Some new practical equations for rapid calculation of <italic>J</italic>-integral in plates weakened by U-notches under bending: Fid-Bau Portal

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Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending

Barati, E. / Alizadeh, Y. / Aghazadeh, J. / Berto, F.

AbstractThe paper deals with calculations of the J-integral for a plate weakened by U-notches under Mode I bending loading in the case of a material obeying a linear elastic law. The main aim of the study is to suggest some new equations suitable for calculations of the J-integral under bending loading. Although some closed-form solutions exist in the literature based on elliptic integrals, some expressions, simple to be implemented, are useful as a rapid engineering tool.The semi-circular arc of the notch, which is traction-free, is assumed as the integration path and the J-integral is given as a function of the strain-energy density. For a numerical investigation of the strain-energy density distribution on the notch edge, the equation W(θ)=Wmaxcos^δ(θ) has been assumed, where the exponent δ has been determined from finite element analyses. The influence on δ of the notch acuity of the specimen width to the notch depth ratio w/a has been investigated by means of several parametric finite element analyses. In particular, the following values of the notch acuity (a/ρ) and notch depth ratio (w/a) have been analyzed: $4  a / ρ  200$ and $2  w / a  100$ .

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Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending

Barati, E. / Alizadeh, Y. / Aghazadeh, J. / Berto, F.

AbstractThe paper deals with calculations of the J-integral for a plate weakened by U-notches under Mode I bending loading in the case of a material obeying a linear elastic law. The main aim of the study is to suggest some new equations suitable for calculations of the J-integral under bending loading. Although some closed-form solutions exist in the literature based on elliptic integrals, some expressions, simple to be implemented, are useful as a rapid engineering tool.The semi-circular arc of the notch, which is traction-free, is assumed as the integration path and the J-integral is given as a function of the strain-energy density. For a numerical investigation of the strain-energy density distribution on the notch edge, the equation W(θ)=Wmaxcos^δ(θ) has been assumed, where the exponent δ has been determined from finite element analyses. The influence on δ of the notch acuity of the specimen width to the notch depth ratio w/a has been investigated by means of several parametric finite element analyses. In particular, the following values of the notch acuity (a/ρ) and notch depth ratio (w/a) have been analyzed: $4  a / ρ  200$ and $2  w / a  100$ .

Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending

Barati, E. / Alizadeh, Y. / Aghazadeh, J. / Berto, F.

AbstractThe paper deals with calculations of the J-integral for a plate weakened by U-notches under Mode I bending loading in the case of a material obeying a linear elastic law. The main aim of the study is to suggest some new equations suitable for calculations of the J-integral under bending loading. Although some closed-form solutions exist in the literature based on elliptic integrals, some expressions, simple to be implemented, are useful as a rapid engineering tool.The semi-circular arc of the notch, which is traction-free, is assumed as the integration path and the J-integral is given as a function of the strain-energy density. For a numerical investigation of the strain-energy density distribution on the notch edge, the equation W(θ)=Wmaxcos^δ(θ) has been assumed, where the exponent δ has been determined from finite element analyses. The influence on δ of the notch acuity of the specimen width to the notch depth ratio w/a has been investigated by means of several parametric finite element analyses. In particular, the following values of the notch acuity (a/ρ) and notch depth ratio (w/a) have been analyzed: $4  a / ρ  200$ and $2  w / a  100$ .

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Title:

Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending

Contributors:

Barati, E. (author) / Alizadeh, Y. (author) / Aghazadeh, J. (author) / Berto, F. (author)

Publication date:

2009-12-11

Size:

8 pages

ISSN:

DOI:

https://doi.org/10.1016/j.matdes.2009.12.025

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

Strain-energy density , <italic>J</italic>-integral , U-notches , Finite element results

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