Crack tip stress fields for thin, cracked plates in bending, shear and twisting : A comparison of plate theory and three-dimensional elasticity theory solutions

A three-dimensional finite element study of crack tip fields in thin plates under bending, shearing, and twisting loads is carried out to study the relation of the plate theory crack tip fields to the actual, three dimensional crack tip fields. In the region r>0.5h the Kirchhoff theory is a good approximation of the three dimensional stress fields for symmetric plate bending. The Reissner theory gives a good approximation in the region r h from the crack tip than in the bending problem. In the case of shear loading the near tip out-of-plane shear stresses do not vary quadratically through the thickness as in plate theory, but are nearly constant, except in the neighborhood of the free surface. Quadratic variation, as predicted by plate theory, is observed for r>h. Energy release rates based on the Kirchhoff and Reissner theories agree well with those computed by means of three dimensional finite element analyses.

Straight cracks near a stiffening element, or curved cracks, in a pressurized shell can be subjected to out-of-plane tearing stresses in addition to normal tensile stresses due to the membrane stresses in the shell. To predict the rate of fatigue crack growth in such situations a theory and a crack growth rate correlation are needed. Such loadings are modelled as a superposition of plane stress tensile fracture (mode I) and Kirchhoff plate theory shearing fracture (mode 2). Finite element analys...

Crack growth in thin sheets loaded under tension and transverse shear is studied experimentally and the mechanics of such problems are reviewed. A small scale yielding approach is adopted that describes the crack tip fields using a combination if Kirchhoff plate theory and plane stress elasticity. Techniques for calculating the relevant stress intensity factors are presented and validated with results from six test cases. Fatigue crack growth rates are measured using a double-edge notch test spe...

Stress intensity factors for a finite crack in an infinite plate are calculated assuming Kirchhoff plate theory. Two problems are considered: a cracked plate subjected to uniform far-field shearing, and a cracked plate subjected to uniform far-field bending moment. In both cases the crack is oriented at an arbitrary angle to the axis of loading.

Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated here for the first time. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's [16] result that the value of the J-integral based on either theory...

For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy. It is shown that the strain energy release rate for the Reissner's plate approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small. By using this result, the limiting expression of the stress intensity factor can be exp...

Cracked plates subjected to out-of-plane tearing loads were investigated using both classical plate theory and Reissner/Mindlin plate theory. It was shown that the total strain energy release rate according to Reissner/Mindlin plate theory converges to that of classical plate theory as the thickness to crack length ratio approaches zero. It was demonstrated that it is not meaningful to separate mode II and mode III strain energy release rates using classical plate theory.

#2David M. Parks(MIT: Massachusetts Institute of Technology)H-Index: 45

Abstract Based on detailed three-dimensional finite clement analysis, the near-tip field of a thin elastic plate remotely subjected to Mode II antisymmctrical loading is investigated. The computed results show the transition to a three-dimensional state to occur near the radial distance from the crack tip of 1.5 times the plate thickness. In the close vicinity of the crack front, the asymptotic stress field is characterized by a combination of plane strain Mode II and anti-plane Mode III singula...

By using the finite element technique, stress intensity factors have been obtained for finite rectangular plates and the results have been given for various h/a, W/a and L/W ratios. By using a three-dimensional isoparametric element, the problem has been considered as a three-dimensional one and the variation of stress intensity factor across the plate thickness has been found to be nonlinear.

#1Zhen-Liang Hu(CSU: Central South University)H-Index: 2

#2Ying Yang(CSU: Central South University)H-Index: 4

Last. Xian-Fang Li(CSU: Central South University)H-Index: 37

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Abstract The bending fracture of an ultra-thin plate containing a thickness-through crack with consideration of surface elasticity is studied in this paper. Based on the Kirchhoff plate theory incorporating surface elasticity, a governing equation is derived for static bending of nanoplates with surface elasticity. The fracture problem of an infinite isotropic elastic nanoplate with a thickness-through crack is presented and solved when the plate is subjected to uniform bending moment, twisting ...

#2Marcelo A. Dias(Edin.: University of Edinburgh)H-Index: 11

Last. Marcelo A. Dias(Edin.: University of Edinburgh)H-Index: 1

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Abstract Over the past decade, kirigami—the Japanese art of paper cutting—has been playing an increasing role in the emerging field of mechanical metamatertials and a myriad of other mechanical applications. Nonetheless, a deep understanding of the mathematics and mechanics of kirigami structures is yet to be achieved in order to unlock their full potential to pioneer more advanced applications in the field. In this work, we study the most fundamental geometric building block of kirigami: a thin...

#1Jan Kraft(Technische Universität Darmstadt)H-Index: 1

#2Carl Fällgren(Technische Universität Darmstadt)H-Index: 1

Last. Michael Vormwald(Technische Universität Darmstadt)H-Index: 25

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Abstract The strain energy release rate is calculated numerically for cracks in shells from shell elements by using the modified crack closure integral. This enables the separation of individual strain energy release rates for the different crack opening modes and the calculation of the corresponding stress intensity factors for mixed mode loading situations. The presented formulas are validated by comparing numerical results for a 3d finite element model with results computed from a plane shell...

Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions ...

Abstract In this work, an extended isogeometric analysis (XIGA) is used for the analysis of through-thickness crack in a homogeneous and isotropic plate. In isogeometric analysis (IGA), non-uniform rational B-splines (NURBS) are used as a basis function. The plate kinematics is modelled by Reddy’s higher-order shear deformation theory (HSDT). The C 1 continuity requirement of HSDT can be easily fulfilled by the NURBS basis functions. In order to obtain the plate fracture parameters (moment inten...

#2Z. L. Han(Hefei University of Technology)H-Index: 1

Last. Naman Récho('ENS Paris': École Normale Supérieure)H-Index: 7

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A new numerical method for calculating the singularity orders of V-notches in Reissner's plate is proposed in this paper. By introducing the asymptotic expansion of the generalised displacement field at the notch tip into the equilibrium equations of a plate, a set of characteristic ordinary differential equations with respect to the singularity order are established. In addition, by adopting the variable substitution technique, the obtained non-linear characteristic equations are transformed in...

#1Bang Cheng Yang(Kunming University of Science and Technology)

#2Jian Xiong Liu(Kunming University of Science and Technology)H-Index: 2

Last. Haiting Xia(Kunming University of Science and Technology)H-Index: 6

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Study on the fractural mechanism of thin sheet metals focuses on how to efficiently fracture and recycle the scrapped vehicles and electrical equipments. By using the experimental fracture mechanics, the failure mode was studied for 10F rimmed steel sheets to be crushed and recycled. In-plane mode I, out-plane mixed mode I /III and mode III fracture tests were conducted under different loading angles. The effects and contributions of mixed mode crack extensions for 10F rimmed steel sheets were a...

#1Meinhard Kuna(Freiberg University of Mining and Technology)H-Index: 31

The goal of a FEM analysis is the calculation of fracture-mechanical loading parameters for a crack in a structure (test piece, component, material’s microstructure) in the case of linear-elastic (isotropic or anisotropic) material behavior. In Sect. 3.2 the relevant loading parameters of LEFM were introduced: the stress intensity factors \(K_\mathrm{{I}}\), \(K_\mathrm{{II}}\), \(K_\mathrm{{III}}\) and the energy release rate \(G \equiv J\). Their values depend on the geometry of the structure,...

Last. Michel Salaün(University of Toulouse)H-Index: 15

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SUMMARY The modelization of bending plates with through-the-thickness cracks is investigated. We consider the Kirchhoff–Love plate model, which is valid for very thin plates. Reduced Hsieh–Clough–Tocher triangles and reduced Fraejis de Veubeke–Sanders quadrilaterals are used for the numerical discretization. We apply the eXtended Finite Element Method strategy: enrichment of the finite element space with the asymptotic bending singularities and with the discontinuity across the crack. The main p...

#2J. B. Lawrie(Brunel University London)H-Index: 13

Smart structures are components used in engineering applications that are capable of sensing or reacting to their environment in a predictable and desired manner. In addition to carrying mechanical loads, smart structures may alleviate vibration, reduce acoustic noise, change their mechanical properties as required or monitor their own condition. With the last point in mind, this article examines the scattering of flexural waves by a semi-infinite crack in a non-ferrous thin plate that is subjec...