An elastic-interface model for the mixed-mode bending test under cyclic loads

AbstractWe have developed a mechanical model of the mixed-mode bending (MMB) test, whereby the specimen is considered as an assemblage of two identical sublaminates, modelled as Timoshenko beams. The sublaminates are partly connected by a linearly elastic–brittle interface, transmitting stresses along both the normal and tangential directions with respect to the interface plane. The model is described by a set of suitable differential equations and boundary conditions. Based on the explicit solution of this problem and following an approach already adopted to model buckling-driven delamination growth in fatigue, we analyse the response of the MMB test specimen under cyclic loads. Exploiting the available analytical solution, we apply a fracture mode-dependent fatigue growth law. As a result, the number of cycles needed for a delamination to extend to a given length can be predicted

Measurement of cohesive laws from mixed bending-tension tests

The mixed bending-tension (MBT) test was proposed by Macedo et al. (2012) to assess the mode I interlaminar fracture toughness of composite laminates with very low bending stiffness and strength. Specimens obtained from such laminates may fail in bending prior to delamination growth, when tested using the double cantilever beam test (ASTM D5528-13). In the MBT test, the specimen with a pre-implanted delamination is adhesively bonded to two metal bars and then loaded in opening mode. Bennati et al. (2015) developed a mechanical model of the MBT test, where the two separating parts of the specimen are connected by a cohesive interface with bilinear traction-separation law. Accordingly, the specimen response can be subdivided into three stages: (i) linearly elastic behaviour, (ii) progressive material damage, and (iii) crack propagation. The theoretical predictions were in good agreement with the experimental results by Macedo et al. (2012) in the linearly elastic stage. Instead, only qualitative agreement was obtained for the subsequent stages. Here, we upgrade the previous model by introducing a piece-wise linear, discontinuous tractionseparation law for the cohesive zone (Valvo et al., 2015). We show how the global response of the specimen depends on the cohesive law parameters. Besides, we present an operative procedure to determine the cohesive law parameters based on the test measures

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 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

INTERFACIAL FRACTURE TOUGHNESS OF UNCONVENTIONAL SPECIMENS: SOME KEY ISSUES

Laboratory specimens used to assess the interfacial fracture toughness of layered materials can be classified as either conventional or unconventional. We call conventional a specimen cut from a unidirectional composite laminate or an adhesive joint between two identical adherents. Assessing fracture toughness using conventional specimens is a common practice guided by international test standards. In contrast, we term unconventional a specimen resulting from, for instance, bimaterial joints, fiber metal laminates, or laminates with an elastically coupled behavior or residual stresses. This paper deals with unconventional specimens and highlights the key issues in determining their interfacial fracture toughness(es) based on fracture tests. Firstly, the mode decoupling and mode partitioning approaches are briefly discussed as tools to extract the pure-mode fracture toughnesses of an unconventional specimen that experiences mixed-mode fracture during testing. Next, we elaborate on the effects of bending-extension coupling and residual thermal stresses often appearing in unconventional specimens by reviewing major mechanical models that consider those effects. Lastly, the paper reviews two of our previous analytical models that surpass the state-of-the-art in that they consider the effects of bending-extension coupling and residual thermal stresses while they also offer mode partitioning

Experimental validation of the enhanced beam-theory model of the mixed-mode bending test

We present the results of an experimental campaign on a set of specimens manufactured from a typical carbon/epoxy unidirectional laminate. Preliminary tests are performed to evaluate the elastic properties of the base laminate. Then, double cantilever beam (DCB) and end-notched flexure (ENF) tests are conducted to assess the delamination toughness in pure fracture modes I and II, respectively, and evaluate the elastic interface constants. Afterwards, mixed-mode bending (MMB) tests are carried out with three values of the lever-arm length. The outcomes of the preliminary and pure fracture mode tests are used as an input to a previously developed enhanced beam theory (EBT) model of the MMB test. Lastly, theoretical predictions and exper-imental results are compared

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

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 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