Digital Image Correlation for latticestructures

By Florent Mathieu, Ceo of EikoSim et Philippe Brammer R&D engineer at EikoSim

Application of digital image correlation to tests on latticestructure obtained by additive manufacturingInterest in lattice structures is growing rapidly for the development of aeronautical and spacecomponents in particular. In addition to the significant mass gains they allow to consider, they offerthe possibility of optimising their behaviour based on their constituent patterns. The strong growthof metallic additive manufacturing technologies allows manufacturing parts composed of latticestructures, with materials known for their mechanical performance, such as nickel-based alloys,titanium alloys or new generations of aluminium alloys. These promising architectural materials arestill not widely used in the design of structural parts, as they require new development methods on acommercial scale (simulation, characterization, manufacturing). In this context, the Institut deRecherche Technologique (IRT) Saint Exupéry, based on the experience of the SIMaP laboratory inthe field of architectural materials, is conducting a 24-month research and development projectcalled LASER (LAttice Structures for Engines and LauncheRs), bringing together major aerospacemanufacturers with the aim of providing them with understanding and design tools for researchdepartments. EikoSim, a young company specialized in the link between tests and simulations,provides the LASER project with its expertise and its software for field measurement using digitalimage correlation. Focus on test and simulation methods.

Tests on lattice structures carried out as part of the LASER project aim to highlight the strainmodes in compression or shear configurations, with different boundary conditions and scale effectsby playing on the number of unit cells constituting the specimens. The diversity of theseconfigurations should allow the development and the validation of a numerical modelling approach.At that time, the study is limited to quasi-static stresses at room temperature as a starting pointfor fixing the methods. The structures tested are made of microbeams with a maximum diameter of 1mm organised according to BCC lattice (Body-Centered Cubic) or BCCZ lattice (Body-CenteredCubic with vertical beams).

Compression test on a BCCZ lattice structure – IRT Saint-Exupéry

To capture the complex kinematics of such lattice structures under mechanical stress, it isimpossible to use a traditional measurement method. Strain gauges, for instance, are very difficultto use at the microbeam scale and would only provide very partial results on the structural response.The measurement of the global displacement is still possible with extensometers and the appliedstress is captured by an essential load cell. In this context, the link between experimental resultsand modelling remains weak, and it seems very difficult to develop a predictive model, which willmake possible the design of more complex structures with a high level of confidence, different fromthose characterized in the laboratory

BCCZ lattice structure after a compression test, characteristic shear belt – IRT Saint-Exupéry

The use of more efficient measurement methods is one way to meet the challenges posed by thesenew geometries. Field measurement, particularly by digital image correlation, is a naturalcandidate for capturing the heterogeneity of strain and the phenomena of local instabilities that

occur.

Compression test instrumented by image correlation

Application of a black speckle on a white background on a lattice structure – IRT Saint-Exupéry

The implementation of digital image correlation involves the application of a speckle (contrastedpattern) on the part, adapted to the scale and the cameras resolution. On lattice structures, it isapplied with an airbrush to reach spots sizes of a few tens of microns.

During the test, two sides of the sample are observed using two pairs of high-resolution cameras.This makes it possible to capture for sure the characteristic strain mode which results in shear beltand all the complexity of kinematics. From a measurement point of view, this can make thetreatment process complex. With an approach based on a finite element mesh, as proposed in theEikoTwin DIC software, the measurement result is directly associated with a point in the 3D spaceof the model part. There is no analytical limit to the number of cameras, which contributes to themeasurement of the displacement of points that are in their respective fields of view.

Instrumentation by 4 cameras of two sides of a lattice structure for a compression test –IRT Saint-Exupéry

Digital image correlation is a technique that tracks the movement of points in a structure byassuming that they maintain the same grey level in the image. Lighting conditions must therefore becontrolled in order to limit measurement uncertainty and ensure the ability to track the structureeven in case of large displacements.

Vertical displacement field measured by image correlation on the simulation mesh,EikoTwin DIC software – IRT Saint-Exupéry

Modeling and Computation

Several modelling approaches of the mechanical behaviour of lattice structures can be considered.The most accurate in terms of geometric representation describes in volume each microbeam. Thediscretization by volume finite elements allows staying as close as possible to the geometry as

designed initially. From a physical point of view, given the strain level expected during thecompression tests, it is important to describe the elasto-plastic behaviour of the structure’scomponents. One difficulty at this point is to describe the local mechanical behaviour by an adaptedlaw. Several approaches are possible in research department:

As a first approach, it is possible to consider the properties of the constituent material fromstandard tests. In this case, it is recommended at least that the standard tests have beencarried out on specimens machined from raw materials obtained by the same additivemanufacturing process as that of lattice structures.A second approach, proposed and implemented in the LASER project, consists incharacterizing the constituent elements of a lattice structure, namely microbeams. Specimengeometries have been designed and manufactured on the same trays as the lattice structuresto access the intrinsic properties of the microbeams according to their orientation (vertical,tilted). The advantage of this approach is that it allows viewing effects related in particular tothe fineness of the geometry, which are relatively well known in additive manufacturing:roughness, shape error (average diameter, cylindricity), thermal history and particularmetallurgy.

“Microbeam” test pieces for the characterization of the constituent elements of a latticestructure – IRT Saint-Exupéry

The application of loading and boundary conditions is an essential part of the modelling. Just asthe differences between the geometry as designed and manufactured, the differences between the“ideal” load and that actually experienced by the structure can have a significant impact on theresponse. However, measurements of these gaps are rarely available for research departments.The modelling chosen at first therefore largely neglects them.

Simulation of the compression test on a 5x5x5 BCCZ lattice structure, solid element mesh,Abaqus software – IRT Saint-Exupéry

The problem of computation time emerges quite quickly for this type of non-linear models,composed of millions of elements. The LASER project is currently working on a simplified approachbased on an approximation of the geometry by linear finite elements with beam kinematics and withthe objective of not deteriorating the accuracy of the simulations.

Test – Simulation comparison

The comparison between measurements and simulation results is often a challenge in itself. Theability to measure displacements on a point cloud is interesting, but it creates new problems whencomparing to the simulation. With the approach implemented in the EikoTwin DIC software, basedon finite elements, the displacement field is measured directly on the numerical simulation mesh, inthe same 3D reference frame. Errors related to the projection of the measurement fields on themesh, or vice versa, are thus avoided. It also saves time for the user. For example, it is possible todirectly visualize a difference between the ideal loading path and the one applied to the part, inorder to correct the simulation model accordingly.

Difference between the measured and simulated vertical displacement field (left), andevolution of the deviation at a point of the mesh as a function of time (right)

Outlook

The next step: modifying initial simulations using measurement results. These tests teach us a lotabout lattice structures, so we want to use these results to improve our simulations and betterunderstand the sources of error. Initially, the displacements measured at the edges can be used asboundary conditions for the simulation.

Then, coupled with the comparison between experimental and simulated stress-displacement curves,this approach will allow the implementation of a reverse identification strategy to refine the modelparameters and reduce the test-simulation gap. The EikoTwin Digital Twin software proposes tointegrate these two essential steps into a single environment. This will allow us to consider thetransfer of these methodologies to the research department in the very short-term and to developthe potential of lattice structures for industrial applications.

Credits

The Institut de Recherche Technologique (IRT) Saint-Exupéry* is an accelerator of science,technological research and transfer to the aeronautics, space and embedded systems industries forthe development of innovative solutions that are safe, robust, certifiable and sustainable. The IRTSaint-Exupéry offers on its sites in Toulouse, Bordeaux, Sophia Antipolis and Montreal an integratedcollaborative environment composed of engineers, researchers, experts and doctoral students fromindustrial and academic environments for research projects and R&T services supported bytechnological platforms in four key areas: high-performance multifunctional materials, moreelectrical aircraft, intelligent systems & communications and systems engineering & modelling.

* The IRT Saint-Exupéry is a technological research institute labelled by the French governmentas part of the Programme d’Investissement d’Avenir (PIA).

* EikoSim is a software company specialized in test-simulation dialogue, which relies in particularon innovative measurement tools by digital image correlation.

The LASER project is owned by the IRT Saint-Exupéry, 50% financed by its industrial members and50% by the French government’s Programme d’Investissement d’Avenir (PIA). It is part of the inter-IRT “LATTICES” initiative, which defines the close collaboration with the DSL (Durabilité desStructures Lattices) project led by IRT SystemX and with the Centre National d’Etudes Spatiales(CNES).

Written by

Philippe Brammer

R&D Engineer – EikoSim

Florent Mathieu

CEO – EikoSim

Dr. Ludovic Barrière

Project Leader : LASER – IRT Saint-Exupéry