Scale Effects in Cellular Metals
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Scale Effects in
Cellular Metals P.R. Onck
Abstract Scale effects in cellular metals can develop when the specimen size is of the order of the cell size. Decreasing the relevant specimen dimensions—height, width, and ligament size (the region between notches in notched specimens)—leads to material strengthening in shear, in indentation, and in notched specimens and to reduced strength and stiffness in uniaxial compression. Experimental size-effect studies were reviewed, and it was concluded from discrete modeling results that scale effects are caused by two different microstructural mechanisms: boundary-layer effects and constraint effects. The first mechanism is active in shear (strong boundary layers) and uniaxial compression (weak boundary layers) and vanishes for specimens larger than two cell sizes and seven cell sizes, respectively. The second mechanism is active in indentation and in notched specimens, leading to a strengthening behavior that is inversely proportional to indenter and ligament size.
of 2. For the closed-cell foam (Alporas), square prisms with a height-to-width ratio of 2 were used. The specimen geometry was kept fixed, while the absolute dimensions were varied. To avoid the effects of early localized plasticity, the unloading modulus was measured for greater accuracy. Figure 1a shows the unloading modulus E* normalized by the bulk value E*bulk valid for very large specimens (E*bulk 943 MPa for Alporas and E*bulk 368 MPa for Duocel). The normalized Young’s modulus was plotted against specimen size L normalized by the cell size d (d 3 mm for Duocel and d 4.5 mm for Alporas). Each
Keywords: cellular metals, mechanical properties, size effects.
Introduction Cellular metals are emerging as a new class of engineering materials with high potential in sandwich structures, energy absorption, and heat dissipation.1,2 They inherit their attractive thermomechanical properties directly from their cellular microstructure. Most commercial metallic foams have cell sizes ranging roughly from 1 mm to 10 mm. Reduction of the cell size to 1 mm is often restricted due to manufacturing constraints. This means that in many applications, the components can have dimensions of only a few cell sizes. Consequently, the cell size becomes an essential length scale in the problem, making the mechanical behavior of cellular solids scale-dependent. An important manifestation of scale dependency is the occurrence of size effects in the mechanical testing of metallic foams. The term ”size effect” designates the influence of the specimen size, relative to the cell size, on mechanical properties like stiffness and strength. Recent experimental studies3,4 have shown that under uniaxial compression, stiffness and strength decrease with decreasing specimen size. Alternatively, in the case of simple shear3,5 and indentation,3,6 strength increases with decreasing specimen/indenter size, as explained in the discussion section of this article.
MRS BULLETIN/APRIL 2003
Another manifestation of scale dependency is the effe
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