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This paper investigates the free vibration and compressive buckling characteristics of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) beams containing open edge cracks by using the finite element method. The beam is a multilayer structure where the weight fraction of graphene nanoplatelets (GPLs) remains constant in each layer but varies along the thickness direction. The effective Young’s modulus of each GPLRC layer is determined by the modified Halpin-Tsai micromechanics model while its Poisson’s ratio and mass density are predicted according to the rule of mixture. The effects of GPLs distribution pattern, weight fraction, geometry, crack depth ratio (CDR), slenderness ratio as well as boundary conditions on the fundamental frequency and critical buckling load of the FG-GPLRC beam are studied in detail. It was found that distributing more GPLs on the top and bottom surfaces of the cracked FG-GPLRC beam provides the best reinforcing effect for improved vibrational and buckling performance. The fundamental frequency and critical buckling load are also considerably affected by the geometry and dimension of GPL nanofillers.

This paper investigates vibrations of the edge-cracked functionally graded graphene reinforced composite (FG-GRC) beam with the piezoelectric actuators. The edge crack is simulated by a rotational massless spring model. The effective Young modulus of the FG-GRC beam is estimated by utilizing the modified Halpin–Tsai model. The rule of mixture is applied to calculate the mass density and Poisson ratio of the FG-GRC beam. The total energy function of the edge-cracked FG-GRC piezoelectric beam is derived through using Timoshenko beam theory and von Kármán nonlinear strain–displacement relationship. The mechanical–electrical governing equations of motion for the edge-cracked FG-GRC piezoelectric beam are obtained by applying the standard Ritz procedure and are solved by the direct iterative method. The effectiveness and accuracy of this approach are verified through comparing the present results with other research results. Both uniformly and functionally graded (FG) distributed graphene nanoplatelets (GPLs) are considered to analyze influences of the GPL weight fraction, crack depth, crack location, boundary condition, thickness of the piezoelectric layer, and applied actuator voltage on the mechanical–electrical linear and nonlinear vibrations of the edge-cracked FG-GRC beam. The numerical results can help us predict the mechanical–electrical dynamic behaviors of the FG-GRC beam with cracks and promote the development of the structural health monitoring.

In this article, the proposed model analyzed shear wave propagation through an orthotropic strip with an edge crack. Dual integral equations have been developed for solution of the governing mixed boundary value problem with the aid of Hankel transform technique. Then, the dual integral equations have been transformed into a second kind Fredholm integral equation employing Abel’s transformation. The numerical calculations of stress intensity factor and crack opening displacement are performed utilizing the Fox & Goodwin method and displayed graphically. Elastic constants of two orthotropic materials have been used to illustrate the influence of material orthotropy and normalized strip width on SIF and COD.

Advanced high-strength steel (AHSS) sheets are developed and applied to automotive parts to enable lightweight and crash safety. Edge crack of AHSS sheets during stretch forming is a typical problem demanding prompt solution. In this work, five AHSS sheets are sheared by laser and a designed blanking test tooling under different clearances and shear angles. Six sheared surfaces with different quality are obtained. Then, micro analyses are performed to investigate the influences of blanking process parameters on the sheared edge quality. Crack and internal voids occur near the junction between burnish zone and fracture zone as well as on fracture zone during blanking. Moreover, a flanging forming test platform based on Digital Image Correlation (DIC) technology is used to evaluate the flanging formability with different edge quality. The maximum edge crack strain (ECS) can be achieved with a blanking clearance range as of 10~13.1% thickness and under flat blade. Based on the observations of the sheared surface damage and flanging fracture morphology, the mechanism of edge cracking during the flanging forming is revealed. The present work is helpful in evaluating sheared edge quality and predicting edge crack through stretch flanging forming simulation, which can promote the industrial application of AHSS sheets.

The size of the fully developed process zone (FDPZ) is needed for the arrangement of displacement sensors in fracture experiments and choosing element size in numerical models using the cohesive element method (CEM). However, the FDPZ size is generally not known beforehand. Analytical solutions for the exact FDPZ size only exist for highly idealised bodies, e.g. semi-infinite plates. With respect to fracture testing, the CEM is also a potential tool to extrapolate laboratory test results to full-scale while considering the size effect. A numerical CEM-based model is built to compute the FDPZ size for an edge crack in a finite square plate of different lengths spanning several magnitudes. It is validated against existing analytical solutions. After successful validation, the FDPZ size of finite plates is calculated with the same numerical scheme. The (FDPZ) size for finite plates is influenced by the cracked plate size and physical crack length. Maximum cohesive zone sizes are given for rectangular and linear softening. Further, for this setup, the CEM-based numerical model captures the size effect and can be used to extrapolate small-scale test results to full-scale.

In this paper, we propose a new method to estimate the hole expansion ratio (HER) using an integrated analysis system. To precisely measure the HER, three kinds of analysis methods (computer vision, punch load, and acoustic emission) were utilized to detect edge cracks during a hole expansion test. Cracks can be recognized by employing both computer vision and a punch load analysis system to determine the moment of crack initiation. However, the acoustic emission analysis system has difficulty detecting the instant of crack appearance since the magnitude of the audio signal is drowned out by noise from the press, which interrupts the differentiation of crack configuration. To enhance the accuracy for determining the HER, an integrated analysis system that combines computer vision with punch load analysis, and improves on the shortcomings of each analysis system, is newly suggested.

This study aimed to present a stochastic fracture approach to evaluate the mean and variance of mixed-mode stress intensity factor (MMSIF) with crack growth and probability of failure analysis (PFA) of edge cracked functionally graded materials (FGMs) plate using the extended finite element method (XFEM) through the second-order perturbation technique (SOPT) via interaction integral method. The single-edge cracked plate was subjected to various in-plane loadings such as uniform tensile loading, shear loading, and a combination of tensile and shear loading with different FGM models like exponential law, power law, Mori-Tanaka, and sigmoid law to show the efficacy and effectiveness of material gradation on MMSIF through user-defined MATLAB code. The elastic properties vary in the direction of width, and in-plane loading is assumed perpendicular to the edge crack. The present simulated results are compared with the published results in the literature to check the effectiveness of the present code.

The mechanical reliability of glass substrates is a key challenge for their adoption in advanced semiconductor packaging. This study employs finite element analysis to systematically evaluate the risk of edge crack propagation in large glass panels during redistribution layer (RDL) fabrication. The influence of critical factors—including crack location, number of RDLs, glass material and thickness, dielectric ABF properties, Cu content, and edge clearance—was examined. Results revealed that top-edge crack near the RDL/glass interface pose the highest failure risk due to elevated peeling stress and increased energy release rate (ERR). The risk of propagation intensifies with more RDLs and thinner glass, while high CTE (coefficients of thermal expansion) glasses such as D263, Gorilla, and ceramic glass markedly suppress crack growth compared with borofloat 33 and fused silica. Among ABF dielectrics, GZ-41 demonstrated superior crack resistance owing to its low CTE and moderate stiffness. Although higher Cu content slightly reduced ERR, its effect remained limited. Edge clearance strongly affects reliability, with ≥300 µm providing effective suppression of crack propagation. These findings provide quantitative design guidelines for glass interposer structures, emphasizing the optimization of dielectric material selection, glass substrate and thickness, and layout constraints such as edge clearance. The proposed methodology and results will contribute to establishing reliable strategies for deploying ultra-thin glass panels in advanced semiconductor packaging.

We use the method of continuously distributed edge dislocations to study the dislocation-free zone between an edge crack tip and a plastic zone in an isotropic elastic half-space with a traction-free surface under applied in-plane shear stress. The equilibrium condition is formulated in terms of a set of two coupled singular integral equations. The set of singular integral equations is solved numerically using the Gauss-Chebyshev integration formula resulting in the dislocation distribution function and the number of edge dislocations in each of the edge crack and plastic zone, the condition on the externally applied shear stress and the mode II stress intensity factor at the edge crack tip.

Edge cracks in hot-rolled sheets of industrial grain-oriented electrical steel significantly affect the yield rate and pose substantial challenges to cold rolling fabrication. Eliminating such structural defects through hot rolling requires a thorough understanding of their formation mechanism. This study investigates the formation mechanism of edge cracks in hot-rolled sheets, which are characterized by coarse strip-like grains with typical thicknesses ranging from 20 μm to 100 μm. Coarse, strip-shaped grains have low fracture stress, which is the cause of edge cracks. They originate from abnormally developed columnar grains in continuous casting slabs after reheating, which is unavoidable in industrial large-scale production. Inadequate fragmentation and insufficient recrystallization during rough rolling result in residual coarse grains of intermediate slabs, and their preferential deformation and outward protrusion lead to the formation of grooves. In the subsequent finishing rolling process, deformed coarse grains near the grooves undergo further elongation, developing into distinct strip-like structures. Based on the above mechanistic understanding, the edge microstructure under various rolling parameters was investigated, and targeted improvement measures for edge cracks were proposed. It is concluded that the edge quality can be significantly enhanced through increasing the total width reduction, additional rough rolling passes, and the implementation of edge heating during rough rolling. Quantitative analysis demonstrates that increasing the rolling passes from D to E significantly reduces the fraction of band structure from 64% to 48% and the average width of elongated grains from 43.5 μm to 38.4 μm.