Cross over point

In rheological test such as a frequency sweep or a time/temperature sweep, the cross over point is a convenient point of reference to indicate a “transition” point of the sample.

Note: although there technically can be a cross over point in an amplitude sweep, this is not mathematically sound (due to using linear maths/analysis), on a non-linear response, and therefore should not be used.

The cross over point is where the Elastic modulusThe complex modulus (elastic component), storage modulus, or G’, is the “real” part of the samples the overall complex modulus. This elastic component indicates the solid like, or in phase, response of the sample being measurement. elastic modulus is equal to the Viscous modulusThe complex modulus (viscous component), loss modulus, or G’’, is the “imaginary” part of the samples the overall complex modulus. This viscous component indicates the liquid like, or out of phase, response of the sample being measurement. viscous modulus, which is where the phase angle= 45°.

It can be considered, in the simplest terms, where the sample transitions from being “elastically” dominated (i.e. G’ > G’’, delta < 45°) to “viscously” dominated  (i.e. G’ > G’’, delta < 45°), and is for timescales related to the applied test frequency.

In a more considered review, whether a sample is “solid like” or “viscous like” requires a consideration of the cross over point across multiple frequencies. As such, this “crossover” reference point where the phase angle = 45° is no more or less significant to when a sample has a phase angle of 35°, for example, or any other value.

The rSpace software for Kinexus is ready for whatever definition of “crossover” is required, with specific cross over analysis, and the ability to use “find value” to quantify where any other criteria is required.

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