Mixed-mode partition theories for one-dimensional delamination in laminated composite beams (original) (raw)
Related papers
2014
A powerful method for partitioning mixed-mode fractures on rigid interfaces in laminated unidirectional double cantilever beams (DCBs) is developed by taking 2D elasticity into consideration in a novel way. Pure modes based on 2D elasticity are obtained by introducing correction factors into the beam-theory-based mechanical conditions. These 2D-elasticity-based pure modes are then used to derive a 2D-elasticity-based partition theory for mixed-mode fractures. Excellent agreement is observed between the present partition theory and Suo and Hutchinson’s partition theory [1]. Furthermore, the method that is developed in this work has a stronger capability for solving more complex mixed-mode partition problems, for example, in the bimaterial case. [1] Suo Z, Hutchinson JW. Interface crack between two elastic layers. International Journal of Fracture Mechanics 1990;43:1–18.
Experimental assessment of mixed-mode partition theories for generally laminated composite beams
2015
Three different approaches to partitioning mixed-mode delaminations are assessed for their ability to predict the interfacial fracture toughness of generally laminated composite beams. This is by using published data from some thorough and comprehensive experimental tests carried out by independent researchers (Davidson et al., 2000 and 2006). Wang and Harvey’s (2012) Euler beam partition theory is found to give very accurate prediction of interfacial fracture toughness for arbitrary layups, thickness ratios and loading conditions. Davidson et al.’s (2000) non-singular-field partition theory has excellent agreement with Wang and Harvey’s Euler beam partition theory for unidirectional layups. Although Davidson et al.’s partition theory predicts the interfacial fracture toughness of multidirectional layups reasonably well, overall Wang and Harvey’s Euler beam partition theory is found to give better predictions. In general, the singular-field approach based on 2D elasticity and the finite element method gives poor predictions of fracture toughness.
Partition of mixed-mode fractures in 2D elastic orthotropic laminated beams under general loading
Composite Structures, 2016
An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic laminated double cantilever beams (DCBs) under through-thickness shear forces, in addition to bending moments and axial forces, is developed by extending recent work by the authors (Harvey et al., 2014). First, two pure through-thickness-shear-force modes (one pure mode I and one pure mode II) are discovered by extending the authors’ mixed-mode partition theory for Timoshenko beams. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II energy release rate (ERR) correction factor. Both correction factors closely follow an elegant normal distribution around a symmetric DCB geometry. The principle of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a general loading condition, including bending moments, axial forces, and through-thickness shear forces. Excellent agreement is observed between the present analytical partition theory and numerical results from finite element method (FEM) simulations.
Mixed mode partition theories for one dimensional fracture
2012
The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. It has caused considerable confusion due to its in-depth subtleness and complex entanglement with different theories and numerical simulations. The present paper presents completely analytical theories based on Euler and Timoshenko beam theories using a brand new approach which reveals the hidden mechanics of the problem. Orthogonal pairs of pure modes are found and used to partition mixed modes. The developed theories are extensively validated against numerical simulations using finite element methods. Moreover, the fracture mode partition space is thoroughly investigated and crack tip running contact is found which results in a region of pure mode II. The theories are finally applied to general one-dimensional fracture in beams and axisymmetric plates.
A theory of one-dimensional fracture
2012
A completely analytical theory is developed for the mixed mode partition of one-dimensional fracture in laminated composite beams and plates. Two sets of orthogonal pure modes are determined first. It is found that they are distinct from each other in Euler beam or plate theory and coincide at the Wang-Harvey set in Timoshenko beam or plate theory. After the Wang-Harvey set is proved to form a unique complete orthogonal pure mode basis within the contexts of both Euler and Timoshenko beam or plate theories, it is used to partition a mixed mode. Stealthy interactions are found between the Wang-Harvey pure mode I modes and mode II modes in Euler beam or plate theory, which alter the partitions of a mixed mode. The finite element method is developed to validate the analytical theories.
2020
This paper reports the authors' recent work on mixed-mode fracture in fiber-reinforced laminated composite beams and plates. The work considers the so-called one-dimensional fracture which propagates in one-dimension and consists of only mode I and mode II fracture modes. Fracture interfaces are assumed to be either rigidly or cohesively bonded. Analytical theories are developed within the contexts of both classical and first-order shear deformable laminated composite theories. When a rigid interface is assumed for brittle fracture, there are two sets of orthogonal pure modes in classical theory, and there is only one set of orthogonal pure modes in shear-deformable theory. A mixed-mode fracture is partitioned by using these orthogonal pure modes. The classical and shear deformable partitions can be regarded as either lower or upper bound partitions for 2D elasticity, and hence approximate 2D elasticity partition theories are developed by 'averaging' the classical and...
Modeling of delamination propagation in composite laminated beam structures
AIP Conference Proceedings, 2012
A numerical method is developed to predict delamination propagation in composite laminated beam structures under lateral and axial loads. Full geometrical nonlinearity is included in the development of beam elements and the interfaces are modeled with imaginary interface springs. The one step crack closure technique, a contact algorithm and tensor symmetrization are employed in the formulation. It is found that asymmetric composite beam elements suffer from membrane locking and this is completely solved in the work. Also, the mode partitioning results are different to those from the existing mode partition theory. A new theory is developed which shows the flaw in the existing theory and demonstrates the validity of the imaginary interface spring model. In general, excellent agreement with existing numerical and experimental results is observed.
Tehnicki vjesnik-Technical Gazette, 2015
Original scientific paper Delamination (fracture) tests have been numerically investigated using various cohesive zone properties. The test utilises asymmetric and symmetric double cantilever beam specimens loaded with bending moment. Energy release rate contributions from mode I and mode II fracture are calculated using a global and local approach. Mode-mixities results are presented and analysed. The numerical partitioning results for different configurations are compared to two analytical partitioning theories, namely, after Williams and after Hutchinson and Suo. Opposite to these theories, partitioning is observed to be dependent on cohesive zone properties.
Delamination Modeling of Double Cantilever Beam of Unidirectional Composite Laminates
Journal of Failure Analysis and Prevention, 2017
Delamination crack growth in a double cantilever beam laminated composites is modeled by using simple stress analysis beam theory combined with simple linear elastic fracture mechanics and consideration of the theory of elastic failure in mechanics of material. Furthermore, advanced finite element (FE) model is built up. The FE approach employs surface cohesive zone model that is used to simulate the debonding and crack propagation. The analytical modeling, moreover, cracks growth and strain measurements, which are obtained from FE models, are compared with the available published experimental work. The predicted results give good agreement with interlaminar fracture toughness and maximum load which correspond to crack initiation point. The FE models results agree well with the available experimental data for both crack initiation and propagation.
Delamination modelling in a double cantilever beam
Composite Structures, 2005
The simulation of the delamination process in composite structures is quite complex, and requires advanced FE modelling techniques. Failure analysis tools must be able to predict initiation, size and propagation of delamination process. The objective of the paper is to present modelling techniques able to predict a delamination in composite structures. Four different ways of modelling delamination growth of a double cantilever beam test (DCB) are proposed. The first two approaches were based on a cohesive zone model: the interface being represented either by using delamination elements or non-linear springs. The idea of the third approach was to use a fracture mechanics criterion, but to avoid the complex moving mesh techniques it often implies. The interface between the two layers was simulated with solid elements representing the matrix, which were eliminated when their energy release rate exceeded the critical value. The energy release rate was computed using the virtual crack closure technique (VCCT). In the last approach, the interface behaviour was modelled by a tiebreak contact. Coincident nodes were tied together with a constraint relation and remained joined, until when the maximum interlaminar stresses was reached. Once this value was exceeded, the nodes associated with that constraint were released to simulate the initiation of delamination. The comparison of the results of the first three modelling techniques with experimental data showed that very good correlation was achieved. Poor results were obtained using tiebreak contact. It was due to the criterion used, since when the critical interlaminar stress was reached, the delamination was experienced before the critical energy release rate was reached.