Strain rate dependency and fragmentation pattern of expanding warheads

Investigating the strength of materials at very high strain rates using electro-magnetically driven expanding cylinders

The effect of strain rate on the yield stress of an Al-Li alloy has been investigated at temperaturesbetween 77 and 523 K and over the strain rate range from 1.77×10 Š4 s 1 to 1.77×10 Š 2 s . At testing temperaturesbelow 373 K, the yield stress is almost independent of strain rate at any aging stage. At testing temperaturesabove 373 K, the yield stress increases linearly with the logarithm of strain rate, and the strain rate dependenceincreases with increasing testing temperature. The yield stresses of under-aged alloy at temperatures between373 and 473 K at high strain rates are greater than the yield stress at 77 K. For the alloy under-aged or agednearly to its peak strength, the temperature range within which the positive temperature dependence of yieldstress appears expands to the higher temperature side with increasing strain rate. The strain rate dependence ofthe yield stress is slightly negative at this aging stage. The yield stress of the over-aged alloy decreases mono-tonically with decreasing strain rate and with increasing testing temperature above 373 K. The modulus normal-ized yield stress is nearly constant at testing temperatures below 373 K at any strain rate investigated. And,strength depends largely both on the aging conditions and on the testing temperature. The peak positions instrength vs. aging time curves shift to the side of shorter aging time with increasing testing temperature. For thespecimens aged nearly to the peak strength, the positive temperature dependence of yield stress is observed inthe temperature range. The shift of peak positions in the aging curves are explained in terms of the positive tem-perature dependence of cutting stress and the negative temperature dependence of by-passing stress.(Received August 30, 2011; Revised September 15, 2011; Accepted October 4, 2011)Key words: aluminum-lithium alloy, mechanical property, strain rate dependence, temperature dependence

This paper describes the strain rate effects on flow and failure properties of pure tantalum. The strain rate dependent plastic behavior was determined from both quasistatic and split Hopkinson bar (SHB) tests. The competing effect of strain rate and inertia on the onset of necking, post-elongation, and strain to failure (ductility) was investigated. The quasistatic tests were performed at strain rates 0.001, 1, and 10/sec. The strain rates in the SHB tests ranged between 700 and 1600/sec. Under quasistatic loading, the strain hardening in tantalum was found to be rate sensitive. The strain hardening coefficient (n) decreased continually from a maximum value of about 0.28 to almost 0 in the quasistatic loading regime. In the SHB tests, it was not possible to determine the shape of the stress-strain curves for strains less than 5% due to spurious wave reflections. Nonzero positive values forn at high strain rates were obtained through viscoplastic, constitutive modeling. The flow stress at SHB strain rate levels was almost twice the quasistatic value at a strain rate of 0.001/sec, indicating significant strain rate sensitivity in tantalum. Both the ductility and ultimate strain decreased with increasing strain rate under the quasistatic loading regime reaching a minimum of 0.36 and about 0.02, respectively, at 10/sec. While the ductility remained at this level in the SHB (dynamic) loading regime, the ultimate strain (at the onset of necking) increased to values greater than 0.1, indicating deformation stability due to inertia.

The response of metallic foams to a high strain or high stress rate loading has received increased attention in recent years due to their potential to absorb large amounts of energy during plastic deformation and crushing (see, e.g., Thornton and Magee [1]). Research of the mitigation of blast effects indicates that the high-energy absorption characteristic of metallic foams makes them very useful as protective layers of critical structural elements. Consequently, understanding the material dynamic properties of metallic foams will enable engineers to better utilize their energy absorption characteristics. Aluminum foam (Al-foam) is a lightweight material with excellent plastic energy absorbing characteristics [2]. The implementation of bare Al-foam as a protective layer is not practical. The material needs to be a part of a multilayer structure (see, e.g., Seitzberger et al. [3]. The foam layer can be exploited as a protective layer in military vehicles where both lightweight and good energy absorption are needed. The ability of aluminum foams to reduce the explosion-generated blast-induced damage from concrete slabs has been demonstrated in the course of high-explosive (HE) field experiments (see, e.g., Hanssen et al. [4, 5] and Sadot et al. [6]). Several studies have been conducted in order to investigate the constitutive model parameters of Al-foams during the past three decades. The effect of the strain rate was one of the important issues needed to be resolved [7]. A constitutive numerical model was validated in the work of Hanssen et al. [4, 5]. The validation procedure was based on three levels: (a) material calibration; (b) non-uniformed compression test at the material level; and (c) numerical validation at the structural interaction level. Several material models from the LS-DYNA library were calibrated. However, discrepancies between the models were found even for relatively simple load configurations. The most important conclusion noted by the authors was the need for further development of more robust fracture models for the Al-foam. This conclusion is crucial especially since there are increasing numbers of Al-foam manufacturers. Various experimental facilities were used to dynamically load the Al-foam at large ranges of strain and stress rates. In the work of Dannemann and Lankford Jr. [8], closed-cell Al-foams were assessed under static and dynamic loads in the strain rate range of 400–2500 s−1. This range was achieved by using split Hopkinson bar apparatuses. It was found that the strain rate effect is significant in high density Al-foams. Deshpande and Fleck [9] suggested that the initial elastic modulus was lower than that of fully dense alloys. Deformation in the cell walls led to stress concentration around the deformation zones, which resulted in a decrease of the modulus. Some inconclusive results regarding the dependence of the stress–strain curve on the strain rate were presented. Deshpande and Fleck [9] and Paul and Ramamurty [10] did not notice any strain rate dependency, in contrast to the findings of Dannemann and Lankford [8] and Paul and Ramamurty [10]. In a later work by Wang et al. [11], experiments were done using an Instron compression machine at strain rates ranging from 10−3 s−1 up to 450 s−1. Strain–stress curves constructed and distinct strain rate dependency was noted. In the work of Bastawros et al. [12] efforts were made to understand the morphology of the Al-foam during its collapse. Explanation was given to the cell deformation. However, some observations have been ignored and not fully explained even though some key elements of the deformation were identified. The dynamic behavior of Hydro/Cymat Al-foam material was investigated by Tan et al. [13] under different load conditions. The plastic collapse, the plateau range, and the strain at which the deformation occurred were found. It was demonstrated that the dynamic response depends on the direction of the load with respect to the plate manufacturing orientation. Some load enhancement was observed and was explained by micro-inertial effects. Postimpact observation of partly crushed specimens revealed that the deformation is through crush bends. Feng et al. [14] conducted experiments to investigate the rate dependence of Al-foams having different relative densities. They found that the effect of strain rate increases while increasing the Al-foam density as was found by others. For Al-foams with a relative density of 15 % there was little effect of the strain rate while for heaver foams significant strain rate effect was noted.

In order to study the mechanical properties of NEPE propellant at low and high strain rates, the quasi-static and impact eperiments of NEPE propellant were carried out by the electronic universal testing machine and split Hopkinson bar, and the stress-strain curves of NEPE propellant under different strain rates (1.667×10−4−4 500 s−1) were obtained by processing the experiment data. By analyzing the stress-strain curve of low and high strain rates experiment, it can be found that NEPE propellant has obvious nonlinear elasticity and strain rate sensitivity. With the increase of strain rate, the strength, yield stress and elastic modulus of the material increase significantly. Compared with low strain rate, the strain rate sensitivity of the material at high strain rate is higher. Under the high speed impact, a large amount of heat is generated inside the material and cannot be released in time, which makes the internal temperature of the material rise, leading to softening effect of the material and reduction of mechanical properties. In this paper, a nonlinear visco-hyperelastic constitutive model is established to describe the mechanical properties of NEPE propellant at low and high strain rates, in which the Rivlin strain energy function is used to describe the static hyperelastic behaviour, and an integral constitutive model is used to characterize the dynamic response of the material. Considering that the relaxation time has strain rate correlation, a rate-dependent relaxation function is adopted in this paper to replace the traditional Prony series. The hyperelastic parameters were obtained by fitting the hyperelastic part of the constitutive model with extremely slow compression experiment data, and then the other parameters were obtained by fitting the constitutive model with quasi-static and dynamic experiment data. It was proved that the model could well describe the mechanical properties of NEPE propellant at low and high strain rates by the good coincidence degree between the prediction curve and the experiment curve under different strain rates.

The split-Hopkinson pressure bar (SHPB) provided a technique to determine the high strain rate response for low density foams and solid ABS and polypropylene plastics. These materials are used in the interior safety panels of automobiles and crash test dummies. Because the foams have a very low impedance, polycarbonate bars were used to acquire the strain rate data in the 100 to 1600 l/s range. An aluminum SPHB setup was used to obtain the solid plastics data which covered strain rates of 1000 to 4000 l/s. The curves for peak strain rate versus peak stress for the foams over the test range studied indicates only a slight strain rate dependence. Peak strain rate versus peak stress curves for polypropylene shows a strain rate dependence up to about 1500 l/s. At that rate the solid poly propylene indicates no strain rate dependence. The ABS plastics are strain rate dependent up to 3500 l/s and then are independent at larger strain rates.

Interface tensile and fracture behavior of the Ti/Al3Ti Metal-Intermetallic Laminate (MIL) composite under quasi-static and high strain rates

Hot tensile tests were carried out to investigate hot ductility behavior and critical temperature range (ΔT) between zero strength temperature (ZST) and zero ductility temperature (ZDT) of tool steel grades AISI L3 and O1. The test specimens solidified from melting at cooling rate of 0.5℃/s and 3℃/s to the test temperature in the range between liquidus and 900℃. The specimens were then strained to failure at strain rate of 2x10⁻³/s and 2x10⁻²/s. Quenching test was carried out in order to investigate the microstructure occurred during hot tensile test. The microstructure that appeared in quenched specimen was then identified with SEM-EDX. It was found that the critical temperature range of the steels solidified at the slow or the fast cooling rate, widened with increasing strain rate. The specimens which solidified at slow cooling rate when tensile strained to failure at low or high strain rate, had wider critical temperature range than the specimens that solidified at fast cooling rate. For steel grade AISI L3, tensile test at high and low strain rate (after solidified at the fast cooling rate) revealed the hot ductility of 35-65%RA between 900-1250℃. Whereas, the hot ductility of the samples which solidified at slow cooling rate and pulled at slow strain rate were markedly higher than those pulled at higher strain rate between 900-1200℃. Precipitation of manganese sulfide in the interdendritic region resulted in deterioration of hot ductility of steel grade AISI L3. For steel grade AISI O1, tensile tests of specimens solidified between 900-1100℃ at slow cooling rate and low strain rate yielded higher hot ductility than those specimens pulled at high strain rate. The hot ductility of samples at fast cooling rate and low strain rate showed no difference to those samples of hot tested at high strain rate. Nevertheless, slow cooling rate affected hot ductility more than fast cooling rate for tensile tests at both high and low strain rate. Carbide precipitates of vanadium, tungsten and chromium along austenite grain boundaries influenced the ductility loss of steel grade AISI O1.

The compressive and tensile behavior of a 0/90 C fiber woven composite at high strain rates

Yucca mountain is being closely studied as a possible repository for high-level radioactive waste. The rock found at the Yucca Mountain site, i.e. Nevada tuff, is, consequently, of immediate interest. Since it is difficult to obtain samples of the actual Nevada tuff the Apache Leap tuff rock, from Arizona, has been chosen as a similar alternative for this study. The Apache rock was tested in compression at low (10 -4 s -1 ) and high ( 10-2 -10 3 s -1 ) strain rates to evaluate its strain rate dependence. Some of the dynamic tests were performed with a pulse shaper. Strain in the sample was measured with strain gages. Numerical simulations of the full Hopkinson Bar with and without pulse shaper were performed with LS-DYNA. These were very useful in understanding interpretation of the experimental results. Both incident and output waves measured in the SHPB compared very well with the waves obtained from LS-DYNA simulations, confirming that the constitutive model used for the rock was a realistic one. The main conclusions from this work are: 1) The SHPB is a reliable method to obtain the constitutive model of the rock at high strain rates. 2) The pulse shaper use is advised but not compulsory to obtain reliable data, 3) the Apache luff rock is not strongly sensitive to strain rate.

The effects of loading-direction and strain-rate on the mechanical behaviors of human frontal skull bone

Short fibre and hybrid carbon fibre PEEK composite materials were tested in tension and compression under quasi-static and high strain rate conditions to observe the strain rate dependence. Multiple temperatures including room temperature, ＋85 and −50 °C were used to investigate the temperature dependence of the materials. The hybrid laminate comprised a consolidated short fibre core reinforced with outer UD plies in the 0°orientation to provide maximum reinforcement whilst minimising the quantity of expensive UD composite used. Under compression, the beneficial effect of the hybridisation strategy was observed for all high-strain rate testing conditions, where the hybrid laminate outperformed the response of the individual constituents in terms of strength and strain rate dependency. The outer unidirectional (UD) layers contributed to confining the short fibre core, providing superior structural integrity. Under tension, the response was dominated by the UD layers with a 288% increase in strength at room temperature over the short fibre material. However, in the high temperature quasi-static case, the strength was dramatically reduced, by 64%, due to the debonding of the UD reinforcement. This study shows the suitability of hybrid composites for impulsive applications and provides material parameters for the future design of composite structures subjected to impact events.

This paper presents an extended method for determining flow curves under shear loading using torsion tests, a technique often used to characterize plastic behavior in metal forming. Torsion tests are advantageous due to their ability to achieve flow curves up to large strains (~3) while maintaining stable specimen geometry during deformation. However, the strain and strain rate distribution across the specimen are non-uniform, increasing radially from the rotation axis. Traditional analytical methods, such as the Fields and Backofen approach, address this non-uniformity by considering average strain and strain rates. Conversely, inverse approaches, which rely on fitting constitutive equations through iterative procedures, are more sensitive to the choice of empirical equations and can be computationally expensive. To address these issues, this study adapts an inverse piecewise flow curve determination method from compression tests for use in torsion tests. A stepwise methodology is proposed to calculate constant strain rates and isothermal flow curves, where flow curves for the lowest strain rates are first determined and subsequently used to derive flow curves at higher strain rates. The proposed approach was applied to the case-hardened steel 16MnCrS5, with tests conducted at temperatures ranging from 900 °C to 1100 °C and strain rates from 0.01 s−1 to 1 s−1. The experimental data obtained were successfully replicated by the flow curves with a maximum deviation of only 1%. The results demonstrate the efficiency and accuracy of the stepwise inverse approach for determining flow curves in torsion tests, making it appropriate for characterizing material behavior for metal-forming applications.

Dynamic mechanical response and fracture mechanism of granite with structural plane containing planar and circular filling simultaneously: The influence of extension length

The main concern of this work is the mechanical characterization of adhesively bonded assemblies under dynamic shear loading ranging from quasi-static (10 −4 s −1) up to high (10 4 s −1) strain rates. The double-lap shear sample is proposed and a bonding procedure is established. The assemblies are made of steel substrates bonded with an epoxy adhesive. Two surface treatments of the substrates are considered: ethanol and sand shooting. The shear strength and the failure strain are measured by taking into account the testing setups accuracy and the non-uniform distribution of the stress and strain fields in the overlap region. The sensitivity of the strength and the failure strain to the strain rate is highlighted; it is found that the failure strain decreases and the shear strength increases with the strain rate until reaching a maximum value then it drops for very high strain rates.