Wedge indentation into elastic-plastic single crystals, 1: Asymptotic fields for nearly-flat wedge

Asymptotic stress and deformation fields under the contact point singularities of a nearly-flat wedge indenter and of a flat punch are derived for elastic ideally-plastic single crystals with three effective in-plane slip systems that admit a plane strain deformation state. Face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal-close packed (HCP) crystals are considered. The asymptotic fields for the flat punch are analogous to those at the tip of a stationary crack, so a potential solution is that the deformation field consists entirely of angular constant stress plastic sectors separated by rays of plastic deformation across which stresses change discontinuously. The asymptotic fields for a nearly-flat wedge indenter are analogous to those of a quasistatically growing crack tip fields in that stress discontinuities can not exist across sector boundaries. Hence, the asymptotic fields under the contact point singularities of a nearly-flat wedge indenter are significantly different than those under a flat punch. A family of solutions is derived that consists entirely of elastically deforming angular sectors separated by rays of plastic deformation across which the stress state is continuous. Such a solution can be found for FCC and BCC crystals, but it is shown that the asymptotic fields for HCP crystals must include at least one angular constant stress plastic sector. The structure of such fields is important because they play a significant role in the establishment of the overall fields under a wedge indenter in a single crystal. Numerical simulations—discussed in detail in a companion paper—of the stress and deformation fields under the contact point singularity of a wedge indenter for a FCC crystal possess the salient features of the analytical solution.     

The effect of crack orientation on fracture behavior of tantalum by multiscale simulation

The quasicontinuum (QC) multiscale method is used to investigate anisotropic fracture behaviors of body-centered cubic (BCC) rare metal tantalum (Ta) loaded in Mode I and different fracture mechanisms are discussed from nanoscopic to continuum perspectives to have a deep understanding of brittle and ductile fracture. Initial crack deflection, brittle fracture by cleaving along low surface energy plane, ductile fracture as a result of dislocation emission and fracture accompanied by deformation twinning are all observed near crack tips of different crystal orientations. Particularly, some of these fracture mechanisms are found to be consistent with the latest experimental results. By examining different fracture behaviors, we find the surface energy and the available slip planes play a combined role in determining the fracture mechanisms near a crack tip. Both isotropic and anisotropic critical stress intensity factors are derived and compared for different crack orientations. A straightforward criterion that is proved to be applicable is used to distinguish brittle fracture from ductile fracture.     

Effect of temperature on dislocation emission from crack tip for BCC metal Mo

The effect of thermally activated energy on the dislocation emission from a crack tip in BCC metal Mo is simulated in this paper. Based on the correlative reference model on which the flexible displacement boundary scheme is introduced naturally, the simulation shows that as temperature increases the critical stress intensity factor for the first dislocation emission will decrease and the total number of emitted dislocations increase for the same external load. The dislocation velocity and extensive distance among partial dislocations are not sensitive to temperature. After a dislocation emission, two different deformation states are observed, the stable and unstable deformation states. In the stable deformation state, the nucleated dislocation will emit from the crack tip and piles up at a distance far away from the crack tip, after that the new dislocation can not be nucleated unless the external loading increases. In the unstable deformation state, a number of dislocations can be emitted from the crack tip continuously under the same external load. The project is supported by the National Natural Science Foundation of China.     

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.     

Anti-plane shear cracks in ideally plastic crystals

Cracks in ductile single crystals are analyzed here for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by Rice (1967, 1984) and Freund (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.     

分子动力学模拟含不同初始缺陷单晶镍的断裂行为与应力演化

断裂是一个跨尺度复杂的物理过程,对宏观尺度的断裂行为已有深入的研究和发展,然而对微观尺度的断裂行为及断裂过程中应力场的变化缺乏深入的理解。本文通过分子动力学模拟,研究了具有不同初始缺陷(尖锐裂纹、钝裂纹和孔洞)的单晶镍的断裂行为和应力分布特征。结果表明,不同的初始缺陷导致了不同的断裂机制、断裂强度和抗断裂性能。含初始孔洞的单晶镍样品有最高的断裂强度和最强的抗断裂性能,这与孔洞扩展过程中堆积层错的形成密切相关。其次是含初始钝裂纹的样品,在裂纹扩展过程中出现由[100]超位错发射引起的裂尖钝化;含尖锐裂纹的样品表现为脆性断裂,裂尖原子没有出现微结构的变化,其强度和抗断裂性能最低。此外,不同的初始缺陷也会导致断裂过程中应力分布的变化,对含有尖锐裂纹的脆性断裂试样,高应力(拉伸应力、平均应力和米塞斯应力)总是出现在扩展裂纹的裂尖。而对于含有钝裂纹或孔洞的韧性断裂试样,高应力不仅分布在裂尖,也分布在位错发射和堆积层错形成的区域,在裂纹/孔洞扩展之前,应力随着加载时间的增加而迅速增加,而一旦裂纹或孔洞开始扩展,应力增加非常缓慢或几乎不增加,但拉伸应力值始终大于平均应力和米塞斯应力值。这表明,在I型...     

Stress and energy density fields near a blunted crack front in power hardening material

Using Jaumann and Dienes rates of Euler stress in elastic-plastic constitutive equations of finite deformation, plane strain finite element analysis for a compact tension specimen with a blunted crack front is made. The Euler stress, Kirchhoff stress and volume strain energy density near a blunted crack tip are computed. Constitutive relations with different deformation rates affect the the near crack tip solution in a region within an order of magnitude of the crack opening displacement. The results differed from the corresponding solution of deformation plasticity (or nonlinear elasticity) with increasing deformation. They are smaller in a local region of about 2 to 10 times of the crack opening distance.The volume energy density near the crack tip is computed, the stationary values of which determine the locations of extensive yielding and possible sites of crack initiation. It remained nearly constant with increasing deformation. Such a character tends to support the volume energy density criterion as a means for quantifying the ductile fracture behavior of metals.     

A finite element study of the near crack tip deformation of a ductile material under mixed mode loading

In ductile fracture, voids near a crack tip play an important role. From this point of view, a large deformation finite element analysis has been made to study the deformation, stress and strain, and void ratio near the crack tip under mixed mode plane strain loading conditions, employing Gurson's constitutive equation which has taken into account the effects of void nucleation and growth. The results show that: (i) one corner of the crack tip sharpens while the other corner blunts, (ii) the stress and strain distributions except for the near crack tip region, can be superimposed by normalizing distance from the crack tip by a crack tip deformation length, i.e., a steady-state solution under a mixed mode condition has been obtained, (iii) the field near a crack tip can be divided into four characteristic fields (K field, HRR field, blunted crack tip field, and damaged region), and (iv) the strain and void volume fraction become concentrated in the sharpened part of a crack tip with increasing Mode II component.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

Quasicontinuum simulation of single crystal nano-plate with a mixed-mode crack

The quasicontinuum (QC) method is employed to simulate a nickel single crystal nano-plate with a mixed-mode crack. Atomic stresses near the crack tip are fitted according to the elastoplastic fracture mechanics equations. It is found that the atomic stress fields neighboring the crack tip are also singular and controlled by the atomic stress intensity factors. And then the critical energy release rates for brittle and ductile fracture are computed and compared in order to predict crack propagation or dislocation emission. Four possible slip directions at the crack tip are pointed out. Finally, the slip direction around the crack tip is determined by the shear stress and it is well consistent with the atomic pictures from the QC simulation.     

Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic–viscoplastic constitutive relation with various hardening–softening–hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip.On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening(or softening–hardening) has a particularly strong effect on the near crack tip stress and deformation fields.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

Mechanics and fracture of crack tip deformable bi-material interface

Novel interface deformable bi-layer beam theory is developed to account for local effects at crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable sub-layers with consideration of crack tip deformation. Unlike the sub-layer model in the literature in which the crack tip deformations under the interface peel and shear stresses are ignored and thus a “rigid” joint is used, the present study introduces two interface compliances to account for the effect of interface stresses on the crack tip deformation which is referred to as the elastic foundation effect; thus a flexible condition along the interface is considered. Closed-form solutions of resultant forces, deformations, and interface stresses are obtained for each sub-layer in the bi-layer beam, of which the local effects at the crack tip are demonstrated. In this study, an elastic deformable crack tip model is presented for the first time which can improve the split beam solution. The present model is in excellent agreements with analytical 2-D continuum solutions and finite element analyses. The resulting crack tip rotation is then used to calculate the energy release rate (ERR) and stress intensity factor (SIF) of interface fracture in bi-layer materials. Explicit closed-form solutions for ERR and SIF are obtained for which both the transverse shear and crack tip deformation effects are accounted. Compared to the full continuum elasticity analysis, such as finite element analysis, the present solutions are much explicit, more applicable, while comparable in accuracy. Further, the concept of deformable crack tip model can be applied to other bi-layer beam analyses (e.g., delamination buckling and vibration, etc.).     

采用显微网格法研究韧性材料平面应力状态下裂尖附近的应变场

用显微网格数字图象处理方法，测量了韧性材料平面应力条件下Ｉ型单边裂纹尖端附近的应变场。实验结果表明：在裂尖两侧存在与裂纹方向夹角约为５０°的大变形带。最大应变位于离裂尖一定距离的大变形带上，随着载荷增加，最大应变的位置逐渐靠近裂纹尖端。应变峰值轨迹线在裂纹顶端呈放射状，载荷增加时，应变峰值的轨迹线位置并不改变。     

Mode I and mode II crack tip asymptotic fields with strain gradient effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material lengthl, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient. The project supported by the National Natural Science Foundation of China (19704100), National Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-20), CAS K.C. Wong Post-doctoral Research Award Fund and Post-doctoral Science Fund of China     

Micro-crack tip fracture of commercial grade aluminum under mixed mode loading

In situ tensile tests were made in a scanning electron microscope (SEM) to investigate the deformation and micro-fracture in the immediate vicinity of a micro-crack tip in commercial pure aluminum with large-size crystal. Examined are the slip line field, stress intensity factor, strain energy density factor and crack tip opening displacement (CTOD) for mixed mode loading. Blunting and sharpening effects are observed. The latter is controlled by localized slip while the former by uniformed slip of the operating slip system with the highest crack tip Schmid factor. The operating slip system depends on the crystallographic orientation of crystal containing micro-cracks.The damage and fracture take place in the blunted region and depend on the coarsening and spacing of uniformed slip lines. The mixed mode micro-crack propagates along the direction where the voids grow and coalesce into the micro-crack. The direction also depends on the orientation of the applied loading. This suggests that the formation of macro-fracture mechanics could be applied. In particular, the minimum strain energy density criterion is suitable for determining the direction of micro-crack instability in the mixed mode. The in situ data were used to yield a nearly constant critical, minimum strain energy density factor for onset of micro-cracking.     

Special rotational deformation effect on the emission of dislocations from a crack tip in deformed nanocrystalline solids

The interaction between the special rotational deformation and the crack in deformed nanocrystalline ceramics and metals is investigated by the complex variable method. We have theoretically described the effects of the disclination quadrupole produced by the special rotational deformation on the emission of lattice dislocations from the crack tip. The complex form expressions of the stress field and the force field are divided. The critical stress intensity factors for the first dislocation emission are calculated. The influence of the disclination strength, the grain size (the quadrupole arms), the location of the disclinations and the angle between the crack plane and one of the quadrupole arms, as well as the crack length on the critical stress intensity factors is discussed in detail. And the results show that, the special rotational deformation has great influence on the dislocation emission from the crack tip.     

氢对体心立方金属裂纹尖端变形过程的影响

利用扫描电镜(SEM)原位拉伸,观察了 Fe-3％Si 单晶体裂尖的变形和断裂过程。用网格法加计算机处理系统测出了裂纹尖端的应变场及氢对应变分布的影响。发现在Ⅰ型载荷下,主裂纹尖端应变呈不对称分布,形变带内应变梯度很大。形变带内应变分布为: ε_(yy)=f(x)exp(-Ar).氢不改变裂纹尖端塑性变形特征,但能明显促进裂纹尖端局部塑性变形的非均匀增加。     

Application of microline/grid methods to temperature dependent microscopic deformation and damage in CFRP laminates

Tensile tests of CFRP symmetric cross-ply laminates are carried out in a scanning electron microscope (SEM), and microscopic interlaminar deformation and damage near the transverse crack tip are visualized by microlines or microgrids printed on the specimen edge surface. The local deformation around the transverse crack tip is observed at 20°C, 80°C, 120°C and 160°C to evaluate the effect of thermal residual stress on the microscopic deformation and damage in the interlaminar region near the transverse crack tip. Temperature dependence of the axial crack opening displacement (COD) is also measured. The displacement field of the specimen edge surface obtained from these experimental results is compared with the theoretical model proposed by Lee, Allen and Harris. The analysis is modified to consider the temperature effect, and a good agreement is obtained between the modified theoretical predictions and experimental results.