The plastic yield behaviour of polymethylmethacrylate

The yield behaviour of an amorphous glassy polymer has been investigated under a system of combined stress in an attempt to define a criterion for yield. Sheets of polymethylmethacrylate were compressed in plane strain and the compressive yield stress was determined as a function of the tension applied in the plane of the sheet. The compressive yield stress was found to decrease with applied tension more rapidly than would be expected if the shear yield stress of the material were independent of pressure. The results have been analysed in terms of a Coulomb yield criterion where the shear yield stress is expressed as a constant plus a friction term proportional to the pressure on the shear plane. Birefringent shear zones were observed in the deformed region after the load was removed and these zones were inclined at 52.9° to the plane of the sheet. It was found that if the stresses at yield were expressed as nominal stresses then the inclination of the shear planes predicted by the yield stress data coincided with the observed inclination. It also appears that it may be possible to define a fracture criterion in terms of the applied stress system.     

Finite-element analysis and experimental study on tensile fatigue behaviour of bitumen–stone adhesion

Tensile fatigue behaviours of bitumen–stone adhesion were investigated using a dynamic mechanics analyser under stress‐controlled mode at two temperatures of 5 and 25°C and various controlled‐stress levels. Failure characteristics including interfacial failure and cohesive failure were examined using image analysis of fracture surfaces. Finite‐element analysis on stress distributions was conducted under different temperatures, film thickness and interfacial bonding conditions. A Coulomb–Mohr like criterion in combination with shear and normal stresses is proposed to deal with the extreme thin adhesive layer, which can be further simplified into an adhesive zone without significant loss of accuracy for stress analysis.     

红砂岩剪切储能与最大剪应变特征试验研究

为了明确干燥和饱水红砂岩剪切强度、剪切储能与剪应变特征,在岩石剪切试验系统进行了不同法向应力作用下干燥和饱水红砂岩剪切试验,详细分析了法向应力和饱水作用对红砂岩剪切强度、剪切应变能密度和剪应变的影响规律。结果表明：剪力-剪切位移曲线,干燥状态线性段明显,饱水状态屈服段明显,法向应力在10 MPa～20 MPa,剪切强度和剪切位移增加显著,法向应力在20 MPa～40 MPa切向位移变化很小;压剪应力状态下的粘聚力和内摩擦角明显低于三轴压缩应力状态下的粘聚力和内摩擦角,饱水使三轴应力路径下的粘聚力和内摩擦角都弱化,而压剪应力路径下只对内摩擦角弱化。法向应力小于20 MPa时,剪切强度劣化率随法向应力的增加线性增大,法向应力在20 MPa～40 MPa时,剪切强度劣化率在一定值上下波动。峰值剪切应变能密度与法向应力之间存在良好线性变化规律,随法向应力增大,饱水对峰值剪切应变能密度的影响增加。干燥和饱水红砂岩峰值剪切应变能密度分别趋于定值1.4579 MJ/m3和1.0033 MJ/m3,饱水使峰值剪切应变能密度的劣化率趋于31.18%。根据峰值剪应变随法向应力的变化规律,构建了干燥和饱水红...     

Dynamic vs. quasi-static shear failure of high strength metallic alloys: Experimental issues

Ductile fracture of metals by void nucleation, growth and coalescence under positive stress triaxiality is well admitted. This is not the case when metals are submitted to negative stress triaxiality. The present work aims at contributing to a better understanding of the competition between micro-mechanisms at the origin of failure of metals when submitted to shear-pressure loading at low and high strain rates. With this aim in view, experiments were carried out on Ti–6Al–4V shear-compression samples involving a stress triaxiality range comprised between −0.2 and −0.5. Results show that the material failure is the consequence of a void growth induced process. At high strain rate, due to the localization of the deformation within adiabatic shear bands, the failure of the material occurs earlier, leading to maximum shear strain smaller at high strain rate than at low strain rate. Impact tests were also carried out on Kalthoff and Winkler type double notched plates. They showed that the interaction between tension and shear waves leads to a complex Mode I–Mode II crack propagation.     

Experimental studies on shear failure of freeze-bonds in saline ice:: Part II: Ice-ice friction after failure and failure energy

This paper is the second of two papers that present and discusses the results from experiments where artificially created freeze-bonds made from saline ice were tested on direct shear with the freeze-bond oriented horizontally. It discusses the friction forces after freeze-bond failure and the failure energy.The friction force showed increasing linear trends with a non-zero intercept when plotted against the normal force. It shows that for low confinements Amonton's law is insufficient. For larger confinements the values of friction coefficient were in the range of previously reported measurements in ice-ice friction. A slightly decreasing trend of the frictional forces was found when the initial ice temperature increased.A Mohr-Coulomb type of model was proposed to model the ice-ice frictional stresses as function of the normal stresses. An empirical model was obtained to describe freeze-bond failure and subsequent deformation by introducing softening of the cohesion and angle of internal friction.The failure energy had similar trends to those observed for the freeze-bond shear strength when plotted against normal confinement, initial ice temperature and submersion time. Quadratic fitting to the data of failure energy as a function of freeze-bond shear strength allowed the estimation of the elastic shear modulus of the freeze-bond by applying a simple rheological model. The values found were between 2 kPa and 6 kPa which are very low compared with the shear elastic modulus for the ice blocks.     

Physically Based Failure Criterion for Dimensioning of Thick-Walled Laminates

The extreme lightweight potential of modern composites for the application in highly strained and thick walled components can only be sucessfully utilized with the help of adapted design procedures. Therefore, the stress and strain analysis of fibre reinforced components has experienced a tremendous improvement in recent years. The derived mechanical methods and the existing computing facilities are now capable of calculating complex and three-dimensional states of stress for single layers within laminated structures. The adequate development of appropriate failure criteria for the evaluation of such stress states has unfortunately not been promoted in the desired manner. In 1980, Hashin proposed a new generation of physically based failure analysis which could only be realized by a considerably increased numerical effort. Recently, Puck made a new attempt based on Hashin's concept using fundamental elements of the failure criterion by Mohr and Coulomb. Applying this model, the three-dimensional state of stress is evaluated in a realistic manner. It is assumed that besides the occurence of fibre failure only tensile stresses and shear stresses in loading planes tangential to the fibre direction induce the inter-fibre failure of the unidirectionally reinforced composite, whereas compressive stresses in these planes obstruct failure.     

Variation in Creep Rupture of γ′ Strengthened Superalloys with Stacking Fault Energy of Matrices

The correlation between the creep rupturebehaviour and the stacking fault energy of matricesof γ′strengthened superalloys has been studied dur-ing constant load creep.At high temperature andintermediate stress,the creep rupture time andstrain strongly depend on the stacking fault energyof matrices rather than the creep friction stress,butat higher stress,the role of grain boundary carbidesbecomes more obvious.However,in the considerably extensive stressrange investigated here,the mean creep rate is apower function of the stacking fault energy ofmatrices and the power index decreases with in-creasing initial applied stress.Particularly,at inter-mediate stresses the product of this index and theinitial applied stress compensated by the shearmodulus is same for two series of superalloys.Hence,this product may be a criterion predictingthat the matrix deformation controls high tempera-ture creep rupture.     

DEM analysis of the size effects on the behavior of crushable granular materials

Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.     

一种椭圆模的建模及其拉拔力的解析研究

目的设计一种能提高产品成材率、降低能量消耗的拉拔模具,并对其进行工艺优化。方法在求解内部塑性变形功率过程中,利用线性的EA(平均面积)屈服准则,克服了非线性的Mises屈服准则积分困难的问题,得到了拉拔时内部塑性变形功率的解析表达式;通过对入口径向速度积分,得到了入口剪切功率的解析表达式;通过对速度场的曲线积分并利用积分中值定理,得到了摩擦功率的解析表达式;最终,基于上界法得到了拉拔力的解析表达式。结果通过有限元模拟,验证了拉拔力解析式的正确性,并与传统锥模进行了比较,最大应力降幅达到17.5%。结论利用椭圆曲线设计得到的椭圆模能够降低应力集中,提高拉拔制品的质量,减少拉拔时的能量消耗,可以为相关工程人员提供科学指导。     

材料三剪屈服准则研究

在分析Tresca屈服准则和双剪屈服准则的基础上,通过考虑十二面体单元主剪面上所有三个主剪应力的共同作用,提出了材料的三剪屈服准则,并对该准则作了极限线分析、应力莫尔圆分析、中间主应力效应曲线分析和滑移面方向分析。结果表明,新准则与统一屈服准则一样表示的是一个屈服准则系列,其中Tresca屈服准则和vonMise屈服准则是该屈服准则的特例。但与双剪统一屈服准则不同,新屈服准则的极限线和中间主应力效应曲线是非线性的,能够描述材料的非线性屈服特性。另外,也克服了双剪统一屈服准则中存在的在某些特定应力状态下会得出双重滑移面并且滑移面方向会发生变化的问题。     

Deformation dynamics at low and ambient temperatures

The variation of tensile yield stress at a constant strain rate as a function of temperature for well-annealed pure metals show, with increasing temperatures, a rather sharp drop in yield stress (low temperature regime), followed by the intermediate temperature regime where yield stress decreases more slowly (and the ratio of yield stress to shear modulus remains more or less constant), which in turn is followed by the high temperature regime where the yield stress drops again rather sharply. The paper discusses the phenomenological framework for studying deformation dynamics in the low and intermediate temperature regimes. The approach adopted is the well-known state variable approach, where the evolutionary nature of deformation structure is described by one or more structure variables such that the current values of mechanical variables and structure variables together completely define the current state of deformation. A critical analysis of experimental results available suggest that at least for deformation at low strain rates, stress-rate is probably not a state variable of deformation. Thus deformation is most conveniently studied in terms of TASRA (thermally activated strain rate analysis) where the stress, plastic strain rate, temperature and structure are interrelated through a Gibb’s free energy for thermal activation by an Arrhenius equation. The stress-dependence of Gibb’s free energy and its maximum value then form the basis of identifying the rate-controlling obstacles. The need for careful experimentation and systematic analysis is illustrated by the example of low temperature deformation of hard hep metals. Modelling for the evolution of deformation structure is also touched upon.     

基于双剪强度理论的混凝土板极限冲切承载力计算方法

将混凝土板的冲切破坏简化为平面应变问题,采用双剪应力三参数强度准则对冲切破坏时的混凝土板剪压区的复合应力进行分析,得到了剪压面上的极限竖向剪应力,利用静力平衡条件求得混凝土板的极限冲切承载力计算公式。与国内外246个试件的试验数据进行比较表明,该公式的计算结果与试验结果吻合良好。计算公式的计算模式概念清晰,可供结构设计时参考。     

Viscoelasticity and shear yielding onset in amorphous glassy polymers

In the present work, the effect of viscoelasticity on the yield behaviour of a polycarbonate, PC, was studied and the identification of a yield criterion which takes into account the effects of the mechanical history on the onset of plastic strain, was attempted. The attention was focused on the shear yielding plastic deformation process and different loading histories were performed under uniaxial compression: constant strain rate at different rates, stress relaxation at different applied strain levels, creep under different stress levels. Some tests were also carried out under shear loading, in which the hydrostatic stress component is equal to zero and its effect on the yield onset can be considered. For the definition of a yield criterion, different quantities, some already proposed in an analogous work on a styrene-acrylonitrile copolymer (SAN), were considered and determined at yield onset for each of the applied loading histories. The results obtained in this work show that the relative ratios of the viscoelastic strain over the overall strain and of viscoelastic energy over the deformation work are fairly constant irrespective of both loading history and stress state. The re-elaboration of the data previously obtained on SAN is consistent with these results. Discussing the experimental data, differences between the mechanical behaviour of the two glassy polymers were pointed out and a more difficult activation of the plastic deformation process of PC than SAN was generally observed.     

Simple shear in 3D DEM polyhedral particles and in a simplified 2D continuum model

We develop a discrete element model (DEM) simulation of mixed regular rounded polyhedra and spheres in simple shear with walls and periodic boundaries in 3-dimensions. The results show reasonably realistic behaviour developing shear and dilation or compaction depending on whether the initial state is dense or loose. Similarly non-coaxiality of principal stress direction and strain rate direction are shown. Polyhedra show more general realistic behaviour than spheres but take significantly longer to run. Particle forces include normal elastic, damping, and tangential friction and rolling friction. No cohesion or interstitial fluid is modelled. A separate simplified dynamic implicit finite difference Eulerian continuum model is developed and its parameters are used to fit the DEM results. This uses mass and momentum balances, a non-linear constitutive model and Mohr–Coulomb failure criterion. It runs in 2D with periodic boundaries effectively making it pseudo-1D. The model can reproduce the general trend of the DEM results and is a good basis for further development and understanding the physics.     

铅剪切阻尼器的阻尼力模型与设计

基于理想弹塑性本构关系,推导了铅剪切阻尼器的两个阻尼力模型。根据能量原理,考虑剪切变形均匀性假设,横截面各点剪应力同时屈服,得到了均匀变形阻尼力模型(均匀模型)。依据剪应力分布规律和变形连续性条件,引进一个剪应变分布函数,用来描述剪切屈服后剪应变随屈服区扩展的变化规律,通过横截面剪力平衡方程,确定了非均匀变形阻尼力模型(非均匀模型)。两个理论模型的滞回曲线与Robinson SeismicLtd公司的实验曲线进行比较。结果表明,小位移时非均匀模型能精确模拟实验曲线,而均匀模型的计算结果明显大于实验数据;大位移时二者均与实验曲线吻合较好。证明了非均匀模型的极限阻尼力是均匀模型的最大阻尼力(屈服剪力)。以极限阻尼力和屈服位移为参数,给出了阻尼器的设计方法。     

Influence of stress condition on adiabatic shear localization of tungsten heavy alloys

Dynamic deformation and failure behavior of a tungsten heavy alloy (93W) under complex stress condition are studied using a split Hopkinson pressure bar (SHPB) apparatus. Cylindrical, step-cylindrical and truncated-conic specimens are used to generate different stress condition in an attempt to induce strain localization in the alloy. The microstructure of the specimens after tests is examined by optical microscopy and scanning electronic microscopy (SEM). It is found that in all the specimens, except the cylindrical ones, intense strain localization in the form of shear bands is initiated at stress concentration sites. In order to analyze the stress condition of different specimen geometry, finite element simulations are also presented. The Johnson-Cook model is employed to simulate the thermo-viscoplastic response of the material. It is found that dynamic deformation and failure modes are strongly dependent on the geometry of the specimens. The stress condition controlled by specimen geometry has significant influence on the tendency for shear band formation. The adiabatic shear band has general trends to initiate and propagate along the direction of maximum shear stress. It is suggested that further studies on the control of the stress condition to promote shear band formation be conducted in order to improve the penetration performance of the tungsten heavy alloy.     

Perforation of rigid-plastic plate by blunt missile

Three rigid plastic models are presented to treat circular plate deformation during perforation by a rigid missile; these models are based on different assumptions for yield. The analysis considers plate bending, stretching and also shear around the periphery of a central plug. An equivalent strain failure criterion is developed that includes the influence of both shear and radial tensile strain on localized failure of the plate. Both this and a pure shear failure criterion of Shadbolt et al. [1] are used together with three structural deformation models to calculate the ballistic limit and final deformed profiles of plates. These calculations are compared with some experimental results for plates of different materials.     

Adiabatic shear failure in brittle solids

Recent studies have revealed microscopic amorphous lamella resulting from inelastic deformation in the ballistic impact of boron carbide ceramic. The possibility that these deformation features are a consequence of adiabatic shear deformation in the impact event is explored. An early theory of adiabatic shear that was limited to the response of rigid-plastic deformation is expanded to include elastic strain energy. The study reveals that elastic strain energy is commonly a small, but not negligible, contribution to impact-induced adiabatic shear in metals. Elastic strain energy is paramount in brittle solids. Relations are developed from the theory to predict the nominal width and spacing of adiabatic shear-bands in brittle solids. Comparisons of the theoretical predictions are consistent with observations of impact-induced deformation features in boron carbide.     

剪切带内部应变(率)分析及基于能量准则的失稳判据

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。