Page 276 - Failure Analysis Case Studies II

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factor must be included to account for the stress riser caused by the abrupt change in pin diameters.
Multiplying thc bend stress by the elastic stress concentration factor (K, = 1.67) produces a
maximum bending stress of approximately 443 MPa. This value is greater than the ultimate stress
of 324 MPa as calculated from the hardness test and equation (1). Even though the maximum
bend stress is greater than the ultimate stress, the pin will not necessarily fail under this loading
scenario. As the material along the top surface of the pin is plastically deformed, the stress level
remains relatively constant and additional loads are redistributed toward the center of the pin.
After the pin has undergone plastic deformation, the elastic beam equation for the bend stress is
no longer valid. Once this happens, an inelastic bending analysis must be performed. The important
point to note from this analysis is' that under the maximum loading scenario, the pin will be
plastically deformed. This fact alone indicates that the pin was poorly designed.

2.4. Fatigue stress concentration

Close examination of the fracture surfaces has indicated a fatigue failure. The elastic stress
concentration factor previously determined is measured under conditions of elastic stress and
cannot be directly applied in fatigue calculations. Experiments have shown that the fatigue stress
concentration factor may differ significantly from the elastic stress concentration factor. From the
microscopic viewpoint, the steep gradients of an elastic stress field may not be sufficient to shuttle
dislocations and nucleate a fatigue crack. Hence, considerable experimental evidence has shown
that the fatigue stress concentration (K,) is less than or equal to the elastic stress concentration
(K,). The elastic concentration factor can be converted to a fatigue stress concentration factor by
the following formula [4],

where q is the notch sensitivity parameter of the given material. The notch sensitivity is dependent
upon the notch root radius and the materials ultimate tensile strength. The notch sensitivity was
determined from a plot of notch root radius versus notch sensitivity for steels, Fig. 8 [4]. In this
case. the notch root radius was 0.8 mm (& in.) and the approximate ultimate tensile strength of the
steel was 324 MPa as calculated from equation (1). Using these values and Fig. 8 produces a notch
sensitivity value of y = 0.58. Using equation (3) and the value for q, the fatigue stress concentration
factor (K,) was calculated to equal 1.38. The fatigue stress concentration factor was incorporated
into the analysis by multiplying the bending stress calculated in equation (2) by Kr.

2.5. Machine usage

To make an accurate prediction of the life of the adjustment pin, it is crucial to determine the
amount of use the machine typically sees. The repetitions at each weight level were recorded over
a period of three weeks. Figure 9 shows a graph of the number of repetitions at each weight level
during the three week period. The majority of the use was between 45 and 135 Ib with only a small
amount of use at the very high weight levels. We will consider the three week time as one period
in the block loading scenario.