Weakest link concept for springs fatigue

Abstract

ABSTRACTIn the present manuscript, a new approach is developed to account the stress gradient effect on fatigue life of springs. The new formula of crack growths per cycle is introduced. The expressions for spring length over the number of cycles are derived in terms of higher transcendental function. The closed-form solutions are used for the estimation of the fatigue life of heterogeneously stressed structural members. The probability distribution of the fatigue limit for heterogeneously stressed structural elements is evaluated. The proposed approach for the stress gradient sensitivity of fatigue life is based on the weakest link concept. The weakest link approach is applied to calculate the number of cycles to crack initiation of structural elements under different probability levels. The effect of stress ratio on elongation of crack is discussed. The developed theory is applied to helical springs under cyclic load. The fatigue sensitivity to stress concentration is addressed in application to springs. Effect of fluctuating stresses on fatigue life of springs is combined with the influence of heterogeneous stress distribution (stress gradient) over the cross-section of wire and time-varying stresses. These two factors lead to complicated evaluation for fatigue life of helical springs. The stress field is inhomogeneous over the cross-section of the wire of spring. The stress distribution is uniquely defined by ratio of the diameter of wire to the diameter of spring body. The calculated lifetimes are compared with the lifetimes obtained from experiments performed on helical springs subjected to cyclic load of constant amplitude.