I have seen some articles that do measurements of hardness and elastic modulus by instrumented indentation (nanoindentation) in different directions of the material (for example: rolling direction, transverse direction and normal direction). Despite some articles discuss these measurements according to the direction tested, they do not make clear if the technique is really directional. Although the intenter moves in a single direction, from my view point, the material during the test will be deformed in 3 dimensions. Hence, the value we obtain is not the value of hardness or elastic modulus in the direction the indenter is moving, but a 3 dimensional response.

Does someone know where I could  get a theory that explains this?

I hope I have made myself clear.

Thank you in advance.

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