Microstructural modeling of crack nucleation and propagation in high strength martensitic steels

A dislocation-density based multiple-slip crystalline plasticity formulation, a dislocation-density grain boundary (GB) interaction scheme, and an overlapping fracture method were used to investigate crack nucleation and propagation in martensitic steel with retained austenite for both quasi-static and dynamic loading conditions. The formulation accounts for variant morphologies, orientation relationships, and retained austenite that are uniquely inherent to lath martensitic microstructures. The interrelated effects of dislocation-density evolution ahead of crack front and the variant distribution of martensitic blocks on crack nucleation and propagation are investigated. It is shown that dislocation-density generation ahead of crack front can induce dislocation-density accumulations and plastic deformation that can blunt crack propagation. These predictions indicate that variant distribution of martensitic blocks can be optimized to mitigate and potentially inhibit material failure.     

Effects of surface diffusion and resolved shear stress intensity factor on environmentally assisted cracking

Hydrogen induced crack-tip plastic deformation has been known as the primary mechanism of hydrogen assisted cracking and stress corrosion cracking. It has been systematically shown that the same mechanism of environmentally assisted crack-tip dislocation emission causes hydrogen assisted cracking, stress corrosion cracking, and liquid metal embrittlement cracking.An embrittling chemical species has to reach a crack tip in order to accelerate crack growth. Very close to a sharp crack tip, surface diffusion is shown to be the dominant transport process of embrittling species for stage-II crack growth. The role of surface diffusion in stage II crack growth is analyzed. The constant cracking velocity is proportional to the surface diffusion coefficient of an embrittling species and inversely proportional to a length parameter, , which is related to the transport process upstream.Dislocation emission at a crack tip is driven by crack-tip resolved shear stress. Crack-tip resolved shear stress field is characterized by resolved shear stress intensity factor, K_RSS·K_RSS is defined, the procedure for its calculation outlined, and its applications to crack-tip dislocation emission and environmentally assisted cracking discussed.     

Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations

We present molecular dynamics simulations of [1 1 0]-oriented Si nanowires (NWs) under a constant strain rate in tension until failure, using the modified embedded-atom-method (MEAM) potential. The fracture behavior of the NWs depends on both temperature and NW diameter. For NWs of diameter larger than 4 nm, cleavage fracture on the transverse (1 1 0) plane are predominantly observed at temperatures below 1000 K. At higher temperatures, the same NWs shear extensively on inclined {1 1 1} planes prior to fracture, analogous to the brittle-to-ductile transition (BDT) in bulk Si. Surprisingly, NWs with diameter less than 4 nm fail by shear regardless of temperature. Detailed analysis reveals that cleavage fracture is initiated by the nucleation of a crack, while shear failure is initiated by the nucleation of a dislocation, both from the surface. While dislocation mobility is believed to be the controlling factor of BDT in bulk Si, our analysis showed that the change of failure mechanism in Si NWs with decreasing diameters is nucleation controlled. Our results are compared with a recent in situ tensile experiment of Si NWs showing ductile failure at room temperature.     

16MnR钢缺口试样解理断裂行为研究

研究了低合金热轧钢16MnR缺口试样在$-196\,{^\circ}$C和$-130\,{^\circ}$C的解理断裂机 理. 拉伸试验、单、双缺口四点弯曲实验、断口形貌观察以及有限元分析结果表明, 缺口试 样发生解理断裂时均起裂于夹杂物粒子, 一种位于缺口根部前端(IC型), 另一种位于距缺口 根部较远的条形裂纹前端(SIC型); 且随温度升高, 起裂源的类型从$-196\,{^\circ}$C下的IC 型转变为$-130\,{^\circ}$C下的SIC型. 微裂纹均形核于夹杂物, 最终的断裂由铁素体晶粒尺 寸的微裂纹扩展控制. 缺口试样IC型解理断裂遵循裂纹形核条 件$\varepsilon_{\rm p} \ge \varepsilon_{\rm pc}$和裂纹扩展条件$\sigma_{yy} \ge \sigma_{f}$, 而SIC型解理断裂条件则演化为$\varepsilon_{\rm p}+\varepsilon_{\rm ps} \ge \varepsilon_{\rm pc}$和$\sigma_{yy} +\sigma_{yy{\rm s}} \ge \sigma_{f}$.     

A statistical, physical-based, micro-mechanical model of hydrogen-induced intergranular fracture in steel

Intergranular cracking associated with hydrogen embrittlement represents a particularly severe degradation mechanism in metallic structures which can lead to sudden and unexpected catastrophic fractures. As a basis for a strategy for the prognosis of such failures, here we present a comprehensive physical-based statistical micro-mechanical model of such embrittlement which we use to quantitatively predict the degradation in fracture strength of a high-strength steel with increasing hydrogen concentration, with the predictions verified by experiment. The mechanistic role of dissolved hydrogen is identified by the transition to a locally stress-controlled fracture, which is modeled as being initiated by a dislocation pile-up against a grain-boundary carbide which in turn leads to interface decohesion and intergranular fracture. Akin to cleavage fracture in steel, the “strength” of these carbides is modeled using weakest-link statistics. We associate the dominant role of hydrogen with trapping at dislocations; this trapped hydrogen reduces the stress that impedes dislocation motion and also lowers the reversible work of decohesion at the tip of dislocation pile-up at the carbide/matrix interface. Mechanistically, the model advocates the synergistic action of both the hydrogen-enhanced local plasticity and decohesion mechanisms in dictating failure.     

TEMPERATURE EFFECT ON LOW-CYCLE FATIGUE BEHAVIOR OF NICKEL-BASED SINGLE CRYSTALLINE SUPERALLOY

The low-cycle fatigue （LCF） behavior of a nickel-based single crystal superalloy with [001] orientation was studied at an intermediate temperature of T0℃ and a higher temperature of To ＋ 250℃ under a constant low strain rate of 10^-3 s^-1 in ambient atmosphere. The superalloy exhibited cyclic tension-compression asymmetry which is dependent on the temperature and applied strain amplitude. Analysis on the fracture surfaces showed that the surface and subsurface casting micropores were the major crack initiation sites. Interior Ta-rich carbides were frequently observed in all specimens. Two distinct types of fracture were suggested by fractogaphy. One type was characterized by Mode-I cracking with a microscopically rough surface at To ＋ 250℃. Whereas the other type at lower temperature T0℃ favored either one or several of the octahedral {111} planes, in contrast to the normal Mode-I growth mode typically observed at low loading frequencies （several Hz）. The failure mechanisms for two cracking modes are shearing of γ＇ precipitates together with the matrix at T0℃ and cracking confined in the matrix and the γ/γ＇interface at To - 250℃.     

Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging

We demonstrate the use of X-ray phase contrast imaging with sub-microsecond temporal resolution to obtain quantitative visualization of dynamic fracture processes in brittle solids. We examine an amorphous solid (fused silica), a ceramic single crystal (single-crystal quartz), and a polycrystalline ceramic (boron carbide), in the form of single-edge notched specimens loaded using a three-point apparatus at nominal strain rates up to \(\sim \)800 s^?1. We observe that the crack tip speed for boron carbide is relatively independent of mode I stress intensity factor rate (\(\dot {K}_{\mathrm {I}}\)) for these rates of loading, while that of fused silica and single-crystal quartz increases with \(\dot {K}_{\mathrm {I}}\). Further, for the amorphous and single crystal cases, we observe the development of a crack tip instability in the form of crack branching as the crack tip speed approaches 45% of the Rayleigh wave speed. This suggests that strain-rate-dependent mechanisms contribute to crack branching. Such mechanisms may, in turn, affect the macroscopic fracture properties of these materials.     

Numerical computation of central crack growth in an active particle of electrodes influenced by multiple factors

Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithium-ion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles \((\hbox {LiMn}_{2}\hbox {O}_{4})\) by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling.     

Nucleation of micro-cracks for polycrystalline metal with anisotropy: micro-stress evaluation

Presented is the local stresses on the crystallographic plane as they are influenced by the metal fracture with anisotropy. It is based on the nucleation of micro-cracks and its unstable equilibrium in a polycrystal with texture. Crystallographic texture causes non-uniform distribution of the crack nucleus orientations owing to their preference to expand or open on certain crystallographic planes. This is the main cause of anisotropy of cleavage fracture stress of textured metal. “Oriented” micro-stresses in textured metal contribute to the anisotropic effect. In view of what has been said, accumulated plastic strains at fracture is analysed.     

Modeling hydrogen attack effect on creep fracture toughness

The effect of high temperature hydrogen attack on creep crack growth rates in steels is studied by modeling the interaction between creep deformation and gaseous pressures generated by hydrogen and methane. The equilibrium methane pressure as a function of hydrogen pressure, temperature and carbide types for carbon steels and Cr–Mo steels is calculated. This gaseous driving force is incorporated into a micromechanics model for void growth along grain boundaries of a creeping solid. Growth and coalescence of voids along grain boundaries is modeled by a microporous strip of cell elements, referred to as the fracture process zone. The cell elements are governed by a nonlinear viscous constitutive relation for a voided material. Two rate sensitivities as well as two types of grain boundaries are considered in this computational study. Simulations of creep crack growth accelerated by gaseous pressures are performed under conditions of small-scale and extensive creep. The computed crack growth rates at elevated temperatures are able to reproduce the trends of experimental results.     

Numerical simulations of crack deflection at a twist-misoriented grain boundary between two ideally brittle crystals

Finite-element simulations are used to model crack propagation across twist-misoriented grain boundaries, which are an important source of toughness in lamellar microstructures such as TiAl. We consider a twist grain boundary (GB) between two adjacent grains, and assume that each grain has a single cleavage orientation. The cleavage planes and GB are modeled as a set of cohesive surfaces, and the crack path and effective toughness of the system are simulated using a dynamic finite-element method (FEM). As the crack approaches the GB under remote mode I loading, it is allowed to either deflect along the GB and/or induce the nucleation of a periodic array of cracks in the adjacent grain. The simulations predict (i) a critical toughness ratio between the GB and the cleavage planes for the crack to propagate into the adjacent grain; (ii) an array of cracks in the GB and the twisted grain; (iii) the macroscopic mode I toughness of the solid as a function of a generalized measure of crack length; and (iv) the influence of GB toughness and twist misorientation on the effective toughness of the solid.     

Dynamic shear-strain localization and inclusion effects in lath martensitic steels subjected to high pressure loads

A three-dimensional multiple-slip dislocation-density based crystalline formulation, specialized finite-element formulations, and specialized Voronoi tessellations adapted to martensitic orientations, were used to investigate shear-strain localization, and dislocation-density evolution in martensitic microstructures under dynamic compressive loading conditions. The formulation is based on accounting for variant morphologies and orientations, secondary-phase structures, and initial dislocations-densities that are uniquely inherent to martensitic microstructures. The effects of strain rate and inclusions on the evolution of shear-strain localization were investigated. The analysis indicates that variant morphology and orientations have a direct consequence on dislocation-density accumulation and inelastic localization in martensitic microstructures, and that lath directions, orientations, and arrangements are critical characteristics of high-strength martensitic dynamic behavior. It is shown that tensile hydrostatic pressure due to the unloading of the plastic waves at the free boundary and extensive shear-strain accumulation occurs at certain triple junctions. Furthermore, plastic shear-slip accumulation between inclusions and the surrounding martensitic matrix results in shear-strain localization and increases in the tensile hydrostatic pressure at critical locations, such as trip junctions.     

Evaluation of fracture behavior of iron aluminides

Comparative fracture tests of three Fe-28%Al iron aluminides showed that alloys with Zr and C addition (FA-187) or with B, Zr, and C addition (FA-189) are extrinsically more susceptible to environmental embrittlement than the base ternary alloy (FA-186) under constant tensile loading condition. This may be caused by the variations of grain boundary morphology (i.e. changes of grain size and grain boundary cohesive strength) caused by the alloy addition. The effect of grain boundary size and cohesive strength are further investigated with reference to the susceptibility of hydrogen embrittlement. Finite element simulation of initial intergranular fracture of two iron aluminides (FA-186 and FA-189) are made. The computational scheme involves coupling the stress and mass diffusion analyses to determine crack-tip stress state and the crack tip hydrogen diffusion. Maximum strain failure criteria was adopted to simulate intergranular fracture. The numerical modeling results correlated well with the experimental data. The result further confirmed that the grain boundary morphology is important as it appears to control the intrinsic and extrinsic fracture behavior of iron aluminides.     

A statistical model of brittle fracture by transgranular cleavage

A model for brittle fracture by transgranular cleavage cracking is presented based on the application of weakest link statistics to the critical microstructural fracture mechanisms. The model permits prediction of the macroscopic fracture toughness, K_Ic, in single phase microstructures containing a known distribution of particles, and defines the critical distance from the crack tip at which the initial cracking event is most probable. The model is developed for unstable fracture ahead of a sharp crack considering both linear elastic and nonlinear elastic (“elastic/plastic”) crack tip stress fields. Predictions are evaluated by comparison with experimental results on the low temperature flow and fracture behavior of a low carbon mild steel with a simple ferrite/grain boundary carbide microstructure.     

Macroscopic and microscopic examination of the relationship between crack velocity and path and Rayleigh surface wave speed in single crystal silicon

The speed of Rayleigh surface waves, denoted C_R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C_R on crack path selection in particular.Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C_R, and thereafter the crack deflects to other cleavage planes. Indeed, C_R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C_R has no influence on the crack deflection phenomenon. However, the misfit in C_R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone.     

伴随微孔洞生长的裂纹弹塑性定常扩展

裂纹在韧性材料中扩展时,将们随着微孔洞的萌生和生长,孔洞的萌生和深化将直接影响着材料的总体断裂韧性和强度,以往的研究主要集中在将裂纹的扩展刻划为微孔洞的萌生、生长和汇合这样一个过程。从传统的断裂过程区模型出发研究微孔洞的萌生和生长对材料总体断裂韧性的影响,通过采用Ｇｕｒｓｏｎ模型,建立塑性增量本构关系,然后针对定常扩展情况直接进行分析,孔洞对材料断裂韧性的影响由本构关系刻划,而在孔洞汇合模型中,上     

Hydride-induced embrittlement and fracture in metals—effect of stress and temperature distribution

A mathematical model for the hydrogen embrittlement of hydride forming metals has been developed. The model takes into account the coupling of the operating physical processes, namely: (i) hydrogen diffusion, (ii) hydride precipitation, (iii) non-mechanical energy flow and (iv) hydride/solid-solution deformation. Material damage and crack growth are also simulated by using de-cohesion model, which takes into account the time variation of energy of de-cohesion, due to the time-dependent process of hydride precipitation. The bulk of the material, outside the de-cohesion layer, is assumed to behave elastically. The hydrogen embrittlement model has been implemented numerically into a finite element framework and tested successfully against experimental data and analytical solutions on hydrogen thermal transport (in: Wunderlich, W. (Ed.), Proceedings of the European Conference on Computational Mechanics, Munich, Germany, 1999, J. Nucl. Mater. (2000a) 279 (2-3) 273). The model has been used for the simulation of Zircaloy-2 hydrogen embrittlement and delayed hydride cracking initiation in (i) a boundary layer problem of a semi-infinite crack, under mode I loading and constant temperature, and (ii) a cracked plate, under tensile stress and temperature gradient. The initial and boundary conditions in case (ii) are those encountered in the fuel cladding of light water reactors, during operation. The effects of near-tip stress intensification as well as of temperature gradient on hydride precipitation and material damage have been studied. The numerical simulation predicts hydride precipitation at a small distance from the crack-tip. When the remote loading is sufficient, the near-tip hydrides fracture. Thus a microcrack is generated, which is separated from the main crack by a ductile ligament, in agreement with experimental observations.     

A combined experimental–numerical investigation of ductile fracture in bending of a class of ferritic–martensitic steel

We present a combined experimental–numerical study on fracture initiation at the convex surface and its propagation during bending of a class of ferritic–martensitic steel. On the experimental side, so-called free bending experiments are conducted on DP1000 steel sheets until fracture, realizing optical and scanning electron microscopy analyses on the post mortem specimens for fracture characterization. A blended Mode I – Mode II fracture pattern, which is driven by cavitation at non-metallic inclusions as well as martensitic islands and resultant softening-based intense strain localization, is observed. Phenomena like crack zig-zagging and crack alternation at the bend apex along the bending axis are introduced and discussed. On the numerical side, based on this physical motivation, the process is simulated in 2D plane strain and 3D, using Gurson’s dilatant plasticity model with a recent shear modification, strain-based void nucleation, and coalescence effects. The effect of certain material parameters (initial porosity, damage at coalescence and failure, shear modification term, etc.), plane strain constraint and mesh size on the localization and the fracture behavior are investigated in detail.     

A quantum-mechanically informed continuum model of hydrogen embrittlement

We present a model of hydrogen embrittlement based upon: (i) a cohesive law dependent on impurity coverage that is calculated from first principles; (ii) a stress-assisted diffusion equation with appropriate boundary conditions accounting for the environment; (iii) a static continuum analysis of crack growth including plasticity; and (iv) the Langmuir relation determining the impurity coverage from its bulk concentration. We consider the effect of the following parameters: yield strength, stress intensity factor, hydrogen concentration in the environment, and temperature. The calculations reproduce the following experimental trends: (i) time to initiation and its dependence on yield strength and stress intensity factor; (ii) finite crack jump at initiation; (iii) intermittent crack growth; (iv) stages I and II of crack growth and their dependence on yield strength; (v) the effect of the environmental impurity concentration on the threshold stress intensity factor; and (vi) the effect of temperature on stage II crack velocity in the low-temperature range. In addition, the theoretically and experimentally observed intermittent cracking may be understood as being due to a time lag in the diffusion of hydrogen towards the cohesive zone, since a buildup of hydrogen is necessary in order for the crack to advance. The predictions of the model are in good quantitative agreement with available measurements, suggesting that hydrogen-induced degradation of cohesion is a likely mechanism for hydrogen-assisted cracking.     

级联碰撞对层状珠光体力学行为的影响

铁素体合金钢是目前在核能工程界应用最为广泛的一种金属结构材料,以渗碳体和铁素体基体构成的层状珠光体是铁素体合金钢中常见的金相结构。深入理解辐照效应对层状珠光体力学性能的影响对高辐照条件下铁素体钢的材料设计与寿命评估有着重要的理论参考意义。基于以上考虑,本文采用分子动力学（MD）模拟,研究了连续低能铁原子级联碰撞对渗碳体/铁素体两相界面的破坏情况,探讨了经历不同程度级联碰撞的两相结构在单向拉伸以及压缩荷载下的初始屈服情况。通过对MD模拟结果的深入分析,得到了以下主要结论：a.辐照会破坏渗碳体/铁素体两相界面的失配位错结构,引起渗碳体的分解,并促进碳原子向铁素体的扩散;b.在单轴拉伸荷载作用下,级联碰撞会使初始屈服机制由{112}<111>位错滑移系的开动转变为间隙原子团簇附近位错环的形核与长大;c.在单轴压缩荷载作用下,级联碰撞会使初始塑性变形机制由{110}<111>滑移系的开动转变为{112}<111>滑移系的开动;d)无论在单轴拉伸还是压缩情况下,级联碰撞（及辐照效应）都会导致位错初始形核应力的提升。本文的研究结果为铁素体合金钢的辐照硬化和辐照脆化行为提供了新的微观解释,对于辐照条件下铁素体合金钢材料的优化设计有一定的参考意义。