Effects of superimposed hydrostatic pressure on fracture in round bars under tension

The effect of superimposed hydrostatic pressure on fracture in round bars under tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that while the superimposed hydrostatic pressure has no noticeable effect on necking, it increases the fracture strain due to the fact that a superimposed pressure delays or completely eliminates the nucleation, growth and coalescence of microvoids or microcracks. The experimentally observed transition of the fracture surface, from the cup-cone mode under atmospheric pressure to a slant structure under high pressure, is numerically reproduced. It is numerically proved that the superimposed hydrostatic pressure has no effect on necking for a damage-free round bar under tension.     

Void coalescence within periodic clusters of particles

The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modelled using a unit cell approach. Three discrete particles are introduced into each unit cell while a secondary population of small particles within the surrounding matrix is represented using the Gurson-Tvergaard-Needleman (GTN) constitutive equations. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined.The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence failure strains. Coalescence of voids within a first-order particle cluster (consisting of three particles) is a stable event while collapse of inter-cluster ligaments leads to imminent material collapse through void-sheeting.     

Characterizing void nucleation in a damage-based constitutive model using notched tensile sheet specimens

An experimental and numerical test programme was conducted to investigate damage-induced ductile fracture in notched tensile sheet specimens of an aluminum–magnesium alloy. An upper bound, damage-based constitutive model was employed to estimate the formability of the material over a range of stress states found in sheet metal forming. Stress- and strain-based nucleation models are evaluated to characterize damage initiation and fracture of the material. The ligament strain-to-failure, elongation-to-failure and load–displacement curves can be captured using either nucleation rule. The advantages of each nucleation model are discussed in relation to quantitative measurements of damage available in the literature. Stress-based nucleation provides a promising approach for characterizing the nucleation behaviour over a range of stress states compared to strain-based nucleation.     

金属塑性变形极限判据

研究出金属材料塑性变形极限判据，它为断裂力学和失效分析提供理论依据。利用这判据，裂纹尖端的临界应变和相应的临界应力可以确定。在板料成形中，拉应力下颈缩失稳的临界应变值可以定出。节省大量试验工作。     

冲击下混凝土试样应变率效应和惯性效应探讨

结合混凝土试件的真三轴静载冲击实验结果,分别运用考虑应变率效应的Holmquist-Johnson-Cook (HJC)模型和考虑静水压效应的Drucker-Prager (DP)模型进行数值分析,以探讨研究混凝土试样应变率效应和惯性效应的方法。在探究混凝土的应变率效应和横向惯性效应的关系时,使用HJC模型的数值模拟结果来拟合DP准则的各个参数。结果表明:随着应变率的升高,混凝土的强度会提高,并且这种强度的提高,也有一部分原因是第一应力不变量I₁的增大所导致的。因此,混凝土试件的应变率效应和横向惯性约束具有较强的耦合作用。理论和数值分析了冲击下试样内部的横向应力分布特征与应变率、静水压和试样尺寸的关系,结果发现:试样内部横向应力的幅值随着应变率、静水压的升高而增大,但随着试样尺寸的增大而减小。为了探讨横向惯性带来的强度提升效果,提出了一个有关冲击方向最大应力σ_x和等效应力σ_e的参数ξ,且ξ=(σ_x?σ_e)/σ_x。此参数具有尺寸效应、应变率效应和静水压效应,但是此参数与应力三轴度的关系表现出应变率无关特性,可为应变率效应的研究提供新的思路。     

An analysis of ductile rupture in notched bars

Ductile fracture in axisymmetric and plane strain notched tensile specimens is analyzed numerically, based on a set of elastic-plastic constitutive relations that account for the nucleation and growth of microvoids. Final material failure by void coalescence is incorporated into the constitutive model via the dependence of the yield function on the void volume fraction. In the analyses the material has no voids initially; but as the voids nucleate and grow, the resultant dilatancy and pressure sensitivity of the macroscopic plastic flow influence the solution significantly. Considering both a blunt notch geometry and a sharp notch geometry in the computations permits a study of the relative roles of high strain and high triaxiality on failure. Comparison is made with published experimental results for notched tensile specimens of high-strength steels. All axisymmetric specimens analyzed fail at the center of the notched section, whereas failure initiation at the surface is found in plane strain specimens with sharp notches, in agreement with the experiments. The results for different specimens are used to investigate the circumstances under which fracture initiation can be represented by a single failure locus in a plot of stress triaxiality vs effective plastic strain.     

Void growth to coalescence in a non-local material

The size-effect in metals containing distributed spherical voids is analyzed numerically using a finite strain generalization of a length scale dependent plasticity theory. Results are obtained for stress-triaxialities relevant in front of a crack tip in an elastic-plastic metal. The influence of different material length parameters in a multi-parameter theory is studied, and it is shown that the important length parameter is the same as under purely hydrostatic loading. It is quantified how micron scale voids grow less rapidly than larger voids, and the implications of this in the overall strength of the material is emphasized. The size effect on the onset of coalescence is studied, and results for the void volume fraction and the strain at the onset of coalescence are presented. It is concluded that for cracked specimens not only the void volume fraction, but also the typical void size is of importance to the fracture strength of ductile materials.     

Load-Inversion Device for the High Strain Rate Tensile Testing of Sheet Materials with Hopkinson Pressure Bars

A high strain rate tensile testing technique for sheet materials is presented which makes use of a split Hopkinson pressure bar system in conjunction with a load inversion device. With compressive loads applied to its boundaries, the load inversion device introduces tension into a sheet specimen. Two output bars are used to minimize the effect of bending waves on the output force measurement. A Digital Image Correlation (DIC) algorithm is used to determine the strain history in the specimen gage section based on high speed video imaging. Detailed finite element analysis of the experimental set-up is performed to validate the design of the load inversion device. It is shown that under the assumption of perfect alignment and slip-free attachment of the specimen, the measured stress–strain curve is free from spurious oscillations at a strain rate of 1,000 s^?1. Validation experiments are carried out using tensile specimens extracted from 1.4 thick TRIP780 steel sheets. The experimental results for uniaxial tension at strain rates ranging from 200 s^?1 to 1,000 s^?1 confirm the oscillation-free numerical results in an approximate manner. Dynamic tension experiments are also performed on notched specimens to illustrate the validity of the proposed experimental technique for characterizing the effect of strain rate on the onset of ductile fracture in sheet materials.     

Characterization of the post-necking strain hardening behavior using the virtual fields method

The present study aims at characterizing the post-necking strain hardening behavior of three sheet metals having different hardening behavior. Standard tensile tests were performed on sheet metal specimens up to fracture and heterogeneous logarithmic strain fields were obtained from a digital image correlation technique. Then, an appropriate elasto-plastic constitutive model was chosen. Von Mises yield criterion under plane stress and isotropic hardening law were considered to retrieve the relationship between stress and strain. The virtual fields method (VFM) was adopted as an inverse method to determine the constitutive parameters by calculating the stress fields from the heterogeneous strain fields. The results show that the choice of a hardening law which can describe the hardening behavior accurately is important to derive the true stress–strain curve. Finally, post-necking hardening behavior was successfully characterized up to the initial stage of localized necking using the VFM with Swift and modified Voce laws.     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.     

Influence of transverse normal stress on sheet metal formability

Since the late 1960's, the strain space forming limit diagram, FLD_ϵ, has been nearly universally employed as a method to help predict sheet metal failure for the open die stamping process. Traditional FLD_ϵ's in use today are based upon a plane stress assumption. However, a plane stress assumption may not always be valid for many sheet metal forming operations. Through the employment of a strain-to-stress space mapping procedure, a new sheet metal formability model that takes into account the through-thickness normal stress (σ₃) is proposed. Good agreement with a limited set of experimental data is found.     

Further study on effect of concrete defense layer on evolution mechanism of stress-waves

The Taylor–Chen–Kuszmaul model, which regards the dynamic fracture process of brittle materials as a continuous accrual of damage, has been successfully applied to simulate rock blast and concrete penetration. This paper employs the TCK damage model to numerical study on the effect of perforated concrete defense layer on evolution mechanism of blast-induced stress waves. The numerical results reveal that the tensile damage near free boundary should be noteworthy under a higher blast loading, and the peak values of hydrostatic pressure beneath an artificial cavity are largely reduced. The effects of cavity dimensions and position on wave evolution and reduction are detailedly explored. One empirical formula is proposed to relate the decay factor of peak hydrostatic pressure to the dimensions and relative position of cavity.     

用三维电镜图像数据测试空穴形状

用碳化硅强化金属基复合材料制作的不同切口的拉伸试样进行了拉伸试验并使用三维电子扫描显微镜对拉伸延性断面进行了微小空穴的三维形状测试，分析了在不同应力三维度下空穴聚合时空穴几何形状的变化，为准确模拟金属基复合材料在多向外载荷下的损伤过程，判断延性损伤机理提供了科学依据。     

Ti-6Al-4V在高应变率下的动态剪切特性及失效机理

采用基于霍普金森压杆的新型加载技术对Ti-6Al-4V材料的动态剪切特性及失效机理进行了测试研究。获得了Ti-6Al-4V材料在超过104 s-1应变率下的剪应力-剪应变曲线及失效参数。研究发现,材料的流动应力存在明显的应变率强化效应;随着应变率的增加,材料的失效应力逐渐增大,而失效应变逐渐减小。采用ABAQUS/Explicit对加载过程进行了数值模拟。结果显示,剪切区材料基本处于平面剪切状态,应力应变场分布较为均匀,计算得到的剪应力-剪应变曲线与实验结果吻合较好。经断口分析可知,随着应变率的升高,Ti-6Al-4V的失效机理存在由韧窝、拉伸韧窝至台阶及河流花样的演化过程,材料的失效模式主要表现为韧性断裂。     

深部回采巷道围岩零应变交界圈现象的模型试验研究

以淮南矿区口孜东矿深部回采巷道为工程背景,采用真三轴模型试验装置模拟了从浅埋静水压力、深埋静水压力、初掘采动应力(K=1.5为1.5倍900m埋深静水压力,后同)到回采动压(K=2~3)等不同应力条件下,大、小两种尺寸的直墙拱形回采巷道围岩应变状态,获得了浅埋条件下巷道围岩浅部拉应变、深部零应变,以及深埋静水压力及初掘采动应力下,巷道围岩出现"零应变交界圈"现象及深埋回采高应力下非线性大应变的围岩应变特征。应变监测结果反映了深部回采巷道围岩变形破坏的动态演化过程,为巷道的稳定性控制提供了一定的思考。     

Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading

A damage plasticity model for ductile fracture is proposed. This model is established on the cylindrical coordinate system of principal stress space. Experimental results show that fracture initiation in uncracked ductile solids is sensitive to the hydrostatic pressure and dependent on the Lode angle. The joint effects of pressure and Lode angle define a fracture envelope in principal stress space. Plastic deformation induced damage is calculated by an integral of the damage rate measured at current loading and deformation status with respect to the fracture envelope. A power law damage rule is proposed to characterize the nonlinearity in damage accumulation. A damage-related weakening factor is adopted to describe the material deterioration. The material parameters are calibrated from standard laboratory tests. The proposed model is numerically implemented. Four simulations with emphasis on crack path prediction are presented.     

轴向拉伸下氮化钛纳米杆变形机制及力学性能的分子动力学研究

本文使用分子动力学软件包lammps并采用第二近邻改进型嵌入原子法(2NN MEAM)模拟了单晶氮化钛纳米杆的轴向拉伸破坏过程,分析了分别沿[100]、[111]晶向的不同截面尺寸、不同拉伸应变率、不同温度下的氮化钛纳米杆的力学性能,详细描述了氮化钛纳米杆拉伸变形过程。研究发现, 拉伸晶向、截面尺寸、拉伸应变率及温度均会对TiN纳米杆的拉伸变形过程及屈服强度、弹性模量等力学性能产生不同程度的影响。 沿[100]晶向的拉伸,截面尺寸越大,屈服强度越低;而沿[111]晶向,截面尺寸越大,屈服强度越大。应变率越大,屈服强度及屈服应变越大,但对于弹性模量几乎无影响。温度越高,材料的屈服强度、屈服应变及弹性模量越小,断裂应变越大。不同拉伸条件下的氮化钛纳米杆的拉伸过程均包括弹性变形、塑性变形与断裂阶段。[100]晶向的弹性模量都要高于[111]晶向。     

液压膨胀环动态拉伸碎裂的有限元模拟

液压冲击膨胀环实验平台能有效地实现韧性金属圆环在高应变率拉伸载荷作用下的动态断（碎）裂。本文采用流固耦合的有限元数值计算方法,模拟了实验过程中金属圆环在高压液体作用下的运动、变形和断裂现象。分析了装置和试件的接触应力对试件碎裂过程的影响并讨论了如何实现液压对试件的有效加载。计算结果表明,实验中的初始接触应力和液体的较长时间加载对试件的碎裂过程没有显著影响;在合理的加载条件下,液压膨胀环实验技术是研究固体动态拉伸碎裂的有效手段。     

ASYMPTOTIC SOLUTIONS OF MODE I STEADY GROWTH CRACK IN MATERIALS UNDER CREEP CONDITIONS

An asymptotic analysis is made on problems with a steady-state crack growth coupled with a creep law model under tensile loads. Asymptotic equations of crack tip fields in creep materials are derived and solved numerically under small scale conditions. Stress and strain functions are adopted under a polar coordinate system. The governing equations of asymptotic fields are obtained by inserting the stress field and strain field into the material law. The crack growth rate rather than fracture criterion plays an important role in the crack tip fields of materials with creep behavior.