Plastic zone boundary and Poisson’s ratio depending on plastic loosening

A more accurate determination of the plastic zone boundary for plane strain and plane stress state is proposed. The plastic zone boundary is determined with regard to plastic loosening, given exact stress distribution and Schleicher yield criterion. The presence of mean normal stress in the Schleicher criterion ensures uniform expansion of the plastic zone. The dependence of Poisson’s ratio and constraint ratio for plastic strain on plastic loosening of material is examined. These parameters peak at the tip or in the immediate vicinity of a stress concentrator and decrease with distance from it. In a small neighborhood of the crack tip, a region is found in which Poisson’s ratio is impossible to determine from the Schleicher criterion. The size of this region is identified with the size of the region of exhausted plasticity.     

A comparative analysis of the mesoscale stress-strain state in two- and three-dimensional polycrystalline specimens

A comparative analysis has been performed of mesoscale stress and strain distributions in sections of 3D polycrystalline specimens and in their 2D cousins under plane strain and plane stress conditions. For similar macroscale stress-strain curves, the mesoscale plastic strain localization patterns are shown to differ essentially both qualitatively and quantitatively in 2D and 3D models. In other words, the same effective mechanical response of the materials can be provided by different mesoscale stress and strain distributions depending on the loading technique used and geometric features of the specimens (thin plates, thick specimens, etc.).     

Local zone wise elastic and plastic properties of electron beam welded Ti–6Al–4V alloy using digital image correlation technique: A comparative study between uniform stress and virtual fields method

Joining of materials using welding results in the formation of material zones with varying microstructure across the weld. Extraction of the mechanical properties of those individual heterogeneous zones are important in designing components and structures comprised of welds. In this study, the zone wise local extraction of the elastic and plastic properties of an electron beam welded Ti–6Al–4V titanium alloy has been carried out using both the uniform stress method (USM) and the virtual fields method (VFM) involving digital image correlation (DIC) technique. The surface strain field obtained using DIC technique from a transverse weld specimen tensile testing is used for extracting the zone wise strain evolution. Initially, using uniform stress assumption, zone wise full range stress–strain curves are extracted. In USM methodology, the elastic and plastic material models are fitted to the zone wise stress–strain curves and required parameters are extracted from it. But inherent disadvantage is lot of images need to be processed for the parameter extraction. Recently, VFM is gaining lot of popularity in characterization domain as it is robust, accurate and faster. VFM is based on the principle of virtual work where, the weak form of local equilibrium equations and kinematically admissible virtual displacement fields are utilized for parameter extraction. Hollomon׳s power law is used here as the hardening rule. Young׳s modulus, Poisson׳s ratio, yield stress, strength coefficient and strain hardening exponent are the parameters extracted zone wise using both USM and VFM. A Vicker׳s microhardness measurement is also conducted across the weld zone towards mapping the strength behavior. Fusion zone has reported higher yield strength, strength coefficient and Poisson׳s ratio. Young׳s modulus value is found decreasing from base metal towards the fusion zone. The trend observed in parameter variation across the weld zone obtained by both USM and VFM compares very well. Due to various advantages associated with VFM technique it is generally recommended for parameter extraction.     

Low-temperature fatigue behaviour and development of dislocation structure in aluminium single crystals with single-slip orientation

Al single crystals oriented for single slip were cyclically deformed under constant plastic strain amplitudes between 1?×?10^?3 and 5?×?10^?2 at 77?K. Al single crystals showed hardening to saturation at all applied shear stress amplitudes. The resultant cyclic stress–strain curve (CSSC) showed a stress plateau in a range of plastic strain amplitude from 2?×?10^?3 to 2?×?10^?2. Surface observation revealed that multiple slip systems were active even at the strain amplitude in the plateau region. At plastic strain amplitudes corresponding to the plateau of the CSSC, persistent slip bands (PSBs) were formed parallel to the primary slip plane. In the PSBs, well-developed dislocation walls parallel to the {100} planes were observed. The microstructure in the PSBs was explained by the fact of multiple activation of the primary and critical slip systems. The above results indicate that the high stacking fault energy of Al is an important factor affecting the fatigue behaviour even at 77?K.     

Emission of stress waves during fracture

Emission of both longitudinal and surface (Rayleigh) waves during fracture of plates under conditions of plane stress and plane strain were studied experimentally. The non-equilibrated tensile stress in the fractured section of the plate creates an elastic wave, which travels radially along the plate at the sound speed. Moreover, the high surface deformation around the crack tip, due to the high stress concentration there, propagates as a surface wave following fracture of this zone, at the respective Rayleigh wave speed with a circular wavefront. The influence of the thickness of the plate and the type of fracture (brittle or ductile) was examined and interesting results were derived, by utilizing a high speed photography technique.     

Local plasticity of Al thin films as revealed by x-ray microdiffraction

Grain-to-grain interactions dominate the plasticity of Al thin films and establish effective length scales smaller than the grain size. We have measured large strain distributions and their changes under plastic strain in 1.5-microm-thick Al 0.5% Cu films using a 0.8-microm-diameter white x-ray probe at the Advanced Light Source. Strain distributions arise not only from the distribution of grain sizes and orientation, but also from the differences in grain shape and from stress environment. Multiple active glide plane domains have been found within single grains. Large grains behave like multiple smaller grains even before a dislocation substructure can evolve.     

激光冲击强化“残余应力洞”的形成机制

利用ABAQUS有限元软件进行了单个圆形高斯光斑的激光冲击强化数值模拟,分析材料表面光斑中心区域形成的"残余应力洞"现象,并通过分析材料的动态力学响应特征揭示了"残余应力洞"的形成机制。结果表明:在冲击波加载时,光斑边界处会产生很强的剪切应力,形成向四周传播的表面稀疏波和向材料内部传播的剪切波。当稀疏波同时传播到光斑中心,发生相遇、汇聚,使材料产生急剧的上下位移过程,造成冲击波加载塑性变形后的二次塑性变形。二次塑性变形中形成了较大的剪切塑性应变,并降低了冲击波加载阶段产生的轴向和径向塑性应变,使残余压应力降低,从而形成"残余应力洞"。     

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.     

2024铝合金激光多次冲击诱导残余应力状态分布规律

采用高功率激光器多次冲击2024铝合金,用X射线衍射技术分析了冲击区域的残余应力,研究了冲击残余应力状态分布规律,并用其评价激光冲击强化效果。研究表明,随着冲击次数增加,塑变量及塑性应变梯度逐渐减小,测点是双向压应力状态,而4次冲击时,塑性应变梯度增大,光斑中心是单向压应力状态,其他点是双向压应力状态。当激光功率密度为2.8 GW/cm2时,3次冲击强化效果最佳,材料是二向压应力状态,残余最大主应力及应力强度的均值最大,方差最小,分布基本均匀,塑性应变梯度较小。     

Externally applied stress sign and film elastic properties effects on brittle film fracture

Rectangular stainless steel samples with TiN film deposited on the front lateral surface were loaded in three-point bending to the maximum normal strain of 6%. Scanning electron microscopy showed that vertical cracks appeared in the tension zone when the tensile strain exceeded 1.5%, while horizontal cracks appeared in the compression zone when the compressive strain exceeded –2.9%. Film cracks in the compressive zone originate from the tensile stress imposed by the plastically deformed substrate due to the Poisson’s expansion. Taking plastic deformation and Poisson’s expansion of the substrate in compression into account, theoretical analysis of normal stress distribution along the cracked film segment in compression is presented. Substrate strain and film elastic properties affect film cracking in the compressive zone. At larger compressive strain, some transverse cracks along with buckling cause the film spallation. The presented method is useful for studying brittle film fracture with variable strain levels in a single sample.     

裂纹顶端的异号位错和无位错区的象力理论

本文改进BCS型裂纹位错模型,并对裂纹顶端范性区的位错密度分布进行了计算。结果指出,在紧靠裂纹顶端的滑移面上出现和裂纹位错异号的位错。这些负号位错将移至裂纹顶端并使之钝化而留下一个无位错区或低位错密度区。本文对无位错区形成的象力理论进行了讨论。 关键词：     

Simulation of plasticity in nanocrystalline silicon

Molecular dynamics investigation of plasticity in a model nanocrystalline silicon system demonstrates that inelastic deformation localizes in intergranular regions. The carriers of plasticity in these regions are atomic environments, which can be described as high-density liquid-like amorphous silicon. During fully developed flow, plasticity is confined to system-spanning intergranular zones of easy flow. As an active flow zone rotates out of the plane of maximum resolved shear stress during deformation to large strain, new zones of easy flow are formed. Compatibility of the microstructure is accommodated by processes such as grain rotation and formation of new grains. Nano-scale voids or cracks may form if stress concentrations emerge which cannot be relaxed by a mechanism that simultaneously preserves microstructural compatibility.     

Analysis of the dependence of the global load on the mechanical parameters of ice under interaction between an ice field and construction

A series of problems concerning interaction between an ice field and a vertically plane construction has been solved numerically using a computing system based on the discontinuous Galerkin method. The results of calculations have been processed, and the maximum global load upon the construction at different physicomechanical parameters of ice has been analyzed based on these data. The chosen parameters were Young’s modulus, the yield stress, tensile stress, and plastic failure strain.     

On the foundations of stochastic dislocation dynamics

A stochastic approach to dislocation dynamics is proposed that starts off from considering the geometrically necessary fluctuations of the local stress and strain rate caused by long-range dislocation interactions during plastic flow. On a mesoscopic scale, a crystal undergoing plastic deformation is thus considered an effective fluctuating medium. The auto- and cross-correlation functions of the effective stress and the plastic strain rate are derived. The influences of dislocation multiplication, storage and cross slip on the correlation functions are discussed. Various analogies and fundamental differences to the statistical mechanics of thermodynamic equilibrium are outlined. Application of the theory of noise-induced transitions to dislocation dynamics gives new insight into the physical origin of the spontaneous formation of dislocation structures during plastic deformation. The results demonstrate the importance of the strain-rate sensitivity in dislocation patterning.     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.     

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.     

Plastic deformation behaviour of layer-grained silver polycrystalline from atomistic simulation

Two types of nanocrystalline polycrystalline silver models in bulk, film and nanowire forms were constructed with layer-grained or equiaxed grain morphologies and average grain sizes of ~7.8 and ~14.7 nm. Uniaxial tensile deformation was performed to investigate the effect of grain morphology and free surface on the plastic deformation behaviour under the strain rate of 5 × 10⁸ and 10⁷ s^?1 at 0.1 K. Grain Boundary (GB) orientation and dimensions in layer-grained morphology promoted the formation of sessile dislocation structures. Some dislocations interacted with each other and some dislocations got obstructed by stacking faults. However, the resulting configurations did not last long enough to cause strain hardening. Strain softening was observed in all models except for the layer-grained models in bulk form, where steady plastic flow was observed after yield. The location and orientation of free surfaces with respect to GBs imposed geometric constraints on the deformation mechanisms (GB sliding and formation of sessile dislocations) which produced asymmetric stress states that influenced the elastic as well as plastic response of the material. The yield stress and flow stress were much smaller at lower strain rate simulations. The proportion of perfect dislocations increased as the strain rate decreased from 5 × 10⁸ to 10⁷ s^?1 due to the decrease of applied stress. Dislocations were mainly emitted from grain boundaries or triple junctions at both high and low strain rate deformations. These results provided insights into the understanding of layer-grained nanocrystalline materials and the synthesis of materials with both high strength and ductility.     

Relation between the Hurst Exponent and the Efficiency of Self-organization of a Deformable System

We have established the degree of self-organization of a system under plastic deformation at different scale levels. Using fractal analysis, we have determined the Hurst exponent and correlation lengths in the region of formation of a corrugated (wrinkled) structure in [111] nickel single crystals under compression. This has made it possible to single out two (micro-and meso-) levels of self-organization in the deformable system. A qualitative relation between the values of the Hurst exponent and the stages of the stress–strain curve has been established.     

Kinetics of pore formation upon plastic deformation of crystals with a cesium chloride structure

The kinetics of pore formation upon plastic deformation of crystals with a cesium chloride structure was studied as the first stage of a first-order phase transition in a deformable media. The shape and the critical dimensions of microvoids depending on the critical shear stress were found. The number of critical microvoids per unit volume arising per unit time on the surface of a slip plane was determined based on the kinetics of formation of pairs of charged vacancies. The volume fraction of pores at the initial stage of plastic deformation in CsBr and CsI crystals was estimated.     

Initial damage induced by thermal residual stress and microscopic failure analysis of carbon-fiber reinforced composite under shear loading

In order to study the mechanical properties and the progressive failure process of composite under shear loading, a representative volume element (RVE) of fiber random distribution was established, with two dominant damage mechanisms – matrix plastic deformation and interfacial debonding – included in the simulation by the extended Drucker–Prager model and cohesive zone model, respectively. Also, a temperature-dependent RVE has been set up to analyze the influence of thermal residual stress. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the in-plane shear fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation. The progressive damage process and final failure mode of in-plane shear model which are based on constitute are very consistent with the observed result under scanning electron microscopy of V-notched rail shear test. Also, a transverse shear model was established as contrast in order to comprehensively understand the mechanical properties of composite materials under shear loading, and the progressive damage process and final failure mode of composite under transverse shear loading were researched. Thermal residual stress changes the damage initiation locations and damage evolution path and causes significant decreases in the strength and fracture strain.