Prediction of Fracture Loads for Gray Iron Bearing Housings
Gray cast iron exhibits very low notch sensitivity. A notched tensile specimen breaks at approximately the same load as a smooth specimen. Under the isotropic and homogeneous assumptions of continuum mechanics, the calculated stresses for notched specimens far exceed stresses calculated for un-notched specimens. Stress-based fracture criteria for brittle materials, including the maximum normal stress and modified Mohr criteria, therefore badly under-predict the breaking strength of notched cast iron specimens. Adjusting the breaking strength by a factor equal to the stress concentration factor matches the observed breaking load for the notched tensile specimen. Calculation of the stress concentration factor requires taking the ratio of the maximum stress to the nominal stress. For the notched tensile specimen, nominal stress amounts to just the load divided by the minimum cross sectional area of the specimen. For the notched tensile specimen geometry, handbook values exist for stress concentrations for linear elastic materials. However, the nonlinear stress/strain curve for cast iron requires calculation of maximum stress by FEA. For the more complex geometry of manufactured parts, such as a roller bearing housing, FEA suffices to calculate maximum stress, but no clear definition suggests itself for the nominal stress. This study describes a technique for estimation of nominal stress from a path plot of stress versus location across the critical cross section of a roller bearing housing. The estimated stress concentration factor then amounts to the ratio of maximum stress calculated in FEA to the estimated nominal stress. Estimated fracture loads then get calculated from FEA maximum stress compared to stress-based fracture criteria, and then multiplied by the stress concentration factor. The estimated fracture loads match experimentally determined fracture strengths for two sizes of housings with less than 10% error for two housing sizes, and match within 20% for a third housing size.
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