Edge Crack Research Articles

Adaptive phase-field modeling for brittle fracture in isotropic/orthotropic piezoelectric materials using multi-patch isogeometric analysis

In this paper, an adaptive multi-patch isogeometric phase-field model is presented for brittle fracture in isotropic/orthotropic piezoelectric materials. The polynomial splines over hierarchical T-meshes (PHT-splines) functions are employed to represent both geometry and field variables. Nitsche’s method provides the continuity of all field variables, including displacement, electric potential, and phase-field at the coupling edge. The local refinement uses a mesh refinement strategy determined by a user-defined threshold for the phase-field variable. An approach that integrates hybrid formulation with staggered solving is utilized for the numerical implementation. The proposed method’s accuracy, reliability, and robustness are demonstrated using several fracture simulations, including tensile tests of rectangular and grooved ceramic plates with an edge crack, plate with a single hole, porous plate, and ceramic laminate with different material orientations.

Modified Study for the Effect of Combined Cycling Loading in Plane on Dynamic Edge Crack Propagation in a Thin Plate

نظرا للأهمية والمخاطر المحتملة المرتبطة بحدوث الشقوق الميكانيكية في التطبيقات الهندسية الهامة، فقد أصبح من الضروري البحث عن نوع معين من انتشار الشقوق. هذه هي حالة شقوق الوضع المختلط التي تنتج عن الوضع الأول والوضع الثاني للتحميل والتي تنتشر في معظم الهياكل، ويتم عرض تلك الشقوق، بالإضافة إلى الظروف التي يمكن أن تحدث فيها، في هذه الحالة. في سياق نظرية ميكانيكا الكسر المرنة الخطية (LEFM)، تم تحقيق توليد إمكانية التحميل غير المتناسب على عينات من سبائك الألومنيوم من خلال تطبيق أحمال الشد الثابتة بالتزامن مع أحمال القص الدورية. باستخدام قانون جريفيث للوضع المختلط I/II لطاقة الشق، تم بناء معادلة نظرية لمعدل نمو الشق الديناميكي. تأخذ هذه المعادلة في الاعتبار تأثير انتشار الكراك الديناميكي. تجريبياً تم تصميم أجهزة مختبرية محلية الصنع وتعديلها لتتناسب مع طبيعة الأحمال المطبقة على عينات ذات شقوق حافة مسبقة من نوعين مختلفين من سبائك الألومنيوم (AA) 6061 و5052، بنظام Uni-Standard بطول شق الحافة تم إجراء مقارنة بين أنواع السبائك المستخدمة للتحقق من صحة النتائج. والتناقض بين مدى قرب النتائج النظرية من النتائج الحقيقية للكسر الذي حدث. وأظهرت النتائج التوافق بين المعادلة النظرية والنتائج العملية. تبدأ العينة 5052 بشكل أسرع وتنتشر الشقوق بشكل أسرع من السبائك 6061.

The mechanism of electric field control in the solidification of welding lines in magnesium alloy casting-rolling

According In this paper, two current loading methods are used to improve the solidification welding line of magnesium alloy casting-rolling from "Ɔ" to "1" shape. The results show that the Joule thermal effect can improve the temperature field distribution in the casting-rolling zone after the magnesium alloy melt is energized. Especially in the case of scheme 1, the temperature field distribution in the casting-rolling zone changes obviously. After the electric field is applied, the range of eddy current increases obviously, the accumulation of high temperature metal liquid appears at the eddy current, and the shape of solidification welding line is improved. When the current density is greater than 2.5 e7A /m2, the distance from the bonding point K to the outlet is less than the distance from K "to the outlet. The casting-rolling force on the edge of plate is small, which is conducive to inhibiting the edge crack of magnesium alloy cast-rolled sheet.

Dual phase‐field model for immiscible fluid flow through fractured unsaturated porous media

AbstractThe immiscible multiphase fluid flow in intact and fractured porous media is relevant to numerous engineering sectors, including industrial processes, geo‐engineering, and civil engineering. These encompass crucial applications that pose significant challenges in modeling, such as carbon dioxide () storage in underground reservoirs, contaminant transport, and desiccation‐induced hydraulic fracturing in unsaturated soils. In this work, a macroscopic framework is developed to describe the transport of immiscible and multiphase fluids in intact and fractured porous materials. The modeling approach utilizes the embedding of two phase‐field models within the continuum Theory of Porous Media (TPM). The case of negligible capillary pressure in the macroscopic scale is associated with many numerical challenges in solving this nonlinear DAEs system, which forms the major subject of the current work. Hence, the problem of the neglected capillary pressure is defined as a target problem. To deal with this, a thermodynamically consistent modified problem is defined, which incorporates an additional artificial macroscopic capillary pressure based on the Cahn–Hilliard phase‐field approach. To increase the robustness and stability of the numerical solution, the Newton–Raphson method is replaced by a homotopy method that allows a gradual transformation of a simpler, solvable problem into the original target problem that usually converges poorly. The sharp crack topology in the fracture regions is approximated by another phase‐field method, which forms a diffusive transition zone across the crack edges of the deformable porous material. For the solid matrix, we consider a small strain assumption with a heterogeneous distribution of the permeability parameter. The inclusion of heterogeneity allows for a more realistic modeling of crack propagation and fluid‐fluid interaction. For the numerical framework, the coupled DAE system is approximated by the finite element method (FEM), implemented in the open‐source project FEniCSx. Appropriate stabilization techniques are also discussed.

A mathematical model for predicting the electro-mechanical behavior of biomimetic crack sensors: Effect of crack depth and gap

Various biomimetic microstructures, such as porous, cracks, wrinkles, micro-pyramids, and micro-domes, are applied to improve the sensing performance of mechanical sensors. Among them, the crack-based strain sensors are widely investigated due to high sensitivity and fast response time. To clearly describe the relationship between crack morphology and sensor sensitivity, a mathematical model is developed for investigating the performance of a poly(3,4-ethylenedioxythiophene)-silicon oxide/polydimethylsiloxane (SiOx/PDMS) based crack strain sensor. First, the displacement field of a crack tip is calculated based on the theory of fracture mechanics, and the mathematical relationship between the crack depth, crack gap, and strain is obtained. The predicted crack depth of the SiOx thin film's thicknesses in 7.91 μm (SiOx/PDMS-7.91) is 2.82 μm, with the error of 3.75% compared to the experimental result. Correspondingly, the deviation of SiOx/PDMS-7.91 is 5.74% between the predicted crack gap and the experimental data. Second, above the aforementioned crack tip characteristics, the mathematical model based on crack edges contacts probability (CECP) is used to construct the relationship between the crack tip characteristics, applied stress, and device sensitivity. The maximum predicted sensitivity can reach 3562.68 compared with the experimental data of 3800.44, and the deviation is about 6.26%. Moreover, the CECP model has good universality with the other reported crack-based strain sensors. It can be concluded that crack morphology affects the distribution and quantity of conductive paths. When the strain sensor is subjected to external forces, brittle thin films generate a certain number of bumped-like elements for microcracks. The wider and deeper crack will increase the relative resistance change and the decrease of conductive paths, resulting in a rapid increase in the sensitivity of the strain sensor.

Mixed FEM implementation of three-point bending of the beam with an edge crack within strain gradient elasticity theory

This paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gradients is applied, simplifying the choice of approximating functions. The concept of energy balance is adopted to calculate the energy release rate with a virtual increase in crack length. The increment of the potential energy of an elastic body is determined by accounting for the strain and stress gradient contribution. Numerical calculations were performed using a quasi-uniform triangular mesh of the cross-type. The mesh refinement was applied in the vicinity of the crack tip, at the concentrated support, and the point of application of the transverse force, and uniform mesh partitioning was utilized in the rest of the beam. The fine-mesh analysis was carried out on the successively condensed meshes in the stress concentration domain for different values of the length scale parameter. The crack opening displacements and the distribution of strains and Cauchy stresses for various values of the length scale parameter are presented. An increase in this parameter increases the stiffness of the crack, which leads to a decrease in the crack opening displacements and a smooth closure of its faces at the crack tip. In addition, accounting for the scale parameter reduces the calculated values of strains and stresses near the crack tip. Based on the energy balance criterion, local fracture parameters such as the release rate of elastic energy at the crack tip and the stress intensity factor are determined for different values of the mesh step. The numerical calculations indicate the convergence of the obtained approximations. The main feature of solutions, which includes the strain gradient contribution, is the decrease in the values of the calculated parameters associated with the fracture energy compared to the classical elasticity theory.

Mechanical Behavior of Multiple Edge‐Cracked Nanobeams by Taking Into Account the Multiple Cracks Effects

ABSTRACTBy exploiting the stress‐driven model, within the Euler–Bernoulli beam theory, a novel nonlocal analytical model is proposed in order to simulate the mechanical behavior of multiple edge–cracked nanobeams by taking into account the multiple cracks effects. According to the present model, the nanobeam is split in correspondence with each of the edge cracks, thus obtaining beam segments, connected to each other by means of massless elastic rotational springs. Firstly, the proposed model is validated by considering experimental data available in the literature, related to bending tests on two cantilever microbeams, each of them containing a single edge crack (i.e., ). Then, the model is employed to simulate a bending test on a cracked cantilever microbeam containing two edge cracks (i.e., ) and a parametric study is performed by varying both the crack depth, the distance between cracks, and the characteristic length of the material in order to investigate the influence of such parameters on the microbeam mechanical response.

Effect of defects on the thermomagnetic instabilities of superconducting radio-frequency cavities with a multilayer structure

Abstract Vortex motion can lead to significant energy dissipation, resulting in hot spots and thermomagnetic instabilities that are detrimental to the application of superconductors. This paper presents a theoretical examination of thermomagnetic instabilities triggered by vortex motion within a Nb3Sn-I-Nb cavity featuring a multilayer structure. The investigation is conducted using Ginzburg–Landau theory in conjunction with the heat diffusion equation. The numerical simulations align well with experimental data from Nb3Sn superconducting cavities. Given that the performance of superconducting radio-frequency (SRF) cavities is highly sensitive to various defects, this study also considers the interaction between vortices and these defects. It reveals the impact of edge cracks on temperature rise and the quality factor. The findings indicate that edge cracks significantly reduce the threshold field for thermomagnetic instability in SRF cavities. The performance of SRF cavities is influenced not only by the RF field amplitude and frequency but also by the length and number of edge cracks. These results offer valuable insights for evaluating the performance of SRF cavities subjected to RF fields.

On a contact problem for a homogeneous plane with a finite crack under friction

An exact solution to the contact problem of indentation of an absolutely rigid punch with a straight base, taking into account friction, into one of the edges of a finite crack located in a homogeneous elastic plane was derived. It is assumed that shear contact stresses are directly proportional to normal contact pressure. In this case, it is assumed that the friction coefficient is directly proportional to the coordinates of the contacting points of the contacting surfaces. The governing system of equations for the problem was derived in the form of the heterogeneous Riemann problem for two functions with variable coefficients and its closed solution is constructed in quadratures. Simple formulas for contact stresses and the normal dislocation component of displacements of crack edge points were obtained. The patterns of changes in contact stresses and crack opening depending on the maximum value of the friction coefficient have been studied.

Multiple edge cracks in a coated semi-infinite medium due to non-Fourier thermal shock

In this wok, based on the non-Fourier C-V model, the problem for multiple edge cracks is investigated for a coating-substrate pair subjected to a sudden temperature drop at the surface of coating. The temperature and resulting thermal stresses without cracks are obtained by the method of Laplace transform. By numerically solving the singular integral equations, the thermal stress intensity factors (SIFs) are evaluated. The results from the Fourier model and C-V heat conduction model are presented for comparison. Two dimensionless quantities are proposed to account for the coupling effects of heat conduction parameters (i.e., thermal conductivity, thermal diffusivity, and thermal relaxation time). Numerical results are presented for the thermal SIF as a function of normalized quantities such as time, crack depth, material constants and crack spacing. The findings in this work are expected to provide references for maintaining the integrity of the coating-substrate pair in the extreme heat transfer applications.

Enhanced anisotropy of Pr-Nd-Fe-B HDDR magnetic powders by regulating the hydrogen decrepitated process

The evolution of microstructures for different hydrogen decrepitated routes was investigated in hydrogenation-disproportionation-desorption-recombination (HDDR) magnetic powders, with particular focus on the fracture of the SC heat-treated alloy during two-step hydrogen decrepitation (HD) and the influence of the first step temperature on magnetic properties. As the temperature increases, the properties of the magnetic powders increase and then decrease, the optimized performance of HDDR magnetic powders was obtained with Br=1.45 T, (BH)max=393 kJ·m−3, DOA=0.79 when the first HD temperature is 65°C. The microscopic analysis shows that there are two problems in the one-step HD route: one is that the particle size is larger ∼150 μm and there are incomplete fractured cracks, the particle surface is more PrNd-rich phase, which leads to different reaction rates between the surface and center in HDDR particles, and the texture orientation of the fine grains at the edge of surface and crack is disordered. The second issue is that HD grains have significant angular difference with the c-axis orientation in incomplete fractured grain clusters, which is directly inherited by the HDDR magnetic powder, resulting in a misalignment texture. In comparison, the two-step HD process effectively addresses the issues derived from one-step HD process. Not only is the grain size of HDDR magnetic powders uniform and the width of the thin grain boundary phases (GBs) is less than the exchange coupling length, but also (Fe+Co) content exceeding 30 at% in GBs with weak magnetism. This is beneficial for enhancing exchange coupling effect between adjacent grains. Moreover, magnetic powder particle exhibits single-domain characteristics, which improves the grain texture orientation. This research provides a new insight for the development of high-orientation and high-performance HDDR magnetic powders.

Study on stress singularities in cylindrical shells with an arbitrary oriented crack using digital gradient sensing technique

In this paper, the transmitted digital gradient sensing (DGS) technique is applied to analyze stress singularity at the tip of an arbitrary oriented crack in a cylindrical shell. A thoretical model of the opitcal path near the tip of the inclined crack in a cylindrical shell under mixed-mode fracture is proposed based on the geometric optical imaging principle. An optical governing equation of DGS technique is established to relate the mixed-mode stress intensity fractors (SIFs) at the crack tip to the shell geometry parameters and the inclined crack sizes, and the angular deflection contours are theoretically plotted using this govering equation. Uniaxial tensile tests are carried out on polymethyl methacrylate (PMMA) cylindrical shells containing an edge crack with different inclined angles, and the optimal calculation area for the exaction of SIFs is determined from linear elasitic fracture mechanics. The effects of shell radius, shell thick, crack length, and crack angle on the mixed-mode SIFs are studied, respectively. These results show that the DGS technique is effective and accurate to evalute the stress singulary around an arbitrary oriented cracks in cylindrical shells.

Local heating at the running crack tip in bcc iron according to molecular dynamics

Abstract This study presents estimates of a possible temperature rise at the crack tip from three dimensional (3D) atomistic simulations of fracture via molecular dynamics (MD) technique. Simulations start from an initial temperature of 0 K. The pre-existing edge crack was loaded in tension mode I. Crack initiation in MD is accompanied by surface dislocation emissions and later by a cross slip of the emitted dislocations into other slip systems. This leads both to stress waves radiation and to local heating in the plastic zone created by these dislocations. The local heating at the crack tip in the surface layers reaches a level of 480–500 K at some atoms, but an average temperature in the plastic zone is lower and depends on a chosen crack tip zone size. In the bulk crystal, where no dislocation emission (i.e. no plastic zone) has been realized, no significant heating is observed at the crack tip. MD results at the free sample surface comply with experimental data for ferritic steels with a pre-existing notch, loaded (quasi-statically) in mode I, as well as with some continuum predictions.

An in-depth analysis of the Radial Point Interpolation Method’s parameters in relation to the accuracy of fracture problem

The fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘ α ≥ 3.5 and shape parameter value between ‘ n = 1.9 -2.1’ yield results of accuracy with error % ≤ 3 % . Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost.

Road Damage Analysis using Surface Distress Index (SDI) and Its Handling on Provincial Road Babat - Jombang (STA 7+000 - 12+500)

The Babat - Jombang road is often traveled by highly loaded vehicles because there are large industries along this section. In addition, the road is damaged by weather and poor subgrade conditions. Thus, resulting in road damage that can interfere with user comfort. Therefore, road damage analysis research was conducted on Babat - Jombang Road (STA 7+000 - 12+500). Road damage analysis in this study using the SDI method. The SDI (Surface Distress Index) method is a road performance scale obtained from visual observations of road damage that occurs in the field. The SDI method is a method that produces an SDI value obtained from the percentage of crack area, crack width, number of holes per 100 m, and the depth of the ruts. From this research, the types of damage on Babat - Jombang Road (STA 7+000 - 12+500) are the hole damage area of 0.11%, longitudinal cracks of 12.05%, transverse cracks of 0.17%, edge cracks of 0.29%, crocodile skin cracks of 79, 66%, shoulder joint cracking by 0.0015%, ruts by 1.48%, bleeding by 1.1%, ravelling by 2.61%, surface layer flaking by 0.13%, patches by 0.26%, upheavel by 0.51%, shoving by 1.6%. Road condition assessment using SDI method shows 87.27% in good condition and 12.73% in moderate condition. Handling carried out is leveling, sealing, hot aggregate sprinkle, and patching holes.

Fracture Behavior of a 2D Imine-Based Polymer.

2D polymers have emerged as a highly promising category of nanomaterials, owing to their exceptional properties. However, the understanding of their fracture behavior and failure mechanisms remains still limited, posing challenges to their durability in practical applications. This work presents an in-depth study of the fracture kinetics of a 2D polyimine film, utilizing in situ tensile testing within a transmission electron microscope (TEM). Employing meticulously optimized transferring and patterning techniques, an elastic strain of ≈6.5% is achieved, corresponding to an elastic modulus of (8.6 ± 2.5) GPa of polycrystalline 2D polyimine thin films. In step-by-step fractures, multiple cracking events uncover the initiation and development of side crack near the main crack tip which toughens the 2D film. Simultaneously captured strain evolution through digital image correlation (DIC) analysis and observation on the crack edge confirm the occurrence of transgranular fracture patterns apart from intergranular fracture. A preferred cleavage orientation in transgranular fracture is attributed to the difference in directional flexibility along distinct orientations, which is substantiated by density functional-based tight binding (DFTB) calculations. These findings construct a comprehensive understanding of intrinsic mechanical properties and fracture behavior of an imine-linked polymer and provide insights and implications for the rational design of 2D polymers.

Enhanced pavement crack segmentation with minimal labeled data: a triplet attention teacher-student framework

ABSTRACT Effective crack detection is critical for pavement maintenance, yet existing methods face significant challenges. Deep learning has become a popular solution due to its superior accuracy and automation capabilities, but supervised methods require extensive labelled data, making it costly and time-intensive. Unsupervised methods, while less data-reliant, struggle with feature extraction, especially for indistinct crack edges. Semi-supervised methods attempt to bridge this gap by using minimal labelled data, enhancing accuracy while reducing manual labelling efforts. However, accurate segmentation remains difficult, particularly with sparse labelled data or complex crack patterns. These limitations highlight the need for a more effective approach. To address these challenges, we propose a novel framework based on a teacher-student model enhanced with triplet attention. Leveraging the Unet architecture, this approach enables efficient feature extraction with minimal labelled data. The teacher model refines predictions using an exponential moving average of the student model’s weights, while the student model is trained with supervised and uncertainty losses. Evaluations on three benchmark datasets demonstrate our framework outperforms fully supervised models, achieving higher intersection-over-union and dice scores with just 2% labelled data. This approach overcomes the limitations of existing methods, enabling accurate crack segmentation with minimal labelled data.

Cracking in semiconductor devices–effect of plasticity under triaxial constraint

A semiconductor device integrates dissimilar materials of small sizes and complex geometries. During fabrication, the materials are deposited at various temperatures. Both deposition and change in temperature cause stresses in the materials. Under the stresses, ductile materials may deform plastically, and brittle materials may crack. Here we focus on how plastic deformation in the ductile materials affects cracking in nearby brittle materials. We study a model structure in which a metal line is encased by a silicon substrate and a brittle oxide layer. In the triaxially constrained metal, the stresses readily exceed the yield strength of the metal. Such high stresses in the metal elevate the stresses in the oxide. The degree of triaxial constraint varies with the aspect ratio of the metal. We compute the stress in the oxide, as well as the energy release rate of an edge crack and a long channel crack. We discuss strategies to avert cracking in the oxide.

Elucidation and verification of cracking behavior in additive manufacturing of alloy 718 based on fractography

This study identified a cracking that occurred continuously in the built direction of an additive manufactured part of alloy 718 by the laser metal deposition method and clarified the cracking behavior. The solidification microstructure of alloy 718 was evaluated by EDS, EPMA, and extraction residue, and it was found that Laves phase, Ti carbides, and Al oxides were formed between the dendrite microstructures. A fracture surface analysis of the cracks revealed that the cracking in the additive manufacturing was hot cracking associated with the liquid film and that the cracking occurred along the grain boundaries. The fracture surface at the beginning of the cracking showed a solidification cracking fracture surface. The experimental investigation for crack propagation during additive manufacturing and the analytical evaluation of the mechanical state around the cracking using thermal elastic-plastic analysis elucidated the cracking behavior during additive manufacturing. If the cracking exists at the fusion boundary, it is suggested that the cracking initiates from the solid-liquid interface towards the solidification direction. Moreover, tensile strain occurred around the cracks during additive manufacturing, particularly the strain was biggest at the crack edge on the fusion boundary. Therefore, the continuous cracking that occurred beyond each layer in the additive manufacturing of alloy 718 in this study can be considered solidification cracking, and its behavior can be further explained as a notch extension cracking that starts from the solidification cracking and continuously occurs in the solid-liquid coexistence temperature region.

Image-driven prediction of fatigue crack growth in metal materials via spatiotemporal neural network

This study proposes an image-driven model based on the SimVP spatiotemporal neural network (STNN) to predict the fatigue crack growth (FCG) in aluminum alloys. This methodology represents a novel usage of STNNs for FCG analysis. It does not require repetitive modeling, extensive computations, or conventional mechanical assumptions. The datasets used during this study were gathered from fatigue experiments with a variety of crack positions, angles, and load levels; they contained a total of 17,925 image frames obtained from DIC measurements. Subsequently, the displacement fields were interpolated onto uniform grids and then augmented, so they could be fitted into an STNN. The proposed method was validated using specimens with edge and central cracks subjected to loads equal to 15.0 % and 20.0 % of the ultimate load. The generalization capability of the proposed method was studied by predicting the FCG under load levels and crack angles outside the training set. In addition, its predictive capability was investigated for both short and long step sizes by employing datasets in which the image data were collected at varying intervals. The overall structural similarity index measurement values were greater than 0.968, and the root mean square errors were held within 0.025 mm. The predicted displacement fields, crack lengths, and crack growth rates agreed well with experimental measurements.