A physically consistent virtual crack closure technique for I/II/III mixed-mode fracture problems

We present a physically consistent virtual crack closure technique (VCCT) that can be applied to three-dimensional problems involving I/II/III mixed-mode fracture. The crack-tip forces exchanged between the nodes of the finite element model along the crack front are decomposed into the sums of three energetically orthogonal systems of forces. The modal contributions to the energy release rate are associated to the corresponding amounts of work done to close the virtually extended crack

A further step towards a physically consistent virtual crack closure technique

The standard virtual crack closure technique may calculate negative values of the modal contributions to the energy release rate when analysing problems with highly asymmetric cracks. To avoid such physically meaningless results, a method is proposed, where the partitioning of fracture modes is based on the decomposition of the crack-tip nodal force into energetically orthogonal components. As an example, a delaminated cantilever beam subjected to bending moments is analysed. Both geometric and algebraic interpretations of the method are discussed

The Effects of Shear on Mode II Delamination

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 mixed-mode fracture. Several fracture mode partition methods of the literature are reviewed with specific attention on the effects of shear forces and shear deformation on the mode II contribution to the energy release rate

On the calculation of energy release rate and mode mixity in delaminated laminated beams

A method is presented for the analysis of laminated beams with general stacking sequences and arbitrarily located, through-the-width delaminations. First, the relative displacements and concentrated forces at the crack tip are determined based on classical lamination theory and Timoshenko beam kinematics. Next, new quantities, called crack-tip displacement rates, are defined as the relative displacements per unit increase in crack length. The previously computed quantities are then used to calculate the energy release rate and its mode I and II contributions via an adaptation of the virtual crack closure technique. Results for homogeneous and bimaterial delaminated beams are presented and compared to the predictions of other methods in the literature. Lastly, applications to some non-standard delamination test specimens are illustrated

MODELLING OF DEPLOYABLE CABLE NETS FOR ACTIVE SPACE DEBRIS REMOVAL

Space debris represent a true risk for current and future activities in the circumterrestrial space, and remediation activities must be set out to guarantee the access to space in the future. For active debris removal, the development of an effective capturing mechanism remains an open issue. Among several proposals, cable nets are light, easily packable, scalable, and versatile. Nonetheless, guidance, navigation, and control aspects are especially critical in both the capture and post-capture phases. We present a finite element model of a deployable cable net. We consider a lumped mass/cable net system taking into account non-linearities arising both from large displacements and deformations, and from the different response of cables when subject to tension and compression. The problem is stated by using the nodal coordinates as Lagrangian coordinates. Lastly, the nonlinear governing equations of the system are obtained in a form ready for numerical integration

An enhanced beam-theory model of the mixed-mode bending (MMB) test – Part II: applications and results

The paper presents an enhanced beam-theory (EBT) model of the mixed-mode bending (MMB) test, whereby the specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. Analytical expressions for the compliance, energy release rate, and mode mixity are deduced. A compliance calibration strategy enabling numerical or experimental evaluation of the interface elastic constants is also presented. Furthermore, analytical expressions for the crack length correction parameters – analogous to those given by the corrected beam-theory (CBT) model for unidirectional laminated specimens – are furnished for multidirectional laminated specimens, as well. Lastly, an example application to experimental data reduction is presented

Explicit expressions for the crack length correction parameters for the DCB, ENF, and MMB tests on multidirectional laminates

We demonstrate the application of the enhanced beam-theory (EBT) model to multidirectional laminated specimens with several stacking sequences and compare our theoretical predictions with experimental results and numerical analyses

An enhanced beam-theory model of the mixed-mode bending (MMB) test – Part I: literature review and mechanical model

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements

Experimental study on the creep behavior of GFRP pultruded beams

The objective of the paper is to explore the validity of the Time-Temperature-Stress Superposition Principle (TTSSP) to describe the creep behaviour of glass fibre reinforced polymer (GFRP) pultruded beams. For this purpose, an experimental programme, including both short- and long-term creep tests, has been carried out. A total of twenty pultruded GFRP beams have been tested in a 4-point bending scheme. Tests have been conducted at controlled room temperature (26°C, 32°C, 41°C) and prescribed percentage of the ultimate load (26%, 35%, 45%). Findley’s law has been used to interpret the results of the short-term experiments. Then, the TTSSP has been applied to build a master curve, usable to predict the results of long-term experiments. The results demonstrate the extent of validity of the TTSSP for predicting the creep behaviour of GFRP composites, at least for the material used and the duration of the tests

An elastic interface model of the mixed bending-tension (MBT) test

The mixed bending-tension (MBT) test has been introduced by Macedo et al. to assess the interlaminar fracture toughness of laminates with low bending stiffness and strength in the longitudinal direction. In the experimental setup, the delaminated specimen is adhesively bonded to two pin-loaded metal beams. We have developed a mechanical model of the test, where the specimen is modelled as an assemblage of two beams connected by an elastic interface, while the metal beams are modelled as rigid beams. An analytical solution has been obtained by applying classical beam theory. Furthermore, to better describe the experimental results, we have developed also a cohesive zone model based on a bilinear traction-separation law