Running Crack Research Articles

Crack Arrest Fracture Toughness Testing of Naval Construction Steels

Abstract A program was undertaken to apply the ASTM E 1221 test method to two submarine steels exhibiting high ratios of toughness to yield stress. The objective was to measure the capacities of these steels and representative shipyard welds to arrest fast running cracks. Although the method is not a measure of dynamic toughness, it was considered to be a procedure capable of comparing the crack arresting abilities of these steels. The work has shown that it is possible to follow ASTM E 1221 and obtain valid crack arrest fracture toughness results for materials with room temperature KJc as high as 240 MPa√m and a yield stress of 690 MPa using specimens of 50-mm thickness. The process did, however, have a high level of unreliability, necessitating a large number of tests and extensive re-testing to obtain valid results. Test temperatures below −60°C were required to obtain run-arrest events, and as such could not easily be related to material qualification procedures such as explosion bulge testing or to submarine operating temperatures.

表層超細粒化による高アレスト鋼板の諸特性

A new type of steel plate with high crack arrestability has been developed by controlling its microstructure especially in surface layers of the plate. The microstructure of the surface layers of the plate is ultra-fine grained (so-called SUF), which provides excellent fracture toughness even at a cryogenic temperature. Crack arrestability of the plate has been further improved by the enhanced formation of side-ligaments (shear-lips) due to SUF, since unstable running crack behaviour is strongly affected by these shear-lips, which are formed in the surface layers of the plate after the unstable brittle crack has propagated in the mid-section of the plate.In the present report, the practical properties of the developed plate (so-called SUF plate) are investigated. Fracture tests confirm that the SUF plate possesses ultra high crack arrestability. The improved value of arrestability due to the SUF effect can be predicted by fracture mechanics.For practical use of the SUF plate, the damage to the surface layers in actual service should be considered, since the SUF region (surface layers) is essential for obtaining ultra high arrestability in the SUF plate. Considering corrosion loss on an un-painted surface of the plate, the SUF plate, which is prepared by cutting down one side surface to remove 'SUF', is evaluated for crack arrestability by ESSO tests. To simulate the welding damage to the SUF plate, bead-on-SUF plate specimens are tested for crack arrestability by ESSO tests. Both test results suggest that the SUF plate possesses sufficient crack arrestability even in actual service.Furthermore, it is also confirmed that the SUF plate has other characteristics, such as weldability and workability, which make it suitable for ship-building use, such characteristics being similar to those of a conventional-steel plate, including TMCP steel plate.

Fracture of interface cracks under combined loading

This paper presents a study of the fracture behaviour of interfacial cracks under combined mode I and mode II loading condition. Experiments were conducted using scarf joints, in which a wide range of mode ratio is obtained by varying the slant angle. Brittle epoxy adhesive was used in the bonding so that plastic deformation is not a major factor. The observed crack paths are inter-layer with the crack running parallel to the interface. The experimental results suggest that the existing criteria established for homogeneous materials are not applicable to the bi-material system. A fracture criterion is proposed based on the principal strain and the hydrostatic tension, reflecting the sensitivity of brittle adhesives to pressure. It is shown that the theory can also provide good correlation to some of the experimental results obtained using different configurations.

A biaxial test specimen for crack arrest studies

A biaxially loaded, single edge notched (SEN) fracture specimen, with mixed modes I and II loading, was used to study the crack arrest capability of a bonded and riveted tear strap without and with simulated multiple site damage (MSD). MSD was modeled by a 50-percent groove without which the running crack would inevitably kink due to KII loading. A total of thirty-one 2024-T3 aluminum specimens with various crack and MSD configurations were tested. The fracture parameters associated with straight and curved crack paths were determined by using the experimenta results to drive a dynamic finite element model of the specimen in its generation mode. The crack kinking and extension criteria were verified by the excellent agreement between the prediction based on these fracture parameters and the measured crack kinking angles. Comparison between the test results generated by the biaxial stress specimens and by those generated by small- and full-scale pressurized fuselage rupture experiments showed that this specimen can be used to prescreen the effectiveness of tear straps and crack arrestors in an airplane fuselage.

Asymptotic crack tip fields for pressure-sensitive materials and dynamic crack growth under plane stress conditions

For the mathematical description of the yield behaviour of elastic-plastic materials the von Mises yield criterion proves to be suitable for the interpretation of the stress and strain curves of metals. However, many materials exhibit a pressure-sensitive yielding. These material properties are not adopted in the von Mises yield criterion. Hence a generalization of the yield criterion is necessary to examine pressure-sensitive materials. In this contribution, a generalization of the von Mises yield criterion is used to investigate the crack tip fields of pressure-sensitive materials like porous metals and certain polymers [1,2]. This extension, which includes a share of the hydrostatic stresses, leads to the so-called Drucker-Prager yield criterion. The factor ~ in this yield criterion is the measure of the pressure-sensitivity and describes the strength of the influence of the hydrostatic stresses on the yield process. A first asymptotic analysis of stress and displacement fields for dynamic crack problems in elastic-plastic solids was performed by Amazigo and Hutchinson [3] by assuming the validity of the J2-flow theory. Achenbach, Kanninen and Popelar [4], Ponte Castaneda [5], Ponte Castarleda and Mataga [6], t3stlund and Gudmundson [7] and Yuan, Yuan and Schwalbe [8,9] generalized those investigations for a dynamic crack propagation including the plastic reloading region on the crack surfaces for a mixed mode loading situation. Studies concerning pressure-sensitive materials using the HRR-field theory were performed by Li and Pan [10], Li [11] and Yuan and Lin [12]. Bigoni and Radi [13,14] advanced the before mentioned investigation [7-9] for pressure-sensitive materials. However, that analysis was restricted to quasistatic crack extension as well as mode I loading. In this paper, the asymptotic stress and velocity crack tip fields for fast running cracks in an elastic-plastic, pressure-sensitive material are determined. The behavior of the singularity exponent s of the stress-singularity was examined for different pressure-sensitivity parameters kt, crack-tip velocities v and hardening coefficients a. The hardening coefficient t~ describes the relation between the shear and the tangent shear modulus. The assumption of homogeneous, isotropic material behaviour showing linear hardening was used. Further, the incremental theory was applied and stationary crack growth under plane stress conditions has been adopted.

The temperature and the infrared luminescence of the uvenil fracture surface of glassy polymer

The fracture of solids is accompanied by such physical and chemical phenomena as emissions of electrons, ions, photons and molecular particles. The understanding of the mechanisms of all these processes is impossible without the knowledge of the uvenil fracture surface (UFS) temperature. In this research the temperature of UFS of glassy polymer polymethylmethacrylate (PMMA) was measured in time range 10–60 μs after the specimen rupture. The emissional infrared (IR) spectroscopy was chosen as an investigation method, that allows to obtain the Planck spectrum of the heat irradiation of the object, and by position of the maximum ( λ max) on the spectral curve with the application of Wien law ( λ max T=2896 μ m · K) to determine the radiating zone temperature of the progressing crack and of the UFS. It was shown that the IR emission spectrum contains two main components: the Planck (or “heat”) component and the characteristic (or luminescent) one. The UFS warming-up of the PMMA does not exceed 200°C. The temperature field in the vicinity of the top of the running crack and UFS of PMMA was calculated with the help of Rosenthal-Weichert-Schonert theoretical model. The kinetics of UFS cooling of PMMA, which is in a good agreement with the experimental one in long time (tens of μs) has been obtained. In the range of short time (smaller than 10 μs) the experimental data are absent while the calculation given the value of maximum warming-up in the same time range (on the top of the running crack) ∼ 250°C.

Dynamic fracture toughness of 4340 VAR steel under conditions of plane strain

Plate impact experiments are conducted to study the dynamic fracture processes in 4340 VAR steel which occur on submicrosecond timescales. These experiments involve the plane strain loading of a planar crack by a plane tensile pulse with a duration of approximately 1 μs. The loading is achieved by impacting a precracked, disk-shaped specimen by a thin flyer plate. Motion of the rear surface of the specimen, caused by waves diffracted from the stationary crack and by waves emitted from the running crack, is monitored at four points ahead of the crack tip using a laser interferometric system. The measured rear surface motion is compared with the calculated motion using the finite element method to gain understanding of the dynamic fields that occur near the crack tip during crack initiation and propagation. For low temperature experiments, the measured rear surface particle velocity fields are in good agreement with the computed profiles obtained for a constant velocity crack propagation model. For the room temperature experiments, the experimental free surface particle velocityvs time profiles show a sharp spike, with a duration of less than 100 ns at the moment of crack initiation. The spike, which is not predicted by the inverse square root singular stress fields of linear elastic fracture mechanics, is understood to be related to the onset of crack growth. Critical values of the fracture toughness are estimated from the crack initiation times determined both from the velocity time profiles and the elastodynamic modeling of crack advance. The toughness values obtained increase with increasing impact velocity and are as large as 170 MPa√m at the highest impact velocity. Such relatively high values appear to be consistent with the ductile mode of crack initiation observed at all impact velocities used in the present study.

Study on Unstable Brittle Crack Arrest Toughness of Newly Developed Steel with Surface Layers with Ultra Fine Grain Microstructure

Unstable running crack behaviour is strongly affected by side-ligaments (shearlips), which is formed in the surface layers of steel plate after an unstable crack has propagated in the mid-thickness of the plate. Since extensive plastic deformation takes place during the formation of shear-lips, enhanced shearlips formation can improve the crack arrestability. Therefore, a new type of steel plate has been developed by controlling the microstructure, especially in the surface layer of the plate. The surface layer of the steel plate has an ultra fine grain ferrite microstructure, which possesses excellent fracture toughness even at a cryogenic temperature.Fracture mechanics investigations confirm that shear-lips can be formed in the surface layers with this microstructure whenever a brittle crack propagates in the developed steel plate at an actual service temperature for ships. Furthermore, the brittle fracture propagation models also confirm that crack arrestability is improved by enhanced shear-lip formation.

Highly transient elastodynamic crack growth in a bimaterial interface: Higher order asymptotic analysis and optical experiments

A higher Order asymptotic analysis of the transient deformation field surrounding the tip of a crack running dynamically along a bimaterial interface is presented. An asymptotic methodology is used to reduce the problem to one of the Riemann-Hilbert type. Its solution furnishes displacement potentials which are used to evaluate explicitly the near-tip transient stress field. Crack-tip fields corresponding to crack speeds up to the lower of the two shear wave speeds are investigated. An experimental study of dynamic crack growth in PMMA steel interfaces using the optical method of CGS and high speed photography, is also described. Transonic terminal speeds (up to 1.4 c PMMA S) and initial accelerations ( $ ̃ 10 8 ms 2) are reported and discussed. Transient effects are found to be severe and more important than in homogeneous dynamic fracture. For subsonic crack growth, these experiments arc used to demonstrate the necessity of employing a fully transient expression in the analysis of optical data to predict accurately the complex dynamic stress intensity factor history.

CHARACTERIZATION OF DUCTILE TEARING RESISTANCE BY ENERGY DISSIPATION RATE

AbstractThe J integral, which is widely used in elastic‐plastic fracture mechanics, is not the true driving force any more if the crack is propagating. This leads to some inconsistencies when ductile tearing resistance is characterized in terms of J, especially for large crack extensions. Instead, Turner has proposed the energy dissipation rate as a physically more meaningful quantity. His concept is discussed and more evidence is given that will provide a better understanding of ductile tearing. It is shown how this quantity can be determined by measuring the heat production ahead of a fast running crack, or calculated in a finite element analysis, or re‐evaluated from J‐R test records of bend and tensile specimens. The energy dissipation rate is decreasing with crack extension in gross plasticity and approaches a stationary state. From these relations, the shapes of the cumulative J‐R curves can be derived for different specimen geometries.

Crack initiation, propagation and arrest criteria for steel structure safety assessment

Linear Elastic Fracture Mechanics (LEFM) constitutes a numerical correlation between the acting tensile stress, the defect size and the fracture toughness. Usually initiation of material separation is considered to be the critical condition. This, however, holds only for those cases, in which the weakest microstructural area can be located and tested. If this is not the case, a crack will be initiated somewhere else and the fact that it will grow from there onwards has to be considered. Crack propagation is possible in ductile or in cleavage manner. If ductile propagation is present, an R- curve approach may be adequate to be applied. However, if cleavage is triggered, timely arrest of the running crack becomes the only possibility to prevent the separation of the piece.

A theory for cleavage cracking in the presence of plastic flow

A theory is proposed for cleavage cracking surrounded by pre-existing dislocations. Dislocations are assumed not to emit from the crack front. It is argued that the pre-existing dislocations, except for occasional interceptions with the crack front, are unlikely to blunt the major portion of the crack front, so that the crack front remains nanoscopically sharp, advancing by atomic decohesion. The fracture process therefore consists of two elements: atomic decohesion and background dislocation motion. An elastic cell, of size comparable to dislocation spacing or dislocation cell size, is postulated to surround the crack tip. This near-tip elasticity accomodates a large stress gradient, matching the nanoscopic, high cohesive strength to the macroscopic, low yield strength. Consequences of this theory are explored in the context of slow cleavage cracking, stress-assisted corrosion, fast running crack, fatigue crack growth, constraint effects, and mixed mode fracture along metal/ceramic interfaces. Computational models and experiments to ascertain the range of validity of this theory are proposed.

Local variations of the dynamic elastic modulus around running cracks

The variation of the dynamic elastic modulus in the immediate vicinity of the tip of the running crack was studied through an iterative procedure, based on the theoretical expressions for the stress-field components and the experimental relation between strain rate and elastic modulus. It was found that the elastic modulus varied strongly around the tip of the crack, both in radial and polar sense. Also it was observed that the polar distribution of the elastic modulus presented clear off-axis extrema in directions that were in good agreement with experimentally measured branching angles, thus indicating a possible relation between these two phenomena.

Asymptotic fields of mode I steady-state crack propagation in non-associative elastoplastic solids

The quasi-static, steady-state propagation of a crack running in an elastoplastic solid with volumetric-non-associative flow law is analyzed. The adopted constitutive model corresponds to the small strain version of that proposed by Rudnicki and Rice. The asymptotic crack-tip fields are numerically obtained for the case of the incremental theory with linear isotropic hardening, under mode I plane-stress conditions. A relevant conclusion of the study is that the singularity of the near-tip fields appears to be mainly governed by the flow-rule, rather than by the yield surface gradient.

Demonstration of crack arrest capability for welds showing low toughness pop-in

Toughness data are presented for three typical structural welds. All the three welds showed significant pop-ins at low toughness (0.02 < δ c < 0.06 mm) in Crack Tip Opening Displacement (CTOD) tests. In spite of this, the structural safety of the welds is demonstrated by their ability to arrest large running cracks at two-thirds yield stress in the double tension wide plate test. A method of deducing an estimate of crack arrest toughness from the CTOD test itself is presented, and shown to be conservative.

Stress Wave Radiation From a Crack Tip During Dynamic Initiation

Plate impact experiments are conducted to study the dynamic fracture processes which occur on submicrosecond time scales. These experiments involve the plane strain loading of a plane crack by a square tensile pulse with a duration of approximately one microsecond. The crack-tip loading rates achieved are K1 ˜ 108MPams−1, which are approximately two orders of magnitude higher than those obtained in other dynamic fracture configurations. Motion of the rear surface caused by waves diffracted from the stationary crack and by waves emitted by the running crack is monitored at four points ahead of the crack tip using a laser interferometer system. The measured normal velocity of the rear surface of the specimen agrees very well with the scattered fields computed using an assumed elastic viscoplastic model, except for the appearance of a sharp spike with a duration of less than 80 nanoseconds. This spike, which is not predicted by the inverse square root singular stress fields of linear elastic fracture mechanics, is understood to be related to the onset of crack growth and coincides with the abrupt and unstable ductile growth of a microstructural void to coalescence with the main crack. The crack initiation process is modeled as the sudden formation of a very small hole at the crack tip. This admits the possibility of dynamic crack-tip stress fields with crack-tip singularities stronger (˜r−3/2) than the inverse square root singular fields of fracture mechanics. The elastodynamic radiation resulting from the formation of a traction free hole at the crack tip is applied first to the case of antiplane shear deformation and then to the corresponding plane strain problem. The radiated fields predicted by the strongly singular solutions are found to be in good agreement with the spikes observed in the experiments. The radius of the hole, which appears as a parameter in the solution for the radiated field, agrees reasonably well with the interparticle spacing.

Non-planar deviation of an initially straight moving crack

The problem of dynamic crack curving in a brittle solid is investigated as a first step towards determining the velocity dependence of the stability of a running crack. By using a perturbation technique and the complex potential method, a solution for the slightly curved deviation of a running crack under mixed-mode loading conditions is presented. To the first order the angular distribution of the singular stress near the curved crack tip for a smooth running crack is found to depend only on the instantaneous crack-tip velocity and is independent of the crack-tip acceleration and the curvature. For steel the analysis indicates that cracks propagating more slowly than the critical branching velocity will exhibit nearly the same characteristics as those for quasi-static crack deviation and stability. The calculations also show that the critical branching velocity may increase with increasing Poisson's ratio of the material. The estimates of the crack path dependence on velocity presented here are consistent with the quasi-static crack growth solution of Sumi et al. [ Int. J. Fracture 21, 67–79 (1983)].

Constant-speed propagation of a penny-shaped interface crack under pure torsion

A transient problem of propagation of a penny-shaped crack in the plane interface between two different media is solved. The body is twisted by a torque at infinity that tends to shear the bond between the two media. A small initial flaw is assumed to expand uniformly in the plane of the interface at a speed less than the smaller of the SH wave speeds of the two media. The solution is carried out by a combination of two methods: a method of rotational superposition of two-dimensional solutions and the Smirnov-Sobolev method of self-similar potentials for twodimensional problems. The dynamic stress intensity factor and the crack tearing displacement are determined. It is found that the stress field near the crack tip has a square root singularity. The maximum crack-tearing displacement is found to occur at close to three-fourths of the way from the crack origin to the running crack tip.

A Theory of Caustics for Mixed-Mode Fast Running Cracks. 4th Report. Higher-Order Theory.

A higher-order theory of caustics for mixed-mode running cracks is developed using the general asymptotic solutions for a dynamically propagating crack-tip. The analytical expressions are obtained for the Jacobian equation that determines the initial curve, and for the image equations on a screen. With the use of the higher-order coefficients determined by the finite-element simulations of actual dynamic fracture experiments, the effects of the higher-order terms on the caustic curve are investigated on the basis of the present theory. It was found that the r1/2 stress field plays an important role in the formation of caustic patterns.

Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.