Transition Strain Rate Research Articles

Appraisal of Pulse-Shaping Technique in Split Hopkinson Pressure Bar Tests for Brittle Materials

Split Hopkinson pressure bar (SHPB) technique has been frequently used to measure the uniaxial compressive stress–strain relation of brittle materials at intermediate strain-rates where pulse-shaping technique is employed to improve the stress uniformity and maintain a nearly constant strain-rate in the specimen during the effective loading period. This paper appraises the functions of the pulse-shaping technique in SHPB tests of brittle samples based on numerical simulations of SHPB tests. It is shown that a proper pulse-shaper can attenuate high frequency oscillations of the incident pulse and increase the rise-time of the pulse, resulting in the improvement of stress equilibrium and uniformity along the axial direction of an SHPB specimen. However, it is found that the inertia-induced confinement in the radial direction of a brittle specimen is still significant even though the shaped incident stress pulse can generate a nearly flat plateau in the reflected pulse in the SHPB test. It implies that the achievement of a nearly constant strain-rate represented by a nearly flat plateau in the reflected pulse in an SHPB test may not give a true nearly constant strain-rate in the SHPB specimen. It is concluded that the application of the pulse-shaping technique in SHPB tests on brittle materials may not change the nature of the observed transition strain-rate, which represents the transition of the stress state from a uniaxial-compressive-stress-dominated state to a confined compressive stress state, rather than the start of significant strain-rate effect. Therefore, inertia-induced radial confinement effect needs to be considered in the interpretation of any SHPB results for brittle materials even though a pulse-shaper is used.

Dynamic behavior of polymers at high strain-rates based on split Hopkinson pressure bar tests

Dynamic behavior of polymers at high strain rates from 10 1 to 10 4 s −1 is frequently investigated by split Hopkinson pressure bar (SHPB) technique. It is found that the apparent strain-rate effect on the dynamic yield stress of polymers based on SHPB tests may include significant contributions from lateral confinement effects when the strain-rate is beyond a transition strain-rate. A methodology based on numerical SHPB tests and the constitutive equation without considering strain-rate effect is proposed to identify this transition strain rate. Experimentally-measured strain-rate dependence of the peak stress up to the transition strain rate is recommended for the determination of the strain-rate dependence of the polymer, which is subsequently implemented into a dynamic constitutive equation including strain-rate and temperature effects. This dynamic constitutive equation together with a kinetic friction model is used to simulate the SHPB tests in independent publications. Reasonably good agreements between numerical predictions and experimental results are observed for a range of polymers at strain rates below 10 4 s −1.

Effects of Strain Rate on Mechanical Properties and Microstructure of V-5Cr-5Ti Alloy

In this work the static and dynamic tensile properties of vanadium alloy V-5Cr-5Ti were investigated at strain rates ranged from 3.3x10-5/s to 1.2x102/s. The material microstructures were analyzed using optical microscope, SEM, TEM, XRD and EDS. Results show that the yield strength a increases with strain rate. The brittle-ductile transition strain-rate is about 101/s to102/s. At room temperature the tensile fracture at a low strain rate occurs via mixed modes of microvoid aggregating and transgranular cracking; at high strain rate the fracture occurs via a brittle mode. The analysis by TEM, XRD and EDX shows the existence of lath martensite, and on there exits precipitate phase of Ti(O,C, N) in grain boundaries.

Modelling plastic deformation of metals over a wide range of strain rates using irreversible thermodynamics

Based on the theory of irreversible thermodynamics, the present work proposes a dislocation-based model to describe the plastic deformation of FCC metals over wide ranges of strain rates. The stress-strain behaviour and the evolution of the average dislocation density are derived. It is found that there is a transitional strain rate (∼ 104 s-1) over which the phonon drag effects appear, resulting in a significant increase in the flow stress and the average dislocation density. The model is applied to pure Cu deformed at room temperature and at strain rates ranging from 10-5 to 106 s-1 showing good agreement with experimental results.

A constitutive model for high strain rate deformation in FCC metals based on irreversible thermodynamics

The present work extends a recent model for plastic deformation of polycrystalline metals based on irreversible thermodynamics. A general dislocation evolution equation is derived for a wide range of strain rates. It is found that there is a transitional strain rate (∼10 3 s −1) over which the phonon drag effects play a dominant role in dislocation generation resulting in a significant raise in the dislocation density and flow stress. The model reduces to the classical Kocks–Mecking model at low strain rates.

Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I: Experiments

Effects of the inertia-induced radial confinement on the dynamic increase factor (DIF) of a mortar specimen are investigated in split Hopkinson pressure bar (SHPB) tests. It is shown that axial strain acceleration is unavoidable in SHPB tests on brittle samples at high strain-rates although it can be reduced by the application of a wave shaper. By introducing proper measures of the strain-rate and axial strain acceleration, their correlations are established. In order to demonstrate the influence of inertia-induced confinement on the dynamic compressive strength of concrete-like materials, tubular mortar specimens are used to reduce the inertia-induced radial confinement in SHPB tests. It is shown that the DIF measured by SHPB tests on tubular specimens is lower than the DIF measured by SHPB tests on solid specimens. This paper offers experimental support for a previous publication [Li QM, Meng H. About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. Int J Solids Struct 2003; 40:343–360.], which claimed that inertia-induced radial confinement makes a large contribution to the dynamic compressive strength enhancement of concrete-like materials when the strain-rate is greater than a critical transition strain-rate between 10 1 and 10 2 s −1. It is concluded that DIF formulae for concrete-like materials measured by split Hopkinson pressure bar tests need to be corrected if they are going to be used as the unconfined uniaxial compressive strength in the design and numerical modelling of structures made from concrete-like materials to resist impact and blast loads.

Damage Kinetics of Glass/Epoxy Composite Materials Under Dynamic Compression

The strain rate sensitivity of glass fiber-reinforced polymer is studied by testing a single laminate configuration at strain rates of 200—2000 s-1. The compressive material properties are determined by testing the laminate systems with different orientations from low to high strain rates. Samples of cubic geometry are tested in in-plane direction for seven fiber orientations, 08, ±208, ±308, ±458, ±608, ±708, and 908. Preliminary compressive stress—strain vs. strain rates data obtained show that the dynamic material strength increases with increasing strain rates. The tests show a strong material sensitivity to dynamic loading and fiber direction. For in-plane tests, there is a transitional strain rate and a transitional fiber orientation in the trends, reflecting the dependencies on strain rate and fiber orientation observed in experiments. Damage investigations have revealed that the failure events differ and depend on composite sequence lay-ups.

Computational micromechanics of dynamic compressive loading of a brittle polycrystalline material using a distribution of grain boundary properties

A two-dimensional finite element model is used to investigate compressive loading of a brittle ceramic. Intergranular cracking in the microstructure is captured explicitly by using a distribution of cohesive interfaces. The addition of confining stress increases the maximum strength and if high enough, can allow the effective material response to reach large strains before failure. Increasing the friction at the grain boundaries also increases the maximum strength until saturation of the strength is approached. Above a transitional strain rate, increasing the rate-of-deformation also increases the strength and as the strain rate increases, fragment sizes of the damaged specimen decrease. The effects of flaws within the specimen were investigated using a random distribution at various initial flaw densities. The model is able to capture an effective modulus change and degradation of strength as the initial flaw density increases. Effects of confinement, friction, and spatial distribution of flaws seem to depend on the crack coalescence and dilatation of the specimen, while strain-rate effects are result of inertial resistance to motion.

An interacting micro-crack damage model for failure of brittle materials under compression

A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.

A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates

In many applications, polymer materials undergo a large variety of mechanical loading conditions, wherein the influences of temperature and strain rate are of prime importance. Mahieux and Reifsnider [Mahieux CA, Reifsnider KL. Polymer 2001;42:3281. [19]] have proposed a statistical model to describe the stiffness variation of polymers over a wide range of temperatures. However, this model does not consider any frequency/strain rate dependence of the stiffness modulus. Starting from this consideration, we propose here to transform this latter model into a robust physically based model for the prediction of the stiffness modulus for a wide range of temperatures and frequencies/strain rates. This new formulation has been successfully validated for two amorphous polymers, polymethylmethacrylate (PMMA) and polycarbonate (PC), using dynamic mechanical analysis and uniaxial compression testing. Good agreement has been found between theory and experiment for the non-linear behavior of the initial Young's modulus, at the very high strain rates.

Dynamic Compressive Response and Failure Behavior of an Epoxy Syntactic Foam

The high-strain-rate compressive behavior of an epoxy syntactic foam is examined in this study. A pulse-shaped split Hopkinson pressure bar (SHPB), modified for low-impedance material testing, was used to ensure that the samples deformed under dynamic equilibrium and at a nearly constant strain-rate. Dynamic stress equilibrium in the specimen was monitored for each experiment using piezoelectric force transducers mounted close to the specimen end-faces. Quasi-static experiments were also conducted to demonstrate rate effects of the foam, as well as to study its failure behavior. It was determined that the compressive strength of the foam increased with strain rate up to a transition strain rate of between 550 and 1030 s 1. For experiments conducted at strain rates above this transition range, strain-rate-induced damage caused the compressive strength of the foam to decrease. Based on the experimental results, a constitutive model with strain-rate and damage effects was developed, which described the test data well.

Deformation behavior of the Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 bulk metallic glass over a wide range of strain-rates and temperatures

The stress-strain relations for the Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 bulk metallic glass (Vitreloy 1) over a broad range of temperatures (room temperature to its supercooled liquid region) and strain rates (10 −5 to 10 3 s −1) were established in uniaxial compression using both quasi-static and dynamic Kolsky (split Hopkinson) pressure bar loading systems. Relaxation and jump in strain rate experiments were conducted to further understand the time dependent behavior of Vitreloy 1. The material exhibited superplastic flow above its glass transition temperature (623 K) and strain rates of up to 1 s −1. The viscosity in the homogeneous deformation regime was found to decrease dramatically with increasing strain rate. A fictive stress model was used to describe the basic deformation features of Vitreloy 1 under constant strain-rate loading as well as multiple strain-rate loading at high temperatures.

Effect of Microstructure on Moisture-induced Embrittlement of L12 Intermetallic Compounds

The effects of grain size and second phase on moisture-induced embrittlement of L1 2 -type Co 3 Ti and Ni 3 (Si, Ti) alloys were investigated by tensile test in air and vacuum as functions of strain rate and temperature, in combination with microstructural and fractographic observation. In both the intermetallic alloys, brittle-ductile transition (BDT) strain rate defined from an elongation vs. strain rate curve decreased with decreasing grain size, meaning that fine-grained microstructure has the effect of reducing the moisture-induced embrittlement. Also, it was found that dispersion of Co solid solution phase and Nb-containing second phase has the effect of reducing moisture-induced embrittlement of the Co 3 Ti and the Ni 3 (Si, Ti)-Nb alloys, respectively, when their second phases are incoherent with the L1 2 matrix. Contrarily, finely precipitated Co solid solution phase that is coherent with the L1 2 matrix has the effect of enhancing moisture-induced embrittlement of the Co 3 Ti alloys. Mechanisms responsible for the microstructural effect on the moisture-induced embrittlement of the L12 intermetallic alloys were presented and discussed.

Strain-rate effects on low cycle fatigue mechanism of eutectic Sn–Pb solder

Low cycle fatigue tests of as-casted Sn–Pb eutectic solder (63Sn/37Pb) were carried out using the non-contact strain-controlled system at 20°C in order to avoid local deformation and stress concentration at contact points between the extensometer and the specimen surface. The fatigue mechanisms were studied by SEM examination of polished surface of specimens and fracture surfaces. Wedge cracking due to grain boundary sliding was the dominant mechanism in the low strain rate regime, while extensive cavitation was observed on the colony boundaries at high strain rate regime. An estimation of the transition strain rate for grain boundary cracking due to sliding ( ε ̇ ∗ w ) yielded a value lowers than that of the experimental result by 2–3 orders of magnitude. Relationship between time to failure and strain rate for the present results and the reported results could be expressed by a double-linear curve with the transition strain rate of approximately 10 −3 s −1.

The Brittle Failure of Ice under Compression

This paper reviews progress during the past decade in understanding the brittle compressive failure of ice. Evidence is presented for the frictional crack sliding-wing mechanism and for the role of localized fragmentation. The ductile-to-brittle transition is explained in terms of the suppression of crack growth and is modeled in terms of Ashby−Hallam wing crack mechanics and Riedel−Rice crack-tip creep. The brittle compressive strength is related to ice−ice friction. Modeling and experiment suggest that the transition strain rate of cracked ice scales as (crack size)-1.5 and that its brittle strength scales as (crack size)-0.5, at least for small specimens. Possible size effects are noted.

Failure of columnar saline ice under biaxial compression: Failure envelopes and the brittle‐to‐ductile transition

Experiments were performed on the compressive failure of columnar saline ice loaded biaxially at temperatures from −40°C to −50°C and at strain rates from 10−6 s−1 to 10−1 s−1. The major stress (σ11) was applied across the columns, and the minor stress was applied proportionally either across the columns (σ22) or along the columns (σ33). The results show that the macroscopic behavior changes from brittle to ductile upon reducing the strain rate to a critical level and that the transition strain rate first increases and then decreases with increasing across‐column confining stress. The brittle strength increases sharply under low degrees of across‐column confinement and then decreases upon increasing σ22 further. This behavior is manifested in a truncated, Coulombic‐type of failure envelope where failure on the rising branch is by splitting (zero confinement) and by shear faulting (moderate confinement) within the loading plane and on the descending branch by spalling out of the loading plane. The ductile strength increases monotonically with increasing confining stress and with both decreasing temperature and increasing strain rate. The ductile failure envelope is semielliptical in shape and can be described by Hills criterion for the yielding of plastically orthotropic materials. Correspondingly, the components of the inelastic “strain vector” in the X1‐X2 plane are reasonably normal to the failure envelope. Neither the brittle nor the ductile strength is affected by a confining stress along the columns (σ33). Brittle behavior is explained in terms of the frictional crack‐sliding wing crack mechanism, and ductile behavior is related to both basal (under low confinement) and nonbasal (under high confinement) dislocation processes. The brittle‐to‐ductile transition is attributed to the relaxation of crack tip tensile stresses and is modeled by incorporating the crack size and the resistance to creep, crack propagation, and frictional sliding.

The ductile-to-brittle transition and ductile failure envelopes of orthotropic ice under biaxial compression

Experiments were performed on orthotropic columnar fresh-water ice of ≈ 6mm column diamter proportionally loaded across the columns under biaxial compression at −10°C under various combinations of strain rate and stress ratio, R = σ 22/ σ 11. The ductile-to-brittle transition strain rate increased from about 8 × 10 −5 s −1 under no confinement to about 3 × 10 −4s −1 under intermediate confinement ( R ⋍ 0.3), and then decreased to about 5 × 10 −5s −1 under full confinement ( R = 1). The ductile failure envelopes are semi-elliptical in shape and conform fairly well to those created with the use of Hill's [9] criterion for the yielding of plastically orthotropic materials. The transition strain rate is rationalized in terms of the effects of the confining stress on the ductile and the brittle failure stresses, and is modelled in terms of the suppression of creep deformation at the tips of wing cracks.

On the ductile-to-brittle transition in ice under compression

Evidence is presented which supports a recent model [Schulson, Acta metall. mater.38, 1963 (1990)] of the ductile-brittle transition in ice under uniaxial compression. Observations on columnar, fresh-water ice show that wing cracks from within both the brittle and the ductile regimes, but that individual wing cracks propagate only within the brittle regime. The ductile-brittle transition strain rate agrees reasonably well with that predicted by the model, including the predicted (grain size)−1.5 dependence. Experiments using artificial cracks again show that when individual wing cracks propagate, brittle behavior is generally observed; when individual cracks do not propagate, ductile behavior is generally observed. When cracked samples are crept under a small load, wing crack propagation is suppressed. These observations are all in accord with the idea (1) that the transition occurs when the size of the crack-tip creep zone becomes too small to prevent wing crack growth under an increasing compressive stress.

The brittle compressive fracture of ice

The brittle compressive fracture under uniaxial loading of fresh-water, granular ice Ih has been studied. Measurements are reported of the fracture stress at temperatures from −10 to −50°C at strain rates of 10 −3 and 10 −1 s −1 for grain sizes from approximately 1 to 10 mm. Also a summary is reported of measurements by Jones et al. (unpublished) of the kinetic coefficient of friction for ice on ice at temperatures from −10 to −40°C at sliding velocities from 5 × 10 −7 m s −1 to 5 × 10 −2 ms −1. Observations via high speed photography of internal cracking during loading are included. The strength, albeit scattered, increases with decreasing grain size, with decreasing temperature and at −10°C with decreasing strain rate. Similarly, the coefficient of friction increases with decreasing temperature and at −10°C with decreasing sliding velocity. Wing cracks were observed on some inclined cracks nucleated during loading. The results are explained in terms of the frictional crack sliding-wing crack model [as developed by Ashby and Hallam, Acta metall. 34, 497 (1986)] of compressive fracture. Finally, a simple model is presented for the transition from ductile to brittle behavior. It is based upon the competition between the building up and the relaxation of internal stresses within the vicinity of the internal cracks, and it leads to a transition strain rate which can be expressed in terms of the fracture toughness, the creep rate, the kinetic coefficient of friction and the microstructural scale of the material.

Plastic flow and microstructure of cast nickel aluminides at 1273 K

Chill-cast nickel aluminides based on Ni3Al were compression-tested in vacuum at 1273 K at strain rates ranging from 10-5 s-1 to 10-1 s-1. As the strain rate increases, the propensity for intergranular cracking increases. The ductile-to-brittle transition strain rate (DBTS) of as-cast Ni-22.5Al-0.5Hf-0.1B (at. pct) is approximately 10-1 s-1. Homogenization lowers this value by three orders of magnitude, to 10-4 s-1 (a homogenized specimen disintegrated completely at a rate of 10-3 s-1). The fine-grained structure of the as-cast alloy plays an important role in its relatively high DBTS. A hafnium-free alloy, Ni-24A1-0.1B, on the other hand, shows only a weak dependence of the DBTS on prior homogenization, and possible reasons for this finding are discussed.