Showing papers on "Paris' law published in 1988"

The practical use of fracture mechanics

Abstract: 1. Introduction.- 1.1. Fracture control.- 1.2. The two objectives of damage tolerance analysis.- 1.3. Crack growth and fracture.- 1.4. Damage tolerance and fracture mechanics.- 1.5. The need for analysis: purpose of this book.- 1.6. Exercises.- 2. Effects of Cracks and Notches: Collapse.- 2.1. Scope.- 2.2. An interrupted load path.- 2.3. Stress concentration factor.- 2.4. State of stress at a stress concentration.- 2.5. Yielding at a notch.- 2.6. Plastic collapse at a notch.- 2.7. Fracture at notches: brittle behavior.- 2.8. Measurement of collapse strength.- 2.9. Exercises.- 3. Linear Elastic Fracture Mechanics.- 3.1. Scope.- 3.2. Stress at a crack tip.- 3.3. General form of the stress intensity factor.- 3.4. Toughness.- 3.5. Plastic zone and stresses in plane stress and plane strain.- 3.6. Thickness dependence of toughness.- 3.7. Measurement of toughness.- 3.8. Competition with plastic collapse.- 3.9. The energy criterion.- 3.10. The energy release rate.- 3.11. The meaning of the energy criterion.- 3.12. The rise in fracture resistance: redefinition of toughness.- 3.13. Exercises.- 4. Elastic-Plastic Fracture Mechanics.- 4.1. Scope.- 4.2. The energy criterion for plastic fracture.- 4.3. The fracture criterion.- 4.4. The rising fracture energy.- 4.5. The residual strength diagram in EPFM: collapse.- 4.6. The measurement of the toughness in EPFM.- 4.7. The parameters of the stress-strain curve.- 4.8. The h-functions.- 4.9. Accuracy.- 4.10. Historical development of J.- 4.11. Limitations of EPFM.- 4.12. CTOD measurements.- 4.13. Exercises.- 5. Crack Growth Analysis Concepts.- 5.1. Scope.- 5.2. The concept underlying fatigue crack growth.- 5.3. Measurement of the rate function.- 5.4. Rate equations.- 5.5. Constant amplitude crack growth in a structure.- 5.6. Load interaction: Retardation.- 5.7. Retardation models.- 5.8. Crack growth analysis for variable amplitude loading.- 5.9. Parameters affecting fatigue crack growth rates.- 5.10. Stress corrosion cracking.- 5.11. Exercises.- 6. Load Spectra and Stress Histories.- 6.1. Scope.- 6.2. Types of stress histories.- 6.3. Obtaining load spectra.- 6.4. Exceedance diagram.- 6.5. Stress history generation.- 6.6. Clipping.- 6.7. Truncation.- 6.8. Manipulation of stress history.- 6.9. Environmental effects.- 6.10. Standard spectra.- 6.11. Exercises.- 7. Data Interpretation and Use.- 7.1. Scope.- 7.2. Plane strain fracture toughness.- 7.3. Plane stress and transitional toughness, R-curve.- 7.4. Toughness in terms of J and JR.- 7.5. Estimates of toughness.- 7.6. General remarks on fatigue rate data.- 7.7. Fitting the da/dN data.- 7.8. Dealing with scatter in rate data.- 7.9. Accounting for the environmental effect.- 7.10. Obtaining retardation parameters.- 7.11. Exercises.- 8. Geometry Factors.- 8.1. Scope.- 8.2. The reference stress.- 8.3. Compounding.- 8.4. Superposition.- 8.5. A simple method for asymmetric loading cases.- 8.6. Some easy guesses.- 8.7. Simple solutions for holes and stress concentrations.- 8.8. Simple solutions for irregular stress distributions.- 8.9. Finite element analysis.- 8.10. Simple solutions for crack arresters and multiple elements.- 8.11. Geometry factors for elastic-plastic fracture mechanics.- 8.12. Exercises.- 9. Special Subjects.- 9.1. Scope.- 9.2. Behavior of surface flaws and corner cracks.- 9.3. Break through: leak-before-break.- 9.4. Fracture arrest.- 9.5. Multiple elements, multiple cracks, changing geometry.- 9.6. Stop holes, cold worked holes and interference fasteners.- 9.7. Residual stresses in general.- 9.8. Other loading modes: mixed mode loading.- 9.9. Composites.- 9.10. Exercises.- 10. Analysis Procedures.- 10.1. Scope.- 10.2. Ingredients and critical locations.- 10.3. Critical locations and flaw assumptions.- 10.4. LEFM versus EPFM.- 10.5. Residual strength analysis.- 10.6. Use of R-curve and JR-curve.- 10.7. Crack growth analysis.- 10.8. Exercises.- 11. Fracture Control.- 11.1. Scope.- 11.2. Fracture control options.- 11.3. The probability of missing the crack.- 11.4. The physics and statistics of crack detection.- 11.5. Determining the inspection interval.- 11.6. Fracture control plans.- 11.7. Repairs.- 11.8. Statistical aspects.- 11.9. The cost of fracture and fracture control.- 11.10. Exercises.- 12. Damage Tolerance Substantiation.- 12.1. Scope.- 12.2. Objectives.- 12.3. Analysis and damage tolerance substantiation.- 12.4. Options to improve damage tolerance.- 12.5. Aircraft damage tolerance requirements.- 12.6. Other requirements.- 12.7. Flaw assumptions.- 12.8. Sources of error and safety factors.- 12.9. Misconceptions.- 12.10. Outlook.- 12.11. Exercises.- 13. After the Fact: Fracture Mechanics and Failure Analysis.- 13.1. Scope.- 13.2. The cause of service fractures.- 13.3. Fractography.- 13.4. Features of use in fracture mechanics analysis.- 13.5. Use of fracture mechanics.- 13.6. Possible actions based on failure analysis.- 13.7. Exercises.- 14. Applications.- 14.1. Scope.- 14.2. Storage tank (fictitious example).- 14.3. Fracture arrest in ships.- 14.4. Piping in chemical plant (fictitious example).- 14.5. Fatigue cracks in railroad rails.- 14.6. Underwater pipeline.- 14.7. Closure.- 15. Solutions To Exercises.

Short and long fatigue crack growth: A unified model

Abstract: In this model the growth of a crack is analysed in terms of the successive blocking of the plastic zone by slip barriers (e.g. grain boundaries) and the subsequent initiation of the slip in the next grain. The discontinuous character of the slip process (slip jumps) plays a fundamental role in the model. The factor governing the transfer of slip across a grain boundary is considered to be the stress concentration ahead of the plastic zone which, for a constant applied stress τ, is found to be dependent only on a parameter n = a/c defining the position of the crack tip relative to the grain boundary. The discrete behaviour of the slip has a strong influence in the short-crack period and hence cannot be neglected in the analysis of the crack growth rate. This period is characterized by large variations in the parameter n. In the long-crack period the slip jumps do not influence the overall description of the growth and the parameter n is almost constant. By making the crack extension per cycle prop...

Mechanics of Fatigue Crack Closure

Abstract: Papers are presented on plasticity induced crack closure, crack closure in fatigue crack growth, the dependence of crack closure on fatigue loading variables, and a procedure for standardizing crack closure levels. Also considered are a statistical approach to crack closure determination, the crack closure behavior of surface cracks under pure bending, closure measurements on short fatigue cracks, and crack closure under plane strain conditions. Other topics include fatigue crack closure behavior at high stress ratios, the use of acoustic waves for the characterization of closed fatigue cracks, and the influence of fatigue crack wake length and state of stress on crack closure.

Role of silicon carbide particles in fatigue crack growth in SiC-particulate-reinforced aluminum alloy composites

Abstract: A study has been made of the mechanistic role of silicon carbide (SiC) particles during fatigue crack propagation in powder metallurgy AlZnMgCu metal matrix composites reinforced with 20 vol.% SiC particulates (SiC p ), with varying sizes of reinforcement phase. Crack growth and accompanying crack tip shielding (principally by crack deflection, closure and bridging) are examined in peak-aged alloys over a wide spectrum of growth rates from 10 −12 to 10 −4 m cycle −1 and are compared with corresponding behavior in the unreinforced matrix alloy. Crack growth resistance in the composites is found to be both superior and inferior to that of the unreinforced alloy, depending on how the SiC and SiC-matrix interface fracture. At low stress intensity ranges ΔK, the predominant fracture of carbides close to the crack tip results in low levels of crack closure and rapid growth kinetics for fine SiC p distributions, whereas for coarse SiC p distributions the rougher fracture surface promotes crack closure from asperity wedging and improved crack growth resistance. With increasing ΔK, the fracture of large carbides farther ahead of the crack tip leads to the development of non-uniform crack fronts, thereby promoting crack bridging via uncracked ligaments and a small improvement in crack growth resistance. At high ΔK levels approaching K Ic , growth rates are faster in the composites owing to their low toughness. On the basis of these results, the overall fatigue crack growth performance of the SiC p Al composites compared with that of the traditional monolithic aluminum alloys is briefly discussed.

A microstructurally-short fatigue crack growth equation

Abstract: — A brief outline of a recently developed model which describes the microstructurally short and the physically short crack periods of fatigue crack growth is presented. A single equation to describe both regimes is discussed and the model applied to data on a medium carbon steel. Good predictions relating to the actual experimental lifetime were achieved. The results are compared with the prediction of fatigue life based on a previously reported two-equation approach.

Chemical and metallurgical aspects of environmentally assisted fatigue crack growth in 7075-T651 aluminum alloy

Abstract: A comprehensive study has been carried out on a 7075-T651 alloy to examine the influence of water vapor on fatigue crack growth. The kinetics of fatigue crack growth were determined as a function of water vapor pressure at room temperature and at 353 K. Detailed fractographic analyses and surface chemistry studies were carried out to identify the micromechanisms and to quantify the chemical interactions for corrosion fatigue crack growth in this alloy. Experiments were also carried out in ultra-high vacuum and in oxygen to provide for comparisons. Two regions of fatigue crack growth response were identified. In the low pressure region (below 67 Pa at 5 Hz), crack growth is controlled by the rate of transport of water vapor to the crack tip, and the response can be described by a model for transport controlled crack growth. At pressures above 67 Pa, additional increases in crack growth rate occurred, which are attributed to the further reactions of water vapor with segregated magnesium in this alloy. Different micromechanisms for crack growth have been identified for vacuum, oxygen, and water vapor. These micromechanisms are considered in relation to the environmental parameters through a modified superposition model for corrosion fatigue.

Effects of SiC reinforcement and aging treatment on fatigue crack growth in an AlSiC composite

Abstract: The effects of SiC reinforcement and matrix aging treatment on fatigue crack growth behavior in a powder metallurgy aluminum 2124 alloy-SiC whisker composite were investigated. The microstructures were designed such that the matrix of the composite material and the unreinforced control aluminum alloy 2124 with an identical processing history had similar hardness and precipitation characteristics. The threshold stress intensity factor range ΔK0 for tensile fatigue crack growth was obtained using a procedure whereby mode I precracks were initiated in uniaxial cyclic compression prior to tension fatigue. The composite exhibits a ΔK0 value which is about twice that of the control alloy. However, ΔK0 is relatively insensitive to variations in both the aging treatment and the mean stress of the fatigue cycle in both the composite and the control alloy. Possible mechanisms underlying this trend are discussed.

Fatigue crack growth resistant nickel-base article and alloy and method for making

Abstract: An article having improved fatigue crack growth resistance is provided through an improved nickel-base superalloy and an improved method which controls grain size and a strain rate found to be critical in processing. The alloy is selected to have a gamma prime content in the range of about 30-46 volume percent and a resistance to cracking upon rapid quenching from a selected supersolvus solutioning temperature to a selected quenching temperature. The article produced has an improved balance and combination of fatigue crack growth resistance and tensile, creep, and stress rupture properties.

Three-Dimensional Finite-Element Simulation of Fatigue Crack Growth and Closure

Abstract: A three-dimensional elastic-plastic finite-element analysis of crack growth and closure under cyclic loading has been performed in order to investigate the behavior of a crack in a finite-thickness middle-crack tension specimen. The cases of both constant-amplitude loading and a single-spike overload are considered. The calculated crack-opening stresses for the exterior of the specimen agree with previous plane-stress results, and those obtained for the interior of the specimen agree with previous plane-strain results.

Applications of Probabilistic Fracture Mechanics to Offshore Structures

Abstract: For offshore structures the fatigue limit state is governing the structural dimensions of several members and joint connections. Safety against fatigue failure is achieved through a combination of design requirements and performance of in-service inspections with repair of detected fatigue cracks. A review of uncertainties involved in fatigue life predictions by fracture mechanics is presented with particular reference to steel structures. Sources of uncertainties considered are: environmental conditions, hydrodynamic loading, global structural analysis, local stress calculation at fatigue sensitive points, and fatigue crack growth modeling by fracture mechanics. A probabilistic model using the fracture mechanics in probabilistic form is presented. This model accounts for uncertainties in loading, initial and critical defect sizes, material parameters, and in the uncertainty related to computation of the stress intensity factor. Failure probabilities are computed by first-order reliability methods and sensitivity factors are determined. Model updating based on in-service inspection results is formulated. Uncertainties with respect to detecting a crack and to correctly sizing a crack are included. Experience on application of the analysis method is presented.

Markov process model for fatigue crack growth

Abstract: Crack propagation analysis is a major task in the design and life prediction of fatigue‐critical structures, yet experimental tests indicate that fatigue crack propagation involves a large amount of statistical variation and is not adequately modeled deterministically. A method of analysis based on Markov process theory is presented for the investigation of fatigue crack propagation. A new fracture mechanics based, lognormal random process model is developed, and without approximation, a boundary value problem is formulated for the statistical moments of the random time to reach a given crack size. A Petrov‐Galerkin finite element method is then used to obtain solutions to the boundary value problem. A parametric study of the power‐law fatigue crack growth model is conducted, and a numerical example is given in which excellent agreement is found between the finite element results and experimental data. The model and problem formulation are consistent with physical phenomena, overcome many objections to pr...

Fatigue crack growth from indentation flaw in ceramics

Abstract: The indentation crack has been used as a model of surface flaw in the strength tests of ceramics. In evaluation of such strength properties, some attention should be paid to the residual stress effect due to indentation. In this study, fatigue crack growth behavior from indentation flaws was investigated in sintered silicon nitride and alumina. In both materials, a V-shaped behavior was observed in the relation between the maximum stress intensity factor and the crack growth rate. The indentation crack was analyzed using fracture mechanics procedure to take account of the residual component. On the basis of the analysis, an effective stress intensity factor for crack growth was successfully evaluated. The growth rate was correlated to the effective stress intensity factor, and the relation was found to be approximated by a power law equation. The fatigue crack growth property obtained as above was applied to an estimation of fatigue life of specimens without artificial flaws. The flaw size effect was also discussed based on the result.

Mode II Cyclic Delamination Growth

Abstract: The end notched flexure (ENF) specimen is employed in an investigation of the inter laminar fracture of unidirectional graphite/epoxy, graphite/polyimide, and graphite/PEEK composites subjected to Mode II fatigue loading. Fatigue crack growth rates are deter mined for the stable delamination growth observed under fully reversed cyclic loading. Within the crack driving force range studied, cyclic crack growth data obeyed a power law dependency on the cyclic strain energy release rate. The response of the various material systems is compared to crack growth under static loading. The importance of the data re duction scheme for the crack growth resistance is discussed. Friction is examined as a potential energy absorbing mechanism in the test by finite element analysis. Suggestions for appropriate experimental geometries minimizing frictional effects are presented. Finally, fatigue fracture surfaces are analyzed with scanning electron microscopy to identify crack growth mechanisms.

Toward an understanding of Mode II fatigue crack growth

Abstract: The Mode II crack flank displacement and crack growth responses of three precracked specimens made from structural steel were measured, using plastic replicas and a crack-tip compliance gage. Crack surface interaction wasfound to dominate behavior: at low stress intensity range (ΔK I I n o m = 9 MPa √m) the precracks did not suffer reversed slip to their tips and no crack growth occurred, while at high stress intensity range (ΔK I I n o m = 19 MPa √m) the effective stress intensity range was less than half that nominally applied. Three sources of crack flank frictional attenuation were identified: compressive residual stresses due to precracking, Mode I wedging over asperities, and gross plastic deformation of interlocking asperities. The measured unlocking response was modeled successfully by assuming that crack flank frictional stresses obeyed a constant interfacial shear stress friction law.

On the Role of Crack Closure Mechanisms in Influencing Fatigue Crack Growth Following Tensile Overloads in a Titanium Alloy: Near Threshold Versus Higher Δ K Behavior

Abstract: A comparative study has been made of the transient fatigue crack growth rate behavior following tensile overloads at low (nearthreshold) and high stress intensity ranges in an o./B -type titanium alloy IMI 550, with specific emphasis of the role of crack closure mechanisms. After tensile overloads, fatigue cracks in both coarsegrained B-annealed and fine-grained o./B microstructures were observed initially to accelerate, followed by significant retardation, before· growth rates returned to their baseline levels. The initial acceleration was attributed to an immediate reduction in near-tip closure, as indicated by metallographic sectioning, and a slight 1Visiting Scientist and Professor, Materials and Molecular Research Division. Lawrence Berkeley Laboratory, and Department of Materials Science and Mineral Engineering, University of California, Berkeley, Ca 1 if 94720, U.S.A. Dr. Ward-C lose is current 1 y at the Roya 1 Aircraft Establishment, Farnborough, Hants, U.K.

Effect of Frequency on Fatigue Crack Growth Rate of Inconel 718 at High Temperature

Abstract: : Fatigue crack growth was studied at 650 deg C as a function of frequency for several ratios of minimum-to-maximum stress intensity, and for two values of maximum stress intensity factor Crack lengths were monitored at low frequencies from compliance calculations based on crack mouth opening displacement measurements At higher frequencies, crack length was measured using a dc electric potential system It was found that fatigue crack growth rate can be characterized in three distinct frequency regions These three regions represent fully cycle dependent, mixed, and fully time dependent crack growth behavior and each region can be modeled by a power law function Observation of micro mechanisms support the existence of these three different regions of crack growth Keywords: Fatigue crack growth, Time dependent growth, Cyclic-dependent growth, Nickel base superalloy, Crack growth rate model, Frequency effects

Fracture of Si3N4–SiC Whisker Composites under Cyclic Loads

Abstract: This communication demonstrates the role of cyclic compressive loads in inducing mode I fatigue crack growth at room temperature in Si3N4 matrix–SiC whisker composite materials containing stress concentrations. The characteristics of stable, cyclic fracture are examined for several volume fractions of the SiC whisker and are compared with those of the matrix material. It is found that the composites with higher volume fractions of SiC whiskers exhibit an inferior resistance to fracture under cyclic compressive loads despite improvements in fracture toughness values.

A review of fatigue crack growth characterisation by linear elastic fracture mechanics (lefm). part i—principles and methods of data generation

Abstract: — The application of linear elastic fracture mechanics (LEFM) to the characterisation of fatigue crack growth has been reviewed. In Part I the present understanding of the factors influencing growth rate is summarised, and the current methods of fatigue crack growth rate data generation are considered in the light of this. In Part II, documents are reviewed which provide advice on the prediction of fatigue crack growth and also those national standards in which fatigue crack growth considerations are implicit.