Mode-I debonding of a double cantilever beam: A comparison between cohesive crack modeling and Finite Fracture Mechanics

Dimitri, Rossana; Cornetti, Pietro; Mantič, V.; Trullo, Marco; Lorenzis, Laura De

doi:10.1016/j.ijsolstr.2017.06.007

Cited by 42 publications

(13 citation statements)

References 66 publications

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“…This solution was revisited and extended to account for a finite length of the specimen and a trapezoidal CZM by Dimitri et al. ( 2017 ). de Morais ( 2013 ) proposed a solution for a DCB with prescribed rotations (loaded with moments) where the arms are modelled as Timoshenko beams and a bi-linear CZM is embedded at the interface.…”

Section: Introductionmentioning

confidence: 99%

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Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

2018

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In this work we develop a complete analytical solution for a double cantilever beam (DCB) where the arms are modelled as Timoshenko beams, and a bi-linear cohesive-zone model (CZM) is embedded at the interface. The solution is given for two types of DCB; one with prescribed rotations (with steady-state crack propagation) and one with prescribed displacement (where the crack propagation is not steady state). Because the CZM is bi-linear, the analytical solutions are given separately in three phases, namely (i) linear-elastic behaviour before crack propagation, (ii) damage growth before crack propagation and (iii) crack propagation. These solutions are then used to derive the solutions for the case when the interface is linear-elastic with brittle failure (i.e. no damage growth before crack propagation) and the case with infinitely stiff interface with brittle failure (corresponding to linear-elastic fracture mechanics (LEFM) solutions). If the DCB arms are shear-deformable, our solution correctly captures the fact that they will rotate at the crack tip and in front of it even if the interface is infinitely stiff. Expressions defining the distribution of contact tractions at the interface, as well as shear forces, bending moments and cross-sectional rotations of the arms, at and in front of the crack tip, are derived for a linear-elastic interface with brittle failure and in the LEFM limit. For a DCB with prescribed displacement in the LEFM limit we also derive a closed-form expression for the critical energy release rate, . This formula, compared to the so-called ‘standard beam theory’ formula based on the assumptions that the DCB arms are clamped at the crack tip (and also used in standards for determining fracture toughness in mode-I delamination), has an additional term which takes into account the rotation at the crack tip. Additionally, we provide all the mentioned analytical solutions for the case when the shear stiffness of the arms is infinitely high, which corresponds to Euler–Bernoulli beam theory. In the numerical examples we compare results for Euler–Beronulli and Timoshenko beam theory and analyse the influence of the CZM parameters.

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Section: Introductionmentioning

confidence: 99%

“…We will refer to the models with quasi-brittle crack as ‘cohesive crack models’ (CCM) (Dimitri et al. 2017 ).…”

Section: Introductionmentioning

confidence: 99%

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

2018

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“…In addition to the 12 BCs defined by the relations (8), other 7 relations are required to determine all the unknown constants. These remaining relations are determined by substituting Equations (14), (16), (20)- (22) into Equation (3). More specifically, the following relations can be applied to evaluate the first six constants independently, namely…”

Section: Analytical Solution Strategymentioning

confidence: 99%

Numerical Study of the Mixed-Mode Delamination of Composite Specimens

Dimitri

Tornabene

2018

J. Compos. Sci.

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The present research deals with the delamination process in multi-layered composite specimens, with a reduced computational effort. The adhesive interface between sublaminates is represented as a continuous distribution of elastic-brittle springs in the normal and/or tangential direction depending on the interfacial mixed-mode condition. Each composite adherend, instead, is modelled according to the Timoshenko's beam theory. The proposed formulation is here enhanced through the Generalized Differential Quadrature (GDQ) method, where the differential equations of the problem are solved directly in a strong form. Thus, the possibility of tracking the delamination response of the specimens is provided locally in a numerical sense, in terms of interface stresses, internal forces and displacements but also in terms of critical fracture energies and mode mixity angles. A further check of the proposed formulation is performed with respect to some standard solutions available in literature. The good agreement between numerical and theoretical predictions verifies the efficiency of the proposed GDQ approach for the study of complex mixed-mode delamination phenomena in composite materials and joints.

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“…For this reason, effective methods of prognosticating the occurrence of this hindrance are intensively researched. Four basic groups of fracture models are used in this research, namely continuous damage mechanics models, porous solid mechanics models, cohesive models and phenomenological models [1][2][3][4][5][6][7][8][9][10]. Application of the last group of models does not allow one to understand the mechanism of fracture, but facilitates the prognostication.…”

Section: Introductionmentioning

confidence: 99%

Rotational Compression of Cylindrical Specimen As a New Calibrating Test for Damage Criteria

et al. 2020

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The subject-matter of the article is the ductile fracture of materials—A phenomenon occurring in numerous metal forming processes. In order to prognosticate the possibility of a fracture, damage criteria are employed. Their effectiveness, however, depends on the accurate determination of the critical values of damage. These values are obtained through calibrating tests, where the stress state has to be as similar to the actual process as possible. The currently employed calibrating tests do not enable one to determine the limit values of the damage function when the Mannesmann effect occurs. Therefore it was not possible to effectively prognosticate the material fracture in the processes of cross- and skew-rolling. A new calibrating test, based on rotational compression of a cylindrical sample, in which the fractures are caused by the Mannesmann effect, was developed at the Lublin University of Technology. This test was discussed in the article, with a particular focus on the stress and strain state in the sample. A practical use of the test was presented on the example of C45 grade steel, formed in the temperature equal 1150 °C. In the research ten material damage criteria were adopted.

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Mode-I debonding of a double cantilever beam: A comparison between cohesive crack modeling and Finite Fracture Mechanics

Cited by 42 publications

References 66 publications

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

Numerical Study of the Mixed-Mode Delamination of Composite Specimens

Rotational Compression of Cylindrical Specimen As a New Calibrating Test for Damage Criteria

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