不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

Loading rate and confining pressure effect on dilatancy,acoustic emission,and failure characteristics of fissured rock with two pre-existing flaws

Investigating the dilatancy, acoustic emission and failure characteristics of fissured rock are significant to ensure their geotechnical stability. In this paper, the uniaxial and triaxial compression experiments with AE monitoring under different loading rates were carried out on fissured rock specimens with the same geometrical distribution of two pre-existing flaws. The dilatancy and AE activity of these specimens were discussed, and the effects of the confining pressure and loading rate on the mechanical parameters and failure characteristics were analyzed. The results show that the exponential strength criterion is more suitable than the Mohr–Coulomb strength criterion to characterize the strength characteristics of fissured rock. The crack evolution and failure characteristics of fissured rock specimens are more complicated than those of intact rock specimens. The failure characteristics of the fissured rock follow the tensile shear coalescence model, crack branching occurs with increasing the loading rate, and the multi-section coalescence model is verified with increasing the confining pressure. The phenomena of stress drop and yield platform usually occur after the dilatancy onset, the specimen does not fail instantaneously, and the propagation and coalescence of cracks cause a sharp increase in the AE signals, circumferential strain, and volumetric strain.     

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.     

三向应力Mohr圆的真实构成及剪应力作用方向的确定

三向应力Mohr圆的构成在传统上是借助公式推证而得，并以平面图形来表示，缺乏三维的真实感和直观性。在应力应变分析中，对于平面应力问题，可以通过平面应力摩尔圆确定过一点不同斜面上的应力分量及其作用方向。对于三维问题，利用摩尔圆图解法可以确定某一斜面上的正应力和剪应力的数值，但不能表示剪应力的作用方向。剪应力的作用方向需要通过另外的图解方法来确定。本文分别从坐标系旋转和数值计算的角度解释了三向应力Mohr圆的构成过程，形象地说明了Mohr圆的物理本质。针对三向应力Mohr圆不能表示剪应力作用方向的问题，通过矢量运算，给出了剪应力作用方向的确定公式。     

An augmented multicrack elastoplastic damage model for tensile cracking

In this paper we present the general formulation and numerical aspects of an augmented multicrack elastoplastic damage model aiming to reflect the crack induced anisotropy in concrete like quasi-brittle materials. Consistent evolution laws for the involved internal variables are derived based on the augmented Lagrangian method. The (time) discrete formulation and the corresponding variational structure are investigated, with the Euler–Lagrangian equations defining the closest-point projection approximation of the proposed model. The numerical aspects, such as the stress updating algorithm and the algorithmic consistent tangent moduli, are also discussed in details. It is found that in the developed numerical algorithm the active loading surfaces are determined in such a posterior manner that potential numerical problems due to the iteratively updating procedure in classical algorithms can be avoided. The proposed model is applied to the modeling of tensile cracking in concrete. The behavior of a single crack is characterized by an elliptical cracking surface and a hyperbolic softening function, with the orientations of potential cracks determined by Mohr’s postulate. The model is verified by calculating the single point stress vs. strain relations of concrete under several typical proportional and non-proportional loading cases. Finally, two benchmark tests of concrete structures, i.e. four-point bending beam under cyclic loading (Hordijk, 1992) and double edge notched specimens under mixed tension/shear forces (Nooru-Mohamed, 1992), are numerically simulated. Both predicted load vs. displacement curves and crack patterns agree well with the experimental data.     

压缩-剪切复合应力下PMMA材料的静态力学特性研究

通过压缩具有一定倾斜角(0°,10°,15°,20°和25°)试件和双剪切模型试件,实现了单轴压缩、压缩-剪切复合应力以及纯剪切三种应力状态,得到PMMA(聚甲基丙烯酸甲酯)在相应应力状态下的应力-应变曲线,同时对不同应力状态下试件的破坏模式进行了分析。结果表明:在不同受力环境中材料的强度和破坏的机理不同;同单轴压缩状态下相比,材料在压缩-剪切复合应力状态下屈服极限、强度极限以及破坏应变均不同程度的增大,呈现明显的"剪切增强"现象。单轴压缩与压缩-剪切应力状态下试件的破坏模式均为在试件短对角面上出现明显的剪切屈服带,由应力分析得出试件剪应力在短对角面上达到最大,引起在此平面上分子链间滑动从而产生应变软化形成剪切屈服带;双剪切试件的破坏模式为与剪切面呈45°的斜面。     

Simulation of ground stress field and fracture anticipation with effect of pore pressure

Triaxial compression tests are carried out on the cores with different confining pressure and pore pressure to study the rupture mode and fracture distribution of carbonate rocks in Kenkiyak pre-salt oilfield, and the cores are made into thin sections after experiment. It shows that shear plane, high angle crack, conjugate shear cracks and net fractures will gradually appear with the effective confining pressure, the rock texture is damaged more and more seriously with the increase of effective confining pressure. Tectonic stress field in Kenkiyak Field is simulated by finite element numerical simulation software ADINA considering the effect of pore pressure, this model contains five faults and assumes that two planes of faults could slip with the force to decompress. The simulation results indicate that the total displacement coincides with the practical formation, the simulated tectonic stress fits with the values measured by acoustic emission testing, and the direction of major horizontal principal stress is consistent with the imaging log interpretation data. The fracture rupture rate and density are predicted according to tension and shear rupture rate which derived by simulation results. The fracture density varies widely in the simulated region and cracks develop easily on the structural high position, near the fault because of the increasing pore pressure and extrusion in the process of the tectonic movements.     

拉压异性材料含受压圆孔大平板的极限分析

探讨了广义双剪应力强度理论在平面应力状态下的屈服轨迹及其方程式,并用于拉压异性材料圆孔受内压的极限分析,得到了与拉压比有关的弹性极限内压力,弹塑性区的应力、塑性内压力与弹塑性分界半径之间的关系、塑性区的最大半径和最大内压力,所得极值均高于用莫尔强度理论分析的结果。     

Matched asymptotic expansions in nonlinear fracture mechanics—II. Longitudinal shear of an elastic work-hardening plastic specimen

Earlier analysis given by T.M. Edmunds and J.R. Willis (1976) is extended to deal with cracks in elastic work-hardening plastic specimens subjected to longitudinal shear loads. Solutions are expressed in terms of a set of parameters that are determined from linear elastic solutions alone. It is proved, for any specimen geometry and any loading symmetric about the plane of the crack, that a ‘plastic-zone correction’, obtained by solving a linear elastic problem for a crack which is a length r_y longer than the actual crack, provides a two-term asymptotic expansion for the J-integral, if r_y is defined suitably in terms of the linear elastic stress concentration factor and the initial slope of the work-hardening curve. The general method is applied in detail to a strip of finite width containing an edge crack, for which the effect of the work-hardening on the maximum extent of the plastic zone and on the J-integral is summarized graphically.     

Nanomechanical Testing of Gum Metal

“Gum Metal” is a newly developed β-Ti alloy that, in the cold-worked condition, has exceptional elastic elongation and high strength. The available evidence suggests that Gum Metal does not yield until the applied stress approaches the ideal strength, and then deforms by mechanisms that do not involve conventional crystal dislocations. To study its behavior, submicron-sized pillars of solution-treated and cold-worked Gum Metal were compressed in situ in a quantitative compression stage in a transmission electron microscope. Solution-treated specimens and half of the cold-worked specimens exhibited essentially monotonic hardening during compression, but with serrated load-deflection curves that included periodic partial relaxations of the stress. The other cold-worked specimens exhibited pronounced shear instability. These samples deformed by a stick-slip motion along a well-defined shear plane, with a serrated load-deflection curve demonstrating partial stress relaxation at each sliding event. The pattern of deformation is consistent with prior work showing deformation by the formation and growth of shear bands and faults in a matrix that is densely decorated with defects.     

Influence of flaw inclination angle and loading condition on crack initiation and propagation

With reference to the experimental observation of crack initiation and propagation from pre-existing flaws in rock specimens under compression, the influences of pre-existing flaw inclination angle on the cracking processes were analyzed by means of finite element method (FEM) and non-linear dynamics method. FEM analysis on the stress field distribution induced by the presence of a pre-existing flaw provided better understanding for the influence of flaw inclination angle on the initiation position and initiation angle of the potential cracks. Numerical analysis based on the non-linear dynamics method was performed to simulate the cracking processes. The resultant crack types, crack initiation sequences and the overall crack pattern were different under different loading conditions. Under a relatively low loading rate or a small magnitude of maximum loading pressure, tensile cracks would tend to initiate prior to shear cracks. In contrast, under a relatively high loading rate and a large magnitude of maximum loading pressure, shear cracks would tend to initiate prior to tensile cracks instead.     

Dynamic crack growth along a polymer composite-Homalite interface

Dynamic crack growth along the interface of a fiber-reinforced polymer composite-Homalite bimaterial subjected to impact shear loading is investigated experimentally and numerically. In the experiments, the polymer composite-Homalite specimens are impacted with a projectile causing shear dominated interfacial cracks to initiate and subsequently grow along the interface at speeds faster than the shear wave speed of Homalite. Crack growth is observed using dynamic photoelasticity in conjunction with high-speed photography. The calculations are carried out for a plane stress model of the experimental configuration and are based on a cohesive surface formulation that allows crack growth, when it occurs, to emerge as a natural outcome of the deformation history. The effect of impact velocity and loading rate is explored numerically. The experiments and calculations are consistent in identifying discrete crack speed regimes within which crack growth at sustained crack speeds is possible. We present the first conclusive experimental evidence of interfacial crack speeds faster than any characteristic elastic wave speed of the more compliant material. The occurrence of this crack speed was predicted numerically and the calculations were used to design the experiments. In addition, the first experimental observation of a mother-daughter crack mechanism allowing a subsonic crack to evolve into an intersonic crack is documented. The calculations exhibit all the crack growth regimes seen in the experiments and, in addition, predict a regime with a pulse-like traction distribution along the bond line.     

The dynamic behaviour of sharp V-notches under impact loading

The dynamic behaviour of sharp V-notches which are either symmetric or oblique to the longitudinal boundary of a homogeneous elastic and isotropic strip subjected to an impact plane pulse was studied by the method of caustics. The stress pulse impinging on the flanks of the notch reflects and diffracts in different ways depending on the geometry of the notch relative to the coming pulse. For compressive stress pulses a stress concentration at the bottom of the notch does not create a crack propagation phenomenon, whereas for tensile pulses there is a possibility for an incubation, nucleation and eventual propagation of a crack. A complete experimental study of the incubation nucleation and propagation of cracks from the bottoms of notches in thin strips under tensile stress pulses was undertaken, whereas for compressive stress pulses the stress concentration at the bottom of the notch was evaluated. Interesting results were disclosed concerning the reinforcement of pulses by reflection and caging in, the evolution of stress concentration at the notch and the mode of crack propagation inside the plate. Dynamic stress intensity factors were evaluated all over the paths of crack propagation indicating a close intimacy between crack velocity and values of SIFs.     

The simulation of dynamic crack propagation using the cohesive segments method

The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.     

Experimental and Numerical Study of Shear Fracture in Brittle Materials with Interference of Initial Double Cracks

A simultaneous experimental and numerical study of shear fracture of concrete-like materials is carried out using Brazilian disc specimens with initial double edge cracks and fourpoint bending beam specimens with double edge-notches.The interference effects of two cracks/notches are investigated through varied ligament angles and crack lengths.It is shown that shear fracturing paths change remarkably with the initial ligament angles and crack lengths.The cracked specimens are numerically simulated by an indirect boundary element method.A comparison between the numerical results and the experimental ones shows good agreement.     

含预制裂纹L形梁柱试件动态断裂过程

针对含预制裂纹L形梁柱试件,为研究预制裂纹动态扩展的力学特征及其对梁柱试件破坏模式的影响,采用数字动态焦散线实验系统,对距节点核心区不同距离l处含有预制裂纹的试件进行落锤冲击实验,得到预制裂纹的扩展轨迹、速度、动态应力强度因子的变化规律。结果表明,l值增大,扩展裂纹在梁下边缘的贯通点与预制裂纹的夹角逐渐增大,曲裂程度变大。裂纹扩展速度随着l的增大振荡性增强,裂纹扩展平均速度逐渐降低。l值为2 mm时,裂尖表现为Ⅰ型断裂,l值增大,裂尖受到剪应力作用增强,Ⅰ型动态应力强度因子减小,Ⅱ型动态应力强度因子增大,断裂逐渐转变为Ⅰ-Ⅱ复合型。     

胶结砂砾石层面直剪试验及破坏行为细观研究

本文采用宏观试验和细观模拟相结合的方法研究胶结砂砾石层面在剪切过程中的破坏行为．首先进行了不同法向应力作用下的胶结砂砾石层面直剪试验,获得了不同的剪切面破坏特征：随着法向应力的不断增加,剪切破坏面凹凸起伏程度、骨料脱落现象越发明显．其次为了深入探究层面破坏现象,按照室内试验采用的骨料级配粒径建立细观颗粒数值模型,结合物理试验对模型进行参数标定,并进行数值模型的层面直剪模拟和细观分析．结果表明,数值模型可以再现宏观直剪试验层面破坏特征;法向应力越大,层面区域颗粒发生错动和翻转的数量越多;层面破坏方式为颗粒间的张拉和剪切混合破坏,裂隙均集中在层面位置,随着法向应力的增加,裂隙的集中区域逐渐由“面”向“带”转变．     

爆炸荷载作用下两平行裂纹对扩展中裂纹的影响规律

用实验和数值模拟方法,研究在爆炸载荷下岩体内部一对平行裂纹对扩展主裂纹的影响规律。实验中,采用带有中心装药孔及预制裂纹的砂岩圆盘试件,利用由示波器、超动态应变仪及裂纹扩展计所组成的测试系统,监测主裂纹扩展速度和扩展距离;数值模拟中,采用了AUTODYN软件进行,模拟了主裂纹及两平行裂纹的扩展规律,对岩石材料,采用线性状态方程及最大拉应力失效准则,并在两平行裂纹间设置相应的观测点记录应力曲线。通过实验与数值模拟分析,得到:爆炸载荷下,紧随冲击波后的稀疏波经过两平行裂纹面反射后变成压缩波,并在两平行裂纹间产生垂直于主裂纹扩展方向的压应力,对裂纹的扩展有压制、止裂作用;而且,这种压应力的大小与两平行裂纹的间距有关,进而导致了不同的止裂效果,影响裂纹的扩展速度及最终扩展长度。     

The effects of the rock bridge ligament angle and the confinement on crack coalescence in rock bridges: An experimental study and discrete element method

The present article investigates the influences of the rock bridge ligament angle, β, and the confinement on crack coalescence patterns by conducting laboratory and numerical tests on rock-like specimens. Laboratory tests show that no coalescence in the rock bridge occurred for low β. With an increase of β, tensile-shear coalescence and tensile coalescences subsequently occurred. In addition, the increase in the confinement first promoted shear coalescence and then restrained crack coalescence for low β, whereas the tensile coalescence was restrained by the increase in confinement for high β. The numerical results corroborate the laboratory tests in the coalescence patterns. In addition, the numerical study shows that tensile and shear cracks subsequently initiated near crack tips because of the concentrated tensile and shear stresses, respectively. Regarding the influence of β on crack coalescence, tensile or shear stress failed to concentrate in rock bridges for low β. Therefore, the cracks failed to coalesce, whereas with the increase in β, tensile and shear stress concentrations occurred in the bridge and led to either tensile shear or tensile coalescence. Regarding the influence of confinement on crack coalescence, the increase in confinement restrained the tensile stress concentrations and further hindered tensile crack coalescence in rock bridges for high values of β.     

Fracture analyses of different pre-holed concrete specimens under compression

Crack propagation processes in specially prepared concrete discs and rectangular specimens containing a single cylindrical hole or multiple holes of varying diameters have been studied both experimentally and numerically.In this research, the cracks coalescence paths in Brazilian disc and rectangular specimens made from rock-like material containing multi-holes are investigated. These concrete specimens are specially prepared from an appropriate mixture of Portland Pozzolana Cement(PPC), fine sands, and water.The pre-holed Brazilian discs and rectangular specimens are experimentally tested under compression. The breakage load in the ring type disc specimens containing an axial hole with varying diameters is measured and the distribution of the induced lateral stress is obtained. The mechanism of cracks propagation in the wall of the ring type specimens is also studied. In the case of multi-hole Brazilian disc and rectangular specimens, the cracks propagation and cracks coalescence are also investigated. These experiments are numerically modeled by a modified higher order displacement discontinuity method. It has been shown that the corresponding experimental and numerical results are in good agreement with each other. The results presented in this research validate the accuracy and applicability of these crack analyses procedures.