Stress measurement with non-indentation Page: 2 of 8
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crack length method to measure fracture toughness has been critically reviewed
recently by C. B. Ponton and R. D. Rawlings.' Of particular significance is Lawn,
Evans, and Marshall's elastic-plastic model of indentation2 which was evaluated
for its utility for toughness testing by G. R. Anstis, P. Chantikul, B. R. Lawn, and
D. B. Marshall.3
The elastic-plastic model can be used also to assess the effect of pre-existing
residual stresses. Accordingly, the critical stress intensity factor (fracture tough-
ness) K, , can be related to the indentation load, P, the post-indentation crack
length, c, and the pre-existing residual stress, oGes , as:
K, = Ps+Yo- (1)
The first term on the right hand side of this equation represents the effect of the
indentation which is characterized by the parameter, X. The second term represents
the effect of the pre-existing local, or residual stress. Implicit in the form of the
second term is the assumption that the indent crack is a half penny surface crack
placed in a uniform residual stress field whose depth is greater than the depth of the
indentation crack. Y is the shape parameter for a half-penny surface crack.
The applicability of the indentation theory has been restricted, by-and-large, to
Vickers indents with fully developed half-penny cracks whose diameter is at least
2.5 times the impression diagonal.1 This restriction led to the use of relatively
large indentation loads by Wu et al.4 in their study to measure stresses in uni-
axially loaded Si3N4 bars with Vickers indentation. Consequently, the length of the
cracks that were analyzed to predict the stress in the test bars were of the order of
hundreds of micro-meters. The purpose of the study presented in this paper was to
assess the applicability of Eq. (1) to measure residual stress on a much smaller
scale using a cube-corner nano-indenter to produce cracks with lengths of several
micro-meters. Such small cracks would enable the use of indentation for the meas-
urement of stress with high spatial resolution.
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Jakus, K.; Evans, N.D. & Hay, J.C. Stress measurement with non-indentation, report, November 1998; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc702873/m1/2/?rotate=90: accessed May 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.