Study on elastic-plastic behaviour of inclusions in cold drawn wire by using reverse analysis and nanoindentation test

The purpose of this study is to investigate the elastic-plastic behavior of inclusions, i.e. SiO2 particles, in cold drawn wire using reverse analysis and nanoindentation test. First, the nanoindentation tests were performed to obtain indentation load P – penetration depth h curves. Second, the reverse analysis which is consisted of various dimensionless functions including change in E∗/ r , Wp/Wt and n was used to extract the elastic-plastic properties of the indented inclusions and metals from indentation responses. To verify the accuracy of calculated properties, uniaxial tensile tests were performed for different materials which are AISI 1045 and AISI 1080. Results (E, y , n) of tensile tests for each material were also compared with those of nanoindentation tests.


Introduction
Nanoindentation test is an efficient method for measuring the mechanical properties of material such as the elastic modulus and hardness using the indentation load -penetration depth curve.Technological advances of numerical and theoretical analysis have recently allowed us to extract the elastic-plastic properties for not only bulk materials but also thin films or coated metal.
The basic relationship between the elastic-plastic behaviour of metal can be generally identified by dimensional analysis [1][2][3].Especially, Lee et al. [3] performed a parametric study of 138 cases with various elastic-plastic parameters using FE analysis of indentation.They proposed a set of dimensionless functions that can investigate the elastic-plastic properties from the indentation response.
This study is designed to calculate mechanical properties of inclusions, i.e.SiO 2 particles, in cold drawn wire by using reverse analysis proposed by Lee et al. [3].The reverse analysis which is consisted of various dimensionless functions including change in C, E * / r , and W p /W t can be extract the elasticplastic properties of indented materials, such as E, y and n.The validity of calculated mechanical properties was verified to nanoindentation and tensile tests.
a Corresponding author: bmkim@pusan.ac.krThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reverse analysis
General P -h curve of the elastic-plastic materials is shown in Fig. 1.In previous studies [2,3], a loading curve in P -h curve is described by Kick's law.
where P , h and C are the indentation load, depth and loading curvature, respectively.An unloading curve can be also expressed as an initial unloading slope dP u /dh hm .The term of W t (= W e + W p ) is the total work performed during whole indentation process.W e and W p represent the elastic work during unload process and the plastic work, respectively.In order to determine the mechanical properties of the inclusions in cold drawn wire, the reverse analysis was performed as described in Ref. [3] and its detailed procedure is shown in Fig. 2. First, the reduced modulus E * is calculated by using 2 function and substituting the C and W p /W t obtained from the Ph curve.Second, the representative stress r is obtained by using 1 function and substituting the C and E * .Third, the representative strain r is determined by substituting E * and r into Eq.( 6).Fourth, the hardness H of the indented material is calculated by using 4 function and substituting E * and W p /W t .Fifth, the strain hardening exponent n is confirmed by 3 function and substituting C, H and E * / r .Finally, the initial yield stress y is obtained by substituting E * , r , r and n into Eq.( 7).

Nanoindentation and tensile tests
To verify the effectiveness of the reverse analysis, both nanoindentation and tensile tests were performed for different materials witch are AISI 1045 and AISI 1080.Only nanoindentation test were carried out to measure mechanical properties of inclusions which is a SiO 2 , as shown in Fig. 3. Indentation specimens were indented on a commercial Nanoindenter XP of MTS with the Berkovich diamond indenter until the indentation load of 100 ∼ 500 mN at a target strain rate of approximately 0.05.Nanoindentation tests were repeatedly conducted by five times per each material.For each materials, test results are shown in Tables 1-3.The results revealed that computational properties are well agreed with experimental values within ±5% and ±9% on E and y , respectively.

Conclusion
Mechanical properties of SiO 2 particles in cold drawn wire were calculated by using the reverse analysis and nanoindentation test.The reverse algorithm consists of various dimensionless functions including change in E * / r , W p /W t and n.To verify the accuracy of calculated properties (E, y and n), uniaxial tensile tests were performed for different materials which are AISI 1045 and AISI 1080.

Figure 1 .
Figure 1.Typical load -penetration depth curve during indentation test with elastic-plastic deformation.

Table 1 .
Results of uniaxial tensile tests.

Table 2 .
Comparisons E * / r , r and r calculated from Dao's and current reverse analysis.

Table 3 .
Comparisons of Dao's and current reverse analysis.