Revelation of a functional dependence of the sum of two uniaxial strengths/hardness on elastic work/total work of indent
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Taihua Zhang State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Chung Wo Onga) Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China (Received 3 August 2005; accepted 19 December 2005)
Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength E,y + engineering tensile strength E,b)/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the sum E,y + E,b according to the data of an instrumented indentation test. The E,y + E,b value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.
I. INTRODUCTION
There has been a long-lasting attempt to correlate the results obtained from indentation test with the fundamental mechanical properties of a material. More than 50 years ago, Tabor1 first reported that the hardness H of some metals obtained from indentation tests by using a conical indenter was ∼3 times a “representative yield stress (Yo),” where Yo was the true yield stress at a 0.08 true yield strain. This finding linked up the hardness with the standard material properties obtained from a uniaxial tensile/compressive test. Along with the development of depth-sensing indentation technique in the past decades, Tabor’s conjecture was reexamined over a larger variety of materials. Cheng and Cheng2 further introduced dimensional and finite element analyses (FEA) for conical indentation, and pointed out that when the ratio of yield
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0111 J. Mater. Res., Vol. 21, No. 4, Apr 2006
strength to Young’s modulus increased from 0.0002 to 0.1, the ratio H/Yo would drop from about 2.8 to 1.7. Dao et al. also reported a similar trend,3 leading to the conclusion that there was no simple proportional relationship between hardness and yield stress. Another line of thought is to correlate the whole set of load–displacement data, rather than hardness value alone, with a group of fundamental material elastoplastic properties, such as Young’s modulus E, yield strength, Poisson’s ratio , and stain-hardening exponent n. 3–5 However, Cheng and Cheng, 6 Capehard and Cheng,7 and Tho et al.8 pointed out t
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