A physically consistent virtual crack closure technique accounting for contact and interpenetration

In some circumstances, the standard formulation of the virtual crack closure technique (VCCT) may yield negative values of the modal contributions to the energy release rate. To avoid such physically meaningless results, a revised formulation is available. However, the revised VCCT does not take into account possible interpenetration of the crack faces, that may be predicted by the linearly elastic solution. The present work extends the revised VCCT formulation by introducing suitable contact constraints to prevent local interpenetration of the crack-tip nodes. By considering open vs. interpenetrated cracks and tensile vs. compressive crack-tip forces, four cases emerge. For each case, a suitable two-step crack closure process is outlined with the two steps respectively corresponding to fracture modes II and I. The contact pressure force, if present, is evaluated and accounted for in the computation of the crack closure work. As a result, novel analytical expressions are derived for the modal contributions to the energy release rate accounting for contact and prevented interpenetration

The ellipse of crack-tip flexibility for the partitioning of fracture modes

A crack in a solid body will generally propagate according to a combination of the three basic fracture modes (I or opening, II or sliding, and III or tearing). Thus, the energy release rate, G, will be the sum of three modal contributions, GI, GII, and GIII. In the finite element context, the virtual crack closure technique (VCCT) is widely used to calculate the energy release rate and its modal contributions. Accordingly, G is related to the work done by the forces, r and -r, applied at the crack-tip nodes to close up the crack, once propagated by a finite length, Da. In I/II mixed-mode fracture problems, the crack-tip relative displacement Ds = [Du, Dw]T = Fr, where F is the crack-tip flexibility matrix. The conic section associated to F turns out to be an ellipse, Gamma, named the ellipse of crack-tip flexibility, similar to Culmann’s ellipse of elasticity. The ellipse of crack-tip flexibility helps visualise the relationship between the crack-tip force, r, and relative displacement, Ds, whose directions correspond to conjugate diameters. Furthermore, the ellipse can be used to decompose the crack-tip force vector, r, into energetically orthogonal components, which enable a physically consistent partitioning of fracture modes

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

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

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

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 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

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