Adiabatic shear localization in α-titanium: experiments, modeling and microstructural evolution

The localization of dynamic shearing deformations in α-titanium is examined using a novel experimental technique (the compression-torsion Kolsky bar) that allows the recovery of specimens within which an adiabatic shear band has been grown as the result of a single torsional pulse. The specimens are circumferentially notched thick-walled cylinders that are subjected to simultaneous, independently controlled, dynamic compression and torsion. Explicit finite element computations are performed to obtain the stress, strain, temperature and pressure distributions within the specimens under the measured boundary conditions. The constitutive behavior input to the computational simulations is obtained from independent high-strain-rate experiments (involving only homogeneous deformations) on the same material. Shear band growth and microstructural evolution in the specimens are investigated by sectioning the specimens at different depths from the outer radial surface. TEM observations across the shear bands reveal the following microstructural evolution: (a) planar dislocation motion and twinning; (b) grouping of dislocations into cells; (c) formation of elongated subgrains along the shear direction, and (d) development of equiaxed nanocrystalline grains 50- in diameter. The microstructures observed are analogous to those reported for severely cold-rolled metals.     

帽型试样动态绝热剪切破坏演化分析

利用分离式霍普金森压杆加载Ta2钛合金扁平闭合帽形受迫剪切试样,结合数字图像相关法和“冻结”试样的微观金相观察,研究剪切区剪切应变的演化、绝热剪切带形成条件等。结果显示：受迫剪切试样在动态加载过程,剪切区剪切应变不断集中,形成绝热剪切带,裂纹沿绝热剪切带发展;随加载率提高,绝热剪切起始临界应变减小;进一步利用数字图像相关法DIC场应变分析及金相微观观测对比,利用卸载回复特性对绝热剪切带起始临界条件进行了讨论,计算的绝热剪切带起始时温升仅为86℃。材料软化可能不是绝热剪切带起始的控制条件,相反是由于绝热剪切带形成造成的应变高度集中发展导致温度急剧升高。     

表面加工塑性层对金属柱壳剪切带自组织单旋起始的影响

在外爆加载金属柱壳高速坍塌过程中, 发生塑性变形失稳形成的剪切带具有高度的自组织特征, 甚至出现剪切带排列的单旋现象—剪切带在顺时针和逆时针两个方向呈现一个方向占优的现象. 柱壳在坍塌时, 最大剪切应力位于柱壳内表面, 剪切带的形核及扩展行为受内表面材料介观状态的影响显著. 本文通过选材和控制柱壳加工工艺, 获得了内表面具有不同厚度塑性层的20钢柱壳, 采用厚壁圆筒实验技术, 研究了表面加工塑性层对金属柱壳绝热剪切带自组织单旋现象起始的影响规律及其物理机制. 研究结果表明, 金属柱壳内表面加工塑性层显著改变了试样剪切带的起始条件, 沿顺时针或逆时针方向排列的剪切带形核数量在总剪切带数量中所占比例取决于表面加工塑性层的厚度和晶粒取向, 具有单一晶粒拉伸方向的较厚塑性层样品更容易形成单向螺旋剪切带结构. 在相同变形条件下, 随着塑性层厚度增加, 剪切带平均形核速率和扩展速率增大, 剪切带平均间距减小. 结果可为理解金属柱壳在高速塌陷过程中绝热剪切带占优取向现象提供有价值的参考.      

Formation of adiabatic shear band in metal matrix composites

A modified single-pulse loading split Hopkinson torsion bar (SSHTB) is introduced to investigate adiabatic shear banding behavior in SiCp particle reinforced 2024 Al composites in this work. The experimental results showed that formation of adiabatic shear band in the composite with smaller particles is more readily observed than that in the composite with larger particles. To characterize this size-dependent deformation localization behavior of particle reinforced metal matrix composites (MMCp), a strain gradient dependent shear instability analysis was performed. The result demonstrated that high strain gradient provides a deriving force for the formation of adiabatic shear banding in MMCp.     

再结晶组织对TA2纯钛绝热剪切行为的影响

使用二辊轧机对TA2工业纯钛进行多道次大应变冷轧处理,制备了冷轧总变形量为70%的TA2纯钛板。通过对冷轧TA2纯钛板进行500℃加热、不同保温时间的退火处理,获得了具有不同再结晶组织的钛板。基于帽形试样和限位环变形控制技术,在分离式霍普金森压杆装置上对不同再结晶组织的试样进行动态冲击冻结实验,结合光学显微镜和扫描电子显微镜表征试样冲击前后微观组织的变化,研究了再结晶组织对TA2纯钛绝热剪切行为的影响。结果表明,随着退火保温时间的延长,试样再结晶晶粒占比逐渐增大,晶粒分布由分散向局部聚集转变;在相同应变和应变率下,在所有试样中都观察到了绝热剪切带,再结晶晶粒占比高的试样更易诱发绝热剪切带中裂纹形核扩展。对比变形前后试样再结晶组织和几何必需位错变化,结合剪切区整体温升分析发现,再结晶晶粒作为材料软化点能够诱发剪切带的形成,而剪切带发展后期产生的绝热温升会促进剪切带内材料发生二次再结晶,提高剪切带内材料的韧性,延缓剪切裂纹的形成。     

The formation of multiple adiabatic shear bands

In a previous paper, Zhou et al. [2006. A numerical methodology for investigating adiabatic shear band formation. J. Mech. Phys. Solids, 54, 904-926] developed a numerical method for analyzing one-dimensional deformation of thermoviscoplastic materials. The method uses a second order algorithm for integration along characteristic lines, and computes the plastic flow after complete localization with high resolution and efficiency. We apply this numerical scheme to analyze localization in a thermoviscoplastic material where multiple shear bands are allowed to form at random locations in a large specimen. As a shear band develops, it unloads neighboring regions and interacts with other bands. Beginning with a random distribution of imperfections, which might be imagined as arising qualitatively from the microstructure, we obtain the average spacing of shear bands through calculations and compare our results with previously existing theoretical estimates. It is found that the spacing between nucleating shear bands follows the perturbation theory due to Wright and Ockendon [1996. A scaling law for the effect of inertia on the formation of adiabatic shear bands. Int. J. Plasticity 12, 927-934], whereas the spacing between mature shear bands is closer to that predicted by the momentum diffusion theory of Grady and Kipp [1987. The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids. J. Mech. Phys. Solids 35, 95-119]. Scaling laws for the dependence of band spacing on material parameters differ in many respects from either theory.     

动态载荷下剪切变形局部化、微结构演化与剪切断裂研究进展

总结和评述了近年来金属与合金变形局部化的形成、微结构演化与剪切断裂方面作者和相关的研究工作成果. 材料包括低碳钢, SS304不锈钢, Fe-15%Ni-15%Cr单晶, Al-Li合金,α-Ti和Ti-6Al-4V, Al/SiCp复合材料等.综述内容主要包括:采用改进的Hopkinson扭杆装置,对剪切变形局部化形成、发展和演化过程进行了实验观察与数值模拟;采用"侧剖"与"对接"等定点方法制备电子显微镜薄膜试样,对剪切带内相变与再结晶、非晶转变、旋涡结构等动态变形现象,以及与宏观动态力学行为对应的位错胞的形成、发展和坍塌等微结构特征进行了观测;提出了应变和应变率同时作为剪切带形成的两个必要条件的直接实验证据;在剪切带内发现了α'$-马氏体相变现象,以及相变产物与母体之间的晶体学关系;通过位错单滑移或交滑移等微观剪切最后发展成为宏观剪切的机制;对剪切带内再结晶结构的观测和对再结晶动力学本构关系的定量描述;对剪切带特别是``白色'腐蚀带(或相变带)的形成机制的分析和新的解释,指出 ``白色'是带内亚结构取向趋于一致,其在光学或扫描显微镜下很难辨认这些亚结构的取向差所致,并非表明剪切带内一定发生了相变;通过截断实验和实时跟踪观测发现,剪切带内微裂纹的萌生与聚合是材料承载能力骤然下降并导致最后断裂的主控因素.此外,本文对近年来在准静态和循环加载下材料的局部化形变与剪切断裂的实验结果予以简要评述,指出其微观机制与动态载荷下的截然不同, 是由位错的平面滑移所控制的,与热效应无关的等温变形.      

A numerical methodology for investigating the formation of adiabatic shear bands

In this paper, we present a numerical approach for analyzing thermo-visco-plastic deformation in one dimension. The method, which is accurate to second order, is based on integration along the characteristic lines. It is able to simulate fully localized plastic flow with high resolution and good efficiency. We apply this numerical scheme to the analysis of shear localization, emphasizing the interactions between a single shear band and its surroundings and among the members of a periodic array of shear bands. It is found that a shear band may grow intermittently due to interactions with other bands. The developed method is specifically adequate for analyzing the self-organized multiple adiabatic formation process, which will be discussed in the follow-up paper.     

Analysis of anisotropy and plastic spin effects on localization phenomena

Summary The main objective of the paper is the investigation of the influence of the anisotrophy and plastic spin effects on criteria for adiabatic shear band localization of plastic deformation. A theory of thermoplasticity is formulated within a framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration such effects as plastic non-normality, plastic-induced anisotropy (kinematic hardening), micro-damage mechanism, thermomechanical coupling and plastic spin. The next objective of the paper is to focus attention on cooperative phenomena in presence of the plastic spin, and the discussion on the influence of synergetic effects on localization criteria. A particular constitutive law for the plastic spin is assumed. The necessary condition for a localized plastic deformation region to be formed is obtained. This condition is accomplished by the assumption that some eigenvalues of the instantaneous adiabatic acoustic tensor vanish. A procedure has been developed which allows us to discuss two separate groups of effects on the localization phenomenon along a shear band. Plastic spin, spatial covariance and kinematic hardening effects are investigated at an isothermal process in an undamaged solid. In the second case, an adiabatic process in a damaged solid is discussed when the spatial covariance terms and the plastic spin are neglected. Here the thermomechanical coupling, micro-damage mechanism and kinematic hardening effects are examined. For both cases, the criteria for adiabatic shear band localization are obtained in an exact analytical form. Particular attention is focused on the analysis of the following effects: (i) plastic non-normality; (ii) plastic spin; (iii) covariant terms; (iv) plastic strain-induced anisotropy; (v) micro-damage mechanism; (vi) thermomechanical couplings. Cooperative phenomena are considered, and synergetic effects are investigated. A discussion of the influence of the plastic spin, kinematic hardening and covariant terms on the shear band localization conditions is presented. A numerical estimation of the effects discussed is given. Received 24 April 1997; accepted for publication 23 December 1997     

Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process

Summary The main objective of the present paper is the development of a viscoplastic regularization procedure valid for an adiabatic dynamic process for multi-slips of single crystals. The next objective is to focus attention on the investigation of instability criteria, and particularly on shear band localization conditions.To achieve this aim, an analysis of acceleration waves is given, and advantage is taken of the notion of the instantaneous adiabatic acoustic tensor. If zero is an eigenvalue of the acoustic tensor, then the associated discontinuity does not propagate, and one speaks of a stationary discontinuity. This situation is referred to as the strain localization condition, and corresponds to a loss of hyperbolicity of the dynamical equations. It has been proved that for an, adiabatic process of rate-dependent (elastic-viscoplastic) crystal, the wave speed of discontinuity surface always remains real and different from zero. It means that for this case the initial-value problem is well-posed. However, for an adiabatic process of rate-independent(elastic-plastic) crystal, the wave speed of discontinuity surface can be equal zero. Then the necessary condition for a localized plastic deformation along the shear band to be formed is as follows: the determinant of the instantaneous adiabatic acoustic tensor is equal to zero. This condition for localization is equivalent to that obtained by using the standard bifurcation method. Based on this idea, the conditions for adiabatic shear band localization of plastic deformation have been investigated for single crystals. Particular attention has been focused on the discussion of the influence of thermal expansion, thermal plastic, softening and spatial covariance effects on shear band localization criteria for a planar model of an f.c.c. crystal undergoing symmetric primary-conjugate double slip. The results obtained have been compared with available experimental observations.Finally, it is noteworthy that the viscoplasticity regularization procedure can be used in the developing of an unconditionally stable numerical integration algorithm for simulation of adiabatic inelastic flow processes in ductile single crystals, cf. [21].The paper has been prepared within research programme sponsored by the Committee of Scientific Research under Grant 3 P404 031 07.     

Multiresolution continuum modeling of micro-void assisted dynamic adiabatic shear band propagation

A thermal-mechanical multiresolution continuum theory is applied within a finite element framework to model the initiation and propagation of dynamic shear bands in a steel alloy. The shear instability and subsequent stress collapse, which are responsible for dynamic adiabatic shear band propagation, are captured by including the effects of shear driven microvoid damage in a single constitutive model. The shear band width during propagation is controlled via a combination of thermal conductance and an embedded evolving length scale parameter present in the multiresolution continuum formulation. In particular, as the material reaches a shear instability and begins to soften, the dominant length scale parameter (and hence shear band width) transitions from the alloy grain size to the spacing between micro-voids. Emphasis is placed on modeling stress collapse due to micro-void damage while simultaneously capturing the appropriate scale of inhomogeneous deformation. The goal is to assist in the microscale optimization of alloys which are susceptible to shear band failure.     

TA2钛合金开口柱壳外爆碎片分布研究

金属柱壳爆炸膨胀断裂机制及其对碎片分布、特征尺寸的影响是应用物理、力学、兵器工程等领域共同关心的重要课题, 但目前除数值模拟外, 考虑断裂机制的简单二维碎裂模型尚未出现.开展TA2钛合金开口柱壳在不同装药条件下的碎裂实验研究, 通过对软回收碎片的统计及微观分析, 探讨金属柱壳外爆断裂模式及二维碎片分布规律, 结果显示:(1) TA2钛合金柱壳在实验爆压(7 $\sim$ 25 GPa)下宏观断口均为剪切断裂模式, 但机制不同, 在较高爆压下柱壳剪切断裂由多重绝热剪切带破坏控制, 在较低压力下为剪切破坏;(2) 与一维拉伸碎裂相比, 柱壳爆炸碎裂不充分, 碎片质量更符合$\beta=1$ (或更接近1)的指数分布; 爆炸碎裂越充分, 碎片越小并趋于均匀, $\beta$趋于较小的值, 趋向Mott和Linfoot提出的泊松统计分布形式;(3) Rayleigh分布可以较好描述柱壳碎片的宽度分布规律, 不同爆压下柱壳碎片宽度归一化尺寸分布具有相似性, 呈现"量子化"特性, 即存在最小的特征尺寸; (4) TA2柱壳碎片特征尺寸远大于G-K剪切断裂公式预测的尺寸, G-K剪切式描述的是多重绝热剪切带间距.本研究为金属柱壳碎片特征、分布规律及其模型分析提供了重要参考.      

表面粗糙度对TC4钛合金柱壳剪切带形成的影响

剪切带是材料在高应变率加载条件下特有的变形和损伤形式之一,关于影响金属材料中剪切带形成的敏感性因素及其机理的研究,一直是科学研究和工程设计中关注的重点问题. 在柱壳高速坍塌过程中,剪切带优先在内表面形核, 其形核及扩展行为受内表面介观状态的影响显著.本文采用爆轰加载厚壁圆筒坍塌实验技术,结合材料表面处理技术、微结构表征技术和剪切带理论模型分析,研究了内表面粗糙度变化对TC4钛合金柱壳剪切带形成影响的细观动力学规律.结果表明, 在爆炸加载形成的高应变率条件下,表面粗糙度对TC4钛合金柱壳中剪切带形成具有明显影响. 在相同的变形条件下,随着试样内表面粗糙度的增大, 剪切带数量、长度和形核速率均增大;表面粗糙度越大, 部分剪切带扩展速率越快, 剪切带长度差异越大,剪切带的屏蔽效应增强. 分析表明,实验获得的剪切带间距与W-O模型和M模型预测结果基本吻合,具体数值受试样内表面粗糙度影响, 随着表面粗糙度的增大,实验结果逐渐小于预测数值.      

Adiabatic shear localization in the dynamic punch test,part I: experimental investigation

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during a dynamic punch test is investigated. Specifically, the possibility and affects of adiabatic shear localization are examined. The three materials are chosen to encompass a wide range of physical properties. Punch tests are conducted at average shear strain rates from 10⁻³ to 10⁴ s⁻¹ on a servo-hydraulic compression machine, a mechanical press, and a Hopkinson bar apparatus. Experimental load displacement curves are obtained and fractographic and metallographic analysis is performed. Finite element simulations of punching operations are performed in the second part of this two part investigation to examine internal deformation not visible during experimental tests. More specifically, the role of adiabatic shear localization in burr formation is determined. Adiabatic shear localization occurs in the titanium alloy for the mechanical press and Hopkinson bar tests, while localization is not present for the 6061-T6 aluminum in any test. The 1018 steel begins to exhibit some transitional behavior toward shear localization in the Hopkinson bar experiments. It is seen that in the materials tested here, a combination of high strength and low strain hardening make a material more susceptible to adiabatic shear localization in punching operations.     

Photoelastic stress analysis of thick-walled closed-end cylinders

A three-dimensional photoelastic stress analysis was conducted on six thick-walled closed-end cylinders subjected to internal-pressure loading. The cylinders were approximately similar in design to the breech chamber of a large-caliber tank weapon. Maximum octahedral shear stresses were determined in the side wall-end wall juncture of essentially flat-ended cylinders (similar to actual weapon component) and in hemispherically-ended cylinders. The purpose of the study was to learn more about the stresses in the closed end of the cylinder so that future components of this type may be designed more efficiently with regard to stress and weight.     

Prediction of the initial thickness of shear band localization based on a reduced strain gradient theory

Plastic flow localization in ductile materials subjected to pure shear loading and uniaxial tension is investigated respectively in this paper using a reduced strain gradient theory, which consists of the couple-stress (CS) strain gradient theory proposed by Fleck and Hutchinson (1993) and the strain gradient hardening (softening) law (C–W) proposed by Chen and Wang (2000). Unlike the classical plasticity framework, the initial thickness of the shear band and the strain rate distribution in both cases are predicted analytically using a bifurcation analysis. It shows that the strain rate is obviously non-uniform inside the shear band and reaches a maximum at the center of the shear band. The initial thickness of the shear band depends on not only the material intrinsic length l_cs but also the material constants, such as the yield strength, ultimate tension strength, the linear hardening and softening shear moduli. Specially, in the uniaxial tension case, the most possible tilt angle of shear band localization is consistent qualitatively with the existing experimental observations. The results in this paper should be useful for engineers to predict the details of material failures due to plastic flow localization.     

分子动力学模拟金属玻璃板拉伸时剪切带的形成和演化过程

金属玻璃在低温高应力条件下容易生成剪切带而导致结构的破坏，大大限制了它的推广应用。本文采用分子动力学模拟研究了三种Cu64Zr36（不带缺口、一侧带缺口、两侧带缺口）金属玻璃板试样在拉伸过程中剪切带的形成和演化过程及其力学性能。结果表明：不带缺口金属玻璃板试样在低温高应力的拉伸过程中会自发出现局部剪切转变区，发生剪切局部化，继续拉伸会在与加载轴大约成45°方向上形成剪切带。剪切带的形成与剪切转变区的分布和局部化有关，带缺口比不带缺口的试样会更早出现应变局部化，即在较低的拉伸应变下便形成剪切带，其拉伸强度也相应较低。相同条件下，一侧带缺口与两侧带缺口的试样在拉伸强度上几乎相同，但两侧带缺口试样的应变局部化程度稍低，主要是两侧缺口处均出现了剪切转变区，导致其分布和局部化不够集中，这也是形成主剪切带和次剪切带的主要原因。以上结果为进一步从原子尺度理解金属玻璃剪切带的形成和演化特征提供了重要的信息。     

分子动力学模拟金属玻璃板拉伸时剪切带的形成和演化过程

金属玻璃在低温高应力条件下容易生成剪切带而导致结构的破坏,大大限制了它的推广应用。本文采用分子动力学模拟研究了三种Cu64Zr36（不带缺口、一侧带缺口、两侧带缺口）金属玻璃板试样在拉伸过程中剪切带的形成和演化过程及其力学性能。结果表明：不带缺口金属玻璃板试样在低温高应力的拉伸过程中会自发出现局部剪切转变区,发生剪切局部化,继续拉伸会在与加载轴大约成45°方向上形成剪切带。剪切带的形成与剪切转变区的分布和局部化有关,带缺口比不带缺口的试样会更早出现应变局部化,即在较低的拉伸应变下便形成剪切带,其拉伸强度也相应较低。相同条件下,一侧带缺口与两侧带缺口的试样在拉伸强度上几乎相同,但两侧带缺口试样的应变局部化程度稍低,主要是两侧缺口处均出现了剪切转变区,导致其分布和局部化不够集中,这也是形成主剪切带和次剪切带的主要原因。以上结果为进一步从原子尺度理解金属玻璃剪切带的形成和演化特征提供了重要的信息。     

The growth of shear bands in composite microstructures

Shear band formation in materials with inhomogeneous and composite microstructures is influenced by factors that usually do not come into play in monolithic materials. Experiments and calculations have shown that inhomogeneities in material properties enhance the localization of deformation. This investigation concerns the propagation of shear bands in a two-phase tungsten composite under the conditions of nominally pure shear deformation. Finite element calculations are carried out to delineate the effects of different grain–matrix morphologies. In the numerical models, the initiation of shear bands is triggered by a notch, simulating the effect of defects such as microcracks and microvoids in materials. Calculations demonstrate that phase morphology, particle size and the relative location of initiation site have significant influences on the development of localized deformation. The work and energy evolutions are tracked for each constituent phase in the microstructures. In addition, the exchange of thermal energy through heat flow between the phases is analyzed. The results show that a strong correlation exists between the course of shear band propagation and the thermomechanical coupling between microscopic phases.