iMechanica - Expansion
https://imechanica.org/taxonomy/term/6095
enExpansion behavior of cellular solids
https://imechanica.org/node/13052
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/609">homogenization</a></div><div class="field-item odd"><a href="/taxonomy/term/1101">swelling</a></div><div class="field-item even"><a href="/taxonomy/term/2173">anisotropy</a></div><div class="field-item odd"><a href="/taxonomy/term/4540">cellular materials</a></div><div class="field-item even"><a href="/taxonomy/term/6004">cellular solids</a></div><div class="field-item odd"><a href="/taxonomy/term/6095">Expansion</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
The expansion behavior of cellular materials is especially attractive for potential applications such as design and development of bio-inspired adaptive materials since most of biological materials have a cellular microstructure at least at one of their hierarchical levels. Wood, bone, bamboo, ice plant and honeybee combs are examples of such natural materials.
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The thermal expansion or hygro-expansion (sometimes referred to as swelling coefficient) of cellular solids are not studied to the same extent as mechanical properties such as elastic behavior, strength, buckling, etc. Lakes and co-workers proposed different configurations of cellular materials with extreme thermal expansions. These models are mainly composed of bi-layer cell walls with contrasting expansion ratio which induces a non-affine deformation in the structure under uniform temperature increase. Inspiring from anisotropic swelling behavior of wood cells, we recently investigated with finite element based homogenization the effective (hygro-)expansion of honeycombs and some interesting trends are captured:
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<span><a href="http://dx.doi.org/10.1016/j.compstruct.2012.08.017">http://dx.doi.org/10.1016/j.compstruct.2012.08.017</a></span>
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<span><a href="http://dx.doi.org/10.1016/j.mechmat.2012.08.002">http://dx.doi.org/10.1016/j.mechmat.2012.08.002</a></span>
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The degree of anisotropy is dependent on the geometry and also the material properties of the cell wall. We can control the anisotropic expansion of cellular materials by tuning the material properties of the cell wall which is promising for stimuli-responsive actuation devices. The cell walls might be intrinsically anisotropic or composed of different isotropic layers with contrasting expansion behavior.
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So far, similar to those relations proposed by Ashby and Gibson for elastic moduli of honeycombs and other cellular solids are not available for thermal or hygro-expansion coefficients. Development of analytical models will enable us to improve our understanding of the expansion behavior of cellular solids.
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</div></div></div>Sun, 02 Sep 2012 00:18:39 +0000Ahmad Rafsanjani13052 at https://imechanica.orghttps://imechanica.org/node/13052#commentshttps://imechanica.org/crss/node/13052Coefficient of Thermal Expansion (CTE) for Carbon Nanofibers
https://imechanica.org/node/9962
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/460">nanocomposites</a></div><div class="field-item odd"><a href="/taxonomy/term/1112">thermal</a></div><div class="field-item even"><a href="/taxonomy/term/1821">Polymer nanocomposites</a></div><div class="field-item odd"><a href="/taxonomy/term/2347">carbon</a></div><div class="field-item even"><a href="/taxonomy/term/2455">residual stresses</a></div><div class="field-item odd"><a href="/taxonomy/term/6092">Vapor</a></div><div class="field-item even"><a href="/taxonomy/term/6093">Grown</a></div><div class="field-item odd"><a href="/taxonomy/term/6094">Nanofibers</a></div><div class="field-item even"><a href="/taxonomy/term/6095">Expansion</a></div><div class="field-item odd"><a href="/taxonomy/term/6096">Coefficient</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Dear iMechanica community,
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One of the biggest difficulties of performing a processing conditions related residual stress analysis and subsequent interfacial fracture assessment for carbon nanofiber containing polymer nanocomposites (especially with aerospace grade epoxies) is the lack of adequate information concerning the range of attainable values of CTEs (Coefficient of Thermal Expansion) for different types of carbon nanofibers. Clearly, the micro-, nanostructure of the nanofiber interior (i.e. orientation of annular graphene layers with respect to the fiber axis, their spacing, defect size/distribution, concentration of synthesis related impurities such as substitutional catalyst particles, the ratio of graphitic/turbostratic contents etc.) and geometric factors such as the extent of the hollow concentric region in case of tubular structures have a combined effect on the resulting CTE range. To circumvent this difficulty I did some first principles based thermomechanical analysis and decided to share the preliminary results with our community to collect your feedback. I think these initial CTE estimates can be implemented with some moderate confidence for predominantly sp2-bonded 1-D carbon nanostructures (nanotubes/nanofibers/nanorods) within the diameter range of 30-500 nm. Also note that a simple sensitivity analysis indicates that the angle between the fiber axis and the inward normal of the basal planes of graphene is the most influential factor in determining the CTE. Let me also note that I set the limits of this orientation angle to 30 and 90 degrees in my analysis and did not consider any periodic/aperiodic waviness of the 1-D structure or localized amorphous carbon presence in the composition. Under these gross assumptions, the values I am getting are the following:
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Coefficient of thermal expansion (CTE) range for carbon nanotubes (CNTs) and carbon nanofibers (CNFs):
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2.7 x 10-6 (1/K) to 4.4 x 10-6 (1/K)
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I looked at the existing literature to see whether these values make any sense and found an experimental paper which mentions a CTE value for the vapor grown carbon nanofibers within the same diameter range as the one in my analysis:
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"Temperature Dependence of Electrical Resistivity in Carbon Nanofiber/Unsaturated Polyester Nanocomposites" by Natsuki, Ni and Wu, published in Polymer Engineering and Science (2008).
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Their value was close to my upper bound with 4 x 10-6 (1/K). If you are aware of CTE values which fall within the above mentioned range or simply want to share your own estimates please reply to this blog. By exchanging ideas and sharing different perspectives on this topic, we can achieve much more in terms of technical and scientific accuracy of these CTE values for carbon nanostructures.
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With my best regards,
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Tanil Ozkan
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</div></div></div>Thu, 17 Mar 2011 05:57:05 +0000TANIL OZKAN9962 at https://imechanica.orghttps://imechanica.org/node/9962#commentshttps://imechanica.org/crss/node/9962