Synchronous Full-Field Strain and Temperature Measurement in Tensile Tests at Low,Intermediate and High Strain Rates

Tensile tests with simultaneous full-field strain and temperature measurements at the nominal strain rates of 0.01, 0.1, 1, 200 and 3000 s^?1 are presented. Three different testing methods with specimens of the same thin and flat gage-section geometry are utilized. The full-field deformation is measured on one side of the specimen, using the DIC technique with low and high speed visible cameras, and the full-field temperature is measured on the opposite side using an IR camera. Austenitic stainless steel is used as the test material. The results show that a similar deformation pattern evolves at all strain rates with an initial uniform deformation up to the strain of 0.25–0.35, followed by necking with localized deformation with a maximum strain of 0.7–0.95. The strain rate in the necking regions can exceed three times the nominal strain rate. The duration of the tests vary from 57 s at the lowest strain rate to 197 μs at the highest strain rate. The results show temperature rise at all strain rates. The temperature rise increases with strain rate as the test duration shortens and there is less time for the heat to dissipate. At a strain rate of 0.01 s^?1 the temperature rise is small (up to 48 °C) but noticeable. At a strain rate of 0.1 the temperature rises up to 140 °C and at a strain rate of 1 s^?1 up to 260 °C. The temperature increase in the tests at strain rates of 200 s^?1 and 3000 s^?1 is nearly the same with the maximum temperature reaching 375 °C.     

Thermomechanical behavior of casting sands: Experiments and elastoplastic modeling

The thermomechanical behavior of casting sands is discussed from an experimental and a theoretical point of view. Uniaxial compression tests at temperatures ranging from 20°C to 950°C and at different values of strain rate (ϵ = 10⁻² s⁻¹, ϵ = 10⁻³ s⁻¹ and ϵ = 10⁻⁴ s⁻¹) have been performed. They show that casting sands exhibit no strain rate effect in the temperature range 20–600°C, and that an elastoplastic model is well suited to describe the experimental results. Three thermoelastoplastic models, derived from Cam Clay and Hujeux models have been developed. These new models take into account the cohesion of the material. The physical parameters needed for these models have been obtained in the temperature range 20–300°C by using triaxial tests, uniaxial compression tests, isotropic compression tests and die pressing tests. An original triaxial apparatus has been built allowing a temperature of 800°C and a pressure of 4 MPa to be reached. In the temperature at which the parameters have been obtained (20–300°C), two additional triaxial compression tests at different confining pressures are used to check the validity of the thermoelastoplastic models used. The best quantitative results are obtained with the revised modified Cam Clay model.     

Experimental analysis of dynamic mechanical properties for artificially frozen clay by the split Hopkinson pressure bar

A device for impact compression experiments is the split Hopkinson pressure bar with a refrigerating attemperator. Data for incident and reflected waves are obtained by the measuring technique with strain gauges, and data for transmitted waves are obtained by the measuring technique with semiconductor gauges. Static compression tests of frozen clay are conducted at an identical temperature and different strain rates of 0.001 and 0.01 sec ⁻¹ . Dynamic stress-strain curves are obtained at strain rates of 360–1470 sec ⁻¹ . The low and high temperatures correspond to high and low strain rates, respectively. It is shown that both the temperature and strain rate affect the frozen soil deformation process. Different dynamic stress-strain curves obtained at the same temperature but different strain rates are found to converge. The test results indicate that frozen soil has both temperature-brittleness and impact-brittleness.     

The effect of pre-thermal history on shear and uniaxial elongational viscosity of a tetrafluoroethylene/hexafluoropropylene copolymer near the crystal melting transition

The melt rheology of a commercially available tetrafluoroethylene/hexafluoropropylene copolymer, which is known as Teflon FEP copolymer, was studied to examine the effect of pre-thermal history during sample preparation conditions on dynamic shear and uniaxial elongational measurements. The first experimental series includes the sample preparation under hot press at 320 °C followed by a rapid cooling. The master curves were successfully obtained at 300 °C from the time-temperature superposition principle. The loss modulus G″ was found to be proportional to the angular frequency in a double-logarithmic plot toward 0.01 (rad/s), while the slope of the storage modulus G′ did not become 2. The elongational viscosity as a function of time under constant strain rates showed weak strain-hardening, which was enhanced with larger strain rates. The second experimental series contain three kinds of samples with different pre-thermal history to control rheological properties. All samples were hot-pressed at 320 °C followed by a rapid cooling to room temperature for the sample A and a slow cooling for the sample B and C. The dynamic shear and elongational measurements were performed at 270 °C for all samples, which were heated from room temperature for the sample A and B, but heated up to 280 °C and cooled down to 270 °C for the sample C. The distance between G″ and G′ become narrower in the order of the sample C, B, and A. In the same order, unexpectedly, the strain-hardening in the elongational viscosity measurements became the strain-softening. These unusual properties were discussed from a residual crystallinity.     

A shear-compression specimen for large strain testing

A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s⁻¹), up to very high strain rates (2×10⁴s⁻¹ in the present case).     

An experimental study of dynamic tensile properties of glass fiber at low-temperatures

Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σ_max and the unstable strain ɛ _b of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σ_max increase; but ɛ _b increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles were also discussed. Project supported by the National Natural Science Foundation of China (No. 19772058).     

Experimental Technique to Characterize the Plastic Behaviour of Metallic Materials in a Wide Range of Temperatures and Strain Rates: Application to a High-Carbon Steel

This paper presents high temperature quasi-static and dynamic tensile testing. Samples are heated by an induction system controlled with a pyrometer. A high-speed camera (500 fps) is used to determine displacement fields with a digital image correlation software. For such tests a specific marking procedure of the sample is applied. This method is used to characterize the mechanical behaviour of a C68 high-carbon steel at temperatures up to 720 °C. Stress-strain curves are given from room temperature up to 720 °C at strain rates ranging from 400 /s to 4 × 10² /s.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

Mechanical and optical characterization of an anelastic polymer at large strain rates and large strains

Two constitutive relations have been determined from test results that characterize, respectively, the uniaxial and photomechanical behavior of a polyester-styrene copolymer for strain rates from 10^?5 to 3×10³ in./in./s and strains up to 40 percent. The high-strain-rate data were obtained by means of a split-Hopkinson-bar apparatus. Intermediate-strain-rate tests, performed with the aid of a drop tower, were reported in an earlier paper. Quasi-static experiments were conducted on a standard testing machine. A nonlinear, four-parameter, elastic-viscoplastic model was constructed which describes the mechanical behavior. The parameters were determined by a least-mean-squares curve-fitting procedure. The viscoplastic parameters were found to obey a power law in strain rate. The photomechanical model was found to be linear with strain well into the plastic-deformation region, while the slope of the strain-birefringence curve for each strain rate also varied by strain rate to a power.     

Critical Stresses in Spalling and Dynamic Rupture of Metals

Results of dynamic rupture tests of a series of metals obtained using a composite Hopkinson bar and shock-wave loading of plane specimens are described. It is shown that the actual rupture strength at a strain rate of 5 · 10³ sec⁻¹ is very close to the spall strength at higher strain rates. Results of testing the same metals using a composite Hopkinson bar within a temperature range of 20–350°C are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 103–107, November–December, 2005.     

High-temperature test facility for repeated pressure loading of cylinders

A test facility capable of subjecting cylindrical specimens to repeated pressure loadings at high temperatures is described. The loading rates range from 480 to 600 cycles per minute. The test pressures range from 310 to 447 MN/m² and the test temperatures are 260°C, 538°C and 816°C. Testing was performed at two strain rates. A “low” strain rate of about 4 per second and a “high” strain rate of about 9.6 per second. The uniqueness of the facility lies in the choice of a solid loading medium to transmit pressure to the specimen. Some typical results are presented.     

Brittle fracture of precompressed steel as affected by hydrostatic pressure,temperature and strain concentration

Highly precompressed 1020 HR steel, 0.65 prestrain at 400°F (204°C), tested in nominally uniform tension at ?80°F (?62°C) fractures at about 110,000 psi (760 MN/m²) with less than 0.02 plastic strain. Yet the addition of a hydrostatic pressure of less than 7000 psi (48 MN/m²) converts this visually brittle fracture to a ductile one with appreciable necking. The explanation of this surprising experimental result is shown to follow directly and simply from the combination of a tensile stress criterion of fracture, strain concentration and the low tangent modulus of the stress-strain curve in tension beyond the Bauschinger transition region of a few percent of plastic strain. Temperature dependence and strain-rate dependence of brittle fracture similarly are predictable in an almost trivial manner from the appropriate stress-strain curves for different amounts of precompression. So also is the amazingly high ductility or fracture toughness of the most complex of perforated or notched statically loaded structures of mild steel in an undamaged or fully annealed state.     

A crystallographic model for the orientation dependence of low cyclic fatigue property of a nickel-base single crystal superalloy

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Effects of laser power density on static and dynamic mechanical properties of dissimilar stainless steel welded joints

The mechanical properties of laser welded joints under impact loadings such as explosion and car crash etc. are critical for the engineering designs. The hardness, static and dynamic mechanical properties of AISI304 and AISI316 L dissimilar stainless steel welded joints by CO₂ laser were experimentally studied. The dynamic strain-stress curves at the strain rate around 10³ s^?1 were obtained by the split Hopkinson tensile bar (SHTB). The static mechanical properties of the welded joints have little changes with the laser power density and all fracture occurs at 316 L side. However, the strain rate sensitivity has a strong dependence on laser power density. The value of strain rate factor decreases with the increase of laser power density. The welded joint which may be applied for the impact loading can be obtained by reducing the laser power density in the case of welding quality assurance.     

Torsional split Hopkinson bar tests at strain rates above 104s−1

The torsional split Hopkinson bar is used for testing materials at strain rates above 10⁴s⁻¹. This strain rate, which is an order of magnitude higher than is typical with this technique, is obtained by using very short specimens. Strain rates of 6.4×10⁴s⁻¹ have been achieved with specimens having a gage length of 0.1524 mm. Results from tests on 1100 aluminum show an increase in rate sensitivity as the strain rate increases.     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.     

Thermo-mechanical response of nylon 101 under uniaxial and multi-axial loadings: Part I,Experimental results over wide ranges of temperatures and strain rates

A comprehensive study of the thermo-mechanical response of a thermoplastic polymer, nylon 101 is presented. Quasi-static and dynamic compression uniaxial and multi-axial experiments (stress states) were performed at a wide range of strain rates (10⁻⁵ to 5000 s⁻¹) and temperatures (−60 to 177 °C or −76 to 350 °F). The material is found to be non-linearly dependent on strain rate and temperature. The change in volume after plastic deformation is investigated and is found to be negligibly small. The relaxation and creep responses at room temperature are found to be dependent on strain rate and the stress–strain level at which these phenomena are initiated. Total deformation is decomposed into visco-elastic and visco-plastic components; these components have been determined at different levels of deformation. Results from non-proportional uniaxial to biaxial compression, and torsion experiments, are also reported for three different strain rates at room temperature. It is shown that nylon 101 has a response dependent on the hydrostatic pressure.     

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.     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Strain-gage installations for adverse environments

Seven projects in which resistance-type bonded strain gages were used in adverse environments are described. The projects involved: (1) force measurements in a 10^?10 torr vacuum, (2) load measurements over a temperature range of 75 to 300° F, (3) displacement measurements in a nonconductive fluid at 500° F, (4) dynamic displacement measurements in an electric field, (5) strain measurements in air at 600° F, (6) dynamic displacement and strain measurements to ?320°F, and (7) strain measurements in water at pressures up to 2500 psi and temperatures up to 300° F. This report provides detailed information about the gage installations, the transducers used and the performance obtained.