Key Engineering Materials Vol. 560

Abstract: Two methods for the extraction of Stress Intensity Factors (SIFs) from three-dimensional (3-D)problems are presented: the Contour Integral Method and the Cutoff Function Method. The formula-tions are tailored for the Generalized Finite ElementMethod andmixed-mode 3-D propagating cracks.The case of crack faces loaded by prescribed tractions is also considered. Another contribution of thispaper is a procedure to control the noise of extracted SIFs based on theMoving Least SquaresMethod.The proposed approach provides a continuous and smooth approximation of 3-D SIF functions foreach fracture mode. Numerical experiments demonstrating the accuracy and robustness of the pro-posed methodology are presented. They include 3-D mixed-mode fatigue crack growth simulationsand the case of a pressurized crack.

Abstract: Distance fields are functions defining the minimum distance between any generic point inspace and the boundaries of an object. This paper shows some important properties of these fields andtheir derivatives. In fact, for polygonal lines, the derivatives of distance fields are discontinuous overthe finite length of the segment, but continuous all around the end-points. An immediate consequenceis their application as intrinsic enrichment of weight functions in meshless methods, for the treatmentof multiple arbitrary cracks. By introducing such explicitly known function for the distance fields,discontinuities can be easily incorporated in the kernel in a simple, multiplicative manner. The result-ing method allows a more straightforward implementation and simulation of the presence of multiplecracks in a meshless framework without using any of the existing algorithms such as visibility, trans-parency and diffraction. Furthermore, one of the main advantages of this approach is the automaticcoalescence of multiple interacting cracks, i.e. no particular enrichment functions are necessary at thejunction points.

Abstract: In this paper multiple fatigue cracks propagation are simulated in two-dimensional plates. Since re-meshing the cracked bodies in each increment of crack extension is a time-consuming and complicated procedure, numerical simulation of mixed-mode crack propagation with FEM is a difficulty. For this purpose, a FEM software is programmed and mesh refinement in each increment of crack is performed by Delaunay Refinement Algorithm. Using different refinement methods, complex boundaries such as multiple cracks and discontinuities which are closed together are easily refined by this algorithm. Crack propagation path is predicted using domain form of J-integral. Modified tensile stress (MTS) criterion is used to predict the crack propagation path in each increment. Different numerical examples illustrate the validation and reliability of present software.

Abstract: Micromechanical cleavage is one of the methods used for isolation of single-and few-layer graphene sheets from bulk graphite. On the surface of peeled graphite flakes, nanosteps of precisely multiple-layer thickness are often observed. The nanosteps are believed to be termination edge of graphene sheets and formed by tearing graphene sheets sandwiched in the mouth of a main cleavage crack during the peeling process. In the present work, we introduce a continuum model to examine the peeling process that involves multiple fractures: the main cleavage fracture at the microscale, delamination of a graphene sheet from bulk graphite at the nanoscale, and tearing fracture of graphene at the atomistic scale. We apply von Karman's plate theory to model the graphene layer, the elastic fracture mechanics for the microscale cleavage crack, and a cohesive zone model for the nanoscale interlayer delamination and for the lattice-scale tearing fracture as well. With a reliable empirical interlayer potential, we could reveal the characteristic length scales involved in the multiscale fracture process. We show that the graphene layer is locally stretched to fracture in mode-I when von Karman's finite deflection effect in a plate is invoked, although the loading by the sandwiching cleavage crack faces is nominally tearing in mode-III.

Abstract: This paper evaluates the stress intensity factors (SIFs) at the crack tips, predicts the crack initiation angles and simulates the crack propagation path in the two-dimensional cracked anisotropic materials using the single-domain boundary element method (SDBEM) combined with maximum circumferential stress criterion. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, degree of material anisotropy, and crack types are presented. Furthermore, the propagation path in Cracked Straight Through Brazilian Disc (CSTBD) specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Additionally, the anisotropic rock slope failure initiated by the tensile crack can also be analyzed by the proposed crack propagation simulation technique.

Abstract: The boundary element method (BEM) is used in this paper for modelling multiple crack propagation in two-dimensional domains. The formulation adopted is based on the dual BEM, in which singular and hyper-singular integral equations are used. An iterative scheme is proposed in order to predict the crack growth path and the crack length increment at each load step. This scheme is accurate enough to simulate localisation and coalescence phenomena, which is the main contribution of this paper. The displacement correlation technique is used to evaluate the stress intensity factors and the theory of maximum circumferential stress is adopted to determine the crack propagation angle and the equivalent stress intensity factor. One application is presented in order to illustrate the robustness and applicability of the proposed model.

Abstract: This article aims at evaluating the extent of the surface region in notched Middle Cracked Tension specimens. Firstly, a fully automatic fatigue crack growth technique is developed to obtain stable crack shapes. After that, the stress triaxiality along the crack front is evaluated for different notch shapes. Then, objective criteria are defined to quantify the extent of the surface region from the stress triaxiality data collected. Next, the extent of the surface region is related to the elastic stress concentration factor of the uncracked geometry by a linear relationship. Finally, empirical two-constant equations able to evaluate the extent of the surface region from the thickness, notch radius, notch depth and elastic stress concentration factor are formulated.

Abstract: In this work, the performance of a new methodology, based on the Dual Boundary Element Method (DBEM) and applied to reinforced cracked aeronautic panels, is assessed. Such procedure is mainly based on two-dimensional stress analyses, whereas the three-dimensional modelling, always implemented in conjunction with the sub-modelling approach, is limited to those situations in which the so-called secondary bending effects cannot be neglected. The connection between the different layers (patches and main panel) is realised by rivets: a peculiar original arrangement of the rivet configuration in the two-dimensional DBEM model allows to take into account the real in-plane panel stiffness and the transversal rivet stiffness, even with a two dimensional approach. Different in plane loading configurations are considered, depending on the presence of a biaxial or uniaxial remote load. The nonlinear hole/rivet contact, is simulated by gap elements when needed. The most stressed skin holes are highlighted, and the effect of through the thickness cracks, initiated from the aforementioned holes, is analysed in terms of stress redistribution, SIF evaluation and crack propagation. The two-dimensional approximation for such kind of problems is generally not detrimental to the accuracy level, due the low thickness of involved panels, and is particularly efficient for studying varying reinforcement configurations, where reduced run times and a lean pre-processing phase are prerequisites.The accuracy of the proposed approach is assessed by comparison with Finite Element Method (FEM) results and experimental tests available in literature.This approach aims at providing a general purpose prediction tool useful to improve the understanding of the fatigue resistance of aeronautic panels.KEYWORDSDBEM, full scale aeronautic panel, 2D/3D crack growth, MSD, doubler-skin assembly, damage tolerance

Abstract: In this paper, the effect of a centrally located cutout (circular and elliptical) and cracksemanating from the cutout on the free flexural vibration behaviour of functionally graded materialplates in thermal environment is studied. The discontinuity surface is represented independent of themesh by exploiting the partition of unity method framework. A Heaviside function is used to capturethe jump in the displacement across the discontinuity surface and asymptotic branch functions areused to capture the singularity around the crack tip. An enriched shear flexible 4-noded quadrilateralelement is used for the spatial discretization. The properties are assumed to vary only in the thicknessdirection. The effective properties of the functionally graded material are estimated using the Mori-Tanaka homogenization scheme and the plate kinematics is based on the first order shear deformationtheory. The influence of the plate geometry, the geometry of the cutout, the crack length, the thermalgradient and the boundary conditions on the free flexural vibration is numerically studied.