Uniqueness of reverse analysis from conical indentation tests
- PDF / 229,062 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 37 Downloads / 213 Views
Z.S. Liu Institute of High Performance Computing, 1 Science Park Road, #01-01, Singapore 117528
K. Zeng Institute of Material Research and Engineering, 3 Research Link, Singapore 117602
J. Hua Department of Civil Engineering, National University of Singapore, Singapore 119260 (Received 27 January 2004; accepted 21 May 2004)
The curvature of the loading curve, the initial slope of the unloading curve, and the ratio of the residual depth to maximum indentation depth are three main quantities that can be established from an indentation load-displacement curve. A relationship among these three quantities was analytically derived. This relationship is valid for elasto-plastic material with power law strain hardening and indented by conical indenters of any geometry. The validity of this relationship is numerically verified through large strain, large deformation finite element analyses. The existence of an intrinsic relationship among the three quantities implies that only two independent quantities can be obtained from the load-displacement curve of a single conical indenter. The reverse analysis of a single load-displacement curve will yield non-unique combinations of elasto-plastic material properties due to the availability of only two independent quantities to solve for the three unknown material properties.
I. INTRODUCTION
Due to the significant improvement in indentation equipment and the pressing need for assessing the mechanical properties of materials on small scales, there is increased interest in instrumented indentation. Several methods have been proposed by researchers to extract the Young’s modulus (E), yield strength (Y), and strainhardening exponent (n) of elasto-plastic materials from indentation load-displacement curves.1–4 It is generally believed that the curvature of the loading curve (C), the gradient at initial unloading (S), and the ratio of residual depth to maximum indentation depth (hr/hmax) are three independent quantities that can be directly obtained from an indentation load displacement curve. The assumption on the independence of these three fundamental quantities implies uniqueness of reverse analysis results due to the existence of three independent relationships to solve for three unknown elasto-plastic material properties. However, Cheng and Cheng,5 Capehard and Cheng,6 and Tho et al.7 have shown that it is possible to find different combinations of elasto-plastic material properties that
give practically identical indentation load-displacement curves. In the present study, the assumption of independence between the three quantities is critically examined for instrumented indentation with conical indenters. A simple relationship between C, S, and hr/hmax is analytically derived. Large deformation finite element analyses are carried out to verify the proposed relationship among the three quantities. This study demonstrates that nonuniqueness of the reverse analysis based on a single conical indenter as observed by Cheng and Cheng,5 Capehard and Cheng,6 and Tho et al.7 can be att
Data Loading...
