Stable Crack Research Articles

The importance of toughness in manufacturing

In manufacturing, the yield strength (k, Pa) of the material being worked determines how easy or difficult it is to achieve permanent deformation and hence the size of equipment required to do the job. In some processes, cracking of the workpiece sets limits, but in others such as slitting and trimming of sheets, can opening, guillotining, punching of holes and so on, separation of parts is required. The transition from plastic flow to cracking is controlled by the fracture toughness (R, J/m2) of the workpiece, which is a measure of the resistances to crack initiation and propagation in tension and in shear. R is employed in the discipline of fracture mechanics. There are standard ways independently to measure fracture toughness, and it is to be emphasised that R is not the same as Charpy values. Furthermore, fracture mechanics applies not only to structural integrity linear elastic cases, but describes cracking in the presence of large irreversible deformations as found in forming. Processes may start as flow (controlled by the laws of elastoplasticity) but then become simultaneous combined flow and fracture (controlled by the laws of elastoplastic fracture mechanics).The initiation of cracks may set limits on processes, and there are many empirical criteria written in terms of stress and/or strain that give limits for different forming processes. However, they are not transferable from one process to another ― even for the same workpiece material ― but they can all be rationalised when expressed in terms of workpiece toughness, a mechanical property that also determines whether the cracks are formed in tension or in shear. Furthermore, in those processes where a number of cracks form, it is toughness that determines how many appear: a criterion of a critical strain at fracture, say, will simply predict when cracking will commence.‘Separation’ is fracture by another name and such processes operate beyond the limits of normal forming. The modelling of all types of cutting (whether algebraic or FEM) should include toughness. Indeed, toughness defines what constitutes a sharp tool. Many experimental observations for which traditional ‘Ernst-Merchant’ theories have no explanation become quantitatively clear when fracture toughness is incorporated. These include workpiece-dependence of the angle of the primary shear plane, and transitions between different types of chip at different uncut chip thicknesses which are the result of cube-square scaling inherent in all fracture problems. That is, the remote work stored elastically or dissipated plastically over the whole workpiece depends on volume, but the work required for fracture depends only on the area of the cracked surface with its boundary layers of highly damaged, and separated, material above and below. Some metal cutters do not believe that fracture can have anything to do with cutting since ‘cracks are not seen ahead of the tool’. In consequence artifices such as adaptive re-meshing are employed in FEM to simulate cutting without a criterion for separation, but that methodology does not represent the physics of what’s happening at the cutting edge, and it also confuses the existence of cracking with the stability of cracking. Better to simulate all manufacturing problems with codes that will show fracture if that is what the physics demands, yet not show fracture if it is not part of the problem.Energy scaling poses the fascinating question of what do we really understand by the classifications of ‘brittle’ and ‘ductile’ as determined by the behaviour of laboratory-size testpieces since glass, for example, can be machined with continuous ribbons at micrometer depths of cut, and ductile metals will split at very large depths of cut. It all comes down to the toughness-to-strength (R/k) ratio.

Unified formulae for evaluating load reduction by change in stiffness of circumferential crack considering general piping systems

The conservatism of leak-before-break (LBB) analysis depends on the methodologies for evaluation of the crack opening displacement (COD) and crack stability analysis, in which the applied load at the cracked section is an important variable. In current procedure, the applied loads are obtained from an uncracked pipe analysis, and the effect of restraint is not assumed in the calculations of COD and the allowable applied moment. When the presence of a crack and the pipe restraint are considered, however, the applied load can be reduced because of the change in the piping system stiffness. In this regard, there have been several proposed analytical expressions to evaluate the restraint effects on COD or crack stability analysis, but the expressions cannot be applied to practical cases because of the limitation of the pipe geometries and applied loading conditions. This study develops unified formulae to evaluate the effective applied loads that enable balanced analyses of both the COD and stability of circumferential cracked pipes. The formulae were developed for a piping system containing a circumferential crack based on the compliance approach. By comparing this with finite element analysis results, the validity of the formulae was demonstrated. It is expected that the proposed formulae can be used as a simple approach to detailed LBB analysis to secure the safety margin before implementing the complex non-linear finite element analysis.

FRACTAL CHARACTERISTICS OF CRACK PROPAGATION IN COAL UNDER IMPACT LOADING

This paper studied the fractal characteristics of crack propagation in coal containing beddings under impact loading condition. Split Hopkinson pressure bar (SHPB) system was applied to determine the prepared notched semi-circular bending specimens. The high-speed camera was used to record the propagation characteristics of cracks. The image processing method and fractal dimension calculation software are combined to further analyze the effects of bedding and loading rate on the fractal characteristics of crack propagation in coal. The experimental results presented that the presence of bedding has a remarkable impact on the crack propagation. The crack velocity of coal samples with [Formula: see text] bedding angle is of the maximum, however, the crack velocity of samples with [Formula: see text] bedding angle is of the minimum. Bedding angles also have obvious influence on the fractal dimension of cracking path, the bedding angle of [Formula: see text] being the largest, and those of [Formula: see text] and [Formula: see text] having the intermediate values, while those of [Formula: see text] and [Formula: see text] being the smallest. Several points of instantaneous fractal crack velocity are close to the Rayleigh wave velocity ([Formula: see text]). The crack velocities of coal specimens with bedding angles of [Formula: see text], [Formula: see text] and [Formula: see text] are prone to the high value.

On the failure mechanism for high pressure die casting A390 hypereutectic alloy in low cycle and high cycle fatique

The fatique failure behavior of A390 hypereutectic aluminum alloy plate was studied with laboratory CT and such technique provided a new method for analyses of the mechanical failure. Results were based on the reconstructed fractography and SEM observation and special attention was paid to crack propagation mechanism in the hypereutectic alloy. The fatique crack surface was separated into crack initiation site around pores, flat crack propagation zone and instantaneous crack zone. While the flat crack propagation zone only occurred in high cycle fatique and the height fluctuation of flat propagation was within 50 µm. The disappearance of flat propagation in low cycle fatique showed the different crack propagation mechanism between hypereutectic and hypoeutectic alloy. Different crack propagation stage changed with the stress intensity of crack tip. The flat propagation zones for high cycle fatique attributed to the relatively parallel extension of crack and debonding between PSPs and matrix in hypereutectic alloy. While under higher stress intensity like the case in LCF or later stage of HCF, the crack branched and extended instantaneously, tortuous crack propagation route formed and many PSPs with minor cracks or striations remained.

Fracture mechanics analysis of Zircaloy-4 tubular samples after laboratory simulated LOCA transient

This paper investigates the room temperature cladding embrittlement of Stress Relieved Annealed (SRA) Zircaloy-4 fuel cladding samples subjected to laboratory steam oxidation tests simulating Loss of Coolant Accident (LOCA) transients at 1200 °C followed by water quenching. These high temperature oxidized tubes are mechanically tested using axial tensile samples with machined gage sections. Formerly performed studies suggested that Linear Elastic Fracture Mechanics (LEFM) could provide a good understanding of the sample failure process, including crack nucleation close to the oxidized surfaces followed by crack instability and sample failure at higher applied loads. However, it was found that when the applied stress intensity was calculated using solutions for plate material given in the Tada and Paris Handbook, with the cracks in the plate corresponding to a crack formed only on the cladding’s outer surface – produced by oxidation on this surface alone – versus two opposing cracks formed on the cladding’s inner and outer surfaces – produced by oxidation on both of these surfaces – the critical stress intensity was different between these two cases. It is shown here that for both of the foregoing configurations the same critical crack intensity values are obtained when the applied LEFM stress intensity values are calculated using three dimensional finite element modeling of the axial tensile samples. The critical stress intensity factors determined by this more accurate method – and calculated as a function of degree of surface oxidation and hydrogen content in the prior-β phase – could, thus be considered to be a true materials parameter correlating well with the experimentally determined effect of hydrogen content on the failure strength of the samples.

Instantaneous Crack Width Calculation for Steel Fiber-Reinforced Concrete Flexural Members

Instantaneous Crack Width Calculation for Steel Fiber-Reinforced Concrete Flexural Members

Mode I fracture of tropical woods using grid method

The cracking properties in opening mode of three tropicals species from the Gabonese forest, namely Iroko (Milicia Excelsa), Okume (Aucoumea klaineana Pierre), and Padouk (Pterocarpus soyauxii), were investigated in this study. Various tests were performed at room temperature and for two different thicknesses. A full-field measurement technique, namely the grid method, was used in order to obtain the displacement and strain maps near the crack during the tests. The mechanical parameters, the specificities of the wood species, the Arcan system and the grid transfer method are first described. For all the specimens, the initial crack length was oriented along the fiber direction (RL). The instantaneous failure tests were performed using two types of specimens: the modified Compact Tension Shear (CTS) and the Mixed Mode Crack Growth (MMCG) specimens. The images of the grid were recorded and analyzed to obtain the displacement maps. The crack opening, the location of the crack tip as well as the strain fields on the surface of the specimens were deduced from these displacement maps. The experimental critical energy release rate Gc was evaluated by the compliance method in imposed displacement. In the case of instantaneous crack with CTS specimens, the comparison of the initial value of Gc for all the samples show that this quantity strongly depends on the thickness and density of the species under study. Crack propagation was observed for a thickness equal to 20 mm only. The results of the crack propagation with the MMCG specimens show the same dependence, and confirm the quasi-brittle fracture behavior of Iroko. The experimental results are scattered, but clear trends can be observed concerning the fracture parameters of the in previous studies described in the literature on wood species with wood species under study. The results are finally compared with those given densities similar to those studied here.

The Evolution of Cracks in Maluanshan Granite Subjected to Different Temperature Processing

The understanding of the change in the physical and mechanical properties of rock before and after heating is of great significance for the site selection of mattamore and the exploitation of geothermal resources. It is known that before and after heating, the changes in wave velocity, wave velocity anisotropy and permeability of rock are due to the evolution of cracks in the rock. In this study, the wave velocity and permeability of granite specimen from the Maluanshan tunnel in Shenzhen, China, were measured after high-temperature processing at atmospheric pressure. The effects of temperature on the properties of rock based on the acoustics and permeability were measured and analyzed. The evolution of the cracks in Maluanshan granite was inverted through the change rule of the cracks, wave velocity anisotropy and permeability with temperature. The main conclusions were as follows: (1) Both granite P and S wave velocities decreased with the increasing temperature, and the thermal cracking occurred in four stages: between 50 and 250 °C, the crack stabilization development stage was in effect; between 250 and 300 °C, an accelerated development stage of the cracks existed; between 300 and 350 °C, a shift stage for the cracks was entered; and finally, from 350 to 700 °C, the cracks continued into a further development stage; (2) The coefficient of variation could be used to reflect the structural feature change of the rocks in the study of the wave velocity anisotropy. The structures of cracks were observed to change before and after 300 °C. (3) The Maluanshan granite permeability increases with the increasing processing temperature. It was observed that the higher the processing temperature, the larger the increase in the permeability rate. A porosity function was used as a variable to analyze the relationship between the porosity function and permeability as follows: from 50 to 200 °C, the permeability was determined by the microcracks; 200–400 °C was the transition stage; and between 400 and 700 °C, the permeability was determined by the macrocracks.

Crack initiation and early growth behavior of TC4 titanium alloy under high cycle fatigue and very high cycle fatigue

Abstract

Fatigue crack propagation under biaxial fatigue loading with single overloads

The crack propagation behavior and the governing crack growth micromechanisms in aluminum alloy under in-plane biaxial fatigue loading with single overloads, of different magnitudes and occurring at different fatigue crack lengths, is investigated. The microscale fracture mechanisms governing crack growth behavior under these conditions are identified through detailed fractography. Crack growth retardation behavior observed due to the occurrence of single overloads is correlated with overload magnitude, instantaneous fatigue crack length, crack-tip plasticity and fracture surface morphology. The results obtained provide insight into the relationship between macroscale crack growth behavior to microstructural mechanisms, which is essential to understanding the fatigue behavior of metallic materials under variable amplitude biaxial loading scenarios.

Unraveling crack stability and strain localization in staggered composites by fracture analysis on the shear-lag model

Bio-inspired composites can achieve excellent toughness while maintaining their strength through hierarchical microstructure designs combining strong and brittle reinforcements and soft yet ductile matrices. The interfaces between reinforcements and matrices transfer loads through shear deformation and deflect cracks along themselves to dissipate a considerable amount of energy. In this way, the catastrophic failure, which is common in monolithic reinforced materials due to the severe stress concentration near the defects, is deferred in hierarchical composites. Yet, recent computations and experiments suggest that strain localization arising from the unstable crack propagation along interfaces leads to the composites failure. In this study, fracture analysis is carried out on staggered composites with the brick-and-mortar structure. An analytical formula predicting the onset of strain localization emerges from the analysis and is validated by finite element analysis. Furthermore, showing good agreements with independent tensile tests on multi-layer graphene assemblies, our model demonstrates its applicability to explain the strain localization in composites consisting of interfaces that function through re-formable bonds. Characteristic length scales emerging from the analysis can be used to guide the composites design to optimize material toughness and ductility.

Effects of crack tunneling and plasticity on the elastic unloading compliance technique for SE(B) – current limitations and proposals

Understanding how cracks behave in high toughness structural materials is critical for high responsibility applications. Design and fitness-for-service activities in this scenario are highly dependent on accurate resistance curves (J-R curves) and fatigue crack growth data (da/dN-ΔK). Such mechanical properties correlate crack driving forces with instantaneous crack size a, determined using real time techniques such as the Elastic Unloading Compliance (EUC). In this method, load P and displacement V (CMOD) allow real-time compliance (V/P) computation, whose increase can be used to predict increasing crack size a. Despite usually accurate, EUC predictions sometimes deviate from post-mortem analyses (errors above 10% were found by the research group) or present spurious effects such as apparent negative crack growth. Several phenomena may affect EUC accuracy, including: stress triaxiality, side-grooves, specimen rotation, closure, crack tip plasticity and crack tip tunneling. This paper investigates the effects of tunneling and plasticity on the EUC technique applied to SE(B) specimens of varying thicknesses and geometrical features. Very refined numerical simulations were conducted considering varying thicknesses, levels of crack depths and five levels of crack curvatures. Regarding tunneling, results show that for the same equivalent ASTM-E1820 straight crack, elastic compliance decreases with the increase of crack front curvature, leading to a predicted crack smaller than ASTM equivalent. No significant deviations were detected within ASTM limits, however, when such limits are violated, significant deviations occur. As a step to improve size predictions for tunneled cracks, a new proposal for determining the equivalent straight crack was developed and expands the applicability of current methods. In terms of plasticity, results revealed that near-tip plasticity causes a decrease followed by an increase in specimen’s compliance, whose deviation varies depending on its geometry and material properties. The effects of varying plasticity levels on crack size estimation could be identified and discussed.

Experimental Investigation on Wellbore Strengthening Based on a Hydraulic Fracturing Apparatus

Lost circulation is a serious problem which always exists in the petroleum industry. Wellbore strengthening by lost circulation materials (LCMs) is a commonly applied method for mitigating lost circulation. This paper presents a hydraulic fracturing apparatus to investigate the effect of material type, concentration, and particle size distribution (PSD) of LCMs on wellbore strengthening behavior. In addition, the characteristics of pressure curves in the fracturing process are analyzed in detail. The results showed that the fracture pressure of the artificial core can be increased by LCMs, and there exists an optimum concentration of LCMs for the maximum wellbore strengthening effect. The LCMs with wide PSD can significantly increase the fracture pressure. However, some LCMs cannot increase or even decrease the fracture pressure; this is resulting from the LCMs with relatively single PSD that makes the quality of mud cake worse. The representative pressure curve in the fracturing process by drilling fluids with LCMs was divided into five parts: the initial cake formation stage, elastic plastic deformation stage, crack stability development stage, crack instability development stage, and unstable plugging stage. The actual fracturing curves were divided into four typical types due to missing of some stages compared with the representative pressure curve. In order to strengthen the wellbore in effective, good LCMs should be chosen to improve the maximum pressure in the elastic plastic deformation stage, extend the stable time of pressure bearing in the crack stability development stage, and control the crack instability development stage.

Cracking isotropic and anisotropic relativistic spheres

We explore the influence of density fluctuations on isotropic and anisotropic configurations, extending the concept of cracking for isotropic general relativistic fluid spheres. This concept, conceived to describe the behaviour of anisotropic matter distributions just after its departure from equilibrium, could provide some insight on potential instabilities and future evolution of relativistic fluids. We have refined the idea of cracking, considering local fluctuations—represented by any function of compact support defined in a closed interval—and their effect on the state variables and gradients through “barotropic” equations of state, P = P(ρ) and [Formula: see text]. Under this approach it is found that both isotropic and anisotropic models could exhibit cracking (or overturning), and that previous results for cracking (and overturning) instabilities on anisotropic matter configurations has to be revised.

Comparison of methods to determine CTOD for SENB specimens in different strain hardening steels

AbstractMethods for determining crack tip opening displacement (CTOD) given in national and international standards are compared for steels with a range of strain hardening characteristics.Crack tip opening displacement measurements were made from single‐edge notched bend notches using a silicone rubber casting method. The finite element model produced good agreements with predictions of these CTOD measurements. The versatility of the finite element model enabled CTOD from the original crack tip and the 45° intercept method to be compared. The 45° CTOD generally underestimates the original crack tip CTOD, and is less useful for conditions with stable crack extension.Apart from the high strain hardening material, CTOD calculated using BS 7448‐1, WES 1108 (JWES), and ASTM E1820 was slightly lower than the values determined from silicone measurements and modelling, which is conservative. ASTM E1820 gave the largest underestimation of CTOD, whilst BS 7448‐1 may be unsuitable for higher strain hardening steels, where the standard predicts higher CTOD than measured from the replica. JWES gives the most consistent estimation of CTOD for steels with a wide range of strain hardening values.

Effects of δ-hydride precipitated at a crack tip on crack instability in Zircaloy-4

A fraction of hydrogen produced due to the waterside corrosion of Zircaloy-4 nuclear fuel cladding diffuses into it. Diffused hydrogen migrates up a stress gradient in the Zircaloy-4 and accrues in the regions of higher stress like a crack tip. When the concentration of hydrogen exceeds terminal solid solubility, it precipitates as brittle hydride phases. Hydride precipitated at the tip of a crack may induce crack instability, causing failure of the cladding. To understand the effects of hydride precipitated at the tip of a crack on crack instability in Zircaloy-4, a numerical investigation is performed on single-edge notched tension specimen by using the extended finite element method. The mechanical properties of the Zircaloy-4 cladding and hydride precipitated in it—used in this numerical analysis—are evaluated by using nanoindentation technique. The crack length is taken between 0.05 and 0.2 mm, while the length of the hydride is varied in the range of 0.1 to 0.2 mm. The influence of hydride dimensions, number of hydrides, orientation of hydrides, and distance of hydride from the crack tip on crack instability is evaluated. The stability of the crack is assessed in stress intensity factor and J-integral for each case. Results reveal that stress distribution around the crack tip is significantly altered by the precipitation of hydride. The circumferential hydride is less detrimental compared with the radial hydride. As the distance of hydride from the crack tip increases, there is a decline in the stress intensity factors and J-integrals, implicating that there may exist a critical distance beyond which hydride precipitation has negligible effect on crack instability.

The impact of print orientation and raster pattern on fracture toughness in additively manufactured ABS

Fused deposition modeling (FDM) has been gaining industrial interest due to its potential to simplify and lower the cost of complex manufacturing. To better understand the mechanical response of these materials—due to potential integration of FDM parts into structural components—compact tension samples of acrylonitrile butadiene styrene (ABS) were printed in three orthogonal orientations to analyze how the fracture toughness varied with mesostructure. Furthermore, in each of these orientations the raster pattern was either an alternating +45/−45° or a 0/90° pattern. When the alignment of extruded filament layers changed from parallel to perpendicular with respect to the crack plane, a 54% increase in fracture toughness was observed. However, the raster pattern only had a significant effect in one of the print orientations; the fracture toughness decreased by 11% when a 0/90° pattern was used in place of a +45/−45° pattern in layers oriented perpendicularly to the crack plane. The orientation of individual tracks of deposited material with respect to the crack tip appeared to have the most pronounced role in altering the fracture toughness of FDM ABS. This research provides useful information and insight to future designers determining how processing affects the crack stability of these new materials used for space hardware

Investigation of cleavage fracture under dynamic loading conditions: Part II numerical analysis

Part I of this study was an extensive fractographic investigation that covered the topics local crack arrest, and cleavage fracture-inducing mechanisms under dynamic loading situations. Also, it produced data regarding the origin of cleavage fracture. Now, this data is used for the numerical part of this study. First, the development of temperature and strain rate increase at the origin of cleavage fracture is conducted, and linked to discrepancies regarding experiments and the Master Curve concept in a phenomenological way. Then, cleavage fracture controlling mechanical field variables at the origin of fracture are analyzed, whereas very similar conditions regarding crack initiation and propagation are found when compared to quasi-static data. The influence of wave phenomena is examined as well. Finally, micromechanical simulations showed that a local temperature increase at the particle–matrix interface does not influence fracture behavior either, and that conclusively, the actual physical mechanism of cleavage fracture initiation (crack initiation and instability) takes place under the same conditions at elevated loading rates as under quasi-static conditions. Ultimately, the mechanisms responsible for the shortcomings of the Master Curve concept under dynamic loading conditions are identified, and current local approach concepts need to be adjusted to consider local crack arrest to be reliable.

“Ductile” Fracture of Metallic Glass Nanolaminates

AbstractMost metallic glasses are brittle as deformation induces low‐density sporadic shear bands and severe shear localization proceeding catastrophic failure. Here, it is demonstrated that the introduction of crystalline nanolayers with appropriate dimension can substantially suppress shear localization in metallic glasses, as manifested by ubiquitous ductile dimples in amorphous phase. Furthermore, dimple sizes can be tailored by tuning the dimension of layer thickness. Additionally unlike instantaneous crack propagation occurring in most metallic glasses, crack propagation occurs in a highly periodic and “zigzag” fashion, and shows clear size dependence for metallic glass nanolaminates. Thus, it is a promising approach to promote ductility in metallic glasses while maintaining high strength by synthesizing metallic glass nanolaminates with certain layer thickness. Molecular dynamics simulations demonstrate that crystalline/amorphous interfaces can block crack propagation in crystalline layers and delocalize strain in amorphous layers, and suggest that “zigzag” crack propagation could be achieved through dislocation slips in crystalline layers.

Comparing the floquet stability of open and breathing fatigue cracks in an overhung rotordynamic system

Rotor cracks represent an uncommon but serious threat to rotating machines and must be detected early to avoid catastrophic machine failure. An important aspect of analyzing rotor cracks is understanding their influence on the rotor stability. It is well-known that the extent of rotor instability versus shaft speed is exacerbated by deeper cracks. Consequently, crack propagation can eventually result in an unstable response even if the shaft speed remains constant. Most previous investigations of crack-induced rotor instability concern simple Jeffcott rotors. This work advances the state-of-the-art by (a) providing a novel inertial-frame model of an overhung rotor, and (b) assessing the stability of the cracked overhung rotor using Floquet stability analysis. The rotor Floquet stability analysis is performed for both an open crack and a breathing crack, and conclusions are drawn regarding the importance of appropriately selecting the crack model. The rotor stability is analyzed versus crack depth, external viscous damping ratio, and rotor inertia. In general, this work concludes that the onset of instability occurs at lower shaft speeds for thick rotors, lower viscous damping ratios, and deeper cracks. In addition, when comparing commensurate cracks, the breathing crack is shown to induce more regions of instability than the open crack, though the open crack generally predicts an unstable response for shallower cracks than the breathing crack. Keywords: rotordynamics, stability, rotor cracks.