A method for estimating contact depth from initial unloading slope is examined.
The differential term in Equation (6) was determined by fitting the initial unloading Ps-δ response with the power function P s = A δ - δ f m, (7).
where S is the stiffness of the test material, which can be determined from the slope of the initial unloading by evaluating the maximum load and the maximum depth, where S = dP/dh.
This is attributed to its higher stiffness as observed during the initial unloading period from the load-unload curve, as shown in Figure 7. Figure 7 Load-unload curve for wet and dry indentations (cases 1 and 2).
where S is the stiffness of the test material, which can be obtained from the initial unloading slope by evaluating the maximum load and the maximum depth, i.e.,S = dP/dh.β is a shape constant that depends on the geometry of the indenter and is 1.034 for the Berkovich tip.
where A is the area of the indentation at the contact depth hc, S = dp/dh is the initial unloading curve at maximum load or stiffness which is proportional to the modulus, and Es, νs, Ei, and νi are the elastic modulus and Poisson's ratio of the specimen and the indenter, respectively.
