Instability and fracture of materials: investigation with holographic interferometry and non-local modelling

PhD at University of Technology of Troyes, supervised by Prof. Manuel FRANCOIS and Dr. Léa Le Joncour

1. Aim of the PhD workThe manufacturing of industrial components with complex shapes requires very advanced numerical models which, in turn, rely on accurate descriptions of the constitutive behavior of the materials. In the case of metal sheet forming by stamping, the formability of the material is limited by an instability phenomenon called necking which leads to the appearance of defects (wrinkles) and, eventually to fracture. Although the onset of the instability is well documented in the scientific literature, from both the experimental and theoretical point of view, much less is known about what happens between this onset and fracture. In our research group, a method using Laser Speckle Pattern Interferometry was developed to investigate the development of necking. In particular, it was shown that the intrinsic dynamics of necking can be studied independently from the geometry of the specimen and that a "master curve" can be found for each material. From this starting point, many questions can be investigated. For instance, what is the origin of this master curve? What is the link between damage development and necking evolution? What is the influence of the deformation rate on necking evolution? A particularly nagging question is: what governs the width of the necking zone and how is it linked to the famous "internal length" of the material that appears in non-local constitutive behavior of materials? A new set-up, based on high speed holographic microscopy and a comparison with non-local modelling of necking will certainly help answering these questions.

Figure 1: necking band in a copper sheet. One can note how straight and regular the band is.

Image M. François, UTT

In parallel some colleagues in our group are developing non-local modelling constitutive behavior (micromorphic) in a thermodynamic based theoretical framework in order to simulate numerically various forming processes, taking into account the softening of the material due to ductile damage. During the PhD project, interaction with these colleagues will enable to compare modelling and experiments.

Figure 2: Interference fringes observed at various stages of the localization process. Left: symmetric hourglass shape at the beginning during diffuse necking, middle: asymmetric X shape at the onset of localized necking,

right: slash shape just before fracture. Each fringe represents a displacement of 600 nm (the resolution is about 20 nm). The color picture is the strain rate field deduced from fringe pictures

2. Detailed description of the research projectThe PhD work will take place through two stages, one mostly experimental and the other one will be modelling.

Experimental work: previous experiments were performed with ESPI at macroscopic scale only. In the proposed work, the ESPI measurements will be completed by in-depth local characterization of the material with X-ray diffraction, SEM observations, instrumental nano-indentation or EBSD. Concerning optical measurements, the existing set-up will be improved to investigate the influence of strain rate on the necking development. The use of Digital Holography will also allow a better resolution and thus get much closer to the fracture than in previous studies. Analysis of the local rotation rate will provide a better understanding of the kinematics and the plastic flow inside the necking bands.

Numerical modelling: As the behavior of the material becomes unstable (loss of ellipsicity), the modelling of necking requires the use of a non-local formulation to regularize the solution. The chosen approach is based on a micromorphic scheme developed in our laboratory (the micromorphic parameters describe both plasticity and damage) or developed by S. Forest in Ecole des Mines de Paris (the micromorphic parameters describe plasticity only). The model will be used to analyze the ESPI measurements and identify the parameters of the constitutive model and retrieve one or two internal length of the material. Once the

internal length is known, a stage of interpretation (and additional experiments) will be necessary to understand its physical meaning. The unicity and the stability of the solution will also be investigated.

Several publications are expected from this work and, at least: One on the local characterization One on the use of Digital Holography, as applied to this problem One or two on the modelling and identification of the internal length(s) and damage

parametersThe project will be performed through a cooperation with partner laboratories such a AGH University of Science and Technology of Krakow (Poland) or Ecole des Mines de Paris (France).

3. Work environmentThe University of Technology of Troyes (UTT):

UTT is a French institution of higher education established in 1994. It is today one of the largest engineering schools in France. Over 2,900 students are registered at the University, enrolled on undergraduate, postgraduate and doctoral study programs. In the renowned yearly ranking of French magazines UTT takes enviable positions. More detailed information is available on http://www.utt.fr/en/about-utt.html.

The LASMIS research team:

The LASMIS research team (about 60 researchers) is part of Charles Delaunay Institute which is associated to CNRS (the French National Center for Scientific Research, equivalent to the Chinese Academy of Science).

The LASMIS team has a significant experience in the field of photomechanics (the use of optical techniques to measure mechanical quantities such as displacement, velocity or strain fields), damage mechanics, numerical modelling of material forming processes and experimental characterization of post-necking behavior of materials. It possesses a recognized know-how in the field of damage mechanics and Electronic Speckle Pattern Interferometry (ESPI/DSPI) (see Tables 1 and 2). Our team cooperates regularly with industrial partners such as Renault, Peugeot SA, Renault SA, AREVA, Arcelor-Mittal, SNECMA or Turbomeca (Safran Group) and academic partners such as University Paris 6, Ecole des Mines ParisTech, Shanghai JiaoTong University, Dortmund Technical University or AGH University of Krakow (Poland).

The international recognition of UTT in the field of damage mechanics and material forming can be seen through the organization by UTT of the 2nd International Congress on Damage Mechanics in 2015 (http://icdm2.utt.fr/) and the 12th International Conference on Numerical Methods in Industrial Forming processes (http://numiform2016.utt.fr/)

Table 1: number of papers published between 2000 and 2016 according to ISI Web of Science with the keyword “ductile damage”. UTT ranks at #2 with 60 papers among other prestigious institutions. The total number of

published papers in this period and indexed in ISI Web of Science is 671. It should be noted that CNRS (rank 1) is not really a laboratories but a group of laboratories (like Chinese Academy of Science).

Table 2: number of papers published between 2000 and 2016 according to ISI Web of Science with the keyword “ESPI”. UTT ranks at #9 with only 16 papers among other prestigious institutions. The total number of published papers in this period and indexed in ISI Web of Science is 990. It should be noted that CNRS (rank 8) is not really

a laboratories but a group of laboratories (like Chinese Academy of Science).

Available equipment: Several optical set-ups for Laser Speckle Pattern Interferometry, including one which

is mounted in-situ on a mechanical testing system

High speed digital holographic microscope

Instrumented nano-indentation system

Two X-ray diffractometers

Numerical microscope

Finite Element codes (ABAQUS, Z-Set).

Every PhD student shares an office with other PhD students. A personal desk is

proposed to each PhD student along with a personal computer and full personal

access to the internet and bibliographic data bases.

PhD supervisors

The PhD work will be supervised jointly by Professor Manuel François and Dr Léa Le Joncour. They have co-supervised one PhD work together: Dr Chengheri Bao (defense in 2016), sponsored by a CSC grant.

Prof. Manuel François, 55, obtained a Master of Engineering from Arts et Métiers ParisTech in 1985, a Master of Science in Metallurgy from University Paris 6 in 1987. He defended his PhD in Arts et Métiers ParisTech in June 1991. After being Associate Professor in University of Nantes from 1993 to 2000, he became full Professor in UTT in 2000 (promoted exceptional class in 2011).He lived one year

in China to teach French language in 1985-1986. He has supervised 18 PhD students and has been involved in 11 others PhD theses. He has published about 248 papers among which 80 in rank A international journals. He has been Dean of the Mechanical Engineering Department of UTT, Development Manager of UTT, member of the Executive Board of UTT and director of the LASMIS research laboratory (51 people, including 21 faculty)

Dr. Léa Le Joncour, 32, obtained a Master of Structure Calculation from Paris-Saclay University in 2007. She defended her PhD in University of Technology of Troyes in 2011. She became an Assistant professor in UTT in September 2012. She already co-directed 2 PhD thesis, and has been involved in 2 others.

In less than 8 years she has performed 6 significant experimental campaigns on Large European Instruments (neutron sources and synchrotron radiation) such as the Center of Accelerators and Nuclear Analytical Method (near Praha), the ISIS research center (near Oxford), ESRF (near Grenoble).

4. Contact and application Prof. Manuel François Tel: +33(0)325 71 56 57 Mail: manuel.francois@utt.fr

The applicant should send his/her detailed CV, a motivation letter, a list of references, a copy of grades sheets and two recommendation letters. Before the final decision, some of the applicants will be interviewed through Skype (or equivalent system).

5. Publications in the last 10 yearsOur publications restricted to the field of ESPI, necking, localization, damage, constitutive behavior and instrumented indentation.

1. Guelorget B., François M., Vial-Edwards C., Montay G., Daniel L., Lu J., Strain rate measurement by Electronic Speckle Pattern Interferometry : a new look at the strain localization onset, Materials Science and Engineering A, 415, n°1-2, 2006, 234-241.

2. Montay G., François M., Tourneix M., Guelorget B., Vial-Edwards C., Lira I., Analysis of plastic strain localization by a combination of the speckle interferometry with the bulge test, Optics and Lasers in Engineering, 45 (2007) 222-228.

3. Montay G., François M., Tourneix M., Guelorget B., Vial-Edwards C., Lira I., Strain and strain rate measurement during the bulge test by electronic speckle pattern interferometry, Journal of Materials Processing Technology, 184 (2007)428-435

4. Guelorget B., François M., Lu J., Microindentation as a local damage measurement technique, Materials Letter, 61 (2007) 34-36

5. Guelorget B., François M., Liu C., Lu J., Extracting the plastic properties of metal materials from microindentation tests: experimental comparison of recently published methods, J. Mater. Res., vol 22, n°6, 2007, 1512-1519.

6. Montay G., Sicot O., Maras A., Rouhaud E., François M., Two dimensions residual stress analysis through incremental groove machining combined with Electronic Speckle Pattern Interferometry, Experimental Mechanics, 49, 2009, 459-469.

7. Guelorget B., François M., Montay G., Strain localization band width evolution by electronic speckle pattern interferometry strain rate measurement, Scripta Materialia 60 (2009) 647-650

8. Petit J., Montay G., François M., Strain rate evolution in aluminium alloy measured by ESPI during tensile test, Materials Science Forum, 614, 2009, 155-162

9. Hfaiedh N., Saanouni K., François M., Roos A., Self consistent intragranular ductile damage modeling in large strain plasticity for FCC polycrystalline materials, Procedia Engineering, 2009, vol. 1, 229-232

10. Petit J., Montay G., François M., Localisation Phenomenon Investigation on SMATed Stainless Steel Samples by Speckle Interferometry. Strain, Vol. 47, issue 4, 2011, 363-371

11. Le Joncour L., Panicaud B., Baczmanski A., François M., Braham C., Paradowska A., Wronski S., Chiron R., Damage in duplex steels studied at mesoscopic and macroscopic scales, Mechanics of Materials 42 (2010) 1048–1063

12. Le Joncour L., Panicaud B., Baczmański A., François M., Braham C., Paradowska A., Large Deformation and Mechanical Effects of Damage in Aged Duplex Stainless Steel, Materials Science Forum, 652, 155-160, 2010.

13. Panicaud B., Saanouni K., Baczmanski A., François M., Cauvin L., Le Joncour L., Theoretical modelling of ductile damage in duplex stainless steels – Comparison between two micro-mechanical elasto-plastic approaches, Computational Materials Science 50 (2011) 1908–1916

14. Panicaud B., Cauvin L., Le Joncour L., Baczmanski A., Saanouni K., François M., Analysis of intergranular interactions during ductile damage – Comparison between micromechanical models and neutron diffraction experiments, Materials Science Forum, vol 681 (2011)91-96

15. Gaj A., Baczmański A., Le Joncour L., Panicaud B., François M., Braham C., Paradowska A., Localization of Stresses in Polycrystalline Grains Measured by Neutron Diffraction and Predicted by Self-consistent Model, Materials Science Forum, vol 681 (2011)103-108, (8th European Conf. on Residual Stresses (ECRS8), June 26th-28th, 2010, Riva del Garda, Italie.)

16. Baczmanski A., Le Joncour L., Panicaud B., Francois M., Braham C., Paradowska A., Wronski S., Amara S., Chiron R., Neutron time-of-flight diffraction used to study aged duplex stainless steel at small and large deformation until sample fracture, Journal of Applied Crystallography, 44 (2011) 966-982.

17. Baczmański A., Le Joncour L., Gaj A., Wroński S., François M., Panicaud B., Braham C., Paradowska A.M., Study of stress localization in polycrystalline grains using self-consistent model and neutron diffraction, Philosophical Magazine, Vol. 92, n°24, 2012, 3015-3035

18. François M., Panicaud B., Le Joncour L., Baczmanski A., Paradowska A., Wronski S., Gadalinska E., Comparison of strain/stress behaviour of duplex stainless steels between mesoscopic and macroscopic scales by neutron measurements including post-necking strains, Thin Solid Films, 530 (2013) 62-65

19. Petit J., Montay G., François M., Strain rate measurements by speckle interferometry for necking investigation in stainless steel, Int. J. of Solids and Structures 51 (2014) 540-550

20. Labergère C., Guelorget B., François M., Strain rate distribution and localization band width evolution

during tensile test, International Journal of Solids and Structures, 51 (2014) 3944-396121. Baczmanski A., Gadalinska E., Wronski S., Braham C., Seiler W., François M., Le Joncour L.,

Panicaud B., Buslaps T., Study of mechanical behaviour of polycrystalline materials at the mesoscale using high energy X-ray diffraction, Advanced Materials Research Vol. 996 (2014) 118-123 (9 th

European Conference on Residual Stresses (ECRS-9), Troyes, France, 7-12 July 2014)22. Bao C., Francois M., Le Joncour L., Influence of Specimen Geometry on Strain Localization

Phenomena in Steel Sheets, Applied Mechanics and Materials Vol. 784 (2015) 514-519. 2nd

International Conference on Damage Mechanics (ICDM2), Troyes, France, July 201523. Li Y., Kanouté P., François M., Disturbance induced by surface preparation on instrumented

indentation test, Materials Science and Engineering A, 642 (2015) 381-39024. Duran A.I., Signorelli J.W., Celentano D.J., Cruchaga M.A., François M., Experimental and numerical

analysis on the formability of a heat treated AA1100 aluminum alloy sheet, Journal of Materials Engineering and Performance, vol. 24, 10 (2015) 4156-4170

25. Baczmański A., Zhao Y., Gadalińska E., Le Joncour L., Wroński S., Braham C., Panicaud B., François M., Buslaps T., Soloducha K., Elastoplastic deformation and damage process in duplex stainless steels studied using diffraction and self-consistent model, International Journal of Plasticity, 81(2016)102-122.

26. Bao C., François M., Le Joncour L., A closer look at the diffuse and localized necking of a metallic thin sheet evolution of the two bands pattern, Strain, 52 (2016) 244-260.

27. Zhu Y., Vaillant J., François M., Montay G., Bruyant A., Co-axis digital holography based on sinusoidal phase modulation using generalized lock-in detection, Applied Optics, vol. 56, n°13, 2017, F97-F104.

28. Baczmański A., Marciszko M., Wroński S., Wróbel M., Zhao Y., Francois M., Panicaud B., Le Joncour L., Tokarski T., Micromechanical behaviour of a two-phase Ti alloy studied using in-situ grazing incidence diffraction and a self-consistent model, accepted in Acta Materialia 2017.