Crack Faces Research Articles

COD and CSD based model for in-plane stiffness of symmetric laminates with cracks in plies and local delaminations: Analysis of crack face sliding

COD and CSD based model for in-plane stiffness of symmetric laminates with cracks in plies and local delaminations: Analysis of crack face sliding

Stress Field near Crack Tips in Pressurized Thick-Walled Cylinders with Single and Multiple Cracks in Linear Elastic Fracture Mechanics: Analytical and Numerical Analysis of Stress Field and Crack Behavior

<div>Arrays of radial cracks often appear at the bore of pressurized cylinders, posing potential safety risks and leading to possible structural failures. This article presents an analytical approach to evaluate the stress field arising from single or multiple uniform radial cracks in thick-walled pressurized cylinders within the context of linear elastic fracture mechanics (LEFM) under mode-I loading. This formulation is based on the fundamental equations of elasticity and approximations of stress intensity factors (SIF) reported in the literature. Hence, the SIF were revisited and their range of validity was highlighted. The study considers two types of internal pressure loading: one applied only to the cylinder’s inner surface with no pressure on the crack faces and another applied to both the inner surface and the crack faces. The influence of the number and length of cracks relative to cylinder thickness on the stress field is analyzed. A finite element model of the pressurized vessel is constructed to verify the proposed analytical solution, showing good agreement with numerical results for a limited number of cracks.</div>

Effect of random variation in input parameter on cracked orthotropic plate using extended isogeometric analysis (XIGA) under thermomechanical loading

Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.

Finite element analyses of rail head cracks: Predicting direction and rate of rolling contact fatigue crack growth

A numerical framework in 3D for predicting crack growth direction and rate in a rail head is presented. An inclined semi-circular surface-breaking gauge corner crack with frictionless crack faces is incorporated into a 60E1 rail model. The investigated load scenarios are wheel–rail contact, rail bending, thermal loading, and combinations of these. The crack growth direction is predicted using an accumulative vector crack tip displacement criterion, and Paris-type equations are employed to estimate crack growth rates. Results are evaluated along the crack front for varying crack radii and crack plane inclinations. Under the combined load cases and in the presence of tractive forces, the crack is generally predicted to go deeper into the rail than under pure contact. Crack growth rates for the combined load cases are higher than (but still close to) that for pure contact. A tractive force will increase growth rates for smaller cracks, whereas a steeper (45°) inclination will decrease the growth rate under the studied conditions as compared to a shallower (25°) inclination. Results should be of use for rail maintenance planning where deeper cracks require more machining efforts.

Experimental and numerical study on the effect of friction between crack faces on fracture parameters of hot mix asphalt concrete

This article investigates the effect of friction between crack faces in ASCB (asymmetric semi-circular bend) specimen on fracture parameters of hot mix asphalt concrete. To achieve this, fracture tests were conducted on ASCB specimens containing cracks with different angles (0, 10, 20, 30, and 40°). In addition to the fracture tests, friction tests were also performed by designing a simple fixture. Subsequently, finite element analyses were carried out, and friction coefficients between crack faces were calculated based on the results of fracture and friction tests. Furthermore, two fracture criteria, ASED (average minimum strain energy density) and MTS (maximum tangential stress), were examined under two different scenarios: assuming zero-friction and non-zero friction between crack faces to predict fracture load and fracture strength. The fracture tests showed that with an increase in the crack angle, the fracture load initially decreased up to the crack angle of 20°, and then increased. Furthermore, the friction tests revealed that an increase in the normal load led to an increase in the friction coefficient. As per finite element results, the crack face contact occurred at a crack angle of 13.1°. Hence, crack faces in the ASCB specimens with the crack angles of 20, 30, and 40° had friction, which significantly affected the fracture parameters. The results also indicated that the average error values for the MTS and ASED criteria compared to the experimental results were 22.8 % and 18.8 %, respectively, when the friction` between crack faces is ignored, and 12.4 % and 4.0 % for the scenario that the friction effect is taken into account. The ASED criterion demonstrated higher accuracy than MTS criterion. Additionally, the average error value of fracture strength predicted by the ASED criterion with assuming non-zero friction was 4 %, indicating good predictive accuracy for fracture strength.

An analysis of the interaction between surface and basal crevasses in ice shelves

Abstract. The prescription of a simple and robust parameterization for calving is one of the most significant open problems in ice sheet modelling. One common approach to the modelling of crevasse propagation in calving in ice shelves is to view crevasse growth as an example of linear elastic fracture mechanics. Prior work has, however, focused on highly idealized crack geometries, with a single fracture incised into a parallel-sided slab of ice. In this paper, we study how fractures growing from opposite sides of such an ice slab interact with each other, focusing on different simple crack arrangements: we consider either perfectly aligned cracks or periodic arrays of laterally offset cracks. We visualize the dynamics of crack growth using simple tools from dynamical systems theory and find that aligned cracks tend to impede each other's growth due to the torques generated by normal stresses on the crack faces, while periodically offset cracks facilitate simultaneous growth of bottom and top cracks. For periodic cracks, the presence of multiple cracks on one side of the ice slab, however, also generates torques that slow crack growth, with widely spaced cracks favouring calving at lower extensional stresses than closely spaced cracks.

Solution of a Dugdale–Barenblatt crack in an infinite strip by a hyper-singular integral equation

This work treats the case of a Dugdale–Barenblatt crack within an infinite strip through the resolution of a hyper singular integral equation. The crack is perpendicular to the strip boundaries and located at its center. The solution approach is based on second order Chebyshev polynomials and requires meticulous treatment of the jump discontinuities within the loading distribution along the crack faces. The relationship between the width of the strip and the length of the cohesive zone has been established. The variation in applied load with the increase in crack length, considering different ratios of the initial crack length to the strip width is illustrated. Furthermore, the crack propagation is simulated. Validation of our approach is achieved through comparison with both the infinite medium case and the work of H. Tada et al. “The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, Pennsylvania. 1973”.

Health monitoring of bonded joints through electrical measurements

The aim of this research work is to explore the possibility of continuously monitoring the presence of damage in bonded joints through electrical measurements. Initially, an analytical model for estimating the crack length based on the electric resistance increase measured across the bond area is presented. The model is successfully validated through finite element analyses and experimental tests on single lap joints made of a conductive adhesive and aluminium or carbon/epoxy adherends. For the last case, the model is extended to account for damage scenarios where a residual conductivity is present across crack faces, due, for instance, to fibre bridging. Eventually, a procedure for predicting the crack length and the stiffness reduction in bonded joint based on electrical measurement is developed.

Numerical solution for the interior electric displacement of the moving DBY‐PS model for semi‐permeable cracked piezoelectric material

AbstractIn this study, we analysed a moving crack at the interface of an infinitely long piezoelectric bilayer using the Dugdale–Barenblatt yield (DBY) model and the polarisation saturation (PS) model. To model the moving crack problem, a Yoffe‐type crack moves at a constant subsonic speed on the interface of an infinitely long piezoelectric bilayer. The crack faces are assumed to be semi‐permeable, and at the boundary of the bilayer, in‐plane electrical and out‐of‐plane mechanical stresses are applied. Due to the application of electro‐mechanical loads, cracks propagate, mechanical yielding zones and electric saturation zones are developed. To arrest the crack from further propagation, mechanical yield stress and saturation electric displacement are applied at the developed zones. To address this problem analytically and numerically, the mixed boundary value problem is transformed into a set of coupled Fredholm integral equations (FIEs) of the second kind using the Fourier transform and the Copson method. The closed‐form analytical expressions for the length of the electrical saturation zone (ESZ), whether longer, shorter or equal to the mechanical yielding zone (MYZ), show dependence on external electro‐mechanical loads under semi‐permeable crack conditions. The algorithm to solve the electric crack condition parameter (ECCP) has been defined using numerical discretization and the bisection method. Illustrative examples demonstrate the proposed technique's effectiveness and suitability for Yoffe‐type moving cracks. The numerical results show the convergence of the ECCP. Furthermore, the numerical results show how mechanical and electrical zone lengths and energy release rate (ERR) are affected by electrical and mechanical loads, strip thickness and crack velocity. In addition, the size of the mechanical yielding zone is consistently promoted by electrical load, while the promotion or prevention of the electrical saturation zone by mechanical load depends on the relative sizes of the nonlinear zones.

Transient heat transfer analysis of a sandwich panel with a cracked honeycomb core

Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face’s midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Extraction of stress intensity factors of biharmonic equations with free boundary conditions on crack faces (III): SIF of a thin plate subjected to the bending moment

The plate bending problems in the Kirchhoff–Love model can be reduced to biharmonic equations. In the previous papers (Kim et al., 2020; Kim et al., 2022), we derived stress intensity factors (SIF) extraction formulas of a biharmonic equation Δ2u=f in a non-convex (cracked, L-shaped) domain with various boundary conditions such as clamped, simply connected, free, and mixed. In previous papers, we could not show a general SIF formula related to Poisson’s ratio ν contained in the free boundary condition. Moreover, the previous SIF extraction formula obtained for a given Poisson’s ratio requires cumbersome line integrals. In this paper, removing the line integrals in the extraction formulas, we show improved SIF extraction formulas applicable to biharmonic equations with free boundary conditions. Thus, the new, improved SIF extraction formulas for free boundary conditions become more straightforward and can be applied to plate bending problems.

Fatigue damage identification based on Kullback-Leibler relative entropy for raw acoustic emission waveform

Acoustic emission (AE) as a non-destructive testing technique is used to identify structural fatigue damage through the evolution of AE characteristic parameters, aiming to prevent significant economic losses and catastrophic consequences caused by fatigue failure. Traditional AE characteristic parameters (counts, hit rate, duration, rise time) are susceptible to the influence of threshold and user-defined acquisition parameters (PDT, HDT, HLT). Inaccurate parameter settings can miss the AE signals of the structural damage, resulting in inaccurate assessment. To reduce the dependency on threshold and other user-defined parameters, the Kullback-Leibler relative entropy (KLRE) is proposed as a feature parameter for identifying structural fatigue damage and performing fatigue life analysis. The effectiveness and feasibility of KLRE were verified through the fatigue tension–compression test on medium carbon steel (MCS) 1045 V-notch specimens. Based on different waveform recording methods, KLRE is divided into the hit KLRE (HKLRE) and waveform stream KLRE (SKLRE). Experimental results demonstrate that:(1) SKLRE outperforms the traditional AE time–frequency domain features in assessing fatigue damage, exhibiting an inflection point in its evolution trend before reaching fatigue critical failure. (2) Node-independent wavelet packet denoising method improves the initial instability of SKLRE caused by work hardening and crack face friction. (3) Amplitude attenuation does not affect the evolution trends of Shannon entropy (SE) and SKLRE. (4) The evolution trend of HKLRE is similar to traditional AE time–frequency domain features, necessitating the use of multiple features together to reduce uncertainty.

Sharp-interface limits for brittle fracture via the inverse-deformation formulation

We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Γ-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non-convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse-strain gradient. They predict spontaneous fracture with exact crack-opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces in the Γ-limit. Accordingly, we construct energy-minimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load.

Moving EMPS model for semipermeable two equal collinear interface cracks in dissimilar magneto-electro-elastic materials

The moving electric-magnetic polarization saturation (EMPS) model is studied for two equal collinear interface cracks in mode-III dissimilar magneto-electro-elastic (MEE) bimaterial under semipermeable crack face conditions. The closed-form solutions of all three possible cases of the proposed EMPS model are derived using the distributed dislocation technique (DDT) and singular integral method. An iterative scheme and explicit expressions of fracture parameters are used to implement the semipermeable crack-face conditions. The study of local energy release rate based on constant electric and magnetic breakdown strength-based saturated conditions concludes that increasing the mismatch of the MEE bimaterial can improve its fracture toughness.

Impact of supercritical carbon dioxide on the frictional strength of and the transport through thin cracks in shale

Understanding the mechanical and transport behavior of thin (i.e. small aperture) cracks slipping under supercritical carbon dioxide (sc-CO2) conditions is essential to evaluate the integrity of sealing formations with buoyant sc-CO2 below and the success of waterless fracturing. The two major items of interest in this work are frictional strength and permeability change of the crack. We used a triaxial cell that permits in situ visualization to conduct and monitor slippage along the faces of narrow cracks subjected to triaxial stresses. Such cracks are analogs to small geological faults. We tested carbonate-rich, 1-inch diameter Wolfcamp shale samples that are saw cut 30° to vertical to create a thin crack. Friction coefficients ranged from about 0.6 to 0.8 consistent with expectations for brittle rocks. The sc-CO2 generally did not alter friction coefficient over the time scale of experiments. From a transport perspective, saturating cracks with sc-CO2 substantially decreased permeability of the crack by 26%–52%, while slip resulted in a variety of permeability responses. Overall, the combined impact of sc-CO2 saturation and slip reduced fault permeability for all tests. Our observations support the notion that the sealing capacity of some caprocks improves when saturated with sc-CO2 and that some slip of small fractures is not necessarily detrimental to caprock integrity.

Mode I fracture propagation and post-peak behavior of sandstone: Insight from AE and DIC observation

Microcracks generated at the crack tip, particularly in quasi-brittle materials such as sandstone, give rise to a non-linear region known as the fracture process zone (FPZ), which cannot be analyzed using linear elastic fracture mechanics (LEFM). To gain insights into the nonlinear fracturing behavior of rock, this study conducted three-point bending experiments on sandstone beams with prefabricated notch. Stable mode-Ⅰ fracture propagation during the post-peak stage was achieved by the monotonic increment of crack mouth opening displacement (CMOD) measured by a clip gauge. The acoustic emission (AE) and digital image correlation (DIC) techniques were utilized to visually track the detailed crack propagation process from both micro and macro perspectives. Nonlinear fracture parameters, including FPZ length, were identified by AE and DIC measurements and compared with the theoretical calculation. A nonlinear fracture criterion relating applied load, equivalent crack length, and stress intensity factor were established, from which the theoretical CMOD-P curve at the post-peak stage were obtained and validated with experimental measurement from MTS machine. The results reveal that microcracks formulating the FPZ materialize in the pre-peak stage, with the majority emerging post-peak to facilitate the propagation of the traction-free crack and FPZ in the loading direction, as evidenced by AE locations and DIC displacement gradient. Throughout the crack propagation process, over 65 % of microcracks are estimated to be tensile mode based on both AF/RA and polarity analysis, aligning with anticipated outcomes from macroscopic three-point bending fracture tests. Energy dissipation primarily occurs within the FPZ to facilitate separation of crack faces, with the dissipated energy region advancing towards the beam boundary. By integrating AE source locations and DIC displacement gradient, the FPZ length of the 3-point-bending sandstone specimens is determined to be lp = 8.1 mm, slightly exceeding the theoretical FPZ lengths calculated by the Irwin model (lp = 7.0 mm) and the Dugdale-Barenblatt model (lp = 7.6 mm). Using a non-linear fracture criterion that incorporates the FPZ and employing the in-time equivalent crack length measured by AE and DIC as an intermediate variable, the theoretical applied load-crack length curve during the post-peak stage is calculated, showing close agreement with load cell measurements with a negligible error of approximately 2 %. Furthermore, the theoretical post-peak CMOD vs. load curve aligns with experimentally obtained results, demonstrating a non-linear crack propagation speed at a constant CMOD rate, wherein crack propagation speed decreases as crack length increases.

Non-break modeling and numerical simulation for non-intact rock failure process

Simulation of the failure process of non-intact rock containing initial cracks, voids, and other discontinuities is a research hotspot in rock mechanics and geotechnical engineering. The damage smear method has attracted wide attention due to its ability to realistically depict the complete failure processes of rock from the microscopic to the macroscopic scale. However, when portraying pre-existed discontinuities, the damage smear method suffers from major difficulties such as mesh dependency and stress singularity. To overcome the limitations of current methodology, this paper proposes a novel non-break modeling strategy inspired by the extended finite element method for dealing with embedded discontinuities, in which the discontinuity of the physical fields across crack faces or the void boundary, as well as the stress singularity at the crack tip, can be characterized by introducing appropriate enrichment functions, and the penalty method is used to impose frictional contact constraints. Applications of the combined method of the improved modeling strategy and damage smear analysis to laboratory-scale and engineering-scale numerical examples show a satisfactory approximation with the analytical solution or experimental observations, indicating that the current modeling strategy can further improve computational accuracy while retaining the advantages of the damage smear method.

Dynamic crack growth in orthotropic brittle materials using an adaptive phase-field modeling with variable-node elements

In this paper, crack growth in orthotropic materials subjected to dynamic loading is numerically studied using an adaptive phase-field method. The study starts with a coarse structured mesh and the adaptive refinement strategy based on a user-defined threshold on the phase-field variable is proposed for computational efficiency, and variable-node elements are employed to treat the hanging nodes as a result of local adaptive refinement. The Hughes-Hilbert-Taylor (HHT) time integration scheme is adopted for temporal discretization. The directionality of orthotropic materials is represented by a penalized second-order structural matrix, which is incorporated in the crack face energy density. Through numerical examples, the influence of the material orientation on the dynamic crack growth in orthotropic materials is studied and the reliability of the proposed framework is validated.

Simulation of crack closure effect on cracked beam vibrations

Vibrations of beams containing cracks are usually investigated by using open or breathing crack models. Neither one of these approaches considers the plasticity induced crack closure (PICC) phenomena which occurs in fatigue crack growth. In this study, PICC is integrated into the vibration analysis of a cracked beam. First, fatigue crack growth at a notch is simulated with elastoplastic finite element analysis. Residual deformations, stresses and the contact pressures on crack faces are obtained. In the second phase, the model which includes these quantities is used for forced vibration analysis under harmonic loading by using implicit finite element method. For comparison, analyses are also running without PICC. Simulation results indicate that PICC has a significant effect on vibrations of cracked beams. For low load amplitude levels, cracked beam behaves like an intact beam. Nonlinear behavior appears only at rather high amplitude levels. It is concluded that PICC could suppress the crack breathing behavior and this could make it difficult to detect a fatigue crack in a beam from its nonlinear vibration response.