Effect of loading frequency upon fatigue crack development

This paper deals with a non-destructive detection method of the generation time, the crack length and the propagation speed of fatigue crack in spot-welded joints under tensile-shear load.In case of spot-welded joints, fatigue cracks generate usually at the neighborhood of nugget tips of the weld interface, and propagate toward outer surfaces of the sheets. Accordingly, it is very difficult to observe and measure the crack length, consequently the generation time and the propagation speed of crack by using conventional measuring devices.Authors developed a non-destructive method of fatigue crack, which the generation time, the crack length and the propagation speed of fatigue crack can be quantitatively estimated by utilizing infomation obtained from the strain gages bonded on the electrode indentations of spot welds. Specimens used in this experiment are made of various kinds of thin steel sheets.Main conclusions obtained in this study are as follows:(1) The propagation length of fatigue crack is related with both mean strain and strain range of out-put of the strain gage, and the changing rate of strain range is specially useful for fatigue crack detection.(2) The generation time and the propagation speed of fatigue crack can be estimated easily from relationship between the number of cycles and the crack length, which is established in advance for an individual test piece.

Experimental observations on the effect of thermal treatment on the crack speed and mode I and II fracture toughness in brittle and ductile rocks

Analyses of the multiple cracking behaviour of brittle hollow cylinders under internal pressure

Study on dynamic fracture behavior of mode I crack under blasting loads

We investigated crack propagation in the drying process of a thin layer of calcium carbonate (CaCO 3 ) paste experimentally. Cracks are induced by uniform desiccation from the top surface of a layer at the approximately same water content for various drying conditions. We found that the crack speed is a nonlinear increasing function of the drying rate at the cracking time although the tensile stresses arising in the bulk of paste do not depend practically on the drying rate. The crack speed does not depend significantly on the layer thickness and decreases in the cases in which glycerol is mixed to increase the viscosity of paste. These results suggest that dynamical crack growth occurs with viscoplastic relaxation in the vicinity of crack tips.

Since the tensile fracture is governed by the load rate, the unstable crack fracture must be observed under the condition in which the load rate is smaller than crack speed. In this paper, the time-dependent stress caused by the compression wave emanated from the rupture section of a notched round bar is observed by the strain gauge method, while the problem of the same condition is theoretically analysed by postulating the crack growth models. The crack speed is determined from a comparison of the experimental result with theoretical result. Furthermore, the present paper experimentally distinguishes the effect of various factors, load rate and stress intensity factor, strain hardening, and area contraction of the material on the crack speed in tensile fracture, and suggests the experimental condition in observing the unstable crack fracture by the tensile test.

Crack propagation speed in ceramic during quenching

A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals

The author has studied the relationship between the stress and the propagating speed of fatigue crack by analysing shelly pattern on fracture surface of shoulder fillet specimens obtained by the tests described in Part 3. This analysis was based upon the assumption of the stress σ on the cros section of fillet as follows : [numerical formula] where η : distance from neutral axis for bending C1, C2 : constants given by stress concentrating factor. As the results of above studies, it has been presumed that the propagating speed of fatigue crack may be reduced due to coaxing effect and strain harding at the tip of fatigue crack, where the speed is smaller than 0.2μ/c. When the speed exceed 0.2μ/c, it may be obtained from the following formula ; [numerical formula] where υσn : stress on edge line of fracture surface kg/mm2. υc : speed of fatigue crack propagation μ/c. σo : fatigue strength of specimen having fine crack kg/mm2. Φr : stress gradient on surface layer of cracking part kg/mm2/mm.

An earlier developed numerical model for three‐dimensional propagation in horizontally stratified fluid/elastic media [H. Schmidt and J. Glattetre, J. Acoust. Soc. Am. 78, 2105–2114 (1985)] has been modified to incorporate seismic moment representations for compact cracks of tensile, dip‐slip, and strike‐slip types. The applied global matrix approach first yields the depth‐dependent Green's function simultaneously in all layers for an arbitrary number of individual source depths. The frequency domain solution for a three‐dimensionally propagating crack is then determined by wavenumber integration over a spatial grid of superpositions of individual source contributions multiplied by the proper phase terms. Finally, the time domain solution over the spatial grid is obtained by simple Fourier synthesis. The present Fourier transform approach has the advantage that many crack propagation scenarios can be treated with only a single computer intensive solution of the wave equation. Once the depth‐dependent Green's function has been determined for the relevant crack type and depths, the field can be evaluated very efficiently by superposition for any crack propagation direction and speed. The developed model has been applied to theoretical analysis of the sound field produced in an Arctic environment by ice cracking, demonstrating the effect of cracking mechanisms, propagation speed as well as environmental parameters in general. [Work supported by ONR.]

The objective of this study is to measure the crack propagation speed in three types of self-compacting concrete reinforced with steel fibers loaded under four different loading rates. Central-notched prismatic beams with two types of fibers (13 mm and 30 mm in length), three fiber volume ratios, 0.51%, 0.77% and 1.23%, were fabricated. Four strain gages were glued on one side of the specimen notch to measure the crack propagation velocity, a fifth one at the notch tip to estimate the strain rates upon the initiation of a cohesive crack and the stress-free crack. A servo-hydraulic testing machine and a drop-weight impact device were employed to conduct three-point bending tests at four loading-point displacement rates, the former to perform tests at 2.2 m/s, 22 mm/s and the latter for those at 1.77 m/s, 2.66 m/s, respectively. With lower fiber contents, smooth mode-I cracks were formed, the crack speed reached the order of 1 mm/s and 20 m/s. However, crack velocities up to 1417 m/s were obtained for the concrete with high content of fibers under impact loading. This value is fairly close to the theoretically predicted terminal crack velocity of 1600–1700 m/s. Numerical simulations based on cohesive theories of fracture and preliminary results based on the technique of Digital Image Correlation are also presented to complement those obtained from the strain gages. In addition, the toughness indices are calculated under all four loading rates. Strain hardening (softening) behavior accounting from the initiation of the first crack is observed for all three types of concrete at low (high) loading rates. Significant enhancement in the energy absorption capacity is observed with increased fiber content.

Corrosion fatigue crack growth of serviced API 5L X56 submarine pipeline

Crack dynamic propagation properties and arrest mechanism under impact loading

Peridynamic simulation of crack propagation of non-homogeneous brittle rock-like materials

The smooth blasting of hard granite tunnel will have problems such as poor fragmentation of the tunnel face. To address these issues, this study investigates the mechanism of empty hole blasting. According to the blasting theory, by deducing the formula of the equivalent damage zone radius of the group hole, and a criterion for defining the blasting effect is proposed. The rationality is verified by numerical simulation and field test. The results show that the empty hole can change the stress distribution of the group hole blasting, and has the effect of directional to crack. With the increase of empty hole‐group hole spacing, the peak stress decreases gradually. Aiming at the damage change, the damage feature transformation coefficient m is proposed to define the blasting effect and m = 0.6 is determined as the damage feature transformation threshold. With the increase of distance, the propagation speed and length of rock cracks gradually weaken, and the regional penetration effect gradually deteriorates. The relationship between damage threshold and vibration velocity is constructed. It is concluded that when the space is greater than the damage threshold, the maximum vibration velocity fluctuation interval gradually increases, and the stress wave propagation velocity gradually weakens. The Sadovsky formula of spacing and vibration velocity peak is constructed to characterize the change law. It provides a reference for the optimization of smooth blasting parameters in hard granite tunnels.