Formation Of Adiabatic Shear Bands Research Articles

Global existence and quenching for a model of adiabatic shear band formation

Global existence and quenching for a model of adiabatic shear band formation

Adiabatic shear band formation in Al-SiCw composites

The objective of this study is to investigate the adiabatic shear band formation in 2124-T6 aluminum composites reinforced with SiC whiskers. The composites were deformed at high strain rates by ballistic impact. Adiabatic shear bands initiated from cracks near the impacted region were observed. The shear bands tended to propagate along the extrusion direction, since they were blocked by SiC whiskers. Within the shear bands, microvoids and microcracks formed, presumably by the temperature rise. Shear bands, together with microvoids and microcracks, deteriorated the impact resistance of target materials. Finally, performance of the composites against ballistic impact loading was discussed by comparing the behavior of shear banding with dynamic fracture toughness.

Adiabatic shear band formation during dynamic torsional deformation of an HY-100 steel

Dynamic torsion experiments have been conducted on thin-walled tubular specimens of a tempered martensitic HY-100 steel, causing adiabatic shear bands to form. The strain rates imposed were ∼ 10 3 s −1 and local temperature increases up to 600°C within the shear bands were measured. The shear band microstructure was examined by transmission electron microscopy (TEM), revealing two distinct microstructures. In some regions, highly elongated narrow subgrains extended in the shear direction, while in other regions, fine equiaxed cells were characteristic. The proportions of the two microstructures varied for different specimens, and the observations were interpreted to indicate that a process of dynamic recovery accompanying large deformation and a high temperature rise occurred within the shear band. Although thermal effects were apparent, there was no evidence to support a phase transformation to austenite followed by martensite formation. On the basis of present findings, it appears that the thermodynamic stability of the original microstructure can influence the tendency toward shear localization under dynamic loading conditions.

On the measurement of local strain and temperature during the formation of adiabatic shear bands

A series of experiments was performed to study the process of adiabatic shear band initiation and formation in steels. The steels include a low carbon cold-rolled steel and three martensitic steels (HY-100 and two tempers of AISI 4340 VAR steel of varying hardness). In each case the specimens are machined as thin-walled tubes that are deformed dynamically in a torsional Kolsky bar (torsional split Hopkinson bar). Shear band initiation and formation are observed by ultrahigh-speed photography of a fine grid pattern deposited on the specimen's surface. It is shown that the critical strain for shear band initiation depends on the magnitude of a preexisting defect, in accordance with the predictions of Molinari and Clifton, J. Appl. Mech., 54 (1991) 806–812. Ultrahigh-speed photographs of the grid pattern show that local strains of 100–1000% may be attained and that the local strain rates reach 10 5 s −1. In addition, the local temperature in the shear band is measured by employing an array of small high-speed infrared detectors that provide a plot of temperature as a function of time and position. Within the shear band region, temperatures of 600 °C have been measured.

Numerical experiments on adiabatic shear band formation in one dimension

Abstract Adiabatic shear band formation in an elastic, thermoviscoplastic, simple material is studied in the context of unidirectional shearing of a slab. The effect of varying the thermal softening behavior of the material on localization strain and postlocalization morphology is studied for a rigid, perfectly plastic material; the material parameters are appropriate for a high-strength steel. In this case it is demonstrated that localization of the strain rate can be transient . A coupling between linear-elastic response and the basic thermoviscoplastic localization mechanism is explored in the absence of strain hardening. Last, the flow law is modified to include strain hardening in order to simulate a high-rate torsion test on OFHC copper. In this case localization is initiated by thermal boundary layer diffusion and the solution takes on a complex, apparently nonperiodic, postlocalization morphology quite different from that in the perfectly plastic cases.

Shear band susceptibility: Work hardening materials

Abstract A phenomenological model of a rigid, work hardening, plastic material, with rate hardening and thermal softening, is analysed to determine susceptibility to the formation of adiabatic shear bands. The approach used is to examine perturbation equations that are linearized about a homogeneous solution of the full nonlinear problem. It is found that, in general, solutions to these linearized equations exhibit a strong initial boundary layer in time and that the traditional approach, that is, analysis of frozen eigenvalues, cannot be relied upon to determine stability against initial perturbations. A variety of special techniques are used to approximate solutions for the fully time-dependent behavior. These techniques include asymptotic expansions of exact representations, WKB analysis of the equations that govern the Fourier components, and numerical analysis by spectral methods of both the linearized and nonlinear equations. Although solutions to the linearized eqautions are valid only for finite time when perturbations are growing, it is still possible to obtain a basic scaling law for comparing susceptibility of different materials.

Formation of adiabatic shear bands in eutectoid steels in high strain rate compression

A detailed study has been made of the localized adiabatic shear band formation in a plain carbon and a low alloy eutectoid rail steel subjected to high strain rate compression at initial deformation temperature of 298, 453 and 623 K. Localized adiabatic shearing due to impact is found to be favored with alloy steels and decreasing temperatures of deformation. It is shown that the deformed and transformed shear bands rather than being two separate phenomena are only an outcome of the extent of adiabatic strain localization occuring during deformation; the deformed bands forming with lesser localized flow and the transformed bands forming with extensive localized flow. This study explains convincingly the formation of the white phase on the surface of the rail heads during wheel-rail contact as due to the coalescence of the numerous adiabatic shear bands.

Mechanical properties and microstructure of extruded 7075 aluminium alloy

The hot deformation behaviour of Stir cast 7075 alloy was studied using processing map technique. The map has been interpreted in terms of the microstructural processes occurring in situ with deformation, based on the values of a dimensionless parameter η which is an efficiency index of energy dissipation through microstructural processes. An instability criterion has also been applied to demarcate the flow instability regions in the processing map using another parameter (ξ). Both the parameters (η and ξ) were computed from the experimental data generated by compression tests conducted at various temperatures and strain rate combinations over the hot working range (300–500 °C and 0.001–1.0 s−1) of the present material. The processing map exhibits one distinct η domains without any unstable flow conditions under the investigated temperature and strain rate conditions. The dynamic recrystallization zone and instable zones, i.e. adiabatic shear band formation, interface crack, and wedge cracking, were identified in the processing map. Microstructural examination was performed for validation. The processing maps can be used to select optimum strain rates and temperatures for effective hot deformation of 7075 alloy.

DYNAMICS OF ADIABATIC SHEAR

The formation of adiabatic shear bands is examined with an approximate analytic model. The shear band is viewed as a propagating feature with a well-defined front. The shear band is further partition into a shear-band process zone within which most of the adiabatic heating and shear stress relaxation occurs, followed by a quasisteady zone within which little dissipation occurs. Although a one-dimensional analysis of the shear-band dynamics is initially pursued, the analysis is then used to calculate properties of the inherently two-dimensional shearband process zone. The length and width of the process zone is calculated along with the shear displacement. The model is further used to calculate the energy dissipation within the shear-band process zone. The flow field within the vicinity of the process zone is also examined. Calculated properties of the shear-band process zone are compared with available experimental data.

A Mechanism for Shear Band Formation in the High Strain-Rate Torsion Test

A numerical study of a one-dimensional model of the high strain-rate torsion test shows that a moving boundary of rigid unloading, starting from the ends of the thin-walled tubular specimen, is a plausible mechanism for adiabatic shear band formation during the test. Even though the dimensionless thermal diffusivity parameter is very small, the moving boundary is due to heat transfer from the specimen through its ends, which are assumed to be isothermal heat sinks. The mathematical model is based on a physical model of thermoelastic-plastic flow and a phenomenological Arrhenius model for the plastic flow surface. The numerical technique used is the semi-discretization method of lines.

Transition in the Failure Behavior of Dynamically Shear Loaded Cracks

An experimental technique is presented for subjecting cracks to high rates of shear (mode-II) loading. By means of the shadow optical method of caustics, the dynamic crack tip loading conditions are investigated for both the phase of loading and the subsequent phase of failure. A failure mode transition is observed when the loading rate exceeds a certain limit. At low rates failure is controlled by fracture processes. At high rates, failure is controlled by the formation of adiabatic shear bands, a process not considered by fracture mechanics so far.

Approximate analysis for the formation of adiabatic shear bands

Parametric solutions are given for the formation of adiabatic shear bands in the context of the onedimensional nonlinear theory where inertia and elasticity are ignored. When heat conduction is also ignored, the exact solution reduces completely to a sequence of quadratures. For a perfectly plastic material with heat conduction, an implicit parametric solution is also constructed. This is similar to the previous one in many ways, but now it involves two quadratures, a single nonautonomous first-order ODE. and two functions that obey heat equations. This solution appears to be very accurate (compared to the full finite element solution) until the time of stress collapse. Results indicate that for weak rate hardening of the power law type, intense localization depends strongly on the initial characteristics of thermal softening and not at all on the high temperature characteristics. Within the context of rigid/perfect plasticity, a scaling law for the critical strain is given, and a figure of merit is defined that ranks materials according to their tendency to form adiabatic shear bands.

Temperature measurements and photographic observations of evolving adiabatic shear bands

Experiments are described in which the local temperature and local strain distribution are measured during the formation of adiabatic shear bands in steels. The specimen employed is a short thin-walled tube loaded dynamically in a torsional Kolsky bar (split-Hopkinson bar). Local temperature is determined by measuring the infrared radiation emanating at 12 neighboring points on the specimen's surface, including the shear band area. Indium-antimode elements are employed for this purpose to give the temperature history during deformation. In addition, high-speed photographs are made of a grid pattern deposited on the specimen's surface, thus providing a measure of the strain distribution at various stages during shear band formation. The results provide a picture of the developing strain localization process, of the temperature history within the forming shear band, and of the consequence loss in the load capacity. It appears that plastic deformation follows a three-stage process that begins with a homogeneous strain state followed by a generally inhomogeneous strain distribution, and finally by a narrowing of the localization into a fine shear band. Experimental results are compared with predictions of various models.

A numerical analysis for the formation of adiabatic shear bands including void nucleation and growth

A new numerical model for the formation of adiabatic shear bands in thin-walled tubular torsion specimens has been developed by considering void nucleation and growth together with thermo-plastic deformation. Using this model, the distributions of the shear strain, strain rate and temperature in the gauge section can be obtained. This model was applied successfully to the explanation of non-central shear banding in low carbon steel and titanum. For materials with low thermal conductivity such as steel and titanium, geometrical imperfections play a more significant role than thermal softening in the location of shear bands.

Adiabatic shear morphology at very high strain rates

The formation and distribution of adiabatic shear bands at very high strain rates is investigated through an elastic-viscoplastic model with thermal coupling, accounting for inertia effects and heat conduction. The calculations provide the band widths, spacing and critical growth time; the results are found to be in good agreement with available experimental data. Special attention is paid to inertia, rate sensitivity, thermal softening and conductivity effects on the morphology of the heterogeneous shear deformation. Shear band interactions are explored.

Localization of plastic deformation in high-speed shock deformation of aluminum and AMg6 alloy

1. Localization of deformation on the microlevel is detected in aluminum at all the three strain rates examined, whereas in AMg6 alloy it was detected only at the highest strain rate (900 m/sec). In AD1 aluminum, localization of deformation is reflected in the local enlargement of the elongated dislocation cells, and in AMg6 alloy it results in the fragmentation of deformed microregions. 2. The high stacking fault energy and the absence of sufficiently effective obstacles to the high-speed motion of the dislocations should be regarded as the criteria for the formation of adiabatic shear bands in pulsed deformation.

Effect of impact on the grinding media and mill liner in a large semiautogenous mill

The introduction of large semiautogenous mills to grind larger pieces of ore necessitates the use of large diameter grinding balls. Grinding balls as large as 127 mm (5 in) in diameter are not rare. The increased height of fall of such grinding balls in these larger mills results in severe impact between the grinding balls and also between the grinding balls and the mill liners. The effect of this impact on the mill liner and the 127 mm diameter grinding balls used in a 8.2 m diameter semiautogenous mill were studied. It was observed that the repeated severe impacts resulted in the formation of adiabatic shear bands below the surface of both the mill liner and the grinding balls. Severe impact also resulted in fatigue failure of the mill liners and a phase transformation below the surface of the grinding balls due to the generation of high temperature. In smaller mills, using smaller grinding balls, considerable work hardening was observed beneath the surface of the grinding balls. The extent of the work hardening increased with increase in the ball and mill diameter.

On stress collapse in adiabatic shear bands

T he dynamics of adiabatic shear band formation is considered making use of a simplified thermo/visco/plastic flow law. A new numerical solution is used to follow the growth of a perturbation from initiation, through early growth and severe localization, to a slowly varying terminal configuration. Asymptotic analyses predict the early and late stage patterns, but the timing and structure of the abrupt transition to severe localization can only be studied numerically, to date. A characteristic feature of the process is that temperature and plastic strain rate begin to localize immediately, but only slowly, whereas the stress first evolves almost as if there were no perturbation, but then collapses rapidly when severe localization occurs.

The initiation and growth of adiabatic shear bands

A simple version of thermo/viscoplasticity theory is used to model the formation of adiabatic shear bands in high rate deformation of solids. The one dimensional shearing deformation of a finite slab is considered. For the constitutive assumptions made in this paper, homogeneous shearing produces a stress/strain response curve that always has a maximum when strain and rate hardening, plastic heating, and thermal softening are taken into account. Shear bands form if a perturbation is added to the homogeneous fields just before peak stress is obtained with these new fields being used as initial conditions. The resulting initial/boundary value problem is solved by the finite element method for one set of material parameters. The shear band grows slowly at first, then accelerates sharply, until finally the plastic strain rate in the center reaches a maximum, followed by a slow decline. Stress drops rapidly throughout the slab, and the central temperature increases rapidly as the peak in strain rate develops.

Approximate linear stability analysis of a model of adiabatic shear band formation

The formation of adiabatic shear bands in ductile metals under dynamic loading conditions is generally thought to result from a material instability, which is associated with a peak in the curve of engineering plastic flow stress vs. engineering shear strain. This instability arises from the effect of thermal softening, caused by irreversible adiabatic heating, which counteracts the tendency of the material to harden with increasing plastic strain. An approximate linear stability analysis of a one-dimensional rigid-thermoviscoplastic model, based on data taken from dynamic torsion experiments on thin-walled tubes of mild steel, shows that shear band formation in this situation can be interpreted as a bifurcation from a homogeneous simple shearing deformation which occurs at the peak in the homogeneous stress vs. strain curve. The asymptotic method of multiple scales is used to show that the growth rate of small perturbations on the homogeneous deformation is controlled by the ratio of the slope of the homogeneous stress vs. strain curve to the material viscosity, i.e., the rate of change of the plastic flow stress with respect to the strain-rate. In addition, it is shown that this growth rate is essentially independent of wavelength in any small perturbation. Numerical methods are used to show that this growth rate beyond the bifurcation point may not be sufficiently large for the model to account for the experimental data, and some suggestions are made on how to modify the constitutive equation so that it better fits the experimental data.