On the transverse indentation moduli of high-performance KM2 single fibers using a curved area function

Nanoindentation of single microscale fibers is a challenging task due to the dimensional similarity of the probing instruments to the single-fiber cross sections. Algorithms customarily used in nanoindentation equipment assume that the indentation occurs in flat surfaces, thus simplifying the local geometry and approximating material properties in curved specimens. A modified Curved Area Function (mCAF) is developed using finite element analysis and tested using nanoindentation measurements of high-performance single microfibers. The mCAF accounts for the dimensions and curvature in the transverse direction of the cylindrical microfiber in conjunction with the contact depth and the impression of the indented area. The transverse direction indentation modulus of a \(12\,\upmu \hbox {m}\) of \(\hbox {Kevlar}^{\textregistered }\) KM2 fiber was estimated as \(7.76\, \pm \,0.22\) GPa. The computational results were corroborated with experimental measurements performed on KM2 single fibers and agreed with literature findings that assumed minor differences in testing equipment, area analysis, and projected surface area. Two geometry-related coefficients \( C_{0}\) and \(C_{1}\) were determined that facilitate simulation of fiber nanoindentations with diameters of \(d = 7, 15, 30, 40,\) and \(50\,\upmu \hbox {m}\) with indentation depths up to, and including, \(2\,\upmu \hbox {m}\). The mCAF provided a narrow measurement error of \(\pm \,0.22\) GPa (2.8%) when compared to published studies using the semi-infinite plane approximation, reinforcing the suitability of the developed model.