Strain-rate effects during reverse torsional shear

When a material is rate sensitive during loading, it may also be expected to be rate sensitive during unloading and reverse loading. To investigate this matter, a series of experiments was performed on a moderately ratesensitive magnesium alloy. A modified torsional split-Hopkinson-bar system was used in which a high shear-strain rate can be suddenly imposed on a short specimen while it is being plastically twisted in the opposite sense at a much lower rate. The torsional pulse has a short rise time and a large amplitude, and is of approximately 1 ms useful duration. This allows the specimen to be unloaded and plastically loaded to fracture in the opposite sense within a few microseconds. Forward loading was kept throughout at a shear-strain rate of about 0.006 s^?1, while the reverse straining occurred at 0.006, 250 and 1100 s^?1. Strain-rate dependence of the reverse loading at various plastic prestrain values ranging from 0.0 to 0.3 is presented and discussed as a macroscopic phenomenon in the context of various ‘Bauschinger-effect’ stress parameters.     

Strain-rate and strain-rate-history effects in several metals in torsion

A machine for testing thin-walled tubes in torsion at shear-strain rates up to 25/sec is described. Results of constant and variable-strain-rate tests are presented for 1100-0 aluminum, AISI 1020 steel, and 50-A titanium. Results indicate that 1100-0 aluminum is very slightly strain-rate sensitive, but steel and titanium are noticeably sensitive to both strain rate and strain-rate history. Variable-rate tests show that subsequent dynamic loading on a statically prestrained specimen causes an increase in the flow stress in steel and a decrease in the flow stress in titanium.     

脆性材料动态强度应变率效应

通过求解波动方程,结合有限结构-时间破坏准则,得到了动态载荷下脆性材料单轴拉伸强度应变 率效应的解析表达式。分析结果表明:材料动态强度的应变率效应具有明显的结构响应特征,即材料动态强 度除与应变率和静态参数相关外,还显著地依赖于外载荷结构及其与材料间的相互作用,因而动态强度不是 表征材料动态破坏的内禀材料性质;此外,由于在不同的外载荷条件下材料将表现出不同的动态强度,这是导 致实验结果离散性大的内在因素。     

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10^?3 and 10³ s^?1 for ?150, ?100, ?50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump. The low strain-rate results show a well-defined elastic limit but no yield drop, a small yield plateau is found at room temperature. The subsequent strain hardening shows a maximum at 200°C, when serrated flow occurs and the ductility is reduced. The high strain-rate results show a considerable drop of stress at yield. The post-yield flow stress decreases steadily with increasing temperature, throughout the temperature range investigated. At room temperature and below, the strain-hardening rate becomes negative at large strains. The adiabatic temperature rise in the dynamic tests was computed on the assumption that the plastic work is entirely converted to heat. This enabled the isothermal dynamic stress-strain curves to be calculated, and showed that considerable thermal softening took place. The initial response to a strain-rate jump is approximately elastic, and has a magnitude which increases with decrease of testing temperature; it is little affected by the amount of prestrain. At 200 and 400° C, a yield drop occurs after the initial stress increment. The post-jump flow stress is always greater than that for the same strain in a constant-rate dynamic test, the strain-hardening rate becoming negative at large strains or low testing temperature. This observed effect of strain-rate history cannot be explained by the thermal softening accompanying dynamic deformation. These and other results concerning total ductility under various strain-rate and temperature conditions show that strain-rate history strongly affects the mechanical behavior of the mild steel tested and, hence, should be taken into account in the formulation of constitutive equations for that material.     

Analyticity and causality of the three-parameter rheological models

In this paper, the basic frequency and time response functions of the three-parameter Poynting–Thomson solid and Jeffreys fluid are revisited. The two rheological models find application in several areas of rheology, structural mechanics, and geophysics. The relation between the analyticity of a frequency response function and the causality of the corresponding time response function is established by identifying all singularities at ω = 0 after applying a partial fraction expansion to the frequency response functions. The strong singularity at ω = 0 in the imaginary part of a frequency response function in association with the causality requirement imposes the addition of a Dirac delta function in the real part in order to make the frequency response function well defined in the complex plane. This external intervention, which was first discovered by PAM Dirac, has not received the attention it deserves in the literature of viscoelasticity and rheology. The addition of the Dirac delta function makes possible the application of time domain techniques that do not suffer from violating the premise of causality.     

45钢柱壳膨胀断裂的应变率效应

采用前照明高速分幅照相技术拍摄到在爆轰加载下45钢柱壳表面裂纹生成、扩展及产物泄漏过程的清晰图像,较准确地测量了膨胀断裂的时间与应变。 45钢柱壳在炸药爆轰加载下,断裂应变随应变率的增加而增加,当应变率达到一定值,断裂应变随应变率的增加而降低,出现了动态断裂中的塑性峰现象。     

Study of plastic/viscoplastic models with various inelastic mechanisms

This paper describes a general framework for the development of plastic or viscoplastic constitutive equations. As the applications are focused on cyclic loadings, only small strains are considered, with an additive decomposition of the total strain into a thermo-elastic part, and several inelastic parts, the evolution of which is determined by several plastic or viscoplastic criteria. Quadratic or linear (crystallographic) criteria could be used, so that the approach is able to describe the contribution of several physical levels, or deformation mechanism, to the inelastic behavior. The present work is restricted to the case of quadratic criteria, and specially to the study of the various interactions which can be introduced between the mechanisms. The most important case is the coupling between kinematic hardening variables which allows to describe: (1) either normal rate sensitivity or inverse rate sensitivity; (2) plasticity-creep interaction; (3) ratcheting for high mean stress but either adaptation or plastic shakedown for lower mean stress.     

Strain-rate history effects and microstructural aspects in lithium fluoride and aluminium single crystals after dynamic loading

Single crystals of LiF and Al are deformed in shear at a number of constant strain-rates in the range 10^–4 to 1600 s^–1. These constant rate tests are supplemented by a series of jump tests in which a sharp increment in strain rate is imposed during the quasi-static straining. Dislocation arrangements are observed by etch-pits technique for LiF crystals and by TEM for Al crystals. It is shown that cell sizes vary inversely with flow stress and strain-rate sensitivity.     

Acoustical validation of the rheological models for a structural bond

The purpose of this study is to characterize by ultrasound a bonded structure metal/adhesive/metal. At first, we investigate the guided modes of the structure for the adhesive layer in its entirety; this is the exact model. Secondly, we assume that the adhesive layer is described by one geometrical interface, with a superficial distribution of longitudinal and transversal springs with or without mass; this is the rheological model. A comparison of the guided modes for the two models allows to determinate the validity limits for the rheological modelling and define the equivalent stiffness coefficients and the mass as a function of the frequency. Some cutoff-frequencies are better evaluated when the springs mass is taken into account.     

An appraisal of rheological models as applied to polymer melt flow

Summary An attempt is made at giving an appraisal of some representative rheological models of both differential and integral type, using the standard rheological measurements of six polymer melts. Experimental data obtained were the steady shear viscosity and the first normal stress difference by means of aWeissenberg rheogoniometer over the range of shear rates: 10^–2 ~ 10 sec^–1, and by means of aHan slit/capillary rheometer over the range of shear rates: 10 ~ 10³ sec^–1. Also measured by means of theWeissenberg rheogoniometer were the dynamic viscosity and dynamic elastic modulus over the range of frequencies: 0.3 × 10^–2 ~ 3 × 10² sec^–1. Rheological models chosen for an appraisal are theSpriggs 4-constant model, theMeister model, and theBogue model.It is found that the capability of the three models considered is about the same in their prediction of the rheological behavior of polymer melts in simple shearing flow. It is pointed out however that, due to the ensuing mathematical complexities, the usefulness of these models is limited to the study of flow problems associated with simple flow situations. Therefore, in analysing the complex flow situations often encountered with various polymer processings, the authors suggest use of the empirical models of the power-law type for both the viscosity and normal stress functions.With 11 figures, 4 schemas and 1 table     

Influence of fiber architecture on the inelastic response of metal matrix composites

This three-part paper focuses on the effect of fiber architecture (i.e. shape and distribution) on the elastic and inelastic response of unidirectionally reinforced metal matrix composites (MMCs). The first part provides an annotated survey of the literature; it is presented as an historical perspective dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix composites and MMCs. A summary of the state of teh art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of MMCs. This micromechanics model, referred to as the generalized method of cells (GMC), can predict the overall inelastic behavior of unidirectional, multiphase composites, given the properties of the constituents. The model is also general enough to predict the response of unidirectional composites that are reinforced by either continuous or discontinuous fibers, with different inclusion shapes and spatial arrangements, in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments on this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third part provides qualitative results generated by using GMC for a representative titanium matrix composite system, SCS-6/TIMETAL 21S. The results presented correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep behavior of MMCs, with both strong and weak fiber/matrix interfacial bonds. Fiber arrangements included square, square-diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes were circular, square, and cross-shaped cross-sections. The effect of fiber volume fraction on the stress-strain response is also discussed, as is the thus-far poorly documented strain rate sensitivity effect. In addition to the well-documented features of the architecture-dependent behavior of continuously reinforced two-phase MMCs, new results are presented about continuous multiphase internal architectures. Specifically, the stress-strain and creep responses of composites with different size fibers and different internal arrangements and bond strengths are investigated; the aim was to determine the feasibility of using this approach to enhance the transverse toughness and creep resistance of titanium matrix composites (TMCs).     

Study of some rheological models with a finite number of degrees of freedom

A large number of rheological models can be covered by the existence and uniqueness theory for maximal monotone operators. Numerical simulations display hysteresis cycles when the forcing is periodic. A given shape of hysteresis cycle in an appropriate class of polygonal cycles can always be realized by adjusting the physical parameters of the rheological model.     

Identification of material parameters for inelastic constitutive models: statistical analysis and design of experiments

In this paper we introduce stochastic methods to describe the influence of scattering test data on the identification of material parameters. We employ the viscoplastic constitutive model of Chan, Bodner, and Lindholm in its uniaxial form. The available test data result from three types of experiments performed at 600 °C on AINSI SS316 stainless steel, namely creep tests, constant strain rate tension tests with intermediate relaxation, and cyclic tension–compression tests. Each test has been performed with 12 specimens at different strain rates and stress rates respectively. However, for a serious statistical evaluation a larger number of experiments is required. In order to increase the number of tests we introduce stochastic simulations based on time series analysis which generate artificial data with the same stochastic behaviour as the experimental data. The method of stochastic simulation presents a widely accepted technique in engineering which does not add complexity to the process of parameter identification, but allows an investigation of the confidence in the fits of the material parameters. To keep the computation time for the identification of the material parameters as low as possible, very efficient numerical methods have to be implemented. The methods applied here for integration and nonlinear optimization are briefly introduced. The optimization strategy contains stochastic elements. Furthermore, we apply the method of statistical design of experiments to derive which combination of tests yields the most important information for an effective identification of material parameters.     

Identification of material parameters for inelastic constitutive models: Stochastic simulations for the analysis of deviations

For parameter identification a distance function between the measured and the simulated data has to be minimized. Therefore, the influence of three different norms used in the definition of such a distance function is investigated. The nonlinear optimization problem is solved using a modified random search algorithm originally proposed by Price (1978). Next a stochastic model for the generation of artificial test data is presented. This model is used for a stochastic simulation of test data (constant strain rate tension with relaxation and creep). From these artificial data the material parameters of the model of Chan, Bodner and Lindholm are identified. To measure the quality of the identified material parameters their mean values and empirical standard deviations are computed. Furthermore, the coefficients of the empirical correlation matrix for the material parameters are computed. The model responses for tensile tests with the parameter vector generated from all tests and with the estimated parameters (from stochastic simulations) differ not considerably. However, for the creep tests the different parameter estimations lead to quite different model responses. Received October 22, 1999