Assoc. Prof. Dr. Cihan Tekoğlu

Department of Mechanical Engineering
  TOBB University of Economics and Technology
Söğütözü Cad. No: 43,
Söğütözü, Ankara, 06560 TURKEY
e-mail: cihantekoglu@etu.edu.tr
phone: +90 (312) 292 40 65
fax: +90 (312) 292 40 91


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My research interests span different areas of macro/micro mechanics of materials, with a particular focus on metamaterials, and understanding and improving the fracture behaviour of metals and composites. Although my main work is devoted to theoretical and computational mechanics, I have recently started conducting experimental studies as well. In the following, I briefly state my expertise and give an outlook on my future research plans.

Metamaterials
Evolutionary optimization has led natural materials to have remarkably efficient mechanical properties: wood has a specific strength comparable with that of the strongest steel, the fracture toughness of bone is an order of magnitude larger than engineering ceramics, etc. Yet, there is nothing special about the mechanical properties of the individual blocks, but it is the arrangement of these building blocks, i.e. the micro-architecture, which optimizes the mechanical performance. The ever-increasing demand for multi-functional engineering materials forces scientists and engineers to develop novel strategies to combine usually contradicting properties, such as high strength and high ductility, or high stiffness and low actuation energy, in a single material. Some topics of interest for me are:

Figure 1: Size-effects observed for 2D Voronoi microstructures under different loading conditions. The contour plots show typical strain localization patterns [4].
Cellular solids, which are a relatively new class of engineering materials with a great potential to be used in strong, stiff and lightweight structures. Despite their superior bulk properties, if one of the structural dimensions of a cellular solid has the same order of magnitude as the cell size, the effectivemacroscopic response of the solid is dictated by the individual excitements of the cells, which results in size-dependent mechanical properties [1]. In order to understand the effect of the cellular morphology on the mechanical behaviour, we performed finite element (FE) calculations on model materials [2, 3, 4], see e.g. Fig. 1. By comparing the results with generalized continuum theories, which incorporate a length scale to capture size effects, we critically assessed the capabilities of different theories in the elastic deformation range. The best agreement is obtained for the strain divergence theory that we proposed, where the divergence of strain is taken as an additional deformation measure [3].

Design of multi-functional materials, which combine mechanical functions (such as stiffness and strength) witho ther properties (such as thermal or electrical conductivity, shape changing capability, etc.). Recent studies have shown that some lattice materials (e.g. two-dimensional (2D) Kagome structure and its 3D equivalent [5]) have a great potential to be used in multi-functional applications: if one of the lattice elements (i.e. beams or rods) is replaced with an actuator, the material can undergo large shape changes when the actuator is deployed, while it provides stiffness against external loads when the actuator is not triggered. The Kagome lattice is a member of the family of semi-regular tessellations of the plane. Two fundamental questions naturally arise: i-) What makes a lattice material suitable for actuation? ii-) Are there other tessellations more effective than the Kagome lattice for actuation? In order to answer these questions, we first established a set of topological criteria to identify micro-architectures suitable for actuation [6], and determined the sufficient symmetry conditions for isotropy of elastic moduli [7]. We then contrived four novel 2D in-plane isotropic lattice materials in light of these criteria [8], see Fig. 2. One of the proposed designs (the Double Kagome lattice, see Fig. 2c) is found to match the optimal elastic properties of the Kagome structure, while it requires less energy for (single member) actuation. The only downside of the DK lattice appears to be that the displacement field induced by actuation attenuates faster than in a Kagome lattice, meaning that the DK lattice has a lower shape changing capacity.


Figure 2: The four newly contrived 2D lattice materials: (a) Kagome with concentric triangles (KT), (b) Kagome with concentric hexagons (KH), (c) Double Kagome (DK), and (d) the Modified Dodecagonal structure (MD).
My quest for stiff/strong shape-morphing lattice materials progresses with fruitful outcomes. Recently, I designed two different families of 2D in-plane isotropic lattice materials, and some members of both families turned out to possess a negative Poisson ratio (NPR). Owing the their underlying architecture, NPR materials offer attractive mechanical properties. For example, unlike a positive Poisson ratio bar or plate, which assumes a saddle shape when bent, NPR materials take convex shapes that are more appropriate for sandwich panels for aircraft or automobiles, see e.g. [9, 10]. With their high resistance to shear and indentation, and high energy absorption capacity and toughness, NPR materials have a large potential to be used in different applications such as fasteners and rivets, sensors, medical applications (e.g. artificial blood vessels), bullet-proof helmets and vests, intelligent textiles, internal structure for adaptive airplane wing box configurations, etc. My research group currently characterizes the mechanical properties of the NPR materials that I designed. These new materials cover a relatively large range of different NPR values, and some of them

have higher stiffness values compared to the existing 2D NPR lattices. In the long term, I am planning to extend (some) of these 2D lattice designs to 3D, that could for example be used in crashworthiness applications.

Ductile fracture of metals and composites
The mechanical properties of structural metallic alloys are continually improved such that cleavage and intergranular fracture mechanisms are mostly successfully avoided, leaving ductile fracture as the main failure mechanism upon overloading. Therefore, together with fatigue and corrosion, ductile fracture is the key ingredient in structural integrity assessment of metals. Most of the ductile fracture models in the literature neglect the presence of second-phase particles and make use of phenomenological stress and/or strain controlled void nucleation laws, where the nucleation stress/strain values are defined with respect to the overall values in the material, and not to the local field quantities in the particles or along the particle-matrix interfaces. If, however, the particle volume fraction is larger than 5-10 %, neglecting the presence of the particles leads to dramatically poor estimates for the fracture strain. In order to explicitly account for the effect of second phase particles on the ductile fracture process, we integrated a damage model based on the Gologanu-Leblond-Devaux (GLD) constitutive behavior with a mean-field homogenization scheme [11]. The integrated model is able to account for the per-phase and overall stress/strain response of the material, and, as importantly, for the softening induced by particle fracture or decohesion, which cannot be captured by regular Gurson type models due to a lack of coupling between void nucleation and particle response [12]. The proposed model is shown to successfully predict the fracture strain of dual-phase (DP) [13]. I have successfully completed a project funded by The Scientific and Technological Research Council of Turkey (T¨UB˙I TAK), entitled “Microstructural optimization of dual-phase (DP) steels”, and I am planning to extend the approach we used to study the DP steels to a wide class of metallic alloys, such as TRIP steels and Titanium alloys.

In order to address the effect of crystal plasticity on growth and coalescence of voids in single crystals, we performed a large set of FE calculations on 3D representative unit cells containing a spherical void. We were able to predict the onset of void coalescence by using the Thomason criterion—which was initially developed in the framework of isotropic perfect plasticity—within 20 % relative error for most cases, and often more accurately [14]. A more challenging task is to provide a constitutive damage model that can account for plastic anisotropy. For this purpose, we coupled the Gurson model with an anisotropic yield criterion, the Facet method, which successfully represents the yield surfaces of both single and polycrystals, even for sharp crystallographic textures [15].

I have also contributed to the extension of the GLD model to account for the rotation of the voids. We proposed a void rotation law and showed that it gives excellent agreement with 3D unit cell calculations [16]. We have also coupled the GLD damage model with a more realistic, Kocks-Mecking type strain hardening law, which explicitly takes into account the two main strain hardening stages observed in metals, referred to as stage III and stage IV in the literature. The predictions of this extended damage model are in very good agreement with the results of the FE voided unit cell calculations [17]. A comprehensive summary for a part of my work on fracture mechanics is explained in a review paper [18].

Although there exists fairly accurate (theoretical/numerical) models for void growth, especially for isotropic materials, proper treatments of void nucleation and localization of plastic deformation leading to final failure are still open research topics. An important part of my work concerning fracture mechanics is therefore devoted to the development ofmicroscopic localization (i.e. void coalescence) criteria incorporating the effect of shear loads [19, 20], and the effect of the presence of a secondary family of voids/particles [21]. I have also worked on macroscopic plastic localization dominated failure, which led to the important conclusion that: “At sufficiently high stress triaxiality, a clear separation exists between the macroscopic and microscopic modes of localization. At lower stress triaxialities, however, the onset of macroscopic localization and coalescence occurs simultaneously” [22]. All these studies on localized deformation gave me the opportunity to build a robust FE framework for performing representative volume element calculations under constant stress triaxiality, Lode parameter, and shear ratio [23]. I have ongoing studies on failure under low stress triaxiality, with a particular interest on the effect of “shear ratio” on ductile fracture. An ambitious target for me is to develop a localization model for randomly distributed and oriented voids/particles under general loading conditions.

Another challenging topic in the field of ductile fracture is the effect of volume fraction, shape, size and spatial distribution of second phase particles on the crack propagation mechanisms. I have recently completed a project funded by T¨UB˙ITAK, entitled “A numerical and experimental investigation of crack propagation mechanisms in ductile metal plates”. The main conclusion of this study was that “large particles with a large volume fraction lead to a slanted or a cupcone crack, while small particles with a small volume fraction lead to a cup-cup fracture surface morphology for ductile plates teared under mode I loading (see Fig. 3)”, which we were able
to demonstrate both in an experimental [24] and in a numerical framework [25].


(a)                                                                                                           (b)
Figure 3: A scanning electron fractograph for a: (a) 1 mm-thick plate with a cup-cup crack, and (b) 5 mm-thick plate with a slanted crack (see also [24]).
References
[1] C. Tekoğlu, 2007. Size effects in cellular solids. PhD Thesis, University of Groningen, The Netherlands. (url)
[2] C. Tekoğlu, P. R. Onck, 2005. Size effects in the mechanical behavior of cellular materials. J. Mater. Sci. 40, 5911-5917. (url)
[3] C. Tekoğlu, P. R. Onck, 2008. Size effects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models. J. Mech. Phys. Solids 56, 3541-3564. (url)
[4] C. Tekoğlu, L. G. Gibson, T. Pardoen, P. R. Onck, 2011. Size effects in foams: Experiments and modeling. Prog. Mater. Sci. 56, 109-138 (url)
[5] N. A. Fleck, V. S. Deshpande and M. F. Ashby, 2010. Micro-architectured materials: past, present and future. Proc. R. Soc. A. (published online). (url)
[6] T. N. Pronk, C. Ayas, C. Tekoğlu, 2017. A quest for 2D lattice materials for actuation. J. Mech. Phys. Solids 105, 199-216. (url)
[7] C. Ayas, C. Tekoğlu, 2018. On the sufficient symmetry conditions for isotropy of elastic moduli. J. Appl. Mech. 85, 074502-074502-5. (url)
[8] W. E. D. Nelissen, C. Ayas, C. Tekoğlu, 2019. 2D lattice material architectures for actuation. J. Mech. Phys. Solids 124, 83-101. (url)
[9] S. R. Lakes, 1993. Advances in negative Poisson’s ratio materials Advanced Materials 5, 293-296. (url)
[10] S. R. Lakes, 2017. Negative-Poisson’s-Ratio Materials: Auxetic Solids Annual Review of Materials Research 47, 63-81. (url)
[11] M. Inanc, T. Pardoen, C. Tekoğlu, 2015. An Enhanced Mori-Tanaka Homogenization Scheme for Incremental, Non-Linear Rate-Independent Plasticity. In: Proceedings of the 5th ECCOMAS Thematic Conference on the Mechanical Response of Composites, COMPOSITES 2015, 07-09 September, 2015, University of Bristol, UK [CD-ROM].
[12] C. Tekoğlu, T. Pardoen, 2010. A micromechanics based damage model for composite materials. Int. J. Plasticity 26, 549-569. (url)
[13] A. P. Pierman, C. Tekoğlu, T. Pardoen, P. J. Jacques, 2009. Nucleation, growth and coalescence of voids in dual phase steels: from model microstructures to microstructure based modeling. In: Proceedings of the 12’th International Conference on Fracture, Ottawa, Canada [CD-ROM].
[14] S. K. Yerra, C. Tekoğlu, F. Scheyvaerts, L. Delannay, P. Van Houtte, T. Pardoen, 2010. Void growth and coalescence in single crystals. Int. J. Solids Structures 47, 1016-1029. (url)
[15] S. K. Yerra, C. Tekoğlu, A. Van Bael, L. Delannay, P. Van Houtte, T. Pardoen, 2010. The Facet-Gurson model for ductile damage process. In: 18’th European Conference on Fracture, August 30 - September 03, 2010, Dresden, Germany, [CD-ROM].
[16] F. Scheyvaerts, P. R. Onck, C. Tekoğlu, T. Pardoen, 2011. The growth and coalescence of ellipsoidal voids in plane strain under combined shear and tension. J. Mech. Phys. Solids 59, 373-397 (url)
[17] L. Lecarme, C. Tekoğlu, T. Pardoen, 2011. Void growth and coalescence in ductile solids with stage III and stage IV strain hardening. Int. J. Plasticity 27, 1203-1223. (url)
[18] T. Pardoen, F. Scheyvaerts, A.Simlar, C. Tekoğlu, P. R. Onck, 2010. Multiscale modeling of ductile failure in metallic alloys. C. R. Physique 11, 326-345. (url)
[19] C. Tekoğlu, J.-B. Leblond, T. Pardoen, 2012. A criterion for the onset of void coalescence under combined shear and tension. J. Mech. Phys. Solids 60, 1363-1381. (url)
[20] M.E. Torki, C. Tekoğlu, J.-B. Leblond, A.A. Benzerga, 2017. Theoretical and numerical analysis of void coalescence in porous ductile solids under arbitrary loadings. Int. J. Plasticity 91, 160-181. (url)
[21] C. Tekoğlu, 2015. Void coalescence in ductile solids containing two populations of voids. Eng. Fract. Mech. 147, 418-430. (url)
[22] C. Tekoğlu, J.W. Hutchinson, T. Pardoen, 2015. On localization and void coalescence as a precursor to ductile fracture. Philos. T. R. Soc. A. 373, 1-9. (url)
[23] C. Tekoğlu, 2014. Representative volume element calculations under constant stress triaxiality, Lode parameter, and shear ratio. Int. J. Solids Struct. 51, 4544–4553. (url)
[24] C. Tekoğlu, S¸ . C¸ elik, H. Duran,M. Efe, K. L. Neilsen, submitted. Experimental Investigation of Crack Propagation Mechanisms in Commercially Pure Aluminium Plates. To: Proceedings of 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials (IWPDF2019), August 22-23, 2019, Ankara, Turkey.
[25] C. Tekoğlu, K. L. Nielsen, 2019. Effect of damage-related microstructural parameters on plate tearing at steady state. Eur. J. Mech. A-Solid. Advance online publication. (url)

Room No.: 120; Phone: +90 (312) 292 40 65; Fax: +90 (312) 292 40 91; e-mail: cihantekoglu@etu.edu.tr