Determining constitutive models from conical indentation: Sensitivity analysis
- PDF / 208,500 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 3 Downloads / 230 Views
Several procedures have previously been advanced for extracting constitutive relations from the force–displacement curves obtained from indentation. This work addresses the specific problem of determining the elastic modulus E, yield stress Y, and hardening exponent n, which define the isotropic strain-hardening model from a single force–displacement curve with a sharp conical tip. The sensitivity of the inversion process was tested through a series of finite element calculations using ABAQUS. Different magnitudes of normally distributed noise were superimposed on a calculated force–displacement curve to simulate hypothetical data sets for specific values of E, Y, and n. The sensitivity of the parameter confidence intervals to noise was determined using the 2-curvature matrix, statistical Monte Carlo simulations, and a conjugate gradient algorithm that explicitly searches the global parameter space. All three approaches demonstrate that 1% noise levels preclude the accurate determination of the strain-hardening parameters based on a single force–displacement curve.
I. INTRODUCTION
A number of studies have previously addressed estimating constitutive relations from the indentation experiments.1–17 Frequently, these estimates were based on inverting the force–displacement curves during indentation and withdrawal to obtain the presumably unique parameters of the constitutive model.7,9–13,16–18 Characterization of an elastoplastic material using the isotropic strain-hardening model based on the piece-wise continuous stress–strain relation =
En Y n−1
⑀n
= E⑀
for ⑀ ⬎Y Ⲑ E ,
(1)
for ⑀ 艋 Y Ⲑ E ,
(2)
(where E is the Young’s modulus, Y is the initial yield stress, and n is the work-hardening exponent) is of particular utility in describing material formability. The strain-hardening model allows both the ultimate strain (limiting value of strain for uniform deformation), ⑀u = n ,
(3)
and the ultimate strength u = E nY1−nnne−n
a)
,
(4)
This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs. org/publications/jmr/policy.html. J. Mater. Res., Vol. 18, No. 4, Apr 2003
http://journals.cambridge.org
Downloaded: 11 Mar 2015
of the material to be directly estimated from its parameters.20 Elastic–perfect plasticity (n ⳱ 0) provides the simplest of the strain-hardening constitutive models, and based on prior work it can be concluded that unique model parameters can be extracted from a single load– displacement curve using both hemispherical and conical indenters.4–6 However, many engineering materials exhibit substantial work hardening (0.1 < n < 0.5),21 and consequently the applicability of the perfect plasticity model is limited. Inverting a load–displacement curve on loading and unloading to obtain its constitutive law is most thoroughly studied for hemispherical indentation. Taljat, Zacharia, and Kosel have shown that for a spherical indenter the force–displacement curve mea
Data Loading...
