Weight functions from virtual crack extension

Parks, David M.; Kamenetzky, E. M.

doi:10.1002/nme.1620141110

Cited by 62 publications

(26 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method has some general advantages over the finite element method (FEM) in that a standard BEM program can be used whereas an FEM program requires modification [4,5] to incorporate the virtual crack extension (VCE) technique. The whole domain must be discretized in FEM calculations, but only the boundary needs to be in the BEM resulting in a much smaller system of equations to solve.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Mixed-mode Bueckner weight functions using boundary element analysis

Aliabadi¹,

Rooke²,

Cartwright³

1987

Int J Fract

View full text Add to dashboard Cite

A Bueckner singular displacement field is incorporated into the boundary element method in order to calculate weight functions for mixed mode stress intensity factor in a two-dimensional cracked body. Weight functions for modes I and II can be calculated independently and hence the factors K~ and KI~" can be obtained for any arbitrary loading on any boundary. Results are obtained for some slant crack problems in finite sheets and compared with known results where available.

show abstract

Section: Discussionmentioning

confidence: 99%

“…In order to avoid the fine mesh that Paris et al [1] required at the crack tip, Parks and Kamenetsky [4] have developed a method for calculating weight functions for crack problems. More recently Sha and Yang [5] have extended this method to non-symmetric mixed mode problems.…”

Section: Introductionmentioning

confidence: 99%

Mixed-mode Bueckner weight functions using boundary element analysis

Aliabadi¹,

Rooke²,

Cartwright³

1987

Int J Fract

View full text Add to dashboard Cite

show abstract

“…The sti ness derivative technique [21] used in the MWF method, also named as the virtual crack extension technique [22], will be used to calculate partial derivatives @U=@a, which can be regarded as the 'weights'. Here, U is the transpose of displacement vector u…”

Section: Calculation Of Partial Derivatives @U=@a and Sti Ness Derivamentioning

confidence: 99%

“…The procedure developed by Sham [13] was based on FEM using the variational principle for determining the singular ÿelds in ÿnite bodies. The procedure developed by Vanderglas [21] and Parks and Kamenetzky [22] was based on the virtual crack extension (VCE) technique. The procedure developed by Zhao and Wu [23,24] and Zhao and Newman et al [25] was based on the slice synthesis technique.…”

Section: Introductionmentioning

confidence: 99%

A novel technique for determination of histories of SIF distributions along 3D crack fronts of a body subjected to thermal shock

Huang

et al. 2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe thermal weight function (TWF) is dependent only on the crack conÿguration and body geometry, and is independent of temperature ÿelds. TWF is independent of time during thermal shock, so the whole variation of transient stress intensity factors (SIFs) can be directly calculated through integration of products of TWF and transient temperatures and temperature gradients. The basic equation for the 3D TWF method for Mode I is derived. Then a novel technique, referred to as the multiple virtual crack extension (MVCE) technique, is proposed to solve the basic equations in the 3D TWF method. The specially selected linearly independent VCE modes are directly used as shape functions for the interpolation of unknown SIFs. The coe cient matrix of the ÿnal system of equations is a triplediagonal matrix and the values of the coe cients on the main diagonal are usually large. The system of equations has good numerical properties. The number of linearly independent VCE modes which can be introduced in a problem is unlimited. The complex situations that the SIFs vary dramatically along the crack fronts can be numerically well simulated by the MVCE technique. Examples show that the scheme is of very high e ciency and of good accuracy. The results show that the histories of SIF distributions along 3D crack fronts are very complex. In order to understand the behaviour of 3D cracks correctly it should be calculated in detail.

show abstract

“…The energy perturbation finite element technique for the weight function determination has been established for homogeneous media with mode I crack [20][21][22][23][24] and mixed-mode crack [25][26]. The weight function evaluations, which are evolved from homogeneous materials to inhomogeneous materials, are briefed herewith as illustrated with the bimaterial interface crack h~al)ix and problem.…”

Section: Weight Functions For Bimaterials Interface Crackmentioning

confidence: 99%

Weight functions for bimaterial interface cracks

Sha

Chen

1991

Int J Fract

View full text Add to dashboard Cite

An efficient approach using the analytically decoupled near-tip displacement solution for bimaterial interface cracks presented in this paper involves: (1) the calculation of the decoupled strain energy release rates G~ and Gn associated respectively with the decoupled stress intensity factors K~ and K. and (2) the extension of Rice's displacement derivative representation of Bueckner's weight function vectors beyond the homogeneous media. It is shown that the stress intensity factors for a bimaterial interface crack predicted by the present approach agree very well with those solutions available in the literature. The computational efficiency is enhanced through the use of singular elements in the crack-tip neighborhood.As reported in the homogeneous case, the calculated weight function for a bimaterial interface crack is loadindependent but depends strongly on geometry and constraint conditions. Due to the coupling nature of the stress intensity factors of a bimaterial interface crack, the invariant characteristics of the dimensionless weight function vectors are different from those of a crack in homogeneous material. In addition, the elastic constants of two constituents can significantly alter the weight function behavior for a cracked bimaterial medium.Due to the load-independent characteristic of the weight functions, the stress intensity factors for a bimaterial interface crack can be obtained accurately and inexpensively by performing the sum of worklike products between the applied loads and the weight functions for the cracked bimaterial body under any loading conditions once the weight functions are explicitly predetermined. The same calculation can also be applied for the identical cracked bimaterial medium with different constraint conditions by including the self-equilibrium forces that contain both the external loads and the reaction forces induced at the constraint locations. Moreover, the physical interpretation of the weight functions can provide a guidance for damage tolerant design application.

show abstract

Weight functions from virtual crack extension

Cited by 62 publications

References 14 publications

Mixed-mode Bueckner weight functions using boundary element analysis

Mixed-mode Bueckner weight functions using boundary element analysis

A novel technique for determination of histories of SIF distributions along 3D crack fronts of a body subjected to thermal shock

Weight functions for bimaterial interface cracks

Contact Info

Product

Resources

About