脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

Large deformation extensional rheology of bread dough

The stress–strain curves of bread dough were derived under uniaxial compression, uniaxial tension and equi-biaxial tension loading conditions. In uniaxial compression, a lubricant was used to eliminate frictional effects between the loading platens and the sample. In uniaxial tension, cylindrical samples with thin flat discs at both ends (‘I’ samples) were tested. The discs at both ends were allowed to air-dry and were subsequently glued onto the loading platens. In equi-biaxial tension, a thin disc of dough was inflated into a bubble using pressurised air. The thickness at the top of the bubble was measured by shining a light through the walls of the bubble and recording the change in light intensity as the wall becomes thinner. All methods ensured that uniform deformation was obtained. Stress and strain were accurately evaluated using image analysis techniques. The tests were performed at various strain rates and speeds that defined the time dependence of the material. A non-linear viscoelastic model based on the Prony series and Van der Waals hyperelasticity was used to predict all test data. The model had a total of five material parameters and two time constants, which were set to represent the actual time scales of the experiments. A reasonable agreement between the experimental data and the chosen material model was observed.     

Constitutive relations of strain, anisotropic degradation, and fracture of filled polymer materials in prevailing-tension processes with varying axis direction and relaxations

In the course of monotone uniaxial tension, filled polymer materials quasi-isotropic in the initial state experience increasing structure fractures (local adhesive separation and cohesive tearing) whose directions are mainly perpendicular to the tension axis. After complete unloading and relaxation, the fracture lips close, and weaker secondary bonds are formed between them. Taking into account the anisotropy of the above-described process of deterioration of the material structure and mechanical properties (degradation), we suggest to characterize the state of each elementary material fiber by its own values of the structure parameters (damage, fracture, and maximum strain), which can be calculated (according to the model equations of uniaxial tension in a constant direction) from the effective strain history of the fiber. It is determined as the product of the current values of two factors, namely, the strain intensity and the influence function, whose argument is the angle between the directions of the fiber under study and the maximum principal strain. The form of the influence function depends on the material and reflects the degree of anisotropy of the damage arising in it. As a model of uniaxial tension in a constant direction, we use the earlier-proposed version of the nonlinear endochronic theory of ageing viscoelastic materials, which, in addition, contains the secondary bond parameter (with its own equation). We show how the proposed constitutive relations permit one to describe the decrease in the resistance and the ultimate strain during the second axial tension compared with a similar tension from the initial state and to determine the dependence of these effects on the angle between the directions of the preliminary and repeated tensions.     

混凝土断裂过程及尺寸效应分析

为研究混凝土裂纹断裂过程和最大承载力计算方法,通过实验机对四种不同尺寸混凝土紧凑拉伸断裂试件进行了加载过程实验,并对其中一个试件进行应变片跟踪测试.由实验结果分析得到了一系列关系曲线,如试件的载荷-加载点位移关系曲线,断裂损伤区变形随载荷变化曲线;并且计算了不同尺寸断裂试件的应力强度因子.结合计算粘聚裂纹应力强度因子的公式与断裂准则,完成了对承载力理论值的计算,并将其与实验峰值平均值进行对比,其结果是两者相比误差较小,表明此种计算裂纹结构最大承载力方法是可行的.     

Multi-cycle deformation of silicone elastomer: observations and constitutive modeling with finite strains

Observations are reported on a medical grade of silicone elastomer in uniaxial tensile tests up to breakage of specimens, short-term relaxation tests, and cyclic tests with monotonically increasing maximum elongation ratios. Experimental data in cyclic tests demonstrate the fading memory phenomenon: stress–strain diagrams for two specimens with different deformation histories along the first n?1 cycles and coinciding loading programs for the other cycles become identical starting from the nth cycle. A constitutive model is developed in cyclic viscoplasticity of elastomers with finite strains, and its adjustable parameters are found by fitting the experimental data. Ability of the stress–strain relations to predict the mechanical response in cyclic tests with various deformation programs is confirmed by numerical simulation.     

An Improved Experimental Method for Determining the Workability Diagram

The workability diagram is often used for ductile fracture predictions in metal forming processes. Its determination requires the measurement of the strain to fracture in several tests in which the triaxiality ratio is supposed to be known and fixed throughout the process of deformation. One of such tests is the uniaxial tension test. In practice, however, it is very difficult (or even impossible) to keep the triaxiality ratio fixed in this test because of necking. It is shown in the present paper that the uniaxial tension test can be replaced with the collar test for obtaining a point of the workability diagram when the fracture criterion based on an average value of the triaxiality ratio is adopted. It is also shown that the collar test provides a more accurate prediction of the strain to fracture. The test carries out at quasi-static strain rates.     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

An experimental study of inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading

An experimental study was conducted on the inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading. Thin-walled tubular specimens were used and small strain gages were bonded on the specimen surface to characterize the local deformation. The controlled loading paths included cyclic tension–compression, cyclic torsion, proportional axial-torsion, 90°-out-of-phase axial-torsion, and fully reversed torsion with a constant axial stress. The maximum stress in each experiment was lower than the lower yield stress of the material. It was found that the cyclic plastic deformation within the gage section of the specimen under multiaxial stress state followed the three-stage process that was observed from uniaxial loading, namely, incubation, propagation, and saturation. The plastic deformation was significantly inhomogeneous during the propagation stage, and the inhomogeneity continued through the saturation stage. The duration of each stage and the saturated strains were dependent on the cyclic stress amplitude and the loading path. Multiaxial stress state reduced the incubation stage. With identical equivalent stress magnitude, the nonproportional loading path resulted in the shortest incubation and propagation stages, and the saturated equivalent plastic strain magnitude was the smallest. Although the deformation over the gage section was inhomogeneous, the plastic deformation in a given local area was found to be practically isotropic.     

Shear Testing of Polypropylene Materials Analysed by Digital Image Correlation and Numerical Simulations

Distributions of shear strains and strain states (triaxiality) were analysed for two in-plane shear test fixtures (Iosipescu and V-notched rail), using digital image correlation and numerical simulations. Three different polypropylene-based materials (two talc-filled compounds and one unfilled homopolymer) were tested. The three materials behaved differently in the shear tests. Most notably, cracks developed in tension near the notches for the particle-filled materials, while the unfilled homopolymer did not fracture. There were also differences between the materials regarding strain localisation between the notches, strain rates vs. strain level (for a given cross-head speed), thickness change in the sheared section, and triaxiality. The yield stresses in shear, uniaxial tension and uniaxial compression showed pressure sensitivity. At least for equivalent strain rates below 1?s^?1, the strain rate sensitivity of the yield stress was approximately the same in these three stress states. The stress?Cstrain curves obtained with the two methods were quite similar for these materials. There were some differences between the methods regarding the ease of mounting and aligning specimens, the complexity of specimen deformation patterns, and the uniformity of the shear strain distribution between the notches.     

超高强度钢AF1410塑性流动特性及其本构关系

在本文中,为揭示超高强度钢AF1410的塑性流动性,并研究其塑性流动本构关系,利用CSS4410电子万能试验机和改进的Hopkinson拉压杆技术,对AF1410钢在温度从100K到600K,应变率从0.001/s到2000/s,塑性应变超过20%的塑性流动特性进行了试验研究。结果表明,拉伸加载下AF1410钢屈服强度低于压缩屈服强度,且随应变率增加,拉压屈服强度差值越来越大;该材料塑性流动应力对应变率敏感性低,而对温度较为敏感;随应变率的提高,该材料拉伸失效应变减小,但温度对失效应变无明显影响。最后基于位错的运动学关系,借助试验数据,获得了AF1410钢的塑性流动物理概念本构模型,并通过与经典J-C模型的结果对比对该物理概念本构模型进行了评估分析,表明该物理概念本构模型在较宽温度和应变率范围能较好的预测AF1410钢的塑性流动应力。     

Ratchetting of viscoplastic material with cyclic softening,part 1: experiments on modified 9Cr–1Mo steel

Uniaxial and multiaxial ratchetting tests were conducted at temperatures between 200 and 600 °C on modified 9Cr–1Mo steel, which exhibits both viscoplastic and cyclic softening behavior. Anomalous behavior was observed in the stress-controlled uniaxial ratchetting tests; the material exhibited outstanding ratchetting in the tensile direction under zero mean stress. Under the uniaxial conditions, the ratchetting deformation significantly depended on the loading rate and hold time in addition to parameters such as the maximum stress and stress ratio. The uniaxial ratchetting was also accelerated to a great extent when cyclic deformation was given before the ratchetting tests. Under the multiaxial conditions, the ratchetting depended on the steady stress, cyclic strain range and strain rate. The ratchetting progressed faster as the steady stress or strain range became larger, or the strain rate became smaller, as expected. Monotonic compression tests were carried out to investigate the reason for the rachetting under no mean stress. Strain range change tests were also conducted to investigate the effect of strain range on the cyclic softening behavior of the material in detail.     

半结晶聚合物损伤演化的实验表征与数值模拟

损伤本构模型对研究材料的断裂失效行为有重要意义, 但聚合物材料损伤演化的定量表征实验研究相对匮乏. 通过4种高密度聚乙烯(high density polythylene, HDPE)缺口圆棒试样的单轴拉伸实验获得了各类试样的载荷-位移曲线和真应力-应变曲线, 采用实验和有限元模拟相结合的方法确定了HDPE材料不同应力状态下的本构关系, 并建立了缺口半径与应力三轴度之间的关系;采用两阶段实验法定量描述了4种HDPE试样单轴拉伸过程中的弹性模量变化, 并建立了基于弹性模量衰减的损伤演化方程, 结合中断实验和扫描电子显微镜分析了应力状态对HDPE材料微观结构演化的影响. 结果表明缺口半径越小, 应力三轴度越大, 损伤起始越早、演化越快; 微观表现为: 高应力三轴度促进孔洞的萌生和发展, 但抑制纤维状结构的产生;基于实验和有限元模拟获得的断裂应变、应力三轴度、损伤演化方程等信息提出了一种适用于聚合物的损伤模型参数确定方法, 最后将本文获得的本构关系和损伤模型用于HDPE平板的冲压成形模拟, 模拟结果与实验结果吻合良好.      

Deformation and fracture of crystalline materials under complex loading-program conditions

In predicting the deformation and conditions of fracture of materials under complex loading program conditions one must consider the entire duration of the deformation process.The problem becomes complicated in cases of a simultaneous operation of various mechanisms of deformation and fracture, e. g., when plastic deformation is superposed (once or repeatedly) on creep.A promising phenomenological approach to this problem may be based on concepts of the mechanical equation of state of materials. A hypothesis of the existence of the equation of state depending on a finite number of structural parameters was formulated by Kröner [1] for the case of the three-dimensional law of plasticity and by Rabotnov [2] for the case of creep and fracture under uniaxial stress state conditions.This article is concerned with the application of the hypothesis of the mechanical equation of state to the problem of deformation and fracture of materials (in the uniaxial case) under complex loading program conditions.     

Effects of stress invariants and reverse loading on ductile fracture initiation

Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.     

Multi-cycle deformation of semicrystalline polymers: Observations and constitutive modeling

Experimental data are reported on isotactic polypropylene in multi-cycle uniaxial tensile tests where a specimen is stretched up to some maximum strain and retracted down to the zero minimum stress, while maximum strains increase with number of cycles. Fading memory of deformation history is observed: when two samples are subjected to loading programs that differ along the first n − 1 cycles only, their stress–strain diagrams coincide starting from the nth cycle. Constitutive equations are developed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and adjustable parameters in the stress–strain relations are found by fitting the experimental data. Results of numerical simulation demonstrate that the model predicts the fading memory effect quantitatively. To confirm that the observed phenomenon is typical of semicrystalline polymers, experimental data are presented in tensile cyclic tests with large strains on low density polyethylene and compressive cyclic tests on poly(oxymethylene).     

Photoplastic stress analysis considering rate effect

The possibilities of cellulose acetate as a photoplastic model material used in the uniaxial tension test were presented by the authors in Ref. 1. Empirical formulas were proposed for photoplastic stress analysis considering the effect of strain rate and temperature. In this paper, the stress-strain-optic laws derived from the uniaxial tension test were confirmed precisely under the biaxial stress field. Consequently, the biaxial stress-strain-optic laws of cellulose acetate can be represented by simply substituting the difference of the principal stress and the difference of the principal strain into the terms of the stress and the strain in the empirical formulas for the uniaxial stress state, respectively. Therefore, the empirical formulas considering the influence of strain rate were obtained for the photo-viscoelastoplastic plane-stress analysis during the usual static loading. This method was applied to an elastoplastic problem of a finite plate with a circular hole under uniaxial tension. The distribution of stress and strain, the stress-concentration factors in the elastoplastic region and the development of the plastic region were obtained experimentally taking the rate effect into account. As a result, the stress on a minimum section in a model increased as head speed increased. On the other hand, the distribution of strain, the development of the plastic region and the stress-concentration factors were almost never influenced by head speed.     

Sequential evaluation of continuous deformation field of semi-crystalline polymers during tensile deformation accompanied by neck propagation

The localized deformation field of high density polyethylene and polypropylene during a tensile test accompanied by neck propagation was quantitatively evaluated based on the network digital image correlation method. In the proposed method, the continuity of the deformation field around a point of interest was introduced for accurate evaluation of the displacement. The accuracy of the proposed method was verified through test images. Using the proposed method, the development of a non-uniform displacement field during tensile tests was evaluated from sequential digital images. The local strain rate was almost uniform until the nominal stress reached its maximum value. After the maximum stress was reached, non-uniform deformation developed at a part of the gauge region of the specimen. A decrease in nominal stress induced a reduction of the local strain rate at regions other than the necked zone. In this study, the cross section average local true stress, strain, and strain rate can be evaluated from the local displacement field. Thus, the relationship between these quantities was evaluated during the tensile tests. Using the proposed method, the local response under wide ranges of strain and strain rate can be evaluated from a few test conditions of tensile strain rate and a small range of tensile strain. Finally, the relationships between gradients of stress, strain, and strain rate under uniaxial tension are discussed. These non-local quantities deviated from those predicted by constitutive equations when the domain size used to evaluate the local quantities was large.     

Strain strengthening effects in Witwatersrand quartzite

A series of uniaxial compression specimens were tested over a range of applied ram displacement rates of 8.9 × 10⁻⁴ to 8.9 mm/sec to elucidate the effects of loading rate on the uniaxial compressive fracture stress of Witwatersrand quartzite. It was demonstrated that even within standard loading rate ranges, considerable scatter in the fracture strength (under uniaxial compression) existed in this particular quartzite rock. Nevertheless, a definite trend of increasing fracture resistance with increasing monotonic loading rate was evident inasmuch that increasing the loading rate (strain rate) by four orders of magnitude increase the fracture strength by almost 2.8 times. Prior fatigue loading also produced a significant strain strengthening as the uniaxial compressive fracture stress tended to increase in a sigmoidal fashion with increasing number of fatigue cycles prior to testing. Indeed, the fracture strength of quartzite was almost doubled in value after 10⁻ cycles. Plane strain fracture toughness tests utilising three point bend specimens were conducted and an average of K_lc = 1.7 MPa√m was realized. In both the uniaxial compression tests and the fracture toughness tests, failure occurred by crack extension predominantly by a transgranular flat cleavage-like mode through pure quartzite (silica) regions. However, crack extension was also observed to occur in an intergranular “ductile-like” mode through areas associated with inclusions prevalent in the quartzite.     

High-rate start-up behaviour of unvulcanised rubber compounds

The recently developed machines, which are shown to be comparable with “established” devices, are used to perform the start-up of uniaxial extension and simple shear at high constant deformation rates. Henky strains in excess of 8 at constant strain rates of over 100 s^?1 are achieved for two highly filled unvulcanised rubber compounds of Butyl and Chloroprene rubbers. In general no steady state is attained in uniaxial extension; the stress reaches a maximum and then declines. It is shown that the time—temperature superposition principle holds for start-up flows resulting in a family of master curves. It is established that the extensional stresses are one or two orders of magnitude greater than the shear stresses at corresponding deformation rates over a wide rate range.     

45钢的J-C损伤失效参量研究

为了在结构碰撞效应的有限元分析中描述材料行为,通过开展45钢在不同应力状态和温度下的准静态材料力学性能实验及拉伸SHB实验,考察了应力状态三轴度、温度和应变率对材料失效应变的影响。由实验数据得到了Johnson-Cook失效模型参量,并通过出现失效的Taylor撞击实验和数值模拟进行了一定的验证,表明模型描述与实验结果的趋势一致。