Maximum Shear Stress Plane Research Articles

Formation, Thermal Stability and Mechanical Properties of Bulk Glassy Alloys with a Diameter of 20 mm in Zr-(Ti,Nb)-Al-Ni-Cu System

Bulk glassy alloy rods with a diameter of 20 mm were produced for Zr61Ti2Nb2Al7:5Ni10Cu17:5 and Zr60Ti2Nb2Al7:5Ni10Cu18:5 by a tilt casting method. The replacement of Zr by a small amount of Ti and Nb caused a distinct increase in the maximum diameter from 16 mm for Zr65Al7:5Ni10Cu17:5 to 20 mm, accompanying the decrease in liquidus temperature and the increase in reduced glass transition temperature. The primary precipitation phase from supercooled liquid also shows a distinct change, i.e., from coexistent Zr2Cu, Zr2Ni and Zr6NiAl2 phases for the 65%Zr alloy to an icosahedral phase for the 61%Zr and 60%Zr alloys. These results allow us to presume that the enhancement of the glassforming ability is due to an increase in the stability of supercooled liquid against crystallization caused by the development of icosahedral shortrange ordered atomic configurations. The 60%Zr specimens taken from the central and near-surface regions in the transverse cross section at the site which is 15 mm away from the bottom surface of the cast glassy rod with a diameter of 20 mm exhibit good mechanical properties under a compressive deformation mode, i.e., Young’s modulus of 81 GPa, large elastic strain of 0.02, high yield strength of 1610 MPa and distinct plastic strain of 0.012. Besides, a number of shear bands are observed along the maximum shear stress plane on the peripheral surface near the final fracture site. The finding of producing the large scale Zr-based bulk glassy alloys exhibiting reliable mechanical properties is encouraging for future advancement of bulk glassy alloys as a new type of functional material. [doi:10.2320/matertrans.MER2008179]

Correlation of adiabatic shearing behavior with fracture in Ti-6Al-4V alloys with different microstructures

The correlation of adiabatic shearing behavior with fracture was investigated in Ti-6Al-4V alloys with bimodal and lamellar microstructures by split Hopkinson pressure bar (SHPB) apparatus and ballistic impact test. The experiment results show that the macrographic characteristic of post-critical fracture is closely related with the behavior of adiabatic shear band (ASB) in these titanium alloys under high strain rate conditions. In bimodal microstructure, adiabatic shear bands are self-organized and distributed in somewhat regularly spaced clusters. These adiabatic bands as well as the correlated cracks spread far off along the maximum shear stress plane, which causes the projectiles fracture along the dominant cluster of adiabatic shear bands, and the fracture surfaces make an acute angle with the flat end of the projectile. In case of lamellar microstructure, the adiabatic shear bands branch off and interconnect with one another into a net-like structure. Such adiabatic shearing cracks can't spread deep resulting from the branching off and interaction of adiabatic shear band, but only to split the specimen into small fragments, which leads to the erosion of the projectile and the resulting fracture surfaces almost parallel to the flat end of the projectile.

Interpreting the change in shear band inclination angle in metallic glasses

Shear bands in metallic glasses subject to uniaxial loading such as tension and compression exhibit the inclination angle different from 45° on the maximum resolved shear stress plane with respect to the loading axis. The cause is often attributed to the effective normal stress acting on the shear plane, which also suggests Coulomb–Mohr yield criterion for metallic glasses. We show here that this argument is conceptually ill justified. Instead, shear band inclination angle can be described by a simple model taking into consideration the volume dilatation and the pressure effects.

Influence of microstructure and strain rate on adiabatic shearing behavior in Ti–6Al–4V alloys

Adiabatic shearing behavior of Ti–6Al–4V alloys with bimodal and lamellar microstructures is investigated at strain rates ranging from 10 3 s −1 to 10 4 s −1 by Spilt Hopkinson Pressure Bar and Taylor impact. The characteristic of fracture is closely related with the behavior of adiabatic shear band in Ti–6Al–4V alloys. In bimodal microstructure at strain rate of 10 3 s −1, the adiabatic shear bands are regularly spaced and orientated along the maximum shear stress plane. In case of the lamellar microstructure, when the strain rates increase from 4000 s −1 to 6000 s −1, the adiabatic shear bands go through the transition from self-organization to branching off and interconnecting into a net-like structure. At strain rate of 10 4 s −1 by Taylor impact, the regularly spaced adiabatic shearing cracks cause that the fracture surface makes an angle of 45° with the impacted end of the projectile in bimodal microstructure. The net-like adiabatic shearing cracks in lamellar microstructure result in the fragmentation of the projectile head, the angle is about 0°.

Fracture behavior of Zr55Cu30Al10Ni5 bulk metallic glass under quasi-static and dynamic compression

Fracture behavior of Zr55Cu30Al10Ni5 bulk metallic glass was investigated under quasi-static compression at strain rate of 10−4/s using an Instron testing machine and dynamic split Hopkinson bar (SHPB) compression with strain rate of about 1900–4300/s. Pronounced strain softening, especially past the peak stress, was observed under SHPB tests and compared with the distinct flow serrations under quasi-static tests. Scanning electron microscope revealed that the angle between the loading axis and major shear plane is less than 45°, deviating from the maximum shear stress plane. Microscopically, unlike the ordinary veinlike pattern found in quasi-static compression, the elongated veinlike pattern was observed at the onset position of rapid shearing under dynamic test. A closely arrayed dendritelike structure dominated the dynamic fracture, consequently, and should be the major pattern representing the rapid shear band propagation. In addition, a transition state from veinlike to dendritelike pattern was observed at the final instantaneous fracture region in quasi-static tests. Evidence revealed the characteristic dimension of dynamic fracture surface complies with Taylor’s meniscus instability criterion. The roles of free volume and adiabatic heating on the fracture strength and stress concentration on the fracture morphology are also discussed.

CMT data inversion using a Bayesian information criterion to estimate seismogenic stress fields

SUMMARY We developed an inversion method to estimate the stress fields related to earthquake generation (seismogenic stress fields) from the centroid moment tensors (CMT) of seismic events by using Akaike’s Bayesian information criterion (ABIC). On the idea that the occurrence of an earthquake releases some part of the seismogenic stress field around its hypocentre, we define the CMT of a seismic event by a weighted volume integral of the true but unknown seismogenic stress field. Representing each component of the seismogenic stress field by the superposition of a finite number of 3-D basis functions (tri-cubic B-splines), we obtain a set of linear observation equations to be solved for the expansion coefficients (model parameters). We introduce prior constraint on the roughness of the seismogenic stress field and combine it with observed data to construct a Bayesian model with hierarchic, highly flexible structure controlled by hyper-parameters. The optimum values of the hyper-parameters are objectively determined form observed data by using ABIC. Given the optimum values of the hyper-parameters, we can obtain the best estimates of model parameters by using a maximum likelihood algorithm. We tested the validity of the inversion method through numerical experiments on two synthetic CMT data sets, assuming the distribution of fault orientations to be aligned with the maximum shear stress plane in one case and to be random in the other case. Then we applied the inversion method to actual CMT data in northeast Japan, and obtained the pattern of the seismogenic stress field consistent with geophysical and geological observations.

Structure, Thermal Stability and Mechanical Properties of Zr<SUB>65</SUB>Al<SUB>7.5</SUB>Ni<SUB>10</SUB>Cu<SUB>17.5</SUB> Glassy Alloy Rod with a Diameter of 16 mm Produced by Tilt Casting

Bulk glassy alloy rods with a diameter of 16 mm and a length of 40 to 45 mm were produced for Zr65Al7:5Ni10Cu17:5 alloy by a tilt casting method. The alloy specimens taken from the different sites which are away by about 10 mm, 15 mm and 30 mm from the bottom surface of the cast rod consist of a glassy phase and their thermal stability, mechanical properties and fracture mode are almost independent of the specimen sites. The glass transition temperature, temperature interval of supercooled liquid region before crystallization and heat of crystallization are about 643 K, 102 K and 55 J/g, respectively, for the specimens taken from the three different sites. Besides, Young’s modulus, yield strength, fracture strength, yield strain and plastic strain of the specimens are about 87 GPa, 1540 MPa, 1580 MPa, 0.018 and 0.005, respectively. The fracture mode consisting of shear plastic deformation along the maximum shear stress plane, followed by an instantaneous final rupture is also independent of the specimen sites. These data indicate that the cast glassy alloy rod with a diameter of 16 mm has nearly the same characteristics, though the cooling rate is significantly dependent on sample sites. The knowledge of producing the Zr-based bulk glassy alloy rod with nearly the same characteristics in the large diameter range up to 16 mm is encouraging for future applications of bulk glassy alloys as a new type of engineering material. [doi:10.2320/matertrans.MER2008127]

Compressive and tensile deformation behavior of consolidated Fe

The deformation behavior was investigated in a consolidated Fe with a grain size ranging from submicrometer to tens of micrometer values under uniaxial compression and tension. In compression, shear banding occurred significantly at grain sizes >500 nm while only a single band was observed in samples with grain sizes of ∼100 nm. For the samples with grain sizes <∼800 nm, the shear banding took place at angles of 48–51°. When the grain sizes were >∼800 nm, the shear banding happened at an angle of 45° (in the maximum shear–stress plane). In tension, premature fracture happened in samples with grain sizes <1 μm while shear banding was observed at grain sizes >1 μm, and the shear banding angle was also close to 45°. For the samples with grain sizes > 2 μm, homogeneous deformation took over in compression with a yield-point phenomenon being observed, but Lüders banding localization occurred in tension.

Multifarious Fracture Features of CuZrAlGd(Ag) Bulk Metallic Glasses

Multifarious fracture features, such as coarse rive-like, micro holes, rugged and flat fracture surface, were systematically investigated in the monolithic Cu46-xZr45Al7Gd2Agx (x=0, 0.5) bulk metallic glasses. The fracture planes presented different angles with the loading direction. These fracture features were completely different from the typical fracture characteristics of amorphous alloys, i.e. vein-pattern and fracturing approximately along the maximum shear stress plane. On the other hand, some tiny strips with about 50 nm intervals were also detected on the flat fracture plane. The preliminary discussions on the formation mechanisms of these exceptional features were presented.

Effects of Undersized Inclusions on Ductile Fracture Behavior of FeNi42 Alloy in Sheet Tension

In-situ tension tests with special designed SEM had been conducted to trace the process of microvoids nucleation, growth and coalescence at the nonmetallic inclusions in FeNi42 alloy. The fracture surfaces were examined by scanning electron microscopy. The main results are as follows. The fracture of the tensile specimen of FeNi42 alloy is along the plane of maximum shear stress (45deg to the tensile axis), and there are a lot of dimples in the fracture surface. So this is a typical ductile fracture. At earlier stages of deformation, microvoids nucleated at bigger inclusions, and grew up independently. When the microvoids grew up to critical size, they began to coalesce. Coalescence of microviods occurs only in localized necked regions. When the space of adjacent microviods is smaller, they coalesced directly. Oppositely, when the space is bigger, they are usually linked by several smaller voids nucleated presumably by fine carbides or very small inclusions as result of the high local strains required to separate the intervening matrix.

Simulation of plasticity in nanocrystalline silicon

Molecular dynamics investigation of plasticity in a model nanocrystalline silicon system demonstrates that inelastic deformation localizes in intergranular regions. The carriers of plasticity in these regions are atomic environments, which can be described as high-density liquid-like amorphous silicon. During fully developed flow, plasticity is confined to system-spanning intergranular zones of easy flow. As an active flow zone rotates out of the plane of maximum resolved shear stress during deformation to large strain, new zones of easy flow are formed. Compatibility of the microstructure is accommodated by processes such as grain rotation and formation of new grains. Nano-scale voids or cracks may form if stress concentrations emerge which cannot be relaxed by a mechanism that simultaneously preserves microstructural compatibility.

Fatigue fracture behavior of a single-slip-oriented Fe-35 wt.% Cr alloy single crystal containing fine-scale Cr-rich precipitates

The fatigue fracture behavior of a [ 1 ¯ 4 9 ] single-slip-oriented Fe-35 wt.% Cr alloy single crystals containing fine-scale Cr-rich precipitates is investigated at constant plastic strain amplitudes ( ɛ pl) ranging from 5.0 × 10 −4 to 5.0 × 10 −3 at ambient temperature in air. In the early stage of cyclic deformation, the initial primary crack nucleates at the specimen surface and develops along the primary slip band. With further cycling the deflection of the primary crack takes place into the nearby soft regions, and eventually the zigzag primary crack forms roughly along the primary slip plane ( 1 ¯ 0 1 ) , accompanied with a few secondary cracks formed in soft regions. In addition, the fracture surface seems to become more brittle-like with increasing ɛ pl. It is suggested that such a fatigue fracture behavior is mainly bound up with the enhanced strain localization resulting from the dissolution of fine Cr-rich precipitates during cycling, and also with the special macroscopic state of stress, namely, the primary slip plane ( 1 ¯ 0 1 ) , which makes an angle of 45° with the stress axis, [ 1 ¯ 4 9 ] , is exactly a maximum shear stress plane.

The Physical Nature of Materials Strengths

The strength of a material is assessed most often by means of a tensile test. For a given material the fracture strength can be calculated by σF = Fmax/A0. For a bulk metallic glassy specimen, it often fails in a shear mode, and the shear fracture surface makes an angle of θT=56° with respect to the tension axis. Such shear fracture behavior has been widely observed in many metallic glasses. Consequently, this gives rise to some interesting and significant questions. Which is the real tensile strength of a metallic glass? Why do metallic glasses often fail neither along the maximum normal stress plane (θT =90°) nor along the maximum shear stress plane (θT = 45°) under tensile loading? What is the physical nature of the materials strength?

How ductile are ductile shear zones?

Three premises of ductile deformation in the middle and lower crust are widely accepted: (1) rocks flow with power-law viscous rheology, (2) localization in ductile shear zones involves strain softening, and (3) fluid flows into and is channelized within ductile shear zones. Ductile (viscous) shear zones should therefore initially develop along planes of maximum shear stress, strain soften, and rotate as material planes into the field of progressive extension. However, the mean stress or pressure within a weak, elongate viscous band being stretched is higher than the surrounding matrix, and this is difficult to reconcile with premise (3). In contrast, Mohr-Coulomb brittle faults always have lower pressure within the fault zone. Flow of fluid and melt into high-temperature shear zones therefore implies that “ductile” shear zones are not perfectly viscous but have a pressure-dependent viscoplastic rheology. The continued pressure dependence may reflect significant microcracking on the grain scale even when localized deformation does not produce larger-scale discrete fractures.

Void formation and cracking of Zr41Ti14Cu12.5- Ni10Be22.5 bulk metallic glass under planar shock compression

Planar shock compression effects on void formation and cracking in Zr41Ti14Cu12.5Ni10Be22.5 bulk metallic glass (BMG) are studied in this paper. Cracking was found to be a result of void linkage in some direction deviation from the maximum shear stress plane. Changing the state of the stress inside the BMG sample led to formation of different void distribution. Nucleation of the microvoids was possibly initiated by release of excess free volume under shock wave compression.

Tensile creep and microstructural characterization of bulk Sn3.9Ag0.6Cu lead-free solder

The microstructural and creep behavior of bulk 63SnPb37 and the Pb-free solder alloy Sn3.9Ag0.6Cu are reported and compared. The Sn3.9Ag0.6Cu alloy showed much lower absolute creep rates than 63SnPb37. The size and distribution of the intermetallic compound (IMC) coarsened with increasing creep temperature. A number of coarsened precipitates of Cu6Sn5 segregate around β-Sn grain boundaries. After creep at 80°C and 115°C. the β-Sn particles in the Sn3.9Ag0.6Cu alloy are strongly aligned at approximately 45° to the uniaxial tension, parallel to the maximum shear-stress planes. The powerlaw-defined stress exponent significantly increases with increasing stress in both the 63Sn37Pb and Sn3.9Ag0.6Cu alloys; therefore, the Dorn model is unsuitable for these materials over large stress and temperature ranges. Both sets of experimental data were successfully fit with the present power-law stress-dependent energy-barrier model and the Garofalo model. However, the application of the present power-law stress-dependent energy model resulted in a significantly lower estimated variance as compared to the Garofalo model.

Fatigue and fracture behavior of bulk metallic glass

Tensile, compressive, cyclic tension-tension, and cyclic compression-compression tests at room temperature were systematically applied to a Zr52.5CU17.9Al10Ni14.6Ti5 bulk metallic glass for comprehensive understanding of its damage and fracture mechanisms. Under tensile loading, the metallic glass only displays elastic deformation followed by brittle shear fracture. Under compressive loading, after elastic deformadon, obvious plasticity (0.5 to 0.8 pct) can be observed before the final shear fracture. The fracture strength under compression is slightly higher than that under tension. The shear fracture under compression and tension does not occur along the maximum shear stress plane. This indicates that the fracture behavior of the metallic glass does not follow the Tresca criterion. The fracture surfaces show remarkably different features, i.e., a uniform vein structure (compressive fracture) and round cores coexisting with the radiating veins (tensile fracture). Under cyclic tension-tension loading, fatigue cracks are first initiated along localized shear bands on the specimen surface, then propagated along a plane basically perpendicular to the stress axis. A surface damage layer exists under cyclic compression-compression loading. However, the final failure also exhibits a pure shear fracture feature as under uniaxial compression. The cyclic compression-compression fatigue life of the metallic glass is about a factor of 10 higher than the cyclic tension-tension fatigue life at the same stress ratio. Based on these results, the damage and fracture mechanisms of the metallic glass induced by uniaxial and cyclic loading are elucidated.

Lüders bands propagation of 1045 steel under multiaxial stress state

Inhomogeneous plastic deformation of 1045 steel under monotonic loading was experimentally studied. Thin-walled tubular specimens were used in the experiments and custom-made small strain gages were bonded on the specimen surface to characterize the local deformation. Experiments were conducted under tension, torsion, and combined tension–torsion. During the propagation of Lüders bands, the local deformation experienced two-stage deformation: an abrupt plastic deformation stage followed by a slower deformation process. In some area of the gage section of the specimen, a small amount of initial plastic deformation occurred before the Lüders front reached. During the propagation of Lüders bands, multiple Lüders fronts can be formed. Under tension, torsion, and combined tension–torsion with a constant axial load, the Lüders front was approximately parallel to the material plane of maximum shear stress. When the combined axial-torsion followed a proportional fashion, the stress–extensometer strain responses were dependent on the axial/torsional loading ratio, and the Lüders fronts were oriented differently and propagated along the specimen axis at a different velocity. The local strain was inhomogeneous even at the work-hardening stage. The relationships between the equivalent stress and the equivalent plastic strain were found to be practically identical for all the loading cases studied.

Ultra-high strength above 5000 MPa and soft magnetic properties of Co–Fe–Ta–B bulk glassy alloys

Glassy Co 43Fe 20Ta 5.5B 31.5 alloy rods with glass transition temperature of 910 K, followed by a large supercooled liquid region of 72 K were produced in the diameter range up to 2 mm by copper mold casting. The glassy alloy rods exhibit ultra-high fracture strength of 5185 MPa, high Young’s modulus of 268 GPa, high specific strength of 6.0 × 10 5 N m kg −1 and high specific Young’s modulus of 31 × 10 6 N m kg −1. The fracture strength, specific strength and specific Young’s modulus obtained by compression test are higher than all previous values reported for any crystalline and glassy alloys. The ultra-high strength of over 5000 MPa persists in the temperature range up to 698 K. The fracture occurred on one major shear band which was declined by 44° to the stress axis implying the slight deviation from the maximum shear stress plane. Excellent formability is manifested by large tensile elongation of 1400% and large reduction ratio in thickness above 90% in the supercooled liquid region. The ultra-high strength alloy exhibits simultaneously good soft magnetic properties: low coercivity of 0.25 A/m and an extremely high permeability of 550,000. The novel alloy is promising as a new ultra-high strength material with good deformability and soft magnetic properties.

Effects of strain and strain-rate on the formation of the shear band in metals

An experimental study on the formation of shear bands was carried out in several metals including pure titanium (α-Ti), 304 stainless steel and aluminium (Al-7075-T6) through the compression of cylinder specimens in a Split-Hopkinson-Bar system. The shear band initiation and the distribution within the specimen were examined under different plastic strains and strain rates. The shear band forms along the maximum shear stress plane. Combining the total plastic strain and the angle between the band and the centrally symmetrical axis with the stress-strain curve, the critical strain (e c ) and stress (σ c ) for the formation of the band can be evaluated. It was found that the multiple developing shear bands were stopped in front of the grain boundary in one grain of Al-7075-T6. The present experimental results agree with Armstrong's dislocation pile-up model for the initiation for shear banding. Based on dislocation dynamics, a new constitutive equation is proposed for description of the formation of shear bands. The formation of the band is caused mainly by the strain softening from the sharp increase of mobile dislocations while the thermal softening enhances the development of the shearing process.