Multiscale Modelling Method for Chosen Functionally Graded Material

Abstract:

The paper deals with the numerical and experimental analyses of functionally graded material structures which are represented by a surface layer of the steel sample hardened during the laser treatment process. A functionally graded parameter of the researched structure was assumed as the hardness value experimentally measured with the use of a Vickers hardness test method. The microstructure of the tested layer was also analyzed for the Vickers test verification. Two homogenization methods were used for the purpose of layer substitute properties for numerical calculations. The first one was to divide the FGM domain into a number of layers in the direction of material gradation and then apply a numerical homogenization method within each layer. The resulting material model describes the FGM as a composite of homogeneous layers. The second method was based on the Mori-Tanaka homogenization theory and was carried out with the use of Digimat software, which is the nonlinear multi-scale materials and structures modelling platform. Both methods were compared and showed good correspondence.

• Periodical: Solid State Phenomena (Volume 199)
• Pages: 593-598
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.199.593
• Online since: March 2013
• Authors: Danuta Miedzińska, Robert Panowicz, Przemysław Jóźwicki
• Keywords: Finite Element Method (FEM), Functionally Graded Material (FGM), Homogenization, Multiscale Modeling, Surface Layer

References

[1] K. Vemaganti, P. Deshmukh, An adaptive global–local approach to modeling functionally graded materials, Comp. Methods Appl. Mech. 195 (2006) 4230-4243.

DOI: 10.1016/j.cma.2005.08.005

[2] L. Sills, R. Eliasi, Y. Berlin, Modeling of functionally graded materials in dynamic analyses, Composites: Part B 33 (2002) 7–15.

DOI: 10.1016/s1359-8368(01)00057-9

[3] S.B. Dong, Global–local finite element methods, State-of-the-art Surveys on Finite Element Technology, American Society of Mechanical Engineers, New York (1983) 451–474.

[4] D. Tabor, A Simple Theory of Static and Dynamic Hardness, Proc. Roy. Society Series A 192 (1947) 247-274.

[5] D. Tabor, The Hardness and Strength of Metals, Oxford Clarendon Press, (1951).

[6] T. Mori, K. Tanaka, Average stress in the matrix and average elastic energy of materials with misfitting inclusions, Acta Metall. Mater. 21 (1973) 571-574.

DOI: 10.1016/0001-6160(73)90064-3

[7] Y. Benveniste, A New Approach to the Application of Mori-Tanaka's Theory in Composite Materials, Mech. Mater. 6 (1987) 147–157.