Crack Tip Plastic Zone Size Research Articles

Dynamic crack propagation in elastic-perfectly plastic solids under plane stress conditions

the phenomenon of steady-state dynamic crack propagation in elastic-perfectly plastic solids under mode I plane stress, small-scale yielding conditions is investigated numerically. An Eulerian finite element scheme is employed. The materials are assumed to obey the von Mises yield criterion and the associated flow rule. The ratio of the crack tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 × 10 4. Two subjects of general interest are discussed. These are the asymptotic structure of the crack tip stress and deformation fields, and the appropriateness of a crack growth fracture criterion based on the far-field dynamic stress intensity factor. The crack-line solution by achenbach and li (Report NU-SML-TR-No. 84-1, Dept. of Civil Engineering, Northwestern University, Evanston, IL 60201, 1984a; in Fundamentals of Deformation and Fracture (edited by B.A. Brilby et al.). Cambridge University Press, 1984b) is discussed and compared to the numerical solution. The results of this study strongly indicate that the crack tip strain and velocity fields possess logarithmic singularities, which is consistent with the assumptions in the asymptotic analysis by Gao ( Int. J. Fracture 34, 111, 1987). However, it is revealed that the crack tip field variations in Gao's solution present features often contrary to the numerical findings. To this end, a preliminary asymptotic analysis is performed in an effort to resolve certain issues. Finally, the critical plastic strain criterion ( mcclintock and irwin, in Fracture Toughness Testing and Its Applications, ASTM STP 381, p. 84, 1964) is adopted to obtain theoretical relations between the critical dynamic stress intensity factor and the crack propagation speed. These relations are found to agree well with experimental measurements by Rosakis et al. ( J. Mech. Phys. Solids 32, 443, 1984) and by zehnder and rosakis ( Int. J. Fracture, to appear 1990), performed on thin 4340 steel plates whose material characteristics match those of the calculation. The results seem to support the existence of a one-to-one relationship between the dynamic fracture toughness of the material and the crack propagation speed, for materials which fail in a locally ductile manner.

A strip model for fatigue crack growth predictions under general load conditions

A strip crack closure model, based on the Dugdale-Barenblatt model but modified to leave plastically deformed material in the wake of the crack tip, was investigated for various aspects of fatigue crack growth behaviour. A constraint factor was introduced into the model to account for the 3D effect at the crack tip to extend the applicable range of the original Dugdale-Barenblatt model to the plane strain condition. Comparisons with experimental data show that the constraint factor in the strip model results in a fairly good prediction for the fatigue crack closure under the plane strain condition. A variable constraint factor makes it possible for the model to account for the gradual change of stress state from plane strain to plane stress when the crack grows large. The change of stress state occurs typically for the fatigue crack in plates where the stress state at the crack tip is mainly determined by the relative ratio for the crack tip plastic zone size and the plate thickness. The change of stress state has a significant influence on fatigue crack growth behaviour. Weight functions were combined in the modified Dugdale model because crack surface displacement solutions can be derived and the stress intensity factors for complex stress fields can be obtained from corresponding weight functions. It has been shown that a great many problems can be solved when approximate weight function techniques are used. Comparisons were made between predictions from the model and experimental data available in the literature. There was very good agreement for the fatigue crack growth under constant amplitude loading with different stress ratios ( R-ratios), for the load interaction effects in both plane stress and plane strain conditions, for the fatigue crack growth in plates under spectrum loading, for the fatigue crack growth in residual stress fields, and for the small crack growth behaviour.

Formulations for fracture stress, CTP zone and [formula omitted

A unified method is proposed to develop crack resistance curves for various materials. In this method, an R- curve is traced as a nonlinear function of the crack tip plastic (CTP) zone size. The sizes of CTP zones are determined by using an elastic-plastic stress solution based on the HRR (Hutchinson-Rice-Rosengren) singularity. The validity of the analysis is established by comparison with test results. In the course of development of this method, it is also shown that the empirically developed Feddersen's fracture stress envelope can also be derived from theoretical analysis.

Fracture mechanics parameters for polystyrene under high speed impact

AbstractA series of commercial polystyrenes was tested using an instrumented impact tester to determine the fracture toughness Kc and critical strain energy release rate Gc. Over the range of Mw, 201,000 to 336,000, Kc increased from 1.38 MN/m3/2 to 1.76 MN/m3/2and Gc from 0.92 kJ/m2 to 1.60 kJ/m2. A linear correlation for Kc and Gc was seen with melt index, and an inverse relationship was obtained against molecular weight. Examination of the fracture surfaces revealed the presence of crack growth bands corresponding to the crack tip plastic zone size. It is suggested that these bands are the consequence of variations in crack growth along crazes that form in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances. The spacing of these bands corresponds to the craze length formed in the plastic zone, and the band spacing increases with molecular weight.

新しい衝撃曲げ試験法による動的破壊じん性の評価

A novel impact bend test procedure is described for determining the dynamic fracture-initiation toughness, KId, at a loading rate KI of the order of 106MPa√m/s. The split Hopkinson pressure bar technique was used to measure dynamic loads applied to a fatigue-precracked bend specimen. The dynamic stress intensity factor history for the bend specimen was evaluated by means of a dynamic finite element code. The onset of crack initiation was detected using a strain gage near a crack tip. The KId value was determined from the critical dynamic stress intensity factor at crack initiation. A series of dynamic fracture tests were performed for a Ti-6246 alloy and a 7075-T6 aluminum alloy. The KId values obtained for both the alloys were compared with the corresponding values obtained under quasi-static loading conditions. The fracture surface morphology was examined with the help of a scanning electron microscope to rationalize the apparent differences in the measured fracture-initiation toughness in response to the change in loading rate. Furthermore, the validity of the KId determination was confirmed by measurements of the crack tip plastic zone size in the interior of the fracture specimens based on the microhardness tests.

High-resolution measurement of crack-tip plastic zone sizes by selected area channelling patterns

Selected area channelling patterns (SACPs) have been used to measure plastic zones (PZ) associated with fatigue cracks in a nickel-based superalloy MA6000. Refinement of the technique has enabled the PZ dimension to be measured to within ±0.5 μm, which represents an order of magnitude improvement on previously reported work. It has been shown, in a series of fatigue tests at various frequencies and temperatures, that the size of the plastic zone at a given value of ΔK varies with the square root of the crack propagation rate.

Elastic Fracture Mechanics Concepts for Interfacial Cracks

Elastic fracture mechanics concepts are reexamined for a crack on the interface between dissimilar solids. A derivation by function theory is given of the form of stress and displacement fields in the vicinity of the crack tip, equivalent to complete Williams expansions of both inner and outer (external to a nonlinear or contact zone) type. The complex stress intensity factor K associated with an elastic interface crack, for which contact is ignored, is discussed and, specifically, its validity as a crack tip characterizing parameter is noted for cases of small scale nonlinear material behavior and/or small scale contact zones at the crack tip. That is, similar values of K for two cracked bodies then imply similar states as the crack tip, so that conditions for crack growth can be phrased in terms of K reaching a critical failure locus in a complex plane. The maintenance of a similar state at a crack tip under change of crack length is shown to require alteration of both the magnitude and phase angle of a combined tension and shear loading. Some possible definitions of stress intensity factors KI and KII of classical type associated with interface cracks are discussed. Also, the scaling of interface crack tip plastic zone size with load under small scale yielding conditions is found to deviate from classical scaling, in proportion to the square of the applied load level, and dependences of the field on distance from the tip and on load phase angle are found to be linked together.

On double limits and asymptotic small scale yielding solutions of crack tip fields

The stress intensity factor emerged as a parameter quantifying the strength of crack tip stress or strain singularities in linear elastic materials but stress and strain intensity factors have also been used extensively to characterize crack tip stress and strain fields in elastic-plastic materials under small scale yielding conditions. A rigorous asymptotic small scale yielding solution must involve the passage to the limit as the two quantities r and R tend to zero, where r is the radius vector centred at the crack tip and R is the maximum crack tip plastic zone size. However, there is no unique solution, i.e. one which does not depend on the manner in which r and R tend to zero. In order to establish some contact between macroscopic continuum models and material microstructure an increasing number of fracture criteria stipulate the existence of a small finite characteristic length associated with the region neighbouring the crack tip, e.g. a process zone size rz. In such cases characterization of the stress and strain states in the region bordering the process zone may be obtained from directed partial limit solutions corresponding to r, R tending to zero but the ratio ρ (= r/R) tending to ρc (= rz/Rc) where Rc is the value of R at the initiation of crack extension. Quantities essentially similar to ρc have appeared in the literature from time to time and have also been encountered in connection with the crack separation energy rate GΔ which was found to have a strong dependence on them.

Determination of the size of crack-tip plastic zone in a thin sheet under uniaxial loading

The shape and size of plastic zone at the tip of a centre crack in a thin sheet under plane stress conditions has been studied by use of the photostress coating method. A simple technique has been adopted for the computation of largest spread of the plastic zone surrounding a crack-tip by use of normal incidence photoelastic data alone. It has been shown that this technique, in conjunction with the Tresca yield criterion, gives the absolute maximum value of the plastic zone size under plane stress condition. The results show reasonable agreement with those obtained from elasto-plastic finite element analysis and those obtained by other researchers.

ON THE IMPACT FATIGUE CRACK GROWTH BEHAVIOUR OF METALLIC MATERIALS

AbstractThe impact fatigue crack growth characteristics of a low carbon steel and an aluminium alloy were studied. An impact fatigue testing machine of the Hopkinson bar type was used in these experiments to conduct a series of crack growth tests under simple impact stresses.The following characteristics of impact fatigue crack growth behaviour were revealed: (1) crack growth rate is higher in impact fatigue than in non‐impact fatigue; (2) crack opening ratio in impact fatigue takes a higher value than in non‐impact fatigue; (3) crack tip plastic zone size is smaller in impact fatigue than in non‐impact fatigue.

Hydrogen induced interior crack-tip morphologies in high strength steel

In this study WOL specimens of high strength 4340 steel were used to obtain information on the interior, or near plane strain, crack-tip morphology resulting from hydrogen assisted crack growth, including the position of secondary cracks in relation to the region of maximum triaxial stress, crack-tip plastic zone size, and grain size. The interior, or near plane strain, regions were revealed by removing thin sections, by a grinding and polishing procedure, from the surfaces of specimens that underwent hydrogen assisted crack growth. The results appear to indicate that advance of the crack occurs by growth of protrusions, or steps, from the main crack front, followed by linkup of these protrusions by sideways growth along grain boundaries.

The influence of crack tip plasticity in the growth of small fatigue cracks

In order to rationalize observed differences in the growth behavior of large and small cracks, local crack tip opening micromechanics have been characterized for both crack size regimes in a high strength aluminum alloy. It is found that crack tip opening displacement, crack tip opening load, and crack opening mode all differ widely for large and small cracks at equivalent cyclic stress intensities (ΔK). High crack tip opening displacements and relatively low, approximately constant, crack opening loads for microcracks account both for their rapid rate of growth relative to large cracks and the absence of a microcrack threshold stress intensity. Crack tip plastic zone sizes also were measured, and it was found that the ratio of plastic zone size to crack length for small cracks is ∼ 1.0, while for large cracks the same ratio is ≪ 1. Simple empirical corrections to ΔK are found inadequate to correlate the growth of large and small cracks. It is concluded that for small cracks, linear elastic fracture mechanics similitude does not apply, and that an alternative crack driving force must be formulated.

Crack tip plasticity and crack growth in a single-crystal superalloy at elevated temperatures

The effect of frequency and temperature on the fatigue crack growth rates of a single-crystal superalloy have been investigated. At elevated temperatures, crack growth rates were found to increase significantly at frequencies below 1 Hz. The crack tip plastic zones from the mid-plane of centre crack tension specimens fatigued at known stress intensities have been analysed. At a constant δK and high frequencies the plastic zone size is relatively insensitive to changes in temperature. At elevated temperatures, lower frequencies give rise to increases in the plastic zone size at a constant δK. The measurements of the crack tip plastic zone size and the strain distribution within the plastic zone are related to the deformation mechanisms determining crack advance.

The effect of dispersoids on the micromechanisms of crack extension in Al-Mg-Si alloys

The effect of an increasingly triaxial stress state on the fracture strain of peak-aged alloys was measured using a series of notched tensile specimens. The alloy ductility was found to increase with dispersoid content and to decrease with increased stress triaxiality. Crack tip plastic zone sizes on the midplane of compact tension specimens were measured experimentally and, for the same applied stress intensity factor, were found to decrease with increasing dispersoid content. SEM analysis of the fracture surfaces revealed that the dominant micromechanism of crack extension was ductile rupture along the grain boundary precipitate free zone. These results are discussed in terms of the influence of dispersoids on slip distribution. The stress and strain distributions in the plastic zones are related to the micromechanisms of crack extension.

The effect of dispersoids on the ductile fracture toughness of AlMgSi alloys

The ductile fracture toughness J Ic of AlMgSi alloys aged to peak hardness is measured as a function of dispersoid volume fraction. It is found that the toughness increases with dispersoid content, for alloys having similar grain sizes and yield strengths, and this increase is attributed to the homogenization of slip distribution. The crack tip plastic zone sizes are determined experimentally as a function of applied stress intensity factor K and a model, based on the crack tip blunting geometry, is proposed to explain the variation in zone size with dispersoid content. A relationship between fracture toughness J Ic and the work per unit area of new fracture surface, dW/dA, bears out the contention that the increased toughness caused by an increased amount of dispersoid particles is due to finer spread-out slip at the crack tip.

The Effect of Plate Thickness on the Fatigue Crack Propagation of Very Thin Steel Plate Specimens

Using very thin steel plate specimens, the effect of the plate thickness on the fatigue crack propagation was studied and the following results were obtained. In very fine grained specimens, the crack propagation rate becomes slow with an increase of plate thickness. Based on the fatigue crack propagation resistance in the plane stress (in case of extremely thin plate specimen) and plane strain (in case of relatively thick specimen) conditions and the crack tip plastic zone sizes under maximum stress and cyclic stress conditions, the effect of plate thickness on fatigue crack propagation was estimated. The experimental results coincide with this estimation.

The effects of dispersoids upon the micromechanisms of crack propagation in AlMgSi alloys

The effect of dispersoids containing Mn or Cr. in a series of peak-aged AlMgSi alloys, upon the crack-tip plastic zone size has been studied by the use of Selected Area Channelling Patterns (SACPs). In the absence of such dispersoids. the alloy fractures in a brittle intergranular fashion; when the particles are present, the alloys are ductile but still fracture in a predominantly intergranular manner but with an increase in the size of the plastic zone associated with the crack tip. It is suggested that the toughening effect of the dispersoid phase is indirect through its effect upon the matrix grain size and upon the distribution of slip. Fracture occurs because slip bands impinge on grain boundaries, causing a local strain concentration which at some critical value nucleates a void, thereby causing an increment of crack extension.

The Relationship of the Resistance Curve and Gcto Specimen Configuration

SummaryFollowing a brief introduction, an examination is presented of the factors which define fracture toughness, resistance-curve relationships and the extent of stable crack extension in thin-sheet failure. Tests have been performed on three aluminium alloys to establish the variations in the shape of resistance curves, using both compliance-indicated and measured absolute values of crack length in compact tension specimens and centre crack sheets. The results show that both the toughness and the resistance curves of the two specimen types are different and that these differences cannot be explained wholly by consideration of crack tip plastic zone sizes.