Showing papers on "Fracture mechanics 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.

Elastic wave propagation in media with parallel fractures and aligned cracks

Abstract: A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.

Fracture of fiber-reinforced materials

Abstract: The fracture behaviour of fiber-reinforced materials is studied in this paper. Using a simple shear lag model, which includes friction at the debonded interface and the Poisson contraction of the fiber, the fiber-matrix debonding problem is solved. This gives the relationship between debonding load and debonded length. Interfacial friction is shown to have a significant effect on the debonding load. The fracture toughness of fiber-reinforced materials due to fiber debonding, frictional dissipation at fibre-matrix interface following debonding and other micro-fracture mechanisms is discussed with reference to strong and weak fibres. Finally, the strength and toughness of short fibre-reinforced materials are given.

Small-scale crack bridging and the fracture toughness of particulate-reinforced ceramics

Abstract: T heoretical analyses of small-scale bridging of crack surfaces by elastic-ideally plastic springs are presented and applied to the study of the fracture toughness of ceramics reinforced by small particles. The dependence of toughening on particle size, concentration, strength, and ductility is explored, and relations between toughening and bridge length at fracture are given. Available experimental information is examined in the light of the analyses.

Fracture testing of silicon microelements in situ in a scanning electron microscope

Abstract: Fracture testing of silicon cantilever beams (thicknesses 10–20 μm) was performed in situ in a scanning electron microscope by means of an equipment specially designed for this purpose. Beams of various sizes and orientations (〈011〉 and 〈001〉) were manufactured in Si (100) wafers by two different micromachining procedures. The beams were tested by simple bending to fracture, and a number of fundamental fracture parameters were determined from an analytical model of elastic fracture. To verify its validity, the model was utilized to evaluate an experimental E modulus, which was found to agree well with previous results. Fracture limits, fracture strains, and initiating flaw sizes were determined. The maximum fracture limit was very high; about 10 GPa. The strengths of different beams scattered from this value down to practically zero strength, with an average close to 4 GPa. The corresponding fracture strains and initiating flaw sizes were 6% and 3 nm, respectively (maximum strength), and 2% and 17 nm (ave...

Fracture energy and strain softening of concrete as determined by means of compact tension specimens

Abstract: Fracture mechanics parameters of concrete are determined by means of the compact tension (CT) test. The effects of ligament length, rate of loading and concrete composition on the specific fracture energy GF and the strain-softening diagram are investigated. As a first approximation of the real softening behaviour of concrete, a bilinear strain softening diagram is used in a finite-element analysis. A parameter study shows that several bilinear diagrams can represent the real behaviour equally well. With the bilinear softening diagram, a good agreement between both calculated and measured load-displacement curves and GF-values is obtained. The determined strain-softening diagrams are transformed into a normalized presentation. For each investigated testing condition, characteristics shapes of this normalized strain-softening diagram are obtained.

Transformation Plasticity of CeO2-Stabilized Tetragonal Zirconia Polycrystals: I, Stress Assistance and Autocatalysis

Abstract: Transformation plasticity in CeO2-stabilized tetragonal zirconia polycrystals due to the tetragonal-to-monoclinic transformation was studied by inducing volumetric and shear deformation under compression and bending between the burst temperature of martensite (monoclinic) formation (Mb) and the burst temperature of austenite (tetragonal) formation (Ab). The stress-strain curve features a load drop, a perfect plastic regime, and an extended strain-hardening regime before the exhaustion of transformation. Macroscopic shear bands formed in the perfect plastic regime. The yield stress has a strong, positive pressure and temperature sensitivity but is strain-rate sensitive only in the last stage of deformation. These results are rationalized in terms of stress assistance to the transformation which, in a homogeneous tetragonal polycrystal, may propagate autocatalytically. Autocatalysis can be impeded by a second phase, such as monoclinic ZrO2 or Al2O3, and is suppressed at higher temperature. Flow localization is found to precede and precipitate crack formation. As a result, the actual fracture energy is much less than the total plastic work. The implications of stress-assisted, autocatalytic transformation on strength and toughness are explored.

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.

The effect of molecular weight on slow crack growth in linear polyethylene homopolymers

Abstract: The rate of initiation and growth of cracks in linear high-density polyethylene with different molecular weights was observed in single-edge-notched tensile specimens under plane strain condition as a function of applied stress, notch depth and temperature. The initial rates of crack initiation all have the form of Cσm a0nexp (−Q/RT) or AKpexp (−Q/RT) where σ = stress, a0 = notch depth and K= stress intensity factor. For the different molecular weights, m, n, P and Q are almost the same where m=5, n=2, P=4.7 and Q=115 kJ mol−1, but the constants C and A varied as (¯Mw−¯Mc)−1 where ¯Mc is a limiting molecular weight for sudden fracture. A molecular model based on tie-molecules has been used to explain the dependence on ¯Mw. The effect of ¯Mw on the fast-fracture strength at low temperature and the relationship to tie-molecules have also been investigated. Quantitative relationships between the concentration of tie-molecules and the fracture behaviour have been obtained.

Modeling mixed-mode dynamic crack propagation nsing finite elements: Theory and applications

Abstract: Previous work in modeling dynamic fracture has assumed the crack will propagate along predefined mesh lines (usually a straight line). In this paper we present a finite element model of mixed-mode dynamic crack propagation in which this constraint is removed. Applying linear elasto-dynamic fracture mechanics concepts, discrete cracks are allowed to propagate through the mesh in arbitrary directions. The fracture criteria used for propagation and the algorithms used for remeshing are described in detail. Important features of the implementation are the use of triangular elements with quadratic shape functions, explicit time integration, and interactive computer graphics. These combine to make the approach robust and applicable to a broad range of problems. Example analyses of straight and curving crack problems are presented. Verification problems include a stationary crack under dynamic loading and a propagating crack in an infinite body. Comparisons with experimental data are made for curving propagation in a cracked plate under biaxial loading.

Rising Fracture Toughness from the Bending Strength of Indented Alumina Beams

Abstract: The analytical function of crack extension to a fractional power is used to represent the fracture resistance of a vitreous-bonded 96% alumina ceramic. A varying flaw size, controlled by Vickers indentation loading between 3 and 300 N, was placed on the prospective tensile surfaces of four-point bend specimens, previously polished and annealed. The lengths of surface cracks were measured by optical microscopy. Straight lines were fitted to the logarithmic functions of observed bending strength versus indentation load in two series of experiments: (I) including the residual stress due to indentation and (II) having the residual stress annealed out at an elevated temperature. Within the precision of measurement these lines have the same slope, being about 32% less than the -1/3 slope which a fracture toughness independent of crack extension would indicate. Considering the criteria for crack extension and specimen failure, the fracture mechanics equations were solved for the conditions of the two series of experiments. Approximately the same values of fracture toughness, rising as a function of indentation flaw size, were obtained from both series of experiments.

Crack Resistance Curves in Magnesia‐Partially‐Stabilized Zirconia

Abstract: Crack growth resistance curves (R curves) for the growth of surface cracks have been measured in a series of magnesia-partially-stabilized zirconia ceramics with varying degrees of transformation toughening. The shapes of the R curves are correlated with strength-toughness relations and the predictions of fracture mechanics analysis of transformation toughening. Results support a previous hypothesis that the peak in the strength-toughness relation is associated with a decreasing slope of the R curve with increasing steady-state toughness. The role of microstructural influences due to localized regions of transformation on crack growth is assessed, and the relation between reversible and irreversible transformation and toughness is examined.

R-Curve Behavior of a Polycrystalline Graphite: Microcracking and Grain Bridging in the Wake Region

Abstract: The contributions of nonlinear fracture processes both in the microcracking frontal process zone and in the following wake region and of grain bridging to crack-growth resistance parameters are discussed in terms of the R-curve behavior of an isotropic polycrystalline graphite. The R-curve behavior of the graphite is characterized by rapidly increasing values at the initial stage of crack extension (Δa≤1 to 2 mm) followed by a steady-state plateaulike region and then a distinct decrease when the primary crack tip approaches the end surface of the test specimen. Scanning electron microscopy of fracture mechanics specimens revealed a dominant role of grain bridging in the following wake regions on the rising R-curve behavior and confirmed the significant size effect of the large-scale microcracking process zone on the falling R-curve behavior. The stress-derived fracture toughness (KR) and the energy fracture toughness (Rc) are discussed in relation to the micro-cracking residual strain.

Short-Crack Growth Behaviour in an Aluminum Alloy: An AGARD Cooperative Test Programme

Abstract: An AGARD Cooperative Test Program on the growth of short fatigue cracks was conducted to define the significance of the short-crack effect, to compare test results from various laboratories, and to evaluate an existing analytical crack-growth prediction model. The initiation and growth of short fatigue cracks (5 micrometer to 2 mm) from the surface of a semi-circular notch in 2024-T3 aluminum alloy sheet material were monitored under various load histories. The cracks initiated from inclusion particle clusters or voids on the notch surface and generally grew as surface cracks. Tests were conducted under several constant-amplitude (stress ratios of -2, -1, 0, and 0.5) and spectrum (FALSTAFF and Gaussian) loading conditions at 3 stress levels each. Short crack growth was recorded using a plastic-replica technique. Over 250 edge-notched specimens were fatigue tested and nearly 950 cracks monitored by 12 participants from 9 countries. Long crack-growth rate data for cracks greater than 2 mm in length were obtained over a wide range in rates (10 to the -8 to 10 to the -1 mm/cycle) for all constant-amplitude loading conditions. Long crack-growth rate data for the FALSTAFF and Gaussian load sequences were also obtained.

Toughening by aligned, frictionally constrained fibers

Abstract: T he M ode I fracture toughness of a brittle material reinforced by aligned brittle fibers is studied theoretically. The fibers are assumed to slip relative to the matrix when a critical interface shear stress is reached, and the toughening action of the fibers is presumed to be due to bridging of crack faces in the vicinity of the crack front. The toughening due to the fiber reinforcement is related to basic parameters associated with the related problem of steady-state matrix cracking in the presence of intact fibers. Bridge lengths at fracture and fracture resistance curves are calculated.

Effect of Temperature and Humidity on Fracture Energy of Concrete

Abstract: Fracture experiments were conducted at temperatures from 20 to 200 C (68 to 392 F) to determine the dependence of the Mode I fracture energy of concrete on temperature as well as the specific water content. The fracture energy values were determined by testing geometrically similar specimens of sizes in the ratio 1:2:4:8 and then applying Bazant's size effect law. Three-point bend specimens and eccentric compression specimmns are found to yield approximately the same fracture energies, regardless of temperature. To describe the temperature dependence of fracture energy, a recently derived simple formula based on the activation energy theory (rate process theory) is used and verified by test results. The temperature effect is determined both for concrete predried in an oven and for wet (saturated) concrete. By interpolation, an approximate formula for the effect of moisture content on fracture energy is also obtained. This effect is found to be small at room temperature but large at temperatures close to 100 C (212 F).

Rupture Initiation in Shear Fracture of Rocks' An Experimental Study

Abstract: We used a torsional geometry to grow shear ruptures in two fine-grained rock types. The sample has a slot that is loaded to produce a strong mode 3 shear stress concentration. The onset and growth of the damage zone is detected by monitoring the elastic stiffness of the samples. We find that the samples continue to harden after the onset of fracture. This is initially accompanied by oblique tensile cracks forming at the stress concentration. The peak in supported load apparently corresponds to the onset of strain localization, with the development of cross-cutting shear fractures. We attempted to estimate the partitioning of energy dissipation between elastic and frictional components with a fracture mechanics analysis. The elastic energy increases with normal stress, but scatter in the inelastic data does not allow identification of convincing trends. The sample is too small to develop a complete transition to a shear rupture. The geometry of the fractures is used to explain the energy relations as well as other experimental observations