Showing papers on "Fracture toughness 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 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.

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.

Mechanisms of fast fracture and arrest in steels

Abstract: Studies of the unstable propagation and arrest of brittle fractures were conducted on four steels: plain carbon steel, 3 pct Si steel, A-517, and 4340. Unstable fractures were initiated in double-cantilever-beam test specimens by forcing a wedge between the two beams under compression. These fractures propagate at essentially constant wedge opening displacement and can be made to arrest within the confines of the specimen. The strain energy stored in the specimen at the onset of propagation was varied systematically by changing the root radius of the starting slot. The experiments show that Ka, the stress intensity at arrest, is not a materials constant but depends on the strain energy stored in the specimen. Values of άrcR, the average energy dissipation rate during propagation, calculated for the four steels, are in the range23- GIc ≲ άcrR ≲ G{Ic}. Detailed metallographic examinations show that brittle fractures appear highly segmented on interior sections, but that the individual segments are interconnected. This morphology is attributed to isolated, difficult-to-cleave regions, comparable in size to the grains, which are bypassed and remain unbroken at relatively large distances behind the crack front. Etching studies conducted on a silicon steel reveal that the plastic deformation attending crack propagation is largely confined to the plastic stretching of the ligaments behind the crack front. Increases in the size, number, and toughness of the ligaments with temperature coincide with the brittle-to-ductile transition. An analytical model consisting of an elastic crack with a regular array of tractions representing the ligaments supports the view that the ligaments are the principal source of brittle crack propagation resistance in the steels.

The Strength and Fracture Toughness of Polycrystalline Magnesium Oxide Containing Metallic Particles and Fibres

Abstract: The transverse rupture strength of hot-pressed and annealed composites of magnesium oxide and dispersed metallic phases (nickel, iron, cobalt) increases with increasing volume fraction of metal and annealing temperature. The strengthening effect of the metal is attributed to an inhibition of grain growth while flaw healing occurs during the annealing of the composites.

Steam Turbine Failure at Hinkley Point ‘A’:

Abstract: The catastrophic failure of Hinkley Point ‘A’ unit No. 5 in September 1969 was the result of spontaneous brittle fracture of a shrunk-on ***l.p. turbine disc, initiated by stress-corrosion cracking in the crown of a keyway in the disc bore. Stress corrosion cracking of disc bores and keyways was also found on a number of other discs. The discs were made of 3 Cr-Mo steel and complied with normal acceptance standards, but due to temper embrittlement, their fracture toughness was low, and cracks only about 1/16 in deep in the concentrated stress field at the keyway crown were large enough to initiate brittle fracture. Investigation of the cause of the stress-corrosion cracking is being separately reported.

Measuring the fracture toughness of cement paste and mortar

Abstract: Synopsis This paper describes two methods that have been used to measure the effective fracture toughness of cement pastes and mortars. The first is a notched-beam technique, combined with compliance measurements to measure the slow crack growth prior to instability. The change of toughness is measured for separate increments of crack growth as the crack propagates. The second method, using a double-cantilever beam, avoids the slow crack growth problem by making a specimen of variable web width such that the length of crack front increases with and exactly compensates for the effect of crack growth. Tests of both pastes and mortars show that the fracture toughness of cement paste is independent of crack growth but that the toughness of mortar increases as the crack propagates. For both materials, the stress intensity required to initiate crack growth was less than that to maintain crack growth at the loading rates used.

The fracture energy of carbon-fibre reinforced glass

Abstract: The fracture energy of carbon-fibre reinforced glass has been measured by the work of fracture technique, using specimens of varied geometry, Meaningful material properties were obtained only when crack propagation was controlled throughout failure. The work of fracture (γ F) depended on strain-rate and fibre volume fraction, and was typically ∼3 kJm−2 for a 40 vol % specimen. Variations of work of fracture due to strain-rates have been related to the microstructure of the fracture surfaces and estimates have been obtained of the fibre-matrix interfacial shear stress during pull-out. Approximate estimates have been made of the fracture initiation energy (γ I) by fracture mechanics analyses, γ I was less than γ F and no strain-rate sensitivity was detected. An attempt has been made to explain γ I in terms of the initial rate of release of strain energy during fibre fracture.

Fracture Mechanics Approach to Adhesive Joints

Abstract: This study investigates the problem of applying fracture mechanics to the opening mode fracture of a two-material (aluminum-epoxy-aluminum) system. The results of a finite element analysis of a two-material, single- edge-notch (SEN) plate are used with a compliance method in order to obtain strain energy rates, g, and with a displacement method to obtain stress intensity factors, K. Approximate relationships between the homo geneous system and the adhesive system for both K and g are determined. The relationship between K and g for the adhesive system is obtained. The experimental investigation provides an experimental compliance calibration for the same adhesive system and loading. Good reproducibility of the fracture toughness values obtained for the two-material system with SEN and tapered DCB specimens indicates the geometry independence of the fracture toughness. The effect of the notch root radius and proper specimen preparation are also considered.

Fracture Toughness of Materials

Abstract: G 2:: Gc = R 1. where G is the energy per unit area given up by the system (strain energy change plus external work) during an incremental extension of the crack and R is the energy absorbed by the material in the process of crack exten­ sion. It is common practice to measure Ge, which is the minimum value of G at which crack extension is observed experimentally. The quantities Rand Gc are indices of the material's fracture toughness and have the units of energy per unit area of crack extension. They are related to two other indices in common use: KIe (a critical stress-field in­ tensity) and 0* (a critical crack-opening displacement). The virtue of these toughness indices is that they describe the combinations of load and crack size (the necessary level of inspection) that will assure safe operation. Evaluations of the fracture toughness of materials draw on two disci­ plines: applied mechanics and materials science. Applied mechanics offers methods for evaluating G and Ge for cracks in different types of test specimens and structural components. These disci­ plines also provide quantitative descriptions of the crack-tip stress-strain environment within which the micro mechanisms of crack extension operate. Materials science is mainly concerned with determination of Rand, thereby, with the control of fracture toughness through an understanding of the effects of composition, microstructure, processing, and the identifica­ tion and analysis of the micro mechanisms of crack extension. This review draws on both of these disciplines to examine our present understanding of the fracture toughness of materials. We first discuss methods of determining G and K, and the relations among Ge, KI .. and 0*. The review then turns to the deformation of the crack tip prior to fracture, both macroscopically and on the atomic scale. With this background, prog-

The energy of crack propagation in carbon fibre-reinforced resin systems

Abstract: The energy expended during controlled crack propagation in unidirectionally reinforced composites of carbon fibre in a brittle resin matrix has been evaluated in terms of the energy dissipated during fibre-snapping, matrix-cracking and fibre pull-out. The work of fracture, γF, is found to depend principally on the frictional shear stress at the fibre/resin interface opposing pulling out of broken fibres. Differences in γF for carbon fibre/resin composites exhibiting a range of interfacial shear strengths and void contents have been explained with reference to variations in fracture surface topography of the fibrous composites. The effect of environment on properties of the interface and work of fracture was also investigated. The energy required to propagate a crack has been compared with the energy for fracture initiation, γI, using a linear elastic fracture mechanics approach. It was found that fibre pull-out energy is the principal contribution to γF, and γI is similar to the elastic strain energy release rate at the initiation of fracture of a brittle, orthotropic solid. For crack propagation parallel to fibres, γF and γI are similar and not unlike the fracture surface energy of the resin alone. The strength of the interface is important only in so far as it affects the value of γI.

Untempered Ultra-high Strength Steels of High Fracture Toughness

Abstract: ULTRA-HIGH strength steels now in use were developed decades ago by trial and error methods and they all have some undesirable characteristics, such as low fracture toughness at high levels of yield strength. So far there has been little effort to use the new concepts of alloying and micromechanics of fracture to improve existing alloys, or to find new ones with better combinations of properties. We are studying the factors that contribute to notch brittleness in high strength steels and we have learned how to increase the fracture toughness of steels having yield strength in excess of 200,000 pound inch−2 by as much as 70%. We use treatments that differ significantly from the normal commercial practice for quenched and tempered low alloy steels, which involves heating to the lower end of the austenite temperature range (to minimize grain size), quenching fast enough to produce martensite and tempering at a temperature that will optimize mechanical properties.

Gaseous hydrogen-induced cracking of Ti-5Al-2.5Sn

Abstract: The kinetics of hydrogen-induced cracking have been studied in the Ti-5Al-2.5Sn titanium alloy having a structure of acicular α platelets in a β matrix. It was observed that the relationship between hydrogen-induced crack growth rate and applied stress intensity can be described by three separable regions of behavior. The crack-growth rate at low stress-intensity levels was found to be exponentially dependent on stress intensity but essentially independent of temperature. The crack-growth rate at intermediate stress-intensity levels was found to be independent of stress intensity but dependent on temperature in such a way that crack-growth rate was controlled by a thermally activated mechanism having an activation energy of 5500 cal per mole and varied as the square root of the hydrogen pressure. The crack-growth rate at stress-intensity levels very near the fracture toughness is presumed to be independent of environment. The results are interpreted to suggest that crack growth at high stress intensities is controlled by normal, bulk failure mechanisms such as void coalescence and the like. At intermediate stress-intensity levels the transport of hydrogen to some interaction site along the α-β boundary is the rate-controlling mechanism. The crack-growth behavior at low stress intensities suggests that the hydrogen interacts at this site to produce a strain-induced hydride which, in turn, induces crack growth by restricting plastic flow at the crack tip.

Fracture toughness of composites reinforced with discontinuous fibres

Abstract: Measurements of the work of fracture of composites of polyester resin reinforced with chopped steel wires of various lengths are compared with the theory developed by Cooper. For composites containing aligned wires the results agree well with the model except where there is excessive resin cracking. The toughness of composites containing wires which are randomly distributed in the resin can be significantly greater than that of aligned composites with wires of similar length. This is probably due to the plastic shearing of wires not lying parallel or normal to the specimen axis.

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.