High strain-rate behavior of ice under uniaxial compression

In the present study, a modified split Hopkinson pressure bar (SHPB) is employed to investigate the dynamic response of ice under uniaxial compression in the range of strain rates from 60 to 1400 s^?1 and at initial test temperatures of ?10 and ?30 °C. The compressive strength of ice shows positive strain-rate sensitivity over the range of strain rates employed; a slight influence of ice microstructure is observed, but it is much less than that reported previously for ice deformation under quasi-static loading conditions [Schulson, E.M., IIiescu, D., Frott, A., 2005. Characterization of ice for return-to-flight of the space shuttle. Part 1 – Hard ice. NASA CR-2005-213643-Part 1]. Specimen thickness, within the range studied, was found to have little or no effect on the peak (failure) strength of ice, while lowering the test temperature from ?10 to ?30 °C had a considerable effect, with ice behaving stronger at the lower test temperature. Moreover, unlike in the case of uniaxial quasi-static compression of ice, the effect of specimen end-constraint during the high rate compression was found to be negligible. One important result of these experiments, which may have important implications in modeling ice impacts, involves the post “peak-stress” behavior of the ice in that the ice samples do not catastrophically lose their load carrying capacity even after the attainment of peak stress during dynamic compression. This residual (tail) strength of the damaged/fragmented ice is sizable, and in some cases is larger than the quasi-static compression strength reported for ice. Moreover, this residual strength is observed to be dependent on sample thickness and the strain rate, being higher for thinner samples and at higher strain-rates during dynamic compression.     

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.     

Failure in notched tension bars due to high-temperature creep: Interaction between nucleation controlled cavity growth and continuum cavity growth

For axi-symmetrically notched tension bars [Dyson, B.F., Loveday, M.S., 1981, Creep Fracture in Nimonic 80A under Tri-axial Tensile Stressing, In: Ponter A.R.S., Hayhurst, D.R. (Eds.), Creep in Structures, Springer-Verlag, Berlin, pp. 406–421] show two types of damage propagation are shown: for low stress, failure propagates from the outside notch surface to the centre-line; and for high stress, failure propagates from the centre-line to the outside notch surface. The objectives of the paper are to: identify the physics of the processes controlling global failure modes; and, describe the global behaviour using physics-based constitutive equations.Two sets of constitutive equations are used to model the softening which takes place in tertiary creep of Nimonic 80A at 750 °C. Softening by multiplication of mobile dislocations is firstly combined, for low stress, with softening due to nucleation controlled creep constrained cavity growth; and secondly combined, for high stress, with softening due to continuum void growth. The Continuum Damage Mechanics, CDM, Finite Element Solver DAMAGE XX has been used to study notch creep fracture. Low stress notch behaviour is accurately predicted provided that the constitutive equations take account of the effect of stress level on creep ductility. High stress notch behaviour is accurately predicted from a normalized inverse cavity spacing d/2? = 6, and an initial normalized cavity radius r_hi/? = 3.16 × 10^?3, where 2? is the cavity spacing, and d is the grain size; however, the constants in the strain rate equation required recalibration against high stress notch data. A void nucleation mechanism is postulated for high stress behaviour which involves decohesion where slip bands intersect second phase grain boundary particles. Both equation sets accurately predict experimentally observed global failure modes.     

Ductile–brittle transitions in the fracture of plastically-deforming,adhesively-bonded structures. Part I: Experimental studies

Rate effects for adhesively-bonded joints in steel sheets failing by mode-I fracture and plastic deformation were examined. Three types of test geometries were used to provide a range of crack velocities between 0.1 and 5000 mm/s: a DCB geometry under displacement control, a wedge geometry under displacement control, and a wedge geometry loaded under impact conditions. Two fracture modes were observed: quasi-static crack growth and dynamic crack growth. The quasi-static crack growth was associated with a toughened mode of failure; the dynamic crack growth was associated with a more brittle mode of failure. The experiments indicated that the fracture parameters for the quasi-static crack growth were rate independent, and that quasi-static crack growth could occur even at the highest crack velocities. Effects of rate appeared to be limited to the ease with which a transition to dynamic fracture could be triggered. This transition appeared to be stochastic in nature, it did not appear to be associated with the attainment of any critical value for crack velocity or loading rate. While the mode-I quasi-static fracture behavior appeared to be rate independent, an increase in the tendency for dynamic fracture to be triggered as the crack velocity increased did have the effect of decreasing the average energy dissipated during fracture at higher loading rates.     

Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress

Uniaxial compression stress–strain tests were carried out on three commercial amorphous polymers: polycarbonate (PC), polymethylmethacrylate (PMMA), and polyamideimide (PAI). The experiments were conducted under a wide range of temperatures (−40 °C to 180 °C) and strain rates (0.0001 s⁻¹ up to 5000 s⁻¹). A modified split-Hopkinson pressure bar was used for high strain rate tests. Temperature and strain rate greatly influence the mechanical response of the three polymers. In particular, the yield stress is found to increase with decreasing temperature and with increasing strain rate. The experimental data for the compressive yield stress were modeled for a wide range of strain rates and temperatures according to a new formulation of the cooperative model based on a strain rate/temperature superposition principle. The modeling results of the cooperative model provide evidence on the secondary transition by linking the yield behavior to the energy associated to the β mechanical loss peak. The effect of hydrostatic pressure is also addressed from a modeling perspective.     

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.     

Ductility of selected metals under electromagnetic ring test loading conditions

Experimental studies on ductility of selected metals differing mechanical properties under strain rates between 4 × 10³ and 2 × 10⁴ s^?1 are presented in this work. The electromagnetic expanding ring experiment was used as the primary tool for examining the ductility behaviour of metals. Through a use of the Phantom v12 digital high-speed camera and specialised TEMA Automotive software, rings expansion velocities were determined with satisfactory accuracy for all ring tests. In this paper, the experimental observations on cold-rolled copper Cu-ETP, aluminium alloy Al 7075, barrel steel and tungsten heavy alloy are reported. Ductility of studied materials was estimated by measuring changes in cross-sectional areas in the uniform strain portions of the recovered ring fragments. In a similar way the metals ductility was defined at the conventional tensile test condition. Moreover, results of analogue investigation for static and dynamic loading at the temperature of about ?40 °C were described. The experimental observations mainly revealed the different ductility behaviour of metals tested at applied dynamic loadings; Cu-ETP and barrel steel demonstrated an increase in ductility, whereas aluminium alloy Al 7075 and tungsten heavy alloy were characterised by lower ductility in comparison to static loading. These results appear to be partially in contrast with the observations reported recently by some other investigators.     

Experimental analysis of the quasi-static and dynamic torsional behaviour of shape memory alloys

This paper investigates experimentally the quasi-static and dynamic torsional behaviour of shape memory alloys wires under cyclic loading. A specifically designed torsional pendulum made of a Ni–Ti wire is described. Results on the quasi-static behaviour of the wire obtained using this setup are presented, giving an overall view of the damping capacity of the material as function of the amplitude of the loading (imposed torsional angle), the frequency and the temperature. The dynamical behaviour is then presented through measured frequency response function between forcing angle at the top of the pendulum and the difference between top and bottom rotation angles in the vicinity of the first eigenfrequency of the wire, i.e. in the range [0.3 Hz, 1 Hz]. The softening-type non-linearity and its subsequent jump phenomenon, predicted theorically by the decrease of the effective stiffness when martensite transformation starts is clearly evidenced and analysed.     

Dynamic rupture of polymer–metal bilayer plates

Recent theoretical assessments of metal/polymer bilayers indicate a potentially significant delay in the onset of ductile failure modes, especially under dynamic loading, due to strain hardening of the polymer. The response of copper/polyurethane bilayers under dynamic and quasi-static loadings is investigated via static tensile, static bulge forming and dynamic bulge forming tests. Two polyurethanes PU1 and PU2 were chosen with a significant contrast in stiffness and ductility: PU1 has a glass transition temperature T_g close to ?56 °C and at room temperature it has a low modulus, low strength and a high tensile failure strain. In contrast, PU2 has a T_g of 49 °C and at room temperature it has a high modulus and strength but a much smaller tensile failure strain. In most of the tests, the polymer coatings were approximately twice the thickness of the metal layer. Under static loadings (tensile and bulge forming) the PU2 bilayer outperformed the uncoated metal plate of equal mass while the PU1 bilayer had a performance inferior to the equivalent uncoated plate. We attribute this to the fact that the PU2 retards the necking of the copper layer and thus increases its energy absorption capacity while the PU1 coating provides no such synergistic effect. The dynamic bulge forming tests indicate that on an equal mass basis, the dynamic performance of the PU2 bilayers with a weakly bonded polymer coating were comparable to the uncoated plates but intriguingly, when the PU2 was strongly adhered to the copper plates the performance of these bilayers was inferior to that of the uncoated plates. Thus, the coatings do not provide dynamic performance benefits on an equal mass basis. However, it is shown that increasing the mass of a plate by adding a polyurethane layer can improve the performance for a given total blast impulse. Given the ease of applying polyurethane coatings they may provide a practical solution to enhancing the blast resistance of existing metallic structures.     

The mechanisms governing the activation of dislocation sources in aluminum at different strain rates

This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 10¹ s⁻¹ to 10¹⁰ s⁻¹ in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 10⁶ s⁻¹, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 10⁶ s⁻¹, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 10⁸ s⁻¹, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×10⁷ s⁻¹ homogeneous nucleation becomes the dominant generation mechanism.     

Static and dynamic compaction of ceramic powders

The static and dynamic compaction of ceramic powders was investigated experimentally using a high-pressure friction-compensated press to achieve static stresses of 1.6 GPa and with a novel gas gun setup to stresses of 5.9 GPa for a tungsten carbide powder. Experiments were performed in the partial compaction region to nearly full compaction. The effects of variables including initial density, particle size distribution, particle morphology, and loading path were investigated in the static experiments. Only particle morphology was found to significantly affect the compaction response. Post-test examination of the powder reveals fracture of the grains as well as breaking at particle edges. In dynamic experiments, steady structured compaction waves traveling at very low velocities were observed. The strain rate within the compaction waves was found to scale nearly linearly with the shock stress, in contrast with many fully dense materials where strain rate scales with stress to the fourth power. Similar scaling is found for data from the literature on TiO₂ powder. The dynamic response of WC powder is found to be significantly stiffer than the static response, probably because deformation in the dynamic case is confined to the relatively narrow compaction wave front. Comparison of new static powder compaction results with shock data from the literature for SiO₂ also reveals a stiffer dynamic response.     

Extreme softness of brain matter in simple shear

We show that porcine brain matter can be modelled accurately as a very soft rubber-like material using the Mooney–Rivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments performed on small rectangular fresh samples (2.5 cm³ and 1.1 cm³) at quasi-static strain rates. They revealed a linear shear stress–shear strain relationship $(R^2>0.97)$, characteristic of Mooney–Rivlin materials at large strains. We found that porcine brain matter is about 30 times less resistant to shear forces than a silicone gel. We also verified experimentally that brain matter exhibits the positive Poynting effect of non-linear elasticity, and numerically that the stress and strain fields remain mostly homogeneous throughout the thickness of the samples in simple shear.     

Dynamic crushing of sandwich panels with prismatic lattice cores

The dynamic out-of-plane compressive response of stainless steel corrugated and Y-frame sandwich cores have been investigated for impact velocities ranging from quasi-static to 200 ms⁻¹. Laboratory-scale sandwich cores of relative density 2.5% were manufactured and the stresses on the front and rear faces of the dynamically compressed sandwich cores were measured using a direct impact Kolsky bar. Direct observational evidence is provided for micro-inertial stabilisation of both topologies against elastic buckling at impact velocities below 30 ms⁻¹. At higher impact velocities, plastic waves within the core members result in the front face stresses increasing with increasing velocity while the rear face stresses remain approximately constant. While the finite element calculations predict the rear face stresses and dynamic deformation modes to reasonable accuracy, the relatively slow response time of the measurement apparatus results in poor agreement between the measured and predicted front face stresses. The finite element calculations also demonstrate that material strain-rate effects have a negligible effect upon the dynamic compressive response of laboratory-scale and full-scale sandwich cores.     

准三维针刺C_f/SiC复合材料室温层向动态压缩力学行为的实验研究

为了研究应变率对准三维针刺碳纤维增韧的碳化硅复合材料(Cf/SiC)层向压缩力学性能的影响,本文利用分离式Hopkinson压杆装置对三维针刺Cf/SiC复合材料进行了应变率为10-4至6.5×103s-1的单轴压缩力学性能测试。实验结果表明,由于材料缺陷,其动态压缩强度分布遵循Weibull分布。破坏时,材料并未表现出典型的脆性破坏,而是在应力达到压缩强度后经历了较大的伪塑性变形才最终破坏。这表明三维针刺Cf/SiC复合材料沿厚度方向针刺的碳纤维有助于提高材料的韧性。同时,材料的压缩强度随应变率的升高显著增大,并与对数应变率近似成线性关系。借助光学显微镜和扫描电镜对压缩断口的观察表明:材料的失效模式随着应变率变化而发生改变。在准静态下,材料主要表现为剪切和分层破坏,而在高应变率下,则主要表现为劈裂。     

The characteristics of plastic flow and a physically-based model for 3003 Al–Mn alloy upon a wide range of strain rates and temperatures

The uniaxial compressive responses of 3003 Al–Mn alloy upon strain rates ranging from 0.001/s to about 10⁴/s with initial temperatures from 77 K to 800 K were investigated. Instron servohydraulic testing machine and enhanced split Hopkinson bar facilities have been employed in such uniaxial compressive loading tests. The maximum true strain up to 80% has been achieved. The following observations have been obtained from the experimental results: 1) 3003 Al–Mn alloy presents remarkable ductility and plasticity at low temperatures and high strain rates; 2) its plastic flow stress strongly depends on the applied temperatures and strain rates; 3) the temperature history during deformation strongly affects the microstructure evolution within the material. Finally, paralleled with the systematic experimental investigations, a physically-based model was developed based on the mechanism of dislocation kinetics. The model predictions are compared with the experimental results, and a good agreement has been observed.     

酚醛层压材料的冲击力学行为及本构模型

为了研究酚醛层压材料的冲击力学行为并获得本构模型,利用万能试验机和整形修正的分离式霍普金森压杆(SHPB)装置,对材料试样进行了应变率范围为10^-3~10³ s^-1的单轴压缩实验,得到了不同加载应变率下的应力应变曲线,对其在准静态、动态载荷下的压缩破坏机理进行了初步探讨。结果表明,酚醛层压材料具有较强的应变率效应,与准静态(1.67×10^-3 s^-1)时相比,在动态载荷(7×10² s^-1)下,峰值应力增加了约10倍;破坏应变减少了约一半;在准静态和动态加载条件下试样力学性能的差异是由于纤维基体界面特性以及不同应变率下破坏模式的不同;采用朱-王-唐本构方程描述了酚醛层压材料力学行为,拟合得到了本构方程的系数,在加载过程中,理论计算值与实验结果吻合较好。

     

Dynamic fracture of concrete compact tension specimen: Experimental and numerical study

Compared to quasi-static loading concrete loaded by higher loading rates acts in a different way. There is an influence of strain-rate and inertia on resistance, failure mode and crack pattern. With increase of loading rate failure mode changes from mode-I to mixed mode. Moreover, theoretical and numerical investigations indicate that after the crack reaches critical velocity there is progressive increase of resistance and crack branching. These phenomena have recently been demonstrated and discussed by O?bolt et al. (2011) on numerical study of compact tension specimen (CTS) loaded by different loading rates. The aim of the present paper is to experimentally verify the results obtained numerically. Therefore, the tests and additional numerical studies on CTS are carried out. The experiments fully confirm the results of numerical prediction discussed in O?bolt et al. (2011). The same as in the numerical study it is shown that for strain rates lower than approximately 50/s the structural response is controlled by the rate dependent constitutive law, however, for higher strain rates crack branching and progressive increase of resistance is observed. This is attributed to structural inertia and not the rate dependent strength of concrete. Maximum crack velocity of approximately 800 m/s is measured before initiation of crack branching. The comparison between numerical and experimental results shows that relatively simple modeling approach based on continuum mechanics, rate dependent microplane model and standard finite elements is capable to realistically predict complex phenomena related to dynamic fracture of concrete.     

Temperature dependent bulge test for elastomers

The bulge test is a particularly convenient testing method for characterizing elastomers under biaxial loading. In addition, it is convenient to utilize this test for validating material models in simulation due to the heterogeneous strain field induced during inflation. During the bulge test the strain field for elastomers covers uniaxial tension at the border to pure shear and equibiaxial tension at the pole. Elastomeric materials exhibit a hyperelastic material behavior, with a dependency on temperature and loading rate. The temperature effect on the mechanical behavior during biaxial loading is considered in the present study. A bulge test setup combined with a temperature chamber is developed in order to characterize this effect, and an exemplary temperature dependent characterization of a poly(norbornene) elastomer is performed with this setup. The equibiaxial stress–strain curves measured at 60 °C, 20 °C and −20 °C are presented.     

An experimental investigation into the kinematics of a concentrated hard-sphere colloidal suspension during Hopkinson bar evaluation at high stresses

The behavior of a concentrated, hard-sphere colloidal suspension is evaluated using the split Hopkinson pressure bar (SHPB) experimental technique. The composition of the suspension is measured using thermograviometric analysis before and after loading. This, combined with recorded pressure distributions, result in the conclusion that the suspension undergoes high rate squeezing flow. Experimental results demonstrate that the suspension exhibits shear thickening consistent with that observed in standard rotational rheometry. At sufficiently high stresses the suspension exhibits a second regime of shear thinning behavior that is consistent with elastohydrodynamic theory that incorporates the shear modulus of the particles themselves. Further increases in stress result in irreversible behavior, i.e., rather than fracturing or crushing, the particles form non-reversible agglomerates during testing. This fact is demonstrated through the use of dynamic light scattering and electron microscopy. This behavior occurs within a regime of viscous material response which is seen to occur at normal strain rates and stresses over 10⁴ s^?1 and 40 MPa, respectively.     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.