Showing papers on "Fracture toughness published in 1974"

Elementary engineering fracture mechanics

Abstract: I Principles.- 1 Summary of basic problems and concepts.- 1.1 Introduction.- 1.2 A crack in a structure.- 1.3 The stress at a crack tip.- 1.4 The Griffith criterion.- 1.5 The crack opening displacement criterion.- 1.6 Crack propagation.- 1.7 Closure.- 2 Mechanisms of fracture and crack growth.- 2.1 Introduction.- 2.2 Cleavage fracture.- 2.3 Ductile fracture.- 2.4 Fatigue cracking.- 2.5 Environment assisted cracking.- 2.6 Service failure analysis.- 3 The elastic crack-tip stress field.- 3.1 The Airy stress function.- 3.2 Complex stress functions.- 3.3 Solution to crack problems.- 3.4 The effect of finite size.- 3.5 Special cases.- 3.6 Elliptical cracks.- 3.7 Some useful expressions.- 4 The crack tip plastic zone.- 4.1 The Irwin plastic zone correction.- 4.2 The Dugdale approach.- 4.3 The shape of the plastic zone.- 4.4 Plane stress versus plane strain.- 4.5 Plastic constraint factor.- 4.6 The thickness effect.- 5 The energy principle.- 5.1 The energy release rate.- 5.2 The criterion for crack growth.- 5.3 The crack resistance (R curve).- 5.4 Compliance.- 5.5 The J integral.- 5.6 Tearing modulus.- 5.7 Stability.- 6 Dynamics and crack arrest.- 6.1 Crack speed and kinetic energy.- 6.2 The dynamic stress intensity and elastic energy release rate.- 6.3 Crack branching.- 6.4 The principles of crack arrest.- 6.5 Crack arrest in practice.- 6.6 Dynamic fracture toughness.- 7 Plane strain fracture toughness.- 7.1 The standard test.- 7.2 Size requirements.- 7.3 Non-linearity.- 7.4 Applicability.- 8 Plane stress and transitional behaviour.- 8.1 Introduction.- 8.2 An engineering concept of plane stress.- 8.3 The R curve concept.- 8.4 The thickness effect.- 8.5 Plane stress testing.- 8.6 Closure.- 9 Elastic-plastic fracture.- 9.1 Fracture beyond general yield.- 9.2 The crack tip opening displacement.- 9.3 The possible use of the CTOD criterion.- 9.4 Experimental determination of CTOd.- 9.5 Parameters affecting the critical CTOD.- 9.6 Limitations, fracture at general yield.- 9.7 Use of the J integral.- 9.8 Limitations of the J integral.- 9.9 Measurement of JIc and JR.- 9.10 Closure.- 10 Fatigue crack propagation.- 10.1 Introduction.- 10.2 Crack growth and the stress intensity factor.- 10.3 Factors affecting crack propagation.- 10.4 Variable amplitude service loading.- 10.5 Retardation models.- 10.6 Similitude.- 10.7 Small cracks.- 10.8 Closure.- 11 Fracture resistance of materials.- 11.1 Fracture criteria.- 11.2 Fatigue cracking criteria.- 11.3 The effect of alloying and second phase particles.- 11.4 Effect of processing, anisotropy.- 11.5 Effect of temperature.- 11.6 Closure.- II Applications.- 12 Fail-safety and damage tolerance.- 12.1 Introduction.- 12.2 Means to provide fail-safety.- 12.3 Required information for fracture mechanics approach.- 12.4 Closure.- 13 Determination of stress intensity factors.- 13.1 Introduction.- 13.2 Analytical and numerical methods.- 13.3 Finite element methods.- 13.4 Experimental methods.- 14 Practical problems.- 14.1 Introduction.- 14.2 Through cracks emanating from holes.- 14.3 Corner cracks at holes.- 14.4 Cracks approaching holes.- 14.5 Combined loading.- 14.6 Fatigue crack growth under mixed mode loading.- 14.7 Biaxial loading.- 14.8 Fracture toughness of weldments.- 14.9 Service failure analysis.- 15 Fracture of structures.- 15.1 Introduction.- 15.2 Pressure vessels and pipelines.- 15.3 "Leak-bcfore-break" criterion.- 15.4 Material selection.- 15.5 The use of the J integral for structural analysis.- 15.6 Collapse analysis.- 15.7 Accuracy of fracture calculations.- 16 Stiffened sheet structures.- 16.1 Introduction.- 16.2 Analysis.- 16.3 Fatigue crack propagation.- 16.4 Residual strength.- 16.5 The R curve and the residual strength of stiffened panels.- 16.6 Other analysis methods.- 16.7 Crack arrest.- 16.8 Closure.- 17 Prediction of fatigue crack growth.- 17.1 Introduction.- 17.2 The load spectrum.- 17.3 Approximation of the stress spectrum.- 17.4 Generation of a stress history.- 17.5 Crack growth integration.- 17.6 Accuracy of predictions.- 17.7 Safety factors.- Author index.

Strain-energy-density factor applied to mixed mode crack problems

Abstract: This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k 1,k 2 are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS cr is related tok 1c alone asS cr = (κ − 1)k 1 2 /8μ. In general,S takes the quadratic forma 1 1 k 1 + 2a 1 2 k 1 k 2 +a 2 2 k 2 whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.

Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations

Abstract: Two related criteria based on stress distribution are presented for predicting the uniaxial tensile strength of laminated composites containing through the thickness discontinuities of a general shape. The criteria result in two parameter (unnotched tensile strength and a characteristic dimension) models which are capable of predicting observed discontinuity size effects without resorting to classical concepts of linear elastic fracture mechanics. As a direct consequence of the stress criteria, however, a relationship between Mode I fracture toughness and unnotched laminate tensile strength is determined. Limited comparison of theory to experimental data for circular holes and straight cracks yields good results. The simplicity of the analytical approach coupled with its generality make it of practical value to the designer.

Brittle fracture in compression

Abstract: The initiation and propagation of microfractures and their contribution to material failure in compression are examined. The early part of the fracture process, the lateral and the axial yield points of the stress-strain curves, are identified with the onset of microfracture, respectively at the tensile and the compressive stress concentrations of the elastic flaw boundary. Later stages, including the initiation of inclined shear fractures, the mobilization of total resistance and the reduction of strength to the residual level, are discussed in terms of a modified Coulomb model.

A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses

Abstract: : A weakest link theory for macroscopically homogeneous isotropic materials containing uniformly distributed, randomly oriented cracks is developed under the assumption that fracture depends only on the stress normal to a crack plane. The function representing the number of cracks failing at each value of normal stress is expanded as a Taylor series with coefficients determined from tensile test data. This function is used without additional assumptions to determine the probability of fracture under arbitrary stress conditions. The results can be readily incorporated into a finite element code to predict the failure probability of any structure to which the code applies. (Author)

Small-Scale Yielding Analysis of Mixed Mode Plane-Strain Crack Problems

Abstract: The small-scale yielding analysis of an elastic-plastic body with a line crack under plane-strain conditions subject to combinations of Mode I and II loadings is examined. The analysis of the near-tip field follows the works of Hutchinson and Rice and Rosengren. Dominant singularity solutions governing the asymptotic behavior of the stresses and strains at the crack tip are obtained for the complete range of loadings between Mode I and II. The results of an accurate finite element technique, which imbeds the dominant singularity solutions, directly relates the near-tip behavior to the elastic stress intensity factors K(I) and K(II). Implications of this study to mixed mode fracture mechanics is also discussed, particularly with respect to the direction of crack initiation and the relation of fracture toughness under mixed modes to that in Mode I. Details of the mixed mode plastic zone sizes and shapes are also given.

Temperature effects in the fracture of PMMA

Abstract: Experiments are described in which the fracture toughness,K c, of PMMA has been determined in the temperature range −190 to + 80° C and over the crack speed range of 10−2 to 102 mm sec−1. Single edge notch tension was used for instability measurements but the other data were obtained using the double torsion method. In the range −80 to + 80°C the variations inK c may be described in terms of modulus changes and a constant crack opening displacement criterion. Crack instabilities are correlated with isothermal-adiabatic transitions at the crack tip. Below −80° C there is an inverted rate dependence associated with thermal effects during post-instability crack propagation.

The effect of austenitizing temperature on the microstructure and mechanical properties of as-quenched 4340 steel

Abstract: The effect of austenitizing temperature on both the plane strain fracture toughness,KIC, and the microstructure of AISI 4340 was studied. Austenitizing temperatures of 870 and 1200°C were employed. All specimens austenitized at 1200°C were furnace cooled from the higher austenitizing temperature and then oil quenched from 870°C. Transmission electron microscopy revealed an apparent large increase in the amount of retained austen-ite present in the specimens austenitized at the higher temperature. Austenitizing at 870°C resulted in virtually no retained austenite; only minor amounts were found sparsely scat-tered in those areas examined. A considerably altered microstructure was observed in specimens austenitized at 1200°C. Fairly continuous 100 to 200A thick films of retained austenite were observed between the martensite laths throughout most of the area exam-ined. Additionally, specimens austenitized at 870°C contained twinned martensite plates while those austenitized at 1200°C showed no twinning. Plane strain fracture toughness measurements exhibited an approximate 80 pct increase in toughness for specimens austen-itized at 1200°C compared to those austenitized at 870°C. The yield strength was unaffected by austenitizing temperature. The possible role of retained austenite and the elimination of twinned martensite in the enhancement of the fracture toughness of those specimens austen-itized at the higher temperature will be discussed.

Adhesive fracture mechanics

Abstract: In studies of fracture mechanics the adhesive fracture energy is regarded as a fundamental property of the adhesive system. It is pointed out that the value of the adhesive fracture energy depends on surface preparation, curing conditions, and absorbed monolayers. A test method reported makes use of a disk whose peripheral part is bonded to a substrate material. Pressure is injected into the unbonded central part of the disk. At a certain critical pressure value adhesive failure can be observed. A numerical stress analysis involving arbitrary geometries is conducted.

The strength, fracture toughness, and low cycle fatigue behavior of 17-4 PH stainless steel

Abstract: The influence of microstructure on the strength, fracture toughness and low cycle fatigue behavior of 17-4 PH stainless steel has been examined. Aging hardening involves initial formation of coherent copper-rich clusters which transform to incoherent fee ∈-copper precipitates upon further aging. The changes in strength level and strain hardening rates observed during aging are consistent with previously suggested models for precipitation hardening based on differing elastic moduli. The fracture toughness and fatigue crack growth rates were shown to be a function of microstructure and environment. At equivalent strength levels overaging resulted in a higher fracture toughness than did underaging. The fatigue crack growth rates increased with increasing strength level and humidity but were not a function of toughness level. Attempts to correlate the fatigue crack growth rates with monotonie tensile properties were unsuccessful. However when final failure obeyed a critical strain criteria, the fracture toughness behavior could be reasonably described and related to preferential void nucleation and growth at δ-ferrite-matrix interfaces.

Effect of hydrogen on fracture and inert-environment sustained load cracking resistance of α- β titanium alloys

Abstract: The fracture toughness and resistance to inert-environment sustained load crack propagation of α-β titanium alloys are usually reduced by increased hydrogen contents. The range of hydrogen contents over which either fracture toughness or threshold stress intensity for sustained load cracking was observed to decrease with hydrogen content is small (0 to 50 ppm) for Ti-6 Al-4 V, but further increases in hydrogen content can cause an increase in cracking rates. Sustained load crack propagation is characterized by a mixture of microvoid coalescence with cleavage, usually on a plane 12 to 15 deg from {0001} of the hep α phase with some {000l} cleavage. Cleavage apparently initiates ahead of the main crack front within a grains, usually near apparent α-β interfaces. Atmospheric moisture is inert with respect to sustained load cracking, that is, it does not cause stress corrosion cracking. Sustained load cracking was demonstrated in Ti-8 Al-1 Mo-1 V, Ti-6 Al-6 V-2 Sn, and several grades of Ti-6 Al-4 V.

Interfacial bonding and the toughness of carbon fibre reinforced glass and glass-ceramics

Abstract: The work of fracture of four different carbon fibre reinforced glass and glass-ceramic composites has been measured to determine the effects of the different properties of the components on fracture behaviour. Differences in fracture energies can be explained in terms of the fibre pull-out model and differences in the fibre-matrix interfacial shear bond. The work of fracture of the glass-ceramic is independent of crack velocity while that of the Pyrex matrix composite decreases with increasing velocity at low velocities, the decrease stopping at higher velocities. Work of fracture values agree well with linear elastic fracture mechanics toughness values.

Fracture Toughness and Spalling Behavior of High‐Al2O3 Refractories

Abstract: The fracture energies and spalling resistance of high-Al2O3 refractories were studied. The fracture energies, γWOF and γNBT, were measured by the work-of-fracture and the notched-beam-test methods, respectively. Spalling resistance, as measured by the relative strength retained in a water quench, correlated well with the thermal-stress resistance parameter applicable to stable crack propagation under conditions of thermal shock, (γWOF/α2E0). Many of the refractories exhibited high ratios of γWOF to γNBT; such high ratios were shown analytically to maximize the parameter (R1111=E0γWOF/S12) which describes the resistance to catastrophic spalling. The increase of crack length with increasing quenching temperature difference (ΔT) was somewhat less than that predicted theoretically; the discrepancy was attributed to an increase of crack density with ΔT. In general, the results show that fracture energy is important in establishing the spalling resistance of high-Al2O3 refractories.

Correlations between fracture surface appearance and fracture mechanics parameters for stage II fatigue crack propagation in TÏ-6AI-4V

Abstract: Stage fatigue crack propagation in Ti-6A1-4V has been studied as a function of various fracture mechanics parameters, including the stress intensity range (ΔK) and both positive and negative ratios of the minimum to maximum stress (R). It was found that the fracture surface appearance undergoes a transition from cyclic cleavage to striations at a ΔKeff of approximately 13 MNm-3/2 (11.8 ksi√in.). It was also observed that the measured striation spacings are generally within a factor of two of the optically measured crack growth rates. Both of these results can be particularly useful for determining unknown component cyclic loadings during failure analysis. The criterion for the cyclic cleavage to striation transition is considered to be a change from primarily single to multiple slip within the individual grains at the crack tip. This occurs when the cyclic plastic zone size becomes approximately equal to the α grain size.

The evolution of brittle fracture in rocks

Abstract: At the macroscopic scale, the process of brittle fracture, leading to the formation of a macroscopic fault, involves several stages of fracture development. The usual sequence of events consists of the following stages: load-parallel tensile fracture, load-normal shear fracture, inclined shear fracture, strength failure, second order fracture and faulting. The first two stages can be defined quantitatively in terms of an elastic flaw concept which is based on the elastic stress distribution existing around the flaw prior to the appearance of the first fracture. The appropriate theories are developed through a stress model which, in departure from other brittle fracture theories, involves the stress gradient along the fracture path. Experimental results are introduced to demonstrate the general validity of the stress gradient model. The initiation of the first inclined shear fracture seems to be contingent on the existence of a quasi-cataclastic state produced by the earlier sets of load-parallel tensile and load-normal shear fractures. Because the original elastic stress distribution, including the stress anomaly around the flaw, is destroyed before the initiation of the inclined shear fracture, later events of fracture cannot be interpreted in terms of the elastic flaw model • Probably a Coulomb-type mechanism, similar to the one involved in the failure of cohesionless, granular materials, controls the initiation and propagation of inclined shear fractures as well as the development of maximum resistance.

Interfacial fracture energy and the toughness of composites

Abstract: The premises upon which prevailing composite toughness theories are based are discussed in the light of observed strength variations in boron-epoxy composites with differing shear strengths of the interfacial bond. None of the extant toughness theories (pull-out, debonding, stress redistribution) successfully predicts the work of fracture of the boronepoxy system. However, incorporation of the work to create new surfaces into the total toughness analysis gives better agreement with experiment, and work of fracture predictions for other sytems, such as carbon-polyester, can also be modified. The approach is more generalized than the Outwater/Murphy debonding explanation for toughness, which in the way usually presented only applies when the filament fracture strain is greater than the matrix fracture strain. The present analysis suggests how to tailor the interfacial shear strength in order to obtain a reasonable toughness yet still maintain strengths of the order of the rule of mixtures.

Application of Fracture Mechanics to Space-Shuttle Windows

Abstract: The fracture properties of an ultralow-expansion glass intended for use in windows for the Space Shuttle were characterized by strength and fracture-mechanics techniques to provide reliable design data. Proof-test diagrams for predicting minimum times-to-failure under specified service loads were developed from measurements of subcritical crack growth in water and air. Failure predictions were confirmed from strength measurements in water. In vacuum (<10−4 torr), the fracture behavior was similar to that of other high-SiO2 glasses, as evidenced by the absence of subcritical crack growth and by insensitivity of the critical stress intensity factor to temperature.

Increased fracture toughness in a 300 grade maraging steel as a result of thermal cycling

Abstract: Systematic changes in the fracture toughness of a 300 grade commercial maraging steel were obtained using a non-standard heat-treating process. Microstructures consisting of variable amounts of retained austenite in an aged martensitic matrix were produced. A mathematical model is presented relating these toughness values to the properties of the individual constituents. Increases in fracture toughness resulting from the non-standard heat-treatment were attributed to the nature of the distribution of the tough phase (retained austenite) in a brittle matrix of precipitation hardened martensite. In some cases, a strain-induced transformation to martensite was observed which greatly added to the toughness. Some improvements in fatigue crack propagation characteristics also resulted from this heat treatment.

Stress analysis of the compact specimen including the effects of pin loading

Abstract: An improved method of boundary collocation was applied to the two-dimensional stress analysis of the compact specimen. The effects of the pin-loaded holes on stress-intensity factors and crack-opening displacements were investigated for various crack-length-to-specimen-width ratios, hole locations, and internal loadings. The stress-intensity factors for the 'standard' compact specimen under plane-stress or plane-strain conditions were found to be within 1 percent of the stress-intensity factors reported in the ASTM Test for Plane-Strain Fracture Toughness of Metallic Materials (E 399-72) over a range of crack-length-to-specimen-width ratios of 0.4 to 0.7. However, for crack-length-to-specimen-width ratios less than 0.4, the pin-load holes (which were not previously accounted for) had a significant effect on stress intensity and crack-opening displacements.

Fracture toughness tests of a rigid polyurethane foam

Abstract: The results of some exploratory tests for determining the fracture toughness of a rigid polyurethane foam are presented. The specimen geometries used included centre- and double-edge-cracked plates, the single-edge-cracked tensile specimen and the double cantilever beam specimen. The validity of applying the concepts of linear elastic fracture mechanics to the fracture of this foam is discussed. Some unique features of the fracture of foam are discussed.