Crack Tunneling Research Articles

Crack growth under constant sustained load at elevated temperature in IN718 superalloy

Crack growth rate ( da/dt) in IN718 nickel base superalloy has been studied at 600 and 700°C, in both compact tension and corner crack specimens, under sustained constant load conditions, generating an intergranular fracture mode. Using the stress intensity factor, K, as the correlating parameter, slower growth rates are found for corner cracks than for the through cracks in CT specimens together with a greater degree of crack tunneling. In the CT specimens, the introduction of lateral side grooves increases the crack growth rate. Disparities found between growth rates in the CC geometry are found to correlate with the incubation time for re-initiation of crack growth, which is attributed to a crack tip blunting and creep mechanism. A limited assessment of the correlation of growth rates using the creep crack growth parameter C* is made.

An energy balance in crack propagation and arrest

The data from temperature gradient double tension tests and dynamic small scale tests on two steels having different toughness levels have been utilised in a quasi-static crack arrest analysis. An energy balance approach using the total initial elastic energy progressively depleted by the absorbed fracture propagation energy predicted arrest temperatures to within 7°C of the values measured at the arrested crack tip in double tension tests. The general criterion for crack arrest including conditions where crack tunnelling by shear occurs is: R s >σ 2 iL/2E(1+a p /W) where R s is the mean impact propagation energy per unit area required for arrest; σ i is the initial applied gross section stress; L is the effective length of the whole of the structure; a p is the length of the arrested crack; W is the width; E is the elastic modulus. The above expression applies to service conditions as well as to laboratory tests. It incorporates the kinetic energy which is a means whereby the total elastic energy is made available for fracture. For linear elastic plane strain conditions with no tunnelling, the equivalent stress intensity factor K s derived from the above is: K s >σ i/(1/(2W tan( πa p /2W))+2a p /WL) 0.5. This expression can only be applied to predict arrest where L and, therefore, the total energy of the structure is low and the slope of d K/d a is negative.

Crack Initiation in Fiber‐Reinforced Brittle Laminates

In fiber‐reinforced brittle laminates, crack growth under monotonic tension generally consists of crack tunneling along the weaker ply (usually the 90° ply) followed by plane strain crack growth through the adjacent, more resistant plies (the 0° plies). In this paper, the details of this transition in crack mode are examined. The tunneling crack configuration is generalized to allow the crack to penetrate the 0° ply during tunneling. The effects of crack bridging in the 0° plies on the energetics of tunneling are computed numerically for general cases and combined with analytical results for certain limits. The nature of the transition from tunneling to plane strain cracking is found to depend on the ratio of the toughnesses of the 90° and 0° plies. Implications for laminate design are discussed.

CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of 2.3-mm thick sheets of 2024-T3 aluminum alloy was experimentally investigated for middle crack tension specimens having initial flaws that were: (a) flat fatigue cracks (low fatigue stress) and (b) 45-deg through-thickness slant cracks (high fatigue stress). The critical CTOA values during stable tearing were measured by two independent methods, optical microscopy and digital-image correlation. Results from the two methods agree well. The CTOA measurements and observations of the fracture surfaces have shown that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness (Δa>B), CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness (Δa>2B), crack tunneling stabilized. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only slightly higher CTOA values during initial crack growth. The amount of tunneling in the high fatigue stress tests was about the same as that in the low fatigue stress tests after the flat-to-slant transition. This study indicates that stress history has an influence on the initial portion of the stable tearing behavior. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack-tip constraint. The measured CTOA reached a constant value of 6 deg for crack growth of about the specimen thickness. This coincided with the onset of 45-deg slant crack growth and a stabilized, slightly tunneled (about 20 percent of the thickness) crack-front shape. For crack growth on the 45-deg slant, the crack front and local field variables are still highly three dimensional.

DUCTILE CRACK GROWTH PREDICTIONS FOR LARGE CENTRE CRACKED PANELS BY DAMAGE MODELLING USING 3‐D FINITE ELEMENT ANALYSIS

Abstract— This paper reports on a three‐dimensional numerical prediction that involves continuum damage theory for the deformation of centre cracked panels under uniaxial and biaxial tensile loading. The predicted differences of crack tip blunting movement, crack tunnelling behaviour and the changing shape of the plane ahead of the crack tip for the two loadings are close to those observed in tests. The material parameters that encapsulate the damage response of the A533 B class 1 steel tested, were selected from a detailed parametric study on laboratory crack‐growth resistance tests on the material.

A numerical study of fracture initiation in a ductile material containing a dual population of second-phase particles—I. Static loading

Some recent experimental studies with pre-notched bend specimens of 4340 steel under both static loading [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] and impact loading [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] have shown that considerable crack tunneling occurs in the interior of the specimens prior to gross fracture initiation on the free surfaces. The final fracture of the side ligaments happens because of shear lip formation. The tunneled region is characterized by a flat fibrous fracture surface. In this work, the above experiments are analyzed using a 2D plane-strain finite-element procedure which is expected to simulate local material failure in the center-plane of the 3D specimen accurately. The rate-independent version of the Gurson model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage, and small particles which require large strains to nucleate voids. Attention is focused on the formation of a discrete void around a simulated inclusion ahead of the notch-tip, its growth and link-up with the notch-tip via a sheet of microvoids. In Part I of the work, the results obtained from the finite-element analysis of the static fracture initiation test [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] are presented. It is found that the value of the J-integral at which material failure near the notch-tip commences in the present simulation agrees well with experimental observations regarding the onset of crack tunneling. The analysis of the impact fracture test of [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] will be taken up in Part II.

THREE‐DIMENSIONAL CONSTRAINT EFFECTS ON STRESS INTENSITY DISTRIBUTIONS IN PLATE GEOMETRIES WITH THROUGH‐THICKNESS CRACKS

AbstractThree‐dimensional finite element analyses of through‐thickness cracks in plate geometries are presented. It is shown that the local constraint variation towards the crack tip causes an increase in stress intensity which is neglected in analyses which assume a constant stress state throughout the geometry. This means that stress intensity factors for these types of crack geometries are a factor (1 — v2)‐0.5 higher than generally reported in stress intensity handbooks.Analyses on crack tunnelling situations show that if plane stress dominates the global behaviour, an almost constant stress intensity across the thickness is reached for a relative tunnelling depth of a 2.5% of the plate thickness. For geometries which are not predominantly in plane stress this value will be somewhat larger. Crack front tunnelling does not influence the mean stress intensity across the thickness.Shear lips are shown to reduce the mean equivalent stress intensity (the mode I stress intensity which has the same energy release rate as the actual combined mode I, II and III loading) by a factor equal to the square root of the ratio between plate thickness and projected length of the crack front. This may explain the reduction in crack growth rate caused by shear lips during fatigue crack growth experiments. The reduction of the mode I stress intensity factor is considerably larger, which may cause a further reduction of fatigue crack growth rate for crack growth mechanisms that depend primarily on the mode I crack tip loading.Analyses on CNT and SENB specimens show that the conclusions reached on infinite plate models also hold for real structures. However for an SENB specimen with an uncracked ligament equal to the plate thickness, the overall constraint is larger than that of a pure plane stress situation, and the effect of stress intensity increases due to the constraint transition is less pronounced.

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.

PbSnSbIn solder alloy: Kawai, K., Fukuma, N. and Matsui, A. Patent: US4869871, USA Mar. 1989, Off. Gaz. Sept. 1989

Fatigue is one of the main problems in the provision of service life and safety of aircraft structures. The menace of fatigue cracking is accentuated in areas of stress concentration, e.g., joints of structural components. An example is the fuselage where riveting is used. One of the techniques for improving the fatigue life of these connections is the cold expansion of the rivet hole. As part of a larger project on the fatigue behaviour of aeronautical structures, an experimental study of open-hole specimens in Al-alloy 2024-T3, with and without hole expansion, is presented. The residual stress field created by the cold expansion was experimentally assessed by using the X-ray technique and predicted by FEA. Fatigue tests were supplemented by SEM measurements of fatigue striation spacing along longitudinal and transverse directions in the crack surface of each specimen. Empirical models and fractographic techniques developed by Nedbal et al. are used for the analysis of the experimental data, and results of quantitative microfractography are presented. Crack tunnelling was quantified based on the reconstituted crack history and on the surface crack growth measurements.

Hydrogen-assisted cracking studies of 4340 steel by using the optical method of caustics

The optical method of caustics is used to measure the effect of hydrogen on the localized deformation within the fracture process zone (PZ). In particular, the role of the PZ in hydrogen-assisted cracking (HAC) of 4340 steel in hydrogen gas at 1 atm is examined. No change in the caustic diameter was detected prior to crack initiation but an “anomalous” enlargement of the caustic diameter as a function of crack growth was observed as a result of crack tunneling. The “center” of the caustic follows the position of the internal crack front, thus providing a simple means to monitor the growth of internal cracks. It is demonstrated that the technique provides a sensitive means for detecting HAC initiation (the smallest crack depth change detected is 35 μm) and insight into the three-dimensional character of the PZ.

The effect of microstructure and stress state on the fracture behaviour of wood

Based on a general fracture mechanics approach, this paper attempts to correlate macroscopic fracture properties with micromechanical behaviour in wooD. In the first part, the influence of orientation, cell size and other structural features of wood on toughness, fatigue resistance and fracture morphology is described. Subsequently, experimental observations of crack tunnelling effects are reported which, coupled with direct crack tip strain measurements and a verification of the influence of specimen thickness on fracture properties, confirm the existence of stress state variations across a crack front in wood, and the corresponding effects on fracture behaviour. Irreversible crack-tip deformation modes are identified, involving intercellular debonding, cell twisting and buckling, and the role of stress triaxiality is discussed. A strain criteria for the fracture of pre-notched bulk wood specimens is developed, based on an observed linear relationship between notch root radius and crack opening displacement for fracture initiation.

Fracture Energy and Crack Tunnelling

Abstract Instrumented impact testing has been used to measure the dynamic fracture-initiation toughness of some precipitation hardened aluminum alloys. The results of these tests have been calculated by the energy method GIc = ω/ηA and by the K calibration formula. The difference in origin and interpretation between the initiation toughness GIc = ω/ηA and specific fracture energy ω/A has been considered. Double-cantilever beam (DCB) specimens of these alloys have been used to measure point values of fracture toughness by the compliance method and average propagation toughness by the specific surface energy method. Fracture propagation is of the semistable type in these non-rate-sensitive alloys, and the toughness values are found to be similar by both methods. An exception is when crack tunnelling develops during crack propagation in thick DCB specimens. Then KIc from the surface energy method tends to be lower than that from the compliance method.

Evaluation of Fracture Energy of Aluminum Alloys

Abstract The fracture toughnesses of some precipitation-hardened aluminum alloys have been evaluated, mainly by the use of precracked three-point bend specimens in instrumented impact testing. A recently developed interpretation of the specific surface energy method has been applied to calculate the initiation values of KIc and these values have been compared with those calculated using stress analysis equations. The value of unity thereby deduced for the geometrical constraint factor in these non-rate-sensitive materials may be appropriate to the type of fracture mode occurring in these alloys, that is, semiductile. The distinction in principle between fracture initiation toughness, expressed as GIc = w/ηA, and the average propagation toughness w/A has been noted and the latter used in studying crack tunnelling during semiductile crack propagation in thick sections of the alloys in the form of large, double-cantilever beam specimens.