Stress intensity factors for three-dimensional cracks

Yamamoto, Yoshiyuki; Sumi, Yôichi

doi:10.1007/bf00032382

Cited by 35 publications

(12 citation statements)

References 17 publications

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“…It is hoped that by this rough procedure the transition from nearly plane strain conditions in the interior into the plane stress state occurring at the surface is better taken into account. Compared with the solution obtained by hybrid elements and by [6], both the results from distorted isoparametric elements (+ and x) show a qualitatively fair agreement of the variation of KT along the crack front, but the absolute values lie about 2.5 percent lower for the former (+> and 6 percent for the latter (x).…”

Section: ~64mentioning

confidence: 77%

Three-dimensional elastic analysis of CT specimen with straight and curved crack fronts

Kuna¹

1982

Int J Fract

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In order to reduce the high computational effort for the stress analysis of a three dimensional (3D) body containing a crack and to take advantage of analytically known solutions, various special crack tip elements have been developed.Encouraged by the good experiences made with hybrid techniques for two-dimensional (2D) crack analysis [1], a 3D hybrid crack tip element HCR60 was developed.The method of construction follows the idea of [2] and is based on a hybrid stress formulation: v(°ij ,~i ) = elements n N + I T n T i ui ds I where oij denotes the stress in the element volume Vn, u i are displacements on the boundary S n of the element and Cijkl is the inverse Hooke's tensor.The surface tractions Ti_= a-,n. are obtained by • J J means of the normal vector nj on Sn, and T i are prescribed surface tractions on the part STn of S n. The crack tip elements HCR60 have the shape of 20-node hexahedra with plane faces.The crack front through the body is approximated by a polygon and each line segment is surrounded by a group of four crack tip elements; see Fig. 1. For the stress state in the element regular polynomials and the well known singular solution for the for the 2D plane strain crack were assumed; see, e.g., [3]. This stress state contains the stress intensity factors K I, KII, and KIII for all three opening modes as unknown variables and satisfies the homogeneous equilibrium conditions and the stress-free condition on the crack faces for elements B and B'. The boundary displacements ui on such faces touching the crack tip take into account the correct radial ~r and angular dependence of the 2D crack tip solution, whereas for the remaining two faces (adjoining the neighbouring standard type elements) quadratic isoparametric shape functions were used.Having integrated the stiffness matrices of HCR60 elements, one can assemble the whole FEM system and solve it for the nodal point displacements, from which the stress intensity factors for each hybrid element are directly obtained.The assumed functions and the construction of the stiffness matrix of the hybrid crack tip elements are described in detail in [4].

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Section: ~64mentioning

confidence: 77%

Three-dimensional elastic analysis of CT specimen with straight and curved crack fronts

Kuna¹

1982

Int J Fract

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“…The results of the real three-dimensional analyses with both networks are shown in Fig of [13] were additionally drawn. The nonlinear variation of K~ is clearly well-reflected by the network CT423 and also by CT421.…”

Section: T !I /mentioning

confidence: 99%

A mixed hybrid finite element for three-dimensional elastic crack analysis

Kuna¹,

Zwicke

1990

Int J Fract

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A new three-dimensional crack tip element is proposed, which is based on a mixed hybrid stress/ displacement model. A truncated series expansion of eigenfunctions for the straight semi-infinite crack is deduced and assumed for the internal stress and displacement fields in the element. The basic approach of constructing these hybrid elements is outlined. Their good capability, efficiency and accuracy for analyzing three-dimensional elastic crack problems are demonstrated by first numerical examples.

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“…In the first case the compact tension (CT) specimen with a straight crack front is considered. This problem is a sort of bench mark problem and a well accepted solution is due to Yamamoto and Sumi [7]. The discretization used is close to the one shown in Fig.…”

mentioning

confidence: 93%

“…The SIF is calculated through the relation G = 1-v 2 KI2/E. The SIFs computed by the displacement method, Shivakumar et al's scheme [4] and the proposed method are compared with the solution of [7] in Fig. 3.…”

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confidence: 99%

Crack closure integral based calculation of sifs in three dimensions

1995

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The calculation of energy release rates or SIFs based on the crack closure integral (CCI) has the advantage that the energies associated with the various modes in a mixed mode problem can be separated. In two dimensions the method has been employed extensively. Various special schemes [1][2][3][4][5] are now available to improve the accuracy of the computation. Some of them have been shown to be useful even in three dimensions. The CCI method has not been exploited to that extent in the three dimensions. In the three dimensions, the method to be fully useful, must permit a determination of the distribution of the SIF over the whole crack front. This issue has received some attention [4,6]. A method is presented in the following for the same purpose. It is suitable for both straight and curved crack fronts. Its effectiveness and accuracy are illustrated with four examples.In the case of a straight crack front, say in mode I, the CCI method can be easily employed to calculate the average energy release rate for an extension of the front by 1 (Fig. 1) from the closure forces on lines CD and OP, and opening at nodes on the lines AB and MN. That is,m is the number of segments on the crack front, n is the number of nodes contributing to the crack closure work, and Pi is the closure force at node i and V i is the corresponding displacement.In order to find the local energy release rate, it is assumed that G is constant along the front over the span of an element. If 1 --~ 0 and node S is released to give way to a virtual crack extension over an element area, the associated energy release is related to the product of the closure force at node S and the opening displacement at node T. Therefore the local energy release rate around S, for a finite but small 1 can be assumed to be proportional to the product of crack closure force at node S and crack opening displacement at node T divided by the area a 2, which is equal to b21. Hence the actual energy release rate is given by Int Journ of Fracture 70 (1994)

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Stress intensity factors for three-dimensional cracks

Cited by 35 publications

References 17 publications

Three-dimensional elastic analysis of CT specimen with straight and curved crack fronts

Three-dimensional elastic analysis of CT specimen with straight and curved crack fronts

A mixed hybrid finite element for three-dimensional elastic crack analysis

Crack closure integral based calculation of sifs in three dimensions

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