If I'm analyzing a series of polymer composites mechanical properties through an Instron device and get the Young Modulus value for those samples and analyze the same composites nanomechanical properties through nanoindentation and get the Reduced Modulus value, do both Modulus have the same variation from one sample to the next? Should they?
Young's Modulus and Reduced Modulus are related but distinct mechanical properties measured through different methods: Young's Modulus is determined via tensile or compressive testing, while Reduced Modulus is obtained from indentation or nanoindentation. While both provide insights into a material's stiffness, variations between samples may differ due to differences in testing methods, loading conditions, sample preparation, and material characteristics. While there may be some correlation between the two moduli, it's not guaranteed that they will vary in the same way from one sample to the next.
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The reduced modulus E *is related to the Young's modulus E with the simple equation E* = E/(1−v2), where v is the sample's Poisson's ratio
Young's modulus E, shear modulus G and Poisson's ratio µ are related to each other by the following relation:
G=E/2(1+ µ )
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