Project Goals
Research Plan and Methods
Forming and mechanical design of metallic and composites structures must become more and more virtual, in order to limit the number of prototypes and decrease the time to industrialization of a new product. Moreover, a virtual approach leads to a safer structure with optimized performances. The main point that controls the reliability of the numerical simulations is the pertinence of the representation or modelling of the thermo-mechanical behaviour of the material and, in particular, the material parameters of the constitutive equations involved in the model. Nowadays, one of the real challenges concerns the determination of the material parameters, on a low-cost basis but with an optimal quantity of information to guarantee the reliability of the predictions.
The aim of this project is to develop an efficient methodology for determining the material parameters of thermo-mechanical models, from a dedicated test that involve non-homogeneous temperature and strain fields. Indeed, this non-homogeneity leads to richer information than more traditional approaches with quasi-homogeneous tests, thus to a decrease of the number of experiments.
Nowadays, there are a few numerical methodologies for extracting the material parameters from full-field strain measurements using digital image correlation (DIC) techniques. However, none of them could address successfully the problem of non-uniqueness of solution and none were used to non-homogeneous temperature and strain field and, consequently, to thermo-elasto-viscoplastic constitutive models.
The Virtual Fields Method (VFM) could be an alternative compared to the Finite Element Model Updating (FEMU) for material parameter identification in the field of thermo-mechanical modelling [8,15]. These 2 methods are based on the use of mechanical fields and their relevance was shown in numerous applications, especially for measure of the Young modulus of composites, in the case of linear anisotropic elasticity, and even for non-linear behaviours in plasticity [8].
However, forming and service life in industrial environments can take place under sever conditions, as warm temperatures (i.e. below one half of the melting temperature), with strain and temperature fields involving high gradients [18,19]. These conditions will require an extension of both VFM and FEMU to thermo-mechanical conditions, which was not dealt with previously.
Indeed, aside the theoretical formulation of the optimization, the temperature dependence entails an increase of the inputs and of the material parameters. Additionally, the use of both techniques in a coupled methodology can solve or efficiently decrease the problem of solution uniqueness.
Therefore, the main goal of this proposal is to develop an innovative methodology suitable for thermo-mechanical material characterization using:
(a)
both temperature and strain heterogeneous full-field measurements of a innovative designed mechanical test and
(b)
an inverse integrated VFM-FEMU strategy with convenient physical constraints. The developed methodology will be used to
(C)
build a database of material constitutive models calibrated to a large number of metal materials, particularly to high strength steels, as requested by the industry and FEA providers and users.
Particularly, this proposal includes the following scientific original items:
(I) Experimental and numerical characterization of mechanical behaviour of metallic materials at warm and high temperatures under complex strain paths;
(II) Design of a suitable temperature and strain heterogeneous mechanical test, using integrated topology-shape optimization procedures;
(III) Use of both coupled-synchronized DIC and thermography techniques;
(IV) Use of different inverse methods to identify the parameters of nonlinear thermo-elasto-viscoplastic constitutive models, written within a phenomenological approach [7,17-19];
(V) Extension of VFM to a non-linear thermo-mechanical behaviour;
(VI) Development of an integrated strategy that gather the advantages of different inverse methods. This strategy will be implemented in an automatic numerical tool able to efficiently determine the material parameters;
(VII) Solving/reducing the problem of non-uniqueness of solutions using an integrated strategy;
The impact and benefits of the proposed project are
A
Increasing the precision of numerical FEA simulations providing accurate input data, filling then a gap of the FEA market and answering to the request of the FEA users;
B
The reduction of engineering metal part development lead-time and the provision of robust solutions with highly improved quality;
C
Developing an automatic, accurate and trustworthy methodology for model material characterization;
D
Reduction of the number of experimental tests required to characterize metal forming materials;
E
Reduction of the cost and time in the overall development process.
This works will be split into four main parts, i.e.:
A task dedicated to the development of a robust and accurate numerical methodology for thermomechanical parameter identification using temperature and strain full-field measurements.
In this task, first, a material parameters identification procedure that couple a finite element simulations with a classical optimization methodology (FEMU) will be developed. This classical calibration procedure find the set of parameters that minimize the difference between the experimental and the numerical observations of direct measurable properties (temperature, strain, and loads) in . Here, past work of the team [7,PT4] will be well spent, however, the novelty will be the use of temperature and strain full-field measurements. Then, it will be developed an original methodology based in the virtual field method (VFM). This methodology must extend the VFM to non-linear thermomechanics. It is very different approach from the FEMU because it uses the principle of virtual works to find the set of parameters and introduces the experimental data directly in this principle (that balance the external with the internal forces). While the FEMU uses external observations to find the parameters, the VFM uses internal balances.
Considering that the coupling of both FEMU and VFM extended approaches should gather the advantages of each one, it will be done in this task producing an integrated multi-optimization methodology.
Both FEMU, VFM and coupled methodologies will be previously validated using virtual experimental data (obtained with known material parameters) for several heterogeneous experimental tests and constitutive models.
A task to design of an heterogeneous temperature and strain full-field test for material characterization using integrated topology and shape optimization.
Considering that the existent classical tests lead to homogeneous thermal and stress-strain fields that do not represent the complex fields occurring in metal-forming operations and this classical procedure require high number of expensive and time consuming tests, it is mandatory for this project to develop a heterogeneous mechanical test. This test can be developed through the design of a new specimen and boundary conditions, as previous made by the team [PT2,PT3,24]. However, using the classical try’nd-error design procedure is not effective and the solutions are limited by the definition of the design boundary. Here, an integrated topology-shape optimization approach is suggested. The design of a specimen for plasticity by topology optimization is surely innovative and can lead to solutions with multiple holes, impossible to achieve with only a shape optimization approach. The design procedure should maximize the number of strain-states and the richness of temperature-strain field [PT2].
This design approach should also take into account (i) the criterion of final fracture which condition how far one can have data before failure and (ii) the imaging requirements. Indeed, DIC is a low pass spatial filter (i.e., gradients will be smoothed out by DIC) and its spatial resolution is a key issue, as well at its noise performance.
A task fully dedicated to the analysis of constraints and search universe in parameter identification of thermelastic-viscoplastic and elastoplastic constitutive models.
For the experience of the project team, the success of the material characterization through numerical constitutive models and their parameters depends of the physical optimization constraints introduced in the identification process. Previous works [23,PT5] show that the non-introduction of correct process constraints lead to set of parameters with no physical meaning, although they lead to low objective functions (in the optimization process). Therefore, this task is of maximum importance and it will have researchers in fully exclusivity for it.
A final task concerning the development of an OpenAcess database with input data for FEA simulation software concerning the material behaviour charaterization (models and their parameters). In this task, data for high strength steels through the methodology developed is also introduced.
This task is a response to the needs of the industry and FEA users. The database will be located in a Website and it will be accessed by credited users from the industry and from Academy. This database should be enlarged by the contributions of all users, both with new constitutive models and identified parameters for all kind of materials, even after the conclusion of the project. Within the project, experimental test with high strength steels (like dual-phase steels, bake-hardening steels) will be performed and their behaviour will be characterized for several thermoviscoplastic models, including the extension of the Johnson-Cook model to thermoviscoplasticity and some internal variable models [7].
The ranges of temperature, strain-rate and strain depend of the material.
The main originality of the work is related to the characterization of the mechanical behaviour of metallic materials at warm and high temperatures under complex strain paths, which is still an experimental challenge. Indeed, the heating system, the control and measure simultaneously of the temperature and strain fields require specific equipment like thermal camera and digital image correlation systems, and synchronized acquisition. Moreover, the increase of the number of data, both input data (temperature and strain fields) and parameters to identify, require the use of robust algorithms and to deal with the uniqueness of the solution, which is a central concern in parameter identification. Finally, the extension of VFM to thermo-mechanical behaviour necessitates more academic investigations.
In all the period of the project, special attention will be made to dissemination of the obtained results and developed tools to both scientific and industry community, in order to establish scientific and industrial milestones of the ongoing work.
In this kind of works, and due to the large technological and research complexity involved, it is mandatory to establish contacts and collaborations with renowned entities, both research centers and Universities. As a result, the efficiency and the global quality of the work developed can then be guaranteed. For the effect, it will be made frequent contacts with three well-known researchers and institutions in the research field: Fabrice Pierron – University of Southampton, UK – and Sandrine Thuillier, IRDL – Université de Bretagne Sud, France. Both accepted to be consultors for this project and are already working with the project team, as can be seen by the publications [1-2, PT1-PT4].
Previous works of the project team demonstrate that, although the workplan is quite ambitious, the risks are controlled. As example, inherent risks such as the difficulty in designing a test that promotes heterogeneities of different fields were addressed in [15,24,PT2,PT3].
A multidisciplinary research team composed by experts from mechanical technology and computational mechanics will perform this project, guaranteeing that there will be very useful work produced in industrial and scientific terms.
This workplan fits into the guidelines of Eixo II of COMPETE2020 and the Call Factories-of-the-Future in H2020.