Q235钢缺口试样拉压低循环疲劳的实验研究

以Q235钢制U型缺口板试样为研究对象,用有限元方法计算其缺口根部等效应变幅对应的试样标距段位移,以此控制试验机进行拉压循环疲劳试验。然后用局部应力应变法对试验测得的寿命结果进行分析。结果表明：无论用有限元还是修正Neuber公式计算缺口根部的应力应变,局部应力应变法的疲劳寿命评估只适用于缺口半径较大的试样;对缺口半径较小试样的估计寿命明显低于实测值,且有限元法比修正Neuber法更保守。进而又对试样缺口区域应变梯度的影响进行了探讨：参照有限元计算的应变梯度,利用Taylor模型估算了缺口根部的屈服应力和流动应力;在此基础上重新计算应变分布并估计试样的疲劳寿命,结果证实考虑应变梯度影响可改善缺口试样的疲劳寿命估计。     

FATIGUE PROPERTY BASED ON NOTCHED SPECIMEN TESTS

缺口件疲劳问题的研究日益引起各国学者的重视. 局部应力-应变法以其简单性在工程中得到了广泛应用, 该方法通常会得到偏于安全的结果. 引入疲劳缺口因子代替弹性应力集中因子针对缺口疲劳进行研究, 仍未能从本质上改善预测结果的准确性. 考虑到"热点应力" 附近的相对应力梯度, 提出了应力梯度法研究缺口件疲劳问题, 这一概念亦被用于应力场强度方法中, 如何准确确定损伤区域是应力场强度方法需要解决的问题. 临界距离理论可将Neuber 律、Peterson 方法及应力场强度方法进行有效统一, 同时有限元方法的发展进一步支持了该理论. 目前, 该方法在高周疲劳研究中取得了较好的效果, 但对低周疲劳寿命预测的有效性仍需进一步的验证.     

A unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading

In this paper, a simplified thermodynamics analysis of cyclic plastic deformation is performed in order to establish an energy transition relation for describing the elastic–plastic stress and strain behavior of the notch-tip material element in bodies subjected to multiaxial cyclic loads. Based on the thermodynamics analysis, it is deduced that in the case of elastic–plastic deformation, Neuber’s rule inevitably overestimates the actual stress and strain at the notch tip, while the equivalent strain energy density (ESED) method tends to underestimate the actual notch-tip stress and strain. According to the actual energy conversion occurring in the notch-tip material element during cyclic plastic deformation, a unified expression for estimating the elastic–plastic notch stress–strain responses in bodies subjected to multiaxial cyclic loads is developed, of which Neuber’s rule and the ESED method become two particular cases, i.e. upper and lower bound limits of the notch stress and strain estimations. This expression is verified experimentally under both proportional and non-proportional multiaxial cyclic loads and a good agreement between the calculated and the measured notch strains has been achieved. It is also shown that in the case of multiaxial cyclic loading, the unified expression distinctly improves the accuracy of the notch-tip stress–strain estimations in comparison with Neuber’s rule and the ESED method. The unified expression of the notch stress–strain calculation developed in this paper can thus provide a more logical approximate approach for estimating the elastic–plastic notch-tip stress and strain responses of components subjected to lengthy multiaxial cyclic loading histories for local strain approach-based fatigue-crack-initiation life prediction.     

A new version of the Neuber rule accounting for the influence of the notch opening angle for out-of-plane shear loads

The paper deals with nonlinear stress and strain distributions at the root of sharp and rounded notches with different opening angles under antiplane shear loading and small scale yielding. In order to make an easier comparison with the Neuber rule, the material is thought of as obeying the particular nonlinear law used in the past just by Neuber.By solving the linear differential equation resulting from the use of the hodograph transformation, a new relationship linking linear and nonlinear stress and strain concentrations is found. The relationship is written also in terms of the relevant notch stress intensity factors. In contrast with the Neuber rule, this relationship strictly depends on the notch opening angle. Even when the notch opening angle is zero, it does not match the Neuber Rule, but results in an additional factor 2 which is in agreement with Hult and McClintock’s solution when the notch tip radius tends to zero and the notch becomes a crack.     

Stress redistribution in notched specimens during fatigue cycling

Most materials exhibit a change in stress-strain relationship when subjected to fatigue stresses. In this work, the effect of this change on the stress distribution across the throat of notched-plate specimens of mild steel is examined. Using a set of strain gages, the strain distribution across the specimens was determined under dynamic conditions for various numbers of cycles. Tests of unnotched specimens were used to obtain the cyclic stress-strain properties for corresponding numbers of cycles, and from these data the stress distribution in the notched specimens was determined. Tests in which the strain amplitude at the notch root was held constant revealed a decreasing maximum stress with fatigue cycles. In another series of tests, in which the load amplitude was constant, the maximum stress amplitude was observed to decrease with number of fatigue cycles, despite an increasing strain amplitude. In both types of tests, the stress-concentration factor was observed to decrease with increasing number of fatigue cycles.     

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.     

Fracture analysis of V-notched components – Effects of first non-singular stress term

The effect of the first non-singular stress term on the fracture behavior of notched structures was investigated under symmetric geometry and loading conditions. According to the Williams series expansion, for a large domain of notch angles the non-singular stress terms of sharp notches are functions of complex eigenvalues and their corresponding complex coefficients. Hence, a new representation of stress field near the notch tip was developed in which the higher order terms are expressed as several explicit functions of real and imaginary parts of both the complex eigenvalues and their complex coefficients. A critical stress criterion was then applied to the new stress formulations to assess the influence of the first non-singular stress term on the apparent fracture toughness. Several finite element analyses were also performed on two laboratory specimens in order to show the effects of first non-singular term on the near field stress distribution of notched specimens. The results demonstrated that neglecting the first non-singular stress term could lead to significant errors in predicting the apparent fracture toughness of notched components.     

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.      

缺口件表象疲劳极限的定量化分析

测定了淬火、高温回火35CrMo钢光滑试样和三种缺口试样的三点弯曲疲劳极限,并利用ANSYS有限元软件计算了缺口试样加载时缺口截面上的应力分布.用“疲劳源形成的微细观过程理论”对试验结果进行了分析,认为,疲劳源的形成虽然发生在个别薄弱晶粒内部,是其中位错往返运动及交互作用的结果,但还必须满足一定的形变协调条件和概率条件,因而必须形成由相当多晶粒组成的“细观屈服区”.对试验结果的分析表明,如取“细观屈服区”临界尺寸(xW)等于11个奥氏体晶粒平均直径,则计算得到的缺口试样的表象疲劳极限,与实测值相比,其综合误差最小.据此计算的三种缺口试样的表象疲劳极限,其误差都小于5％.该xW可认为是材料的特征参量.     

Strain gage method for determining stress intensities of sharp-notched strips

An efficient and simple strain gage method for determining the stress intensities of sharp-notched strips is proposed. The bisector of the notch angle is inclined to the edge so that the mixed-mode loading is created simultaneously at the notch tip. A theory of determining the stress intensities using strain gages is described on the basis of the two-dimensional theory of elasticity. Experiments on specimens with various notch shapes are carried out to verify the theoretical results. Experimental results are in good agreement with theoretical results.     

Notch strengthening in titanium aluminides under monotonic loading

An important concern for titanium aluminides is their limited ductility and its consequences for TiAl components containing stress concentrators. In recent experiments, evidence of notch strengthening has been found in one TiAl alloy under monotonic loading. The goal of this study is to fully explore this issue through tests on two cast alloys, one with a microstructure consisting of predominantly equiaxed gamma grains and the other having a fully lamellar microstructure. Tests involve monotonic tensile loading of notched specimens at room temperature under conditions of plane stress, where the notch radii are large relative to grain size. For each material, results from the testing of three notched specimen geometries are presented and finite element models are used to interpret the test results. This includes using the numerical models to apply Weibull statistical methods to predict notch strengthening in the specimens. It is shown that notch strengthening is clearly seen in both alloys tested and thus is likely to be a characteristic of TiAl alloys in general; however, strengthening is not as great as would be predicted by Weibull statistical methods as applied to brittle materials.     

割口单向叠层板的拉伸应力集中与强度

基于剪滞理论,建立一种分层剪滞模型,分析了含割口的单向叠层板在拉伸载荷作用下的应力重新分布问题,获得了割口前缘完整纤维的应力集中因子.在此基础上,采用细观统计破坏理论,研究了割口单向叠层板的拉伸破坏强度,得到了与现有实验较吻合的结果.     

Verification of a neuber-based notch analysis by the companion-specimen method

Measurements of actual notch-root stress-strain behavior by means of the companion-specimen method are compared with predictions of the notch analysis using both a constant (long-life) fatigue-notch factor and a variable fatigue-notch factor determined from fatigue-life data. The results, using cyclicly stabilized specimens, show thatK _f is dependent upon the stress level of the degree of local straining. The amount of error incurred in the use of either the variable or constantK _f was about 7 percent in the prediction of the local strains. In addition, test results using specimens that had not been cyclicly hardened, and specimens subjected to a random-load history, indicated the effects of material-deformation phenomena such as cyclic hardening, stress-strain hysteresis-loop shape, and material memory, on local stress-strain predictions.     

Elastic-viscoplastic notch correction methods

Neuber’s type methods are dedicated to obtain fast estimation of elastic–plastic state at stress concentrations from elastic results. To deal with complex loadings, empirical rules are necessary and do not always give satisfying results. In this context, we propose a new approach based on homogenization techniques. The plastic zone is viewed as an inclusion in an infinite elastic matrix which results in relationships between the elastic solution of the problem and estimated stress–strain state at the notch tip. Three versions of the notch correction method are successively introduced, a linear one which directly uses Eshelby’s solution to compute stresses and strains at the notch, a non-linear method that takes into account plastic accommodation through a β$\beta$-rule correction and, finally, the extended method that is based on the transformation field analysis methods. All the notch correction methods need calibration of localization tensors. The corresponding procedures are proposed and analyzed. The methods are compared on different simulation cases of notched specimens and the predictive capabilities of the extended method in situations where plasticity is not confined at the notch are demonstrated. Finally, the case of a complex multiperforated specimen is addressed.     

A study of cyclic plastic stresses at a notch root

An experimental study is presented for cyclic plastic stresses at notch roots in specimens under constant-amplitude repeated tension and reversed loading. Edge-notched,K _T=2, 2024-T3 aluminum-alloy sheet specimens were cycled until local stress conditions stabilized. Local stress histories were determined by recording local strain histories during cycling and reproducting these histories in simple, unnotched specimens. The fatigue lives for these notched specimens were estimated using stabilized local stresses and an alternating vs. mean stress diagram for unnotched specimens of the same material. These predictions compared favorably with lives from S-N data for the notch configuration tested. In addition, an expression is presented for calculating local first-cycle plastic stresses. An acceptable correlation is shown between predicted stresses and experimental data within the scope of the investigation.     

General stress-strain relations in non-linear theory of viscoelasticity for large deformations

Conclusion General phenomenoligical stress-strain relations in non-linear theory of visco-elasticity for large deformations have been presented.In the first place, according to V. V. Novozhilov 1 we express the generalized equilibrium equation for large deformations in the Lagrange representation, and we apply the generalized Hamilton's principle to the equation of energy conservation, which denotes that the sum of the elastic energy and the dissipative energy is equal to the work done by the body force and the surface on the substance; so that we obtain the required general stress-strain relations in comparison with the above two equations.On the condition that the elastic potential is a function only of the strain, and the dissipation function is a function of the rate of strain and of strain; such a substance is reduced to the Voigt material necessarily, and the stresses which act on the substance are given by the sum of elastic- and viscous stresses, and the stress-strain relations are reduced to the so-called Lagrangian form.If elongations, shears and angles of rotation are small and also the strains and rates of strain are sufficiently small, the stress-strain relations are expressed by a linear Voigt model constituting a Hookian spring in parallel with a Newtonian dashpot.Non-linearity in the theory is classified into two groups i. e. the geometrical non-linearity and the physical non-linearity. The former is introduced into the theory through the definition of the generalized strain and of the generalized stress and through the equilibrium equation for large deformation, and the latter through the general stress-strain relations.The main result of this paper is that the general stress-strain relations in viscoelasticity are deduced necessarily from the physically appropriate assumptions.     

Experimental evaluation of incremental theories for nonproportionate loading of thin-walled cylinders

An experimental investigation was undertaken to evaluate incremental-strain theories which have been proposed in the literature to predict the loads on thin-walled cylinders subjected to nonproportionate loading which follow prescribed strain histories. Test data were obtained for two materials, annealed SAE 1035 steel and normalized 4340 steel. Material-property tests for the SAE 1035 steel indicated that the stress-strain diagram was flat topped and the material followed the Tresca flow condition. Similar tests for the SAE 4340 steel indicated that this steel was a linear strain-hardening material that followed the von Mises flow condition. Two incremental-strain theories were developed for thin-walled cylinders made of SAE 1035 steel. Both were based on the Tresca flow condition. One theory called the Tresca-Tresca theory used the stress-strain relations for the Tresca theory. The other theory called the Tresca-Mises theory used the Prandtl-Reuss stress-strain relations. In general, the test data fell between the two theories. The incremental theory developed for thin-walled cylinders made of the SAE 4340 steel, called the Mises-Mises theory, was based on the von Mises flow condition and the Prandtl-Reuss stress-strain relations. The agreement between theory and experiment was poor.     

缺口复合材料层合板疲劳性能的试验研究

对带各种缺口的复合材料层合板的疲劳性能进行了研究。设计了不同类型的制品试件,分别进行静态和疲劳试验。试验数据表明,缺口对复合材料的静强度和静刚度的影响不大,缺口试样的疲劳寿命带高于缺口试样,与金属材料相比,复合材料对缺口不敏感。采用条状试样获得的力学性能不参代表复合材料的真实性能,实现表明自由边的缺口对结构提高疲劳寿命是有利的。文中还对疲劳过程中复合材料的刚度变化进行了研究,对文中所研究的层合板,     

Prediction and observation of crack tip microstructure in shape memory CuAlNi single crystals

The formation of martensite at a notch tip in a CuAlNi shape memory alloy loaded in tension is studied. The geometry of the initial martensite plate to form at the notch is predicted theoretically, using the stress field at a crack tip in an anisotropic linearly elastic body together with a listing of all possible austenite-martensite interfaces from the Crystallographic Theory of Martensite (CTM). The stress field and CTM analyses are combined through a selection criterion based on computing the work available from the stress field to transform to each austenite-martensite interface. The resulting predictions are compared to experimentally observed microstructures in notched specimens of single crystal CuAlNi loaded in tension for eight notch orientations. Results show that the available work criterion accurately predicts the orientation, number and order of the austenite-martensite interfaces that initially form near a crack.     

准静态条件下金属材料的临界断裂准则研究

本文针对9种金属材料完成了具有不同约束程度的10类试样的延性断裂试验, 获得了发生拉、压、扭和裂尖断裂等破坏形式构型试样的载荷-位移试验关系; 基于圆棒漏斗试样拉伸试验所得直至破坏的载荷-位移曲线, 采用有限元辅助试验(finite-element-analysis aided testing, FAT)方法得到了9种材料直至破坏的全程等效应力-应变曲线, 以此作为材料本构关系通过有限元分析获得了各类试样直至临界破坏的载荷-位移关系模拟. 载荷-位移关系模拟结果与试验结果有较好的一致性, 表明用于解决试样颈缩问题的FAT方法所获得的全程材料本构关系针对各向同性材料具有真实性和普适性. 对应9种材料、10类试样的36 个载荷-位移临界断裂点, 通过有限元分析获得了对应的材料临界断裂应力、应变与临界应力三轴度, 研究表明, 第一主应力在延性变形过程中为主控断裂的主导参量; 通过研究光滑、缺口、裂纹等构型试样的断裂状态, 提出了$-1$至3范围的应力三轴度下由第一主应力主控的统一塑性临界断裂准则.