Macroscopic model with anisotropy based on micro–macro information

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.     

Double-shearing theory applied to instability and strain localization in granular materials

An account is given of the non-dilatant double-shearing theory of plane flow of granular materials, and it is shown that the theory may be formulated as a special form of hypoplasticity theory. It is shown that according to this theory, simple shearing flows may be supported by a time-independent stress field, but that this solution is unstable. An alternative solution in which the stress in time-dependent is also derived, and shear flow takes place under decreasing shear stress. The strain localization theory of Rudnicki and Rice is applied in conjunction with the double-shearing theory, and it is shown that the theory admits bifurcations in which shear bands form on planes that coincide with the shear plane. Similarly, in pure shear, there exists an unstable solution with time-independent stress, and a solution with time-dependent stress in which the compressive load falls as the deformation increases, and shear bands may form at surfaces on which, according to the Coulomb criterion, the critical shear stress is mobilized. The double-shearing theory for axially symmetric flow is summarized, and applied to compression of a circular cylinder. Again there is an unstable constant stress solution, a time-dependent stress solution in which the axial pressure decreases as the compression of the cylinder increases, and conical shear bands may form on conical surfaces on which the critical shear stress is mobilized.     

Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and Its Alloys

α-titanium and its alloys with a dual-phase structure (α β) were deformed dynamically under strain rate of about 104 s-1. The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate (9×105 s-1) deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations inthe bands can be constricted and developed into cell structures; the phase transformation from α to α2 within the bands was observed, and the transformation products (α2) had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10μm in diameter observed within the bands are proposed to be the results of recrystallization.     

新型高密度合金的组织与性能

基于面心立方固溶体结构和时效强化机理,设计出一种新型高密度合金NiW750。利用SEM,TEM对合金微观组织进行观察,采用分离式Hopkinson压杆实验研究合金在动态压缩条件下的特点,并将此合金与其领域常用材料超高强度钢G50及钨合金93WNiFe进行对比。结果表明:NiW750合金在3种材料中综合性能最好。在750℃/5h时效后,合金抗拉强度可达1746MPa,冲击韧度( a kU )可达113J/cm^2。在动态加载条件下,材料存在应变率硬化效应,其动态流变应力可达到2250MPa左右。试样在与中心轴线成45°方向形成绝热剪切带,在应变率约5500s -1 条件下,带宽80~150μm,过渡区较宽,避免材料剪切断裂过早出现。     

工业纯钛TA2剪切带中微观组织的演变

剪切变形局域化是结构材料经受冲击时的一种重要失效机制,为研究密排六方晶体结构金属材料的绝热剪切带形成条件与扩展规律,采用HOPKINSON压杆装置对精加工后的工业纯钛帽形样品进行高速冲击,利用扫描电镜和高分辨透射电镜研究了剪切带形貌和剪切带微观组织的演化过程.结果表明,工业纯钛TA2经高速冲击后,在帽形样品的韧带部位形成了明显的剪切带,剪切带组织由细小的再结晶晶粒组成,剪切带内没有相变发生,剪切带内的动态再结晶过程通过渐进式亚晶位相差再结晶机制完成.     

Analysis of intrinsic stability criteria for isotropic third-order Green elastic and compressible neo-Hookean solids

Internal stability of isotropic nonlinear elastic materials under homogeneous deformation is studied. Results provide new insight into various intrinsic stability measures, first proposed elsewhere, for generic nonlinear elastic solids. Three intrinsic stability criteria involving three different tangent elastic stiffness matrices are considered, corresponding to respective increments in strain measures conjugate to thermodynamic tension, first Piola–Kirchhoff stress, and Cauchy stress. Primary deformation paths of interest include spherical (i.e., isotropic) deformation, uniaxial strain, and simple shear; unstable modes are not constrained to remain along primary deformation paths. Effects of choices of second- and third-order elastic constants on intrinsic stability are systematically studied for physically realistic ranges of constants. For most cases investigated here, internal stability according to strain increments conjugate to Cauchy stress is found to be the most stringent criterion. When third-order constants vanish, internal stability under large compression tends to decrease as Poisson’s ratio increases. When third-order constants are nonzero, a negative (positive) pressure derivative of the shear modulus often promotes unstable modes in compression (tension). For large shear deformation, larger magnitudes of third-order constants tend to result in more unstable behavior, regardless of the sign of the pressure derivative of the shear modulus. A compressible neo-Hookean model is generally much more intrinsically stable than second- and third-order elastic models when Poisson’s ratio is non-negative.     

Effects of particulate reinforcement and strain‐rates on deformation and fracture behavior of Aluminum 6061‐T6 under high velocity impact

Aluminum matrix composites (AMC) exhibit an attractive combination of mechanical and physical properties such as high stiffness and low density, which favors their utilization in many structural applications. Thus, increasing the structural applications of AMC is the driving force for the need to adequately understand their deformation and failure mechanisms under various types of loading conditions. In this study, plastic deformation of alumina particle reinforced Aluminum 6061‐T6 matrix composite is investigated and compared to that of an un‐reinforced Aluminum 6061‐T6 alloy at high strain‐rates under compressive loading. Dynamic stress‐strain curves are obtained using direct impact Split Hopkinson Pressure Bar (SHPB). Particulate reinforcement increases the deformation resistance of the aluminum alloy at high strain‐rates. Strain localization along narrow adiabatic shear bands is observed in both the reinforced and un‐reinforced alloy. Whereas the microstructure of shear bands in un‐reinforced alloy showed finer grain size compared to that of the bulk material, the shear bands observed in the AMCs are darker than the bulk material and the reinforcing particles are observed to be more closely spaced along the shear bands.     

Comparison of plasticity models for tantalum and a modification of the PTW model for wide ranges of strain,strain rate,and temperature

Four well-known constitutive models for plastic deformation of materials, i.e., Johnson–Cook (JC), Zerilli–Armstrong (ZA), Voyiadjis and Abed (VA), and Preston–Tonks–Wallace (PTW), have been compared with reference to existing deformation data of tantalum in wide ranges of strain, strain rate, and temperature. All of these models reasonably describe the flow stress and the strain-hardening behavior only in the certain ranges of strain, strain rate, and temperature for which the models were developed. The PTW model with appropriate parameters most effectively describes the effects of strain rate and temperature in a wider range, except for strain hardening. The strain-hardening term of PTW was thus modified in the current work and the modified PTW demonstrated very good prediction for the constitutive behavior of tantalum in wide ranges of strain, strain rate, and temperature.     

Adiabatic Shear in annealed and shock-hardened iron and in quenched and tempered 4340 steel

Adiabatic shear localization is a catastrophic failure mechanism which can occur in ductile metals under high strain rate loading. This mechanism is driven by a thermal instability process in which rapid temperature rise due to plastic work couples with thermal softening to cause uniform deformation to collapse into narrow bands of intense shear within which material ductility is exhausted. Adiabatic shear localization is studied in three ferrous metals: annealed Armco and as-received Remco iron, both of which are high purity alpha iron; shock-hardened Remco iron; and 4340 steel quenched and tempered to a range of hardness levels. Using a compressive split-Hopkinson bar, punching-shear experiments were performed at room and elevated initial temperatures at shear strain rates of up to 45000 s^–1. Optical and scanning electron microscopy was performed on the deformed shear specimens to determine the extent of shear localization and mode of failure. Experimental evidence showed that the tempered 4340 steels were susceptible to localization through adiabatic shear banding; however, as-received and shock-hardened Remco iron and annealed Armco iron were not. Finite element simulations of the experiments were performed utilizing a user material subroutine developed as part of this research. This constitutive routine incorporates two adiabatic shear failure criteria, namely (i) maximum shear stress with a minimum critical shear strain rate and (ii) flow localization. These criteria proved to be capable of predicting the onset of an instability; however, the deformation which follows the instability was not predicted well.     

Influence of stress condition on adiabatic shear localization of tungsten heavy alloys

Dynamic deformation and failure behavior of a tungsten heavy alloy (93W) under complex stress condition are studied using a split Hopkinson pressure bar (SHPB) apparatus. Cylindrical, step-cylindrical and truncated-conic specimens are used to generate different stress condition in an attempt to induce strain localization in the alloy. The microstructure of the specimens after tests is examined by optical microscopy and scanning electronic microscopy (SEM). It is found that in all the specimens, except the cylindrical ones, intense strain localization in the form of shear bands is initiated at stress concentration sites. In order to analyze the stress condition of different specimen geometry, finite element simulations are also presented. The Johnson-Cook model is employed to simulate the thermo-viscoplastic response of the material. It is found that dynamic deformation and failure modes are strongly dependent on the geometry of the specimens. The stress condition controlled by specimen geometry has significant influence on the tendency for shear band formation. The adiabatic shear band has general trends to initiate and propagate along the direction of maximum shear stress. It is suggested that further studies on the control of the stress condition to promote shear band formation be conducted in order to improve the penetration performance of the tungsten heavy alloy.     

剪切带内部应变(率)分析及基于能量准则的失稳判据

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。     

On the combined influences of Young''s modulus and stress ratio on the LEFM fatigue crack growth process: A new mechanistic approach

A new mechanistic approach (NMA) was used recently to examine the physical aspects of LEFM (long) fatigue crack growth (FCG) process in crack-ductile materials in stages I and II. In this paper, NMA is extended to examine both the physical and analytical aspects of the combined effects of Young's modulus, E and stress ratio, R, in the same stages of the same materials. It is shown that, (i) with submicroscopic cleavage or reversed shear mechanism operating in the pure form, E is the most influential intrinsic “material” property controlling FCG, (ii) E-dependence of da/dN is a natural consequence of near-crack-tip displacement control proposed previously, and (iii) the demonstrated similarity of FCG curves and the existence of characteristic “pivot points” on these curves for a “class of materials” results from E-influence which continues even at a higher R. A simple analytical model based on “strain intensity factor,” K₀, which contains E-influence implicitly and controls da/dN in all materials irrespective of class, is proposed. Model-predicted K₀-based theoretical values of threshold, “Idealised Master Growth Curves (IMGCs)” and mechanism transition point, all agreed excellently with experimental data for at least three classes of materials, i.e. steels, Al-alloys and Ti-alloys at extreme R-values of 0 and ≥ 0.6. The K₀-parameter concept is used here to raise the status of the analysis of the E-effect from a simple “normalisation” to that of direct data “representation”. Using NMA existing empirical relations are given some sound theoretical base. In addition to aiding in a clearer physical understanding of the FCG process, the unique IMGCs developed for different R-values are considered useful in quick, accurate and conservative life estimations, and performing failure analyses usually required in selection and design of materials.     

Effect of processing parameters on shear bands in non-isothermal hot forging of Ti -6Al -4V

Abstract

The alloy system Ti- 6Al- 4V is the prominent Ti alloy system for aerospace and biomedical applications, as a result of its mechanical property balance and biocompatibility. Since the mechanical characterisation of Ti- 6Al- 4V is strongly sensitive to processing parameters there is relationship between processing variables, i.e. strain rate and temperature, microstructure, and properties under different loading conditions. Two phase (α + β) titanium alloys undergo flow instabilities and are susceptible to shear bands or regions of localised deformation crossing many grains during hot forging under non-isothermal conditions (dies and workpiece at different temperatures). Under such conditions shear bands can be generated even in materials without flow softening attributes. This occurs if the forging parameters lead to large amounts of heat transfer between the dies and the workpiece. This study investigates the occurrence of shear bands during non-isothermal, hot forging of Ti -6Al- 4V in order to evaluate the process parameters that generally lead to shear bands in conventional hot forging of metals. Upset compression tests on cylindrical specimens were conducted in a mechanical press and lateral side pressing tests on long, round bars were performed in either a mechanical press or a hydraulic press. The tests ranged from axisymmetric to plane strain compression. In upset specimens shear bands occurred at an angle of 45° to the compression axis and bands of intense deformation separated chill zones from the deforming bulk. Observation also demonstrated that the fracture might be owing to microvoids nucleated at weak points in sections of the shear surfaces. For plane strain deformation, shear bands were found to initiate along zero extension directions in a manner analogous to the formation and propagation of shear bands in isothermal hot forging. Although the shear band features at hot forging temperatures were similar to each other, there was a difference in the hardness and thickness of the shear bands depending on deformation mode, amount, and temperature.     

Shear Band Evolution in Polymer Bonded Explosives Subjected to Punch Loading

The shear band development and potential hot‐spot initiation of polymer‐bonded explosive were investigated under low‐rate punch loading and combined punch and thermal loading. The digital image correlation method was used for deformation analysis. The obtained results showed that the initiation and development of shear bands at room temperature occur in three stages and demonstrated that the material suffers a prolonged shear stress concentration in a local area. Large shear was shown to lead to the formation of slip bands in the hard‐phase area, indicating that this region has the highest potential to initiate hot‐spots even under low‐rate punching. For high temperatures, the initiation and development of shear bands occur in two stages, with the resulting flow field being close to Hill's solution except for a small area directly underneath the punch. Large plastic flow rate was shown to be another important feature besides shear banding.     

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Dry granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasi-static, large deformation. This system is studied in the presence of contact adhesion, using the discrete element method (DEM). Several continuum fields like the density, the deformation gradient and the stress tensor are computed locally and are analyzed with the goal to formulate objective constitutive relations for the flow behavior of cohesive powders. From a single simulation only, by applying time- and (local) space-averaging, and focusing on the regions of the system that experienced considerable deformations, the critical-state yield stress (termination locus) can be obtained. It is close to linear, for non-cohesive granular materials, and nonlinear with peculiar pressure dependence, for adhesive powders—due to the nonlinear dependence of the contact adhesion on the confining forces. The contact model is simplified and possibly will need refinements and additional effects in order to resemble realistic powders. However, the promising method of how to obtain a critical-state yield stress from a single numerical test of one material is generally applicable and waits for calibration and validation.     

A uniaxial nonlinear viscoelastic constitutive model with damage for M30 gun propellant

The nonlinear viscoelastic mechanical response of a conventional tank gun propellant, M30, is modeled using a “modified superposition integral” that incorporates the effects of microstructural fracture damage. Specifically, a linear, time-dependent kernel is convolved with the first-time derivative of a power-law function of stress and a damage “softening” that accounts for damage evolution by a microcrack growth mechanism. The microcrack damage function is a master curve formed from shifted isothermal, compressive, uniaxial constant strain rate (0.01 s⁻¹ to 420 s⁻¹) data on solid, right-circular cylinders of M30 gun propellant. An attractive feature of the model is its ability to predict work-softening behavior under conditions of monotonically increasing deformation. Time-dependent predictions of stress versus time, failure stress versus failure time, and failure stress versus strain rate, quantitatively agree with experimental results from constant strain rate tests on the propellant. Theoretical predictions of time-dependent stresses for Heaviside and “ballistic-like” strain histories are also provided.     

Morphology of adiabatic shear bands in cylindrical specimens of AISI 4340 steel impacted by Hopkinson pressure bar

Abstract

Cylindrical specimens of AISI 4340 steel, which were heat treated by quenching in oil followed by tempering at either 315 or 425°C, were impacted in a Hopkinson pressure bar at different impacting speeds. It was found that when strain and strain rate reached certain values, adiabatic shear bands (or plastic deformation zones) were formed in the specimens. The adiabatic shear bands appeared either in a circle on the transverse section, a hyperbola on different longitudinal sections without the central axis of the cylinder, and a triangle on the longitudinal section through the central axis of the cylinder. From these observations, it can be concluded that the plastic deformation localisation zone is limited in a thin conical shell in three dimensions. It was further confirmed that the adiabatic shear bands initiated along the maximum shear stress directions. In addition, the adiabatic shear bands in the specimens tempered at 315°C appeared white, while those in specimens tempered at 425°C had deformation characteristics. This indicates that the appearance of adiabatic shear bands is related to the hardness and microstructure of the tested steel.     

Continuous shear thickening and discontinuous shear thickening of concentrated monodispersed silica slurry

Concentrated slurry is known to exhibit shear thickening behavior, in which viscosity increases as the shear rate ascends. However, to identify the differences between this shear thickening behavior and rapid increases in viscosity (such as the dilatancy behavior of starch, sand, and other concentrated slurries) and the smooth increases in viscosity exhibited by concentrated slurries, this research investigated the rheological behavior of a polyethylene glycol suspension containing monodispersed silica particles with a size of 2.5 μm. The results found that the increases in viscosity as the shear rate ascends or the increases in elasticity as the strain ascends change consecutively from smooth and reversible behavior (i.e., continuous shear thickening (CST)) to rapid and irreversible behavior (i.e., discontinuous shear thickening (DST)) simply by increasing the concentration of the slurry, even in the case of concentrated slurries comprising of the same particles. DST is a manifestation of dilatancy in which a jamming transition occurs due to collisions between particles. Because CST transitions successively to DST, and the on-set shear stress of shear thickening of CST is almost the same with that of DST, shear thickening in the CST region may, therefore, also be regarded as the result of friction due to collisions between particles. This supports the research by Seto, Mari, Poon et al., which stated that shear thickening occurs due to friction from particle collisions.     

Rheology of Superplastic Ceramics

Constitutive equation of rheology describing a phenomenological level of superplastic deformation as functional correlation between tensor components of stress and strain rate has been analyzed for the case of superplastic ceramic flow. Rheological properties of material are taken into account by means of scalar rheological coefficients of shear and volume viscosity, which are functions of temperature, effective stress (or strain rate) and density of material.