A contact size-independent approach to the estimation of biaxial residual stresses by Knoop indentation

• Biaxial residual stresses are extracted from Kick's law coefficient C.
• The ratio of residual stresses can be estimated directly from the C ratio.
• C values for the biaxial residual stresses case are converted to equivalent C.

The presence of residual stresses (RS) in a material causes a shift of the indentation load–displacement curve. The resulting change in the Kick's law coefficient C can hence be exploited to estimate these RS. By contrast with axisymmetric indenters, when employing the Knoop indenter with its large aspect-ratio, C is further sensitive to the indenter's orientation with respect to the principal RS directions. For a wide range of material properties, maximum and minimum C values are obtained by finite element analysis. It is observed that the RS ratio can be estimated directly from the C ratio, independent of magnitude and sign of RS. Further, the finding that C values for the non-equibiaxial RS case can be converted to equivalent C values for two equibiaxial RS cases, made for conical indentation (J.H. Lee et al., 2010, J Mater Res 25: 2212–2223), is shown to apply to Knoop indentation, too. The magnitude of RS can thus be determined from the equibiaxial RS case. The equibiaxial RS case is investigated in detail and mapping functions are established between C and the corresponding RS value. Finally the method is validated experimentally by comparison with Knoop indentation of bended cross-shaped steel specimens.

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