Experimental investigation of the regularities of inelastic deformation of metals in complex processes of loading under conditions of elevated temperatures

The article describes the study of the regularities of inelastic deformation of metal in isothermal complex processes of loading on paths in the form of two-link broken lines. The results of the experiments under complex loading of tubular specimens of heat-resistant alloy ÉI437 showed that the slope of the strain vector to the path of loading depends on the length of the arc of this path up to the point of its break; however, with the development of plastic deformations this dependence becomes weaker, and it may be neglected. The change of the slope of the strain vector to the path of loading depends on the temperature, and it does not depend on the speed of the loading process within the limits of its change by one order of magnitude; with angles of break of the path of loading exceeding /2 the dependence of the above-mentioned slope of the strain vectors on the length of the arc of the path of loading past the point of its break is not universal.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. 12, pp. 3–8, December, 1989.     

EVALUATION OF LOW CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

Abstract— A series of low cycle fatigue experiments have been conducted on a 42CrMo steel under tension-torsion loading. Thin-walled tube specimens were used. Low cycle fatigue under various loading paths, including circular and square paths, have been investigated.
The plastic work criterion for low cycle fatigue failure has previously been generally accepted, but it is difficult to calculate stress and strain for complex loading paths, especially for non-proportional loading. This present study suggests a simple method for the calculation of the stable cyclic stress and strain values based on a Modified Endochronic Constitutive Theory (MECT) that redefines an intrinsic time scale. The loading path effect under non-proportional loading is also considered when evaluating fatigue life.
The results show that the plastic work approach using the MECT method in multiaxial fatigue calculations correlates reasonably well the data and is a reflection of loading path dependence.     

Accumulation of Damage in A336 GR5 Structural Steel Subject to Complex Stress Loading

Abstract: Changes in the mechanical characteristics of the structural steel because of fatigue damage accumulation are investigated in this article. Cyclic loading was performed in a complex stress state. Tubular specimens were loaded by axial force and torque, with loading performed along proportional and non‐proportional paths in the strain space. Material characteristics in the form of the stress–strain curve and yield surface were determined in the ‘as received’ state and after cyclic loading. It was found that accumulation of the fatigue damage because of cyclic loading in a complex stress state along proportional and non‐proportional paths in the strain space is manifested by the increase in inelastic response. The rate of damage was found to be higher for non‐proportional (circular) loading paths than that for proportional loading with the same strain amplitude.     

DEVELOPMENT OF A CONSTITUTIVE MODEL FOR BIAXIAL LOW-CYCLE FATIGUE

Abstract— A version of the endochronic theory of plasticity for the modelling of nonproportional cyclic loading has been developed. To describe an additional hardening of a material a new engineering method for defining a nonproportionality parameter is proposed for a wide class of cyclic strain paths with a prescribed maximum range of plastic or total strains. This parameter makes it possible to establish an unambiguous linear dependence between the cyclic strain path shape and the stress level in a stabilized state. Conjugation conditions have been formulated to describe complex histories of nonproportional cyclic loading. The results of the modelling are shown to be in fair agreement with the experimental data.     

Modelling of fatigue lifetime under non-proportional multiaxial alternating loading

This paper presents two approaches to lifetime prediction under non‐proportional multiaxial alternating loading; a phenomenological approach using the Manson–Coffin relation and a microstructural approach. Both models have in common the use of a new multiaxiality factor. The data sets for the adaptation and validation of both models are taken from the authors' own experiments. In these tests, both the load paths and the phase shift are varied. The biaxial test apparatus allows for an application of fixed principal stress or strain directions even under non‐proportional loading. A fairly good agreement with our multiaxial lifetime results is obtained with both models. For an advanced assessment of the quality of the approaches used, the models are compared with several other well‐known models from the literature. An additive yardstick is used for the comparison of the different models.     

The effect of thermal loading on the yield surface of aluminium. An experimental investigation

Summary Paper presents the results of an experimental investigation dealing with the effects on the motion and deformation of the room temperature yield curve and on the plastic strain resulting from a substantial penetration of the yield surface by: (1) loading paths with constant stress combined with variable temperature and (2) isothermal loading paths. The results are interpreted with the help of the concept of the equilibrium stress-strain curves which is expanded to include both increasing and decreasing stress as well as changing temperature.With 17 FiguresThis research was supported by the National Science Foundation.     

Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading

The present paper is concerned with multi-axial ductile fracture experiments on sheet metals. Different stress-states are achieved within a flat specimen by applying different combinations of normal and transverse loads to the specimen boundaries. The specimen geometry is optimized such that fracture initiates remote from the free specimen boundaries. Fracture experiments are carried out on TRIP780 steel for four different loading conditions, varying from pure shear to transverse plane strain tension. Hybrid experimental–numerical analyses are performed to determine the stress and strain fields within the specimen gage section. The results show that strain localization cannot be avoided prior to the onset of fracture. Through-thickness necking prevails under tension-dominated loading while the deformation localizes along a band crossing the entire gage section under shear-dominated loading. Both experimental and simulation results demonstrate that the proposed fracture testing method is very sensitive to imperfections in the specimen machining. The loading paths to fracture are determined in terms of stress triaxiality, Lode angle parameter and equivalent plastic strain. The experimental data indicates that the relationship between the stress triaxiality and the equivalent plastic strain at the onset of ductile fracture is not unique.     

Modeling the impact behavior of AD85 ceramic under multiaxial loading

This paper presents an advanced constitutive model to describe the complex behavior of ceramic materials under impact loading conditions. The governing equations utilize a set of microphysically based constitutive relationships to model deformation and damage processes in a ceramic. The total strain is decomposed into elastic, plastic and microcracking components. The model parameters for AD85 ceramic were determined using the data from split Hopkinson bar and bar-on-bar experiments under uniaxial stress state and plate impact experiment under uniaxial strain state. To further validate the generality of the model parameters, modeling of a diagnostic ballistic experiment in which a steel projectile impacted a AD85 ceramic-front-faced thick aluminium plate, was considered. In this experiment, stress histories were measured in the target by embedded manganin and carbon stress gauges. The results from the numerical simulations of the ballistic experiment using a shock-wave propagation based finite element code, successfully matched the measured stress history.     

Version of the endochronic theory of plasticity for describing complicated cyclic loading histories

Equations of state for the endochronic theory of plasticity are suggested for describing processes of nonproportional cyclic deformation of materials. New rules are introduced for characteristics of isotropic and kinematic strengthening with regard to the nonproportionality parameter of the plastic deformation cycle path. Basic experiments are considered with the aim of specifying characteristic relationships. As applied to different complex plastic deformation paths, stress distribution is determined in single-crystal tubular specimens with the combined action of an axial force and torsional moment in relation to the number of loading cycles. Calculated and experimental data are compared.Translated from Probiemy Prochnosti, No. 5, pp. 3–12, May, 1993.     

高强轨道钢双轴压-扭棘轮行为的实验和模拟

在室温下对高强轨道钢进行了单轴和非比例双轴压-扭循环变形行为的实验,讨论了不同加载路径对轨道钢棘轮变形行为的影响。结果显示:该轨道钢呈现出明显的循环软化效应和压缩方向的棘轮行为,且棘轮行为的演化表现出强烈的加载路径相关性;在椭圆路径下,棘轮应变较其他四种路径更小。进而建立了基于Abdel Karim-Ohno非线性随动硬化律的非比例多轴循环棘轮本构模型,并通过在随动硬化和各向同性软化律中引入非比例因子来考虑非比例路径对双轴压-扭棘轮行为的影响。实验结果和模拟结果的对比表明:该本构模型能够较好地模拟高强度轨道钢的非比例双轴压-扭棘轮行为。     

Method for the experimental investigation of laws governing the deformation of materials under nonisothermal complex loading

A method for the testing of thin-wall tubular specimens formed from metallic materials under an axial force, torsional moment, and temperature effects on an TsDMU-30t testing machine equipped with systems for the measurement and recording of loads and strains, and a heating unit, as well as programmed units for automatic loading and heating in the 273–1273 K range is described.The results of two programs for the complex loading of specimens formed from heat-resistant alloy ÉI437 along paths with intermediate unloading at 973 K, which confirm the correctness of the postulate of isotropy for this class of loading processes, are presented, and the applicability of this method to study of laws governing the deformation of materials under complex loading at high temperatures is demonstrated.Mechanics Institute, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. 11, pp. 57–61, November, 1989.     

钛合金管件高压气胀成形工艺研究进展

高压气胀成形是在内高压成形基础上发展起来的管件成形技术,采用气体介质加载,可在高温下成形钛合金构件。以Ti-3Al-2.5V钛合金管材为实验材料,开展了矩形截面构件和大截面差构件高压气胀成形工艺研究,提出了气压阶梯加载方法和气压与轴向位移匹配的加载方法。结果表明,利用Ti-3Al-2.5V钛合金在一定温度和应变速率范围的应变和应变速率双硬化机制,采用合理的加载路径,能够消除开裂缺陷,以较高的效率实现钛合金异形管件的成形制造,并且构件壁厚相对均匀,形状和组织性能均可得到有效控制。     

Comparative study on biaxial low-cycle fatigue behaviour of three structural steels

In this study the uniaxial/biaxial low‐cycle fatigue behaviour of three structural steels (Ck45 normalized steel, 42CrMo4 quenched and tempered steel and AISI 303 stainless steel) are studied, evaluated and compared. Two parameters are considered for estimating non‐proportional fatigue lives: the coefficient of additional hardening and the factor of non‐proportionality. A series of tests of uniaxial/biaxial low‐cycle fatigue composed of tension/compression with cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Several loading paths were carried out, including proportional and non‐proportional ones, in order to verify the additional hardening caused by different loading paths. The experiments showed that the three materials studied have very different additional hardening behaviour. Generally, the transient process from the initial loading cycle to stabilized loading cycle occurs in a few cycles. The stabilized cyclic stress/strain parameters are controlling parameters for fatigue damage. A factor of non‐proportionality of the loading paths is evaluated based on the Minimum Circumscribed Ellipse approach. It is shown that the microstructure has a great influence on the additional hardening and the hardening effect is dependent on the loading path and also the intensity of the loading.     

Validating generality of recently developed critical plane model for fatigue life assessments using multiaxial test database on seventeen different materials

The present studies are aimed at validation of a newly developed critical plane model with respect to large variety of engineering materials used for different applications. This newly developed model has been recently reported by present authors. To strengthen general applicability of this model, multiaxial test database consisting of a wide variety of multiaxial loading paths have been considered. The strain paths include pure axial, pure torsion, in‐phase axial‐torsion, out‐of‐phase axial‐torsion with phase shift angles varying from 30° to 180° having sine/trapezoidal/triangular strain waveforms, with/without mean axial/shear strains and asynchronous axial‐torsion strain paths of different frequency ratios etc. The materials covered in present study are mainly categorized as ferrous and nonferrous alloys. In ferrous alloy category, material grades from plain carbon steel (mild steel, 16MnR, SA333 Gr. 6, E235 and E355), low‐alloy steel (1Cr‐Mo‐V and S460 N) and austenitic stainless steel (SS304, SS316L and SS347) have been considered. In nonferrous alloy category, aluminium alloys (2024T3‐Al, 7075T651‐Al, and PA38‐T6‐Al), titanium (pure titanium and TC4 alloy), cobalt base super‐alloy (Haynes 188), and nickel alloy (Inconel‐718) have been considered. The predicted and test fatigue lives are found in good agreement for all these materials and complex multiaxial loading paths.     

Zur thermischen Ermüdung der Magnesium‐Basislegierung AZ91

Thermal fatigue of magnesium‐base alloy AZ91 Thermal fatigue tests of the magnesium‐base alloy AZ91 were carried out under total strain control and out‐of‐phase‐loading conditions in a temperature range between ‐50°C and +190°C. Specimens produced by a vacuum die casting process were loaded under constant total strain and uniaxial homogeneous stress. To simulate the influence of different mean stresses, experiments were started at different temperature levels, e.g. the lower, mean or upper temperature of the thermal cycle. The thermal fatigue behavior is described by the resulting stress amplitudes, plastic strain amplitudes and mean stresses as a function of the number of thermal loading cycles. Depending on the maximum temperature and the number of loading cycles, cyclic softening as well as cyclic hardening behavior is observed. Due to the complex interaction of deformation, recovery and recrystallization processes and as a consequence of the individual temperature and deformation history, thermal fatigue processes of the material investigated cannot be assessed using results of isothermal experiments alone. The upper temperatures or the resp. temperature amplitudes determine the total fatigue lifetime.     

不同应力路径下堆石料的动力变形特性试验研究

采用大型多功能静动三轴试验机,对堆石料分别进行了常规三轴循环加载、等p循环加载和等q循环加载三种不同应力路径下的动力变形试验研究,探讨了不同应力路径下围压﹑固结应力比及动应力比等因素对体应变和偏应变的影响规律及其变形机制。试验结果表明:在循环荷载作用下,不同应力路径对堆石料体应变和偏应变的发展规律影响较大;在等p循环加载作用下引起的往返体应变为负值,即发生剪胀现象,且在轴向剪切时达到最大剪胀值,反向剪切时基本不发生剪胀;在等q循环加载作用下产生较大的残余体应变和残余偏应变,两者均不可忽略不计,主要与堆石料的各向异性和颗粒破碎有关。     

堆石料真三轴条件下力学特性试验研究进展

该文综述了国内外岩土真三轴仪的发展、堆石料力学特性及机理相关的研究现状。重点介绍了该研究团队开发的大型岩土静动真三轴试验机及在堆石料力学特性试验研究方面取得的初步成果。按加载方式,土的真三轴仪可以分为3类:刚性加载真三轴仪、柔性加载真三轴仪和混合型加载真三轴仪。堆石料真三轴试验具有试样尺寸大、承压高、各方向相互干扰强、试样变形后荷载对中难、加压板与试样间摩擦效应强、试样安装和量测复杂等诸多困难。因而,目前适用于堆石料的真三轴仪和试验成果均较少。考虑堆石料真三轴及复杂应力路径条件下的颗粒破碎、各向异性等,研究其力学特性并开发相应的本构模型是该课题发展的趋势。清华大学大型岩土静动真三轴试验机中联合采用了椭圆形试样帽和异形乳胶膜的封样方式,可很好地解决真三轴试样的高压密封、拆装、量测和耐久性等一系列难题。对堆石料进行了一系列真三轴复杂应力路径试验,结果表明真三轴试验中堆石料表现出更明显的应力诱导各向异性和应力状态依赖性,特别是对小主应力-应变关系、球应力-体应变关系和广义剪应力-剪应变关系的影响更显著。球应力和广义剪应力对体积应变和广义剪应变之间存在着明显的交叉影响。     

LOW-CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

A series of strain-controlled, low-cycle fatigue experiments have been conducted on 42CrMo steel under various loading paths including circular, square, cruciform, and rectangular paths. Present experiments have shown that there is additional hardening under non-proportional cyclic loading. Non-proportional cyclic additional hardening also results in a shorter life for multiaxial low cycle fatigue. A non-proportionality measure of strain path based on both a physical basis and macromechanical phenomena is proposed. The loading path effect on additional hardening is also described well. Low-cycle fatigue damage accumulation and the evolution process under non-proportional loading is analysed via the Continuum Damage Mechanics Model of Chaboche. A non-proportinality measure is introduced in the damage evolution equation and a modified Coffin-Manson type formula is derived. A novel fatigue life prediction approach based on the critical-plane concept of Brown and Miller is proposed.     

Response of boron carbide subjected to high-velocity impact

This article presents an evaluation of the response of boron carbide (B₄C) subjected to impact loading under three different conditions. Condition A is produced by plate-impact experiments where the loading condition is uniaxial strain and the stresses and pressures are high. Under plate-impact loading the material fails at the Hugoniot Elastic Limit (HEL) and the failed material undergoes high confining pressures and relatively small inelastic strains. Condition B is produced by projectile impact onto thick targets where the stresses and pressures are dependent on impact velocity, but they are generally lower than those from plate impact. Under thick-target impact/penetration most of the material fails under compression, the inelastic strains are large and the material appears to exhibit more ductility than under condition A. Lastly, condition C is produced by projectile impact and perforation of thin targets where the stresses and pressures are a combination of compression and tension. Under thin-target perforation the material fails in both tension and compression. The Johnson–Holmquist–Beissel (JHB) constitutive model is used to evaluate the material behavior for each of the three conditions, but it is not possible to accurately reproduce the experimental results of the three conditions with a single set of constants. Instead, three different sets of constants are required to accurately model the three impact conditions. These three models/constants are used to provide insight into the complex response of B₄C, and to identify possible mechanisms that are not included in the JHB model.