Abstract
Recently, numerous papers have been conducted to study the fracture mechanism of adhesively bonded joints in mixed mode I + II fracture. Nevertheless, the lack of an efficient fixture to capture mixed mode I + III fracture is seen in these studies. The first aim of this paper is representing a fixture that provides pure fracture modes I and III and different combinations of these modes. In the next parts of the paper, this testing configuration has been used to evaluate the accuracy of the cohesive zone modeling (CZM) in predicting the mixed mode I + III fracture at the adhesively bonded structures. A series of fracture tests and finite element simulations have been conducted on the adhesively bonded double cantilever beam specimens using the suggested fixture to determine the cohesive laws of the Araldite 2015 adhesive under mixed mode I + III loading situation. The cohesive laws have been calculated through a direct method from the experimental examinations and implemented in the FEM simulations of the tests. Eventually, the comparison between force-crack opening displacement curves resulting from the experimental tests and the numerical simulations in various combinations of the modes I and III loading states demonstrate the accuracy of the cohesive model in these loading conditions.
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Abbreviations
- a:
-
Initial crack length
- \(B\) :
-
Specimen width, crack width, thickness of the beam specimen
- \(E\) :
-
Young’s modulus of adherents
- \(H\) :
-
Specimen height
- \(I\) :
-
Moment of inertia around the neutral axis in the transversal cross section of the beam specimen
- \({J}_{ext}\) :
-
J integral which its integration path is defined on the peripheral boundaries
- \({J}_{ext}^{I}\) :
-
J integral which its integration path is defined on the peripheral boundaries under mode I loading
- \({J}_{ext}^{III}\) :
-
J integral which its integration path is defined on the peripheral boundaries under mode III loading
- \({J}_{loc}\) :
-
J integral which its integration path is defined locally along the crack faces and crack tip
- \({J}_{R}\) :
-
Fracture resistance
- \({J}_{ss}\) :
-
Steady State fracture resistance
- \({K}_{I}\),\({K}_{II}\),\({K}_{III}\) :
-
Stress intensity factors (mode I, mode II and mode III, respectively)
- \({K}_{Im}\) :
-
The maximum value of the mode I stress intensity factor through the crack front
- \(l\) :
-
Moment arm
- \({M}_{I}\) :
-
Bending moment applied to the end of beam specimen caused mode I fracture
- \({M}_{III}\) :
-
Bending moment applied to the end of beam specimen caused mode III fracture
- \(P\) :
-
Created force through the wire
- \({t}_{A}\) :
-
Adhesive thickness
- \(z\) :
-
Location of crack front relative to the mid-section
- \(z/Z\) :
-
Normalized parameter to show the considered points through the crack front
- \({\Gamma }_{\mathrm{loc}}\) :
-
Integration path extended ahead of the crack tip
- \(\delta \) :
-
Local opening of the crack tip
- \({\delta }_{n}\) :
-
Normal crack openings along the integration path
- \({\delta }_{n}^{c}\) :
-
Critical normal crack opening
- \({\delta }_{n}^{*}\) :
-
The crack opening in normal direction at the end of the cohesive zone
- \({\delta }_{t}\) :
-
Transversal crack opening along the integration path
- \({\delta }_{t}^{c}\) :
-
Critical transversal crack opening
- \({\delta }_{t}^{*}\) :
-
The crack opening (sliding) in transversal direction at the end of the cohesive zone
- \({\delta }^{*}\) :
-
The crack opening at the end of the cohesive zone
- \(\theta \) :
-
The angle that the transverse arm creates with longitudinal symmetry plane of the testing specimen, angle of applied moments to specimens
- \(\kappa \) :
-
Curvature of the beam
- \(\nu \) :
-
Poisson’s ratio
- \(\sigma \) :
-
Stress across the fracture process zone
- \({\sigma }_{n}\) :
-
Normal stress
- \({\sigma }_{t}\) :
-
Transversal stress
- \({\sigma }_{11}\) :
-
Axial stress of a beam parallel to the direction of the crack
- \(\phi \) :
-
Potential function for the cohesive Stresses \({\sigma }_{n}\) and \({\sigma }_{t}\)
- CT:
-
Compact tension
- COD:
-
Crack opening displacement
- CZM:
-
Cohesive zone model
- DBM-DCB:
-
Dual bending moment double cantilever beam
- DCB:
-
Double cantilever beam
- ENDB:
-
Edge notched disc bend
- ENF:
-
End-notched flexure
- FEM:
-
Finite element method
- MC-DCB:
-
Mixed-mode controlled double cantilever beam
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Jahanshahi, S., Chakherlou, T.N., Rostampoureh, A. et al. Evaluating the validity of the cohesive zone model in mixed mode I + III fracture of Al-alloy 2024-T3 adhesive joints using DBM-DCB tests. Int J Fract 240, 143–165 (2023). https://doi.org/10.1007/s10704-022-00679-3
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DOI: https://doi.org/10.1007/s10704-022-00679-3