scholarly journals Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

2020 ◽  
Vol 87 (4) ◽  
Author(s):  
Kazem Alidoost ◽  
Meng Feng ◽  
Philippe H. Geubelle ◽  
Daniel A. Tortorelli
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Three Dimensional ◽  
Topological Derivative ◽  
Two Dimensional ◽  
Surface Cracks ◽  
Small Surface ◽  
Refined Meshes ◽  
Boundary Location

Abstract The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

Three-Dimensional Interface Cracks in Anisotropic Bimaterials: The Non-Oscillatory Case

1998 ◽  
Vol 65 (4) ◽  
pp. 1048-1055 ◽  
Author(s):  
Jianmin Qu ◽  
Yibin Xue
Keyword(s):  
Stress Intensity ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Formal Solution ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interface Cracks ◽  
Penny Shaped Crack ◽  
Anisotropic Bimaterials

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available. In this paper, a penny-shaped crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two-dimensional elasticity in conjunction with the Fourier transform method. Fracture mechanics parameters such as the stress intensity factor, crack-opening displacement, and energy release rate are obtained in terms of the interfacial matrix M. To illustrate the solution procedure, a circular delaminations in a unidirectional and a cross-ply composite are considered. Numerical results for the stress intensity factors and energy release rate along the crack front are presented.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

2017 ◽  
Vol 34 (4) ◽  
pp. 495-504
Author(s):  
V. I. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Delamination Fracture

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.

scholarly journals Applications of Energy Release Rate Techniques to Part-Through Cracks in Experimental Pressure Vessels

1982 ◽  
Vol 104 (4) ◽  
pp. 308-316 ◽  
Author(s):  
B. R. Bass ◽  
R. H. Bryan ◽  
J. W. Bryson ◽  
J. G. Merkle
Keyword(s):  
Energy Release Rate ◽  
Thermal Shock ◽  
Energy Release ◽  
Release Rate ◽  
Three Dimensional ◽  
Pressure Vessels ◽  
Test Vessel ◽  
Deformation Plasticity ◽  
Cracked Structures ◽  
Virtual Crack Extension Method

In nonlinear applications of computational fracture mechanics, energy release rate techniques are used increasingly for computing stress intensity parameters of crack configurations. Recently, deLorenzi used the virtual-crack-extension method to derive an analytical expression for the energy release rate that is better suited for three-dimensional calculations than the well-known J-integral. Certain studies of fracture phenomena, such as pressurized-thermal-shock of cracked structures, require that crack tip parameters be determined for combined thermal and mechanical loads. A method is proposed here that modifies the isothermal formulation of deLorenzi to account for thermal strains in cracked bodies. This combined thermo-mechanical formulation of the energy release rate is valid for general fracture, including nonplanar fracture, and applies to thermo-elastic as well as deformation plasticity material models. Two applications of the technique are described here. In the first, semi-elliptical surface cracks in an experimental test vessel are analyzed under elastic-plastic conditions using the finite element method. The second application is a thick-walled test vessel subjected to combined pressure and thermal shock loading.

scholarly journals Calculation and 3D analyses of ERR in the band crack front contained in a rectangular plate made of multilayered material

2018 ◽  
Vol 16 (1) ◽  
pp. 516-519
Author(s):  
Arzu Turan Dincel ◽  
Surkay D. Akbarov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Rectangular Plate ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Geometrical Parameters ◽  
3D Fem ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

AbstractAn investigation into the values of the Energy Release Rate (ERR) at the band crack’s front in the rectangular plate made of multilayered composite material is carried out for the opening mode. The corresponding boundary-value problem is modelled by using threedimensional linear theory and solved numerically by using 3D FEM (Three Dimensional Finite Element Method). The main purpose of the current investigation is to study the influence of mechanical and geometrical parameters on the Energy Release Rate (ERR) at this crack front. The numerical results related to the ERR, and the effect of the mechanical and other problem parameters on the ERR are presented and discussed.

Thickness Effects Are Minor in the Energy-Release Rate Integral for Bent Plates Containing Elliptic Holes or Cracks

1981 ◽  
Vol 48 (2) ◽  
pp. 320-326 ◽  
Author(s):  
J. G. Simmonds ◽  
J. Duva
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Relative Error ◽  
Release Rate ◽  
Plate Theory ◽  
Semimajor Axis ◽  
Elliptic Hole ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Classical Plate Theory

The exact value of Sanders’ path-independent, energy-release rate integral I for an infinite, bent elastic slab containing an elliptic hole is shown to be approximated by its value from classical plate theory to within a relative error of O(h/c)F(e), where h is the thickness, c is the semimajor axis of the ellipse, and F is a function of the eccentricity e. This result is based on Golden’veiser’s analysis of three-dimensional edge effects in plates, as developed by van der Heijden. As the elliptic hole approaches a crack, F(e)~In (1−e). However, this limit is physically meaningless, because Golden’veiser’s analysis assumes that h is small compared to the minimum radius of curvature of the ellipse. Using Knowles and Wang’s analysis of the stresses in a cracked plate predicted by Reissner’s theory, we show that the relative error in computing I from classical plate theory is only O(h/c)In(h/c), where c is the semicrack length. Our results suggest that classical plate and shell theories are entirely adequate for predicting crack growth, within the limitations of applying any elastic theory to an inherently inelastic phenomenon.

Prediction of Energy Release Rate for Mixed-Mode Delamination Using Classical Plate Theory

1990 ◽  
Vol 43 (5S) ◽  
pp. S281-S287 ◽  
Author(s):  
R. A. Schapery ◽  
B. D. Davidson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Mixed Mode ◽  
Plate Theory ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Classical Plate Theory

Prediction of the energy release rate (ERR) and its components for mixed-mode delamination of composite laminates is discussed. A classical plate theory (CPT) version of Irwin’s virtual crack closure method is developed and used for the ERR, first for plane strain and then for three-dimensional deformations. It is shown that CPT does not provide quite enough information to obtain a decomposition of ERR into its opening and shearing mode components. Results from a continuum analysis are needed to complete the decomposition; but analysis of only one loading case is required for two-dimensional and certain three-dimensional problems. In two example problems the finite element method is used with CPT to complete the mode decomposition. Results from CPT and the finite element method are then compared for several cases.

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