Energy Release Rates for the ENF Specimen Using a Beam on an Elastic Foundation

Corleto, Carlos R.; Hogan, Harry A.

doi:10.1177/002199839502901101

Cited by 51 publications

(16 citation statements)

References 9 publications

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“…Corleto and Hogan [58] modelled the ENF test by considering the upper half laminate as a Timoshenko beam on a generalised elastic foundation consisting of extensional and rotational distributed springs. They found that the energy release rate is independent of the shear stiffness of the sublaminate, 5/6 GzxBh, but not of the shear modulus of the material, Gzx, which enters the expressions of the elastic constants of the foundation.…”

Section: Elastic-interface Modelsmentioning

confidence: 99%

The Effects of Shear on Mode II Delamination

Valvo

2018

Frattura Ed Integrità Strutturale

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ABSTRACT. The paper focuses on the effects of shear deformation and shear forces on the mode II contribution to the energy release rate in delaminated beams. A critical review of the relevant literature is presented, starting from the end-notched flexure test as the prototype of delaminated laminates subjected to pure mode II fracture. Several models of the literature are recalled from simple beam theory to more refined models. The role of first-order shear deformation in line with the Timoshenko beam theory is investigated as distinct from the local crack-tip deformation related to the shear modulus of the material. Then, attention is moved on to a general delaminated beam with an arbitrarily located through-the-width delamination, subjected to mixedmode fracture. Several fracture mode partition methods of the literature are reviewed with specific attention on the effects of shear on the mode II contribution to the energy release rate.KEYWORDS. Delamination; Mixed-mode fracture; Mode II fracture; Beam theory; Shear deformation; End-notched flexure test.Citation: Valvo, P.S., The effects of shear on Mode II delamination: a critical review,

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Section: Elastic-interface Modelsmentioning

confidence: 99%

The Effects of Shear on Mode II Delamination

Valvo

2018

Frattura Ed Integrità Strutturale

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“…Wang and Williams [17] derived an additional length of V ℎ to the original crack length by introducing a correction factor V. Then the ERR was evaluated by the formulation of classical beam theory (CBT) using the adjusted crack length. Corleto and Hogan [5] employed two-parameter semi-infinite elastic foundation to the Timoshenko beam model to obtain the compliance and ERR of ENF specimens, in which the crack tip deformation was considered in their model. Ding and Kortschot [18] adapted a simplified analysis of a beam supported on a shear spring without accounting for the transverse shear deformation in order to find a simple and precise analytical solution.…”

Section: Advances In Materials Science and Engineeringmentioning

confidence: 99%

“…In the literature, there has been much study of fracture toughness [5][6][7][8][9][10][11][12][13]. However, it is the stable cracking problem that should be investigated in the interfacial debonding test.…”

Section: Introductionmentioning

confidence: 99%

“…The end-notched flexure (ENF) test and the four-point bend end-notched flexure (4-ENF) test have been commonly employed to determine the mode II bonding fracture toughness. The original ENF test is essentially unstable and requires to measure the crack sliding displacement of the specimen during the experimental process [5]. This test procedure is too complex to achieve accurate results.…”

Section: Introductionmentioning

confidence: 99%

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Mode II Fracture of GFRP Laminates Bonded Interfaces under 4-ENF Test

Zhong

Liu

2017

Advances in Materials Science and Engineering

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This experiment studies the mode II fracture behavior of an adhesively bonded joint composed of GFRP laminates. A new beam model is presented to calculate the mode II ERR for GFRP bonded 4-ENF specimens. In this model, the deformation of 4-ENF specimens caused by the relative deflection angle between the upper and lower layers and by the bending deformation of the upper and lower layers, respectively, is introduced; the effect of the adhesive layer deformation is presented. The closed-form analytical solutions of compliance and energy release rate based on the crack compliance method are obtained. The high accuracy of present analytical solutions are verified by finite element analysis through bonded GFRP 4-ENF specimens and compared to the rigid joint model and the CBT model. The interfacial crack propagation is numerically simulated using shear fracture toughness determined in this experiment, from which the predicted critical load results are in good agreement with the experimental results. The conclusion indicates that the compliance and ERR can accurately be predicted using the new bonded 4-ENF beam model.

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“…Shu and Mai (1993) used both the "rigid" and "soft" joint models to evaluate the upper and lower bounds of buckling and vibration of bimaterial split beam. A better solution of compliance and ERR with consideration of local deformation at the crack tip (Williams, 1989;Wang and Williams, 1992;Corleto and Hogan, 1995;Ozil and Carlsson, 1999;Qiao et al, 2003a,b) was obtained by using a beam on elastic foundation model pioneered by Kanninen (1973Kanninen ( , 1974 and the local deformation was captured as the "elastic foundation effect" with two foundation stiffness coefficients. However, the beam on elastic foundation model could only be employed to model one sub-beam.…”

Section: Introductionmentioning

confidence: 99%

Analysis of beam-type fracture specimens with crack-tip deformation

Wang

Qiao

2005

Int J Fract

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A novel bi-layer beam model is developed to account for local effects at the crack tip of a bimaterial interface by modeling a bi-layer composite beam as two separate shear deformable beams. The effect of interface stresses on the deformations of sub-layers, which is referred to as the elastic foundation effect in the literature, is considered in this model by introducing two interface compliance coefficients; thus a flexible joint condition at the crack tip is considered in contrast to the "rigid joint" condition used in the conventional bi-layer model. An elastic crack tip deformable model is presented, and the closed-form solutions of local deformation at the crack tip are then obtained. By applying this novel crack tip deformation model, the new terms due to the local deformations at the crack tip, which are missing in the conventional composite beam solutions of compliance and energy release rate (ERR) of beam-type fracture specimens, are recovered. Several commonly used beam-type fracture specimens are examined under the new light of the present model, and the improved solutions for ERR and mode mixity are thus obtained. A remarkable agreement achieved between the present and available solutions illustrates the validity of the present study. The significance of local deformation at the crack tip is demonstrated, and the improved solutions developed in this study provide highly accurate predictions of fracture properties which can actually substitute the full continuum elasticity analysis such as the finite element analysis. The new and improved formulas derived for several specimens provide better prediction of ERR and mode mixity of beam-type fracture experiments.

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Energy Release Rates for the ENF Specimen Using a Beam on an Elastic Foundation

Cited by 51 publications

References 9 publications

The Effects of Shear on Mode II Delamination

The Effects of Shear on Mode II Delamination

Mode II Fracture of GFRP Laminates Bonded Interfaces under 4-ENF Test

Analysis of beam-type fracture specimens with crack-tip deformation

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