A framework for statistical modelling of plastic yielding initiated cleavage fracture of structural steels

The well established consensus that cleavage fracture is preceded by plastic deformation in structural steels implies that plastic yielding is the threshold stress state for a volume element to incur cleavage fracture. An accurate compliance with this consensus underlies the normalisation of cumulative cleavage fracture probability and the justification of constraint effect on cleavage fracture. These understandings lead to the proposal of a framework for statistical modelling of cleavage fracture in structural steels. The framework takes the spatial microcrack distribution into account to formulate the cumulative failure probability model that allows for a pertinent physical interpretation of Weibull statistics, and derives the fracture probability of an elemental volume in conformity with the yielding condition from a set of commonly adopted microcrack size or strength distributions. Alternative approaches to calibrating model parameters are suggested based on frequency analysis of brittle particles as cleavage initiators and on statistical analysis of cleavage fracture stress. The strict adherence to plastic yielding as a prerequisite to cleavage fracture also reveals the probabilistic nature of notch brittleness and ductile-to-brittle transition behaviour.     

New aspects of the plastic deformation of silicon – prerequisites for the reshaping of silicon microelements

New shapes of silicon microelements which can be partially situated outside the wafer plane can be created by the combination of wet anisotropic etching and plastic deformation at high temperatures. Therefore new applications become possible. In order to characterize the plastic behaviour of the silicon microelements bending tests in the 3-point manner were carried out at monocrystalline, differently orientated beams with variation of temperature, bending rate and maximum bending. Additionally the fracture strength at room temperature of deformed and undeformed beams was determined. The dislocation content introduced during the deformation was analysed by the etch pit technique. The deformation is characterized by the formation of dislocations, a pronounced yield point effect, and an orientation-dependent strengthening. The yield points depend strongly on temperature. Because of the strong dependence on the deformation parameters it is possible to create the same amount of irreversible deformation at different stages of the stress–bend diagrams resulting in different dislocation contents and therefore different properties. The analysis of the fracture strength values by means of the Weibull statistics shows a slightly decreased average fracture strength of the deformed material in comparison to the undeformed silicon but a strongly increased Weibull modulus. Received: 22 September 1998 / Accepted: 29 January 1999 / Published online: 28 April 1999     

Deformation mechanisms of ultra-thin Al layers in Al/SiC nanolaminates as a function of thickness and temperature

The mechanical properties of Al/SiC nanolaminates with layer thicknesses between 10 and 100 nm were studied by nanoindentation in the temperature range 25 to 100 °C. The strength of the Al layers as a function of the layer thickness and temperature was obtained from the hardness of the nanolaminates by an inverse methodology based on the numerical simulation of the nanoindentation tests by means of the finite element method. The room temperature yield stress of the Al layers showed a large ‘the thinner, the stronger’ effect, which depended not only on the layer thickness but also on the microstructure, which changed with the Al layer thickness. The yield stress of the Al layers at ambient temperature was compatible with a deformation mechanism controlled by the interaction of dislocations with grain boundaries for the thicker layers (>50 nm), while confined layer slip appeared to be dominant for layers below 50 nm. There was a dramatic reduction in the Al yield stress with temperature, which increased as the Al layer thickness decreased, and led to an inverse size effect at 100 °C. This behavior was compatible with plastic deformation mechanisms controlled by grain boundary and interface diffusion at 100 °C, which limit the strength of the ultra-thin Al layers.     

A study of the effect of laser beam geometries on laser bending of sheet metal by buckling mechanism

Laser beam forming has emerged as a new and very promising technique to form sheet metal by thermal residual stresses. The objective of this work is to investigate numerically the effect of rectangular beam geometries, with different transverse width to length aspect ratio, on laser bending process of thin metal sheets, which is dominated by buckling mechanism. In this paper, a comprehensive thermal and structural finite element (FE) analysis is conducted to investigate the effect that these laser beam geometries have on the process and on the final product characteristics. To achieve this, temperature distributions, deformations, plastic strains, stresses, and residual stresses produced by different beam geometries are compared. The results suggest that beam geometries play an important role in the resulting temperature distributions on the workpiece. Longer beam dimensions in the scanning direction (in relation to its lateral dimension) produce higher temperatures due to longer beam–material interaction time. This affects the bending direction and the magnitude of the bending angles. Higher temperatures produce more plastic strains and hence higher deformation. This shows that the temperature-dependent yield stress plays a more dominant role in the deformation of the plate than the spread of the beam in the transverse direction. Also, longer beams have a tendency for the scanning line to curve away from its original position to form a concave shape. This is caused by buckling which develops tensile plastic strains along both ends of the scanning path. The buckling effect produces the opposite curve profile; convex along the tranverse direction and concave along the scanning path.     

Deformation and fracture processes in graphene nanoribbons with linear quadrupoles of disclinations

The deformation and fracture processes in graphene nanoribbons containing linear quadrupoles of disclinations are investigated by the method of molecular dynamics. Special attention is given to estimating the effect of the curvature formed by disclinations and free boundaries in graphene nanoribbons with linear quadrupoles of disclinations on their mechanical characteristics (the stress–strain curve, the strength at the single-axis tension, and the degree of plastic deformation).     

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.     

Plasticity limit of metals during hot plastic deformation

A model of plasticity limit has been derived in the condition of hot plastic deformation, where dynamic recrystallization takes place, through the ratio between the rate of grain boundary sliding and the overall deformation rate. If fracture occurs preferentially at the grain boundaries we can replace the grain boundary deformation through the energy needed to cause fracture and express the temperature influence on the deformation stress. The plasticity limit is then the function of Zener-Hollomon parameter and deformation stress, where the exponent of deformation stress has a value of –4·3.     

Size effects and stochastic behavior of nanoindentation pop in

A statistical model for pop in initiated at preexisting dislocations during nanoindentation is developed to explain size-dependent pop-in stresses. To verify theoretical predictions of this model, experiments were performed on single-crystal Mo, utilizing indenter radii that vary by over 3 orders of magnitude. The stress where plastic deformation begins ranges from the theoretical strength in small volumes, to 1 order of magnitude lower in larger volumes. An intermediate regime shows wide variability in the stress to initiate plastic deformation. Our theory accurately reproduces the experimental cumulative probability distributions, and predicts a scaling behavior that matches experimental behavior.     

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT

The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.     

关於固体的现实应力空间(续)

前文[1]综合四理论[2],[3],[4],[5]构成固体现实应力空间之一初步理论,大体反映固态静力学性质,对金属较对非金属固体反映得当,后者受范形变曲面有异于弥氏圆柱。总起来看,前文仅涉及原则概念,未触及具体问题。为使此理论对金属压力加工及材料试验研究有所帮助,本文进一步研究几个问题:1)由应力空间图形比较不同金属的静力学性质;2)受范形变效率及其计算;3)形变过程之轨迹;并得到一定数量或质量上的结论。同时,附带对前文[1]中一个实验记录图的错误作修正,包括在附录内。     

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.     

Elastic–plastic transition in three-dimensional random materials: massively parallel simulations,fractal morphogenesis and scaling functions

Elastic–plastic transitions were investigated in three-dimensional (3D) macroscopically homogeneous materials, with microscale randomness in constitutive properties, subjected to monotonically increasing, macroscopically uniform loadings. The materials are cubic-shaped domains (of up to 100?×?100?×?100 grains), each grain being cubic-shaped, homogeneous, isotropic and exhibiting elastic–plastic hardening with a J ₂ flow rule. The spatial assignment of the grains’ elastic moduli and/or plastic properties is a strict-white-noise random field. Using massively parallel simulations, we find the set of plastic grains to grow in a partially space-filling fractal pattern with the fractal dimension reaching 3, whereby the sharp kink in the stress–strain curve of individual grains is replaced by a smooth transition in the macroscopically effective stress–strain curve. The randomness in material yield limits is found to have a stronger effect than that in elastic moduli. The elastic–plastic transitions in 3D simulations are observed to progress faster than those in 2D models. By analogy to the scaling analysis of phase transitions in condensed matter physics, we recognize the fully plastic state as a critical point and, upon defining three order parameters (the ‘reduced von-Mises stress’, ‘reduced plastic volume fraction’ and ‘reduced fractal dimension’), three scaling functions are introduced to unify the responses of different materials. The critical exponents are universal regardless of the randomness in various constitutive properties and their random noise levels.     

AlCrFeCuNi高熵合金力学性能的分子动力学模拟

高熵合金具有传统合金无法比拟的高强度、高硬度和高耐磨耐腐蚀性,具有广阔的应用前景。为研究AlCrFeCuNi高熵合金(High entropy alloy,HEA)在轴向载荷作用下的力学性能,采用分子动力学方法,模拟高熵合金的实验制备过程并建立原子模型,研究温度和Al的含量对AlCrFeCuNi高熵合金力学性能的影响,从材料学角度分析了变形过程及其具有高塑性的原因。模拟结果表明,AlCrFeCuNi高熵合金在拉伸载荷作用下依次经历弹性、屈服、塑性3个变形阶段。在屈服阶段,开始出现孪晶和层错,孪晶和层错的产生和生长是合金产生不均匀塑性变形的主要原因之一。高熵合金的杨氏模量和屈服应力随着Al含量的增加近似线性降低,同时具有很强的温度效应,温度越低,Al含量越小,其杨氏模量和屈服应力的下降幅度越大。     

脆性断裂统计理论

本文试图用统计方法,将金属脆性断裂的微观过程与宏观过程结合起来,把断裂理论建立于微裂纹发展动力学的统计基础上。脆性断裂实质上是在小的范性变形过程中微裂纹成核长大的非平衡统计过程和单个主裂纹的传播过程。本文导出了描述这种非平衡统计过程的微分积分方程,并从位错机理出发研究了微裂纹动力学,从而解出了微裂纹的分布函数,求出了金属试样的断裂几率,进而导出了延伸率、断裂强度、范性功、裂纹扩展力、断裂韧性、临界裂纹长度、范性-脆性转变温度以及它们的统计偏差与其它有关物理量之间的函数关系。 关键词：     

光电桅杆水动力作用下的模态分析

通过对光电桅杆在复杂海洋工况下的水动力学分析,得到了光电桅杆的相关力学参数。在理论分析的基础上,通过对光电桅杆进行有限元模型的建立、材料定义、加载和求解,分析了光电桅杆在受到复杂水动力作用下的静态受力变形和动态固有频率和固有振型,为桅杆的最优化设计提供了设计依据。     

脆性断裂的统计理论

本文试图从位错理论出发来探索晶体脆性断裂的统计理论。脆性断裂过程,实质上是微裂缝在极小的范性形变过程中形成长大和传播的随机过程。本文导出了描述这种随机过程的微分方程,利用微裂缝形成长大的位错机理,解出了微裂缝大小的统计分布函数。文中给出了范性形变、加工硬化和活动位错源数目与微裂缝数目和大小之间的函数关系。过去研究脆性断裂时,范性变形只是含糊地包括在有效表面能之内,而加工硬化和活动位错源数目则一向被略去。从微裂缝大小的统计分布函数和微裂缝的传播条件,导出了强度的统计分布函数,从而求得了脆性断裂判别式、脆性断裂强度及脆性-范性转变温度。     

Development of dislocation-based unified material model for simulating microstructure evolution in multipass hot rolling

Dynamic recrystallization and recovery are two competing processes. Both may continue after hot deformation, such as during passes in multipass hot rolling processes, reducing dislocation density of materials and allowing larger plastic deformation to be achieved. The main objective of this research is to develop a set of mechanism-based unified viscoplastic constitutive equations which model the evolution of dislocation density, recrystallization and grain size during and after hot plastic deformation. This set of constitutive equations are determined for a C-Mn steel using an evolutionary programming (EP) optimization technique and implemented into the commercial finite element (FE) solver ABAQUS for process simulations. Numerical procedures to simulate multipass rolling are developed. FE analysis is carried out to simulate the evolution of grain size, dynamic/static recrystallization and recovery, and to rationalize their effects on the viscoplastic flow of the material in a two-pass hot rolling process.     

Effects of Filler Content on Mechanical Properties of Macroporous Composites

The mechanical properties of hydroxyapatite related macroporous biocomposites (MPBs) are influenced by a number of factors, such as the pore size, the filler content and the properties of the matrix and the inclusion. Failure often occurs when the strength of the implant cannot bear the applied mechanical load. In this study, the effects of filler content on the mechanical properties of MPBs have been investigated. A finite element (FE) unit cell model of a macroporous hydroxyapatite–polyetheretherketone (HA–PEEK) biocomposite structure with uniform and interconnected pores has been constructed. In the FE model, the HA particles were assumed to have random distribution, and particle volume fraction would be varied in the PEEK matrix. The material behaviours of both HA and PEEK have been implemented in the ABAQUS finite element code. HA was modelled to exhibit elastic behaviour and undergo plastic softening to a residual strength when a critical stress was reached, while the PEEK matrix would follow elastic–plastic behaviour. The macroscopic compressive stress–strain relations of the macroporous biocomposite structures have been predicted. Increasing particle volume fraction could lead to an increase in the compressive elastic modulus of the structures but a reduction in the compressive strength. The von Mises stress distribution and the effect of stress concentration in the structures with different filler content are also discussed. The proposed model could provide macro-structural and microscopic information of the macroporous biocomposite structure to the designers in order to facilitate the fabrication of this kind of structure with optimum mechanical properties.     

Energy release rate and stress field calculation for debonding crack extension at the fibre-matrix interface during single-fibre pull-out

For the micromechanical modelling of the macroscopic failure of fibre-reinforced composites the formulation of a critical parameter for initiation and extension of debonding cracks at the fibre-matrix interface is essential. This point is discussed for the 'fibre pull-out' specimen, a test commonly used to measure the adhesion quality of fibre-matrix systems. Some of the simplifying assumptions fundamental to shear lag theory-based models of the fibre pull-out test are compared with results from a detailed finite element (FE) model to examine their validity. The FE model strongly contradicts assumptions made with the shear lag theory that the axial stress gradient in the matrix can be neglected from the equilibrium equation. A critical interface shear strength is commonly used as a measure of adhesion quality. But for elastic materials the nature of the stress concentrations at the fibre end and interface crack-tip are singular. Therefore a fracture mechanic approach is better suited for a debonding criterion than a simple finite shear strength. The energy release rate shows a minimum for short crack lengths and may stabilize the moving crack.