Showing papers on "Crack closure published in 1991"

Fatigue of materials

Abstract: Preface 1. Introduction and overview Part I. Cyclic Deformation and Fatigue Crack Initiation: 2. Cyclic deformation in ductile single crystals 3. Cyclic deformation in polycrystalline ductile solids 4. Fatigue crack initiation in ductile solids 5. Cyclic deformation and crack initiation in brittle solids 6. Cyclic deformation and crack initiation in noncrystalline solids Part II. Total-Life Approaches: 7. Stress-life approach 8. Strain-life approach Part III. Damage-Tolerant Approach: 9. Fracture mechanics and its implications for fatigue 10. Fatigue crack growth in ductile solids 11. Fatigue crack growth in brittle solids 12. Fatigue crack growth in noncrystalline solids Part IV. Advanced Topics: 13. Contact fatigue: sliding, rolling and fretting 14. Retardation and transients in fatigue crack growth 15. Small fatigue cracks 16. Environmental interactions: corrosion-fatigue and creep-fatigue Appendix References Indexes.

A Comparison of the J -lntegral and CTOD Parameters for Short Crack Specimen Testing

Abstract: This study investigates the applicability of the J-integral test procedure to test short crack specimens in the temperature region below the initiation of ductile tearing where J 1 c cannot be measured. The current J-integral test procedure is restricted to determining the initiation of ductile tearing and requires that no specimen demonstrates brittle cleavage fracture. The J 1 c test specimen is also limited to crack-depth to specimen-width ratios (a/W) between 0.50 and 0.75. In contrast, the crack tip opening displacement (CTOD) test procedure can be used for testing throughout the entire temperature-toughness transition region from brittle to fully ductile behavior. Also, extensive research is being conducted to extend the CTOD test procedure to the testing of short crack specimens (alW ratios of approximately 0.15). The CTOD and J-integral fracture parameters are compared both analytically and experimentally using square (cross-section) three-point bend specimens of A36 steel with a/W ratios of 0.50 (deep crack) and 0.15 (short crack). Three-dimensional elastic-plastic finite element analyses are conducted on both the deep crack and the short crack specimens. The measured J-integral and CTOD results are compared at various levels of linear-elastic and elastic-plastic behavior. Experimental testing is conducted throughout the lower shelf and lower transition regions where stable crack growth does not occur. Very good agreement exists between the analytical and experimental results for both the short crack and deep crack specimens. Results of this study show that both the J-integral and the CTOD fracture parameters work well for testing in the lower shelf and lower transition regions where stable crack growth does not occur. A linear relationship is shown to exist between J-integral and CTOD throughout these regions for both the short and the deep crack specimens. These observations support the consideration to extend the J-integral test procedure into the temperature region of brittle fracture rather than limiting it to J 1 c at the initiation of ductile tearing. Also, analyzing short crack three-point bend specimen (a/W < 0.15) records using the load versus load-line displacement (LLD) record has great potential as an experimental technique. The problems of accurately measuring the CMOD of short crack specimens in the laboratory without affecting the crack tip behavior may be eliminated using the J-integral test procedure.

The effect of non-singular stresses on crack-tip constraint

Abstract: The effect of the T-stress on the small-scale yielding field of a crack in plane strain conditions has been examined using modified boundary layer formulations. The numerically calculated stresses at the crack tip are represented by slip line fields for small-strain theory. Positive T-stresses cause plasticity to envelop the crack tip and exhibit a Prandtl field, corresponding to the limiting solution of the HRR field for a nonhardening material. Moderate compressive T-stresses reduce the direct stresses within the plastic zone by decreasing the hydrostatic stress by T. This causes a loss of J-dominance, and a stress distribution represented by an incomplete Prandtl field.

Size Effect in Fatigue Fracture of Concrete

Abstract: Crack growth caused by load repetitions in geometrically similar notched concrete specimens of various sizes is measured by means of the compliance method. It is found that the Paris law, which states that the crack length increment per cycle is a power function of the stress intensity factor amplitude, is valid only for one specimen size (the law parameters being adjusted for that size) or asymptotically, for very large specimens. To obtain a general law, the Paris law is combined with size-effect law for fracture under monotonic loading, proposed previously by Bazant. This leads to a size-adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of size-adjusted stress intensity factor. The crack growth is also characterized in terms of the nominal stress amplitude.

Mechanics of Dynamic Debonding

Abstract: Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined Emphasis is placed on extending an established framework for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity This simplifies the problem, rendering the Stroh techniques applicable In general, the singularity oscillates, similar to quasistatic cracks The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials Implications on crack branching and substrate cracking are discussed Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol'dshtein and Dugdale problems Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed

A three-dimensional analysis of crack trapping and bridging by tough particles

Abstract: The toughness of a brittle material may be substantially improved by adding small quantities of tough particles to the solid. Three mechanisms may be responsible. Firstly, the front of a crack propagating through the solid can be trapped by the particles, causing it to bow out between them. Secondly, the particles may remain intact in the wake of the crack, thereby pinning its faces and reducing the crack tip stress intensity factors. Finally, the toughness may be enhanced by frictional energy dissipation as particles are pulled out in the wake of the crack. This paper estimates the improvement in toughness that might be expected due to these mechanisms, by means of a three-dimensional model. The analysis considers a semi-infinite crack propagating through a brittle matrix material, which contains a regular distribution of tough particles. Particles in the wake of the crack are modelled by finding an appropriate distribution of point forces that pin the crack faces; and the effect of the crack bowing between obstacles is included by means of an incremental perturbation method based on work byRice [J. Appl. Mech.56, 619 (1985)]. The calculation predicts the shape of the crack as it propagates through the solid; the resulting R-curve behaviour; and the length of the bridged zone in the wake of the crack.

On the temperature distribution at the vicinity of dynamically propagating cracks in 4340 steel

Abstract: T he heat generated due to plastic deformation at the tip of a dynamically propagating crack in a metal causes a large local temperature increase at the crack tip which is expected to affect the selection of failure modes during dynamic fracture and to thus influence the fracture toughness of the material. The distribution of temperature at the tips of dynamically propagating cracks in two heat treatments of AISI 4340 carbon steel was investigated experimentally using an array of eight high speed indium antimonide, infrared detectors. Experiments were performed on wedge loaded, compact tension specimens with initially blunted cracks, producing crack speeds ranging from 1900 to 730 m/s. The measurements provide the spatial distribution of temperature increase near the crack tip on the specimen surface. Temperature increases were as high as 465° C over ambient and the region of intense heating (greater than 100° C temperature rise) covered approximately one third of the active plastic zone on the specimen surface. The observed temperature increase profiles clearly show the three-dimensional nature of the fracture process near the specimen surface and provide valuable information regarding the dynamic formation of shear lips and their role in the dissipation of energy during dynamic crack growth. Preliminary temperature measurements performed on side-grooved specimens are also reported.

The consequences of short crack closure on fatigue crack growth under variable amplitude loading

Abstract: Opening and closure of short cracks has been examined experimentally using small strain gauges fixed to unnotched specimens very close to short fatigue cracks. The results of completely reversed tension-compression constant amplitude tests are that crack opening stresses decrease with increasing stress amplitude and that crack closure occurs at nearly the same strain as crack opening. In variable amplitude loading the crack is subjected to a low crack opening level resulting from larger cycles. Based on the results of this experimental investigation some simple approximation formulas are proposed with which decrease as well as increase of crack opening levels can be described. Using these formulas it is possible to compute crack opening strains for any load sequence. The findings of the investigations have been merged to build an algorithm for the prediction of fatigue lives to initiation of cracks of technical sizes in case of variable amplitude loading. The improvement in accuracy of life predictions compared to results of an existing damage accumulation concept is demonstrated for two materials and two load sequences.

Determination of higher-order terms in asymptotic elastoplastic crack tip solutions

Abstract: A METHODOLOGY for the calculation of higher-order terms in asymptotic elastoplastic crack tip solutions is developed. The J2-deformation plasticity theory with power law hardening is used to describe the constitutive behavior of the continuum. A two-term expansion of the solution in the near crack tip region is developed. Plane stress and plane strain solutions for a crack in a homogeneous material as well as for a crack lying along the interface between a rigid substrate and an elastoplastic medium are obtained. For the case of a plane strain crack in a homogeneous material, it is shown that, when the hardening capacity of the material is small, the effects of elasticity enter the asymptotic solution to third order or higher, when there is substantial hardening, however, elastic effects enter the solution to second order and the magnitude of the second term in the expansion of the solution is controlled by the J-integral. THE CHARACTERIZATION of the stress and deformation fields in the region near the tip of a crack is essential for the development of sound fracture criteria. HUTCHINSON (1968) and RICE and ROSENGREN (1968) developed the elastoplastic asymptotic solution for the near-tip stresses in a homogeneous material (known as the HRR solution) and showed that the magnitude of the dominant term in the expansion of the solution is determined by the J-integral (RICE, 1968). If the region of dominance of the leading-order term in the expansion of the solution is sufficiently larger than the region over which the fracture micro-mechanisms take place, then the J-integral can be used as the fracture parameter. If the region of J-dominance, however, is smaller than the fracture process zone, then two or more parameters may enter the fracture criterion. LI and WANG 0986) suggested the use of a parameter k2, which is the magnitude of the second term in the near-tip stress plastic solution, as the second parameter to be used together with the J-integral in the fracture criterion. BETEGrN and HANCOCK (1991) used a modified boundary layer formulation of the small-scale yielding problem, in which the boundary conditions are defined in terms of the mode I stress intensity factor Kt and the constant stress term T that enters the near-tip expansion of the elastic solution (LARSSON and CARLSSON, 1973; RICE, 1974), and

The crack problem in bonded nonhomogeneous materials

Abstract: The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

Three-Dimensional Stress Fields of Elastic Interface Cracks

Abstract: Various aspects of stress fields near an interface crack in three-dimensional bimaterial plates are investigated. Due to the nature of the resulting deformation field, three-dimensional effects are more critical in a bimaterial plate than in a homogeneous plate. In the close vicinity of the crack front, the stress field is characterized by the asymptotic bimaterial K -field, and its domain size is a very small fraction of a plate thickness. Unlike a homogeneous case, the asymptotic field always consists all three modes of fracture, and an interface crack must propagate under mixed-mode conditions. Furthermore, computational results have shown that the two phase angles representing the relative magnitudes of the three modes strongly depend on the bimaterial properties. It has been also observed that a significant antiplane (Mode III) deformation exists along the crack front, especially near the free surface. Since experimental investigations have shown that critical energy release rate G c is highly dependent on the phase angles, accurate prediction of the interface fracture behavior requires not only the G distribution but also the variations of phase angles along the crack front.

An analysis of dynamic, ductile crack growth in a double edge cracked specimen

Abstract: Dynamic crack growth is analysed numerically for a plane strain double edge cracked specimen subject to symmetric impulsive tensile loading at the two ends. The material behavior is described in terms of an elastic-viscoplastic constitutive model that accounts for ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, including large inclusions or inclusion colonies with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The crack growth velocities determined here are entirely based on the ductile failure predictions of the material model, and thus the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Different prescribed impact velocities, inclusion spacings and values of the inclusion nucleation stress are considered. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed.

Fatigue of Yttria‐Stabilized Zirconia: I, Fatigue Damage, Fracture Origins, and Lifetime Prediction

Abstract: ~Uniaxial tension-compression fatigue behavior of 3-mol%yttria-stabilized tetragonal zirconia polycrystals was investigated. Hysteresis in the stress-plastic strain curve featured cumulative plastic strain and weakened elastic stiffness. Fracture statistics in terms of cycle-to-failure depends strongly on the maximum stress and less on the stress amplitude. Preexisting processing flaws were identified as the fracture origins in all cases. We suggest that microcracking is the dominant mechanism of fatigue damage, that nucleation of fatigue crack is usually not necessary, and that fatigue lifetime is primarily controlled by crack propagation, which is most sensitive to the maximum stress. [Key words: fatigue, fracture, zirconia, cracks, stress.]

The fracture resistance of a model metal/ceramic interface

Abstract: Crack propagation has been measured for the Al2O3/Au interface subject to conditions that exclude stress corrosion. Crack growth has been shown to occur with a rising resistance, governed by intact metal ligaments in the crack wake. The level of resistance also increases as the metal layer thickness increases. Crack extension occurs by a combination of plastic void growth and interface debonding. The fracture energies are much larger than the work of adhesion, but appreciably smaller than those expected for ductile interface fracture. The fracture energy is nevertheless dominated by plastic dissipation, which increases at larger metal layer thicknesses.

Crack closure and plastic zone sizes in fatigue

Abstract: — An elastic-plastic finite element simulation of growing fatigue cracks which accounts for plasticity-induced crack closure is used to study the size of the forward and reversed plastic zones at the crack tip. Forward plastic zone widths for fatigue cracks and stationary, monotonically loaded cracks are compared and found to be similar. The width of the forward plastic zone at the tip of a fatigue crack is not significantly influenced by closure. The traditional Irwin-Rice estimate for crack tip plastic zone size in plane stress is found to be generally consistent with the finite element results. The width of the reversed plastic zone at the tip of a growing fatigue crack in plane stress is found to be considerably less than one-fourth the size of the forward plastic zone, the traditional Rice estimate. This decrease appears to be due to fatigue crack closure. A simple model is developed which permits estimation of the reversed plastic zone size for any stress ratio from information about maximum and minimum stresses and the closure stress. The predictions of this model agree closely with plastic zone sizes calculated by the finite element analysis. These observations appear to be consistent with experimental measurements of forward and reversed plastic zones sizes reported in the literature.

The determination of crack bridging forces

Abstract: A method is presented for determining the bridging tractions acting on the fracture surfaces of cracks from measurements of the crack opening profile. The tractions may be expressed either as a function ϕ(x) of position in the crack or a function p(u) of the crack opening displacement. The feasibility of deducing ϕ(x) or p(u) from noisy displacement data is demonstrated by numerical simulations. It is found that the most complete information is contained in profiles of cracks growing from notches. Improved estimates of p(u) can also be found by analzying data from several cracks at different stress levels simultaneously.

Effects of crack depth on elastic-plastic fracture toughness

Abstract: Short crack test specimens (a/W ≪ 0.50) are frequently employed when conventional deep crack specimens are either inappropriate or impossible to obtain, for example, in testing of particular microstructures in weldments and in-service structures containing shallow surface flaws. Values of elastic-plastic fracture toughness, here characterized by the crack tip opening displacement (CTOD), are presented for square (cross-section) three-point bend specimens with a/W ratios of 0.15 and 0.50 throughout the lower-shelf and lower-transition regions. Three dimensional, finite-element analyses are employed to correlate the measured load and crack mouth opening displacement (CMOD) values to the corresponding CTOD values, thus eliminating a major source of experimental difficulty in previous studies of shallow crack specimens. In the lower-transition region, where extensive plasticity (but no ductile crack growth) precedes brittle fracture, critical CTOD values for short crack specimens are significantly larger (factor of 2–3) than the CTOD values for deep crack specimens at identical temperatures. Short crack specimens are shown to exhibit increased toughness at the initiation of ductile tearing and decreased brittle-to-ductile transition temperatures. Numerical analyses for the two a/W ratios reveal large differences in stress fields ahead of the crack tip at identical CTOD levels which verify the experimentally observed differences in critical CTOD values. Correlations of the predicted stresses with measured critical CTOD values demonstrate the limitations of single-parameter fracture mechanics (as currently developed) to characterize the response.

Defect assessment in components : fundamentals and applications

Abstract: Fundamentals of ductile fracture numerical studies on stable crack growth j integral calculations in mixed-mode elastic - plastic crack problems j integral for thin shells on stress relaxation at the tip of a crack under normal tension assessment of crack initiation and crack growth in multiphased materials using FEM and microstructural models an energy analysis of elastic - plastic fracture on the crack extension energy rate in elastic - plastic bodies thermoelastic - plastic FEM-analysis of a semi-elliptical surface crack in a cylinder under non-axi-symmetric cooling finite element fracture simulation of A533B steel sheet specimens on the criteria of fracture mechanics and local parameters based on the energy - momentum tensor (part contents)

On crack extension in ductile/brittle laminates

Abstract: The problem of crack progression in a laminate consisting of alternate brittle and ductile layers has been addressed. A finite element analysis has been used to calculate stresses in the vicinity of a crack and the results rationalized on the basis of low and high stress bounds associated, respectively, with small-scale yielding and with a shear lag at the interface. Preliminary experiments conducted on Al2O3/Al laminates have been used to assess the crack extension criterion, upon comparison with the stress analysis. Implications for the strength and toughness of laminates are briefly presented.

Finite element visualization of fatigue crack closure in plane stress and plane strain

Abstract: Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction Finite element analyses indicate that crack closure does occur under pure plane strain conditions The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction This in-plane contraction also leads to the generation of complex residual stress fields The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain

Fatigue of Yttria-Stabilized Zirconia: II, Crack Propagation, Fatigue Striations, and Short-Crack Behavior

Abstract: Fatigue crack propagation in 3Y-TZP was investigated using controlled surface flaws. A unique growth law strongly dependent on the maximum stress intensity factor and quadratically dependent on the amplitude of the range of stress intensity factor was established. This growth law was found to apply for both surface flaws and internal flaws and could be used to predict fatigue lifetime. The presence of residual stress altered the growth mechanics so that an inverse growth rate dependence on the applied stress, reminiscent of the so-called "short-crack behavioe was manifested. Fatigue striations resulting from alternate overload fracture and fatigue fracture during stress cycling were observed. The appearance of striations varied with the R ratio and was very sensitive to the loading condition and crack geometry.

Relationships between fracture parameters and fracture surface roughness of brittle polymers

Abstract: Fracture parameters such as crack velocity a, stress intensity factor Kd and a specific crack extension resistance R* were measured for Homalite-100, PMMA and epoxy in the course of fast crack propagation using a Cranz-Schardin type high speed camera. Fracture surface roughness λ was evaluated as a function of crack length a so that it could be correlated with the fracture parameters above. The results showed that none of those parameters could be uniquely related to λ. Instead, there was a good correlation between λ and a product R*a.