Formulas for Stress and Strain

Roark, Raymond J.; Young, W. C.; Plunkett, R.

doi:10.1115/1.3423917

Cited by 879 publications

(648 citation statements)

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“…They used analytical methods based on the beam theories of Timoshenko and Goodier [19], and Roark and Young [20] to relate several properties (the modulus and plastic yield strength, amongst others) of a foam under compression or tension to its relative density, ρ * . The relationships put forward by…”

Section: A the Gibson-ashby Modelmentioning

confidence: 99%

Mechanical Properties of Ti-6Al-4V Selectively Laser Melted Parts with Body-Centred-Cubic Lattices of Varying cell size

et al. 2015

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. (2015) Mechanical properties of Ti-6Al-4V selectively laser melted parts with body-centred-cubic lattices of varying cell size. Experimental Mechanics, 55 (7). pp. 1261 -1272 . ISSN 1741 -2765 Access from the University of Nottingham repository: http://eprints.nottingham.ac.uk/31973/1/Accepted_manuscript.pdf Copyright and reuse:The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence. For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdf A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk Significant weight savings in parts can be made through the use of additive manufacture (AM), a process which enables the construction of more complex geometries, such as functionally graded lattices, than can be achieved conventionally. The existing framework describing the mechanical properties of lattices places strong emphasis on one property, the relative density of the repeating cells, but there are other properties to consider if lattices are to be used effectively. In this work, we explore the effects of cell size and number of cells, attempting to construct more complete models for the mechanical performance of lattices. This was achieved by examining the modulus and ultimate tensile strength of latticed tensile specimens with a range of unit cell sizes and fixed relative density. Understanding how these mechanical properties depend upon the lattice design variables is crucial for the development of design tools, such as finite element methods, that deliver the best performance from AM latticed parts. We observed significant reductions in modulus and strength with increasing cell size, and these reductions cannot be explained by increasing strut porosity as has previously been suggested. We obtained power law relationships for the mechanical properties of the latticed specimens as a function of cell size, which are similar in form to the existing laws for the relative density dependence. These can be used to predict the properties of latticed column structures comprised of body-centred-cubic (BCC) cells, and may also be adapted for other part geometries. In addition, we propose a novel way to analyse the tensile modulus data, which considers a relative lattice cell size rather than an absolute size. This may lead to more general models for the mechanical properties of lattice structures, applicable to parts of varying size.

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Section: A the Gibson-ashby Modelmentioning

confidence: 99%

Mechanical Properties of Ti-6Al-4V Selectively Laser Melted Parts with Body-Centred-Cubic Lattices of Varying cell size

et al. 2015

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“…8 The effect of the stripping of the shells on an increase of MWNT flexibility can be evaluated by calculating the bending stiffness ͑flexural modulus͒ of the MWNT. The bending stiffness for the MWNT tip is given by 46 k NT = 3 Er 4 4l 3 . ͑2͒…”

Section: Force-distance Curvesmentioning

confidence: 99%

Adhesion and friction of a multiwalled carbon nanotube sliding against single-walled carbon nanotube

et al. 2008

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The adhesion and friction at crossed nanotube junctions were investigated in ambient by using an atomic force microscope ͑AFM͒ in tapping mode. A multiwalled carbon nanotube ͑MWNT͒ tip attached to a conventional AFM probe was scanned across a single-walled carbon nanotube ͑SWNT͒ suspended over a 2-m-wide trench. The interaction between nanotubes was found to critically depend on the morphology of the MWNT tip, which was determined from force-distance curves and scans performed against hard trench surface. The interaction between nanotubes caused the attenuation of vibrational amplitude of AFM cantilever, from which the frictional force between nanotubes was obtained by analyzing the dissipated vibrational power of cantilever. The adhesive force between nanotubes was measured from the vertical cantilever deflection when the MWNT tip end detached from the shell of the SWNT. From the friction and adhesion data, an experimental value of coefficient of friction of 0.006Ϯ 0.003 is obtained for the sliding between nanotubes, which is comparable to the reported value of graphite on nanoscale. The shear strength between nanotubes is derived to be 4 Ϯ 1 MPa by using a continuum model, which is in accordance with the value of 2 MPa reported for the sliding of MWNT on graphite in ambient. It is nearly 2 orders of magnitude larger than the interlayer shear strength of 0.05 MPa reported for MWNT in vacuum. We attribute the difference between the intertube and the interlayer frictions to the presence of water at the nanotube-nanotube interface in ambient.

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“…The design requirements are as follow, 1. The Von Misses stress of design shall be less than Mild Steel yield stress [3]. The minimum factor of safety shall be more than 1.00.…”

Section: Methodsologymentioning

confidence: 99%