Antiplane-inplane shear mode delamination between two second-order shear deformable composite plates

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton’s principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results

Interface fracture in orthotropic composite plates using second-order shear deformation theory

The second-order shear deformation theory is used in this study to calculate the stresses and the energy release rates in orthotropic composite plates. A novel double-plate system is utilized with the imposition of the proper kinematic constraints in the interface plane of a double-plate system. The governing equations of the system were derived and as a demonstrative example a simply supported plate subjected to a point force was analyzed. Using Levy plate formulation, the plate problem was solved by a state-space model, incorporating four different regions. The distribution of the stress resultants and the interlaminar stresses in the uncracked part were also determined. Moreover, the distributions of the mode-II and mode-III energy release rates along the crack front were calculated by the J-integral. The 3D finite element model of the plate was created providing reference data for the analytical model. The results show reasonably good agreement between the analytical and numerical results. Also, the present model eliminates the physical inconsistency of previous models and reveals that under mixed-mode II/III condition, the energy release rate is not contributed by the bending, twisting moments and shear forces at all

Bending solution of third-order orthotropic Reddy plates with asymmetric interfacial crack

In this paper Reddy’s third-order shear deformable plate theory is applied to asymmetrically delaminated orthotropic composite plates under antiplane–inplane shear fracture mode. A double-plate system is utilized to capture the mechanical behavior of the uncracked plate portion. An assumed displacement field is used and modified in order to satisfy the traction-free conditions at the top and bottom plate boundaries. Moreover, the system of exact kinematic conditions was also implemented into the novel plate model. An important improvement of this work compared to previous papers is the continuity condition of the shear strains at the interface of the double-plate system. Applying these conditions it is shown that the nineteen parameters of the third-order displacement field can be reduced to nine. Using the simplified displacement field the governing equations are derived, as well. The solution of a simply-supported delaminated plate is presented using the state-space model and the displacement, strain and stress fields are determined, respectively. The energy release rate and mode mixity distributions are calculated using the 3D J-integral. The analytical results are compared to those by finite element computations and it is concluded that the present model is the most accurate one among the previous plate theory-based approaches

Natural vibration induced parametric excitation in delaminated Kirchhoff plates

This paper revisits the problem of free vibration of delaminated composite plates with Lévy type boundary conditions. The governing equations are derived for laminated Kirchhoff plates including through-width delamination. The plate is divided into two subplates in the plane of the delamination. The kinematic continuity of the undelaminated part is established by using the system of exact kinematic conditions. The free vibration analysis of orthotropic simply supported Lévy plates reveals that the delaminated parts are subjected to periodic normal and in-plane shear forces. This effect induces parametric excitation leading to the susceptibility of the plates to dynamic delamination buckling during the vibration. An important aspect is that depending on the vibration mode the internal forces have a two-dimensional distribution in the plane of the delamination. To solve the dynamic stability problem the finite element matrices of the delaminated parts are developed. The distribution of the internal forces in the direction of the delamination front was considered. The mode shapes including a half-wave along the width of the plate accompanied by delamination buckling are shown based on the subsequent superimposition of the buckling eigenshapes. The analysis reveals that the vibration phenomenon is amplitude dependent. Also, the phase plane portraits are created for some chosen cases showing some special trajectories

Analysis of classical and first-order shear deformable cracked orthotropic plates

The Kirchhoff and Mindlin plate theories are applied in this study to calculate the stresses and the energy release rates in delaminated orthotropic composite plates. A novel double-plate system is developed with the imposition of the kinematiccontinuity constraints in the interface plane. The governing equations of the system were derived in both cases. As a demonstrative example a simply-supported plate subjected to a point force was analyzed using Levy plate formulationand the problem was solved by a state-space model. The distribution of the stress resultants and the interlaminar stresses in the uncracked part were also determined. Moreover, the distributions of the mode-II and mode-III energy release rates along the crack front were calculated by the J-integral. The 3D finite element model of the plate was created providing reference data for the analytical model. The results show that the displacement and stress fields obtained from the Kirchhoff and Mindlin theories are quite similar, but in the case of the energy release rates, transverse shear effect is necessary to consider to obtain reasonably good agreement between the analytical and numerical results

Application of prestressed transparent composite beams in fracture mechanics

This work presents the mixed-mode I/II/III version of the prestressed end-notched flexure system for the general delamination characterization of composite materials. The novel fracture mechanical configuration combines the traditional mode-I double-cantilever beam and the mode-II end-notched flexure specimens with the mode-III modified split-cantilever beam. First, a steel roller with a given diameter - which should not exceed the critical crack opening - is inserted to the delamination front, this fixes the mode-I part of the total energy release rate. Second, the prestressed specimen is put into the special rig of the MSCB specimen, and with the help of a prestressing screw the mode-III part of the total energy release rate is also fixed. Third, the prestressed specimen is put into a simple three-point bending setup and the mode-II part of the total energy release rate is increased up to fracture initiation. Using this method, i.e. varying the crack opening displacement by the steel roller and the crack te aring displacement by the MSCB rig the fracture surface in the GI-GII-GIII space can be obtained. To demonstrate the applicability and limitations of the novel system experiments on glass-fiber reinforced polyester specimens were performed including separated mode-I, mode-II, mode-III, mixed-mode I/II, II/III, I/III and I/II/III fracture tests. To reduce the measured data a previously validated improved beam theory scheme is applied. Finally, the surface of the fracture criterion is constructed by the generalization of the traditional criterion by Williams

COMPARISON OF SOME DATA REDUCTION SCHEMES FOR COMPOSITE DELAMINATION SPECIMENS

Three different solutions for orthotropic, beam-like fracture specimens were compared in the current work. A beam theory-based approach was developed previously by the author. Another solution based on refined plate theory was also considered. Finally, equations based on a numerical calibration technique were utilized as a third solution. These solutions were extended for the case of composite double-cantilever beam, end-loaded split and single-cantilever beam fracture specimens. All the three solutions give reliable expressions for the double-cantilever beam. In contrast for the end-loaded split and the single-cantilever beam coupons the three models give quite distinct results, especially for the mode ratio of the single-cantilever beam specimen

J-integral for delaminated beam and plate models

In this work the J-integral is applied to calculate the energy release rate in simple beam and plate models. Four examples are considered: the mode-I double-cantilever beam, the mode-II end-notched flexure, the mixed-mode I/II single-leg bending specimens and a delaminated plate with simply-supported edges, respectively. In each example the details of calculation are given, in the latter case the distribution of the energy release rate along the crack front is calculated. While for delaminated beams the literature presents the energy release rates in numerous studies, the J-integral calculation is not trivial in theses cases. Moreover for delaminated bent plates the application of the J-integral is not documented. It is shown that considering the classical plate theory there are serious limitations to calculate representative energy release rates