FCC晶体中晶体取向对孔洞长大和聚合的影响

通过编制率相关有限元用户子程序，采用包含一个和两个球形孔洞的单胞探求了FCC晶体中晶体取向对孔洞长大和聚合的影响。计算结果表明：晶体取向对孔洞长大的影响较大，孔洞的形状和长大方向与晶体取向密切相关：由于变形不均匀，孔洞在晶界处产生尖角，易形成裂纹。由于约束较少，孔洞周围和两孔洞间的区域塑性变形较大，晶体的转动和滑移主要集中在孔洞周围以及两孔洞间的区域。     

Simulation of lattice orientation effects on void growth and coalescence by crystal plasticity

A three dimensional rate-dependent crystal plasticity model is applied to study the influence of crystal orientation and grain boundary on the void growth and coalescence. The 3D computational model is a unit cell including one sphere void or two sphere voids. The results of three different orientations for single crystal and bicrystals are compared. It is found that crystallographic orientation has noticeable influences on the void growth direction,void shape, and void coalescence of single crystal. The void growth rate of bicrystals depends on the crystallographic orientations and grain boundary direction.     

Correlations Among Void Shape Distributions,Dynamic Damage Mode,and Loading Kinetics

Three-dimensional x-ray tomography (XRT) provides a nondestructive technique to characterize the size, shape, and location of damage in dynamically loaded metals. A shape-fitting method comprising the inertia tensors of individual damage sites was applied to study differences of spall damage development in face-centered-cubic (FCC) and hexagonal-closed-packed (HCP) multicrystals and for a suite of experiments on high-purity copper to examine the influence of loading kinetics on the spall damage process. Applying a volume-weighted average to the best-fit ellipsoidal aspect-ratios allows a quantitative assessment for determining the extent of damage coalescence present in a shocked metal. It was found that incipient transgranular HCP spall damage nucleates in a lenticular shape and is heavily oriented along particular crystallographic slip directions. In polycrystalline materials, shape distributions indicate that a decrease in the tensile loading rate leads to a transition to coalesced damage dominance and that the plastic processes driving void growth are time dependent.     

镍基单晶超合金中孔洞长大的试验和有限元分析

在高温状态下，镍基单晶超合金的变形、损伤及断裂分析中，孔洞的长大都起着主要的作用。本研究进行了系列的蠕变、疲劳及热机械疲劳（TMF）试验。对试件的断面进行的SEM观察表明，所有的断面都是有许多小断面构成，在断面的中心，至少有一个孔洞。孔洞的尺寸与加载的条件相关。使用晶体塑性有限元程序对单胞模型进行分析，模拟孔洞的长大规律。给出了蠕变和弹塑性两种条件下的模拟结果及不同的晶体取向对孔穴长大的影响结果。对孔洞长大的有限元分析有助于对实验结果的理解。     

Coupled Crystal Plasticity–Phase Field Fracture Simulation Study on Damage Evolution Around a Void: Pore Shape Versus Crystallographic Orientation

Various mechanisms such as anisotropic plastic flow, damage nucleation, and crack propagation govern the overall mechanical response of structural materials. Understanding how these mechanisms interact, i.e. if they amplify mutually or compete with each other, is an essential prerequisite for the design of improved alloys. This study shows—by using the free and open source software DAMASK (the Düsseldorf Advanced Material Simulation Kit)—how the coupling of crystal plasticity and phase field fracture methods can increase the understanding of the complex interplay between crystallographic orientation and the geometry of a void. To this end, crack initiation and propagation around an experimentally obtained pore with complex shape is investigated and compared to the situation of a simplified spherical void. Three different crystallographic orientations of the aluminum matrix hosting the defects are considered. It is shown that crack initiation and propagation depend in a non-trivial way on crystallographic orientation and its associated plastic behavior as well as on the shape of the pore.     

Modeling void growth in polycrystalline materials

Most structural materials are polycrystalline aggregates whose constituent crystals are irregular in shape, have anisotropic mechanical properties and contain a variety of defects, resulting in very complicated damage evolution. Failure models of these materials remain empirically calibrated due to the lack of a thorough understanding of the controlling processes at the scale of the materials’ heterogeneity, i.e. the mesoscale. This paper describes a novel formulation for a quantitative, microstructure-sensitive three-dimensional mesoscale prediction of ductile damage of polycrystalline materials, in the important void growth phase of the process. Specifically, we have extended a formulation based on fast Fourier transforms to compute growth of intergranular voids in porous polycrystalline materials. In this way, two widely used micromechanical formulations, i.e. polycrystal plasticity and dilatational plasticity, have been efficiently combined, with crystals and voids represented explicitly, to predict porosity evolution. The proposed void growth algorithm is first validated by comparison with corresponding finite-element unit cell results. Next, in order to isolate the influence of microstructure on void growth, the extended formulation is applied to a face-centered cubic polycrystal with uniform texture and intergranular cavities, and to a porous material with homogenous isotropic matrix and identical initial porosity distribution. These simulations allow us to assess the effect of the matrix’s polycrystallinity on porosity evolution. Microstructural effects, such as the influence of the Taylor factor of the crystalline ligaments linking interacting voids, were predicted and qualitatively confirmed by post-shocked microstrostructural characterization of polycrystalline copper.     

含铸造微孔镍基单晶合金蠕变损伤和裂纹萌生的模拟计算

基于镍基单晶合金蠕变变形过程中的细、微观组织结构变化及损伤特点,建立了考虑材质劣化和孔洞损伤的双参数蠕变损伤本构方程。利用所建模型对裂纹前缘含铸造缺陷（孔洞）的镍基单晶合金紧凑拉伸（CT）试样蠕变损伤和裂纹萌生进行了模拟计算,并考虑了晶体取向偏差和随机性的影响。计算结果表明：晶体取向和孔洞位置对试样蠕变损伤和裂纹萌生行为有着显著的影响。当孔洞距切口根部距离较近时,裂纹形核于切口附近的孔洞表面,裂纹形核时间较短;孔洞距切口根部距离较远时,裂纹形核位置位于切口表面,具体位置取决于试样的晶体取向,裂纹形核时间较长。随着加载轴晶体取向偏角的增大,裂纹形核时间明显缩短,其分散性加大,最大有34.7%的变化幅度;试样在2个不受控的晶体取向变化时,在偏角为45°和80°出现极值,裂纹形核时间最大偏差达3倍。     

Void growth in metals: Atomistic calculations

Molecular dynamics simulations in monocrystalline and bicrystalline copper were carried out with LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to reveal void growth mechanisms. The specimens were subjected to tensile uniaxial strains; the results confirm that the emission of (shear) loops is the primary mechanism of void growth. It is observed that many of these shear loops develop along two slip planes (and not one, as previously thought), in a heretofore unidentified mechanism of cooperative growth. The emission of dislocations from voids is the first stage, and their reaction and interaction is the second stage. These loops, forming initially on different {1 1 1} planes, join at the intersection, if the Burgers vector of the dislocations is parallel to the intersection of two {1 1 1} planes: a 〈1 1 0〉 direction. Thus, the two dislocations cancel at the intersection and a biplanar shear loop is formed. The expansion of the loops and their cross slip leads to the severely work-hardened region surrounding a growing void. Calculations were carried out on voids with different sizes, and a size dependence of the stress threshold to emit dislocations was obtained by MD, in disagreement with the Gurson model which is scale independent. This disagreement is most marked for the nanometer sized voids. The scale dependence of the stress required to grow voids is interpreted in terms of the decreasing availability of optimally oriented shear planes and increased stress required to nucleate shear loops as the void size is reduced. The growth of voids simulated by MD is compared with the Cocks–Ashby constitutive model and significant agreement is found. The density of geometrically necessary dislocations as a function of void size is calculated based on the emission of shear loops and their outward propagation. Calculations are also carried out for a void at the interface between two grains to simulate polycrystalline response. The dislocation emission pattern is qualitatively similar to microscope observations.     

一种镍基单晶高温合金持久各向异性行为

研究了一种镍基单晶高温合金DD499的[001],[011]和[111]3个晶体取向在典型应力条件下的持久性能。结果表明,持久寿命的取向依赖性与温度和应力有关。760℃,790MPa时,[001]取向的持久寿命明显高于[011]和[111]取向;1040℃,165MPa时,持久寿命由大到小顺序为[111]>[001]>[011],但不同取向的各向异性减弱。利用SEM观察持久断裂后的断口和组织结构表明,760℃,790MPa时,[001]取向试样的断裂特征为解理和准解理混合型断裂,[011]取向为单系滑移引起的剪切断裂,而[111]取向为多系滑移引起的剪切断裂;1040℃,165MPa时,3种取向都为微孔聚集型断裂。     

A phase field model for electromigration-induced surface evolution

In this study, a phase field model is presented to study the effects of electromigration on the surface evolution of single crystal Al metal interconnects. Two dimensional computer simulations are performed for the surface evolution of metal interconnects due to electromigration in various conditions, such as anisotropy in diffusivity, different initial void sizes, and different crystallographic directions compared to the direction of the ambient electric field. From the results of computer simulations, it may be seen that the types of anisotropy and the relative direction of the diffusivity are the decisive factors in motion and shape change. As the symmetry of anisotropy in diffusivity decreases, the void evolves into a more unstable shape. Moreover, the voids of the system with two-fold diffusion symmetry are most likely to evolve into slits when the crystallographic direction is toward a specific orientation compared to the direction of the ambient electric field. This article is based on a presentation made in the 2002 Korea-US symposium on the “Phase Transformations of Nano-Materials,” organized as a special program of the 2002 Annual Meeting of the Korean Institute of Metals and Materials, held at Yonsei University, Seoul, Korea on October 25–26, 2002.     

Investigation of the tensor character of mesoscopic internal stresses in tensile-deformed nickel single crystals by X-ray diffraction

X-ray diffraction profiles of tensile-deformed nickel single crystals with two different orientations of the loading axis were investigated. To characterize the internal elastic strain state on a mesoscopic scale, the profile shapes of different Bragg reflections were analysed. The asymmetric profile broadening is interpreted on the basis of a two-component model for internal stresses in a dislocation cell structure. A least-squares method was applied to determine the stress tensor for the cell interior from the asymmetry parameters of at least six independent reflections. Furthermore, this method was advanced to evaluate the distribution of the plastic deformation across the slip systems. Taking into account an inclusion approximation, by this way the calculated internal stresses were correlated with the plastic strain in the cells. The orientation of the principal axes of the stress tensor and the heterogeneity of slip in the slip systems found agree with model assumptions for the tensile deformation.     

Compressive response of NiTi single crystals

The deformation of NiTi shape memory single crystals are reported under compression loading for selected crystal orientations and two different Ti₃Ni₄ precipitate sizes. For the [148] orientation, selected for highest recoverable strains, the peak aging treatment decreased the transformation stress from austenite to martensite. At the same time, peak aging raised the flow stress of both the austenite and martensite compared to the overaged case by increasing the resistance of the material to dislocation motion. The transformation proceeds beyond the stress plateau region and extends until martensite yielding occurs. This results in recoverable strain levels equivalent to the theoretical estimate of 6.4%. The [112] orientation was chosen to produce two variant formations and in this case, the transformation proceeded over an ascending stress–strain curve compared to the nearly plateau response for the [148] case. Since the austenite and martensite yield levels are reached at a smaller strain level in this case, the maximum recoverable strain was limited to 3.5% even though the theoretical estimates are near 5.1%. The theoretical estimates of transformation strains were established for Type I and Type II twinning cases to cover all possible habit plane and twin systems. TEM investigations support that slip in austenite occurs concomitant with increasing transformation strains. In the [001] orientation, the unfavorable slip systems for dislocation motion in the austenite inhibit slip and permit recoverable strains similar to the theoretical estimates (nearly 4.2%). The [001] orientation exhibits a continuous increase of flow stress with temperature beyond 360 K unlike any other orientation. The results point out that in order to optimize the material performance, close attention must be paid to the selection of the crystallographic orientation, and the precipitate size through heat treatment.     

Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper

An efficient full-field formulation based on fast Fourier transforms (FFTs) for the prediction of the viscoplastic deformation of polycrystals is applied to the study of the subgrain texture and microstructure evolution in polycrystalline Cu deformed under tension. Direct input from orientation imaging microscopy (OIM) images is used in the construction of the initial unit cell. Average orientations and misorientations predicted after 11% tensile strain are directly compared with OIM measurements, showing good agreement. The differences between misorientations of surface grains compared with bulk grains are estimated, and the orientation dependence of intragranular misorientations is studied. Measurements and simulations agree in that grains with initial orientation near 〈1 1 0〉 tend to develop higher misorientations. This behavior can be explained in terms of attraction towards the two stable orientations and grain interaction. Only models that account explicitly for interaction between individual grains, like the FFT-based formulation, are able to capture these effects.     

A probabilistic crystal plasticity model for modeling grain shape effects based on slip geometry

A new statistical theory is introduced that takes into account the coupling between grain size, shape and crystallographic texture during deformation of polycrystalline microstructures. A “grain size orientation distribution function” (GSODF) is used to encode the probability density of finding a grain size D along a direction (given by unit vector n) in grains with orientation g. The GSODF is sampled from the input microstructure and is represented in a finite element mesh. During elastoplastic deformation, the evolution of grain size D (in direction θ) and the orientation g is tracked by directly updating the GSODF probabilities using a Lagrangian probability update scheme. The effect of grain shape (e.g. in high aspect ratio grains) is modeled by including the apparent grain size as seen by various different active slip systems in the grain within the constitutive law for the slip system resistance. The prediction of texture and strains achieved by the statistical approach is compared to Taylor aggregate and finite element deformation analysis of a planar polycrystalline microstructure. The role of grain shape and size in determining plastic response is investigated and a new adaptive GSODF model for modeling microstructures with multimodal grain shapes is proposed.     

单晶Nb拉伸,压缩及恒应变疲劳后的滑移系和滑移特征

研究了单滑移位向和多滑移位向Ｎｂ单晶在拉伸，压缩及循环变形时的滑移系，根据试样表面滑移线的方向，在极图上确定滑移面，单滑移位向（［３２１］）的单晶，在拉伸时的滑移系为（１０１）［１１１］，在压缩时是（１０１）［１１１］和（２１３）［１１１］．根据ｂｃｃ晶体变形特点，分析了拉伸，压缩和循环变形的滑移系之间的关系，用光学显微镜和透射电镜复型观察了试样的表面形貌，确定了多滑移位向（［１１０］位向）单晶滑     

Void growth by dislocation emission

Laser shock experiments conducted at an energy density of 61 MJ/m² revealed void initiation and growth at stress application times of approximately 10 ns. It is shown that void growth cannot be accomplished by vacancy diffusion under these conditions, even taking into account shock heating. An alternative, dislocation-emission-based mechanism, is proposed for void growth. The shear stresses are highest at 45° to the void surface and decay with increasing distance from the surface. Two mechanisms accounting for the generation of geometrically necessary dislocations required for void growth are proposed: prismatic and shear loops. A criterion for the emission of a dislocation from the surface of a void under remote tension is formulated, analogous to Rice and Thomson’s criterion for crack blunting by dislocation emission from the crack tip. The critical stress is calculated for the emission of a single dislocation and a dislocation pair for any size of initial void. It is shown that the critical stress for dislocation emission decreases with increasing void size. Dislocations with a wider core are more easily emitted than dislocations with a narrow core.     

1种新的模拟铝合金铸态组织的随机性方法

采用1种新的随机性模拟方法并与宏观传热过程相耦合，对铝合金的微观组织进行了模拟研究。计算中采用了简化的枝晶形状。建立了简化的枝晶形状的物理与数学模型，并提出了1种形状函数来描述晶粒的外部轮廓。基于简化的晶粒形状，采用坐标变换技术来描述过冷液相中晶粒的生长过程及其对周围节点的捕获过程。连续形核模型被用来处理异质形核现象，在生长模型中则考虑了枝晶尖端生长动力学和择优生长方向。开发了等轴晶生长的模拟程序，并进行了二维计算。进行了浇注金属型和砂型试样的模拟验证实验。结果表明，对两种不同的工艺，所得到的晶粒组织不同，金属型铸造时得到的晶粒尺寸较小，砂型铸造的较大。模拟结果与金相观察结果相符。     

Yielding behavior of aluminum-rich single crystalline γ-TiAl

The yielding behavior of Al-rich single crystalline γ-Ti 55.5 at% Al has been measured along near [0 0 1], [0 1 0] and orientations in both tension and compression and as function of temperature. All three orientations displayed anomalous yielding and a pronounced tension/compression asymmetry. The relative strength of the material, location of the anomalous yielding peak, and tension/compression asymmetry are all orientation dependent. A micromechanical superdislocation model addressing crystal geometry, sense of the applied load, Escaig forces and the Yoo torque is presented to explain the observed experimental results.     

Texture evolution of the γ- and the α/α2-phase during hot rolling of γ-TiAl based alloys

Multiple hot rolling experiments were performed in the upper area of the α+γ phase field of the γ-TiAl based alloy Ti46Al9Nb (in atomic percent). The texture evolution for both the γ- and the α/α₂-phase has been investigated by X-ray diffraction. In the γ-phase textures comparable to those known from fcc-metals evolve. The texture components and fibers were separated and described with respect to the lower symmetry of the L1₀-structure. Computer simulations of the deformation texture evolution allow to attribute specific texture components to the predominant activity of ordinary dislocations, super dislocations and twinning, respectively. The accompanying recrystallization appears to be orientation dependent. In the α/α₂-phase transversal and basal type textures similar to those found after hot rolling of two-phase titanium based alloys have been identified. Based on the literature about titanium-based alloys specific orientations were correlated with characteristic slip activity. The underlying mechanisms of texture evolution and orientation dependent recrystallization are discussed for both phases.     

Void initiation in fcc metals: Effect of loading orientation and nanocrystalline effects

It is shown, through molecular dynamics simulations, that the emission and outward expansion of special dislocation loops, nucleated at the surface of nanosized voids, are responsible for the outward flux of matter, promoting their growth. Calculations performed for different orientations of the tensile axis, [0 0 1], [1 1 0] and [1 1 1], reveal new features of these loops for a face-centered cubic metal, copper, and show that their extremities remain attached to the surface of voids. There is a significant effect of the loading orientation on the sequence in which the loops form and interact. As a consequence, the initially spherical voids develop facets. Calculations reveal that loop emission occurs for voids with radii as low as 0.15 nm, containing two vacancies. This occurs at a von Mises stress approximately equal to 0.12G (where G is the shear modulus of the material), and is close to the stress at which dislocation loops nucleate homogeneously. The velocities of the leading partial dislocations are measured and found to be subsonic (～1000 m s^?1). It is shown, for nanocrystalline metals that void initiation takes place at grain boundaries and that their growth proceeds by grain boundary debonding and partial dislocation emission into the grains. The principal difference with monocrystals is that the voids do not become spherical and that their growth proceeds along the boundaries. Differences in stress states (hydrostatic and uniaxial strain) are discussed. The critical stress for void nucleation and growth in the nanocrystalline metal is considerably lower than in the monocrystalline case by virtue of the availability of nucleation sites at grain boundaries (von Mises stress ～0.05G). This suggests a hierarchy of nucleation sites in materials, starting with dispersed phases, triple points and grain boundaries, and proceeding with vacancy complexes up to divacancies.