The reason for this initial increase followed by a decreasing trend is that when cracks are at their early stages (micro-cracks) the two surfaces of the cracks come into contact as the waves propagate through them, causing contact acoustic nonlinearity (CAN) and the SPC-I value increases.
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A Comparative Study of Geometric Phase Change- and Sideband Peak Count-Based Techniques for Monitoring Damage Growth and Material Nonlinearity.
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The sentences
When input excitations increase, an increasing trend is observed for the square root stress–strain relationship while a decreasing trend is found for the quadratic stress–strain relationship.