• PDF / 359,975 Bytes
• 6 Pages / 612 x 792 pts (letter) Page_size
• 94 Downloads / 298 Views

DOWNLOAD

REPORT

---

esearch Letters

Relationships between the work recovery ratio of indentation and plastic parameters for instrumented spherical indentation Chang Yu, Rong Yang, Yihui Feng, and Yong Huan, State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China Guangjian Peng and Taihua Zhang, College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China Address all correspondence to Taihua Zhang at [email protected] (Received 31 October 2014; accepted 23 February 2015)

Abstract This paper aims to obtain an analytical expression for the ratio of unloading work of indentation (Wu) to total loading work of indentation (Wt) (work recovery ratio of indentation) in instrumented spherical indentation. The expanding cavity model and Lamé solution are used. Three typical stress–strain relations (elastic-perfectly plastic, linear hardening, and power-law hardening) are analyzed. The results of finite-element method coincide with the expressions. The expressions show that the work recovery ratio of indentation is just related to plastic parameters. Furthermore, elastic work (We) are obtained, and it is proved that We should be distinguished from Wu in spherical indentation.

Introduction In recent studies, interest has been intensifying in the development of indentation-based methods to extract material elastic– plastic properties. One category of previous studies aimed to obtain the stress–strain curve from a load–depth curve.[1] In another category of studies, many fitting parameters were involved.[2] In this case, it was easy to determine the relationship between the mechanical parameters and the measurement parameters tested. However, these methods led to complex formulations and the parameters. Ogasawara et al. obtained elastic–plastic parameters from measurements at several depths, a process that mimics the dual/plural sharp indentation method.[3] There is a common problem in these methods. That is lack of sufficient theoretical analysis. In our previous work,[4] it was found that a stable solution can be obtained by the use of work recovery ratio of indentation (Wu/Wt). It seemed to be correlative only with plastic parameters in the power-law hardening material by instrumented spherical indentation. To improve that assumption, and enlarge the scope of the assumption, three typical stress–strain relations are considered to obtain an analytical expression for work recovery ratio of indentation. A general stress–strain relation for the material can be written as


s˜ =

E 1˜ f (˜1)

(˜1 , 1y ) , (˜1 ≥ 1y )

(1)

where s˜ and 1˜ are the equivalent stress and strain, respectively, E is the elastic modulus, and εy is the yield strain.

The function f (˜1) is the constitutive equation of material, which for elastic-perfectly plastic materials takes the form,

s˜ = E1y ,

(2)

while for linear hardening materials, it can be written as

s˜ = Ep 1˜ + (E − Ep )1y ,

(3)

and for power-law hardening materials, it can be written as

s˜ = E1y1−n 1˜ n