Showing papers on "Stress concentration published in 1972"

Fracture under complex stress — The angled crack problem

Abstract: Experiments are described in which thin plates of polymethylmethacrylate were fractured with cracks set at various angles to an applied uniaxial stress. While there is substantial agreement with previous analytical predictions, it is shown that inclusion of the stress component parallel to the crack can improve the correlation between linear theory and experiment, using a critical stress at a critical distance interpretation of the stress intensity factor criterion.

The strength of brittle materials containing second phase dispersions

Abstract: Cracks in brittle materials can be impeded by obstacles in the form of second phase dispersions. The crack tends to bow out between obstacles forming secondary semi-elliptical flaws. The strength is determined by the stress to propagate these secondary cracks. Stress calculations show that this depends on the ratios of the obstacle dimensions and the obstacle spacing and, except for large relative obstacle spacings, the stress is larger than the stress to extend the primary crack. Second phase dispersions will usually increase strength, therefore, through an effect equivalent to the ‘line tension effect’ observed for dislocation motion. A comparison of the calculated ‘line tension effect’ with observed increases in strength in brittle matrix composites shows that line tension is the major contribution to the strength increase for brittle obstacles, but only a minor contribution for fibre composites, and probably a minor contribution for ductile obstacles.

Crack propagation in an elastic solid subjected to general loading—II. Non-uniform rate of extension

Abstract: The stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to general loading is determined. The loading is applied in such a way that a state of plane strain exists and that crack extension takes place in Mode I. The crack tip is initially at rest and then moves in an arbitrary way in the plane of the crack. In the process of obtaining the stress intensity factor, the complete elastic field is determined for a crack which starts from some initial position, extends at a constant rate for some time, and then suddenly stops. Once the stress intensity factor is known for arbitrary motion of the crack tip, the Griffith fracture criterion is applied to obtain an equation of motion for the crack tip which is consistent with the assumptions of this criterion. Numerical results are included for the stress intensity factor and for the velocity-dependent term in the equation of motion.

Crack opening displacement and the rate of fatigue crack growth

Abstract: Using a direct proportionality between the rate of fatigue crack growth and crack opening displacement above a threshold, it is shown that fatigue crack growth data for a wide variety of different materials can be accurately described in terms of the mechanical properties and two material constants; the constant of proportionality A and the threshold stress intensity factorKth. Some 65 sets of data for tests atR ≅ 0 were analysed by computer and it is shown that the approach is valid to growth rates up to about 10−4 in./cycle, i.e. until the onset of crack propagation by dimple formation. It is found thatA can be related to the yield strain for crack growth in non-aggressive environments, and is increased by increasingly severe environments, whileKth is decreased. These changes provide a measure of the severity of the environment. Crack growth rate in non-aggressive environments is shown to be independent of the yield stress and proportional to the strain intensity factor above the threshold. The tabulation ofA andKth values as a function of material, environment and loading conditions provides a systematic engineering approach to estimating rates of fatigue crack growth and in determining the residual lifetimes of flawed structures.

The fracture mechanics of slit-like cracks in anisotropic elastic media

Abstract: U sing the method of continuously distributed dislocations, the problem of a slit-like crack in an arbitrarily-anisotropic linear elastic medium stressed uniformly at infinity is formulated and solved. The crack faces may be either freely-slipping or loaded by arbitrary equal and opposite tractions. If there is no net dislocation content in the crack, then the tractions and stress concentrations on the plane of the crack are independent of the elastic constants and the anisotropy; the same is true of the elastic stress intensity factors. The crack extension force depends on anisotropy only through the inverse matrix elements Kmg−1, where [K] is the pre-logarithmic energy factor matrix for a single dislocation parallel to the crack front. Numerical results for crack extension forces are presented for three media of cubic symmetry.

Brittle fracture in compression

Abstract: The apparent paradox of two theories of fracture depending on whether the applied load is tensile or compressive is resolved. Although in compression, fracture seems to occur when the maximum tensile stress around a hole reaches a critical value it is suggested that fracture occurs when the crack extension force at the tip of a microcrack in the neighbourhood of the crack tip reaches a critical value. An essential difference in behaviour under tension and compression is that whereas in tension the crack extension force increases with crack growth, in compression a maximum value of the crack extension force is reached with further crack growth causing a decrease in its value. If the defects, which must exist at the edge of a machined hole, are small, then the crack extension force is controlled by the maximum tensile stress at the surface of the hole. The degree of smallness is different for tension and compression. In tension, the defects must be less than one fifth of the root radius of the tip of the hole and if the hole is sharp enough, the defects will be larger than this value and the crack extension force will be given by the usual fracture mechanics expressionG = σ2 πc/E. In compression the defects must, in the limiting case, be greater than the root radius of the tip of the hole (in a more typical case, greater than twice the root radius) if the crack extension force is not to be controlled by the maximum tensile force. Such large defects are impossible since the sharpness of the root radius is limited by the defect size and thus in compression, fracture from machined notches will always be controlled by the maximum tensile stress.

Stress Distribution at the Interface Between Tool and Chip in Machining

Abstract: Stress distribution along a tool rake face were measured directly in the orthogonal machining of various metals. The method of measurement was based on the use of a composite tool which was divided into two parts parallel to a cutting edge in order to measure separately the force acting on one section of the tool. The stress distributions under actual cutting conditions were revealed, and the relationship between the nature of stress distribution and the mechanical properties of work material was clarified. It was ascertained that the nature of stress distribution was closely connected with the strain hardening index of work material and the frictional coefficient between tool and material.

Fracture mechanics of composites

Abstract: The concepts of linear-elastic fracture mechanics are introduced and their application to the interpretation of fracture behavior of composite materials is illustrated. Linear-elastic fracture mechanics is based on a description of the linear-elastic stress field around the tip of a crack. The equations for stresses close to a crack tip in a homogeneous, isotropic plane plate are developed. These equations lead directly to the definition of the stress-intensity factor K, a single-parameter characterization of the crack-tip stress field. The level of K corresponding to crack extension and fracture is a measure of the fracture toughness of a material. For fibrous composites, crack-tip stress field equations and the stress-intensity factors for a linear-elastic special orthotropic homogeneous material are introduced. Small-scale plastic behavior at the crack tip and its influence on the crack-tip stress field and stress-intensity factor K are discussed. Crack extension force Ĝ is defined and related to the stress-intensity factor K. Crack-tip stress fields for two-material members with cracks at and near the interface are presented. Fracture analysis for two particulate composite systems, a WC-reinforced cobalt alloy and a W-particle reinforced glass composite are reviewed. A parallel filament glass-epoxy composite is traced through a failure analysis, as well as experiments designed to investigate the applicability of fracture mechanics, using a special orthotropic homogeneous material model, to describe the observed crack extension behavior. The general features of crack extension behavior, specifically the observed relation between Ĝ and crack speed a are discussed and illustrated for epoxy-aluminum adhesive joints. The influence of moisture and sustained loads on the crack extension behavior of epoxy adhesive joints are reported. This article concludes with a discussion of the areas of fracture mechanics, both analytical and experimental, that require attention to develop improved composite materials and structural systems.

The Strength of Glass

Abstract: The search for new high strength materials has always been one of the more active areas in the materials sciences, and while glass is not normally catagorized with high strength metallic alloys and crystalline ceramics, it does have particular properties which will warrant, or necessitate, its use in many new applications.

Fundamental Investigations of Fretting Fatigue : Part 6, Effects of Contact Pressure and Hardness of Materials

Abstract: Fretting fatigue tests have been made about the effect of clamping pressure, p0, and hardness of materials on the initiation of non-propagating cracks and also complete fracture under the conditions where the relative slip is fully controlled. The main results obtained are as follows. (1) Fretting fatigue strength based on the initiation of fatigue cracks, σw1, decreases linearly with the increase of p0. (2) Fretting fatigue strength based on fracture, σw2, decreases gradually with the increase of contact pressure, and reaches a critical strength when p0 is beyond a certain value. (3) These results in (1) and (2) are analogous to fatigue phenomena of notched specimens, when the stress concentration caused by fretting is considered. (4) When the relative slip of fretting is relatively large, σw1 is affected by the susceptibility of materials to wear.

The role of mechanical properties in low-stress fatigue crack propagation

Abstract: An experimental investigation was undertaken to study the relationship between mechanical properties and low stress fatigue crack propagation. Attention was focused on the “fatigue” or “reversed plastic zone” at the crack tip, since it was felt that material properties in this region were of prime importance in the crack propagation process. An effort was made to simulate this region through fully reversed strain-cycling tests on tensile specimens. Mechanical properties obtained from a number of materials before and after strain cycling were correlated with crack propagation data from the same materials. Evidence indicated that while monotonic tensile properties are inadequate for correlation purposes, the cyclic strain-hardening coefficient, the cyclic yield strength, and the elastic modulus appear to be important parameters. This was felt to be an indication of the importance of strain cycling in the reversed plastic zone in influencing the rate-governing mechanisms in fatigue crack growth.

Visco-elastic and thermal effects on crack growth in PMMA

Abstract: An approximate visco-elastic analysis is described for crack growth in PMMA. It is shown that there is a change in the fracture criterion from a constant energy to a constant crack opening displacement when cracks are run below and above their initiation speeds respectively. This analysis is coupled with a prediction of temperature rises at the crack tip and it is shown that this results in a marked maximum in the stress intensity factor crack versus speed curve which corresponds closely to the instability value.

Effect of cyclic stress wave form on corrosion fatigue crack propagation in al-zn-mg alloys

Abstract: Fatigue crack growth rates of a 7075 type aluminum alloy were measured as a function of environment, frequency, stress wave form, alloy chemistry, and thermomechanical treatment. At low ΔK values (belowKISCC), the crack growth rates in a 3.5 pct sodium chloride solution were ten times greater than those in a reference argon environment. Comparison of the effects of a square wave, a negative-sawtooth wave, and a positivesawtooth wave at different frequencies indicates that the synergistic interaction with the environment occurs during the loading part of each cycle. Overaging the alloy and limiting the alloy impurity content results in a reduced corrosion fatigue crack growth rate, but a thermomechanical treatment leading to a grain size refinement increases it.