Experimental analysis and constitutive modeling for the newly developed 2139-T8 alloy

Mechanical behavior of recently emerged 2139-T8 aluminum alloy, which is based on an Al–Cu–Mg–Ag system, has been characterized by uniaxial compression and tension experiments over a wide range of strain rates from 10⁻⁴ to 10⁴ s⁻¹ and for temperatures from −60 to 300 °C. Driven by experimental results, modifications to widely used Johnson–Cook constitutive model has been proposed, and model parameters have been determined. It has been shown that modified Johnson–Cook (MJC) model satisfactorily captures rate- and temperature-dependent variations in flow stress through enhanced coupling between temperature and strain hardening as well as temperature and strain-rate sensitivity. The modified model also provides flow stress prediction over the entire range of quasi-static and dynamic regimes by a single continuous function.     

Mechanical properties of Epon 826/DEA epoxy

Polymers are becoming increasingly used in aerospace structural applications, where they experience complex, non-static loads. Correspondingly, the mechanical properties at high strain rates are of increasing importance in these applications. This paper investigates the compressive properties of Epon 826 epoxy resin cured with diethynolamine (DEA) across strain rates from 10⁻³ to 10⁴ s⁻¹. Specimens were tested using an Instron mechanical testing machine for static loading, traditional split Hopkinson pressure bars (SHPBs) for high strain rates, and a miniaturized SHPB for ultra-high strain rates. Additionally, the material was tested using dynamic mechanical analysis to determine the effects of time and temperature equivalences on the strain rate behavior of the samples. The experimental data is used to fit the Mulliken-Boyce model, modified for one-dimension, which is able to capture the compressive mechanical properties over a range of strain rates.     

Constitutive analysis to predict high-temperature flow stress in modified 9Cr–1Mo (P91) steel

Constitutive analysis for hot working of modified 9Cr–1Mo (P91) ferritic steel was carried out employing experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1373 K), strains (0.1–0.5) and strain rates (10⁻³–10² s⁻¹). The effects of temperature and strain rate on deformation behaviour were represented by Zener–Hollomon parameter in an exponent-type equation. The influence of strain was incorporated in the constitutive equation by considering the effect of strain on different material constants. Activation energy was found to vary with strain in the range 369–391 kJ mol⁻¹. The developed constitutive equation (considering the compensation of strain) could predict flow stress of modified 9Cr–1Mo steel over the specified hot working domain with very good correlation and generalization.     

Mechanical behavior of glass/epoxy tubes under combined static loading. Part II: Validation of FEA progressive damage model

Experimental results from a series of biaxial static tests of E-Glass/Epoxy tubular specimens [±45]₂, were compared successfully with numerical predictions from thick shell FE calculations. Stress analysis was performed in a progressive damage sense consisting of layer piece-wise linear elastic behavior, simulating lamina anisotropic non-linear constitutive equations, failure mode-dependent criteria and property degradation strategies. The effect of accurate modeling of non-linear shear stress–strain response, dependent on the plane stress field developed, was proved of great importance for the numerical FEA predictions, concerning macroscopic stress–strain response. Ultimate load prediction was influenced more decisively when degradation strategies for the compressive strength along the fiber direction were considered.     

Constitutive equations to predict high temperature flow stress in a Ti-modified austenitic stainless steel

The experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1523 K) and strain rates (10⁻³–10² s⁻¹), were employed to develop constitutive equations in a Ti-modified austenitic stainless steel. The effects of temperature and strain rate on deformation behaviors were represented by Zener-Holloman parameter in an exponent type equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of strain on material constants. The constitutive equation (considering the compensation of strain) could precisely predict the flow stress only at 0.1 and 1 s⁻¹ strain rates. A modified constitutive equation (incorporating both the strain and strain rate compensation), on the other hand, could predict the flow stress throughout the entire temperatures and strain rates range except at 1123 K in 10 and 100 s⁻¹. The breakdown of the constitutive equation at these processing conditions is possibly due to adiabatic temperature rise during high strain rate deformation.     

Application of neural networks to predict the elevated temperature flow behavior of a low alloy steel

In order to study the workability and establish the optimum hot forming processing parameters for 42CrMo steel, the compressive deformation behavior of 42CrMo steel was investigated at the temperatures from 850 °C to 1150 °C and strain rates from 0.01 s⁻¹ to 50 s⁻¹ on Gleeble-1500 thermo-simulation machine. Based on these experimental results, an artificial neural network (ANN) model is developed to predict the constitutive flow behaviors of 42CrMo steel during hot deformation. The inputs of the neural network are deformation temperature, log strain rate and strain whereas flow stress is the output. A three layer feed forward network with 12 neurons in a single hidden layer and back propagation (BP) learning algorithm has been employed. The effect of deformation temperature, strain rate and strain on the flow behavior of 42CrMo steel has been investigated by comparing the experimental and predicted results using the developed ANN model. A very good correlation between experimental and predicted result has been obtained, and the predicted results are consistent with what is expected from fundamental theory of hot compression deformation, which indicates that the excellent capability of the developed ANN model to predict the flow stress level, the strain hardening and flow softening stages is well evidenced.     

High temperature compressive properties over a wide range of strain rates in an AZ31 magnesium alloy

High temperature compressive properties in AZ31 magnesium alloy were examined over a wide strain rate range from 10^–3 to 10³ s^–1. It was suggested that the dominant deformation mechanism in the low strain rate range below 10^–1 s^–1 was dislocation creep controlled by pipe diffusion at low temperatures, and by lattice diffusion at high temperatures. On the other hand, analysis of the flow behavior and microstructural observations indicated that the deformation at high strain rates of 10³ s^–1 proceeds by conventional plastic flow of dislocation glide and twinning even at elevated temperatures.     

A constitutive model for fcc crystals with application to polycrystalline OFHC copper

Based on the results of a series of experiments on commercially pure OFHC copper (an fcc polycrystal), a physically based, rate- and temperature-dependent constitutive model is proposed for fcc single crystals. Using this constitutive model and the Taylor averaging method, numerical calculations are performed to simulate the experimental results for polycrystalline OFHC copper. The model calculation is based on a new efficient algorithm which has been successfully used to simulate the flow stress of polycrystalline tantalum over broad ranges of temperature, strain rate, and strain (Nemat-Nasser, S., Okinaka, T., Ni, L., 1998. J. Mech. Phys. Solids 46, 1009). The model effectively simulates a large body of experimental data, over a broad range of strain rates (0.001–8000 s⁻¹), and temperatures (77–1096 K), with strains close to 100%. Few adjustable constitutive parameters of the model are fixed at the outset for a given material. All other involved constitutive parameters are estimated based on the crystal structure and the physics of the plastic flow.     

Work hardening of mild steel within dynamic strain ageing temperatures

An investigation has been performed on the plastic behaviour of a mild steel within the region of dynamic strain ageing. For this purpose tension tests have been performed on annealed XC18 steel within a range of temperatures, from 305–776 K, and a range of strain rates, from 1.0×10^–4–1.85×10^–1s^–1. An analysis of experimental results is presented using a model for plastic deformation based on dislocation multiplications.     

Effect of sulfide ions on the stress corrosion behaviour of Al-brass and Cu10Ni alloys in salt water

The stress corrosion cracking (SCC) behavior of Al-brass and Cu10Ni alloys was investigated in 3.5% NaCl solution in absence and in presence of different concentrations of Na₂S under open-circuit potentials using the constant slow strain rate technique. The results indicated that the Cu10Ni alloy is more susceptible to stress corrosion cracking than as-received Al-brass at strain rate of 3.5 × 10^–6 s^–1 in 3.5% NaCl in presence of high concentration of sulfide ions (1000 ppm). The sulfide ions (up to 500 ppm) has no effect on the stress corrosion cracking of the annealed Al-brass in 3.5% NaCl at two strain rates of 7.4 × 10^–6 and 3.5 × 10^–6 s^–1. The results support film rupture for Al-brass and sulfide stress corrosion cracking assisted with pitting corrosion for Cu10Ni at slip steps as the operating mechanisms.     

Contact thermal resistance of machined metal surfaces in vacuo

The paper presents the results of an experimental investigation of contact thermal resistances of stainless steel and molybdenum samples for the range of compressive loads between 1.5 and 58 · 10^–5 N/m² and for an absolute pressure of the surrounding medium of 10^–4 mm Hg. An equation describing the dependence of the contact heat exchange in vacuo for small compressive loads was derived based on experimental data published in the literature.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 2, pp. 259–269, February, 1970.     

The hardness of Al-Si eutectic alloys

The Vickers hardness values of Al-Si eutectic alloys, solidified unidirectionally at rates ranging from 2.8×10^–5 to 1 cm sec^–1, have been determined. These are compared with associated tensile and compressive properties. It is shown that there is no close correlation of hardness and strength over the entire range of growth rates although similar trends are seen between hardness and compressive yield strength. It is concluded that caution should be exercised when inferring strength from hardness data.     

Strain and relaxation in Si-MBE structures studied by reciprocal space mapping using high resolution X-ray diffraction

High resolution X-ray diffraction measurements have been done on Si(001)-based structures grown by molecular beam epitaxy (MBE). By systematically varying the angle of incidence and the diffraction angle, the diffraction intensity data can be displayed in a two-dimensional X-ray diffraction intensity map that can be interpretted as a reciprocal space map of the reciprocal lattice points. The experimental technique is described and results for studies of the strain and the strain relaxation with high temperature annealing are described for the following material systems: strained Si/Si_1–xGe_x heterostructures, highly B-doped Si layers on Si and highly B-doped Si_1–xGe_x layers on Si. The strain relaxation in Si_1xGe_x layers occurs via generation of misfit dislocations creating a shift and a characteristic mosaic broadening of the layer peak in the reciprocal space maps. A summary of how the degree of relaxation, as measured from reciprocal space maps, depends on the annealing temperature and the layer thickness is given. The relaxation of the strain induced by B, for doping concentrations up to 5 × 10²⁰ cm^–3, is obtained by diffusion of B into the substrate. For a Si_0.82Ge_0.18 layer with partially compensated compressive strain due to a B concentration of 3 × 10²⁰cm^–3, the maps show a combination of strain relaxation via misfit dislocations and B diffusion into the substrate.     

A new methodology for determining the mechanical behavior of polymers exploiting Lie symmetries: application to a stick-like material

Dynamic tests at high strain rates involving a weight dropped from different heights have been carried out on acrylic stick cylindrical specimens, in order to determine their mechanical behavior. The experimental device consists of a mass M dropped from an initial height H₀, impacting the plate of a compressive apparatus lying on the upper surface of the specimen. The stress and the strain are derived from measurements of the compressive force and relative displacement of the upper plate. Regarding theoretical aspects, a novel strategy for a constitutive model, based on a combination of measurements and the use of Lie groups analysis, is proposed. The methodology consists in condensing experimental data obtained for different initial drop heights into master curves, which are further interpreted as Lie symmetries of the postulated constitutive equation for the stick sample. The constitutive model involves two functions of the strain rate, obtained from the Lie symmetry condition; this condition expresses the postulated invariance of the material behavior when the impact conditions vary. The material parameters are obtained from the adjustment of the constitutive model with experimental data. The model is found to be similar to the one used in [Naik, N.K., Perla, Y., 2008. Mechanical behavior of acrylic under high strain rate tensile loading. Polymer Testing 27, 504–512] for acrylic. Predictions of the model at constant strain rates show a viscoelastic behavior typical of such polymers.     

Mechanical properties of amorphous alloy compacts prepared by different consolidation techniques

Amorphous alloy compacts of Fe₇₈B₁₃Si₉ prepared by three different techniques (explosive consolidation, high hydrostatic pressure consolidation and warm extrusion) were deformed in compression between 573 and 723 K at a strain rate ranging from 8.3×10^–5–4.2×10^–4s^–1. Explosively consolidated compacts had high strength ranging from 1.9–2.5 GPa below 623 K and could be plastically deformed to a strain of more than 50% at 673 K while preserving the amorphous state. Amorphous alloy compacts prepared by high hydrostatic pressure consolidation showed lower compressive strength. Those produced by warm extrusion were anisotropic in strength, the highest strength being as high as 2.74 GPa. It was also found that the geometry of the starting powders had a profound effect on the strength of the product compacts. Compacts prepared from flaky powders were stronger than those prepared from spherical ones. It is concluded that the mechanical properties of the amorphous alloy compacts depend on the consolidation technique, powder geometry and surface conditions of the powders, especially existence of oxide films.     

Low temperature stress relaxation of nanocrystalline nickel

Stress relaxation in nanocrystalline nickel within the temperature range 523–673 K in a uniaxial compression regime is studied in the present investigation. The results obtained for coarser grained nickel are given for comparison. An average strain rate of nanocrystalline nickel within the investigated range of temperatures is 1.75 × 10^–5–3.03 × 10^–5s^–1. The presence of two types of stress relaxation dependencies are shown. The most likely strain mechanism is grain boundary sliding controlled by grain boundary diffusion for temperatures between 623 and 673 K.     

Effects of strain rate and temperature on the stress–strain response of solder alloys

To ensure reliable design of soldered interconnections as electronic devices become smaller, requires greater knowledge and understanding of the relevant mechanical behavior of solder alloys than are presently available. The present paper reports the findings of an investigation into the monotonic tensile properties of bulk samples of three solder alloys; a lead–tin eutectic and two lead-free solders (tin–3.5 copper and a tin–3.5 silver alloy). Temperatures between–10 and 75°C and strain rates between 10^–1 and 10^–3 s^–1 have been studied. Both temperature and strain rate may have a substantial effect on strength, producing changes well in excess of 100%. Strength is reduced by lowering strain rate and increasing temperature, and Sn–37 Pb is usually most sensitive to the latter. Expressions for strain and strain rate hardening have been developed. The Sn–0.5 Cu alloy is usually the weakest and most ductile. Sn–37 Pb is strongest at room temperature but with increasing temperature and lower strain rates it becomes inferior to Sn–3.5 Ag. Ductility changes with temperature and strain rate for all three alloys are generally small with inconsistent trends. The role of such data in stress analysis and modeling is considered and the paramount importance of employing data for conditions appropriate to service, is emphasized.     

High-speed testing and material modeling of unfilled styrene butadiene vulcanizates at impact rates

High-speed tensile tests were performed on unfilled SBR strip and sheet specimens at room temperature. Uniaxial dynamic stress-extension ratio curves indicated three distinct regions of rate-dependent behavior when strain rates were below 180 s^–1, between 180–280 s^–1and above 280 s^–1. With increasing strain rate, the toughness increased in the first region, remained roughly constant in the second region, and decreased in the third region. Time-temperature shift on SBR near the glass transition temperature used to obtain high strain rate tensile strength at room temperature did not give the same results as those found in the impact tensile test. The dynamic toughness was used to predict failure of rubber sheets under impact loads using ABAQUS Explicit. Predicted values of the sheet extension at the onset of failure were within 10% of experimental values.     

Stress-strain rate relations for high-temperature deformation of two-phase Al-Cu alloys

Al-Cu alloys containing 6, 11, 17, 24 and 33 wt% Cu, annealed for 0.5–100 h, were deformed by the differential strain-rate test technique over a strain-rate range of 4×10^–6 to 3×10^–2s^–1 at temperatures ranging from 460–540°C. Superplastic behaviour, with strain-rate sensitivity, m0.5, and activation energy, Q=171.5 kJ mol^–1, is shown by the Al-24Cu and Al-33Cu alloys at lower strain rates and higher temperatures. All the alloys show m0.20 at higher strain rates, but the average activation energy for deformation of the Al-6Cu, Al-11Cu, and Al-17Cu alloys is evaluated to be 480.7 kJ mol^–1, in contrast to a lower value of 211 kJ mol^–1 for the Al-24Cu and Al-33Cu alloys. Instead of grain size, the mean free path between particles is suggested to be a more appropriate microstructural parameter for the constitutive relationship for deformation of the Al-Cu alloys.