the notch acuity effect effectively making the notch sharper than what is normally experienced with steel. Cast iron and steel respond differently to a notch. This causes the nodu- lar cast iron to show a lower Charpy-V energy for the same fracture toughness compared to steel.
Ductile Fracture Toughness Estimation
It is possible to derive a theoretical lower bound estimate of the CV-US
energy based on the J R -curve information. The derivation has been presented elsewhere.3
It is based on the
estimation of the total energy needed to fracture a Charpy V- Notch (CVN) size ligament in half. It assumes a deep crack, quasi-static loading and J-controlled crack growth through the entire ligament. The tearing resistance curve is approxi- mated as a simple power law (Eqn. 1). The resulting theo- retical estimate has the form of Eqn. 2.3
Eqn. 1 Eqn. 2
with limited fracture toughness curves, J1mm
shallow notch and the dynamic loading combined with fric- tion effects will increase the total absorbed energy. Fur- thermore, J-dominance will be lost in a real fracture of the ligament, increasing the required energy. Thus, ETOT always be smaller than CV-US
The above energy estimate will be a theoretical lower bound estimate of the CV-US
should
. If Eqn. 2 is used for materials gets the value
corresponding to instability and m becomes 0. The present derivation of Eqn. 2 is provided by Wallin.3
A similar deri-
vation yielding (in practice, an identical equation) has been discovered earlier,4 purpose as Eqn. 2.
even though it was not used for the same
The ductile fracture toughness is usually not expressed in the form of the full tearing resistance curve, but in the form of a standard JIC JIC
flow stress (σf
can be estimated from the J1mm ) by Eqn. 3.2
value. The mostly used ASTM definition of and m information and the
Eqn. 3 General Upper Shelf Relation
structural metals, has been developed using a total of 162 multi-specimen J-R -curve data sets.3
An upper shelf relation between the J-R-curve and CV-US The analysis was re-
stricted to multi-specimen data to minimize possible experi- mental inaccuracies. The data sets corresponded to room tem- perature or temperatures below 100˚C (212˚F). Since ductile tearing is insensitive to temperature in this temperature range, temperature was not a fitting parameter in the data sets. The material’s yield strengths varied in the range 171 to 993 MPa and the Charpy-V-notch upper shelf energies in the range 20 to 300 J. The materials tested included mostly structural and
International Journal of Metalcasting/Volume 8, Issue 2, 2014 , for energy. In a real Charpy-V-test, the The Relation Between Charpy-V and Fracture
pressure vessel steel and their welds, with some Duplex, stain- less and cast steel and even one aluminium alloy.3
Figure 4 shows the resulting relation3
correspond to a pre-cracked specimen. As expected, all the CV-US
the J-integral value at 1 mm crack growth. The dotted line in Figure 4 depicts the theoretical ETOT
between CV-US and estimate that would
values lie clearly above the theoretical lower bound estimate. The few points lying close to the lower bound es- timate are likely due to experimental errors in the J-integral tests. The material’s yield strength does not affect the rela- tion, because the yield strength affects the J-integral and the Cv
value in a similar way.
The exponent m can be expected to be controlled by the overall tearing resistance and the strain hardening properties of the material. The exponent m data for the materials of the general relation are plotted against J1mm clear that m is related to J1mm
in Figure 5.3 It is even though the scatter is con-
siderable. A great deal of the scatter is, however, expected to be due to inadequate quality of many of the data sets. For en- gineering purposes, it is sufficient to use the mean estimate of m as given in Figure 5.
Figure 4. Relation between CV-US at 1 mm crack growth.3
and the J-integral value
Figure 5. Shape of J-R –curve, described by exponent m, is dependent on J1mm.
3 83
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