Numerical approaches and experimental verification of the conical indentation techniques for residual stress evaluation

Abstract

Conical indentation methods to determine residual stress are proposed by examining the finite element solutions based on the incremental plasticity theory. We first note that hardness depends on the magnitude and sign of residual stress and material properties and can change by up to 20% over a specific range of elastic tensile and compressive residual stress, although some prior indentation studies reported that hardness is hardly affected by residual stress. By analyzing the characteristics of conical indentation, we then select some normalized indentation parameters, which are free from the effect of indenter tip rounding. Adopting dimensional analysis, we present practical conical indentation methods for the evaluation of elastic/plastic equi- and nonequi-biaxial residual stresses. The validity of developed approaches is confirmed by applying them to the experimental evaluation of four-point bending stress.

A study on robust indentation techniques to evaluate elastic–plastic properties of metals

“…Thereupon, we set f = 0.3, since Coulomb friction coefficient between general metals is about 0.1-0.4. Lee (2006) contrived a way of minimizing the frictional effect on estimated properties by suitably selecting the regression range of strain, the summary of which is given in Section 5.2. If we use low h max /D, because of relatively small indentation load and contact area for a given indenter radius, we can reduce specimen size and minimize deformation of indenter.…”

“…With Young's modulus still fixed, varying yield strain through its entire range in Table 2 then makes the coefficients as double polynomial functions of strainhardening exponent and yield strain. Note that for each value of varying yield strain, strain-hardening exponent varies again through its entire range in Table 2 1.5, 2, 2.5, 3, 4, 5, 7, 10, 13, 20, 50 formulas for three normalized indentation variables (Lee, 2006). We also plotted the regression lines generated from Eqs.…”

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

“…However, the sensitivity of C to RS is rather low here (especially in combination with a high n), making the approach less appropriate for these materials. Lee et al [22] found for conical indentation that the maximum load (or C) for indentation on a specimen with σ R1 and σ R2 is equal to the mean average of the maximum loads (or C) from two indentations (same depth) on specimens with equibiaxial RS σ RI = σ R1 and σ RII = σ R2 . Assuming that this holds also for Knoop indentation, we can write in terms of Kick's law coefficients in a similar fashion …”

“…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.…”

“…Although the approach was in a good agreement with experiments on steel, the possible influence of material properties was not discussed. To obtain non-equibiaxial RS from the load-depth curve, Lee et al [22] developed a conical indentation-based approach, but which requires preknowledge of the RS ratio. Groth and Mann [23] exploited the reduction of the short diagonal of the Knoop impression (due to elastic recovery during unloading) to estimate RS.…”