Finite Fracture Mechanics extension to dynamic loading scenarios

The coupled criterion of Finite Fracture Mechanics (FFM) has already been successfully applied to assess the brittle failure initiation in cracked and notched structures subjected to quasi-static loading conditions. The FFM originality lies in addressing failure onset through the simultaneous fulfilment of a stress requirement and the energy balance, both computed over a finite distance ahead of the stress raiser. Accordingly, this length results to be a structural parameter, thus able to interact with the geometry under investigation. This work aims at extending the FFM failure criterion to dynamic loadings. To this end, the general requisites of a proper dynamic failure criterion are first shortlisted. The novel Dynamic extension of FFM (DFFM) is then put forward assuming the existence of a material time interval that is related to the coalescence period of microcracks upon macroscopic failure. On this basis, the DFFM model is investigated in case a one-to-one relation between the external solicitation and both the dynamic stress field and energy release rate holds true. Under such a condition, the DFFM is also validated against suitable experimental data on rock materials from the literature and proven to properly catch the increase of the failure load as the loading rate rises, thus proving to be a novel technique suitable for modelling the rate dependence of failure initiation in brittle and quasi-brittle materials

Size effects on spheroidal voids by Finite Fracture Mechanics and application to corrosion pits

The present work aims at investigating the failure size effect of a spheroidal void in an infinite linear elastic solid under remote tension by means of the coupled Finite Fracture Mechanics (FFM) approach. The opening stress field and the stress intensity factor (SIF) of an annular crack surrounding the cavity -necessary for the FFM implementation- are obtained numerically through parametric axisymmetric finite element analyses (FEAs): The spheroid aspect ratio is varied between 0.1 and 10 and Poisson's ratio between 0.1 and 0.5. Accordingly, semi-analytical functions approximating the stress concentration factor and the SIF are put forward. Finally, the failure size effect on spheroidal voids is reported, and FFM predictions are compared with experimental results on the fatigue limit arising from corrosion pits, showing a fairly good agreement

Analytical development on impact behaviour of composite sandwich laminates by differentiated loading regimes

Given the widespread usage of composite components in critical structures within the aerospace and automotive industries, it is deemed as an essential task to determine the effect of normal operation phenomena on its performance in impact. In particular, the present study aims for providing the developed analytical modelling techniques which are needed for describing the low velocity impact dynamic response of sandwich laminated structures. Alongside the analytical models, experimentally validated high-fidelity numerical models are used to check both the validity of the assumptions made as well as the accuracy of the analytical results in the different considered scenarios. An extensive analysis of the sandwich laminate impact performance has been studied, eventually resulting in a much improved, herein developed analytical formulation which is capable of accounting for the differentiated loading, unloading and reloading indentation regimes as well as for the lower facesheet local deflections. These considerations, which are normally neglected in equivalent studies, allow a precise capture of the energy absorption mechanisms

Analytical solutions to predict impact behaviour of stringer stiffened composite aircraft panels

This paper aims to develop an analytical method to predict the low-velocity impact response of simply supported stringer stiffened panels. Since the combination of stringer and panel provides aircraft structure with variable thicknesses, significant mathematical modelling is required to predict the transverse impact response of this type of designs. Within this analysis, the effect of variable stiffness distribution due to the stringer presence has been included. The performance of various layups is investigated to find the most suitable combination for panel-stringer laminate under impact loading. Analytical models were developed based on a spring-mass system to predict the dynamic behaviour of the striker-plate domain and, finally, determine the contact force history, which shows the main novelty of this research. Compared with Finite Element results, the model developed proved to successfully predict stringer stiffened composite panels' response with a range of layups and geometry designs under low-velocity impact loading conditions. The analytical results agree with the available data in the literature, and the error is less than 5%

Spherical voids by finite fracture mechanics

The apparent weakening of a uniaxially tensioned infinite domain that contains a single spherical void and is anywhere else filled with a homogeneous and linear elastic material is investigated through two Finite Fracture Mechanics approaches. Resultant charts depicting the respectively predicted relation of the weakening ratio with the void's radius clearly show that the fracture toughness drives the transition between the strength-dominated extreme solutions, namely voidless and large void. Eventually, the Finite Fracture Mechanics predictions are compared with experimental results, yielding a reasonably good agreement

Coupled versus energetic nonlocal failure criteria: A case study on the crack onset from circular holes under biaxial loadings

The phenomenon of brittle crack onset stemming from a circular hole in an infinite plate subjected to remote biaxial loading is herein investigated. A thorough analysis on the influence of the loading biaxiality reveals the existence of a wide casuistry in the sign and trend distributions of the stress field and Stress Intensity Factor, thus rendering it an exhaustive case study for assessing different failure criteria. Subsequently, three different approaches are used to determine the biaxial safety domains, two of which rely on the coupling of stress and energy conditions for failure, namely Finite Fracture Mechanics and Cohesive Zone Model, plus the purely energy-driven Phase Field model of fracture. Noteworthy, Finite Fracture Mechanics predicts the existence of a region in the loading space where failure is exclusively governed by the energy condition. Likewise, it is mathematically proven that the system of equations governing Dugdale's Cohesive Zone Model is equivalent to the first-order minimization condition of the energy balance, the resultant predictions being fairly close to those obtained by Finite Fracture Mechanics. Lastly, the Phase Field model of fracture is numerically implemented in the context of Finite Elements while paying special attention to the choice of the energy decomposition, whereof two are implemented: No-Decomposition and No-Tension decomposition. Specifically, the latter showcases satisfactory agreement with both Finite Fracture Mechanics and Dugdale's Cohesive Zone Model, thus posing a solid contender for studying complex fracture scenarios upon combined tension-compression stress states