High-strength cellular ceramic composites with 3D microarchitecture Jens Bauera,1, Stefan Hengsbachb, Iwiza Tesaria, Ruth Schwaigera, and Oliver Krafta aInstitute for Applied Materials and bKarlsruhe Nano Micro Facility, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany Edited* by William D. Nix, Stanford University, Stanford, CA, and approved January 9, 2014 (received for review August 12, 2013) To enhance the strength-to-weight ratio of a material, one may try Cellular topologies may be divided into bending- and stretch- to either improve the strength or lower the density, or both. The ing-dominated ones (8). Foams generally behave in a bending- lightest solid materials have a density in the range of 1,000 kg/m3; dominated manner (1, 8, 9). When abstracted to pin-jointed only cellular materials, such as technical foams, can reach consid- frameworks, open-cell foams consist of unit cells that are stati- erably lower values. However, compared with corresponding bulk cally indeterminate (8), e.g., cubic cells. Their topology would materials, their specific strength generally is significantly lower. allow the struts to rotate around the joints leading to a collapse Cellular topologies may be divided into bending- and stretching- under loading (11). However, the joints of foams are frozen dominated ones. Technical foams are structured randomly and rather than pin-jointed, causing the struts to bend. Gibson and behave in a bending-dominated way, which is less weight effi- Ashby (1) showed that the mechanical properties of such bend- ρp=ρ cient, with respect to strength, than stretching-dominated behav- ing-dominated foams depend on the relative density, s, where ρp ρ ior, such as in regular braced frameworks. Cancellous bone and and s are the densities of the foam and the corresponding other natural cellular solids have an optimized architecture. Their solid material, respectively. The compressive strength of the foam basic material is structured hierarchically and consists of nanometer- ðρp=ρ Þ1:5 scales with s or even with higher exponents, depending size elements, providing a benefit from size effects in the material on the failure mechanism. strength. Designing cellular materials with a specific microarch- Stretching-dominated structures are considered to have much itecture would allow one to exploit the structural advantages of better mechanical properties (8, 9, 12). The struts of a frame- stretching-dominated constructions as well as size-dependent work, which is rigid when regarded as pin-jointed, are loaded in strengthening effects. In this paper, we demonstrate that such mate- tension or compression largely without bending (8). In two rials may be fabricated. Applying 3D laser lithography, we produced dimensions, a triangle is the only statically determinate polygon. and characterized micro-truss and -shell structures made from alu- In three dimensions, fully triangular structures, such as tetrahe- mina–polymer composite. Size-dependent strengthening of alumina dral truss constructions as initially developed by Bell (13), reach shells has been observed, particularly when applied with a character- a maximum of rigidity and stretching-dominated behavior (8). istic thickness below 100 nm. The presented artificial cellular materi- Designing foam materials in such a manner facilitates a linear als reach compressive strengths up to 280 MPa with densities well scaling behavior of the strength and the stiffness with the relative 3 below 1,000 kg/m . density (8, 9). However, the specific properties of bulk material still are not quite reached (9). he suitability of a material for lightweight applications is Bone and other biological materials with a similar funda- Tdetermined mainly by two properties: the specific strength mental structure, such as shells (14) and teeth (15), achieve and the specific stiffness, here defined as the strength and stiff- improved strength of their basic material as a result of the ap- ness of a material divided by its density. In the past century, pearance of mechanical size effects (16). On the lowest level of major advancements have been made in optimizing classical hierarchy, bone consists of mineral crystal platelets with thickness lightweight materials, such as aluminum alloys or composite materials, with respect to these properties. However, the lightest Significance solid materials have a density in the range of 1,000 kg/m3 (1). Natural lightweight materials, such as bone and wood, are not It has been a long-standing effort to create materials with low fully dense and may exhibit considerably lower values (1). They density but high strength. Technical foams are very light, but contain several levels of hierarchical structuring down to the compared with bulk materials, their strength is quite low be- – nanometer scale (1 3), leading to remarkable specific mechani- cause of their random structure. Natural lightweight materials, – cal properties (1 4). For instance, cancellous bone is built of such as bone, are cellular solids with optimized architecture. truss- or shell-like framework architectures grown adaptively to They are structured hierarchically and actually consist of ENGINEERING the loading situation (5, 6). The material thickness and the ori- nanometer-size building blocks, providing a benefit from me- entation of the individual structural elements depend on the chanical size effects. In this paper, we demonstrate that magnitude and orientation of loading. This leads to an optimized materials with a designed microarchitecture, which provides topology, in which each structural element is aligned with the both structural advantages and size-dependent strengthening principal stress trajectories (5, 6). effects, may be fabricated. Using 3D laser lithography, we Technical foams are materials with open- or closed-cell po- produced micro-truss and -shell structures from ceramic–poly- rosity of comparable low density and are used in lightweight mer composites that exceed the strength-to-weight ratio of all components, such as foam-core sandwich panels (1, 7). However, engineering materials, with a density below 1,000 kg/m3. their specific strength and stiffness are limited by their charac- teristic stochastic architecture. Typically, considerably lower Author contributions: J.B., I.T., and O.K. designed research; J.B., S.H., and R.S. performed values of specific strength and stiffness compared with the cor- research; J.B., S.H., I.T., and O.K. analyzed data; and J.B. wrote the paper. responding bulk materials are reached (1, 7). In addition to the The authors declare no conflict of interest. material properties, the architecture strongly affects the me- *This Direct Submission article had a prearranged editor. chanical behavior of such cellular solids (1, 8, 9). Buckling, in- Freely available online through the PNAS open access option. homogeneity, and local stress concentrations (10) occur, because 1To whom correspondence should be addressed. E-mail: [email protected]. foams cannot be considered only as materials but also as struc- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. tures (1, 7). 1073/pnas.1315147111/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1315147111 PNAS | February 18, 2014 | vol. 111 | no. 7 | 2453–2458 Downloaded by guest on September 30, 2021 on the order of a few nanometers integrated in a collagen matrix with design control down to the nanometer scale. We describe the (17). The strength of both ductile (18) and brittle (19–21) materials design, processing, and mechanical characterization of several ce- typically increases with decreasing dimensions. In the early 20th ramic–polymer composite structures with submicron feature size. century, Griffith (22) proposed the relationship Although to date 3D-DLW is strongly limited in achievable sample volume, it allows for production of almost arbitrary polymeric ge- σ ∝ p1ffiffiffi [1] ometries (26). In conjunction with coating techniques, such as f c atomic layer deposition (ALD) (27), multimaterial composites (28),aswellasmetallic(29)orceramic(30)structuresinwhichthe between the fracture strength, σf , and the critical size of a flaw, c, polymer has been removed, may be fabricated. We present truss for brittle materials such as ceramics. A flaw cannot be larger constructions with different structuralpropertiesaswellasashape- than the component in which it is located. Assuming c correlates optimized honeycomb design (Fig. 1). All structures were fabri- with the material thickness, t, of a structural element (16), Eq. 1 cated from polymer (IP-Dip; Nanoscribe GmbH) by 3D-DLW and may be written as homogeneously coated with alumina (Al2O3)layersofdifferent thicknesses using ALD. The alumina coating carries tensile and 1 compressive forces, whereas the light polymeric core serves to σf ∝ pffiffi : [2] t prevent early face buckling and to improve toughness. For me- chanical characterization, uniaxial in situ and ex situ compression Thus, the smaller the component, the higher is its fracture tests were performed. strength. It has been argued that when fabricated thin enough, When coatings were applied with a characteristic thickness materials might even exhibit strength values close to the below 100 nm, a substantial increase was observed in the mate- theoretical strength when a critical thickness in the nanometer rial strength of alumina. Surpassing all technical foam materials, range is reached (16). Assuming that failure no longer is gov- the trusses reach compressive strength