27 resultados para Reidemeister torsion
Resumo:
Table of Contents
1 | Introduction | 1 |
1.1 | What is an Adiabatic Shear Band? | 1 |
1.2 | The Importance of Adiabatic Shear Bands | 6 |
1.3 | Where Adiabatic Shear Bands Occur | 10 |
1.4 | Historical Aspects of Shear Bands | 11 |
1.5 | Adiabatic Shear Bands and Fracture Maps | 14 |
1.6 | Scope of the Book | 20 |
2 | Characteristic Aspects of Adiabatic Shear Bands | 24 |
2.1 | General Features | 24 |
2.2 | Deformed Bands | 27 |
2.3 | Transformed Bands | 28 |
2.4 | Variables Relevant to Adiabatic Shear Banding | 35 |
2.5 | Adiabatic Shear Bands in Non-Metals | 44 |
3 | Fracture and Damage Related to Adiabatic Shear Bands | 54 |
3.1 | Adiabatic Shear Band Induced Fracture | 54 |
3.2 | Microscopic Damage in Adiabatic Shear Bands | 57 |
3.3 | Metallurgical Implications | 69 |
3.4 | Effects of Stress State | 73 |
4 | Testing Methods | 76 |
4.1 | General Requirements and Remarks | 76 |
4.2 | Dynamic Torsion Tests | 80 |
4.3 | Dynamic Compression Tests | 91 |
4.4 | Contained Cylinder Tests | 95 |
4.5 | Transient Measurements | 98 |
5 | Constitutive Equations | 104 |
5.1 | Effect of Strain Rate on Stress-Strain Behaviour | 104 |
5.2 | Strain-Rate History Effects | 110 |
5.3 | Effect of Temperature on Stress-Strain Behaviour | 114 |
5.4 | Constitutive Equations for Non-Metals | 124 |
6 | Occurrence of Adiabatic Shear Bands | 125 |
6.1 | Empirical Criteria | 125 |
6.2 | One-Dimensional Equations and Linear Instability Analysis | 134 |
6.3 | Localization Analysis | 140 |
6.4 | Experimental Verification | 146 |
7 | Formation and Evolution of Shear Bands | 155 |
7.1 | Post-Instability Phenomena | 156 |
7.2 | Scaling and Approximations | 162 |
7.3 | Wave Trapping and Viscous Dissipation | 167 |
7.4 | The Intermediate Stage and the Formation of Adiabatic Shear Bands | 171 |
7.5 | Late Stage Behaviour and Post-Mortem Morphology | 179 |
7.6 | Adiabatic Shear Bands in Multi-Dimensional Stress States | 187 |
8 | Numerical Studies of Adiabatic Shear Bands | 194 |
8.1 | Objects, Problems and Techniques Involved in Numerical Simulations | 194 |
8.2 | One-Dimensional Simulation of Adiabatic Shear Banding | 199 |
8.3 | Simulation with Adaptive Finite Element Methods | 213 |
8.4 | Adiabatic Shear Bands in the Plane Strain Stress State | 218 |
9 | Selected Topics in Impact Dynamics | 229 |
9.1 | Planar Impact | 230 |
9.2 | Fragmentation | 237 |
9.3 | Penetration | 244 |
9.4 | Erosion | 255 |
9.5 | Ignition of Explosives | 261 |
9.6 | Explosive Welding | 268 |
10 | Selected Topics in Metalworking | 273 |
10.1 | Classification of Processes | 273 |
10.2 | Upsetting | 276 |
10.3 | Metalcutting | 286 |
10.4 | Blanking | 293 |
Appendices | 297 | |
A | Quick Reference | 298 |
B | Specific Heat and Thermal Conductivity | 301 |
C | Thermal Softening and Related Temperature Dependence | 312 |
D | Materials Showing Adiabatic Shear Bands | 335 |
E | Specification of Selected Materials Showing Adiabatic Shear Bands | 341 |
F | Conversion Factors | 357 |
References | 358 | |
Author Index | 369 | |
Subject Index | 375 |
Resumo:
A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments.
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利用量纲分析研究限定型高压扭转(HPT)变形的相关因素,在此基础上用有限元分析不同侧边摩擦条件和不同径厚比和不同侧面摩擦约束大小对纯铜试样角位移场的特点,讨论理想高压扭转公式适用的范围.量纲分析揭示,试样上变形与几何位置、径厚比、施加压力、材料弹性参数以及模具侧面的摩擦状况相关.有限元分析结果表明,可用幂函数形式的角位移约束来简化侧面摩擦,当幂指数不小于8时,试样上非HPT变形区域大小趋于稳定;当径厚比不小于5时,试样中心存在一个可用纯扭转变形描述的区域,非理想HPT区域大小不超过试样厚度尺寸;当径厚比不大于2时,试样上不存在理想HPT区域.
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Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.
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A new framework of non-local model for the strain energy density is proposed in this paper. The global strain energy density of the representative volume element is treated as a non-local variable and can be obtained through a special integral of the local strain energy density. The local strain energy density is assumed to be dependent on both the strain and the rotation-gradient. As a result of the non-local model, a new strain gradient theory is derived directly, in which the first and second strain gradients, as well as the triadic and tetradic stress, are introduced in the context of work conjugate. For power law hardening materials, size effects in thin metallic wire torsion and ultra-thin cantilever beam bend are investigated. It is found that the result predicted by the theoretical model is well consistent with the experimental data for the thin wire torsion. On the other hand, the calculation result for the micro-cantilever beam bend clearly shows the size effect.
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通过高压扭转对Cu试样施加不同程度的变形,利用OM,TEM及差示扫描量热仪(DSC)对变形组织微观结构及其热稳定性进行了分析.在较小的变形程度下,变形组织为高位错密度的位错胞、亚晶组织,试样的变形储能随变形量的增大而增大,在切应变等于13时达到最大,为0.91 J/mol,DSC曲线显示的放热峰随变形量的增大向低温方向偏移;进一步变形,动态回复加剧,高位错密度的亚晶组织逐渐演化成无位错的等轴状晶粒组织,试样的变形储能减小,组织的稳定性提高.显微硬度随退火温度的提高而减小,晶粒的明显长大导致显微硬度急剧减小.出现明显晶粒长大的温度较DSC曲线显示的放热峰起始温度低45℃左右,这主要是由于变形组织的回复再结晶过程是退火温度与时间的函数,降低处理温度并延长处理时间能达到与高温短时处理相同的效果.
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通过高压扭转(HPT)技术在不同转速条件下实现了Cu试样的晶粒细化.利用光学显微镜(OM),透射电镜(TEM)及显微硬度计观察并测试了组织的结构与性能,并基于有限元计算了变形诱导试样的温升,研究了转速对Cu试样的组织细化与性能的影响.结果表明:转速由1/3r.min-1增大至1r.min-1,经1圈扭转变形,试样温度由40.8℃升高到54.1℃,变形组织均为100~600nm的高位错密度位错胞/亚晶组织,显微硬度由初始态的52HV0.05增大至140HV0.05;经16圈扭转变形,试样温度由50.4℃升高到97.4℃,组织细化到200nm.慢速扭转变形试样晶内位错密度高,微观组织处于严重变形状态;而快速扭转试样晶内衬度均匀,位错较少,微观组织经历明显的动态回复,显微硬度较慢速扭转变形试样低6%
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The fully relaxed single-bond torsional potentials and orientation-related rotational potentials of 2,2'-bithiophene (BT) under the interaction of an external electric field (EF) constructed by point charges have been evaluated with semi-empirical AMI and PM3 calculations. The torsional potentials are sensitive to both EF strength and direction. While the EF is parallel to the molecular long axis, the torsional barrier around C-x-C-x' bond obviously rises with increasing the EF strength, whereas the relative energies of syn and anti minima show a slight change. The interaction between the EF and the induced dipole moment has been proposed to elucidate this observation. On the other hand, the relative energy difference between the syn and anti minima shows an obvious change, while the EF is perpendicular to the molecular long axis. This feature has been ascribed to the interaction between the EF and the permanent dipole moment of BT. Furthermore, conformational and orientational analyses in two dimensions have been carried out by changing the torsional and rotational angles in the different EF. The conformation and orientation of a gas-phase BT in the EF are governed by both the above factors.
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Copolymers based on monomers phenolphthalein (PP)/4,4'-thiodiphenol (Bis-T)/4,4'-dichlorodiphenylsulfone (DCDPS) were prepared by a route involving the toluene, N-methyl-2-pyrrolidone and anhydrous potassium carbonate synthesis. The range of optimum reaction temperature was between 185 and 195 degrees C. The copolymers were characterized by C-13 NMR, differential scanning calorimetry (DSC) and torsion braid analysis. It was found that all of the copolymers were random and homogeneous and their glass transition temperatures (T-g) decreased linearly with an increase of Bis-T contents in the copolymers. The thermal stability determined by thermogravimetry analysis in air atmosphere indicated that the copolymer had better resistance to thermo-oxidative degradation. Dynamic mechanical measurement showed that (PP/Bis-T) PES copolymers containing 0-50 mol% of Bis-T components had two secondary relaxations. (C) 1998 Elsevier Science Ltd. All rights reserved.
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The crystal structure of poly(ether ketone ketone) (PEKK) is predicted by using Cerius2 software according to the wide angle X-ray diffraction (WAXD) experiment result. The predicted structure has a planar zigzag chain conformation between ether oxygen and ketone carbons in an orthorhombic lattice. Average zigzag angle is 126 degrees and average torsion angle is 30.32 degrees. The WAXD powder pattern calculated from the crystal packing model is in good agreement with the experiment result.
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本文在Bruker AM-400 NMR谱仪上,在不同温度下研究了线形脑啡肽(N-Tyr~1-Gly~2-Gly~3-Phe~4-Leu~5)在DMSO中的NMR溶液构象。由NMR测试结果,得到了NH化学位移温度梯度系数、扭转角φ、χ'约束和~1H-~1H NOE距离约束,用目标函数法计算了脑啡肽的溶液构象,分析了优势边链构象。研究结果指明了多肽骨架的柔变性且处于构象平衡中。
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结合生产应用实际,根据扭杆在实际应用中的情况,利用扭床进行模拟,从而测试扭杆的机械特性及相关的各项指标,为扭杆生产提供可靠的质量保证。