Fracture mechanics of plate debonding: Validation against experiment
Research highlights
► Global-energy-balance-based Fracture Mechanics can predict FRP plate debonding. ► Strain energy can be calculated using a modified form of Branson’s equation. ► Fracture Energy of concrete depends on compressive strength and the aggregate type. ► Values for Fracture Energy can be assumed if not quoted. ► The predictions agree well with experimental results reported in the literature.
Introduction
In an earlier paper [1], the authors have presented an analysis of the problem of premature debonding of FRP from concrete beams that relies on fracture mechanics and an assessment of the global energy balance. This paper provides experimental confirmation of the validity of that analysis by comparing the predictions with experiments carried out by others.
Premature plate debonding hampers efficient use of externally bonded FRP plates in flexural strengthening of concrete beams. Existing research mostly concentrates on finite element (FE) modelling of the concrete–FRP interface, but the sort of model that could be used in a FE analysis to follow the debonding-crack-tip behaviour requires far more detail than will ever be available to the designer or analyst, who would be forced to make unwarranted assumptions about interface properties [2]. Furthermore, the values returned by a FE program are governed by the smallness of the elements used: for example, there is an infinite stress concentration at the plate end which is detected when very fine meshes are used. None of the existing models have received wide acceptance and most have only been calibrated against each researchers’ own set of test data, which is usually limited in extent.
The concepts that underlie fracture mechanics better simulate failures taking place at interfaces of dissimilar materials and have been used effectively in interface debonding studies in thin-layered elastic materials (e.g. [3]). There has been some recent work that applied fracture-mechanics concepts to FRP debonding from concrete, but these have directly used linear-elastic-fracture-mechanics (LEFM) concepts as applied to the analysis of thin-layered elastic materials (e.g. [4]). A reliable FE analysis to determine the crack-tip stress field in concrete cannot be obtained because of the unknowable microstructure. In addition, the assumptions on which the LEFM is based are not justified for concrete because of the large fracture process zone [2].
The present fracture mechanics model assumes that flaws are inevitable in the interface and investigates how the global energy balance of the beam changes during a small potential crack extension; an existing crack will propagate if the energy release rate (i.e. energy available for crack to propagate – GR) exceeds the interface fracture energy (i.e. the energy needed to form the required new surfaces – GF). The energy evaluation of the beam is based on a revised version of Branson’s model which determines the moment–curvature behaviour of a cracked beam, subject to an external compressive force (the reaction to the tension force in the FRP); this analysis is described elsewhere [1], [5]. Debonding will propagate in whichever of the concrete, adhesive, or an interface (concrete–adhesive or adhesive–FRP) that provides the least resistance; GF is thus the fracture energy of that weakest phase. Determination of GF is not trivial; however, justifiable estimations, within the accuracy expected in the analysis of concrete beams, can be made. That work is briefly reviewed below but described in a separate publication [6].
The plate end, where abrupt curtailment of the plate causes a change in geometry and where there is also a variation in strength, is one of the areas most susceptible to the initiation of debonding. Others are the locations where the widening of flexural and/or flexural-shear cracks cause interface cracks; the two modes are referred to as “plate-end (PE) debonding” and “intermediate-crack-induced (IC) debonding” respectively (Fig. 1); the model analyses both modes. Despite the crack-tip stress field not being amenable to precise analysis, the energy level of the whole beam can still be calculated to a reasonable accuracy because the Branson’s model represents the average moment–curvature (and hence the energy levels) of beam cross sections distributing all complex stress conditions that will be present in beam sections. The unreliable stress predictions in the crack-tip vicinity are therefore not critically significant to the energy balance of the whole system, whereas the crack-tip stress field would solely govern an analysis based on LEFM [1].
Section snippets
Critical crack concept for the debonding analysis
The model is intended to determine “the longest interface crack that can be sustained without causing debonding under a given applied load”, or alternatively, “for a given crack geometry what is the maximum load that can be sustained?”.
Despite numerous cracks inevitably being present in the interface, usually none is long enough nor weak enough to cause failure by itself. Nevertheless, they can coalesce by growing slowly, and subsequently form a longer crack that can propagate steadily,
Interface fracture energy
A critical parameter in the present analysis is the magnitude of the interface fracture energy (GF), but despite considerable research, none of the existing studies provides a reliable estimate. There exist many conceptual misunderstandings; for example, failure phase, fracture mode, size effects of concrete etc. have not been properly taken into account. A wide range of arbitrary values have been selected that correlate well with results from individual test programmes.
Experimental
Identification of critical parameters
Plate end (PE) debonding propagates into the beam whereas intermediate-crack-induced (IC) debonding propagates towards the nearest beam end (Fig. 1). The plate end location is most influential on PE debonding whereas the interface crack length and its location within the beam govern IC debonding [1].
Comparisons with tests: overview
The model has been validated against a database of test results, collected from the literature, covering all possible forms of PE and IC debonding. Due to space constraints, only a limited number of such comparisons are shown here, but they have been selected to cover test specimens with a large variety of material and geometric properties. It is also shown that the model can also be used for debonding analysis of beams strengthened with steel plates, when the steel plates remain within elastic
Examples: plate-end debonding initiating in the actual plate-end vicinity
The variation between the actual plate end (L0) and predicted effective plate end location (L0_eff) is expressed in terms of the depth of the cover (c): results are normally fitted between L0 − 2c and L0 + 2c. The best possible agreement between theory and test would be for failure at P = Pfailure; GR = GCI to occur at the observed L0_eff.
Comparisons with experimental results: intermediate-crack-induced debonding
IC debonding is more complex than PE debonding since the likely length of the existing debonding crack must be investigated together with its location in the beam. Neither parameter can be known precisely; justifiable assumptions can however be made.
As is shown below, most beams failed due to propagation of cracks 2–3 mm long, caused by the widening of flexural cracks, whereas in much shorter beams, longer interface flaws, about 5 mm long that result from the widening of flexural/shear cracks,
Discussion
Whilst it is clear that the model can be used to explain why a particular test beam fails, a comprehensive understanding of the likely sizes and locations of interface cracks is required prior to design. There is thus a significant difference between analysing the mechanism of failure of a laboratory test and designing a structure for use in the real world. This paper explains why it may be impossible ever to predict the exact failure load of beam that is being designed.
Conclusions
The study has shown that the phenomena of plate debonding can be studied by means of a global-energy-balance based fracture-mechanics approach, which obviates the need for a finite-element analysis of dubious validity. Debonding often propagates in the concrete just above the interface and it has been assumed that extension of debonding is a Mode I propagation as an average, even if the local details may not be Mode I governed; comparisons with test data validate this assumption.
Knowledge of
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