Maximum Shear Stress Plane Research Articles

Single crystal yield criterion for chromium based on atomistic studies of isolated 1/2[111] screw dislocations

Using the recently developed Bond Order Potential for Cr, we investigate the mobility of isolated 1/2[111] screw dislocations under stress at 0 K. These studies provide the dependence of the critical resolved shear stress (i.e., the Peierls stress) on the orientation of the maximum resolved shear stress plane and on the shear stress perpendicular to the slip direction. Similar studies are made for loading in tension and compression to show that the onset of yielding in Cr single crystals can be described using a combination of the shear stresses parallel and perpendicular to the slip direction. Based on these results, we develop a single crystal yield criterion for Cr that includes all non-Schmid contributions to the Peierls stress. This criterion is used to predict the shape of the yield surface and compare it with the regular Tresca's hexagon arising from the Schmid law. For all directions of uniaxial load, the criterion is used to quantify the character and magnitude of the tension-compression asymmetry.

Subsurface Facet-fisheye Induced Failure of Titanium Alloy under Very High Cycle Fatigue

Very high cycle fatigue test under pulsating tension was performed to investigate the subsurface failure mechanism of a titanium alloy. A peculiar region, called “facets cluster zone (FCZ)”, is located at the center of fisheye. The slip-like patterns on facet surface, coalescence of nanoscale cracks and growth of microcracks in the maximum shear stress plane are observable. Combined with the evaluation of stress intensity factors at crack tips, the subsurface failure processes are summarized as: (a) localization of plastic strain, (b) occurrence of slip lines, (c) nucleation of microcracks, (d) coalescence and growth of microcracks, (f) occurrence of the FCZ, (g) formation of fisheye and (i) unstable crack growth until final fracture.

How a strong low-angle normal fault formed: The Whipple detachment, southeastern California

AbstractMany low-angle normal faults (dip ≤30°) accommodate tens of kilometers of crustal extension, but their mechanics remain contentious. Most models for low-angle normal fault slip assume vertical maximum principal stress σ1, leading many authors to conclude that low-angle normal faults are poorly oriented in the stress field (≥60° from σ1) and weak (low friction). In contrast, models for low-angle normal fault formation in isotropic rocks typically assume Coulomb failure and require inclined σ1 (no misorientation). Here, a data-based, mechanical-tectonic model is presented for formation of the Whipple detachment fault, southeastern California. The model honors local and regional geologic and tectonic history and laboratory friction measurements. The Whipple detachment fault formed progressively in the brittle-plastic transition by linking of “minidetachments,” which are small-scale analogs (meters to kilometers in length) in the upper footwall.Minidetachments followed mylonitic anisotropy along planes of maximum shear stress (45° from the maximum principal stress), not Coulomb fractures. They evolved from mylonitic flow to cataclasis and frictional slip at 300–400 °C and ∼9.5 km depth, while fluid pressure fell from lithostatic to hydrostatic levels. Minidetachment friction was presumably high (0.6–0.85), based upon formation of quartzofeldspathic cataclasite and pseudotachylyte. Similar mechanics are inferred for both the minidetachments and the Whipple detachment fault, driven by high differential stress (∼150–160 MPa). A Mohr construction is presented with the fault dip as the main free parameter. Using “Byerlee friction” (0.6–0.85) on the minidetachments and the Whipple detachment fault, and internal friction (1.0–1.7) on newly formed Reidel shears, the initial fault dips are calculated at 16°–26°, with σ1 plunging ∼61°–71° northeast. Linked minidetachments probably were not well aligned, and slip on the evolving Whipple detachment fault probably contributed to fault smoothing, by off-fault fracturing and cataclasis, and to formation of the fault core and fractured damage zone.Stress rotation may have occurred only within the mylonitic shear zone, but asymmetric tectonic forces applied to the brittle crust probably caused gradual rotation of σ1 above it as a result of: (1) the upward force applied to the base of marginal North America by buoyant asthenosphere upwelling into an opening slab-free window and/or (2) basal, top-to-the-NE shear traction due to midcrustal mylonitic flow during tectonic exhumation of the Orocopia Schist. The mechanical-tectonic model probably applies directly to low-angle normal faults of the lower Colorado River extensional corridor, and aspects of the model (e.g., significance of anisotropy, stress rotation) likely apply to formation of other strong low-angle normal faults.

Faceted crack induced failure behavior and micro-crack growth based strength evaluation of titanium alloys under very high cycle fatigue

Very high cycle fatigue properties of titanium alloys under symmetrical and asymmetrical loads were experimentally examined to clarify the failure behavior. An inhomogeneous microstructure zone (IMZ) containing facets is observable. By focused ion beam testing, the interior micro-crack extends along the maximum shear stress plane and the facet plane is about 45°. By the modeling of growth rate and the definition of controlling line, a strength evaluation approach with the failure behavior was well proposed. This reflects that the micro-crack growth rate in IMZ stage is below one Burger’s vector.

Torsional Fatigue Cracking and Fracture Behaviors of Cold-Drawn Copper: Effects of Microstructure and Axial Stress

The fatigue cracking and fracture behavior of cold-drawn copper subjected to cyclic torsional loading were investigated in this study. It was found that with increasing stress amplitude, the fracture mode of cold-drawn copper gradually changes from a shear fracture on transverse maximum shear stress plane to a mixed shear mode on both transverse and longitudinal shear planes and finally turns to the shear fracture on multiple longitudinal shear planes. Combining the cracking morphology and the relationship between torsional fatigue cracking and the grain boundaries, the fracture mechanism of cold-drawn copper under cyclic torsional loading was analyzed and proposed by considering the effects of the microstructure and axial stress caused by torsion. Because of the promotion of the grain boundary distribution on longitudinal crack propagation and the inhibition of axial stress on transverse crack grown, the tendency of crack propagation along the longitudinal direction increases with increasing stress levels.

Fatigue crack initiation and propagation behavior in Al – 7075 alloy under in-phase bending-torsion loading

Fatigue crack initiation and propagation behavior were investigated on a tubular specimen of Al 7075 alloy subjected to multiaxial mixed mode bending-torsional loadings. Tests under pure bending and pure torsional loadings were also conducted to segregate the effect of multiaxiality. A single crack nucleated on the plane of maximum shear stress in all the tests, except for pure torsion. For pure bending, crack propagated on the plane of maximum shear stress in a mixed mode condition tracing an inverted S-shaped trajectory; whereas, crack trajectory under combined bending-torsional load consisted of mode I dominant region, transition region, and pure mode II region. Furthermore, analyses of fracture surfaces were conducted to determine the micro-mechanisms governing crack initiation and propagation behavior.

Mechanical, deformation and fracture behaviors of bulk metallic glass composites reinforced by spherical B2 particles

Ti45Cu40Ni7Zr5Sn2.5Si0.5 alloys were prepared under various cooling rate conditions during solidification. The alloys exhibited different volume fractions of B2 particles with 0 ~ 40 vol% in an amorphous matrix. Monolithic bulk metallic glass of 1 mm diameter showed no macroscopic plasticity and exhibited the typical vein patterns in a maximum shear stress plane on the fracture surface. However, a bulk metallic glass composite containing the B2 particles revealed obvious plasticity (~ 5.6%) with a remarkable work-hardening behavior that resulted from a stress-induced martensitic transformation of the B2 particles. Moreover, the composite displayed the complicated fracture morphologies containing of three types of fracture features. Through detailed investigations on the microstructural evolution, mechanical, deformation and fracture characteristics, the influence of B2 particle on overall behavior of the TiCu-based bulk metallic glass composites was elucidated.

Effect of inclusion and microstructure on the very high cycle fatigue behaviors of high strength bainite/martensite multiphase steels

We studied the mutual and relative effect of inclusion and microstructure on very high cycle fatigue (VHCF) behavior of bainite/martensite (B/M) multiphase steel by designing four combinations of various inclusion sizes and microstructures. Results show that the fatigue crack initiations are mostly induced by inclusions in the specimens with large inclusion size, whereas the “non-inclusion induced crack initiations” (NIICI) are observed in the specimens whose microstructure is coarse. Unlike the inclusion induced cracks that grow along the plane of maximum tensile stress, the early non-inclusion induced cracks within micro-facet propagate along the plane of maximum shear stress (i.e., Stage I crack), which is related to the strain localization in oriented B/M laths during cyclic loading. Finally, with the assistance of scanning electron microscopy, electron backscatter diffraction, 3-Dimensional surface profile, focused ion beam and transmission electron microscopy, we proposed the NIICI mechanism of coarse B/M microstructure, and found the orientation and size of coarse B/M block and blocky retained austenite (RA) are crucial microstructural factors in facilitating the formation of NIICI within VHCF regime.

Ductile-to-brittle transition in tensile failure due to shear-affected zone with a stress-concentration source: a comparative study on punched-plate tensile-failure characteristics of precipitation-hardened and dual-phase steels

The effect of shear-affected zone (SAZ), with a stress-concentration source induced by the punching process, on tensile properties was investigated. Tests using honed specimens (which have the same shapes and stress-concentration without any SAZ) and smooth specimens were conducted to compare the effect with that of the punched specimens. Dual-phase steel, which has a high work-hardening ability and low yield strength, and precipitation-hardened steel, which has a low work-hardening ability and high yield strength, were used in the tests. Materials with two tensile strength grades were prepared from both types of steel. Only the precipitation-hardened steel with higher strength grade punched specimen showed a brittle fracture with extremely short fracture-elongation, whereas the other specimens showed a ductile fracture. The fracture surface analysis revealed that cracks initiated in the maximum shear stress plane of the SAZ under tensile loading at first. We call the crack “shear crack.” The steel which showed brittle fracture used in this study easily exhibited plastic-strain localization compared with the other steels. If the shear crack is sharp, then the transition from ductile to brittle failure tends to occur. Furthermore, the strength characteristics of the punched specimen depend on the crack length dependency of the strength resistance and the failure phenomenon of the original material.

Shear stress triggering brittle shear fracturing of rock-like materials

Contact fracturing of rock-like brittle materials indented by rigid cylindrical punches with flat ends is studied. Contrary to the classical shear fracturing mechanism of brittle materials explained in terms of multi-tensile-stressed micro-cracks in materials [1], a new mechanism dominant in brittle shear fracturing is found, namely, shear stress triggered fracturing orientation existing in nature, and the contact crack initiation angle for such kind rock-like materials is also revealed. This phenomenon is very different from such as Hertzian or Roesler’s [2] crack generation mechanism, as cracks are directed inwards rather than outwards. The theoretical predictions are validated by our experimental results. This finding testifies that for a rock-like brittle material shear fracturing along its maximum shear stress plane is possible under some special confinement, which has important implications for seismology and rock-mass stability, as well as rock engineering.

Microscopic Failure Mechanism Analysis of Sandstone Under Triaxial Compression

Mineral composition and microstructure changes under loading greatly influence the macroscopic mechanical strength of rocks. In this study, the chemical and mineral composition of sandstone from a coal mine in China were analyzed with energy dispersive spectrometry and X-ray diffraction. Triaxial compression tests of three sandstone samples with different compositions were carried out by using a servo-controlled rock mechanics testing system to obtain macroscopic failure characteristics and complete stress–strain curves. Fracture morphologies of the sandstone samples were observed by scanning electron microscopy (SEM), and the fracture origins, defects, grain size, pore structure and distribution, microfracture characteristics and grain boundaries were determined. Finally, the fracture mechanism of the rocks was analyzed, and the microstructure and fracture characteristics of three samples were obtained. The results showed that the stress–strain curve of samples under triaxial compression can be divided into four stages: microfractures compressed-closed, elastic deformation, plastic-failure and post-failure. Under triaxial compression, shear failure occurred in the samples, and the slip occurred along the plane of maximum shear stress. The SEM results showed grooves and steps on the fracture surface, where the debris was piled up in angular and granular shapes. Higher quartz and feldspar content is positively correlated with sample strength. There were some microcracks in the fracture surface of the clastic sandstone with higher hydrophilic clay minerals, which indicates the fracture was easily extended during the shear process. Thus, tensile fractures are more likely to be generated along the bedding plane, resulting in the low strength of clastic sandstone.

Shear Fracture and Industrial Overload Failure of Mechanical Fuse Shear Pin

The science and engineering application of fracture is attractive and complex in nature. The notch provided shear pin geometry design for lower and known stress concentration factor engineered for premature shear pin fracture failure. The shear pin is one among type of mechanical fuse, safeguard bigger industrial rotary components by premature failure. The notch provided in shear pin act as reduced notch toughness where crack initiation and propagation starts from notch surface due to overload stress in the system. Advancement in technologically of mechanical fuses is one such key area, with which design of engineered microstructure analysis of shear failure discussed extensively. In the present investigation, shear pin failure were characterized to determine root cause analysis. Visual examination of fracture surface reveals pure ductile adiabatic shear fracture and metallographic examinations reveals non uniform size of spheroidal cementite carbide particles distributed uniformly slipping in coarse ferrite matrix plane of maximum shear stress causes the reason for shear fracture phenomena during crack propagation.

The role of twinning and nano-crystalline ω phase on the fatigue behavior of the metastable β Ti-15Mo alloy

This work evaluated in depth the fatigue and fracture behavior of the metastable β Ti-15Mo alloy considering the presence of deformation twins and athermal nano-crystalline ω phase in the microstructure. Regardless of the microstructural condition studied, the as-received and the solution treated and quenched materials, ω phase remained unchanged, guaranteeing the static mechanical properties at acceptable levels. The mechanism of fatigue fracture was related to the existence of twins and maximum shear stress planes near the direction of screw dislocation motion in the BCC structure. The significant amount of deformation twins in the initial microstructure did not alter the fatigue limit, because the solution treated and quenched material unexpectedly developed twins during the fatigue test.

Analysis of Fracture Behaviour of Exploded Metal Cylinders with Varied Charge

Explosively driven fragmentation of ductile metals cylinders is a highly complex phenomenon. In this work, the fracture characteristics of exploded TA2 titanium alloy cylinder with varied charge were investigated numerically and experimentally. The results show that the fracture surfaces of fragments lie along planes of maximum shear stress for either a higher or a lower detonation pressure, but their mechanism is different. The finite element analysis demonstrated that the equivalent plastic strain in the middle of the wall is always larger than that of inner and outer wall for metal cylinder during the stage of shock wave driven period. For the high explosive pressures, the micro-cracks originated firstly in middle zone of wall during the stage of shock wave driven, and extend to the inner and outer wall in the direction of maximum shear stress. Explosives which generate lower detonation pressures, the shear fracture of cylinder originated from the inner wall and propagate to the outer wall in an angle of 45° or 135° to radial, the crack begin at the stage of free expansion. The simulated analysis of the process of deformation and fragmentation for exploded metal cylinder agree with the experimental results.

Fatigue and Fracture Behavior of a Cold-Drawn Commercially Pure Aluminum Wire.

Fatigue properties and cracking behavior of cold-drawn commercially pure aluminum wires (CPAWs) widely used as the overhead transmission conductors were investigated. It was found that the fracture surface of the CPAWs shows an obvious four-stage fracture characteristic, i.e., crack initiation, planar crack propagation, 45°-inclined crack propagation and final rapid fracture. The crack growth mechanisms for the CPAWs were found quite different from those for the conventional coarse-grained materials. The cracks in the CPAWs firstly grow along the grain boundaries (Stage I crack growth), and then grow along the plane of maximum shear stress during the last stage of cycling (Stage II crack growth), leading to the distinctive fracture surfaces, i.e., the granular surface in the planar crack propagation region and the coarse fatigue striations in the 45°-inclined crack propagation region. The grain boundary migration was observed in the fatigued CPAWs. The increase in fatigue load enhances the dislocation recovery, increases the grain boundary migration rate, and thus promotes the occurrence of softening and damage localization up to the final failure.

Comparison of crack paths in a forged and extruded aeronautical titanium alloy loaded in torsion in the gigacycle fatigue regime

This paper discusses features of fatigue crack initiation and growth in an extruded and forged VT3-1 titanium alloy loaded in pure torsion in the gigacycle regime. Torsion fatigue tests were performed at 20kHz up to a fatigue life of 109 cycles. It has been shown that regardless of the manufacturing process both surface and subsurface crack initiation may appear under ultrasonic torsion loads despite the fact that the maximum shear stress amplitude is located at the specimen surface. In the two cases cracks initiate on planes of maximum shear stress amplitude (mode II). After reaching a certain length the cracks turn and propagate in mode I. Surface crack initiation and growth mechanisms in VHCF regime are similar to HCF ones. Subsurface crack forms a typical “fish-eye” pattern on fracture surface with three different zones: (1) small crack growth in the plane of maximum shear stress, (2) crack growth on the plane of maximum normal stress with the formation of a quasi-flat failure surface covered by fretting debris, (3) crack branching under mixed mode loading conditions (I+II+III) with the formation of several secondary cracks. Subsurface crack initiation sites are located below the specimen surface (at a depth of approximately 200μm) for both the forged and the extruded materials. Subsurface crack growth is observed on the failure surface as being less rough. The mechanisms of subsurface crack initiation seems to be similar to these observed under fully reversed tensile loads.

Determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading

A weight function method for the determination of the critical plane is here proposed for the case of specimens under combined bending and torsion in the high cycle fatigue regime. The critical plane is assumed to be coincident with the mean maximum absolute shear stress plane, which is calculated by averaging the instantaneous angle between the specimen axis and the normal to the maximum absolute shear stress plane. Two kinds of weight functions are proposed to determine such a plane. The proposed method to determine the critical plane is verified by employing fatigue data available in the literature in terms of experimental fracture planes, and the multiaxial fatigue life is also predicted by a reformulation of the criterion proposed by Carpinteri et al. to verify the determined critical plane. The results show that the proposed method can be applied to determine the critical plane under both constant and variable amplitude loading.

Fatigue crack initiation and growth on an extruded titanium alloy in gigacycle regime: comparison between tension and torsion loadings

This paper is focused on the analysis of fatigue crack initiation and growth mechanisms in defect free VT3-1 titanium alloy (similar to Ti6Al4V) in VHCF regime under tensile and torsion loadings. Fully reversed fatigue tests were carried out between 107 and 109 cycles at 20 kHz under constant amplitude loadings (no pulse-pause). SEM observations of the specimens fracture surfaces were carried out in order to compare the crack initiation mechanisms and the different crack growth stages under different loadings. It has been shown that subsurface crack initiation may appear under tension (as usual in gigacycle regime) but in our experiments no inclusion was observed in the “fish-eye”. Furthermore, subsurface crack initiation was observed under torsion loading too, despite the maximum shear stress location at the specimen surface. Under this loading, a “fish-eye” was observed too, but again without any inclusion in its center. The suspected microstructural reasons responsible for subsurface crack initiations under torsion loading could not be observed due to significant destruction of the fracture patterns (crack lips friction under mixed mode). The results of the fatigue tests show a principal difference in crack initiation and early crack growth stage between tensile and torsion loadings. Torsion crack initiates on a plane of maximum shear stress (like in HCF regime) while tensile crack is on a plane of maximum normal stress. Sequences of changes in fracture surface roughness is the same for tensile and torsion loadings.

Growth behavior of fatigue cracks in ultrafine grained Cu smooth specimens with a small hole

In order to study the growth mechanism of fatigue cracks in ultrafine grained copper, stresscontrolled fatigue tests of round-bar specimens with a small blind hole as a crack starter were conducted. The hole was drilled on the surface where an intersection between the shear plane of the final ECAP processing and the specimen surface makes an angle of 45° or 90° with respect to the loading axis. At a low stress ( ? a = 90 MPa), the direction of crack paths was nearly perpendicular to the loading direction regardless of the location of the hole. Profile of crack face was examined, showing the aspect ratio (b/a) of b/a = 0.82. At a high stress ( ? a = 240 MPa), although the growth directions inclined 45° and 90° to the loading-axis were observed depending on the location of the drilling hole, crack faces in these cracks were extended along one set of maximum shear stress planes, corresponding to the final ECAP shear plane. The value of aspect ratios was b/a = 0.38 and 1.10 for the cracks with 45° and 90° inclined path directions, respectively. The role of deformation mode at the crack tip areas on crack growth behavior were discussed in terms of the mixed-mode stress intensity factor. The crack path formation at high stress amplitudes was affected by the in-plane shear-mode deformation at the crack tip.

In situ micropillar deformation of hydrides in Zircaloy-4

Deformation of hydrided Zircaloy-4 has been examined using in situ loading of hydrided micropillars in the scanning electron microscope and using synchrotron X-ray Laue microbeam diffraction. Results suggest that both the matrix and hydride can co-deform, with storage of deformation defects observed within the hydrides, which were twinned. Hydrides placed at the plane of maximum shear stress showed deformation within the hydride packet, whilst packets in other pillars arrested the propagation of shear bands. X-ray Laue peak broadening, prior to deformation, was associated with the precipitation of hydrides, and during deformation plastic rotation and broadening of both the matrix and hydride peaks were observed. Post-mortem TEM of the deformed pillars has indicated a greater density of dislocations associated with the precipitated hydride packets, while the observed broadening of the hydride electron diffraction spots further suggests that plastic strain gradients were induced in the hydrides by compression.