Damage initialization techniques for non-sequential FE propagation analysis of delaminations in composite aerospace structures

The experimental effort required to develop, damage tolerant, aerospace composite structures could be significantly reduced if reliable numerical simulations were used to perform engineering studies of complex damaged structures. Finite element (FE) simulations of impact damaged structures typically follow a sequential approach that require large computational resources to reproduce complex damage scenarios. A numerical tool capable to reconstruct such scenarios using data from previous impact simulations or NDI could noticeably improve the simulation workflow for damaged composite structures. The paper proposes a method to inizialize the damage variables in numerical analyses aimed at assessing damage propagation, and that are potentially able to evaluate the residual strength of damaged structures. The approach is developed within FE software ABAQUS, and uses SDVINI subroutine to initialize damage variables defined by a user-material-subroutine (UMAT), that provides the constitutive models of the lamina and of the interlaminar layers. Albeit the proposed technique might deal with both inter-laminar and intra-laminar damage, the paper is focused on delaminations. A user defined traction-separation law is coded in an UMAT that endows ABAQUS cohesive elements with damage initialization capabilities. Then, results of test cases, of increasing complexity, are presented in order to assess the damage initialization procedure and verify the performances of its different operating modes. Two test-cases are based on plate-like specimens for which literature data exist: the first is relevant to a circular artificial delamination while the second presents multiple delaminations caused by an impact and measured via NDI techniques. The last test-case is a stiffened panel which incorporates the typical complexities of aerospace structures, but is still tractable with the sequential simulation approach whose results are used as a term of comparison

A numerical micro-mechanical study of the influence of fiber–matrix interphase failure on carbon/epoxy material properties

A finite element micromechanical study of unidirectional carbon–epoxy system is performed in order to investigate the role of fiber–matrix debonding in the degradation of mechanical properties and in the onset of failure for this class of composite materials. The presence of interphase flaws, that can be induced during the manufacturing processes, into micro-scale FE models is obtained by means of an original damage injection technique developed by the authors. The fibers are considered as transversally isotropic solids and the matrix is modeled as an isotropic, elasto-plastic, material with damage. The effect of fiber–matrix debonding is analyzed by means of a quasi 3-D unitary cell with a single fiber, with periodic boundary conditions, for different loading cases. Subsequently, multi-fiber representative volume elements are investigated with the same boundary and loading conditions. Finally, the effect of a 3-D debonding propagation is studied via single fiber model with an increased fiber-wise depth

Low-velocity impact tests on carbon/epoxy composite laminates: A benchmark study

Low-velocity impacts (LVI) on composite laminates pose significant safety issues since they are able to generate extended damage within the structure, mostly delaminations and matrix cracking, while being hardly detectable in visual inspections. The role of LVI tests at the coupon level is to evaluate quantities that can be useful both in the design process, such as the delamination threshold load, and in dealing with safety issues, that is correlating the internal damage with the indentation depth. This paper aims at providing a benchmark of LVIs on quasi-isotropic carbon/epoxy laminates; 2 laminates are tested, 16 and 24 plies and a total of 8 impact energies have been selected ranging from very low energy impacts up to around 30 J. Delamination threshold loads, shape and extension of délaminations as well as post-impact 3D measurements of the impacted surface have been carried out in order to characterize the behavior of the considered material system in LVIs. The analysis of test results relevant to the lowest energies pointed out that large contact force fluctuations, typically associated to delamination onset, occurred but ultrasonic scans did not reveal any significant internal damage. Due to these unexpected results, such tests were further investigated through a detailed FE model. The results of this investigation highlights the detrimental effects of the dissipative mechanisms of the impactor. A combined numericale-experimental approach is thus proposed to evaluate the effective impact energies

Quasi-trivial stacking sequences for the design of thick laminates

Quasi-trivial (QT) sequences have largely proven to be an extremely powerful tool in the design and optimisation of composites laminates. In this paper new interesting properties of this class of stacks are derived. These properties allow to obtain QT sequences by superposing (according to some prescribed rules) any number of QT elementary stacks. In this way, QT solutions with arbitrary large number of plies can be readily obtained, overcoming the computational issues arising in the search of QT solutions with huge number of layers. Moreover, a general version of the combinatorial algorithm to find QT stacks is proposed in this work. It is also proven that the previous estimation of the number of QT solutions, for a given number of plies and saturated groups, is not correct because a larger number of solutions has been found in this study

Multi-scale optimisation of thin-walled structures by considering a global/local modelling approach

In this work, a design strategy for optimising thin-walled structures based on a global-local finite element (FE) modelling approach is presented. The preliminary design of thin-walled structures can be stated in the form of a constrained non-linear programming problem (CNLPP) involving requirements of different nature intervening at the different scales of the structure. The proposed multi-scale optimisation (MSO) strategy is characterised by two main features. Firstly, the CNLPP is formulated in the most general sense by including all design variables involved at each pertinent scale of the problem. Secondly, two scales (with the related design requirements) are considered: i) the structure macroscopic scale, where low-fidelity FE models are used; ii) the structure mesoscopic scale (or component-level), where more accurate FE models are involved. In particular, the mechanical responses of the structure are evaluated at both global and local scales, avoiding the use of approximated analytical methods. The MSO is here applied to the least-weight design of an aluminium fuselage barrel of a wide-body aircraft. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one thanks to the implementation of a sub-modelling approach. The whole process is completely automated and, once set, it does not need any further user intervention.This paper presents part of the activities carried out within the research project PARSIFAL (Prandtlplane ARchitecture for the Sustainable Improvement of Future AirpLanes), which has been funded by the European Union under the Horizon 2020 Research and Innovation Program (Grant Agreement n.723149

A NON-LINEAR MODEL FOR IN-PLANE SHEAR DAMAGE AND FAILURE OF COMPOSITE LAMINATES

Composite material characterization is typically carried out by time-consuming and expensive experimental tests aimed at establishing strengths at both lamina and laminate levels. In this scenario, numerical analyses are valuable tools in order to reduce the number of tests and to gather, at the same time, knowledge about the complex interactions of the composite damage mechanisms. The paper presents a new constitutive model for the non-linear shear behavior of composite laminates, which has been implemented in an user-defined Fortran routine (UMAT) to be used within ABAQUS non-linear FE code. A numerical model of the ASTM Standard V-notch specimen shear test has been developed in order to identify the key parameters of the non-linear shear constitutive model. This has been achieved by means of a systematic comparison of the numerical results with experimental data. Material anisotropy and the geometry of the notch have been found to cause the shear strain field to be non-uniform in the notch section. This prevents a direct measure of the shear constitutive law parameters, which must be alternatively evaluated through an indirect procedure. A modified notch geometry, which mitigates strain non-uniformities, has been evaluated and assessed through numerical simulations

A non-linear model of large radial tyres for the simulation of aircraft braking

A model is presented of the in-plane behaviour of a radial tyre, suitable to be employed within the simulation of aircraft braking. The model is developed on the basis of an energy-balance approach that allows the determination of the effects of braking on rolling friction and on the lever-arm of vertical load. The model is tuned and validated through the correlation between simulated and experimental results relevant to a large aircraft tyre. The method proposed is tuneable on a specific tyre using a limited number of parameters, that are those usually recorded during standard braking tests and it is extendible to the braking tests of an aircraft. This would overcome the limitations intrinsic of current tyre dynamometer facilities that are able to test large aircraft tyres over a modest range of vertical loads compared with those experienced under service conditions

Models of Wheel Contact Dynamics: an analytical study on the in-plane transient responses of a brush model

This paper deals with the dynamics of the contact between the pneumatic tyre and the ground, in particular with reference to braking manoeuvres of aircraft. The transient response of the braking force is analytically evaluated in terms of the transfer functions that link the variation of the braking force to the variation of physical inputs affecting the interaction between the tread and the ground, in the longitudinal plane. The proposed models have been formulated in order to account for the effects of different reference conditions of steady braking on gains, zeros and poles of such transfer functions

Finite-element-based assessment of analytical methods for the design of fuselage frames

The paper presents the results of a number of finite-element analyses carried out to support the development of an analytical design procedure for fuselage frames of a transport aircraft. The numerical simulation by means of finite-element method has the aim of developing an adequate sensitivity about the advantages and the limitations of the analytical approach and in quantifying the magnitude of such limitations with respect to more refined design tools. In particular, the final objective is to achieve a deeper insight into some of the design aspects of the frames, such as the influence of realistic load cases and the effects of the frames on the behaviour of the structure in their vicinity. The results indicate that the analytical design method is capable of describing correctly the influence of the frame on the stress state of the structure at a sufficient distance from the frame location, in the simplifying hypothesis of negligible effects of adjacent loaded frames. In the immediate surroundings of the frame and within the frame itself, the analytical method can provide a first approximation of the stress fields

SENSITIVITY OF MATRIX-DOMINATED FAILURE MODES TO CARBON/EPOXY CONSTITUENT PROPERTIES VIA COMPUTATIONAL MICROMECHANICS

A micromechanical approach can promote understanding of composite material failure mechanisms and increase our knowledge of the key parameters that control intralaminar damage. Such knowledge is vital in order to develop mesoscale (ply level) damage models of composite materials. Classical micromechanics can predict the elastic properties of a lamina, but capturing intralaminar failure modes needs finite-element based approaches that incorporate the modeling of damage for each of the constituents. The response of micromechanical models of unidirectional composite plies is affected by many factors; among them there are: the randomness of fibers distribution, the constitutive and failure models of each constituent and the mechanical characteristics of the matrix-fiber interface layer (interphase). Sensitivity studies to volume fraction, to fiber distribution and to the explicit simulation of the interphase do exist in recent literature. Yet, the influence on failure stresses and modes of constituent properties and damage parameters is still an open issue. The authors present a sensitivity study of micromechanically computed strengths to the most relevant constituent parameters which affect matrix dominated failure modes (transverse traction, transverse compression and shear). For this purpose finite-element (FE) Representative Volume Elements (RVEs) are generated in SIMULIA-ABAQUS by means of a dedicated Python script. The script applies multiple sets of boundary conditions in order to guarantee the periodicity of the microstructure and to reproduce the different load cases. Global RVE mechanical responses, i.e. averaged stresses vs. strains, are obtained by homogenization. The size of the RVEs is selected so that the homogenized stress fluctuations are vanishingly small for any random distribution of fibers generated using the probability density function that, according to recent studies, produces the smallest FE model for RVEs. The typical non-linear behavior of epoxies is reproduced by means of a pressure-dependent elasto-plastic constitutive relation, characterized by an exponential hardening followed by a linear softening law. The interphase is modeled using ABAQUS cohesive elements modified through an ad-hoc traction-separation constitutive model. Both matrix and interphase constitutive laws are implemented via user-defined material routines (UMAT). The systematic comparison of the mechanical responses, in terms of homogenized stress vs. strain curves, is used in order to discover correlations between the constituents properties and lamina failure stresses for modes of interest. The insight gained with the proposed approach will also constitute the basis for the development of specific tests aimed at determining the most relevant micromechanical parameters whose measure is a major challenge for current experimental procedures