The 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) = Wmax cos 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. © 2009 Elsevier Ltd. All rights reserved.

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.. - In: MATERIALS & DESIGN. - ISSN 0264-1275. - 31:6(2010), pp. 2964-2971. [10.1016/j.matdes.2009.12.025]

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

#### Abstract

The 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) = Wmax cos 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. © 2009 Elsevier Ltd. All rights reserved.
##### Scheda breve Scheda completa
2010
Finite element results; J-integral; Strain-energy density; U-notches
01 Pubblicazione su rivista::01a Articolo in rivista
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.. - In: MATERIALS & DESIGN. - ISSN 0264-1275. - 31:6(2010), pp. 2964-2971. [10.1016/j.matdes.2009.12.025]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1688605`
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