Simulation of high speed deformation of copper single crystals

Plastic deformation of copper single crystals was simulated by molecular dynamics using an embedded atom potential. The time step of molecular dynamics is on the order of 1 fs which corresponds to ultra high speed deformation. This paper reports the results of tension, bending, and compression tests. On notched tension surfaces, Heidenreich-Shockley partial dislocations formed near the tip of the notch as expected. In the absence of notch, creation of dislocations was quite difficult under tension. On compression surfaces, partial dislocations were generated near the wrinkle of the possibly redundant slip plane.     

Creation and motion of dislocations and fracture in metal and silicon crystals

By making a step on one surface ( ) of a rectangular small paralellepiped copper crystal, dislocations could be created by the molecular dynamic method. The dislocation created was not a complete edge dislocation but a pair of Heidenreich-Shockley partial dislocations. Each time a dislocation was created, the stress on the surface was released. Small copper crystals having a notch were pulled (until fracture), compressed and buckled by use of the molecular dynamic method. An embedded atom potential was used to represent the interaction between atoms. Dislocations were created near the tip of the notch. A very sharp yield stress was observed. The results of high speed deformations of pure silicon small crystals using the molecular dynamics are presented. The results suggest that plastic deformation may be possible for the silicon with a high speed deformation even at room temperature. Another small size single crystal, the same size and the same surfaces, was compressed using molecular dynamic method. The surfaces are {110}, {112} and {111}. The compressed direction was [111]. It was found that silicon crystals are possible to be compressed with a high speed deformation. This may suggest that silicon may be plastically deformed with high speed deformation.     

镍基单晶合金切口圆棒试样三维晶体弹塑性应力场的数值模拟

建立了镍基单晶切口试样的三维晶体弹塑性有限元模型,研究了不同尺寸的"U"型和"V"型切口试样的应力分布和滑移系开动特性,给出了八面体分切应力沿切口截面径向和周向的分布情况.结果表明切口尺寸对分切应力有显著影响:对于这两种类型切口,随着切口半径的减小,最大分切应力增加,并且切口半径越小,分切应力沿切口截面周向波动的幅度越大;相应的开动滑移系也不同.     

Computer simulation of deformation and fracture of small crystals by molecular dynamics method

Body-centred cubic iron whiskers having [100] and [110] axes were pulled in a molecular dynamics simulation using a supercomputer. The upper yield stress close to the theoretical strength was found. Above the upper yield stress, phase transformation was observed; at the same time the stress was greatly reduced. A new possible mechanism of twinning is proposed. The whiskers were pulled until they had broken into two pieces. Copper small crystals with and without a notch were sheared. It was observed that the edge dislocations were created at the surface and moved through and escaped from the crystals. Copper small single crystals with a notch were pulled. A half-dislocation was created near the tip of the notch. Sharp yield stress was observed. In medium deformation dislocations on different slip planes were created. Due to the cutting of dislocations the tensile stress increased.     

Shear yielding modes of polycarbonate

The modes of shear yielding in edge-notched sheets of polycarbonate have been studied under slow tensile loading. Optical microscope techniques were used to characterize the flow lines through the thickness of the plastically deformed region. Three modes are observed, namely core yielding, hinge shear and intersecting shear. Core yielding consists of two families of shear flow lines contained in the centre region where the stress is highest. In the nearly plane strain condition, the dominating shear mode is hinge shear which is through-thickness yielding on inclined planes above and below the notch. Intersecting shear dominates in the nearly plane stress condition. In this case, yielding occurs through the entire thickness by slip along planes parallel to the width direction that make an angle with the plane of the sheet. It produces a necking effect in front of the notch. The thickness dependent transition from hinge shear to intersecting shear follows conditions suggested by Hahn and Rosenfield.     

Simulation of deformation and lifetime behavior of a fcc single crystal superalloy at high temperature under low-cycle fatigue loading

This work deals with the formulation of a three-dimensional crystallographic time-incremental lifetime rule for face-centered cubic (fcc) single crystals used for gas-turbine blade applications. The damage contribution rate of each slip system to the total damage is governed by the current values of the resolved shear stress and the slip rate on the corresponding slip system. The damage rule is combined with a crystallographic viscoplastic deformation model. For the nickel-base single-crystal superalloy CMSX4 at 950 °C, various strain- and stress-controlled uniaxial cyclic tests with and without hold-times can be described for different crystal orientations by one set of material parameters. For verification, simulation results for a single-crystal specimen with a notch have been compared with corresponding experimental results. The predicted lifetime is within the factor of two of the measured one.     

A simple unified critical plane damage parameter for high-temperature LCF life prediction of a Ni-based DS superalloy

A simple unified critical plane damage parameter (i.e., the modified resolved shear strain range ?γ _mod) based on a slip mechanism-related critical plane concept was proposed in this paper, integrating life prediction of low cycle fatigue (LCF) behavior affected by anisotropy, load ratio and stress concentration into one framework, where the critical plane is determined as the slip plane on which the damage parameter is the maximum during the cycle. For notched specimens, this procedure was specially carried out at the fatigue initiation sites located on the notch surface, which were well predicted by the distribution of Von-Mises stress range ?σ _Mises. The applications of this damage parameter in a directionally solidified superalloy at high temperatures showed that the LCF lives resulting from complicated loading conditions (i.e., variable material orientation, temperature, loading ratio and notch feature) were well simulated consistently, and the predicted fatigue life is within a scatter band of ±3.     

Deformation of single crystals of the L21 ordered Ag2MgZn

The orientation and temperature dependence of slip geometry and yield stress in single crystals of the L2₁ ordered Ag₂MgZn has been studied in compression in the temperature range 290 to 580 K. The slip direction in Ag₂MgZn is exclusively 1 1 1 in this temperature range, but the slip plane varies with crystal orientations; slip occurs on (¯2 1 1) for orientations near the [0 1 1]-[¯1 1 1] boundary, while for the other orientations in the [0 0 1]-[0 1 1]-[¯1 1 1] unit triangle it occurs on the (¯1 0 1). The critical resolved shear stress (CRSS) for slip on both the (¯1 0 1) [1 1 1] and (¯2 1 1) [1 1 1] systems increases abnormally with increasing temperature and reaches a maximum peak at about 0.92 of the critical temperature T _c, for the L2₁-type order. The peak temperature and the shape of the CRSS versus temperature curve are independent not only of crystal orientation but also of the operative slip system. It is suggested that the strength anomaly in Ag₂MgZn be interpreted in terms of the mechanism based on the transition from unit dislocations to superdislocations.     

Investigation on crystallographic behaviors of nickel‐base single crystal alloy cooling holes with different spanwise injection angles

Film cooling as an important thermal protection technology is widely used in aviation and ground gas turbine blades. But film cooling holes reduce the strength of blade seriously, which have become a key region of crack nucleation. In this paper, the plastic behaviors of nickel‐base single crystal alloy turbine cooling holes in spanwise injection angles range from 0° to 40° are investigated on basis of crystallographic constitutive theory. The results show that there are both higher stress regions and lower stress regions around multi‐column cooling holes, where suffer stress interference. The maximum Mises stress occurs at the hole in the center column. The places where the maximum resolved shear stresses occurs change with load and spanwise injection angle. The maximum Mises stress around holes with injection angle of 0° is lowest. With the injection angle increases, the maximum Mises stress increases until injection angles up to 30°. In all the slip systems, the resolved shear stress of hexahedral slip system is most sensitive to the changing of spanwise injection angle and load.     

Calculation of stress intensity factors for straight cracks in grooved and ungrooved shafts

Stress intensity factors have been calculated by finite element methods for a straight edged crack in a plane normal to the axis of rotation of a circular cylinder under tension and bending, and for a similar crack at the base of a symmetric groove in a shaft under tension and bending and under compressive stresses on the cylindrical surface. Satisfactory agreement with results of simplified approximations was found in most cases. A simple formula for determining the effect of the crack on the stiffness of the shaft in bending has also been derived.For the crack in an ungrooved cylinder, the stress intensity factor due to tensile or bending loads was highest at the centre, and lower than that due to a semi-elliptical notch in a slab of the same thickness under the same load. For bending loads on cracks of depths up to a tenth of the cylinder diameter, the stress intensity factor is approx. $\text{1}\text{1}\text{2}\text{σ√l}$ (where $\text{l}$ is the maximum crack depth and σ the maximum stress in the absence of the crack). For cracks in shallow grooves, the maximum stress intensity under tensile and bending loads is also at the centre but that for cracks in deep grooves is at the surface. The maximum stress intensity factor due to shrink fit is near the surface for both types of groove.     

Influence from geometrical features on the growth rate of a micro-structurally short fatigue crack

The influence on the crack growth rate on a micro-structurally short edge crack subjected to fatigue loading from changes in crack length, distance to grain boundaries and applied load has been investigated. The crack is assumed to grow in a single shear mechanism due to nucleation, glide and annihilation of dislocations along preferred slip planes in the material. The external geometry is modelled by distributed dislocation dipole elements in a boundary element approach under quasi-static and plane strain conditions. The evolving plasticity is described by individual discrete dislocations along a slip plane emanating from the crack in the crack direction. The crack growth rate is shown to be controlled by the plasticity, which in turn is controlled by geometrical parameters in combination with the external load.     

A Dislocation barrier model for fatigue crack growth threshold

The primary mechanism of fatigue crack growth is crack-tip dislocation emission followed by the glide of the emitted dislocations. Both of these two processes are controlled by the crack-tip resolved shear stress field, which is characterized by the resolved shear stress intensity factor, . A dislocation barrier model for fatigue crack growth threshold is constructed. The model assumes that a fatigue crack stops growing when crack-tip slip bands are incapable of penetrating the primary dislocation barrier. The derived and deduced threshold behaviors agree with the observed constant threshold K_max,th in the low R region and constant threshold ΔK_th in the high R region. K_max,th is the K_max at the threshold. The constant K_max,th is related to the resistance of the primary dislocation barrier, which in most of cases is grain boundary; and the constant ΔK_th is related to the resistance of secondary barriers. Furthermore, the analysis shows that K_max,th is proportional to √d, where d is the grain size. The relation has been observed in steels. The model also helps to explain the characteristics of, and the transition from, microstructure-sensitive to microstructure-insensitive growth. This revised version was published online in July 2006 with corrections to the Cover Date.     

镍基单晶合金TLP焊接件破坏特性研究

为研究镍基单晶合金的高温焊接性能,通过三点弯曲试验和扫描电镜对单晶体焊接件和单晶体试件在高温下的破坏机理进行了研究,并从晶体滑移理论出发,采用有限元方法对两种不同试样在相同载荷下的Mises应力分布和最大分切应力进行了数值分析.研究结果表明:对于采用TLP焊接连接的单晶焊接件,试样的破坏形式主要表现为脆性断裂,试样的抗弯强度明显低于单晶体试样;对于焊接连接的单晶体结构,由于焊缝处材料性质的差异,在焊缝附近出现明显的应力不连续性,对晶体界面附近的最大分切应力产生明显影响,引起界面附近分切应力分布梯度的显著增加,使试样的破坏特性发生改变,引起试样的脆性破坏,降低了试样的抗弯曲强度.     

Prediction of the yielding behaviour of rolled polyoxymethylene

The yield stress anisotropy of rolled polyoxymethylene (a semicrystalline polymer) is predicted by treating the polymer as a polycrystalline aggregate having two types of crystal slip system. The model first predicts the texture development on cold rolling, then the angular variation in yield stress for various uniaxial stress and plane strain compression tests. At present the model has four disposable parameters (the critical resolved shear stresses for chain and prism slip, a strain hardening coefficient and a minimum yield stress on reverse yielding), which are amenable to experimental confirmation.     

Strengthening via deformation twinning in a nickel alloy

Nanograins and nanotwins are produced in specimens using one processing technique to allow direct comparison in their nanohardnesses. It is shown that the hardness of nanotwins can be close to the lower end of the hardness of nanograins. The resistance of nanotwins to dislocation movement is explained based on elastic interactions between the incident 60° dislocation and the product dislocations. The latter includes one Shockley partial at the twin boundary and one 60° dislocation in the twinned region. The analysis indicates that a resolved shear stress of at least 1.24 GPa is required for a 60° dislocation to pass across a twin boundary in the nickel alloy investigated. It is this high level of the required shear stress coupled with a limited number of dislocations that can be present between two adjacent twin boundaries that provides nanotwins with high resistance to dislocation movement. The model proposed is corroborated by the detailed analysis of high-resolution transmission electron microscopy.     

Effect of loading direction and initial imperfections on the development of dynamic shear bands in a FCC single crystal

Summary We study plane strain dynamic thermomechanical deformations of a FCC single crystal deformed at an average strain-rate of 1 000 s^–1 along the crystallographic direction [380] with the plane of deformation parallel to the plane (001) of the single crystal. Four different situations are studied; in the first two there is no initial imperfection assumed in the crystal and it is either compressed or pulled, and in the other two the crystal is compressed but either the initial temperature is nonuniform or a small region around the centroid of the cross-section is misoriented relative to the rest of the cross-section. In each case, all twelve slip systems are assumed to be potentially active, and the crystal material is presumed to exhibit strain hardening, strain-rate hardening, and thermal softening. These effects are modelled by using a simple combined isotropic-kinematic hardening expression for the critical resolved shear stress, proposed by Weng, and modified to incorporate the effect of thermal softening of the material. It is found that each one of the slip systems , and contributes essentially equally to the plastic deformations of the crystal and these slip systems become active soon after the load is applied. The same holds for the slip systems , and except that they are active in a region different from that of the previous one. The remaining four slip systems either stay inactive throughout the deformation process, or become active at late stages of the deformation.     

采用数字图像相关方法的莫来石纤维增强气凝胶复合材料力学试验

基于V型缺口试样双轨剪切法设计了面内剪切试验方案,开展了莫来石纤维增强气凝胶复合材料的室温面内剪切和弯曲性能试验,采用数字图像相关方法对试样表面的位移场和应变场进行测量,并分析了力学行为和破坏模式。结果表明:设计的试验方案可以在测试区域获得均匀的剪切应变场,适用于莫来石纤维增强气凝胶复合材料的面内剪切性能测试。试验获得的面内剪切模量和强度分别为248 MPa和0.95 MPa,弯曲模量和强度分别为294 MPa和2.08 MPa。面内剪切载荷下,试样的裂纹萌生于缺口尖端附近,并沿两缺口连线方向扩展。根据弯曲正应变场的分布特点,发现试样中性层与几何对称面不重合,验证了该材料拉压模量不同的性质。采用数字图像相关方法获得的中性层位置和理论计算值比较接近,相对误差在10%左右。     

A study of the loading path and crystal orientation effects on size-dependent limit strength

To better understand the loading path and crystal orientation effects on size-dependent material strength, molecular dynamics (MD) simulations are performed with the use of single crystal diamond (SCD) of various sizes under uniaxial tension and simple shear loading conditions. In the MD simulations, mechanical responses of SCD blocks with three different sizes under 〈1 0 0〉 and 〈1 1 0〉 tensions, and under {1 0 0}〈0 1 0〉, {1 0 0}〈1 1 0〉 and {1 1 0}〈0 0 1〉 shear slips at different loading rates are studied. Based on the simulation data, a power scaling law is proposed to predict the size effect on the material strength of pristine diamond under given loading conditions.     

Influence of crystal orientation on ECAP of aluminum single crystals

A single crystal of high purity aluminum, oriented with the {1 1 1} slip plane and the 1 1 0 slip direction rotated by 20° in a clockwise sense from the theoretical shear plane and the shear direction, was processed by equal-channel angular pressing (ECAP) through a single pass. This configuration was designated the 20° orientation and the results are compared with earlier data obtained on a similar high purity aluminum single crystal in the 0° orientation with the (1 1 1) slip plane and the 1 1 0 slip direction lying parallel to the shear plane and the shear direction. The results show that in both orientations the long axes of the subgrains lie parallel to the slip traces of the primary slip system and the average subgrain widths are 1.3 μm. However, the shearing characteristics are different because the 0° specimen exhibited a conventional B-type rolling texture whereas the 20° specimen deformed by slip on the primary slip system and this system rotated by 40° in a counter-clockwise sense as the specimen passed through the shear zone of the ECAP die.     

Creep mechanisms of U720Li disc superalloy at intermediate temperature

The microstructures of U720Li disc superalloy have been investigated by transmission electron microscopy (TEM) before and after creep test at 725 °C/630 MPa. The evolution of the crept microstructures was marked as three different stages (I, II and III) corresponding to gradually increased strain 0.1%, 5% and 27%, respectively. At stage I, dislocations bypassed secondary γ′ via Orowan loops. At stage II, partial dislocations started to shear secondary γ′, leaving stacking fault (SF) behind and microtwins formed in part of grains. At stage III, grain boundary sliding occurred due to very large strain and increased effective stress. The results indicated that the creep mechanisms of U720Li at 725 °C/630 MPa evolved with gradually increased strain. Orowan looping process combining dislocation slip and climb and partial dislocations shearing precipitates were the main creep mechanisms. It is suggested that decreasing the interparticle spacing of secondary γ′, strengthening secondary γ′ and decreasing stacking fault energy (SFE) of γ matrix may be effective methods to improve the creep property at relatively higher temperatures.