Page 126 - Biaxial Multiaxial Fatigue and Fracture

Long-Life Multiaxial Fatigue of a Nodular Graphite Cast Iron 111

limit under equi-biaxial tension would be greater than for either uniaxial tesion or pure torsion.
Unfortunately, equi-biaxial tension fatigue data is rarely published.

EXPERIMENTS

Materials

Nodular cast iron is extensively used in the production of vehicles and heavy machinery
components. When compared to grey iron, nodular cast irons have significantly higher fatigue
strengths at long lives that can be used to great advantage in design. For complex parts, loading
is often multiaxial and in some cases is also highly non-proportional.
Material in this investigation was a nodular cast iron GRS 500 I IS0 1083 cast as ingots
100x100~300 mm in size. Castings were slow cooled but no post cast heat treatment was
performed. Measured tensile properties were Rp0.2 = 340 MPa and Rm = 620 MPa.
Microstructure was predominantly pearlite with small regions of ferrite surrounding the
graphite nodules. Figure 3 shows the typical microstructure for the material tested.
Fractography of failed specimens cycled just above the fatigue limit has shown that failure is
dominated by the nucleation and growth of individual cracks from shrinkage pores near the
specimen surface 114,151. Shrinkage pores several hundred microns in diameter are a common
feature of thick-section castings such as the ingots in this investigation.
Figure 4 shows the extreme value distribution of maximum defect size for a 3400-mm3 test
volume. Defect sizes were approximated as the square root area of the smallest ellipse or semi-
ellipse that just enclosed the defect. Ellipses were used for internal defects while semi-ellipses
were used for surface breaking or near surface defects. The vertical axis in Fig. 4 is based on
rank probability analysis. Measured defect sizes are ordered from smallest to greatest and
assigned a rank number, i, that varies from 1 to n where n is the total number of defects
measured. The value Prank is an estimate of the cumulative probability of finding a defect
larger than that corresponding to rank number i and is approximated using the formula:

i - 0.3
prm? = -
n + 0.4

The value y = 0.37, therefore, corresponds to the median defect size while y = 6 corresponds to
the defect size greater than 99.7% of all defects in the sample [24].
Also shown in Fig. 4 is a similar measured defect distribution for casting defects from a
nominally identical material obtained from a different foundry. In this case the median defect
size is clearly larger than for the median defect in the ingots and the reduced slope in the
resulting regression line is an indication of a greater scatter in the sample.
The statistical method described here is essentially identical to the inclusion rating method
by statistics of extremes (IRMSE) proposed by Murakami [25] for evaluating the cleanliness of
steels. The method has been shown to be especially powerful in its ability to discriminate
between different ultra-clean bearing steels and to predict the size of defects larger that those
found in a series of inspection domains. Such statistical methods are valuable for quality
control monitoring and for specifying maximum allowable stresses for high reliability design.