Nisitani Hironobu

Significance of initiation, propagation and closure of microcracks in high cycle fatigue of ductile metals

Abstract The initiation, propagation and closure behavior of microcracks were investigated through successive observations of fatigue process on the plain specimen surface in rotating bending tests of a mild steel, an α-brass and Al-alloys. The essential difference of crack initiation process and the behavior of microcracks was recognized between an age-hardened Al-alloy and the other annealed metals. Based on the results, the characteristics in fatigue under various loading conditions, such as 1. (i) fatigue behavior under two-steps loading, 2. (ii) coaxing effect of a low carbon steel and 3. (iii) size effect of a notched specimen and fatigue notch sensitivity, were consistently explained with special reference to the behavior of fatigue microcracks.

Behavior of a tip of non-propagating fatigue crack during one stress cycle

Abstract Measurements and observations were made on the crack closure for the so-called non-propagating crack of notched specimens and for the non-propagating microcrack of unnotched specimens, which were formed in a rotating bending test of annealed carbon steel. Under the condition which produces the non-propagating crack, the ratio of stress range where the crack tip is open, to the full range of the cyclic stress tends gradually to zero with the increase in length of the crack initiated from a notch root. The tip of a non-propagating microcrack on the surface of a plain specimen is also recognized to be closed under the maximum stress level after 10 7 cycles of the repetitions of the stress slightly below the fatigue limit. From these facts, it can be said that the tip of a so-called non-propagating crack or a non-propagating microcrack is hardly damaged by the repetition of stress which has produced each crack.

Stress concentration of a strip with a single edge notch

Abstract This paper deals with the stress concentration analysis of a semicircular and a 60° V-shaped single edge notch in an infinite strip under three different types of loading conditions: (a) uniform tension, (b) in-plane bending and (c) pure tension. The stress field induced by a point force in the semi-infinite plate, Greens function in a closed form, is used to solve those problems. The results show that Neubers formula gives an underestimated stress concentration factor when the notch is sharp and shallow. The stress concentration factors of 60° V-shaped notches are represented by diagrams for wide use.

Stress concentration of a strip with double edge notches under tension or in-plane bending

Abstract The stress concentration analysis of 60° V-shaped or partially-circular double edge notches in an infinite strip under tension or in-plane bending is discussed. The stress field induced by a point force in an infinite plate is used to solve these problems. The present results for semicircular notch are in close agreement with other reports. The results calculated on the 60° V-shaped notches show that the Neuber formula gives an underestimated stress concentration factor of about 11% for tension case and in about 9% for bending case. These errors exist for a wide range of notch depth. However, in the case of blunt notches, the Neuber solution of deep hyperbolic notches still gives a sufficient accuracy in engineering use. In addition, the stress concentration factors of 60° V-shaped notches are also represented by diagrams for wide use.

Analysis of the delaying effects of overloads on fatigue crack propagation

Abstract In this paper a simulation analysis of fatigue crack propagation was carried out in order to investigate the delaying effects of overload on fatigue crack propagation. The analysis was based on the Dugdale hypothesis, but the method of analysis used here is the extended body force method, which has been developed recently by the authors and is applicable to a wide range of problems. Based on the results analysed the retardation of crack propagation due to overloads was discussed quantitatively. The results of simulation analysis were compared with the experimental data obtained by other researchers.

Detection of a crack by body force method

Abstract A new practical method is proposed to determine the location and the size of a crack and the loading stresses based on the data of measured strains in the structure. The unknown parameters are determined by the condition which minimizes an objective function. The objective function is denned as the square sum of the residuals between the computed and measured values. The method of gradient search is employed to find out the optimal set of parameters. The body force method is used to calculate the strain field around the crack. In order to avoid problems due to the local minimum in the gradient searching process, the starting point of the gradient search is efficiently selected based on the basic concept of the body force method. In order to shorten the calculation time, the strain field around the crack is represented by several concentrated force doublets. Numerical experiments are carried out, which show that the unknown parameters are determined efficiently with good accuracy and in a short time.

Stress concentration of a strip with V- or U-shaped notches under transverse bending

Abstract This paper deals with the stress concentration analyses of a 60°V-shaped single edge notch, a U-shaped single edge notch, 60°V-shaped double edge notches and U-shaped double edge notches in an infinite strip under transverse bending. The moment field induced by a moment in a semi-infinite plate is used as a fundamental solution to solve those problems. The results show that the Neuber formula gives underestimated stress concentration factors for the wide range of the notch depth. However, in the case of blunt notches, the Neuber solution of deep hyperbolic notches still gives a sufficient accuracy. The stress concentration factors of the 60°V-shaped notches and of the U-shaped notches are represented by diagrams. In addition, the stress concentration factors of a V-shaped notch in a semi-infinite plate and the effect of the notch angle on the stress concentration factor are also discussed in the appendix.

Fatigue crack acceleration and closure in rotating bending tests of 0.54% carbon steel

Abstract Rotating bending fatigue tests were carried out under constant stress amplitudes and two-step stress amplitudes, in order to study the influence of multiple overloads on fatigue crack growth in two kinds of steels, i.e. an annealed 0.54% carbon steel and a quenched-and-tempered 0.54% carbon steel. The measurement of opening displacements of fatigue cracks formed at the rim of a small blind hole was made successively at various stress levels during one stress cycle. Experimental results were discussed in the light of the concept of crack closure. The main results obtained are as follows: 1. (1) In constant amplitude loading fatigue tests, when the crack length l is small, the rate of crack propagation dl/dN is nearly proportional to σ a n l , where σ a is a stress amplitude. The value of n is 7.5 for an annealed steel and 3 for a quenched-and-tempered steel. The main reason why the values of n are different in both materials is that the influences of σ a , on Δσ eff /Δσ are different from material to material, where Δσ eff means the stress range in which the crack is open at the crack tip and Δσ means the full stress range 2σ a . 2. (2) In two-step loading fatigue tests of lo-hi-lo type, crack growth acceleration in the second lower stress level is recognized just after applying higher stresses in an annealed steel, but not in a quenched-and-tempered steel. The above-mentioned acceleration of dl/dN is due primarily to the marked increase in Δ eff /Δσ caused by the preceding repetitions of the higher stress amplitude.

Effect of elastic constants on stress in multi-phases under plane deformation

Abstract The reduction of the elastic parameters necessary to describe the stress field in a composite under plane deformation is discussed based on the body force method and the eigenstrain theory. When the composite body subjected to prescribed surface tractions consists of N different elastic phases and each phase is characterized by M γ ( γ = 0,1,…, N − 1) independent elastic constants, the stress fields generally depend on (∑ γ =0 N −1 M γ ) − 1 parameters involving the elastic constants. If the vector sums of the tractions on holes vanish for every individual hole, however, the stress depends on the elastic constants through only (∑ γ =0 N −1 M γ )− 2 parameters formed from ∑ γ =0 N −1 M γ elastic constants.

Versatile Analysis of Antiplane Shear Problems Based on Body Force Method.

A versatile method for analyzing various antiplane shear problems was presented. The method used here is based on the body force method (BFM) which is a type of boundary method. In this paper, the boundaries of an elastic body are approximated by broken lines to eliminate the necessity of using the numerical integrals. The present method is excellent in accuracy and calculation efficiency, as shown in many numerical examples.