Effect of electric current on the migration of hydrogen interstitial atoms in the region of a crack tip in a crystal

The effect of a constant electric current on the migration of interstitial atoms dissolved in a crystal in the region of a tensile crack tip is estimated. The calculation takes into account plastic deformation that is produced in the vicinity of the crack tip in the loaded sample by dislocation motion in active slip planes of the crystal under the action of mechanically and electrically induced shear stresses, Joule heat release, the Thomson effect, and ponderomotive forces and allows for the effect of gas exchange near the crack edges on the evolution of the distribution of interstitial impurity atoms. The time dependence of the stress intensity factor is found for both the cases of the presence and absence of a constant electric current near the crack tip. Numerical calculations are performed for an α-Fe crystal.     

On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate

Elastic–plastic stress analysis has been carried out for the plastic zone size and crack tip opening displacement of a sub-interface crack with small scale yielding. In our study, the shape of plastic zone is assumed as a long, slim strip at both crack tips. In the plastic zone, both normal stress and shear stress exist and are considered due to the bi-material interface. The values of the plastic zone size, normal stress and shear stress are determined by satisfying the conditions where both Modes I and II stress intensity factors vanish and Von Mises yield criterion is met. In the present paper, the sub-interface crack is simulated by continuously distributed dislocations which will result in singular integral equations. Those singular integral equations can be solved by reducing them to a set of linear equations. The values of the plastic zone size and crack tip opening displacement are obtained through an iterative procedure. Finally, the effect of normalized loading, normalized crack depth (distance to the interface) and Dundurs’ parameters on the normalized plastic zone size and the normalized crack tip opening displacement is discussed.     

Evolution of the concentration of point defects at the tip of a crack

The evolution of the distribution of interstitial impurity atoms in the plastic zone around the tip of a tension crack is analyzed. The transport of point defects is determined by: 1) the hydrostatic component of the elastic stress at the crack tip, created by the superposition of the elastic fields of the crack and dislocations; 2) the elastic field of moving dislocations (“sweeping out” of interstitial impurity atoms); 3) the dislocation-driven transport of point defects present in the dislocation cores. The contributions of each mechanism of transport of point defects to the crack tip are calculated over the entire time from the start of loading of a sample containing a crack until an equilibrium distribution of plastic deformation is established after the cessation of loading. Numerical calculations are carried out for interstitial hydrogen atoms dissolved in an α-Fe crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1580–1585 (September 1997)     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

α-Fe裂纹的分子动力学研究

通过分子动力学方法，模拟了α-Fe裂纹的单轴拉伸实验中的形变过程.研究了不同晶体取向裂纹的形变特点和断裂机理，观察到各种形变现象，如位错形核和发射，位错运动，堆垛层错或孪晶的形成，纳米空洞的形成与连接等.计算结果表明，裂纹扩展是塑性过程和弹性过程相结合的过程，其中塑性过程表现为由裂尖发射的位错导致的原子切变行为，而弹性过程的发生则是由无位错区中的原子断键所导致.同时还研究了α-Fe裂纹的形变特点和断裂机理与温度场和应力场的依赖关系.     

Analysis of the plasticizing effect of hydrogen dissolved in a crystal on the evolution of plastic deformation at the tip of a crack

The effect of interstitial hydrogen atoms on the evolution of plastic deformation in a crystal at the tip of a tensile crack is estimated taking into account gas exchange at the crack banks. It is found that, for an initial concentration of not less than 10^?4, the plasticizing effect of dissolved hydrogen causing a dislocation expulsion is significant and can be responsible (at least, partially) for plasticization. As regards the evolution of the distribution of hydrogen atoms, a monotonic drain of dissolved hydrogen atoms into the hollow of the crack is observed for concentrations below 5×10^?4, while at higher concentrations the impurity concentration at the banks of the crack varies periodically: complete drain is replaced by the accumulation of hydrogen corresponding to a “blocking” of the drain by the gas pressure. Numerical calculations are made for an α-Fe crystal.     

Effect of stress state on deformation and fracture of nanocrystalline copper:Molecular dynamics simulation

Deformation in a microcomponent is often constrained by surrounding joined material making the component under mixed loading and multiple stress states. In this study, molecular dynamics(MD) simulation are conducted to probe the effect of stress states on the deformation and fracture of nanocrystalline Cu. Tensile strain is applied on a Cu single crystal,bicrystal and polycrystal respectively, under two different tension boundary conditions. Simulations are first conducted on the bicrystal and polycrystal models without lattice imperfection. The results reveal that, compared with the performance of simulation models under free boundary condition, the transverse stress caused by the constrained boundary condition leads to a much higher tensile stress and can severely limit the plastic deformation, which in return promotes cleavage fracture in the model. Simulations are then performed on Cu single crystal and polycrystal with an initial crack. Under constrained boundary condition, the crack tip propagates rapidly in the single crystal in a cleavage manner while the crack becomes blunting and extends along the grain boundaries in the polycrystal. Under free boundary condition, massive dislocation activities dominate the deformation mechanisms and the crack plays a little role in both single crystals and polycrystals.     

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.     

Analytical estimation of dislocation distribution at the tip of arrested cracks

Computer simulation technique is used for studying the plastic flow at the tip of an arrested crack in lithium fluoride crystals. Two stages of the dislocation structure formation at the tip of a crack are analyzed: the formation of slip lines at the instant of crack arresting, and their evolution after sample unloading and partial healing of the crack. The size and the number of dislocations in a slip line are determined as functions of the loading force at the instant of crack arresting and on frictional stresses. It is shown that, during sample unloading and healing, some dislocations emerge at the plane of the crack under the action of mutual repulsion and image forces, so that the dislocation density attains its maximum value at a distance from the crack tip. A finite region free of dislocations exists in the immediate vicinity of the crack tip.     

晶体相场法研究应力状态及晶体取向对微裂纹尖端扩展行为的影响

采用晶体相场模拟研究了单向拉伸作用下初始应力状态、晶体取向角度对单晶材料内部微裂纹尖端扩展行为的影响, 以(111)晶面上的预制中心裂纹为研究对象探讨了微裂纹尖端扩展行为的纳观机理, 结果表明: 微裂纹的扩展行为主要发生在<011>(111)滑移系上, 扩展行为与扩展方向与材料所处的初始应力状态及晶体取向紧密相关. 预拉伸应力状态将首先诱发微裂纹尖端生成滑移位错, 进而导致晶面解理而实现微裂纹尖端沿[011]晶向扩展, 扩展到一定程度后由于位错塞积, 应力集中, 使裂纹扩展方向沿另一滑移方向[101], 并形成锯齿形边缘; 预剪切应力状态下, 微裂纹尖端首先在[101]晶向解理扩展, 并诱发位错产生, 形成空洞聚集型长大的二次裂纹, 形成了明显的剪切带; 预偏变形状态下微裂纹尖端则直接以晶面解理形式[101]在上进行扩展, 直至断裂失效; 微裂纹尖端扩展行为随晶体取向不同而不同, 较小的取向角度会在裂纹尖端形成滑移位错, 诱发空位而形成二次裂纹, 而较大的取向角下的裂纹尖端则以直接解理扩展为主, 扩展方向与拉伸方向几近垂直.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Atomistic simulation of microtwinning at the crack tip in L12 Ni3Al

The mechanisms of deformation at the crack tip in L1₂ Ni₃Al have been studied by molecular dynamics simulations. The stress-induced microtwinning is found to occur at the crack tip when a sufficiently high stress concentration exists. The formation mechanism of the microtwinning is discussed. It is found to be achieved by the emission of Shockley partial dislocations from the crack tip and then slip of the Shockley partial dislocations on adjacent {111} planes. Furthermore, the mechanism of the microtwinning is also discussed from the standpoint of stress.     

Elastic interaction of a dislocation array with a phase boundary

The equilibrium configuration of an array of dislocations in parallel equidistant slip planes under an external shear stress near a welded boundary between two isotropic half-spaces having different elastic constants is computed. For large external stress, the dislocations are arranged into an arc concave when seen from the boundary. It is concluded that such an arc is formed at the tip of a twin or of a martensitic plate near a phase boundary. The tensile stress across the boundary due to an edge dislocation array is discussed in connection with the formation of an interfacial crack.     

Yielding of glassy polymer on a microstructural level

Based on recent studies of the morphology and of shear bands and crazes in amorphous polymers it is suggested that shear is the basic mechanism of plastic deformation. Three stages are proposed for the formation of crazes, shear yielding at a defect or craze tip due to stress concentration, nodular movement resulting in fibril formation, followed by void formation between the fibrils.     

Fracture of solids in aggressive gases

An interrelation between the surface energy of a material and the work of plastic deformation at a crack tip is analyzed. Theoretical relationships for the limiting stress intensity factors of a crack tip in a medium of aggressive gases and in vacuum are derived. The results of the calculations are compared with the experimental data.     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.     

Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

Crack tip dislocation emission and nanoscale deformation fields in silicon

A micro-crack in silicon was experimentally investigated by using a combination of transmission electron microscopy and geometric phase analysis. The strain fields of the crack tip, with scales of a few tens of nanometers, were mapped. The crack tip dislocation emission and stress relief by dislocation generation around a crack tip can be proved. And, the strain field of an edge dislocation was compared with the Peierls–Nabarro dislocation model at the scale of a dislocation width. We show that the Peierls–Nabarro model is the appropriate theoretical model to describe the deformation fields of the dislocation core.     

Atomistic study of dislocation loop emission from a crack tip

We report the first atomistic calculation of the saddle-point configuration and activation energy for the nucleation of a 3D dislocation loop from a stressed crack tip in single crystal Cu. The transition state is found using reaction pathway sampling schemes, the nudged elastic band, and dimer methods. For the (111)[110] crack, loaded typically at 75% of the athermal critical strain energy release rate for spontaneous dislocation nucleation, the calculated activation energy is 1.1 eV, significantly higher than the continuum estimate. Implications concerning homogeneous dislocation nucleation in the presence of a crack-tip stress field are discussed.     

Analysis of near weld stress field based on strain measurement and physical mesomechanics

Stresses induced by welding are analyzed from the viewpoint of material deformation behavior. Strain gages are used to measure the residual stresses, and electronic speckle-pattern interferometry is used to analyze the response of the welded work to external force. A tensile load is applied to a butt-welded, thin-plate steel specimen, and the resultant strain field is analyzed with the electronic speckle-pattern interferometry. Comparison is made with the case of a nonwelded specimen of the same material and dimension. The analysis indicates that the residual stress due to welding makes the normal strain due to the external tensile load asymmetric. The asymmetry enhances shear and rotational modes of deformation, generating stress concentration at a point away from the weld where the residual stress is substantially negligible. The observed features are discussed based on physical mesomechanics. Analysis reveals plastic deformation like behavior in the response of the welded specimen to the external force.