Biomimetic structures for mechanical applications by interfering laser beams: More than solely holographic gratings
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A variety of biological materials composed of hierarchical phase composites can be found. These biological materials successfully combine impressive toughness with high stiffness and strength. Deposition techniques combined with high-power laser beams can imitate biological structures in technical systems. Interference phenomena, such as surface scattering, Lloyd’s mirror arrangements, or interference of coherent beams, can be used to create these biomimetic long-range ordered structures on the scale of nanometers to micrometers. These structures are not limited to topographic texturing, as in the case of holographic gratings; rather, they can also create composite structures and phase transformations. This article presents a brief overview of interference techniques, their possibilities, and their limits.
I. INTRODUCTION A. Periodic biological structures
In nature, a huge variety of structures exhibit either mechanical stability or dynamic surface and functional properties. Bone is the most researched biological high-strength and light-weight material1–3 (Fig. 1), but other materials with optimized mechanical properties can also be found in nature, e.g., nacre or shells.4–6 Bone material shows a complex hierarchical structure with a short-range ordered distribution of fibers and particles and a long-range ordered periodic structure on each of several hierarchical levels, from nanometers to micrometers and even as large as millimeters.2,7–9 The smallest structures are periodically staggered mineral nano-crystals in a collagen matrix. Their mechanical behavior has been analyzed and modeled by Jäger and Fratzl.3 The scaling behavior of periodic laser-structured surfaces was further analyzed by Daniel et al.10 B. Scaling effect in the natural bone system
Jäger and Fratzl intensively analyzed the mechanical behavior of bone.3 The principal model consists of staggered mineral crystals in a collagen matrix and is shown in Fig. 2. The staggered mineral crystals have significantly higher stiffness than the matrix, and an applied strain will mainly be accommodated in the matrix. The a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0256 2098 http://journals.cambridge.org
primary structure can be quantified by the length and the width of the crystals and their spacing. If an elastic load is imposed, a virtual dimensionless Young’s modulus E⬘, parallel to the staggered crystals, can be calculated as the sum of two pairs of tensile and shear stress states3: E⬘ =
冉 冊冉 冊 冉 冊冉 c d
l+a 1 b + a 2 d
l+a +1 a
冊
tensile stress states
冉 冊冉 冉 冊冉
冊 冊
共1 − a兲共l + a兲 1+
+
1 1 8 bd
+
1 1 4 共d + b兲d
a共l + a兲 1+
,
shear stress states
where a is the length of the mineral crystals, b is the perpendicular distance of the mineral crystals, c is the crystal width, d is the overall spacing of the mineral crystals (i.e., d ⳱ b + c), l is the crystal length, and is Poisson’s ratio. A contour plot of Young’s modulus as a function of the composite’s dimensions b and c is shown in Fig.
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