Shear band formation in plane strain compression

Shear band formation during plane strain compression of single crystals and polycrystals of an Al-3 wt% Cu alloy was studied. X-ray and electron diffraction, optical microscopy, and electron (TEM/STEM) microscopy were used to document the structure and micromechanisms of the localization process. Complementary finite element studies were performed using the measured single crystals' single slip system strain hardening data. The experimental observations and the computed deformation response are in very close agreement, and indicate that localization, through macroscopic shear band formation, occurs in continuously strain hardening, damage-free material. Shear band formation was preceeded by the development of very coarse slip which, like the shear bands, propagated across entire grains and, in single crystals, across the entire crystal. The computations and experiments showed that geometrical softening, caused by nonuniform lattice reorientation, is an important micromechanical influence on the localization process in both single crystals and polycrystals. Also, the propagation of shear bands across grain boundaries in polycrystals was looked at experimentally and computationally. Particular attention was paid to the crystallography of shear band transmission through grain boundaries.     

An analysis of nonuniform and localized deformation in ductile single crystals

The nonuniform and localized deformations of ductile single crystals subject to tensile loading are analyzed numerically. The crystal is modelled by a rate independent, elastic-plastic relation based on Schmid's law which precisely accounts for lattice rotations. Both self hardening and latent hardening of the slip systems are included in the model. The crystal geometry is idealized in terms of a planar double slip model. Initial imperfections are specified in the form of slight thickness inhomogeneities and the calculations follow the crystal deformation through diffuse necking and the formation of shear bands. The pattern of shear bands depends on the initial imperfection, but, independent of the particular small imperfection, the material planes of the bands are inclined at a characteristic angle to the slip planes. Also, the lattice misorientation across the shear band, which is such as to cause geometrical softening of the bands, is not sensitive to the imperfection form. For high strength, low hardening crystals a comparison with existing experimental data shows remarkably good qualitative and quantitative agreement between the calculations and observations. We also model a relatively soft high hardening crystal which undergoes more diffuse necking than the strong high hardening crystal. Diffuse necking leads to lattice rotations which produce geometrical softening and hence promote shear band formation. Furthermore, we carry out a calculation for a high strength low hardening crystal with the latent hardening rate prescribed somewhat larger than for isotropic hardening. In this case a ‘patchy’ pattern of slip emerges. However, the course of shear band development is unaffected.     

Material rate dependence and localized deformation in crystalline solids

Nonuniform deformations of rate dependent single crystals subject to tensile loading are analyzed numerically. The crystal geometry is idealized in terms of a planar double slip model. In addition to allowing the effects of material rate sensitivity to be explored, the present rate dependent formulation permits the analysis of a range of material strain hardening properties and crystal geometries that could not be analyzed within a rate independent framework. Two crystal geometries are modeled. One is a planar model of an f.c.c. crystal undergoing symmetric primary-conjugate slip. For this geometry, a direct comparison with a previous rate independent calculation shows that material rate sensitivity delays shear band development significantly. Our present rate dependent formulation also enables a more complete exploration of the effects of high (i.e. greater than Taylor) latent hardening ratios on “patchy” slip development. In particular we show that strong latent hardening and patchy slip can give rise to kinematical constraints that prevent shear bands from propagating completely across the gage section. The second geometry models a b.c.c. crystal oriented so that there is approximately a double mode of slip with the slip systems inclined by more than 45° to the tensile axis. This calculation displays the formation of a localized band of conjugate slip. The lattice rotations accompanying this mode eventually lead to a decrease in the resolved shear stress on the more active system in the band so that the bands do not accumulate large strains and catastrophic shear bands do not form. The implications of material rate sensitivity for uniqueness are also discussed with reference to implications for the prediction of mechanical properties of polycrystals.     

Geometrical effects in the inhomogeneous deformation of ductile single crystals

Non-uniform deformation in ductile single crystals is studied using a simple model for a crystal undergoing symmetric double slip in tension. The model, when interpreted in terms of the crystallography of face-centred or body-centred cubic crystals, demonstrates, in particular, that shear bands may form when the slip plane workhardening rates are positive and, thus, without either ideal plasticity or strain softening. Localized plastic flow is viewed as a shearing bifurcation in the uniform tensile deformation of the crystal model and the critical stresses and workhardening rates for localized shear are worked out. The importance of yield vertexes and geometrical softening phenomena related to lattice rotations during deformation are given special attention in the development of the constitutive laws and in the results for the critical conditions for localized shear.     

Stability Problems in Soil‐Structure Interfaces: Experimental Observations and Numerical Study

This article presents experimental results of tests on soil‐structure interfaces carried out on a new “ring simple shear” apparatus specially developed at Ecole Nationale des Ponts and Chaussées, Paris, for such studies. In this apparatus strain localization takes place at or near the surface of the rotating steel drum that forms the soil‐structure interface. Depending on the conditions of tests, in terms of surface roughness, special instrumentation is capable of recording local as well as global response. Three tests on Hostun gravel at different confining radial pressures have been conducted and a deviatoric hardening model with nonassociated flow rule has been adopted for their numerical simulations. The point of inception of strain localization based on various theoretical considerations has been discussed and experimentally verified. The post‐peak behavior is simulated by employing a homogenization technique in which the soil sample is treated as a composite material consisting of a shear band surrounded by intact material. A deviatoric strain softening model has been adopted for the shear band. It is shown that the mechanism of failure and the response of the soil sample is reasonably well simulated. Although there are some concerns regarding the homogeneity of the sample, the post‐peak stage and the overall mechanical response of gravel‐steel interface are rather well reproduced.     

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.     

Conditions for Compaction Band Formation in Porous Rock Using a Two-Yield Surface Model

Compaction bands, a form of localized deformation found in field and laboratory specimens of high porosity rock, consist of planar zones of pure compressional deformation that form perpendicular to maximum compression. Experimentalists report compaction bands and/or shear bands (angled to maximum compression) in high porosity sandstone during a transitional loading regime with multiple active deformation mechanisms. Conditions for localized deformation are determined using a two-yield surface constitutive model and bifurcation theory. The shear yield surface corresponds to a dilatant, frictional mechanism while the cap corresponds to a compactant mechanism. Unlike a single yield surface model, the two-yield surface model predicts both experimentally observed band types for reported values of key material parameters. Observed and predicted shear band angles generally agree. Theory suggests that shear band formation may coincide with activation of the shear yield surface by a previously active cap. If the bulk hardening modulus, k, equals zero (corresponding to localization on the peak or plateau of the mean stress–volume strain curve) compaction band conditions are more favorable than for small positive values of k.     

The formation of cell structures in fatigued iron crystals

Single crystals of α-Fe have been fatigued in constant stress amplitude reversed plane bending. TheS-N curve, the plastic strain amplitude variation, and the dislocation substructures developed in the crystals during fatigue have been studied. The formation of a cell structure was found to occur once a critical dislocation density had accumulated, the nature of which was influenced by the crystallography of the specimen and underwent changes with continued testing. The evolution of a continuous cell structure with testing coincided with a large decline in the level of plastic strain amplitude, and it appears that it is these substructures which account for fatigue hardening. From the observations of crack formation and the mode of dislocation movement during saturation, a mechanism for crack initiation is suggested.     

The structure of adiabatic shear bands in metals: A critical review

A review of the structure of adiabatic shear bands in metals is presented. Shear bands are redefined as being either “transformed” or “deformed” according to how the prior shear deformation is partitioned between two discrete zones in metallographic section. Metals are then classified by their general tendency to form these two types of shear zone during adiabatic shear deformation, based on available literature. Metals of low thermal diffusivity and of low resistance to adiabatic shear localization tend more readily to form “transformed” shear bands; these metals are also capable of transforming to other phases at elevated temperature (and pressure), and forming martensite on rapid cooling to room température. Shear bands of “transformed” appearance can also form in other metals during extremely localized adiabatic shear deformation resulting from the effect of localized plastic flow and elevated temperature alone. The role of phase transformations themselves in promoting the formation of “transformed” shear bands cannot be isolated using the arguments presented in this work, and may even by incidental.     

Microstructural study of adiabatic shear band

This article presents a study of the microstructural development of the adiabatic shear band in an HY-100 steel. The steel was deformed at a high strain rate by ballistic impact, and subsequent metallographic observations along with electron microscopy were performed. A number of white- etched shear bands were found near the perforated region, and three typical microstructural features of the adiabatic shear band were observed: elongated grain structure at the boundary between the shear band and matrix, fine equiaxed grain structure with high dislocation densities in the middle of the shear band, and relatively coarse-grained structure located between the above two structures. These microstructures might be formed in an extremely short time by the combined effects of the large temperature rise and the highly localized deformation. Since very complex phenomena might occur within the shear band, possible mechanisms, such as dynamic recovery and strain-induced dynamic phase transformation, are suggested to explain the micro- structural development of the adiabatic shear band.     

Non-schmid effects on the behavior of polycrystals—with applications to ni3al

The elastoviscoplastic single crystal constitutive model incorporatingnon-Schmid effects developed by Dao and Asaro (Mater. Sci. Eng. A, 1993, vol. 170, pp. 143-60) is introduced into Asaro and Needleman’s (Acta Metall., 1985, vol. 33, pp. 923-53) Taylor-like polycrystal model as well as Harren and Asaro’s (J. Mech. Phys. Solids, 1989, vol. 37, pp. 191-232) finite element polycrystal model. The single crystal non-Schmid effects, strain hardening, latent hardening, and rate sensitivity, are all described on the individual slip system level, while polycrystal mechanical properties on macroscale are predicted. In general, it is found that non-Schmid effects can have important influences on the “constant offset plastic strain yield surfaces,” stress-strain behavior, texture development, and shear band formation. Finite element calculations show that with moderate non-Schmid effects, localized deformation within a polycrystal aggregate tends to initiate earlier and form sharper and more intense shear bands. Heavy shear banding is found to produce less pronounced textures, which is consistent with existing experimental evidence on Ni₃Al. Examples with Ni₃Al demonstrate that the kind of non-Schmid effects existing in Ni₃Al can increase the generalized Taylor factor to values much higher than 3.06, raise the polycrystal strain hardening rate much higher than that which would be obtained using Schmid’s rule, and influence the deformation texture.     

Mn-Si-Cr系Q&P钢的准静态、动态力学行为对比

利用万能试验机和分离式霍普金森压杆装置(SHPB)对Mn-Si-Cr系Q&P钢分别进行了准静态和动态压缩试验。在应变速率为0.001、0.01、0.1 s-1和900、1 500、2 200、3 000 s-1情况下分别得到了准静态和动态压缩真应力-真应变曲线,并利用扫描电子显微镜进行压缩后的显微组织和断口分析,利用X射线衍射仪(XRD)对压缩变形试样进行物相分析。结果表明,准静态和动态压缩变形条件下,试验钢的真应力-真应变曲线均可大致分为弹性变形和塑性变形2个阶段,且没有明显的屈服平台。准静态压缩条件下应变速率强化效果不明显但应变强化效应较显著。动态压缩条件下应变强化效应不明显,但展现出一定的应变速率强化效应。准静态变形后,试样中心区域板条组织倾向沿近水平方向(垂直于压缩方向)定向排布。动态变形后,约有1/3试样发生了断裂,未发生断裂的试样中心出现45°方向剪切带,其附近板条组织发生了“屈曲”。准静态变形后残余奥氏体含量下降明显,而动态压缩试样中,残余奥氏体含量只有略微下降,且块状M/A岛内部出现扭曲变形与开裂,这可能是导致部分试样断裂的诱因。动态压缩破坏试样断口整体呈现45°剪切断裂,一端发生微孔聚集性断裂,另外一端发生剪切断裂。     

Mn-Si-Cr系Q&P钢的准静态、动态力学行为对比

利用万能试验机和分离式霍普金森压杆装置(SHPB)对Mn-Si-Cr系Q&P钢分别进行了准静态和动态压缩试验。在应变速率为0.001、0.01、0.1 s-1和900、1 500、2 200、3 000 s-1情况下分别得到了准静态和动态压缩真应力-真应变曲线,并利用扫描电子显微镜进行压缩后的显微组织和断口分析,利用X射线衍射仪(XRD)对压缩变形试样进行物相分析。结果表明,准静态和动态压缩变形条件下,试验钢的真应力-真应变曲线均可大致分为弹性变形和塑性变形2个阶段,且没有明显的屈服平台。准静态压缩条件下应变速率强化效果不明显但应变强化效应较显著。动态压缩条件下应变强化效应不明显,但展现出一定的应变速率强化效应。准静态变形后,试样中心区域板条组织倾向沿近水平方向(垂直于压缩方向)定向排布。动态变形后,约有1/3试样发生了断裂,未发生断裂的试样中心出现45°方向剪切带,其附近板条组织发生了“屈曲”。准静态变形后残余奥氏体含量下降明显,而动态压缩试样中,残余奥氏体含量只有略微下降,且块状M/A岛内部出现扭曲变形与开裂,这可能是导致部分试样断裂的诱因。动态压缩破坏试样断口整体呈现45°剪切断裂,一端发生微孔聚集性断裂,另外一端发生剪切断裂。     

Deformation Mapping and the Role of Carbides on the Microstructure and Properties of Evolved Adiabatic Shear Bands

Impacting hardenable steel such as 4340, results in the formation of adiabatic shear bands (ASBs). Previous studies have shown that the presence of carbides/second-phase particles in the pre-deformation microstructures of 4340 steel increases their susceptibility to the formation of ASBs. The current study examines the role of carbides on the microstructure and properties within evolved ASBs in 4340 steel after impact. Geometric phase analysis was used to map local deformation fields within the evolved ASBs. It was observed that carbide fragmentation due to plastic deformation of carbides produces both residual carbides and residual carbide particles in regions away from the shear bands. Extensive carbide fragmentation produces fine residual carbide particles which are redistributed within the ASBs. This is attributed to strain localization within the ASBs which result in higher local strain and strain rates within the shear bands than in regions outside the bands. In addition, it is observed that the residual carbide particles trap and pin dislocations within the shear bands and contribute to an increase in local hardening. A more homogenous distribution of narrower and shorter rotational and shear-strain fields were revealed by the local deformation maps within the evolved ASBs. Lattice deformation mapping revealed that the ferrite matrix, prior to impact, had broader and longer rotational and shear-strain fields perpendicular to the direction of impact. This is attributed to lattice-invariant deformation and shape deformation processes that occur on specific crystallographic planes during martensitic transformation. It is concluded that strain localization during high strain rate deformations does not occur on specific crystallographic planes. This results in a more regular distribution of internal lattice rotational and strain fields within the evolved ASBs.     

The study of adiabatic shear band instability in a pearlitic 4340 steel using a dynamic punch test

The formation of adiabatic shear band instabilities in a pearlitic 4340 steel using a dynamic punch test has been studied. The dynamic punch-impact test produced white-etching adiabatic shear bands. The average strain of 0.5 was sufficient to produce adiabatic shear bands in this steel at an average strain rate of 18,000 s⁻¹. Nanohardness variations found across the adiabatic shear band are thought to be caused by the fragmentation and spheroidization of the Fe₃C and the overall deformation and work hardening of the pearlitic microstructure. The cracks formed at the termination of the adiabatic shear band caused the sample to fracture in a ductile mode.     

Behavior of an Austenitic–Martensitic VNS9-Sh Sheet TRIP Steel during Static and Cyclic Deformation

The properties of austenitic–martensitic VNS9-Sh (23Kh15N5AM3-Sh) sheet TRIP steel during static and cyclic loading are studied. The specific features of the mechanical behavior of the steel during static tension that are related to shearing, twinning, and martensite formation processes are detected. The static stress–strain curve of the steel has a developed microyield stage, a long yield plateau, and a serrated stage of strain hardening (Portevin–Le Chatelier effect). The shear mechanisms at the initial stages of cyclic deformation and fatigue crack propagation mechanisms are investigated.