Cracks In Sheets Research Articles

Dynamics of cracks in torn thin sheets

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of nonlinear terms.

Detection of cracks in metal sheets using pulsed laser generated ultrasound and EMAT detection

A pulsed Nd:YAG laser with an approximately Gaussian beam shape is directed onto the surface of an aluminium sheet at an energy density below which damage by laser ablation occurs, generating Lamb waves in the sheet. The laser beam is raster scanned across the surface of the sample. The Lamb waves travel radially outwards from the generation point and are detected some distance away by an electromagnetic acoustic transducer with sensitivity to in-plane displacements of the sheet. A number of static EMATs are located around the edges of the sheet, some distance from the generation point. The presence of a crack-like defect on the sheet can be detected by either a sudden change in the ultrasonic waveform or by an enhancement in the frequency content of the waveform when the laser beam illuminates directly onto the crack.

Effects of Constituents and Lay-up Configuration on Drop-Weight Tests of Fiber-Metal Laminates

Impact responses and damage of various fiber-metal laminates were studied using a drop-weight instrument with the post-impact damage characteristics being evaluated through ultrasonic and mechanical sectioning techniques. The first severe failure induced by the low-velocity drop-weight impact occurred as delamination between the aluminum and fiber-epoxy layers at the non-impact side. It was followed by a visible shear crack in the outer aluminum layer on the non-impact face. Through-thickness shear cracks in the aluminum sheets and severe damage in the fiber laminated layers (including delamination between adjacent fiber-epoxy laminae with different fiber orientations) developed under higher energy impacts. The impact properties of fiber-metal laminates varied with different constituent materials and fiber orientations. Since it was punched through easily, the aramid-fiber reinforced fiber-metal laminates (ARALL) offered poorer impact resistance than the glass-fiber reinforced fiber-metal laminates (GLARE). Tougher and more ductile aluminum alloys improved the impact resistance. GLARE made of cross-ply prepregs provided better impact resistance than GLARE with unidirectional plies.

Evidence for sea‐level falls in the Permian‐Triassic transition in the Ziyun area, South China

AbstractThe sedimentology of three sections showing the Permian–Triassic (P–T) transition on an Upper Permian reef in Ziyun, Guizhou Province, southwest China provides evidence of sea‐level fall in this area. The P–T transition in the Gendan section, which covers a reef‐front sequence, contains a subaerial exposure surface and various desiccation cracks (including rolled‐up chips, in‐chip cracks, pyramid cracks, vertical cracks and sheet cracks), indicating sea‐level falls. The P–T transition in the Shitouzhai section, which covers a reef‐core sequence, contains three micritic beds with abundant pseudomorphs of tabular gypsum crystals replaced by calcite. The underlying centimetres of deposits are composed of fine‐crystalline dolostone, and have a sharp contact with the underlying reef‐core facies. The association of gypsum pseudomorphs and fine‐crystalline dolostone suggests an origin related to a supratidal evaporative environment. The P–T transition in the Tanluzhai section, which covers a back‐reef sequence, is fine‐crystalline dolostone, and shows a laminated algal structure indicating tidal‐flat environments. The middle part of the dolostone interval has become a collapse breccia composed of dolostone fragments and a matrix of micrites or crustose multi‐generation calcite cements. The formation of the collapse breccia is interpreted to be related to the dissolution of the evaporite interbeds originally present between the thin dolostone beds. The formation of the evaporite deposits requires a supratidal condition. Copyright © 2009 John Wiley & Sons, Ltd.

Measurement of Fracture Parameters for a Mixed‐Mode Crack Driven by Stress Waves using Image Correlation Technique and High‐Speed Digital Photography

Abstract: Measurement of fracture parameters for a rapidly growing crack in syntactic foam sheets using image correlation technique and high‐speed photography is presented. The performance of a rotating mirror‐type multi‐channel high‐speed digital camera to measure transient deformations is assessed by conducting benchmark tests on image intensity variability, rigid translation and rigid rotation. Edge‐cracked foam samples are subjected to eccentric impact loading relative to the initial crack plane to produce mixed‐mode loading conditions in a three‐point bend configuration. High‐speed photography is used to record decorated random speckles in the vicinity of the crack tip at a rate of 200 000 frames per second. Two sets of images are recorded, the first set before impact and the second after impact. Using image correlation methodology, crack‐tip displacement field histories and dominant strains from the time of impact up to complete fracture are mapped. Over‐deterministic least‐squares analyses of crack‐tip radial and tangential displacements are used to obtain mixed‐mode fracture parameters. The measurements are compared with complementary finite element results. The fracture parameters determined from radial displacements seem more robust even when fewer number of higher order terms in the crack‐tip asymptotic expansion are used.

Formation of ultrafine-grained microstructure in HSLA steel profiles by linear flow splitting

Linear flow splitting is a new cold forming process for the production of branched sheet metal structures in integral style. It induces extremely high deformation degrees without formation of cracks in the split sheets due to hydrostatic compressive stresses. Investigations on a HSLA steel (ZStE 500) show the formation and fragmentation of a dislocation cell structure in the severely deformed regions of the steel sheet. This results in ultrafine-grained microstructures and improved mechanical properties, similar to SPD processes as Equal Channel Angular Pressing (ECAP) or High Pressure Torsion (HPT). EBSD measurements reveal a gradient in grain size with an increase in direction perpendicular to the surface, whereas micro hardness decreases in the same direction. Based on these results, basic principles of linear flow splitting and its expected potential are discussed.

Anomalies concerned with interpreting fatigue data from two-parameter crack growth rate relation in fracture mechanics

Early studies on metal fatigue have concerned primarily with testing the bulk properties of smooth or notch specimens. The fine line crack configuration became a standard ASTM specimen when local effects were recognized to play a decisive role in failure initiation. The size of the failure initiation crack can range from a few cm to a few mm or smaller depending on the application that can involve through cracks in metal sheets, surface cracks extruding grain boundaries and embedded cracks interior to the material microstructure. The state-of-the-art in fracture control for the most part is to monitor the length of an equivalent crack, say “ a”, such that the corresponding rate d a/d N can be related to the integrity of the system depending on the geometry, load and material. Consistent data interpretation has been a concern because of the enormous range of physical defect size that the design must cover to assure the effective application of the failure criterion from nano to structural scale size. The design may have to demonstrate that nanocracks are controlled in miniature devices as macrocracks are kept in the sub-critical state for larger structures, As more nanostructures are being used, consideration of small cracks in the damage evolution process is becoming the rule rather than the exception. Whether the ordinary two-parameter d a/d N versus Δ K representation referred to Regions I–III would still accommodate microcrack and/or nanocrack behavior is an issue that deserves attention. Because of the empirical nature of the current d a/d N approach, different physical meanings can be attached to the same crack growth rate data. The final decision will invariably favor the best fit of the data to certain pre-conceived condition. Non-uniqueness of the physical interpretation must therefore be kept in mind. Often, it is the a priori assumption based on physics that determines the outcome. Some of the possible differences are discussed with emphases placed on using an equivalent crack length and a corresponding energy density state such that the segmented state of affairs at the different scales can be connected. The time history of material damage including the degradation of the microstructure should be the primary concern in determining the system integrity. Scale segmentation avoids over stretching the ability of theories, most of which are short ranged. The dual scale approach will be offered as the basis for developing multiscale models. Advent of the modern electronic computer offers the opportunity for optimizing several unknown variables at the same time to arrive at the desired solution that can correspond to the design specification.

Crack repair using an elastic filler

The effect of repairing a crack in an elastic body using an elastic filler is examined in terms of the stress intensity levels generated at the crack tip. The effect of the filler is to change the stress field singularity from order 1 / r 1 / 2 to 1 / r ( 1 - λ ) where r is the distance from the crack tip, and λ is the solution to a simple transcendental equation. The singularity power ( 1 - λ ) varies from 1 2 (the unfilled crack limit) to 1 (the fully repaired crack), depending primarily on the scaled shear modulus ratio γ r defined by G 2 / G 1 = γ r ε , where 2 π ε is the (small) crack angle, and the indices (1, 2) refer to base and filler material properties, respectively. The fully repaired limit is effectively reached for γ r ≈ 10 , so that fillers with surprisingly small shear modulus ratios can be effectively used to repair cracks. This fits in with observations in the mining industry, where materials with G 2 / G 1 of the order of 10 - 3 have been found to be effective for stabilizing the walls of tunnels. The results are also relevant for the repair of cracks in thin elastic sheets.

Facies analysis of Lofer cycles (Upper Triassic), in the Argolis Peninsula (Greece)

The Upper Triassic carbonate sediments of Argolis Peninsula are part of the Upper Triassic–Lower Jurassic extensive and thick neritic carbonate formations (Pantokrator facies) that formed at the passive Pelagonian margin and are considered as Dachstein-type platform carbonates. Facies analysis of the Upper Triassic “Lofer-type” lagoonal–peritidal cycles in the Dhidimi area, proved that cycles, although mostly incomplete, were regressive shallowing-upward. The ideal elementary cyclothems are meter-scale in thickness and begin with a subtidal bed (Member C), represented by a peloidal dolostone with megalodonts (wackestone or packstone), being followed by a stromatolitic intertidal dolomitic mudstone and/or fenestral intertidal dolomitic mudstone (Member B) that is overlain by dolocrete (terrestrial stromatolites or pisoidic dolomite) or a supratidal “soil conglomerate” in red micritic matrix (Member A). Lofer-cycle boundaries are defined at the erosional surfaces and accordingly the Lofer cyclothems are unconformity-bounded units. Due to common post-depositional truncation of the subtidal and intertidal facies, the supratidal members prevail, being developed, in places, directly upon subaerial exposure surfaces (erosionally reduced cyclothems). Peritidal layers are characterized by a well-expressed lamination, sheet cracks, tepee structures, fenestral pores and karst dissolution cavities. The studied lagoonal–peritidal cycles are considered to have been deposited in a tidal-flat setting (inner platform), repeatedly exposed under subaerial conditions, in the context of a broader tropical rimmed platform. Although the studied area was tectonically active due to rift-activity and the autocyclic processes should also be taken in consideration, the great lateral correlatability of cycles, the facies shifting and the widespread erosion that resulted in superposition of supratidal-pedogenic facies directly upon subtidal members (subaerial erosional unconformity), indicating a sea-level drop, reflect allocyclic control via high-frequency eustatic sea-level oscillation (orbital forcing). Sediment deposition occurred during low-stand system tract (LST), that probably continued also in the transgressive system tract (TST) and reflects an overall sea-level fall. Under these conditions dissolution and cement precipitation episodes, as well development of paleosols and karsts, were triggered, during a relatively less arid interval.

Carbon isotope evidence for widespread methane seeps in the ca. 635 Ma Doushantuo cap carbonate in south China

Distinctive sedimentary structures, textures, and extremely negative δ 13 C carb values from the Ediacaran Doushantuo cap carbonate (ca. 635 Ma) in south China were taken as evidence for a methane hydrate destabilization event, but existing data for a methane-derived δ 13 C carb signature were reported from a single locality in the Yangtze Gorges area. Here we report negative δ 13 C carb values as low as −48‰ (Vienna Peedee belemnite) from two additional sections ~6 km and 55 km from the original locality. These negative δ 13 C carb values were obtained from isopachous cements that fill stromatactis-like cavities, sheet cracks, and fractures, and from partially recrystallized carbonate crusts, consistent with carbonate precipitation at cold methane seeps. The new data support a widespread methane release event following the Nantuo glaciation in south China (ca. 635 Ma), which may have contributed to the origin of unusual sedimentary and isotope features of cap carbonates.

Slow crack growth: Models and experiments

.The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.

Barite-bearing cap dolostones of the Taoudéni Basin, northwest Africa: Sedimentary and isotopic evidence for methane seepage after a Neoproterozoic glaciation

The Taoudéni Basin of the West African craton contains one of the few genuine terrestrial records of a Neoproterozoic ice age. In the Adrar region of Mauritania, an extensive permafrost landscape, lithified moraines (tillites) and striated pavements are draped by a thin, generally <5-m thick dolostone, which is lithologically and isotopically similar to other basal Ediacaran cap dolostones worldwide. In Adrar, the cap carbonate unit exhibits a complex depositional history with significant lateral facies variation related to the irregular post-glacial, topographic relief and the complex interplay between glacioeustasy and isostatic rebound. The Adrar cap carbonate package consists of one or two dolostone units, with an intervening siliciclastic package of up to 40 m thickness, and a laterally extensive, thin limestone bed that disconformably overlies the uppermost dolostone. The cap dolostone comprises mechanically laminated beds that are disrupted by fitted-brecciation, sheet cracking, tepee formation, karstic dissolution and chaotic vein networks of silica, calcite and barite. The overlying thin bed of limestone breccia comprises volcaniclastic and detrital debris and authigenic barite crystals, cemented and commonly replaced by marine calcite. The close association between relative sea-level changes, glacier retreat and cap dolostone deposition across the Taoudéni Basin implies that cap dolostones formed largely over a period of ∼10 4 years, the maximum interval over which isostatic rebound is likely to operate. Barite has been reported from identical stratigraphic levels overlying terrestrial glacial deposits throughout NW Africa and formed locally during fluid mixing on, and in cavities beneath the seafloor during late stages of the post-glacial marine transgression. Samples of barite were collected from two distant localities in the Taoudéni Basin, in Mauritania and Mali. 87Sr/ 86Sr ratios exhibit an unusually narrow range for barite that closely matches contemporaneous seawater 87Sr/ 86Sr (0.7077–8). Barite δ 34S values range widely between 20‰ and 45‰ CDT, which indicates that sulphate derived from seawater and was subsequently modified by microbially mediated sulphate reduction. The consistent stratigraphic level and irregular distribution of barite deposits are consistent with a sedimentary exhalative origin for the barite, whereby Ba-rich fluids from shallow locations within the rock pile interacted with sulphate-bearing seawater; a hydrothermal origin for these fluids can be excluded. Isotopic constraints and the association of barite with terrestrial glacial deposits across the West African craton suggest that methane seepage from underlying permafrost may be one possible mechanism for Ba sequestration. The occurrence of seafloor barite precipitates at the contact between cap dolostones and overlying post-glacial limestones worldwide implies that changes in ocean composition, in particular increases in the sulphate content of ambient seawater provided an overriding control on barite mineralisation.

Application of the digital moiré method in fracture analysis of a cracked rubber sheet

This paper deals with the mode I crack problem of a cracked rubber sheet under plane stress condition using the delicate digital moire technique. Through the four step phase-shifting method of automated fringe analysis, the displacement fields in the Cartesian coordinate system are given. By the coordinate-transform equation, the radial and circular displacement distributions in the polar coordinate system are obtained. The displacement isoline distributions and displacement vector distributions near the crack tip are discussed. The strain isoline distributions near the crack tip are also analyzed in this paper. Finally, the distribution rules for the mechanical fields near the crack tip are discussed with the sector division method.

Molar tooth structures of the Neoarchean Monteville Formation, Transvaal Supergroup, South Africa. I: Constraints on microcrystalline CaCO3 precipitation

AbstractMolar tooth (MT) structures are enigmatic, contorted millimetre‐ to decimetre‐long veins and spheroids of microcrystalline calcite that formed during very early diagenesis in Precambrian sediments. MT structures in the ca 2·6 Ga Monteville Formation are 600–800 Myr older than previously reported occurrences and establish that conditions necessary for MT genesis were met locally throughout much of the Precambrian. In the Monteville Formation, MT structures were formed shallow subtidally, extending to depths near storm wave base, in shale host sediments intercalated with storm‐generated carbonate sand lenses. They are filled with microcrystalline calcite and rare pyrite. Microcrystalline calcite identical to that in MT structures fills other pore space, including porosity between grains in carbonate sand lenses, moldic porosity in sand grains, sheet cracks in columnar stromatolites, and shallow cracks on sandy bedding planes. Relationships in the Monteville Formation demonstrate that microcrystalline CaCO3 precipitated in fluid‐filled cracks and pores; microcrystalline calcite characteristics, as well as the paucity of carbonate mud in host rocks, are inconsistent with injection of lime mud as the origin of MT structures. Locally, MT cracks were filled by detrital sediment before or during precipitation. Precipitation occurred in stages, and MT CaCO3 evolved from granular cores to a rigid mass of cores with overgrowths – allowing both plastic and brittle deformation of MT structures, as well as reworking of eroded MT structures as rigid clasts and lime mud. Crystal size distributions and morphology suggest that cores precipitated through nucleation, Ostwald ripening and size‐dependent crystal growth, whereas overgrowths formed during size‐independent crystal growth.

Stratigraphy, Sedimentary Structures, and Textures of the Late Neoproterozoic Doushantuo Cap Carbonate in South China

Abstract The 3- to 5-m-thick Doushantuo cap carbonate in south China overlies the glaciogenic Nantuo Formation (ca. 635 Ma) and consists of laterally persistent, thinly laminated and normally graded dolomite and limestone indicative of relatively deep-water deposition, most likely below storm wave base. The basal portion of this carbonate contains a distinctive suite of closely associated tepee-like structures, stromatactis-like cavities, layer-parallel sheet cracks, and cemented breccias. The cores of tepees are composed of stacked cavities lined by cements and brecciated host dolomicrite. Onlap by laminated sediment indicates synsedimentary disruption of bedding that resulted in a positive seafloor expression. Cavities and sheet cracks contain internal sediments, and they are lined by originally aragonitic isopachous botryoidal cements with acicular radiating needles, now replaced by dolomite and silica. Pyrite and barite are common, and calcite is locally retained as a primary mineral. These features share morphological and petrographic attributes with modern and ancient methane seeps in which methane gas and fluids provide both a force for physical disruption from buoyancy and a source of alkalinity for significant cementation. The presence of δ13C values as low as −41‰ in well preserved limestone crusts and cements within and immediately above the tepee-like structures provides unequivocal evidence for methane influence, and the widespread distribution of identical sedimentary structures and paragenetic cement sequences across the entire basin at the same basal cap carbonate level is consistent with gas hydrate destabilization and the development of methane seeps as a result of postglacial warming of the ocean. Considering the broad distribution of similar features at the same stratigraphic level in other cap carbonates globally, we suggest that the late Neoproterozoic postglacial methane release may have influenced the oceanic oxygen level as well as contributed to postglacial warming via the greenhouse effects of methane.

Cyclic palaeokarst surfaces in Aptian peritidal carbonate successions (Taurides, southwest Turkey): internal structure and response to mid-Aptian sea-level fall

The sedimentology and cyclic stratigraphy of palaeokarst structures in Aptian peritidal carbonate successions are interpreted using field and laboratory microfacies analyses of closely spaced samples from measured outcrop stratigraphic sections in southwest Turkey. Cycles displaying shallowing-upward metre-scale cyclicity are generally composed of lime mudstones/wackestones/packestones at the bottom and stromatolites or lime mudstones with charophytes and ostracods at the top. Subaerial exposure structures such as in situ karst breccias, dissolution vugs/pipes, mud cracks and sheet cracks are encountered at the top of the cycles. The presence of limestone layers between the successive karst breccia levels indicates that they are in situ palaeokarst structures, not recent karstifications or deep penetration from the upper palaeokarst surface down to the older strata. Palaeokarst breccia deposits are interpreted as mantling breccia formed as a result of epikarstification. Three main palaeokarst levels are recorded in nearly all sections. The sedimentology of the palaeokarst breccias, their position in cyclic peritidal carbonates and the biostratigraphic framework are used to trace the record of the global mid-Aptian sea-level fall in the southwest Taurides. The successive occurrences of three karst breccia levels close to the mid-Aptian sea-level fall correspond to falling periods of high-amplitude sea-level fluctuation within a late high-stand or early fall condition of a third-order sea level.

Scattering of flexural waves by multiple narrow cracks in ice sheets floating on water

An explicit solution is derived for the reflection and transmission of flexural-gravity waves propagating on a uniform elastic ice sheet floating on water which are obliquely incident upon any number, N, of narrow parallel cracks of arbitrary separation. The solution is expressed in terms of a system of 2 N linear equations for the jumps in the displacements and gradients across each of the cracks. A number of interesting features of the problem are addressed including the scattering by periodically spaced arrays of cracks, and examples of non-uniqueness, or trapped waves, in the case of four cracks. The problem of wave reflection by a semi-infinite periodic array of cracks is also formulated exactly in terms of a convergent infinite system of equations and relies on certain properties of the so-called Bloch problem for wave propagation through infinite periodic array of cracks.

異方性を有する純アルミニウム冷間圧延薄板の特異な疲労き裂進展経路に及ぼす圧下率並びに結晶組織と結晶方位の影響

Effects of rolling ratios, microstructures and crystal orientations on the fatigue cracks that grow on the rolling direction as mixed mode I + II cracks in pure aluminum sheets were investigated by conducting fatigue tests. The CCT specimens were used and made from cold-rolled pure aluminum sheets with rolling ratio of 50%, 75%, and 90%. It was found that the cracks grow to the rolling direction as mixed mode I + II cracks in the specimens with rolling ratio above 75%. It was also confirmed that microstructures in the high rolling ratio specimens are smaller and more elongated to the rolling direction than those with lower rolling ratio. However, there was no effect of microstructure size on the fatigue crack path. The crystal planes on the fracture surfaces and the slip plane of aluminum, (111) planes in the sheets were measured using X-ray diffraction. It was found that (111) planes mainly existed on the fracture surface of the crack that grew on the rolling direction. In addition, there were strong textures of (111) planes on the rolling direction of specimens with rolling ratio higher than 75%. It was clarified that the fatigue cracks, which grow to the rolling direction as mixed mode I + II cracks, are caused by strong textures of (111) planes on the rolling direction that exist in the maximum shear-stress region.

Behavior of Fatigue Crack Growth Paths in Peculiar Anisotropic Commercial Pure-Aluminum Sheets (A1100P)

Behavior of fatigue crack that grows to the rolling direction about 30 degrees to the loading direction as a mixed mode I + II crack in peculiar anisotropic commercial pure aluminum sheets (A 11110 p) was investigated using CCT specimens. From fatigue tests, it was found that the crack started to change the direction from mode I to the rolling direction when mode I stress intensity factor range was 4.2 MPa·mm1/2 and crack grew continuously to the rolling direction when mode II stress intensity factor range was 4.3 MPa·mm1/2 under small scale yielding state. However, in the case of specimen annealed in 563 k, 30 minutes, the crack did not grow to the rolling direction. The crack that grew on the rolling direction changed direction to mode I direction, due to the nominal stress which was about 80 percent of yield stress. According to the measurement on crystal planes using X ray diffraction, it was found that the slip plane of aluminum. (III) plane dominantly existed on the fracture surface of the crack that grew to the rolling direction. From pole figures, it was also verified that strong textures of (III) planes existed in rolling direction, so that the shear strength on the rolling direction was low as confirmed by shear test. Due to the strong textures of (III) planes that exist around the maximum shear stress region, the mode II crack component becomes easily to occur that makes the mixed mode I+II crack to grow to the rolling direction around 30 degrees towards loading direction.

Failure of sandwich beams consisting of alumina face sheet and aluminum foam core in bending

Applications of sandwich structures, comprising alumina face sheets and aluminum foam core, depend critically on their mechanical performance. Four point bend tests are performed on sandwich beams with varying geometries to identify competing failure modes, such as core indentation, face sheet cracking and core shear. Analytical formulae for the identified failure modes are obtained. A failure mode map was constructed based on the analytical calculations in the non-dimensional parameters of beam geometry for a given face sheet to core strength ratio. The tested geometries are simulated using a finite element program: the beam stiffness and the failure load calculations were found to be in good agreement with the experimental and analytical results within experimental scatter.