Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

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.     

Standard Uncertainty Evaluation for Dynamic Tensile Properties of Auto-Body Steel-Sheets

This paper is concerned with the standard uncertainty of the true stress–true strain curve as the tensile properties of auto-body steel sheets at intermediate strain rates ranged from 1 to 100 s^?1. A procedure to obtain true stress–true strain data is properly designed for the experiment and data acquisition. An analytic model is then established to evaluate the standard uncertainty of the measurand. The measurand in this case is the true stress which is a function of the input quantities: the tensile load; the initial length, the thickness and the width of a specimen; and the deformed length of a specimen. Sources of uncertainties of the input quantities are evaluated for the high speed tensile test with their associated sensitivity coefficients. Uncertainty of the stress data acquired is also considered in the procedure of the fast Fourier transform (FFT) smoothing process used to remove unnecessary signals acquired from experiments. Image analysis using a high speed camera is carried out to measure deformation of the specimen during high speed tensile tests with proper uncertainty evaluation. A combined standard uncertainty is evaluated from the uncertainties of the input quantities as well as the influence factor for the true stress of auto-body steel sheets at intermediate strain rates. Consequently, the true stress–true strain data are obtained with proper standard uncertainty evaluation.     

Obtaining a Wide-Strain-Range True Stress–Strain Curve Using the Measurement-In-Neck-Section Method

Background

Measuring true stress–strain curve over a large-strain-range is essential to understand mechanical behavior and simulate non-linear plastic deformation. The digital image correlation (DIC) technique, a non-contact full-field optical measurement technique, is a promising candidate to obtain a long-range true stress–strain curve experimentally.

Objective

This paper proposes a method for measuring true stress–strain curves over a large-strain-range during tensile testing using DIC.

Methods

The wide-strain-range true stress–strain curves of dual-phase and low carbon steels were extracted on the transverse direction in the neck region. The axial strain on the neck section was estimated by averaging the inhomogeneous deformation on the cross-section of the tensile specimen. The true stress was calculated from the engineering stress and the cross-sectional area of the neck.

Results

The validity of the proposed method was assessed by comparing the experimental load–displacement responses during tensile testing with the finite element method (FEM) simulation results. The stress and strain on the neck section estimated using the FEM and DIC, respectively, were proven to satisfy the uniaxial condition and successfully obtained.

Conclusions

The experimental results agree well with the FEM results. The proposed concept can be applied to various deformation modes for accurately measuring long-range true stress–strain curves.

     

A Study of Large Plastic Deformations in Dual Phase Steel Using Digital Image Correlation and FE Analysis

Large plastic deformation in sheets made of dual phase steel DP800 is studied experimentally and numerically. Shear testing is applied to obtain large plastic strains in sheet metals without strain localisation. In the experiments, full-field displacement measurements are carried out by means of digital image correlation, and based on these measurements the strain field of the deformed specimen is calculated. In the numerical analyses, an elastoplastic constitutive model with isotropic hardening and the Cockcroft–Latham fracture criterion is adopted to predict the observed behaviour. The strain hardening parameters are obtained from a standard uniaxial tensile test for small and moderate strains, while the shear test is used to determine the strain hardening for large strains and to calibrate the fracture criterion. Finite Element (FE) calculations with shell and brick elements are performed using the non-linear FE code LS–DYNA. The local strains in the shear zone and the nominal shear stress-elongation characteristics obtained by experiments and FE simulations are compared, and, in general, good agreement is obtained. It is demonstrated how the strain hardening at large strains and the Cockcroft–Latham fracture criterion can be calibrated from the in-plane shear test with the aid of non-linear FE analyses. An erratum to this article can be found at     

Quasi-Static and Dynamic Large Strain Shear-Tension Testing

A new shear specimen is designed, evaluated and tested quasi-statically and dynamically. The specimen consists of a long cylinder having a horizontal gauge section created by two diametrically opposed semi-circular slots machined parallel to the longitudinal axis. This geometry imposes a rather uniform stress state, close to pure shear in the gauge section. Quasi-static and dynamic tension-shear tests up to a strain rate of 10⁴ 1/s were carried out on 1020 cold-drawn steel specimens. The obtained stress–strain curves and ductility were validated numerically. The new specimen can be used to study the shear mechanical characteristics of a material using tensile testing.     

An Experimental Method to Determine the Tensile Strength of Concrete at High Rates of Strain

In the present work, dynamic tensile strength of concrete is experimentally investigated by means of spalling tests. Based on extensive numerical simulations, the paper presents several advances to improve the processing of spalling tests. The striker is designed to get a more uniform tensile stress field in the specimen. Three methods proposed in the literature to deduce the dynamic strength of the specimen are discussed as well as the use of strain gauges and a laser extensometer. The experimental method is applied to process data of several tests performed on wet micro-concrete at strain rates varying from 30 to 150/s. A significant increase of the dynamic tensile strength with strain-rate is observed and compared with data of the literature. In addition, post-mortem studies of specimens are carried to improve the analysis of damage during spalling tests.     

Techniques for measuring stress-strain relations at high strain rates

The qualitative dependence of the mechanical behavior of some materials on strain rate is now well known. But the quantitative relation between stress, strain and strain rate has been established for only a few materials and for only a limited range. This relation, the so-called constitutive equation, must be known before plasticity or plastic-wave-propagation theory can be used to predict the stress or strain distribution in parts subjected to impact stresses above the yield strength. In this paper, a brief review of some of the experimental techniques for measuring the stress, strain, strain-rate relationship is given, and some of the difficulties and shortcomings pointed out. Ordinary creep or tensile tests can be used at plastic-strain rates from 10^?8 to about 10^?1/sec. Special quasi-static tests, in which the stress- and strain-measuring devices as well as the specimen geometry and support have been optimized, are capable of giving accurate results to strain rates of about 10²/sec. At higher strain rates, it is shown that wave-propagation effects must be included in the design and analysis of the experiments. Special testing machines for measuring stress, strain and strain-rate relationships in compression, tension and shear at strain rates up to 10⁵/sec are described, and some of the results presented. With this type of testing machine, the analysis of the data requires certain assumptions whose validity depends upon proper design of the equipment. A critical evaluation of the accuracy of these types of tests is presented.     

Effects of strain rate and moisture content on the behaviour of sand under one-dimensional compression

The influence of strain rate and moisture content on the behaviour of a quartz sand was assessed using high-pressure quasi-static (10^?3 s^?1) and high-strain rate (10³ s^?1) experiments under uniaxial strain. Quasi-static compression to axial stresses of 800 MPa was carried out alongside split Hopkinson pressure bar (SHPB) experiments to 400 MPa, where in each case lateral deformation of the specimen was prevented using a steel test box or ring, and lateral stresses were recorded. A significant increase in constrained modulus was observed between strain rates of 10^?3s^?1 and 10³s^?1, however a consistently lower Poisson’s ratio in the dynamic tests minimised changes in bulk modulus. The reduction in Poissons ratio suggests that the stiffening of the sand in the SHPB tests is due to additional inertial confinement rather than an inherent strain-rate dependence. In the quasi-static tests the specimens behaved less stiffly with increasing moisture content, while in the dynamic tests the addition of water had little effect on the overall stiffness, causing the quasi-static and dynamic series to diverge with increasing moisture content.     

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.     

Dynamic Tensile Characterization of a 4330-V Steel with Kolsky Bar Techniques

Dynamic tensile experimental techniques of high-strength alloys using a Kolsky tension bar implemented with pulse shaping and advanced analytical and diagnostic techniques have been developed. The issues that include minimizing abnormal stress peak, determining strain in specimen gage section, evaluating uniform deformation, as well as developing pulse shaping for constant strain rate and stress equilibrium have been addressed in this study to ensure valid experimental conditions and obtainment of reliable high-rate tensile stress–strain response of alloys with a Kolsky tension bar. The techniques were applied to characterize the tensile stress–strain response of a 4330-V steel at two high strain rates. Comparing these high-rate results with quasi-static data, the strain rate effect on the tensile stress–strain response of the 4330-V steel was determined. The 4330-V steel exhibits slight work-hardening behavior in tension and the tensile flow stress is significantly sensitive to strain rate.     

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.     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes

The elastic-plastic behaviour of dual-phase, high-strength steel sheets under two-stage strain-path changes has been investigated. Three different loading sequences, namely monotonic, 45° tensile path changes and orthogonal tensile path changes complied by sequences of simple uniaxial tensile tests, were analysed at room temperature. From the experiments, it was found that there is a considerable reduction of the initial flow stress over the strain-path changes. The transient softening phenomenon is observed to be a function of orientation, and the period of the transient behaviour following the strain-path change is lengthened with the amount of pre-strain. A constitutive model is adopted that includes combined isotropic and kinematic hardening and is capable of describing the marked transient softening behaviour after the pre-straining. The experimental stress–strain behaviour subsequent to the strain path change is predicted with reasonable accuracy, while the model fails to accurately describe the transient, deformation-induced anisotropy in the plastic flow.     

Stress–strain behaviour of aluminium alloys at a wide range of strain rates

The stress–strain behaviour of extruded AA6xxx and AA7xxx aluminium alloys in T6 temper was studied at a wide range of strain rates. Tensile tests at low to medium strain rates were performed in a standard tensile test machine, while a split-Hopkinson tension bar was used to carry out tests at high rates of strain. Extruded aluminium alloys have anisotropic mechanical properties, and tests were therefore done in three directions with respect to the extrusion direction. It is found that the AA6xxx alloys exhibit no significant rate sensitivity in the stress–strain behaviour, while moderate rate sensitivity was found for the AA7xxx alloys. There seems to be no significant difference between the rate sensitivity in the three tensile directions. The experimental data were used to identify the parameters of a thermo-viscoplastic constitutive relation for the extruded alloys, which includes the effects of strain hardening, strain-rate hardening, thermal softening and plastic anisotropy.     

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.     

一种改进的金属材料的高温动态拉伸实验技术

在旋转盘冲击拉伸实验装置上,利用金属材料自身的导电特性,对试样施加电流.使其在电流作用下发热,实现自加热,形成了试件快速加热而波导杆温升很小的金属材料的动态高温高应变率拉伸实验技术.应用该实验技术获取了45 #钢从室温到1000℃温度范围和应变率650s-1时的材料动态拉伸应力—应变曲线.实验结果表明,45 #钢具有明显的热软化效应,其流动应力和屈服应力随温度的升高而降低.     

Influence of Specimen Geometry on Split Hopkinson Tensile Bar Tests on Sheet Materials

In recent years numerous studies on the high strain rate behaviour of sheet materials using split Hopkinson tensile bar set-ups have been reported in literature. For these experiments mostly dogbone-shaped specimens are used. However, widely divergent specimen dimensions can be found. In the present study the influence of this specimen geometry on the test results is investigated experimentally. An extensive series of Hopkinson tests on a steel sheet material using different specimen geometries is performed. An advanced optical technique is used to obtain the true distribution of the deformation along the length of the specimen. Important issues such as the contribution of the deformation of the transition zones to the total deformation and the (non-)homogeneity of the strain in the specimen are thus determined. From the experiments it is clear that the influence of the specimen geometry on the observed behaviour cannot be neglected. It is shown that inconsistencies between the assumed and real specimen behaviour account for these differences. For the TRIP steel considered in the study, accurate deformation values are only guaranteed if the length to width ratio of the central zone is larger than 1.25 and if the radius of the transition zone is sufficiently small.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

A New Experimental Technique for the Multi-axial Testing of Advanced High Strength Steel Sheets

This paper deals with the development of a new experimental technique for the multi-axial testing of flat sheets and its application to advanced high strength steels. In close analogy with the traditional tension-torsion test for bulk materials, the sheet material is subject to combined tension and shear loading. Using a custom-made dual actuator hydraulic testing machine, combinations of normal and tangential loading are applied to the boundaries of a flat sheet metal specimen. The specimen shape is optimized to provide uniform stress and strain fields within its gage section. Finite element simulations are carried out to verify the approximate formulas for the shear and normal stress components at the specimen center. The corresponding strain fields are determined from digital image correlation. Two test series are performed on a TRIP-assisted steel sheet. The experimental results demonstrate that this new experimental technique can be used to investigate the large deformation behavior of advanced high strength steel sheets. The evolution of the yield surface of the TRIP700 steel is determined for both radial and non-proportional loading paths.