Strain Softening Region Research Articles

Study on dynamic deformation-damage-ignition mechanism of GAP/RDX/TEGDN propellant

ABSTRACT Investigations on high-energy and low-vulnerability propellants can provide a better understanding for improving the operational effectiveness and survivability of strategic and tactical missiles. In the present study, the dynamic compressive mechanical properties and damage-ignition response mechanism of the GAP/RDX/TEGDN (GRT) propellant under high strain rates have been studied using a split Hopkinson pressure bar apparatus and a high-performance high-speed camera. The experimental results suggested that the mechanical properties of the GRT propellant, in terms of yield stress, initial compressive modulus, and ultimate stress, were greatly affected by the loaded strain rate. The true stress-strain curves exhibited an initial linear elasticity region followed by yielding a subsequent strain hardening and strain softening region stage. It has been found that the yield stress and ultimate stress increased with the strain rates. Moreover, at higher strain rates, the impulse increases significantly, leading to earlier and more intense ignition. The critical strain rate and the critical impulse of the GRT propellant are 5000 s−1 and 13.28 N · s, respectively. A judgment basis for GRT propellant ignition is established. Finally, according to the high-speed images and the posttest SEM images, it has been concluded that the dominant ignition mechanism of GRT propellant is flow at the macroscopic level and internal frictional heating at the mesoscopic level.

Numerical investigation of the penetration of torpedo anchors in sand-overlying-nonhomogeneous clay deposit

This study presents a comprehensive investigation of torpedo anchors penetrating into sand-overlying-nonhomogeneous clay deposit, with the main objective of predicting the anchor embeddment depth after it penetrates through the top sand layer. The behavior of the torpedo anchor and soil failure mechanisms during the installation process are analyzed using large deformation finite element (LDFE) methods. To validate the numerical models, comparisons are made with data from existing centrifuge and field tests. An extensive parametric study is then conducted, exploring a wide range of soil properties, soil layer thickness, anchor velocities, and parameters related to torpedo anchor geometry. Two intriguing findings emerge from the analysis. Firstly, there is an evolving soil failure, with the strain-softening region expanding in the clay near the boundary between the two soil layers. Secondly, the velocity profile during both the acceleration and deceleration stages varies with different sand layer thicknesses, displaying a nonlinear relationship with the anchor's final embedment depth. Based on the findings, a simple design procedure is developed to account for the influencing factors on the anchor installation depth. This procedure is expected to be valuable for engineers seeking to estimate the behavior of torpedo anchor installations in sand-overlying-nonhomogeneous clay soil deposits.

A Study on the Effect of Doping Metallic Nanoparticles on Fracture Properties of Polylactic Acid Nanofibres via Molecular Dynamics Simulation.

All-atom molecular dynamics simulations are conducted to elucidate the fracture mechanism of polylactic acid nanofibres doped with metallic nanoparticles. Extensional deformation is applied on polymer nanofibres decorated with spherical silver nanoparticles on the surface layer. In the obtained stress-strain curve, the elastic, yield, strain softening and fracture regions are recognized, where mechanical parameters are evaluated by tracking the stress, strain energy and geometrical evolutions. The energy release rate during crack propagation, which is a crucial factor in fracture mechanics, is calculated. The results show that the presence of doping nanoparticles improves the fracture properties of the polymer nanofibre consistently with experimental observation. The nanoparticles bind together polymer chains on the surface layer, which hinders crack initiation and propagation. The effect of the distribution of nanoparticles is studied through different doping decorations. Additionally, a discussion on the variation of internal energy components during uniaxial tensile loading is provided to unravel the deformation mechanism of nanoparticle-doped nanofibres.

POST-PEAK RESPONSE AUTOMATIC SOLUTIONS IN STRUCTURAL ENGINEERING PROBLEMS – A REVIEW

The ill-condition of stiffness matrix at the unstable region for example at the strain-softening region, the load control method will not be valid to give the solution therefore the displacement control method is essential to use. The stiffness matrix is changed at different steps by used load control and solution is found using any nonlinear solution method of Newton’s family. Therefore, Newton’s method will not give a solution to the unstable region. The iteration method and solution process may also stop when the diagonal element of the stiffness matrix becomes negative or zero if Newton's method is adopted. These difficulties need to be overcome and a non-positive definite stiffness matrix is retained and used for iteration in the arc-length method. A scientific review of literature has been made to pinpoint the difficulties faced in the prediction of complete load-displacement response of structures and techniques available to overcome the same. Displacement control methods have been reviewed with emphases on the arc length methods which can be integrated with the traditional finite element method.

Triaxial tension-induced damage behavior of nanocrystalline NiTi alloy and its dependence on grain size

This study focused on the effect of grain size (GS) on dynamic damage performance of nano-crystalline nickel titanium (NC NiTi) alloy. Molecular dynamics simulations were conducted to triaxially expand it at a high strain rate (4 × 109 s−1), while the temperature and initial pressure remained 300 K and 0 bar, respectively. It was discovered that the superelastic NiTi alloy exhibited the similar damage response as ductile metallic materials, which was vividly characterized by void nucleation, growth, and coalescence. The stress-strain curves demonstrated that the void nucleations always occurred near the start of the strain softening region at various grain sizes. Interestingly, it was discovered that the void evolution was characteristic of an almost double-linear behavior, and the piecewise linearity became more prominent for the void volume fraction increase at larger grain size. More importantly, the fracture behavior was found to be strongly dependent upon the grain size in the NC NiTi alloy. For small grain size, the existing voids propagated along the grain boundaries and in the grains, leading to intergranular and transgranular fracture. Contrarily, the intergranular-dominated fracture was responsible for the void propagation in the large grain. In addition, the starting time, ending time, and threshold of void nucleation were found to be weak sensitivity to GS, and a reverse effect was appropriate to the void growth. The results highlighted that as the GS increased, more complete stress relaxation and shorter duration time were produced, leading to larger void volume fraction and faster growth rate.

Structural Evolution of LLDPE-LMW/HMW Blend during Uniaxial Deformation as Revealed by In Situ Synchrotron Radiation X-ray Scattering

The structural evolutions of LLDPE-LMW/HMW blend during uniaxial deformation at temperatures of 80 and 120 °C were investigated by the in situ synchrotron radiation small- and wide-angle X-ray scattering (SR-SAXS/WAXS). The magic sandwich echo (MSE) sequence was used to detect a virtually dead-time-free induction decay (FID) for solid-state NMR analysis. The thermal property of the blend was first checked by DSC, and the temperature dependence of the overall crystallinity was obtained by MSE-FID. The onset melting temperature is determined to be 116 °C (DSD), and the enhanced π-flip motions in the crystalline domains are clearly observed at T > 60 °C by MSE-FID. For deformation at 80 °C, the lamellae become staggered in the strain-softening region as shown by the four-point SAXS pattern, whereas further deformation leads to the melting-recrystallization in the strain-hardening region. For deformation at 120 °C, the six-point SR-SAXS signal appears just after the four-point SR-SAXS signal, which indicates the formation of new lamellae along deformation direction. In addition, no phase transition occurs in the whole deformation process at both temperatures. Current work shows the detailed temperature dependence microstructural evolution of LLDPE-LMW/HMW blend. This is expected to provide more structural information for correlating microscopic structure with macroscopic mechanical performance.

Compression Behavior of Al-Mg Phases, Molecular Dynamics Simulation

Aluminum alloys development always exit in the manufacturing process. Al/Mg alloys have been attracted significant attention because of their excellent mechanical properties. The microstructural evolution and deformation mechanisms are still challenging issues, and it is hard to observe directly by experimental methods. Accordingly, in this paper atomic simulations are performed to investigate the uniaxial compressive behavior of Al/Mg phases; with different ratio of Mg ranging from 31% to 56%. The compression is at the same strain rate (3.1010s⁻¹), at the same temperature (300K) and pressure, using embedded atom method (EAM) potential to model the interactions and the deformation behavior between Al and Mg.From these simulations, we get the radial distribution function; the stress–strain responses to describe the elastic and plastic behaviors of β-Al3Mg2, ε-Al30Mg23, Al1Mg1and γ-Al12Mg17phases with 31, 41, 50 and 56% of Mg added to pure aluminum, respectively. The mechanical properties, such as Young’s modulus, elasticity limit and rupture pressure, are determined and presented. The engineering equation was used to plot the stress-strain curve for each phase.From the results obtained, the chemical composition has a significant effect on the properties of these phases. The stress-strain behavior comprised elastic, yield, strain softening and strain hardening regions that were qualitatively in agreement with previous simulations and experimental results. These stress-strain diagrams obtained show a rapid increase in stress up to a maximum followed by a gradual drop when the specimen fails by ductile fracture. Under compression, the deformation behavior of β-Al3Mg2and γ-Al12Mg17phases is slightly similar. From the results, it was found that ε-Al30Mg23phase are brittle under uniaxial compressive loading and γ-Al12Mg17phase is very ductile under the same compressive loading.The engineering stress-strain relationship suggests that β-Al3Mg2and γ-Al12Mg17phases have high elasticity limit, ability to resist deformation and also have the advantage of being highly malleable. From this simulation, we also find that the mechanical properties under compressive load of ε-Al30Mg23phase are evidently less than other phases, which makes it the weakest phase. The obtained results were compared with the previous experimental studies, and generally, there is a good correlation.The Al-Mg system was built and simulated using molecular dynamics (MD) software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator).

Variable-order fractional description of compression deformation of amorphous glassy polymers

In this paper, the variable order fractional constitutive model is adopted to describe the compression deformation of amorphous glassy polymers. In order to keep the fractional order within the definition of viscoelasticity, a three-regions- fitting-method is proposed. By using this, the value of fractional order is found to be a constant in viscoelastic region, and decreases linearly in both strain softening and strain hardening regions. The corresponding mechanical property evolution revealed by fractional order is proved to be reasonable based on the molecular chains conflict theory. And a comparison study is conducted to show the advantage of using the variable order fractional model with higher accuracy and fewer parameters. It is then concluded that the variable order fractional calculus is an efficient tool to predict the compression deformation of amorphous glassy polymers.

Formation of liquid crystal/gel emulsions to nano-emulsions constructed by polyalkoxylated fatty alcohol (PAFA)-based mixed surfactant systems

In the construction of ternary phase diagrams, the polyalkoxylated fatty alcohol (PAFA)-based mixed surfactant systems including PAFA-AS (alkyl sulfonate), PAFA-CB (cocamidopropyl betaine) and PAFA-APG (alkyl polyglucosides) were used to develop self-standing liquid crystal/gel emulsions containing rapeseed oil methyl esters (ROME) and water. The formation of liquid crystal/gel emulsions are observed at semi-dilute regions of the phase diagrams. A pre-emulsion was chosen from each of PAFA-AS, PAFA-CB and PAFA-APG systems for minor modification with sodium silicate. Upon aqueous dilution of the modified pre-emulsions to weight fractions (Φw) of 0.8 and 0.6 and with an isothermal shaker agitation, the samples demonstrate dramatic increases in apparent viscosity with flow resistance and shear thinning behaviour. In oscillatory amplitude study, the emulsions show linear viscoelastic (LVE) plateau (G’>G”) and strain softening region (G”>G’) indicating the samples promote a viscoelastic behaviour. Further affirmation by Cole-Cole plots reveal the emulsion samples behave as a Maxwell fluid. The optical microscope study verifies the emulsions of PAFA-AS, PAFA-CB and PAFA-APG systems comprising of multilamellar vesicles, bicontinuous cubic phase and multilamellar phase, respectively. Upon aqueous dilution of the liquid crystal/gel emulsions with an isothermal agitation, the formation of nano-emulsion droplets is confirmed by transmission electron microscopy (TEM) and dynamic light scattering studies. The nano-emulsions display spherical and elliptical shapes with mean droplet sizes are in the range of 158.37 to 206.43 nm and zeta potential values are in the range of –12.07 to –32.79 mV.

Durability of ultra-high performance concrete in tension under cold weather conditions

Freezing and thawing resistance is a key characteristic for concrete materials in cold weather conditions. In this study, the tensile properties and elastic modulus of ultra-high performance concrete (UHPC) under accelerated freeze-thaw cycles are characterized. Six series of UHPC specimens are experimentally tested with a well-designed direct tension test (DTT) method to capture complete tensile stress-strain responses. Both the dynamic and wave moduli of elasticity of UHPC are measured at specific cycles using the standard impact test and self-designed “smart aggregate” technology, respectively. Long term freezing and thawing cyclic conditioning of UHPC samples results in reductions of elastic modulus, tensile strength, strain capacity, and energy absorption capacity. The tensile stress-strain curves of UHPC demonstrate distinct descending with increasing freeze-thaw cycles, particularly in the strain softening region. The energy-based approach is found to be more sensitive and effective than the elastic modulus-based approach when evaluating material deterioration over time and capturing accumulative material degradation subjected to rapidly-repeated freezing and thawing actions. As from the test results, UHPC is characterized as a very durable cementitious material, but it is not inherently unconquerable. Extended freezing and thawing actions can still lead to deterioration of the material, with respect to its elastic modulus, tensile strength, energy absorption capacity, etc. As demonstrated, the DTT method can be used to effectively characterize the long-term performance of UHPC in tension under cold weather conditions.

Determination of time-dependent strengths of salt pillars based on strain energy principle

The objective of this study is to determine the time-dependent strengths of salt mine pillars in the Maha Sarakham formation, northeast of Thailand. Strain rate-controlled triaxial compression tests have been performed on salt specimens under confining pressures from 0 MPa to 12 MPa. The strain rates are from 10−7 s−1 to 10−4 s−1. The axial stresses and lateral strains are monitored through the strain-softening region. The results indicate that the strengths and elastic moduli increase exponentially with the strain rates. The power creep law parameters are calibrated with the test results, and hence allows constructing series of strain-time curves for the salt pillars under different depths and extraction ratios. The strain energy density principle is applied to develop a strength criterion for the salt pillars. Combining this criterion with the series of the strain-time curves the time-dependent strengths of the salt pillars for different extraction ratios can be predicted.

Aging-dependent strain localization in amorphous glassy polymers: From necking to shear banding

This study investigates the influence of physical aging on the tensile deformation behaviors of poly(ethylene terephthalate)-glycol. The polymers are subjected to a quenched and an annealed heat treatment, followed by deformation in tension. The digital image correlation (DIC) is used to capture the surface strain. The DIC results show that the deformation localization occurs in the post-yield strain softening region. The quenched and annealed polymers exhibit different localization types, representing as necking for quenched polymers and shear banding for annealed polymers. With the help of the DIC, the nucleation and propagation of the localization zones are fully captured. The DIC results show that the reference location with the maximum strain does not change with the deformation. At the same strain level, the maximum strain in the shear bands is much larger than that in the necks, which explains the failure strain of the annealed polymers is smaller than the quenched polymers. The stretch rate also has a strong effect on the localization behaviors. A larger stretch rate results in a stronger localization due to an increase in the amount of strain softening.

Disentanglement induced by uniaxial pre-stretching as a key factor for toughening poly(l-lactic acid) sheets

Poly(l-lactic acid) (PLLA) sheets with dramatic improvement of mechanical properties, especially toughness, were obtained by uniaxial pre-stretching around Tg. It was found that a network structure consisting of cohesional entanglements was formed during the usual compression molding process, leading to the brittleness of PLLA, and the destruction of the network structure due to disentanglement after pre-stretching, leading to the toughness of PLLA. The network structure could not be destroyed when pre-stretching ratio (PSR) was in the elastic deformation region I and strain softening region II (PSR < 0.2). However, when PSR got into the strain hardening region III (PSR = 0.2), the network structure was destroyed resulting from the disentanglement, leading to the brittle to ductile transition. With PSR increasing from 0.2 to 0.4, the orientation was formed in pre-stretched PLLA, leading to further increase of the elongation at break. And then the degree of orientation increased along with the occurrence of the mesophase (PSR ≥ 0.5), therefore, the modulus and strength increased, while the elongation at break decreased. However, the elongation at break was still larger than that of undrawn PLLA.

Revealing the deformation mechanism of amorphous polyethylene subjected to cycle loading via molecular dynamics simulations.

Despite tremendous efforts being devoted to the study of the deformation behavior of polyethylene, the deformation mechanism of an amorphous polyethylene polymer under cycle shear-loading remains largely unknown. Here, we report the cycle shear deformation mechanism of an amorphous polyethylene polymer using molecular dynamics (MD) simulations. The stress–strain behaviors, including the elastic, yield, strain hardening, and strain softening regions, are qualitatively in agreement with the previous results. The values of the yield stress, Young's modulus and ultimate strength obtained from MD simulations are consistent with the previous data. The effects of the shear strain rate, temperature, and cycle shear-loading number on the stress–strain behaviors are investigated. Higher strain rate and a lower temperature result in a higher strength in the amorphous polyethylene polymer, attributed to the agglomeration of high local strains. With the increase of the cycle shear-loading number, the high strain region gradually expands from the upper and lower surface to the interior of the polyethylene polymer matrix, which provides the origin of crack initiation. The energy contributions are used in elucidating the inherent deformation mechanisms within the elastic, yielding, strain hardening, and strain softening regions, and the variation trend of energy is consistent with the stress–strain response.

Learning the deformation mechanism of poly(vinylidine fluoride-co-chlorotrifluoroethylene): an insight into strain-induced microstructure evolution via molecular dynamics.

Learning the micro-mechanisms of fluorinated polymers during mechanical response is more difficult than that of common polymers due to the unique intrinsic characteristics of the fluorine element. In this paper, we applied molecular dynamics simulations to study deformation mechanisms of poly(vinylidine fluoride-co-chlorotrifluoroethylene) during uniaxial tension. We analyzed the variations of individual energy components and structural distribution curves versus strain in addition to the commonly used stress-strain curves and microstructure evolutions during stretching. The elastic limit is ɛ = 0.02, ɛ = 0.06 is the yield point, ɛ = 0.24 is the termination of the softening, necking occurs at 0.24 < ɛ < 0.5, strain hardening occurs at 0.5 < ɛ < 2.6, and ɛ = 2.6 is the damage or brake point. The elastic behavior of the material does not rely on strain rate, the obvious effect of strain rate can be seen at the yield region and strain softening region, and the stress values are not influenced by strain rates at the softening and hardening stages. Overall, total potential energy is mainly correlated with non-bonded energy, and the proportion of ΔEcoul overwhelms all the others. The energy components are ordered: ΔEcoul > ΔEvdwl > > ΔEangle > ΔEdihed > ΔEbond. The chain conformation at yield point is almost unchanged compared with the pre-stretching conformation. The chain conformations at the end of strain softening changes more obviously than that at yield point. The molecular chains maintain random coil structure before strain hardening, and switch into a stretch chain conformation gradually during strain hardening. The maximum change in bond angle during the stretching process is F-C-H, the largest change in bond length is the C-Cl bond, and the largest change in dihedral angle is H-C-C-H. The change of non-bonded interaction in the poly(VDF-co-CTFE) system is much larger than the bonding interaction, and the main factor affecting bonding interaction is the change of angles. Graphical abstract Poly(vinylidine fluoride-co-chlorotrifluoroethylene) during tensionᅟ.

Hardening-softening transition in pre-annealed and slightly deformed Ni70Fe30 nanoalloy

The Effect of slight deformation on microstructure evolution and microhardness variation in pre-annealed Ni70Fe30 nanoalloy has been investigated. An obvious hardening-to-softening transition is observed at the rolling strain of ∼6%. Further x-ray diffraction analysis and transmission electron microscopy observation reveal a accumulation of dislocation, stacking fault and twin fault before the sample deformed to ∼6%, which is considered the dominant contribution to strain hardening. Moreover, despite of rolling the sample at a relative small strain level, obvious grain growth takes place overall deformation process. With the increasing grain size, Ni70Fe30 nanoalloy enters into strain softening region due to a decrease in the quantity of defect densities when the rolling strain exceeds ∼6%.

Combined hardening and localized failure with softening plasticity in dynamics

We present for one-dimensional model for elastoplastic bar with combined hardening in FPZ - fracture process zone and softening with embedded strong discontinuities. The simplified version of the model without FPZ is directly compared and validated against analytical solution of Bazant and Belytschko (1985). It is shown that deformation localizes in an area which is governed by the chosen element size and therefore causes mesh sensitivity and that the length of the strain-softening region tends to localize into a point, which also agrees with results obtained by stability analysis for static case. Strain increases in the softening domain with a simultaneous decrease of stress. The problem unloads elastically outside the strain-softening region. The more general case with FPZ leads to more interesting results that also account for induced strain heterogeneities.

Chemorheology investigation of a glassy epoxy thermoset on tensile plastic flow and fracture morphology

Reproducible and uncharacteristic tensile stress–strain behavior of cured glassy epoxy-amine networks produces distinctive fracture surfaces. Test specimens exhibiting plastic flow result in mirror-like fracture surfaces, whereas samples that fail during yield or strain softening regions possess nominal mirror-mist-hackle topography. Atomic force microscopy and scanning electron microscopy reveal branched nodule morphologies in the 50-nm size scale that may be responsible for the unusual tensile properties. Current hypothesis is that plastic flow of the glassy thermoset occurs through the existence and deformation of these nodular nanostructures. The thermal cure profile of the epoxy-amine thermoset affects the size and formation of the nodular nanostructure. Eliminating vitrification during thermoset polymerization forms a more continuous phase, reduction in size of the nodules, and eliminates the capacity of the material to yield in plastic flow. This maximizes nanostructure connectivity of the glassy epoxy-amine thermoset and reduces strain to failure significantly. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1333–1344.

Effect of 110 keV electrons on the deformation mechanisms of low density polyethylene

The deformation mechanisms of low density polyethylene (LDPE) irradiated by 110 keV electrons with different fluences are discussed basing on the deformation behaviors and the structural evolution during uniaxial tensile deformation. The structural evolution is in-situ obtained from small angle X-ray scattering (SAXS) and wide angle X-ray diffraction (WAXD). It is found that the 110 keV electrons with low fluence change the transition strains of different regions (strain-hardening region, strain-softening region, secondary strain-hardening region, plateau in the strain-softening region and sub-stages in the second strain-hardening region) for LDPE. The 110 keV electrons with high fluence lead to disappearance of the strain-softening region and quick break of the samples. From SAXS and WAXD analyses, it is known that the 110 keV electrons have no effect on the disintegration of the original lamellae and the rotation of the lamellae, only slow down the formation of the new crystals. It is concluded that the crosslinking strengthening generated by 110 keV electrons is the dominant reason for the changes of the deformation behaviors of LDPE.

SPH as a nonlocal regularisation method: Solution for instabilities due to strain-softening

Within the framework of continuum damage mechanics (CDM), mechanical loading leads to material damage and consequent degradation of material properties. This can result in strain-softening behaviour, which when implemented as a local model in the finite element (FE) method, leads to an ill-posed boundary value problem, resulting in significant mesh sensitivity of the solution. It is well-known that the addition of a characteristic length scale to CDM models, a non-local approach, maintains the character of the governing equations. In this paper, the similarities between the Smooth Particle Hydrodynamic (SPH) method and non-local integral regularisation methods are discussed. A 1D dynamic strain-softening problem is used as the test problem for a series of numerical experiments, to investigate the behaviour of SPH. An analytical solution for the test problem is derived, following the solution for a 1D stress state derived by Bažant and Belytschko in 1985. An equivalent SPH model of the problem is developed, using the stable Total-Lagrange form of the method, combined with a local bi-linear elastic-damage strength model. A series of numerical experiments, using both SPH and FE solvers, demonstrate that the width of the strain-softening region is controlled by the element size in FE, but in SPH it is controlled by the smoothing length rather than the inter-particle distance, which is the analogous to the element size in the FE method. This investigation indicates that the SPH method is inherently non-local numerical method and suggests that the SPH smoothing length should be linked to the material characteristic length scale in solid mechanics simulations.