Effect of strain rate on cushioning properties of molded pulp products

Molded pulp product is widely used in distribution chains as a cushioning packaging of industrial products due to its favorable cushioning capability. How to evaluate the cushioning capability of molded pulp product is the key issue many scholars are interesting in. The load carrying capacity and energy absorbing of the molded pulp products used in the cushion packaging of mobile phones both in the static compression and dynamic impact were investigated in this paper by applying the experiment and finite element analysis. The static compression was conducted with the compression speed of 12 mm/min corresponding to the nominal strain rate 3.8 × 10⁻³ s⁻¹, and the dynamic impact tests were conducted with three drop heights of 25, 50 and 80 cm corresponding respectively to the nominal strain rates 4.2 × 10¹, 6.0 × 10¹ and 7.5 × 10¹ s⁻¹. The high speed camera was used to record the dynamic impact process and deformation. The finite element model of molded pulp product was built, and the stress and displacement nephograms, the dynamic impact deformation process, the load–displacement curve and the energy absorption curve of the molded pulp product were archived. The comparison between the finite element analysis and the experiment was made. The load–displacement curve of the finite element analysis is in agreement with that of the experiment in the static compression, and the energy absorption curves of the finite element analysis with different nominal strain rates are in agreement with that of the experiment in the area of the point of optimum energy absorption. However, a growing gap between the finite element analysis and the experiment appears with the nominal strain rate increasing, which may be induced by the use of the static stress–strain curve of the material in the finite element analysis of dynamic impact. The molded pulp product experiences the process from structural deformation, local stress concentration, first local buckling, redistribution of stress, global buckling, to structural dilapidation and densification. Two obvious buckling processes occur because of its complicated structure and two layers in structure. However, some additional local buckling also occur before the global buckling of structure in the case of dynamic impact with higher nominal strain rate. The deformation processes of molded pulp product from the finite element analysis and the experiment recorded by high-speed camera are coincident. With the nominal strain rate increasing, the yield stress of molded pulp product increases obviously, and the shoulder point of the energy absorption curve moves upward to the right. The yield stress under the dynamic impact at a drop height of 80 cm increases 59.4% compared with that under the static compression, and the corresponding optimum energy absorption increases 85.4%. The effects of strain rate on the load carrying capacity and the energy absorption of molded pulp product are remarkable. The results can be applied to the design of molded pulp products.     

Strain rate dependent plastic mutation in a bulk metallic glass under compression

This paper reported a strain rate dependent plasticity in a Zr-based bulk metallic glass (BMG) under axial compression over a strain rate range (1.6 × 10⁻⁵–1.6 × 10⁻¹ s⁻¹). The fracture strain decreased with increasing strain rate up to 1.6 × 10⁻³ s⁻¹. A “brittle-to-malleable” mutation occurred at strain rate of 1.6 × 10⁻² s⁻¹, subsequently, the macro plasticity vanished at 1.6 × 10⁻¹ s⁻¹. It is proposed that the result is strongly related to the combined action of the applied strain rate, the compression speed, and the propagating speed of the shear band. When the three factors coordinated in the optimal condition, multiple mature shear bands were initiated simultaneously to accommodate the applied strain, which propagated through the specimen and distributed homogeneously in space, dominating the overall plastic deformation by consuming the entire specimen effectively.     

Hot tensile deformation behaviors and constitutive model of 42CrMo steel

The hot tensile deformation behaviors of 42CrMo steel are studied by uniaxial tensile tests with the temperature range of 850–1100 °C and strain rate range of 0.1–0.0001 s⁻¹. The effects of hot forming process parameters (strain rate and deformation temperature) on the elongation to fracture, strain rate sensitivity and fracture characteristics are analyzed. The constitutive equation is established to predict the peak stress under elevated temperatures. It is found that the flow stress firstly increases to a peak value and then decreases, showing a dynamic flow softening. This is mainly attributed to the dynamic recrystallization and material damage during the hot tensile deformation. The deformation temperature corresponding to the maximum elongation to fracture increases with the increase of strain rate within the studied strain rate range. Under the strain rate range of 0.1–0.001 s⁻¹, the localized necking causes the final fracture of specimens. While when the strain rate is 0.0001 s⁻¹, the gage segment of specimens maintains the uniform macroscopic deformation. The damage degree induced by cavities becomes more and more serious with the increase of the deformation temperature. Additionally, the peak stresses predicted by the proposed model well agree with the measured results.     

The flying wedge: A method for high-strain-rate tensile testing. Part 1. Reasons for its development and general description

The flying wedge is a dynamic tensile testing facility which is capable of generating strain rates from around 10² s⁻¹ up to in excess of 10⁴ s⁻¹. While the wedge concept was originally conceived as stop-gap method of making use of an existing facility, it was recognised that such an arrangement offered the advantage of simultaneously applied, true tensile loading at both ends of a test piece. The device has provided a valuable facility for conducting tests to explore the effects of strain rate, state-of-stress and temperature on the deformation and fracture of ductile materials and for the validation of DYNA codes for use in this area.     

The mechanical properties of ionoplast interlayer material at high strain rates

Ionoplast material has been recently introduced and extensively used as interlayer material for laminated glass to improve its post-glass breakage behavior. Due to its sound mechanical performance, the applications of laminated glass with ionoplast interlayer have been widely extended to the protection of glass structures against extreme loads such as shock and impact. The properties of this material at high strain rates are therefore needed for properly analysis and design of such structures. In this study, the mechanical properties of ionoplast material are studied experimentally through direct tensile tests over a wide strain rate range. The low-speed tests are performed using a conventional hydraulic machine at strain rates from 0.0056 s⁻¹ to 0.556 s⁻¹. The high strain-rate tests are carried out with a high-speed servo-hydraulic testing machine at strain rates from approximately 10 s⁻¹ to 2000 s⁻¹. It is found that the ionoplast material virtually exhibits elasto-plastic material properties in the strain rate range tested in this study. The testing results show that the material behavior is very strain-rate dependent. The yield strength increases with strain rate, but the material becomes more brittle with the increase in strain rate, with the ultimate strains over 400% under quasi-static loading, and decreasing to less than 200% at strain rate around 2000 s⁻¹. The testing results indicate that simply applying the static material properties in predicting the structure responses of laminated glass with ionoplast interlayer subjected to blast and impact loads will substantially overestimate the ductility of the material and lead to inaccurate predictions of structure response. The testing results obtained in the current study together with available testing data in the literature are summarized and used to formulate the dynamic stress–strain curves of ionoplast material at various strain rates, which can be used in analysis and design of structures with ionoplast material subjected to blast and impact loads.     

Modeling quasi-static and high strain rate deformation and failure behavior of a (±45) symmetric E-glass/polyester composite under compressive loading

Quasi-static (1 × 10⁻³–1 × 10⁻² s⁻¹) and high strain rate (∼1000 s⁻¹) compressive mechanical response and fracture/failure of a (±45) symmetric E-glass/polyester composite along three perpendicular directions were determined experimentally and numerically. A numerical model in LS-DYNA 971 using material model MAT_162 was developed to investigate the compression deformation and fracture of the composite at quasi-static and high strain rates. The compressive stress–strain behaviors of the composite along three directions were found strain rate sensitive. The modulus and maximum stress of the composite increased with increasing strain rate, while the strain rate sensitivity in in-plane direction was higher than that in through-thickness direction. The damage progression determined by high speed camera in the specimens well agreed with that of numerical model. The numerical model successfully predicted the damage initiation and progression as well as the failure modes of the composite.     

The high strain-rate fracture behaviors of gray iron under compressive loading

This research studied the high strain-rate fracture behavior of a brittle metallic material under compressive loading. Gray cast iron was chosen as an ideal metal for such purpose. Split Hopkinson pressure bar test was used as experimental method for testing the specimens at the high strain-rate of 762–2526 S⁻¹. Static compression test was performed at a slow rate of 2.4×10⁻⁴ S⁻¹ for comparison purpose. The results indicated that the brittle metallic material does not clearly exhibit strain-rate sensitivity behavior, i.e. the difference between static and dynamic compression energy absorbed values tested at various strain-rates was insignificant. However, the fracture mechanisms were somewhat different. At slow rate, the fracture of gray iron was resulted from the crack propagating gradually and branching together along longitudinal directions of flake graphites. At high rate, it instantaneously appeared that large numbers of microvoids/cracks occurred and coalesced at the sites of flake graphites leading to the final fracture. Metallography and scanning electron microscopy (SEM) were performed to correlate the properties attained to the microstructural features.     

Constitutive modeling for flow stress of 55SiMnMo bainite steel at hot working conditions

The hot deformation behavior of 55SiMnMo bainite steel was studied through isothermal hot compression tests conducted using a Gleeble 3500 at 950–1100 °C, with strain rates of 0.01 s⁻¹ to 10 s⁻¹. A constitutive equation was established using the experimental results to describe the stress–strain relationship based on the dislocation density variation, considering the influence of the dynamic softening mechanism. When dynamic recovery is the only softening mechanism, a constitutive equation for flow stress was obtained from the variation of the dislocation density during hot deformation based on work hardening and dynamic recovery. When dynamic recrystallization occurs, the relationship between the dislocation density and the volume fraction of dynamic recrystallization was used to predict the flow stress after the peak. The reliability of the model was verified through a comparison between the predicted flow stress curves from the model and the experimental data.     

Strain rate and gage length effects on tensile behavior of Kevlar 49 single yarn

In the present paper, Kevlar® 49 single yarns with different gage lengths were tested under both quasi-static loading at a strain rate of 4.2 × 10^?4 s^?1 using a MTS load frame and dynamic tensile loading over a strain rate range of 20–100 s^?1 using a servo-hydraulic high-rate testing system. The experimental results showed that the material mechanical properties are dependent on gage length and strain rate. Young’s modulus, tensile strength, maximum strain and toughness increase with increasing strain rate under dynamic loading; however the tensile strength decreases with increasing gage length under quasi-static loading. Weibull statistics were used to quantify the degree of variability in yarn strength at different gage lengths and strain rates. This data was then used to build an analytical model simulating the stress–strain response of single yarn under dynamic loading. The model predictions agree reasonably well with the experimental data.     

Experimental study on influence of section thickness on mechanical behavior of die-cast AM60 magnesium alloy

Influence of section thickness on mechanical behavior of die-cast AM60 magnesium alloy has been experimentally studied. Tension, compression and shear tests with this material were performed on a universal test machine at strain rates from 5 × 10⁻⁴ s⁻¹ to 5 × 10⁻² s⁻¹. Specimens were cut from plates with five as-cast section thicknesses of 6.5 mm, 5.2 mm, 3.9 mm, 2.6 mm and 1.3 mm. According to the test results, flow stress becomes less sensitive to section thickness with larger section thickness, and the influence of strain rate on flow stress is also decreasing with larger section thickness. At different stress states, the tested material follows the von-Mises yield criterion. And stress state is found to be the main factor influencing the fracture behavior.     

Temperature dependent work hardening in Ti–6Al–4V alloy over large temperature and strain rate ranges: Experiments and constitutive modeling

The plastic deformation behaviors of Ti–6Al–4V alloy over wide ranges of strain rate (from 10⁻⁴ to 10⁴ s⁻¹) and temperature (from 20 to 900 °C) are investigated by the quasi-static and dynamic uniaxial compression tests. The microstructure evolution of Ti–6Al–4V alloy at different temperatures is discussed. Material generates higher ductility and formability when temperature is higher than 500 °C, which leads to the decrease of work hardening rate. The true stress–strain responses are modeled with the JC, modified JC, KHL and modified KHL models. In detail, a temperature dependent work hardening function is introduced into the original JC and KHL models. The parameters of the four models for Ti–6Al–4V alloy are calculated by GA optimization method. The average standard deviations between the experimental and calculated flow stresses range from 4% to 13%, which validates the accuracy of the models. In addition, comparison of flow stresses at dynamic (10,000 s⁻¹), the work hardening rates at dynamic (7500 s⁻¹), as well as the quasi-static jump experiments were proposed to further validate the models. The modified JC and modified KHL models could characterize the temperature dependent work hardening effect for Ti–6Al–4V alloy over large strain rate and temperature ranges.     

Microstructure characteristic for high temperature deformation of powder metallurgy Ti–47Al–2Cr–0.2Mo alloy

Hot compression tests of a powder metallurgy (P/M) Ti–47Al–2Cr–0.2Mo (at. pct) alloy were carried out on a Gleeble-3500 simulator at the temperatures ranging from 1000 °C to 1150 °C with low strain rates ranging from 1 × 10⁻³ s⁻¹ to 1 s⁻¹. Electron back scattered diffraction (EBSD), scanning electron microscope (SEM) and transmission electron microscope (TEM) were employed to investigate the microstructure characteristic and nucleation mechanisms of dynamic recrystallization. The stress–strain curves show the typical characteristic of working hardening and flow softening. The working hardening is attributed to the dislocation movement. The flow softening is attributed to the dynamic recrystallization (DRX). The number of β phase decreases with increasing of deformation temperature and decreasing of strain rate. The ratio of dynamic recrystallization grain increases with the increasing of temperature and decreasing of strain rate. High temperature deformation mechanism of powder metallurgy Ti–47Al–2Cr–0.2Mo alloy mainly refers to twinning, dislocations motion, bending and reorientation of lamellae.     

Failure of AA 6061 and 2099 aluminum alloys under dynamic shock loading

Microstructural aspects of the deformation and failure of AA 6061 and AA 2099 aluminum alloys under dynamic impact loading are investigated and compared with their responses to quasi-static mechanical loading in compression. Cylindrical specimens of the alloys, heat-treated to T4, T6 and T8 tempers, were subjected to dynamic compressive loading at strain rates of between 2800 and 9200 s⁻¹ and quasi-static compressive loading at a strain rate of 0.0032 s⁻¹. Plastic deformation under the dynamic impact loading is dominated by thermal softening leading to formation of adiabatic shear bands. Both deformed and transformed shear bands were observed in the two alloys. The shear bands offer preferential crack initiation site and crack propagation path in the alloys during impact loading leading to ductile shear fracture. While cracks propagate along the central region of transformed bands in AA 6061 alloy, the AA 2099 alloy failed by cracks that propagate preferentially along the boundary region between the transformed shear bands and the bulk material. Whereas the AA 2099 alloy shows the greatest propensity for adiabatic shear banding and failure in the T8 temper condition, AA 6061 alloy is most susceptible to formation of adiabatic shear bands and failure in the T4 temper. Deformation under quasi-static loading is dominated by strain hardening in the two alloys. Rate of strain hardening is higher for naturally aged AA 6061 than the artificially aged alloy, while the strain hardening rate for the AA 2099 alloy is independent of the temper condition. The AA 2099 alloy shows a superior mechanical behaviour under quasi-static compressive loading whereas the AA 6061 shows a higher resistance to impact damage.     

The dynamic mechanical response of SiC particulate reinforced 2024 aluminum matrix composites

The compression properties of the aluminum alloy 2024 metal matrix composites reinforced with 50 vol.% SiC particles were investigated using Instron testing machine and split Hopkinson pressure bar (SHPB) in this paper. The compression stress–strain curves were obtained at the strain rates ranging from 1 × 10^− 3 to 2.5 × 10³/s. The fracture surfaces were characterized by scanning electron microscopy. The results showed that SiCp/2024 Al composites exhibited high strain-rate sensitivity. The strength of composites tended to increase–decrease with increasing of strain rates. The effect of the strain rate on elongation was also discussed.     

Effect of processing parameters on the hot deformation behavior of as-cast TC21 titanium alloy

Isothermal compression tests of as-cast Ti–6A1–2Zr–2Sn–3Mo–1Cr–2Nb (TC21) titanium alloy are conducted in the deformation temperature ranging from 1000 to 1150 °C with an interval of 50 °C, strain rate ranging from 0.01 to 10.0 s⁻¹ and height reductions of 30%, 45%, 60% and 75% on a computer controlled Gleeble 3500 simulator. The true stress–strain curves under different deformation conditions are obtained. Based on the experimental data, the effects of deformation parameters on the hot deformation behavior of as-cast TC21 alloy were studied. The deformation mechanisms of the alloy in the whole regimes are predicted by the power dissipation efficiency and instability parameter and further investigated through the microstructure observation. It is found that at the height reductions of 30%, 45% and 60%, the softening of stress–strain curves at high strain rate (>1.0 s⁻¹) is mainly associated with flow localization, which is caused by local temperature rise, whereas at low strain rate, the softening is associated with dynamic recrystallization (DRX). However, the instability showed in flow localization occurs at low strain rate of 0.01 s⁻¹ when the height reduction reaches 75%. In addition, the effects of strain rate, deformation temperature and height reduction on microstructure evolution are discussed in detail, respectively.     

Modeling the constitutive relationship of powder metallurgy Al–W alloy at elevated temperature

The deformation behavior of Al–W alloy was researched with isothermal compression tests at various deformation temperatures and strain rates to evaluate the deformation activation energy and to develop the constitutive relationship equation, which is in pursuit of revealing the dependence of the flow stress on the strain, strain rate and deformation temperature. The compression tests were conducted in the temperature range between 420 and 570 °C and at strain rates between 0.001 and 5.0 s⁻¹. With the help of determination of related material constants (such as A, β and α) and activation energy Q (451.15 kJ mol⁻¹), the Arrhenius-type constitutive relationship equation of Al–W alloy is developed. It was found that the correlation coefficient R and the AARE is 0.997% and 4.08%, respectively. The results show that the Arrhenius-type model, which considers the combined influence of strain rate and deformation temperature, is able to provide the accurate prediction of high temperature flow stress for the researched alloy.     

Influence of dynamic strain ageing on mixed mode I/III fracture toughness of Armco iron

Fracture toughness tests under mode I and mixed mode I/III loading were carried out at different test temperatures ranging from ambient to 673 K. The dynamic strain ageing (DSA) range in Armco iron was identified to be between 383 and 573 K. A marked increase in fracture toughness was observed in the DSA regime and this correlated with the increase in the strain hardening exponent. The magnitude of fracture toughness, however, decreased with increasing loading angle. The extent of decrease was high at temperatures below the DSA regime (≤383 K) which can be understood in terms of the nature of the stress field ahead of a mixed mode I/III as well as the operative fracture mechanism. However, at higher temperatures, the effect of mode III in this respect diminished in the DSA regime (383–573 K) due to DSA causing the opposite effect, that is fracture toughness to increase.     

Combined effect of strain-rate and mode-ratio on the fracture of lead-free solder joints

The critical strain energy release rate for the solder joint fracture was measured as a function of the strain rate and the mode ratio of loading. These data are useful in predicting the fracture of solder joints loaded under arbitrary combinations of tension and shear during the impact conditions typical of falling portable electronic devices. In this study, strain rates from quasi-static (close to 0 s^− 1) to 61 s^− 1 were investigated at phase angles from 0 to 60°, typical of the range found in microelectronic devices. Copper–solder–copper double cantilever beam (DCB) model specimens were prepared using SAC305 solder at cooling rates and times above liquidus typical of actual ball grid arrays (BGAs). A drop tester was designed and built to achieve different strain rates at various mode ratios. The critical initiation strain energy release rate, J_ci, increased about 70% from quasi-static to intermediate strain rates, before decreasing by more than 67% from intermediate strain rates to 42 s^− 1.     

Effects of strain rate on transverse tension properties of a carbon/epoxy composite: studied by moiré photography

The dependence on strain rate of the mechanical properties of a high performance carbon fibre/epoxy composite loaded in transverse tension has been investigated. Dog-bone shaped specimens have been tested in quasi-static and dynamic loading conditions. The dynamic tests were performed in a split Hopkinson bar at strain rates between 100 and 800 s⁻¹. A moiré technique combined with high-speed photography, at framing rates of 0.25–1 MHz, was used for extraction of the local strain fields. The transverse mechanical properties were found to have weak or no dependence on strain rate. The average transverse modulus did not depend on strain rate, whereas the strain to and stress at failure were found to increase slightly with increased strain rate. For these dog-bone shaped specimens the strain evaluated by conventional Hopkinson bar technique was found to underestimate the true strain field measured by moiré technique. Finally, the moiré technique facilitated crack-propagation monitoring in real time. Crack speeds up to 2300 m s⁻¹ were measured at transverse crack propagation.     

Hot deformation behavior and microstructural evolution of a modified 310 austenitic steel

To study the hot deformation behavior and microstructural evolution of a new modified 310 austenitic steel, hot compression tests were conducted at the temperature range from 800 to 1100 °C with strain rate of 0.1–10 s⁻¹ and strain of 30–70% using Gleeble 3500 thermal–mechanical simulator. The results showed that the serrated flow curves were caused by the competitive interaction between solute atoms and mobile dislocations. There were some coarsened precipitates on the high angle grain boundaries (HAGBs), which facilitated the nucleation of dynamic recrystallization grains. But these precipitates inhibited the growth of the recrystallization grains, and changed the deformation texture in the matrix. Low angle grain boundaries (LAGBs) decreased, while twin GBs and random HAGBs and increased as dynamic recrystallization occurred. Dynamic recrystallization occurred more readily at evaluated temperature or high strain rate. The true stress decreased with the reduction of LAGBs percent. The internal connections between mechanics and microstructures were also discussed.