Showing papers in "International Journal of Fracture in 1981"

Influence of voids on shear band instabilities under plane strain conditions

Abstract: The effect of microscopic voids on the failure mechanism of a ductile material is investigated by considering an elastic-plastic medium containing a boubly periodic array of circular cylindrical voids. For this voided material under uniaxial or biaxial plane strain tension the state of stresses and deformations is determined numerically. Bifurcation away from the fundamental state of deformation is analysed with special interest in a repetitive pattern that represents the state of deformation inside a shear band. Both in the fundamental state and in the bifurcation analysis the interaction between voids and the details of the stress distribution around voids are fully accounted for. Comparison is made with the shear band instabilities predicted by a continuum model of a ductile porous medium. Based on the numerical results an adjustment is suggested for the approximate yield condition in this model of dilatant, pressure sensitive plastic behaviour.

Practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage

Abstract: Simple procedures are presented for treating cumulative fatigue damage under complex loading history using either the Damage Curve concept or the Double Linear Damage Rule. A single equation is provided for use with the Damage Curve approach; each loading event providing a fraction of damage until failure is presumed to occur when the damage sum becomes unity. For the Double Linear Damage Rule, analytical expressions are provided for determining the two phases of life. The procedure involves two steps, each similar to the conventional application of the commonly used Linear Damage Rule. When the sum of cycle ratios based on Phase I lives reaches unity, Phase I is presumed complete, and further loadings are summed as cycle ratios based on Phase II lives. When the Phase II sum reaches unity, failure is presumed to occur. No other physical properties or material constants than those normally used in a conventional Linear Damage Rule analysis are required for application of either of the two cumulative damage methods described. Illustrations and comparisons of both methods are discussed.

Fatigue growth threshold of small cracks

Abstract: The effects of grain size and crack length on the threshold condition of fatigue growth of small cracks are analysed both theoretically and experimentally. The theoretical model is based on the assumption that the threshold condition is determined by whether the crack-tip slip band blocked by the grain boundary propagates into an adjacent grain or not. By comparing the model analysis with the experiments of mild steel, it was found that the threshold stress estimated from the fatigue limit of the smooth specimen gave the effective components of the applied stress. When the threshold stress normalized by the fatigue limit of the smooth specimen was correlated to the crack length normalized by a certain crack length, the theoretical relation was found to agree well with the experimental data. From a further analysis of the published data of various materials, the theoretical normalized relation was found to give a lower bound of the threshold values of the stress and the stress intensity factor. A deviation from the theoretical relation seen in the cases of hard metals was explained through an extension of the model by regarding that hard metals contained initial, inherent flaws even in the smooth specimen.

Requirements for a one parameter characterization of crack tip fields by the HRR singularity

Abstract: Detailed crack tip stress and strain fields are generated for the edge crack bar subjected to bending and the center cracked panel and single cracked panel subjected to tensile loads. These fields are compared with the singular fields, due to Hutchinson and Rice and Rosengren, at the same level of applied J. The comparisons show that the size R of the region at the crack tip dominated by the HRR singularity is substantially larger in the bend specimen than in the center-cracked panel for contained and large scale plasticity. Hardening properties also have a strong influence on R. The implications of these results on the minimum size requirement essential to a one parameter fracture criterion based on the J-integral or crack tip opening displacement are discussed.

Cyclic deformation and fatigue behaviour of α-iron mono-and polycrystals

Abstract: The reported studies are based on a series of cyclic deformation tests that were conducted at room temperature on decarburized high-purity α-iron specimens in mono-and polycrystalline form. The experimental data cover plastic strain ranges Δe pl in the regime 10−4 ≲ Δe pl ≲ 10−2 and variations in cyclic plastic strain rates έ pl between ∼10-5 and ∼10−2 s−1. In the case of single crystals, the effect of solute carbon (∼30 wt. ppm) was investigated as well. The mechanical data were supplemented by detailed studies of the dislocation arrangements by transmission electron microscopy and of the surface patterns by scanning electron and optical microscopy. Detailed accounts are given of the following topics: cyclic hardening and saturation, dislocation mechanisms, shape changes due to asymmetric slip of serew dislocations, cyclic stress-strain response and fatigue crack initiation. Under conventional conditions of “high” έ pl (≲10−4 s−1) the fatigue behaviour of α-iron at room temperature reflects the low mobility of the screw dislocations which is characteristic of the lowttemperature mode of deformation of body-centred cubic (b.c.c.) metals. As a consequence the behaviour exhibits significant differences with respect to that of fatigued face-centred cubic (f.c.c.) metals such as: strongly impeded dislocation multiplication below Δe pl ∼ 5 × 10−4, appreciable secondary slip at higher Δe pl leading to a cell structure (persistent slip bands do not form), shape changes due to asymmetric slip of screw dislocations and a relatively high effective stress level. The reduction of έ pl and the presence of solute carbon atoms modify this behaviour significantly, making it more similar to that of f.c.c. metals. In all cases it was found that only the athermal component of the peak (saturation) stress but not the latter itself represents a suitable measure of the properties of the dislocation substructure. On the basis of the cyclic deformation behaviour and of observations of trans-and intergranular fatigue crack initiation it was concluded that the fatigue limit of α-iron is an intrinsic property of the b.c.c. structure whose characteristics, however, are affected sensitively by interstitial impurity content and by the strain rate of the fatigue test.

The asymptotic stress and strain field near the tip of a growing crack under creep conditions

Abstract: The asymptotic stress and strain fields near the tip of a slowly growing crack are derived for elastic-nonlinear viscous materials, which deform in tension according to the law % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuyTduMbai% aacqGH9aqpcuqHdpWCgaGaaiaac+cacaWGfbGaey4kaSIaamOqaiab% fo8aZnaaCaaaleqabaGaamOBaaaaaaa!428D!\[\dot \varepsilon = \dot \sigma /E + B\sigma ^n \]. The nonlinear viscous term describes power law creep. Based on (small strain) continuum mechanics, a stress analysis is carried out for anti-plane shear (Mode III), plane stress and plane strain (Mode I).

Probability distributions for the strength of composite materials II: A convergent sequence of tight bounds

Abstract: A sequence of convergent upper bounds is developed for the probability distribution of strength of composite materials. The analysis is based on the well-known chain-of-bundles model, and local load sharing is assumed for the nonfailed fiber elements in each bundle. The bounds are based on the occurrence ofk or more adjacent broken fibers in a bundle, an event which is necessary but not sufficient for the failure of the material. However, we find that given the loadL on the composite, some value ofk denotedk*(L) is critical in that a group of failed elements once reaching sizek*(L) will catastrophically increase in size with virtual certainty. IfL happens to be approximately the median strength of the composite, then the bound based onk =k*(L) adjacent breaks is virtually identical to the true probability distribution of composite strength; indeed, the convergence of the sequence of bounds becomes virtually complete ask exceedsk*(L). We show that the strength distribution for the composite essentially has weakest link structure in terms of a characteristic distribution functionW(x),x ≧ 0 which depends on the load sharing and on the probability distribution for fiber element strength. Typical cases are considered under a Weibull distribution for fiber strength and under a double version which has the effect of putting a ceiling on fiber strength. We show that in typical situations, predictions using the double Weibull distribution are not as one might guess, and its use is unjustified in many cases.

Recent progress in understanding environment assisted fatigue crack growth

Abstract: Metal fatigue has been well recognized as an important cause for failure of engineering structures. In most applications, fatigue damage results from the conjoint actions of the cyclically applied stress and the external (chemical) environment, and is therefore time dependent. Understanding of this load-environment interaction is essential to the formulation of rational life prediction procedures and to the development of realistic materials evaluation and qualification tests. Research over the past 15 years has led to the suggestion that the rate of fatigue crack growth in an aggressive environment, (da/dN)e, is the sum of three components—the rate of fatigue crack growth in an inert environment, (da/dN)r, which represents the contribution of “pure” fatigue, a cycle-dependent component, (da/dN)cf, that requires the synergistic interaction of fatigue and environmental attack, and the contribution by sustained-load crack growth (i.e., stress corrosion cracking) at K levels above K Iscc, (da/dN)scc. Recent fracture mechanics and surface chemistry studies have provided a clearer understanding of the cycle-dependent term, and, hence, a more complete understanding of environment assisted fatigue crack growth. (da/dN)cf results from the reaction of the environment with fresh crack surfaces produced by fatigue, and is a function of the extent of reaction during one loading cycle. For highly reactive alloy-environment systems, this contribution depends also on the rate of transport of the aggressive environment to the crack tip. The experimental basis and the development of models for transport and surface reaction controlled fatigue crack growth are reviewed. Interpretation of the effects of partial pressure of the aggressive environment and cyclic load frequency in terms of surface reaction and transport processes is discussed. Implications in terms of service performance and life prediction procedures are considered.

Probability distributions for the strength of composite materials I: two-level bounds

Abstract: An upper bound is obtained on the probability distribution for the strength of composite materials. The analysis is based on the chain-of-bundles probability model, and local load sharing is assumed for the nonfailed fiber elements in each bundle. The bound is based on the occurence of two or more adjacent broken fibers in a bundle. This event is necessary but not sufficient for the failure of the material. Two distributions are assumed for fiber strength: the usual Weibull distribution and a more realistic double version which has much the effect of putting a ceiling on fiber strength. For large composite materials, the upper bound becomes a Weibull distribution but with a shape parameter which is twice that for the individual fibers. The bound is always conservative, but it is extremely tight when the variability in fiber strength is low. In typical cases, the use of the double Weibull distribution for fiber strength is shown not to affect the behavior of the bound significantly. In view of the additional experimental and computational labor involved, its use in practice may not be justified in such cases. However, its use does shed light on fracture processes in composite materials.

A theory of warm prestressing: experimental validation and the implications for elastic plastic failure criteria

Abstract: A theoretical explanation of warm prestressing (WPS) is proposed based on the J-integral. This is defined so that only elastic strains and distortions are included in the integrand compared with the definition of J common in finite element computation where total strains and distortions are used. The physical meaning of J as used here is that it represents the force on singularities (e.g., dislocations) enclosed by the contour of integration. Therefore, it is path dependent if the contour cuts through the plastic zone.

Stress-intensity factors and crack-opening displacements for round compact specimens

Abstract: A two-dimensional, boundary-collocation stress analysis was used to analyze various round compact specimens. The influence of the round external boundary and of pin-loaded holes on stress-intensity factors and crack-opening displacements was determined as a function of crack-length-to-specimen-width ratios. A wide-range equation for the stress-intensity factors, like that developed for the “standard” rectangular compact specimen, was developed. Equations for crack-surface displacements and load-point displacements were also developed.

A micromechanistic approach to the warm pre-stressing of ferritic steels

Abstract: Warm pre-stressing of a cracked body can result in an apparent elevation of its fracture toughness at lower testing temperatures. This effect has been observed in mild steel pre-loaded at room temperature and tested at −150°C, when the apparent toughness elevation can be as great as a factor of two. This toughness elevation is produced both when the pre-load is maintained during cooling and when the pre-load is completely removed prior to cooling.

Linear elastic fracture mechanics computations of cracked cylindrical tensioned bodies

Abstract: The variation of the stress intensity factor along the crack front and the strain energy release rate were computed, by the boundary integral equation method, for semi elliptical cracks on the surface of cylindrical bodies strained in tension or in bending. The results were checked by the compliance method. The fracture toughness of high strength steel wires was measured on notched cylindrical specimens. The value which was found to be 80 MPa √m, was used to predict the fracture loads of cracked wires with various crack configurations, and they compared well with the experimental results. The evolution of the cracks during fatigue was followed as a function of the number of cycles and the fatigue life could be predicted making use of Paris law.

On the bending stress distribution at the tip of a stationary crack from Reissner's theory

Abstract: A general solution is developed for the symmetric bending stress distribution at the tip of a crack in a plate taking shear deformation into account through Reissner's theory. The solution is obtained in terms of polar coordinates at the crack tip and includes the complete class of solutions satisfying all the three boundary conditions along the crack. The solution has arbitrary multiplicative constants and in specific problems, these constants can be determined from conditions on the exterior boundary by well-known numerical techniques such as collocation, successive integration. Results of a numerical solution for a square plate with a central crack subject to uniaxial bending are presented along with a critical discussion of the sensitivity of the numerical solution which is associated with the exponential character of Bessel terms in this higher order analytical solution.

Cracking in particulate composites due to thermalmechanical stress

Abstract: Numerical computations of the strain energy release rate for cracks propagating around the interface between a spherical particle and a matrix have been used to determine the strain energy release rate function for the case where stresses arise due to differential thermal contraction. The strain-energy release rate function was found to exhibit a maximum as a function of crack length consistent with the theoretical conditions for crack extension and arrest proposed by Lange. The calculations show that a critical particle size exists below which crack extention does not occur for a given thermalmechanical stress. The predicted critical particle size correlates well with experimental results.

Cyclic deformation behavior of a low carbon steel in the temperature range between room temperature and 850 K

Abstract: Stress-controlled uniaxial push-pull fatigue tests were carried out with cylindrical specimens of low carbon steel with a carbon content of 0.1 percent. Resistent heated grips provided testing temperatures up to 550°C. During all fatigue tests the time-dependent strain was measured. The strain at zero load, the plastic strain amplitude plotted against the number of cycles is known as the cyclic deformation curve. At room temperature, this curve depends on the applied stress amplitude. The shape of the cyclic deformation curve at the same stress amplitude is strongly temperature-dependent. In the temperature region of blue brittleness the endurance shows a maximum connected with a very low plastic strain amplitude. Also the cyclic stress strain curves have a different appearance within varied temperature ranges.

Fatigue failure criteria for combined cyclic stress

Abstract: Failure criteria for combined cyclic stress are represented in terms of parametric families of failure surfaces in stress space. Quadratic approximations and symmetry arguments are employed in systematic fashion to construct isotropic failure criteria for general three dimensional states of cyclic stress. Particular attention has been directed to the important cases of normal stress-shear stress (bending-torsion) and biaxial stress cyclings. It is shown that failure criteria for cycling with and without mean stress (reversed cycling) have different forms, the latter admitting simpler representations.

On some numerical methods for the solution of the plane elasticity problem for bodies with cracks by means of singular integral equations

Abstract: Comparison is given of the accuracy of calculation of stress intensity factors at the crack tips by various methods when solving plane elasticity problems for bodies with cruciform and edge cracks. It is shown that, within the range of quadrature formulas for singular integrals discussed, the type of the formula chosen for the solution of an equation, if used correctly, affects negligibly the accuracy of the stress intensity factor evaluation at the crack tip, and in view of this a method is proposed based on simple relationships.

On a relationship between stretched zone parameters and fracture toughness of ductile structural steels

Abstract: Quantitative stereofractographic analysis of the stretched zone at the crack tip is performed on specimens of two ductile steels used for determining fracture toughness. The effect of temperature, loading rate, stress-state mode and specimens size on the stretched zone formation is studied. A correlation is obtained of the stretched-zone height and width with fracture toughness of materials and the crack tip opening displacement value which is determined by means of various mathematical models.

The effect of water vapor on fatigue crack tip stress and strain range distribution and the energy required for crack propagation in low-carbon steel

Abstract: The formation of a subgrain structure by the passage of a fatigue crack in low-carbon steel has been detected by backscattered electron imaging in the SEM. The distribution of subgrain sizes has been measured as a function of cyclic stress intensity and environment, and from this data the cyclic stress and strain range distributions have been determined, as has the energy dissipated during propagation of the fatigue crack. These results are compared to theoretical and other experimental findings. The energy equivalent (per unit area of incremental crack advance) of the environment is found to be 106 times the surface energy of iron. In an inert environment, the maximum cyclic stress range developed at the crack tip is found to be approximately 2.3 times the yield stress, independent of cyclic stress intensity. Water vapor effectively lowers this stress range, and causes it to assume a dependence upon cyclic stress intensity.

The early stage of fatigue crack growth in martensitic steel

Abstract: In low ductility and high strength steels, the early stage fatigue behavior associated with non-metallic inclusions is a highly localized phenomenon near the inclusions. However, the nature of the fatigue crack initiation process is not clear. In this paper, a special emphasis is placed on the possible differences in the mechanism of initiation and the early growth of fatigue cracks between a martensitic steel and ordinary ductile materials. The poor adhesion between matrix and aluminum oxide inclusion leads to the formation of an inclusion pit which serves as a simple stress raiser. The fatigue crack originates at the periphery of this inclusion pit at an angle of 45 degrees to the principal stress direction. Metallurgical and micro-fractographical observations revealed that the initiation and early growth of fatigue cracks from non-metallic inclusion are of the shear rather than the tensile mode. Thus, it is concluded that, though the fatigue process is quite localized in the vicinity of inclusion, the mechanism for an initiation and early growth of fatigue cracks is essentially the same as that for ductile materials. The effects of metallurgical heterogeneities in the martensite, such as the prior austenite grain boundaries, packets, and plates on the initiation and early growth of the cracks, are also discussed from the mechanical-metallurgical viewpoint.

The stress-wave radiation from growing cracks

Abstract: Explicit formulae are given for the stress discontinuities radiated by a suddenly starting two-dimensional crack under tension, in an ideal elastic body. These formulae also give, with a change in sign, the stress discontinuities radiated by a suddenly stopping crack, and, with a geometrical deformation, those radiated by a three-dimensional crack. The stress in the primary radiation due to short crack-jumps is thus shown to vary in essentially the same manner as does the crack speed during the jump. The diffraction of the primary radiation from one tip of a centre-crack by the other tip produces a secondary radiation, whose properties depend mainly on the nature of the surface wave associated with the primary radiation. Since this first diffraction can lead to crack extension, further diffractions would be difficult to study analytically. If it is possible to isolate the primary radiation experimentally, however, it should give directly the essential characteristics of the source. This could be used to separate source-characteristics from specimen and transducer effects in acoustic emission studies of fatigue cracking, or stress-corrosion cracking.

Mechanisms of cyclic softening in precipitation-hardening alloys—A ball model approach and tests at 78 K

Abstract: Tests of random, alternating cuts on a ball-model of θ″ in Al−Cu alloy have been run to check the kinetics at which disordering occurs in an initially ordered precipitate subject to cyclic strain. In addition, fatigue tests at low temperature (78 K) and various microscopical observations have been made on Al−Ag alloy containing GP zones to check whether a structure containing an initially disordered precipitate will cyclically soften or not. It was thus found that the θ″ ball model disorders as a function of accumulated plastic strain consistently with the kinetics of cyclic softening in actual material. Further, Al−Ag alloy was found not to soften at 78 K. Both of these results supoort the disordering hypothesis of cyclic softening over the “dissolution” or “shearing-off” mechanisms, although other systems may be subject to these mechanisms. In spite of the low temperature at which the Al−Ag alloy was tested, small γ′/γ precipitates were found to have formed in the longest lived test; however, this result did not interfere with the validity of the experiment as it did previously at room temperature. The fatigue lives at 78 K were much longer than those previously measured at room temperature although the failure mechanisms were not affected at high strain and only somewhat affected at low strain (there was increased incidence of transgranular crack nucleation and propagation).

Energy considerations in fatigue crack propagation

Abstract: The concept of Griffith fracture theory was extended to fatigue crack propagation problems by defining the Gibbs free energy of solids under cyclic loading.

Fatigue microcrack growth in a nickel-base superalloy

Abstract: The growth of very small fatigue microcracks was studied in a powder metallurgy nickel-base superalloy. A novel specimen containing a small crack was used, with crack growth rates being measured optically at high magnification. Interaction between the crack and the material microstructure was observed in a cyclic loading stage within a scanning electron microscope.

A multi-test piece approach to the fracture characterisation of linepipe steels

Abstract: The energy for fully shear fracture in CT tests has been measured for controlled rolled, normalised and also quenched and tempered materials. Equations have been derived relating the energy per unit area for fracture to the ligament length, (W−a), of the test piece, both at ambient temperature and also at lower temperatures; these are of the form: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGvbaabaGaamOqamaabmaabaGaam4vaiabgkHiTiaadggaaiaawIca% caGLPaaaaaGaeyypa0JaamOuamaaBaaaleaacaWGJbaabeaakiabgU% caRiaadofadaWgaaWcbaGaam4yaaqabaGccaGGOaGaam4vaiabgkHi% TiaadggacaGGPaaaaa!47C3!\[\frac{U}{{B\left( {W - a} \right)}} = R_c + S_c (W - a)\] where B is the thickness and Rc and Sc are constants. The first term is the energy absorbed per unit area of fracture whereas the second term is the energy absorbed per unit volume of plastic deformation remote from the fracture surface. Increasing the strain rate or decreasing the temperature slightly increased the energy for fracture; however, there was an increase in the maximum contraction with increasing strain rate whereas there was a decrease with decreasing temperature. This indicated that high strain rate tests could not be correctly simulated by testing at lower temperatures. Similar equation constants were obtained from the results of SENB tests, but for tension tests there was a significantly higher Rc value although the Sc value was similar. Results of impact tests were also found to fit the same expression, with Rc and Sc values greater than for the slow rate tests. A number of sub-thickness CT test pieces were tested, but only a small, if any, decrease in toughness was observed.

Influence of thickness on critical crack opening displacement (COD) and J values

Abstract: The effect of specimen thickness on the critical values of COD and J integral at fracture was studied in a carbon manganese steel plate 100 mm thick. Ductile brittle transition data from preferred geometry bend specimens showed that K IJ values obtained from J Ic in 10 mm thick specimens can overestimate K Ic measured in 100 mm thick specimens. Relaxation of stress triaxiality and changes in micromode of crack initiation with decreasing specimen thickness are considered to be factors causing the discrepancy between K IJ and K Ic. The problems associated with using K IJ values, obtained from thin specimens, to predict defect sizes in thick structures are discussed.

Comparison of J testing techniques and correlation J-COD using structural steel specimens

Abstract: J integral and COD measurements were made simultaneously on three-point bend specimens of 50D structural steel (specification BS4360). Tests were performed at temperatures over the range -100°C up to room temperature, and at each temperature a series of specimens with a/W ranging from 0.2 to 0.8 were tested.