Hello everyone, I have one question about the measurement of micro-mechanical properties in single crystal. Suppose we measured one kind of properties like Young's modulus or hardness... at different crystal direction, E[110] and E[189]. If the crystal is cubic crystal, will there be any significant difference between E[110] and E[189]? If we change the crystal type to hcp or other crystal with lower symmetry compared with cubic system, can we find any difference between the mechanical properties measured at different crystal direction inside the single crystal? If exist, is there any parameters we can employed to quantify this difference?
For same crystal type, properties along different slip planes in a single crystal will be same. But when it comes to different crystal type (FCC, BCC, HCP) , properties vary because of varying atomic packing factor.
Young's modulus anistropy in micromechanics; Have a look at
https://www.researchgate.net/publication/231957150_Measuring_anisotropy_in_Young's_modulus_of_copper_using_microcantilever_testing
Hardness anisotropy: there is a lot of literature on this.
Most recent papers will cite the early and comprehensive study by C. A. Brookes, 1. B. O'Neill, and B. A. W. Redfern, Proc. R. Soc. London, Ser. A 322,73 (1971). I did soem work a bit later, updating their model somewhat, e.g
https://www.researchgate.net/publicationhttps://www.researchgate.net/publication/231748707_Knoop_hardness_anisotropy_on_001_faces_of_germanium_and_gallium_arsenide
and
https://www.researchgate.net/publication/232827072_Knoop_Hardness_Anisotropy_and_Predicted_and_Observed_Slip_Patterns_in_MgO
Plastic anisotropy in micromechanics: try for starters
https://www.researchgate.net/publication/279314261_a_Prismatic_a_basal_and_ca_slip_strengths_of_commercially_pure_Zr_by_micro-cantilever_tests
Steve Roberts
Article Measuring anisotropy in Young’s modulus of copper using micr...
Article Knoop hardness anisotropy on {001} faces of germanium and ga...
Article Knoop Hardness Anisotropy and Predicted and Observed Slip Pa...
Article 〈a〉 Prismatic, 〈a〉 basal, and 〈c+a〉 slip strengths of commer...
The anisotropic character of mechanical properties does not solely depend on the crystal system. For instance, the elastic properties of a Cu single crystal are very anisotropic while the elastic properties of a W single crystal are almost isotropic though both the Cu and W single crystals are cubic crystals.
As a result, though different directions will probably lead to different Young's modulus values, the variations do not uniquely depend on the crystal system.
For a given property (Young's modulus, Yield stress...), to make a quantitative comparison, you might compare the ratio between the maximum and minimum values obtained for all the possible directions. While this might be difficult from an experimental point of view, this is probably much easier with an appropriate constitutive model. For instance, if you know the single crystal elastic constants of the material you are interested in, the maximum and minimum values of the Young's modulus are easily calculated.
Pranav Shinde, Steve's work has already shown us there will be variation in the mechanical properties even inside one kind of single crystal.
Professor Steve, Thanks for your answer and files attached. It's clear that the differential distribution of atoms in different orientation controls the interaction between crystal and deformation behavior, especially for the Young's modulus in Cu or other crystals shown in your paper. However, I have another question that suppose the young's modulus varies with the orientation in certain single crystal , then, whether we can predict that other mechanical properties （like yielding stress）would varies in a similiar way or not. Be specific, I wonder my idea (in bold) is correct or not. Thank you!
Chuanyun
Hi Charles Mareau, thank you for your helpful suggestion. As you have already told me, the anisotropy of mechanical properties in single crystal would be affected by crystal structure and material, I have two questions to be settled.
1) suppose the variation exists, would the young's modulus vary in a similar way with yield stress in the same orientation range?
2) Is there any places I can find the anisotropy of mechanical properties of different materials like Co and its alloys (FCC)? Thank you so much!
Chuanyun
Prof. Roberts have already given you good references. For introduction to anisotropic properties of crystals you could look up the classic text by Nye
J.F. Nye, Physical Properties of Crystals, Their Representation by Tensors and Matrices, Clarendon Press, Oxford 1985.
Chapter VIII of this book entitled "Elasticity: Fourth Rank Tensors" contains the description and formulas for how Young's modulus varies with direction in various crystal systems. Co is hexagonal close-packed. This requires 5 elastic compliances s11, s12, s13, s33 and s44. Once these are known the Young's modulus can be calculated in any direction from a formula given in the book. But of course, you will first need the data for 5 compliances for Co which is not given in this book.
The yield strength (plastic property) will also show anisotropy but the variation is not expected to be the same as Young's modulus (elastic property). Another classic book deals with it
E. Schmid and W. Boas Plasticity of Crystals, Chapman and Hall, London 1968.
- Badges
- Science topic
- Similar topics
- Engineering
- Materials Engineering