An Experimental Compliance Calibration Strategy for Mixed-mode Bending Tests

AbstractWe have developed an enhanced beam theory model of the mixed-mode bending (MMB) test, where the delaminated specimen is schematised as an assemblage of sublaminates connected by an elastic interface. We show how the interface parameters can be estimated through an experimental compliance calibration strategy. First, double cantilever beam (DCB) and end notched flexure (ENF) tests are conducted and the specimens’ compliance is measured. Then, a nonlinear least squares fitting procedure furnishes the values of the elastic interface constants. Such calibrated values can be used to interpret the results of MMB tests

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

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

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 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 elastic-interface model for buckling-driven delamination growth in four-point bending tests

The paper presents a mechanical model of a four-point bending test on a delaminated specimen, considered as an assemblage of laminated beams partly connected by an elastic interface. A differential problem with suitable boundary conditions is formulated to describe the model. Then, an analytical solution is determined for both the pre- and post-critical stages. A mixed-mode fracture criterion is applied to predict the onset of delamination growth. The model is il-lustrated through comparison with some experimental results taken from the literature

An elastic-interface model for buckling-driven delamination growth in composite panels under bending

Delamination is a major failure mode for composite laminates. Such phenomenon can have multiple causes, such as manufacturing defects and low-energy impacts. Delamination cracks propagate under both static and cyclic loads [1]. In this paper, we analyse the delamination growth promoted by local buckling in a laminate subjected to four-point bending [2]. The model considers the specimen as an assemblage of sublaminates of different thicknesses, partly connected through an elastic interface, consisting of a continuous distribution of normal and tangential springs. In particular, the specimen is subdivided into three zones with different behaviour: a first zone, between the support and the load application point, where the laminate is schematised as a single extensible and flexible beam undergoing small elastic deformations; a second zone, between the load application point and the delamination front, in which the laminate consists of two sublaminates connected by the elastic interface, modelled as extensible and flexible beams, again under small deformations; one last zone, where the two sublaminates are considered as extensible and flexible beams undergoing large displacements. The different modelling assumptions in the three zones are justified by the lower stiffness of the delaminated region, which turns out to be the region with higher compression and slenderness. The model is described by a system of differential equations, accompanied by suitable boundary conditions. The differential problem is solved analytically and the value of the critical load of instability is determined through the numerical solution of a suitable transcendental equation. The model provides an overall non-linear mechanical response. In the post-critical regime, also the energy release rate and mode mixity are evaluated. Such quantities are then compared with the fracture toughness to predict the growth of the delamination crack

A cohesive-zone model for steel beams strengthened with pre-stressed laminates

We analyse the problem of a simply supported steel beam subjected to uniformly distributed load, strengthened with a pre-stressed fibre-reinforced polymer (FRP) laminate. According to the assumed application technology, the laminate is first put into tension, then bonded to the beam lower surface, and finally fixed at both its ends by suitable connections. The beam and laminate are modelled according to classical beam theory. The adhesive is modelled as a cohesive interface with a piecewise linear constitutive law defined over three intervals (elastic response, softening response, debonding). The model is described by a set of differential equations with suitable boundary conditions. An analytical solution to the problem is determined, including explicit expressions for the internal forces and interfacial stresses. For illustration, an IPE 600 steel beam strengthened with a Sika® Carbodur® FRP laminate is considered. First, the elastic limit state load of the unstrengthened beam is determined. Then, the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate for the strengthened beam are calculated. As a result, the increased elastic limit state load of the strengthened beam is obtained

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