Stress concentration factors for shoulder fillets in round and flat bars under various loads

Abstract

The stress concentration problem of shoulder fillets in round and flat bars under various loads is often encountered in machine design of shafts. Also it is important for test specimens used to investigate the mechanical properties of materials. Accurate stress concentration factors (SCFs) have been given in a recent analysis of the body force method. However, the results of the solutions have been presented in tabular form which is not suitable for engineering applications. For notched bars, Neuber proposed the simple approximate formula K tN which is useful for a wide range of notch shape: 1/( K tN − 1) m = 1/( K ts − 1) m + 1/( K td − 1) m and m = 2. Here, K ts and K td are exact solutions for shallow and deep notches, respectively. Neuber's simple formula has been used for >40 years in the design of notched bars because of its convenience. In this study, similar convenient equations K tN are initially proposed as an extension of Neuber's formula to the problem of shoulder fillet. In this formula new definitions of K ts and K id are used corresponding to two extreme cases of shoulder fillet in round and flat bars. Next, the most suitable exponent m is determined so as to minimize the difference between K tN and accurate K t, that is, the results of the body force method. Next, by applying the least squares method to the ratio K t/ K tN more accurate formulas are proposed. The formulas proposed in this paper are found to give the stress concentration factors with better than 1 % accuracy. In addition, the stress concentration factors are also provided in a graphical way on the basis of the formula so they can be used easily in design or research.