Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

— A modification to Brown and Miller's critical plane approach is proposed to predict multiaxial fatigue life under both in-phase and out-of-phase loading conditions. The components of this modified parameter consist of the maximum shear strain amplitude and the maximum normal stress on the maximum shear strain amplitude plane. Additional cyclic hardening developed during out-of-phase loading is included in the normal stress term. Also, the mathematical formulation of this new parameter is such that variable amplitude loading can be accommodated. Experimental results from tubular specimens made of 1045 HR steel under in-phase and 90° out-of-phase axial-torsional straining using both sinusoidal and trapezoidal wave forms were correlated within a factor of about two employing this approach. Available Inconel 718 axial-torsional data including mean strain histories were also satisfactorily correlated using the aforementioned parameter.

A critical plane approach to multiaxial fatigue damage including out-of-phase loading

This paper summarises the keynote talk opening the session on ‘Critical Distance Theories of Fracture’; my aim is to describe the methodology used, to demonstrate its applicability in predicting experimental data on fracture and fatigue, to discuss the fundamental basis of the theory and, to suggest areas for future work in this field. The Theory of Critical Distances (TCD) is the name which I have given to a group of theories used for predicting the effects of notches and other stress-concentration features. These theories have a long history, but currently they are being investigated by only a small number of researchers worldwide. This is a pity, because the TCD is capable of accurate predictions in a wide variety of situations. The essential elements are an elastic stress analysis and a material-dependent critical distance, a parameter which we call L. The value of L can be written in terms of other material parameters as: 

$$ L = \frac{1} {\pi }\left( {\frac{{K_c }} {{\sigma _o }}} \right)^2 $$

(1)

The Theory of Critical Distances

Brittle failure of components weakened by cracks or sharp and blunt V-notches is a topic of active and continuous research. It is attractive for all researchers who face the problem of fracture of materials under different loading conditions and deals with a large number of applications in different engineering fields, not only with the mechanical one. This topic is significant in all the cases where intrinsic defects of the material or geometrical discontinuities give rise to localized stress concentration which, in brittle materials, may generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. Whereas cracks are viewed as unpleasant entities in most engineering materials, U- and V-notches of different acuities are sometimes deliberately introduced in design and manufacturing of structural components. Dealing with brittle failure of notched components and summarizing some recent experimental results reported in the literature, the main aim of the present contribution is to present a review of some local approaches applicable near stress raisers both sharp and blunt. The reviewed criteria allowed the present authors to develop a new approach based on the volume strain energy density (SED), which has been recently applied to assess the brittle failure of a large number of materials. The main features of the SED approach are outlined in the paper and its peculiarities and advantages accurately underlined. Some examples of applications are reported, as well. The present review is based on the authors’ experience over more than 15 years and the contents of their personal library. It is not a dispassionate literature survey.

Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches

Quantitative evaluation of effects of non-metallic inclusions on fatigue strength of high strength steels. I: Basic fatigue mechanism and evaluation of correlation between the fatigue fracture stress and the size and location of non-metallic inclusions

Fracture toughness and fatigue crack propagation in high strength steel from room temperature to −180°c

Effects of ferrite grain size, notch acuity and notch length on brittle fracture stress of notched specimens of low carbon steel

The computer simulation is presented of the dynamic behaviour of linear arrays of edge dislocations emitted from a source under a constant rate τ of application of stress for the case when stress τ and velocity v are related by the expression v = Mτm . It is shown that the number N of dislocations emitted is controlled only by the dynamic factor: τ ≈ τ(m+1/m+2) t, where t is time. For large values of N, N is given by A0η m+1, where A0 is a material constant. The dynamic behaviour, such as the position of, the effective stress on, and the velocity of the lead dislocation is deduced. The possibility of the application of the results to the kinetic theory of fatigue crack propagation is discussed.

Computer simulation of dislocation emission from a stressed source

An attempt has been made to examine any differences in behavior between uni-axial fatigue and repeated torsion fatigue. In order to eliminate the stress gradient effect, thin-walled hollow cylindrical specimens were used. Low cycle fatigue tests of mild steel were conducted in uni-axial and torsional loading at constant strain amplitude.

Low cycle fatigue of thin-walled hollow cylindrical specimens of mild steel in uni-axial and torsional tests at constant strain amplitude

Fatigue crack growth behaviour under mixed modes I and II was studied by applying in-phase alternating tensile and torsional loading to a thin-walled hollow cylindrical specimen with an initial crack.



In the linear region of a log-log plot where da/dN=A(ΔK)m, da/dN at first decreases with increasing ΔK110 component and then approaches a minimum close to the value of ΔK110/ΔK10∼ 0.58; here ΔK110/ΔK10 is the ratio of the initial ΔKII to the initial ΔK1., When ΔK110/ΔK10 increases further, da/dN increases. Under shear mode, da/dN becomes higher than that under mode I. The ΔK1, and ΔK11 components during fatigue crack growth under mixed mode loading increase and decrease, respectively, with an increase in da/dN In the low crack growth rate region the fatigue crack growth rates accelerate with an increase of the initial ΔK11 component, ΔK110. Fatigue life increases with increase of ΔK110/ΔK10 under the test condition of equivalent stress range being kept constant and the pre-crack length being the same.

Takeo Yokobori

Papers

Fracture toughness and fatigue crack propagation in high strength steel from room temperature to −180°c

Effects of ferrite grain size, notch acuity and notch length on brittle fracture stress of notched specimens of low carbon steel

Computer simulation of dislocation emission from a stressed source

Low cycle fatigue of thin-walled hollow cylindrical specimens of mild steel in uni-axial and torsional tests at constant strain amplitude

Fatigue crack growth under mixed modes i and ii