Adiabatic shear banding and scaling laws in chip formation with application to cutting of Ti–6Al–4V

The phenomenon of adiabatic shear banding is analyzed theoretically in the context of metal cutting. The mechanisms of material weakening that are accounted for are (i) thermal softening and (ii) material failure related to a critical value of the accumulated plastic strain. Orthogonal cutting is viewed as a unique configuration where adiabatic shear bands can be experimentally produced under well controlled loading conditions by individually tuning the cutting speed, the feed (uncut chip thickness) and the tool geometry. The role of cutting conditions on adiabatic shear banding and chip serration is investigated by combining finite element calculations and analytical modeling. This leads to the characterization and classification of different regimes of shear banding and the determination of scaling laws which involve dimensionless parameters representative of thermal and inertia effects. The analysis gives new insights into the physical aspects of plastic flow instability in chip formation. The originality with respect to classical works on adiabatic shear banding stems from the various facets of cutting conditions that influence shear banding and from the specific role exercised by convective flow on the evolution of shear bands. Shear bands are generated at the tool tip and propagate towards the chip free surface. They grow within the chip formation region while being convected away by chip flow. It is shown that important changes in the mechanism of shear banding take place when the characteristic time of shear band propagation becomes equal to a characteristic convection time. Application to Ti–6Al–4V titanium are considered and theoretical predictions are compared to available experimental data in a wide range of cutting speeds and feeds. The fundamental knowledge developed in this work is thought to be useful not only for the understanding of metal cutting processes but also, by analogy, to similar problems where convective flow is also interfering with adiabatic shear banding as in impact mechanics and perforation processes. In that perspective, cutting speeds higher than those usually encountered in machining operations have been also explored.     

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.     

加载速率对40Cr钢Ⅱ型动态断裂特性的影响

采用新型Ⅱ型动态断裂测试技术,对高强钢40Cr在高加载速率下的Ⅱ型动态断裂特性进行了测试研究。基于新设计的Ⅱ型动态断裂试样和分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）技术,通过实验-数值方法确定了裂尖在加载过程中的应力强度因子曲线。采用应变片法确定了试样的起裂时间,最终得到40Cr的Ⅱ型动态断裂韧性值,并对其加载速率相关性和材料的失效机理进行了研究。结果表明,在1.08～5.53 TPa·m1/2/s的加载速率范围内,40Cr的Ⅱ型动态断裂韧性基本表现为与加载速率成正相关的变化趋势。通过对试样断口形貌的分析,确定了材料的失效模式及机理,发现随着加载速率的增加,存在拉伸型失效向绝热剪切型失效模式转变的现象。     

平头弹穿透间隙式双层靶的穿甲模式

平头弹贯穿单层金属靶,随着靶厚的增加和弹速的增高,穿甲模式均可能由剪切冲塞向绝热剪切冲塞转换。因此,对于双层或多层靶的穿甲,其不同层的靶板失效模式可能是不同的。本文中对相关的平头弹穿甲Weldox 700E单层及双层间隙式钢靶的实验数据进行分析,讨论其穿甲模式。弹速较高时,贯穿第1层靶发生绝热剪切失效,弹速降低,贯穿第2层靶板发生绝热剪切失效或剪切冲塞失效, 最终失效模式为绝热剪切和剪切冲塞混杂。     

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。     

An analysis of the shear failure of rigid-linear hardening beams under impulsive loading

A theoretical rigid-plastic analysis for the dynamic shear failure of beams under impulsive loading is presented when using a travelling plastic shear hinge model which takes into account material strain hardening. The maximum dynamic shear strain and shear strain-rate can be predicted in addition to the permanent transverse deflections and other parameters. The conditions for the three modes of shear failure, i.e., excess deflection failure, excess shear strain failure and adiabatic shear failure are analyzed. The special case of an infinitesimally small plastic zone is discussed and compared with Nonaka's solution for a rigid, perfectly plastic material. The results can also be generalized to examine the dynamic response of fibre-reinforced beams.     

双相高强钢FeNiAlC的动态剪切行为及微结构机理

绝热剪切带是金属材料在高应变率载荷下常见的一种失效模式。利用霍普金森压杆装置,对双相钢Fe-24.86Ni-5.8Al-0.38C不同微结构的帽形样品施加冲击载荷,研究它的动态剪切变形行为及微结构机理。先通过对固熔处理得到的粗晶态样品进行大应变冷轧获得冷轧态样品,再使用透射电子显微镜和扫描电子显微镜表征两种样品冲击前后微结构的变化差异。结果表明,双相钢FeNiAlC拥有较优异的动态剪切性能,剪切强度达1.3 GPa,均匀剪切应变达1.5。变形前,材料由奥氏体相和马氏体相构成,马氏体体积分数约为20%。变形过程由位错滑移和孪生变形主导,但因应变速率较高致使马氏体相变被抑制。不同微结构样品内均形成绝热剪切带,带内发生动态再结晶,形成超细晶粒,平均晶粒尺寸约300 nm,且剪切带内不发生相变;冷轧态剪切带宽度的实验值（14.6 μm）与理论计算值(12.3 μm)较好吻合,而粗晶态剪切带宽度的实验值（14.6 μm）与理论计算值（30 μm）相差甚远,初步分析可能是因为粗晶态样品应变较大基本不满足完全绝热的理论条件。在变形过程中,粗晶态因塑性变形做功产生的绝热温升高达720 K,而冷轧态的只有190 K。通过实验结果与热塑模型分析,得出绝热温升不是形成绝热剪切带的唯一因素,而应考虑材料的微观结构和局部化变形等的共同影响。     

Effect of stress-state and spacing on voids in a shear-field

Unit cell model analyses are carried out for a material with a periodic array of voids, subject to shear loading. Thus the focus is on ductile fracture in conditions of low stress triaxiality. It has been shown recently that voids in shear are flattened out to micro-cracks, which rotate and elongate until interaction with neighboring micro-cracks gives coalescence, so that the failure mechanism is very different from that under tensile loading. In the present studies the plane strain unit cell has fully periodic boundary conditions, so that any combination of the stress components in the overall average stress state can be prescribed. This also allows for studies of the effect of different initial void spacing in the two in-plane coordinate directions. The stress states considered are essentially simple shear, with various levels of tensile stresses or compressive stresses superposed, i.e. low positive stress triaxiality or even negative stress triaxiality. For high aspect ratio unit cells a clear localization band is found inside the cell, which actually represents several parallel bands, due to periodicity. In the materials represented by a low aspect ratio unit cell localization would also occur after that the maximum shear stress has been passed, but this is not shown when periodicity is enforced. The effect of superposed tensile or compressive stresses is found to be bigger for high aspect ratio unit cells than for low aspect ratios.     

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.      

内爆炸载荷作用下7A55铝合金的动态性能及断裂行为

采用圆筒爆炸实验研究了内爆炸载荷作用下7A55铝合金的动态性能,用扫描电镜和光学显微镜 对破裂样品的断口形貌、金相组织等进行了微观分析。结果表明:在本文实验条件下,7A55铝合金能够承受 360MPa的内部爆炸加载;合金的断裂方式为剪切断裂,裂缝与筒壁的径向近似成45角;靠近圆筒内侧组织 中存在剪切变形带、绝热剪切带和裂纹,沿最大剪切应力面向外扩展。     

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.      

Self-organization of adiabatic shear bands in OFHC copper and HY-100 steel

We study the self-organization process of adiabatic shear bands in OFHC copper and HY-100 steel taking into account strain hardening factor. Starting from mathematical model we present a new numerical approach, which is based on Courant–Isaacson–Rees scheme, that allows one to simulate fully localized plastic flow. To prove the accuracy and efficiency of the following method we give solutions of two benchmark problems. Next we apply the proposed method to investigate such quantitative characteristics of self-organization process of ASB as average stress, temperature, localization time and distance between ASB. Then we compare the obtained results with theoretical predictions by other authors.     

绝热剪切研究进展

从实验技术、分析手段和数值模拟技术等三方面对近年来绝热剪切研究相关的工作成果进行了总结和评述,指出了现有工作的不足,即:尚不明了绝热剪切带内微观组织演化规律及尚未建立相应的力学模型;绝热剪切带的静水压相关性仍有待进一步探索;描述绝热剪切的自组织行为的模型需进一步完善;绝热剪切数值模拟精度有待提高等。最后,结合国内外最新的研究动态对绝热剪切研究的发展趋势提出了自己的观点。     

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。     

Modeling adiabatic shear failure from energy considerations

The numerical simulation of dynamic structural failure by localized shear is quite complex in terms of constitutive models and choice of adequate failure criteria, along with a pronounced mesh-sensitivity. As a result, the existing numerical procedures are usually quite sophisticated, so that their application for design purposes is still limited. This study is based on the implementation of a simple energy-based criterion, which was developed on experimental considerations (Rittel et al., 2006), and uses a minimal number of adjustable parameters. According to this criterion, a material point starts to fail when the total strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual structural behavior. The criterion was embedded into commercial finite element software and tested by simulating numerically four typical high-rate experiments. The first is the dynamic torsion test of a tubular specimen. The second concerns the failure mode transition in mode II fracture of an edge crack in plain strain. The last two involve dynamic shear localization under high rate compression of a cylindrical and a shear compression specimen. A very good adequation was found both qualitatively and quantitatively. Qualitatively, in terms of failure path selection, and quantitatively, in terms of local strains, temperatures and critical impact velocity. The proposed approach is enticing from an engineering perspective aimed at predicting the onset and propagation of dynamic shear localization in actual structures.     

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB).Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior.The goal of this paper is to present a new combined experimental–numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment.Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.     

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

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.     

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.     

Adiabatic shear localization in the dynamic punch test,part II: numerical simulations

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during the dynamic punch test is investigated using the finite element method. Specifically, the possibility and effects of adiabatic shear localization and its role in burr formation are examined, and comparisons to experimental tests in the first part of this two part study are made. A maximum stress criterion involving strain and strain rate hardening and thermal softening is used to determine the occurrence of shear localization in the simulations. It is observed that adiabatic shear localization occurs in the simulations of the titanium alloy. This material exhibits narrow regions of concentrated shear strain during the deformation, and the shear localization criterion is satisfied in these regions. The strain is more widely distributed in the other two metals, and the same criterion is not satisfied. In the calculations of the shear localization criterion it is seen that strain rate hardening has a significant effect when compared to strain hardening and thermal softening. Also, contact between specimen and punch is lost around the center of the punch during operation. This loss of contact is important as it leads to higher stress concentrations at the punch corner and dishing of the blank.