Multiresolution continuum modeling of micro-void assisted dynamic adiabatic shear band propagation

A thermal-mechanical multiresolution continuum theory is applied within a finite element framework to model the initiation and propagation of dynamic shear bands in a steel alloy. The shear instability and subsequent stress collapse, which are responsible for dynamic adiabatic shear band propagation, are captured by including the effects of shear driven microvoid damage in a single constitutive model. The shear band width during propagation is controlled via a combination of thermal conductance and an embedded evolving length scale parameter present in the multiresolution continuum formulation. In particular, as the material reaches a shear instability and begins to soften, the dominant length scale parameter (and hence shear band width) transitions from the alloy grain size to the spacing between micro-voids. Emphasis is placed on modeling stress collapse due to micro-void damage while simultaneously capturing the appropriate scale of inhomogeneous deformation. The goal is to assist in the microscale optimization of alloys which are susceptible to shear band failure.     

THEORETICAL ANALYSIS ON THE NUCLEATION OF MICRO-DAMAGE IN CEMENT MORTAR UNDER COMPRESSIVE LOADING AND SULFATE ATTACK

Effect of uniaxial compression on the nucleation of micro-damage in cement mortar under sulfate attack is investigated.Shape and size of micro-voids in cement mortar is detected using Micro Computed Tomography techniques.The formation of delayed ettringite crystal is analyzed using scanning electron microscope and energy disperse spectrum methods.Deformation of micro-voids and the distribution of stress at the surface of a micro-void are calculated.It is found that the nucleation of micro-cracks is caused by the tensile stress at the voids’ surface,and such damage nucleation will be speeded up by the remote uniaxial compressive load.     

Influence of void nucleation on ductile shear fracture at a free surface

An approximate continuum model of a ductile, porous material is used to study the influence of the nucleation and growth of micro-voids on the formation of shear bands and the occurrence of surface shear fracture in a solid subject to plane strain tension. Bifurcation into diffuse modes is analysed for a plane strain tensile specimen described by these constitutive relations, which account for a considerable plastic dilatancy due to void growth and for the possibility of non-normality of the plastic flow law. In particular, bifurcation into surface wave modes and the possible influence of such modes triggering shear bands is investigated. For solids with initial imperfactions such as a surface undulation, a local material inhomogeneity on an inclusion colony, the inception and growth of plastic flow localization is analysed numerically. Both the formation of void-sheets and the final growth of cracks in the shear bands is described numerically. Some special features of shear band development in the solid obeying non-normality are studied by a simple model problem.     

Deformation and failure mechanism in AISI 4340 steel under ballistic impact

Deformation and failure mechanism in quench-hardened AISI 4340 steel under ballistic impact is investigated. The influence of microstructure on damage evolution is also evaluated. Strain localization and shear failure along adiabatic shear bands are the dominant deformation and failure mechanisms. The time and critical strain for the commencement of strain localization is influenced by strain rate and microstructure. The microstructure of the steel sample also influenced the type of adiabatic shear bands formed during impact. Failure mechanism involves nucleation of micro-voids, which clusters to form bigger pores. Extremely fine micro-cracks are initiated adjacent to the pores and in shear flow direction along the shear bands. These micro-cracks become interconnected and grow to macro-cracks, which cause fracture of some of the investigated cylindrical steel samples under impact. The susceptibility of the adiabatic shear bands to cracking increases with decreasing tempering temperature of the steel.     

Identification of damage mechanism and validation of a fracture model based on mesoscale approach in spalling of titanium alloy

The subject of this paper is identification of the physical mechanisms of spalling at low impact velocities for Ti–6Al–4V alloy and determination of the macroscopic stress of spalling via meso-macro approach. Spalling is a specific mode of fracture which depends on the loading history. The aspects of the initial microstructure and its evolution during plastic deformation are very important. In order to identify the spalling physical mechanisms in titanium alloy, numerous pictures by the optical microscopy of the spall surfaces created by plate impact technique have been taken. The scenario of failure observed is in complete agreement with known physical micro-mechanisms: namely nucleation, propagation and coalescence by adiabatic shearing of micro-voids. The most interesting point in spall fracture of Ti–6Al–4V alloy is the nucleation of micro-voids. A significant amount of small micro-voids in the region of the expected spall plane has been observed. It appears that microstructural effects are important due to dual α–β phase microstructure, called Widmanstätten structure. The orientation of microstructure has a direct influence on nucleation mechanism by means of distribution of nucleation sites and decohesion between the softer particles (α-phase lamellae) and the harder lattice (β-phase). According to these observations, a fracture model has been developed. This model is based on the numerous post-mortem microscopic observations of spall specimens. The goal is to determine the macroscopic stress of spalling in function of loading time and damage level via a meso-macro approach.     

Experimental and Numerical Investigation of Second Harmonic Generation by Creep Induced Micro-voids

Background: Identification of damage at an early stage is crucial for critical structural components. Objective: Creep induced micro-voids in heat treated polycrystalline pure copper are experimentally and numerically characterized. Methods: This is accomplished by the use of non-linear ultrasonic waves. Numerically, the study is carried out on an elastic material with randomly located micro-voids. The finite difference in time domain method is used. Results: Experimentally it is found that material damage due to micro-voids that are developed before 40% creep life may effectively be detected with nonlinear ultrasonic waves in the low power regime. Increase in second order nonlinearity parameter with percentage creep life is observed along with the corresponding increase in micro-void concentration. Optical metallography and micro-hardness measurements were used to corroborate the experimental results. For the numerical studies, void dimensions selected for study are much lower than the probing wave length. Concentration of micro-voids is varied from 0.01% to 3%. The second order nonlinearity parameter showed a slight increase in the initial stages and an abrupt increase with higher micro-void concentration in simulations. This agrees with experimental trends. Conclusion: The feasibility of detecting micro-voids in the early stages of creep using nonlinear ultrasonic waves is experimentally demonstrated and a simple model with voids is numerically studied to show the sensitivity of the second order nonlinearity parameter to micro voids.

     

Predicting failure modes and ductility of dual phase steels using plastic strain localization

Ductile failure of metals is often treated as the result of void nucleation, growth and coalescence. Various criteria have been proposed to capture this failure mechanism for various materials. In this study, ductile failure of dual phase steels is predicted in the form of plastic strain localization resulting from the incompatible deformation between the harder martensite phase and the softer ferrite matrix. Microstructure-level inhomogeneity serves as the initial imperfection triggering the instability in the form of plastic strain localization during the deformation process. Failure modes and ultimate ductility of two dual phase steels are analyzed using finite element analyses based on the actual steel microstructures. The plastic work hardening properties for the constituent phases are determined by the in-situ synchrotron-based high-energy X-ray diffraction technique. Under different loading conditions, different failure modes and ultimate ductility are predicted in the form of plastic strain localization. It is found that the local failure mode and ultimate ductility of dual phase steels are closely related to the stress state in the material. Under plane stress condition with free lateral boundary, one dominant shear band develops and leads to final failure of the material. However, if the lateral boundary is constrained, splitting failure perpendicular to the loading direction is predicted with much reduced ductility. On the other hand, under plane strain loading condition, commonly observed necking phenomenon is predicted which leads to the final failure of the material. These predictions are in reasonably good agreement with experimental observations.     

Post-critical plastic deformation in incrementally nonlinear materials

The formation of multiple macroscopic shear bands is investigated as a mechanism of advanced plastic flow of polycrystalline metals. The overall deformation pattern and material characteristics are determined beyond the critical instant of ellipticity loss, without the need of introducing an internal length scale. This novel approach to the modelling of post-critical plastic deformation is based on the concept of a representative nonuniform solution in a homogeneous material. The indeterminacy of a post-critical representative solution is removed by eliminating unstable solution paths with the help of the energy criterion of path instability. It is shown that the use of micromechanically based, incrementally nonlinear corner theories of time-independent plasticity leads then to gradual concentration of post-critical plastic deformation. The volume fraction occupied by shear bands is found to have initially a well-defined, finite value insensitive to the mesh size in finite element calculations. Further deformation depends qualitatively on details of the constitutive law. In certain cases, the volume fraction of active bands decreases rapidly to zero, leading to material instability of dynamic type. However, for physically hardening materials with the yield-vertex effect, the localization volume typically remains finite over a considerable deformation range. At later stages of the plane strain simulation, differently aligned secondary bands are formed in a series of bifurcations.     

Hydrogen induced shear localization of the plastic flow in metals and alloys

Hydrogen enhanced localized plasticity (HELP) is a viable mechanism for hydrogen embrittlement supported by experimental observations. According to the HELP mechanism, hydrogen induced premature failures result from hydrogen induced plastic instability which leads to hydrogen assisted localized ductile processes. The objective of this work is to reveal the role of hydrogen in possibly localizing the macroscopic deformation into bands of intense shear using solid mechanics methodology. The hydrogen effect on material deformation is modeled through the hydrogen induced volume dilatation and the reduction in the local flow stress upon hydrogen dissolution into the lattice. Hydrogen in assumed to reside in both normal interstitial lattice sites (NILS) and reversible traps associated with the plastic deformation. The analysis of the plastic deformation and the conditions for plastic flow localization are carried out in plane strain uniaxial tension. For a given initial hydrogen concentration in the unstressed specimen, a critical macroscopic strain is identified at which shear localization commences.     

An analysis of dislocation nucleation near a free surface

Molecular dynamics analyses of defect-free aluminum single crystals subject to bending are carried out to investigate dislocation nucleation from free surfaces. A principal aim of the analyses is to provide background for the development of dislocation nucleation criteria for use in discrete dislocation plasticity calculations. The molecular dynamics simulations use an embedded atom potential for aluminum. Bending is imposed on a strip by specifying a linear variation of displacement rate on opposite edges. The overall bending response is determined and the character of the dislocations nucleated is identified. It is found that the stress magnitudes at the instant of dislocation nucleation are nearly an order of magnitude smaller than for homogeneous bulk dislocation nucleation. The characterization of dislocation nucleation in terms of various phenomenological nucleation criteria is explored, in particular: (i) a critical resolved shear stress; (ii) the onset of an elastic instability; and (iii) a critical stress-gradient criterion. It is found that dislocation nucleation is not well-represented by a critical value of the resolved shear stress but is reasonably well-represented by the critical stress-gradient criterion.     

Shear failure of tungsten alloy at mesoscale modeled by Movable cellular Automata

Shear failure and deformation localization are studied for tungsten alloy undergoing impact failure and “self-sharpening” in ordnance. Movable cellular Automata (MCA) method is employed to simulate the interior-structure of tungsten alloy such that shear deformation failure at mesoscale level under shear loading can be analyzed. The results show that the velocity of every automaton would vary continuously with deformation. A large velocity vortex sweeping throughout the specimen occurs at the initial loading stage. This corresponds to uniform deformation. Subsequently, the deformation adopts a pattern with more localized vortices. The vortex-morphology would change continually to sustain the global deformation field. The contact between the local vortices induces stress concentration. This means that the deformation of certain automaton pairs would not accommodate the equilibrium of vortex rotation. The different mechanisms of micro-damage mechanisms along the interface between the W grain and matrix are developed quickly throughout the whole specimen. Such shear instability leads to failure. It is also shown that the W grain size effect is sufficient to cause premature shear deformation instability of the tungsten alloy, even at low shear stress.     

Transformation toughening of a ceramic in stable crack growth under plane stress conditions

A finite element study of stable crack growth in ceramics that can undergo a stress-induced martensitic phase transformation is performed under plane stress and small scale transforming conditions. The finite element method is based on the continuum model developed by Budiansky et al. (Int. J. Solids Structures 19, 1983). To guarantee the subcritical transformation behavior without loss of ellipticity of the governing equations, the possibility of strain localization is first re-examined. It is found that the plane stress conditions greatly favor transformation instability in that supercritical transformation occurs when the bulk modulus ¯B during transformation is below –G/3, instead of –4G/3 for three-dimensional or plane strain cases, whereG is the shear modulus. Next, transient crack extension under continuously increasing tensile load is simulated by a node release technique. Transformation zones and crack growth resistance curves are obtained.     

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.     

Secondary instability of large scale structure in free turbulent shear layer

The secondary instability theory is used to study the behavior of spatially growingdisturbance in free turbulent shear layer.The numerical results indicate that secondaryinstability of subharmonic mode shows a strong choice of spanwise wavenumber andthe maximum growth two dimensional case.In contrast to that secondary instabilities of the fundamental mode occur in a wide scope of spanwise wavenumber.We have found so called translative at β=0 and bifurcation phenomenon for an amplitude of the KH wave larger than 0.06.Dey words instability,large scale structure,bifurcation     

高强度榴弹钢的破片机理研究

对高强度榴弹钢５０ＳｉＭｎＶＢ和５８ＳｉＭｎ的破片机理进行了研究。破片的表面形貌和组织变化表明，在初始阶段，榴弹内壁破片裂纹沿法线与半径方向呈／４夹角的平面绝热剪切而形成。５０ＳｉＭｎＶＢ钢的晶界弱化使其临界绝热剪切应变小于５８ＳｉＭｎ钢，从而表现出两者破片质量分布的差异。     

表面加工塑性层对金属柱壳剪切带自组织单旋起始的影响

在外爆加载金属柱壳高速坍塌过程中, 发生塑性变形失稳形成的剪切带具有高度的自组织特征, 甚至出现剪切带排列的单旋现象—剪切带在顺时针和逆时针两个方向呈现一个方向占优的现象. 柱壳在坍塌时, 最大剪切应力位于柱壳内表面, 剪切带的形核及扩展行为受内表面材料介观状态的影响显著. 本文通过选材和控制柱壳加工工艺, 获得了内表面具有不同厚度塑性层的20钢柱壳, 采用厚壁圆筒实验技术, 研究了表面加工塑性层对金属柱壳绝热剪切带自组织单旋现象起始的影响规律及其物理机制. 研究结果表明, 金属柱壳内表面加工塑性层显著改变了试样剪切带的起始条件, 沿顺时针或逆时针方向排列的剪切带形核数量在总剪切带数量中所占比例取决于表面加工塑性层的厚度和晶粒取向, 具有单一晶粒拉伸方向的较厚塑性层样品更容易形成单向螺旋剪切带结构. 在相同变形条件下, 随着塑性层厚度增加, 剪切带平均形核速率和扩展速率增大, 剪切带平均间距减小. 结果可为理解金属柱壳在高速塌陷过程中绝热剪切带占优取向现象提供有价值的参考.      

Site of ductile fracture initiation in cold forging: A finite element model

Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. In this study a new ductile fracture condition that based on the microscopic phenomena of void nucleation, growth and coalescence was proposed. Using this condition and combining with finite element model to predict the fracture locations in bulk metal forming, the results show that it is in close accordance with observations of some experimental specimens. However, in order to obtaining the high trustiness many experiments have to be carried out.     

金属材料平面应变拉伸变形局部化有限元分析

本文对于涉及韧性金属大变形中颈缩与剪切带断裂一类高度非线性变形局部化问题进行了弹塑性有限元数值模拟。采用改进的Ｊ２形变理论微分形式公式与交叉三角形四边形单元有限元网格，详细研究了应变硬化指数及初始表面不均匀特性的平面应变拉伸颈缩和剪切带形成的综合影响，给出此类问题的断裂机制图。     

On the deformation and fracture of porous materials

The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors. These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison is made between theoretical and experimental results.     

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.