesh, and the crack trajectory is usually represented as a chain of elements with degraded properties. The accuracy of the solution is heavily dependent on the choice of mesh topology, the degree of mesh refinement in the unpredictable crack propagation zone, and correct crack surface loading in this case is impossible. The algorithm proposed in this paper is based on the ANSYS Mechanical APDL language for stepwise geometry reconstruction and mesh modification in accordance with the current configuration of a growing crack and assures a more accurate description of its shape. The crack propagation process is divided into stages. Each subsequent stage differs from the previous one by the crack shape modified due to the crack length increment in the calculated direction, and the linear stationary boundary value problem of elasticity is solved under the assumption of small deformations. To check the adequacy of the model, an experiment on crack propagation in glass samples with an initial cutoff under uniaxial compression has been performed. Samples of size 200×100 mm with a 2.5×40 mm central cutout at an angle of 30 ° to the horizontal axis are made from 4 mm thick window glass. Vertical loading is increased until the crack passes through the sample. The relative difference between the calculated and experimental crack paths does not exceed 5%. The numerical model developed is used to solve the problem of secondary crack growth for different values of stress field anisotropy in the oil ground layer. The factors of crack propagation re-fracturing along the normal to the crack primary gap are defined: 1) stress anisotropy ratio> 0.8; 2) growth of discharge pressure; 3) increase of primary crack disclosure.

An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

Stage-I fatigue crack propagation is investigated using 3D discrete dislocation dynamics (DD) simulations. Slip-based propagation mechanisms and the role of the pre-existing slip band on the crack path are emphasized. Stage-I crack growth is found to be compatible with successive decohesion of the persistent slip band/matrix interface rather than a mere effect of plastic irreversibility. Corresponding crack tip slip displacement magnitude and the associated crack growth rate are evaluated quantitatively at various tip distances from the grain boundary. This shows that grain boundaries systematically amplify slip dispersion ahead of the crack tip and consequently, slow down the stage-I crack growth rate. The results help in developing an original crack propagation model, accounting for the boundary effects relevant to polycrystals. The crack growth trend is then evaluated from calculations of the energy changes due to crack length increments. It is shown that the crack necessarily propagates by increments smaller than 10 nm.

Determination of fracture mechanics parameters by measurements of local displacements due to crack length increment

ABSTRACTNew experimental technique for a determination of the stress intensity factor and the non‐singular T‐stress is developed, verified and implemented. The approach is based on combining the crack compliance method and optical interferometric measurements of local deformation response on small crack length increment. Initial experimental information has a form of in‐plane displacement component values, which are measured by electronic speckle‐pattern interferometry at some specific points located near a crack tip. The first four coefficients of Williams' series are derived. A determination of initial experimental data at the nearest vicinity of crack/notch tip is the main feature of the developed approach. In this case, it is not necessary to use complex numerical models, which are connected with geometrical parameters and loading conditions of the object under study in a stage of experimental data interpretation. Moreover, an availability of high‐quality interference fringe patterns, which are free from rigid body motions, serves as a reliable indicator of real stress state in the vicinity of the crack tip. Experimental verification of the proposed method is performed for specially designed specimen of double cantilever beam type. Distributions of the stress intensity factor and the T‐stress for two cracks in different residual stress fields in the vicinity of friction stir welding joints are presented as an example.

Modeling of Ductile Tearing for RAFM Steel Eurofer97

The contribution describes experiments and numerical modelling performed to deal with ductile tearing for RAFM steel Eurofer97. Based on results of tensile testing and results of FEA a micromechanical model of ductile fracture Gurson-Tvergaard-Needleman (GTN) was calibrated. This model was then applied for simulation of measured J-R curve. To successfully simulate J-R curve by GTN model, crack length increment was separated into increment created by crack tip blunting (stretch width zone increment) and by ductile tearing itself. J-R curve corrected to crack tip blunting was satisfactory described by GTN model choosing suitable element size in the region of crack propagation.