Paolo Sebastiano Valvo

A revised virtual crack closure technique for physically consistent fracture mode partitioning

The virtual crack closure technique (VCCT) is a well-established method for computing the energy release rate when analysing fracture problems via the finite element method. For mixed-mode fracture problems, the VCCT is also commonly used to partition the fracture modes, i.e. to determine the energy release rate contributions related to the three classical fracture modes. A perhaps little known fact, however, is that in some circumstances the standard VCCT predicts physically inconsistent, negative values for the modal contributions to the energy release rate. Focusing on I/II mixed-mode problems, this paper presents a revised VCCT which furnishes a physically consistent partitioning of fracture modes by associating the mode I and II contributions to the amounts of work done in a suitably defined two-step process of closure of the virtually extended crack. Deeper investigation pinpoints the origins of the physically inconsistent predictions of the standard VCCT in the lack of energetic orthogonality between the crack-tip force components used to compute the modal contributions. Further insight into the problem is offered by a geometric construction, which introduces the ‘ellipse of crack-tip flexibility’. In closing, the phenomena of contact, interpenetration, and friction between the crack surfaces are briefly touched upon.

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.

Evaluation of the increased load bearing capacity of steel beams strengthened with pre-stressed FRP 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. We assume that the laminate is first put into tension, then bonded to the beam bottom 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. As an application, we consider the standard IPE series for the steel beam and the Sika® CarboDur® system for the adhesive and laminate. For each considered cross section, we first carry out a preliminary design of the unstrengthened steel beam. Then, we imagine to apply the FRP strengthening and calculate the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate. Lastly, we take into account the ultimate limit state corresponding to the plasticisation of the mid-span steel cross section and evaluate the increased load bearing capacity of the strengthened beam. KEYWORDS. Steel beam; FRP strengthening; Adhesive; Beam theory; Cohesive-zone model; Analytical solution; Pre-stressing; Ultimate limit state; Load bearing capacity.

Frattura interlaminare secondo il modo I in un laminato composito

Si propone un modello meccanico per il provino DCB (Double Cantilever Beam), comunemente utilizzato per la determinazione sperimentale della resistenza alla frattura interlaminare secondo il modo I nei laminati compositi. A tal fine, si schematizza il provino come l’assemblaggio di due sublaminati collegati fra loro da un’interfaccia elasto-fragile. Grazie alla relativa semplicita del modello, e possibile ricavare esplicitamente gli spostamenti dei due sublaminati, le tensioni interlaminari e, conseguentemente, la velocita di rilascio dell’energia potenziale totale del sistema. L’adozione di un opportuno criterio di frattura consente, quindi, di valutare il valore critico del carico o dello spostamento di estremita, come funzioni esplicite dell’ampiezza della zona delaminata. Il confronto con alcuni risultati sperimentali presenti in letteratura appare molto buono.

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.

Numerical and analytical modeling of the end-loaded split (ELS) test specimens made of multi-directional coupled composite laminates

The paper deals with the numerical and analytical modelling of the end-loaded split test for multi-directional laminates affected by the typical elastic couplings. Numerical analysis of three-dimensional finite element models was performed with the Abaqus software exploiting the virtual crack closure technique (VCCT). The results show possible asymmetries in the widthwise deflections of the specimen, as well as in the strain energy release rate (SERR) distributions along the delamination front. Analytical modelling based on a beam-theory approach was also conducted in simpler cases, where only bending-extension coupling is present, but no out-of-plane effects. The analytical results matched the numerical ones, thus demonstrating that the analytical models are feasible for test design and experimental data reduction.The paper deals with the numerical and analytical modelling of the end-loaded split test for multi-directional laminates affected by the typical elastic couplings. Numerical analysis of three-dimensional finite element models was performed with the Abaqus software exploiting the virtual crack closure technique (VCCT). The results show possible asymmetries in the widthwise deflections of the specimen, as well as in the strain energy release rate (SERR) distributions along the delamination front. Analytical modelling based on a beam-theory approach was also conducted in simpler cases, where only bending-extension coupling is present, but no out-of-plane effects. The analytical results matched the numerical ones, thus demonstrating that the analytical models are feasible for test design and experimental data reduction.

An Interface Model for Mixed-Mode, Buckling-Driven Decohesion of Superficial Layers

There are several situations in which the local phenomena acting in structural elements can lead to the partial detachment of a superficial layer from its underlying substrate. In the case of fibre-reinforced composite laminates, for example, delamination is one of the most insidious events that can compromise their mechanical performance. Analogous decohesion phenomena can be observed, for instance, in film coatings, sandwich plates, etc. (Hutchinson and Suo [1]).