Stress Upturn Research Articles

Crack tip stress intensification in strain-induced crystallized elastomer

Natural rubber (NR) exhibits strain-induced crystallization (SIC), enhancing tearing strength and crack resistance. However, the reinforcement mechanism along with nonuniform strain around a crack tip remains unclear. We reveal the nonuniform stress field around a crack tip using the DIC-based deformation field data and a hyperelasticity approach. A hyperelastic strain energy density function (W) is derived to be able to replicate stress-strain data across various deformations, encompassing equal and unequal biaxial, uniaxial, and pure shear stretching. These data cover the full range and magnitude of deformations around the crack tip. SIC significantly impacts the singular behaviors of strain and stress near the crack tip, causing a pronounced stress increase and strain decrease within the SIC zone that extends up to approximately 100 μm away from the crack tip. This results in a distinct crossover in singularity power-law index between the SIC zone and the fully amorphous zone. With increasing crack opening, the stress upturn intensifies, and the crossover shifts away from the crack tip due to SIC zone enlargement and local crystallinity increase. These findings deepen our understanding of the physics of SIC near crack tips and its reinforcement mechanism in strain-induced crystallizable soft solid materials.

Revisiting the strain rate sensitivity of the flow stress of copper: Theory and experiment

One of the most important issues related to the strength of metals is the strain rate sensitivity of the flow stress. In this study, an analytical model of the flow stress as a function of strain rate is derived theoretically. The model can reproduce the strain rate sensitivity of the flow stress of copper over a wide range of strain rates (up to 109 s−1) quantitatively. Our theoretical derivations indicate that the strain rate sensitivity of the flow stress, especially that above 103 s−1, is a result of both the variation of the dislocation mobility mechanism with stress and the particular stress dependence of dislocation density but is not a result of each single mechanism. In particular, the stress dependence of the dislocation density and the initial dislocation density are critical to the quantitative relation of the flow stress–strain rate at high strain rate and the strain rate threshold, under which the upturn of the flow stress occurs, respectively. Moreover, experiments with copper of different initial dislocation densities at moderate and high strain rate are performed. The strain rate threshold of the flow stress upturn observed in the experiments grows considerably as initial dislocation density increases, which is in accordance with theoretical prediction by our model.

Mechanical properties and microstructure of the heterogeneous DZ2 axle steel under high-strain-rate compression at ambient temperature

This study aims to clarify the mechanical properties and deformation characteristics of the newly-developed DZ27CrNiMo (DZ2) axle steel for the China standard electric multiple units under dynamic loadings along the diameter direction of the axle at room temperature. The DZ2 axle steel has a heterogeneous band structure consisting of equiaxed grain and lath morphology tempered martensite. When being impacted at the strain rate range from 500 s−1 to 2440 s−1, its yield strength, compressive strength, and plastic strain increase. The flow stress upturn after yielding mainly depended on the strain rate effect rather than the work hardening due to the suppressed dislocation cross-slip. Meanwhile, the steady plasticity was consistent with the presence of uniformly distributed dislocations and microbands within the heterogeneous laminates. Although the nanoscale adiabatic shear bands (ASBs) and micro-cracks were found to initiate at the high strain rate of 2440 s−1, their propagation could be inhibited by the hard-tempered sorbate laths. As a consequence, an excellent resistance for impact-induced fracture was realized in DZ2 axle steel. Taking the thermal activation damage evolution into account, a modified Zerilli-Armstrong (ZA) constitutive model was proposed to describe the dynamic mechanical behavior of DZ2 axle steel. The modeling results were consistent with the experimental data, indicating a high prediction accuracy and good application availability in the operation and maintenance of DZ2 axle.

High-Rate Stress Upturn of Brittle Materials

High-Rate Stress Upturn of Brittle Materials

Ductile Materials Stress Upturn at High Strain Rates

Ductile Materials Stress Upturn at High Strain Rates

Research of strain induced crystallization and tensile properties of vulcanized natural rubber based on crosslink densities

Natural rubber (NR) has excellent mechanical properties than synthetic rubber for its strain induced crystallization (SIC) property. It is known that crosslink density has significant influences on SIC, but mechanism of SIC enhanced tensile properties based on crosslink densities has not investigated clearly. In this study, vulcanizates of NR and NR devoid of non-rubber components, characterized by varying crosslink densities, are prepared. Mechanical and crystallization properties and the structure evolution of the systems occurring during stretching are analyzed by conducting tensile tests and using the in-situ (WAXD) technique. Results reveal that the crosslink density significantly affects the mechanical properties and SIC of the NR materials. The maximum tensile strength is recorded when the crosslink density is 1.84 × 10−4 mol/cm3. The structural evolution of the NR vulcanizates characterized by varying crosslink densities is reported, and the strengthening mechanism associated with the systems is proposed. The stretching process associated with the NR vulcanizates can be divided into three stages, namely stages I, II, and III, based on the crystallization process. The NR vulcanizates characterized by low crosslink densities are primarily reinforced by a series of crystallites in stage II of stretching. Stress upturn is realized following the formation of a large number of crystallite networks in stage III. NR vulcanizates characterized by high crosslink densities form parallel reinforcements with the surrounding network post crystallization in stage II, and this can be attributed to the presence of a large number of crosslink chains in the system. Stress upturn can be realized even in the presence of a small number of crystallite networks in stage III. Furthermore, the results indicate that the process of crystallization significantly affects the elongation at break. The influence of crystallization on the elongation at break has different results divided by a critical crosslink density 0.75 × 10−4 mol/cm3. When the crosslink density is lower than the critical crosslink density, the ideal elongation at break is smaller than real elongation at break. While that is higher than the critical crosslink density, the ideal elongation at break is higher than the real. This is because crystallization in stages II and III determine the final elongation at break.

Rod-like Cellulose Regenerated by Bottom-Up Assembly in Natural Rubber Latex and Its Reinforcement.

As a renewable biomass material, nano-cellulose has been investigated as a reinforcing filler in rubber composites but has seen little success because of its strong inclination towards aggregating. Here, a bottom-up self-assembly approach was proposed by regenerating cellulose crystals from a mixture of cellulose solution and natural rubber (NR) latex. Different co-coagulants of both cellulose solution and natural rubber latex were added to break the dissolution equilibrium and in-situ regenerate cellulose in the NR matrix. The SEM images showed that the sizes and morphologies of regenerated cellulose (RC) varied greatly with the addition of different co-coagulants. Only when a 5 wt% acetic acid aqueous solution was used, the RC particles showed an ideal rod-like structure with small sizes of about 100 nm in diameter and 1.0 μm in length. The tensile test showed that rod-like RC (RRC)-endowed NR vulcanizates with pronounced reinforcement had a drastic upturn in stress after stretching to 200% strain. The results of XRD and the Mullins effect showed that this drastic upturn in stress was mainly attributed to the formation of rigid RRC-RRC networks during stretching instead of the strain-induced crystallization of NR. This bottom-up approach provided a simple way to ensure the effective utilization of cellulosic materials in the rubber industry.

Unusual Stress Upturn in Elastomers Prepared Using Macro Cross-Linkers with Multiple Vinyl Side Groups.

In this study, the unique tensile properties of acrylate elastomers prepared using macro cross-linker polymers with multiple vinyl side groups are analyzed. For the preparation of the macro cross-linker, poly(ethyl acrylate) copolymers bearing hydroxy functional groups are synthesized, followed by the hydroxy-isocyanate reaction with 2-isocyanatoethyl acrylate. Subsequently, the elastomers samples are prepared by UV polymerization of ethyl acrylate in the presence of the macro cross-linkers. The tensile properties of the elastomers in the small elongation region are similar to those of typical elastomers prepared using divinyl cross-linkers, whereas the stress upturn in the large elongation region is considerably different. The stress upturn varies based on the fraction of vinyl side groups in the macro cross-linkers, whereas stress in the small elongation region remains unchanged. These properties are analyzed using various theoretical models. The results reveal that there is artificial inhomogeneity in the cross-link density for samples prepared by the macro cross-linkers, where the short poly(ethyl acrylate) strands inside the macro cross-linker limit the overall chain stretchability. On the whole, this study demonstrates a new method for tuning elastomer properties, especially at large deformation.

Yield Surfaces and Plastic Potentials for Metals, with Analysis of Plastic Dilatation and Strength Asymmetry in BCC Crystals

Since the 1980s, constitutive modeling has steadily migrated from phenomenological descriptions toward approaches that are based on micromechanics considerations. Despite significant efforts, crystal plasticity remains an open field of research. Among the unresolved issues are the anomalous behavior of metals at low temperatures and the stress upturn at extreme dynamics. This work is focused on the low-temperature responses of body-centered-cubic (bcc) metals, among them, molybdenum (Mo). At these conditions, the plastic flow strength is governed by the motion of screw dislocations. The resultant non-planarity of core structures and slip causes the following: the shear stress includes non-glide components, the Schmid law is violated, there is a tension-compression asymmetry, and the yield surface and plastic potential are clearly decoupled. We find that the behavioral complexities can be explained by atomistically resolved friction coefficients in macroscopic yield and flow. The plastic flow mechanisms establish the departure point into the follow-up analysis of yield surfaces. For example, we know that while the von Mises stress is explained based on energy considerations, we will also show that the stress has a clear geometric interpretation. Moreover, the von Mises stress is just one case within a much broader class of equivalent stresses. Possible correlations among non-Schmid effects (as represented macroscopically by friction coefficients), volume change (i.e., residual elastic dilatation) from dislocation lines, and elastic anisotropy are investigated. Extensions to the shock regime are also established.

Reinforcement Behavior of Chemically Unmodified Cellulose Nanofiber in Natural Rubber Nanocomposites.

We investigated the reinforcement behavior of small amounts of chemically unmodified cellulose nanofiber (CNF) in eco-friendly natural rubber (NR) nanocomposites. For this purpose, NR nanocomposites filled with 1, 3, and 5 parts per hundred rubber (phr) of cellulose nanofiber (CNF) were prepared by a latex mixing method. By using TEM, a tensile test, DMA, WAXD, a bound rubber test, and gel content measurements, the effect of CNF concentration on the structure-property relationship and reinforcing mechanism of the CNF/NR nanocomposite was revealed. Increasing the content of CNF resulted in decreased dispersibility of the nanofiber in the NR matrix. It was found that the stress upturn in the stress-strain curves was remarkably enhanced when the NR was combined with 1-3 phr CNF, and a noticeable increase in tensile strength (an approximately 122% increase in tensile strength over that of NR) was observed without sacrificing the flexibility of the NR in the NR filled with 1 phr CNF, though no acceleration in their strain-induced crystallization was observed. Since the NR chains were not inserted in the uniformly dispersed CNF bundles, the reinforcement behavior by the small content of CNF might be attributed to the shear stress transfer at the CNF/NR interface through the interfacial interaction (i.e., physical entanglement) between the nano-dispersed CNFs and the NR chains. However, at a higher CNF filling content (5 phr), the CNFs formed micron-sized aggregates in the NR matrix, which significantly induced the local stress concentration and promoted strain-induced crystallization, causing a substantially increased modulus but reduced the strain at the rupture of the NR.

High-Rate Stress Upturn of Ductile and Brittle Materials

Since the 1980s some researchers performed tests on ductile materials (mainly metals) at different strain rates, and saw a substantial increase of stress beyond strain rates of about 103-104/s. They termed this phenomenon high-rate stress upturn. Some 20 years later, other researchers observed a similar behavior in brittle materials (mainly concrete), but here the upturn started at a much lower rate of 1-10/s. Other researchers assumed that stress upturn is the same as flowstress upturn, according to the common approach to viscoplasticity since the 1960s. As a result, they didn’t believe that stress upturn may exist, and performed tests to show that doesn’t. This led to what has been known as the stress upturn controversy. Here we first describe high-rate stress upturn in ductile materials and in brittle materials, and then discuss the stress upturn controversy. We claim that viscoplasticity should be treated with our overstress approach and not with the widely used flowstress approach. When stress upturn is treated in this way, there is no reason to disclaim or deny the existence of stress upturn, and there’s no room for a stress upturn controversy.

Influence of Sepiolite Addition Methods and Contents on Physical Properties of Natural Rubber Composites

The influence of sepiolite loadings (1-10 phr) and sepiolite addition procedures (mill and latex mixing approaches) on properties improvement of natural rubber composites was investigated. The viscosity, curing behavior, and tensile test were used to assess the property changes whereas the rubber-filler interactions was confirmed by using stress relaxation, swelling, Mooney-Rivlin and rheological methods. It was found that the characteristics of rubber composites influenced by both mixing methods and filler contents. Comparing between two different mixing methods, the slower stress relaxation rate and less swelling capability were achieved from mill mixing technique. This method also lowered the strain where the upturn of stress was occurred as suggested by Mooney-Rivlin plot. The greater properties enhancement of composites was obtained from milling method because of the better rubber-filler interactions, probably as a result of the nature of filler used. The greatest tensile strength improvement was achieved at 1 phr sepiolite loading where the smallest damping characteristics (tan ????) indicating the highest elastic behavior were obtained as revealed by rheological measurements. The simplicity of production and shortened step of milling procedure would be more favorable than the latex mixing approach for fabrication sepiolite filled rubber composites.

High-Strength Heat-Elongated Thermoplastic Polyurethane Elastomer Consisting of a Stacked Domain Structure.

We found that a high-strength elastomer was obtained by the heat elongation of a thermoplastic polyurethane (TPU) film consisting of a high content of crystalline hard segments (HS). The stress upturn continuously increased with the elongation ratio without a decrease in the strain recovery by heat elongation, i.e., the stress at break of a quenched TPU film was increased from 55 to 136 MPa by heat elongation at an elongation ratio of 300%. The results of small-angle X-ray scattering, DSC, and AFM observations revealed that: (1) anisotropically shaped HS domains were stacked at a nanometer scale and the longer direction of the HS domains was arranged perpendicular to the elongated direction due to the heat elongation, (2) the densification of the HS domains increased with increases in the elongation ratio without a significant increase in the crystallinity, and (3) the stacked domain structure remained during the stretching at 23 °C. Thus, the strengthening of the elongated TPU might be attributed to the densification of the HS domains in the stacked structure, which prevents the fracture of the HS domains during the stretching.

Validation of a Microstructure-Based Model for Predicting the High Strain Rate Flow Properties of Various Forms of Additively Manufactured Ti6Al4V(ELI) Alloy

To increase the acceptance of direct metal laser sintered Ti6Al4V(Extra Low Interstitial—ELI) in industry, analytical models that can quantitatively describe the interrelationships between the microstructural features, field variables, such as temperature and strain rate, and the mechanical properties are necessary. In the present study, a physical model that articulates the critical microstructural features of grain sizes and dislocation densities for use in predicting the mechanical properties of additively manufactured Ti6Al4V(ELI) was developed. The flow stress curves of different microstructures of the alloy were used to obtain and refine the parameters of the physical model. The average grain size of a microstructure was shown to influence the athermal part of yield stress, while the initial dislocation density in a microstructure was seen to affect the shape of the flow stress curve. The viscous drag effect was also shown to play a critical role in explaining the upturn of flow stress at high strain rates. The microstructure-based constitutive model developed and validated in this article using experimental data showed good capacity to predict the high strain rate flow properties of additively manufactured Ti6Al4V(ELI) alloy.

Role of tantalum concentration, processing temperature, and strain-rate on the mechanical behavior of copper-tantalum alloys

Microstructural instability in traditional nanocrystalline metals limits the understanding of the fundamental effect of grain size on mechanical behavior under extreme environmental conditions such as high temperature and loading rates. In this work, the interplay between Ta concentrations and processing temperature on the resulting microstructure of a powder processed, fully dense Cu-Ta alloy along with their tensile and compressive behavior at different strain rates are investigated to probe the possibility of manipulating or tuning microstructurally dependent parameters to control the flow-stress upturn phenomenon. Consequently, the results reveal that there is a crucial length scale, i.e., small grain size and appropriate cluster spacing, below which such upturn is damped out. The observation of changes in flow stress upturn behavior is consistent with the observed changes in measured high-rate plasticity, which enhances below the critical length scale. Furthermore, tension-compression asymmetry also tends to be suppressed in nanocrystalline Cu-Ta alloys, while it becomes evident as the grain size increases to an ultrafine regime. Overall, this work presents a systematic approach to control or engineer reduced high strain rate flow stress upturn behavior in metallic alloys, for high-rate applications.

Mechanisms-Based Transitional Viscoplasticity

When metal is subjected to extreme strain rates, the conversation of energy to plastic power, the subsequent heat production and the growth of damages may lag behind the rate of loading. The imbalance alters deformation pathways and activates micro-dynamic excitations. The excitations immobilize dislocation, are responsible for the stress upturn and magnify plasticity-induced heating. The main conclusion of this study is that dynamic strengthening, plasticity-induced heating, grain size strengthening and the processes of microstructural relaxation are inseparable phenomena. Here, the phenomena are discussed in semi-independent sections, and then, are assembled into a unified constitutive model. The model is first tested under simple loading conditions and, later, is validated in a numerical analysis of the plate impact problem, where a copper flyer strikes a copper target with a velocity of 308 m/s. It should be stated that the simulations are performed with the use of the deformable discrete element method, which is designed for monitoring translations and rotations of deformable particles.

Factors influencing green strength of commercial natural rubber

Abstract The factors influencing the green strength of commercial solid rubbers were investigated in the present study through characterization of commercial natural rubber (NR). Various solid commercial rubbers such as standard Vietnam rubber (SVR10), standard Indonesia rubber (SIR10), India standard natural rubber (ISNR10), ribbed smoked sheets (RSS3), and FNR (commercial Sumitomo Rubber) were used as a source. Purification of the samples was carried out through acetone extraction and purified samples were characterized by nuclear magnetic resonance (NMR) and Fourier-Transform infrared spectroscopy. Degradation was found for SVR10, ISNR10, and SIR10 but not for RSS3 and FNR through the assignment of 13C-NMR signals. Acetone extraction was found to improve the green strength of commercial NR due to the removal of impurities. Linked fatty acids and proteins contributed to the upturn of stress at small strain. However, the network structure of degraded rubbers had an insignificant role in enhancing the green strength of commercial NR.

Modeling stress upturn at high strain rates for ductile materials

Ductile materials (mainly metals) exhibit a sharp upturn of stress at strain rates around 103 to 104/s, which is not specific to a certain type of material. It is important to consider stress high rate upturn when dealing with high rate loading, such as shock loading and unloading. Using classical strength models, usually calibrated at not so high rates, may lead to errors with high rate loading and not so high pressures. Here we model high rate upturn on the macroscale. We assume that the upturn mechanism is also responsible for the 4th power law mechanism put forward by Swegle and Grady. In the past we calibrated our overstress dynamic viscoplasticity model for aluminium from 4th power law data. Here we use this calibration to predict the high rate stress upturn.

Molecular Dynamics Simulation Study of Polymer Nanocomposites with Controllable Dispersion of Spherical Nanoparticles.

Through coarse-grained molecular dynamics simulation, we construct a novel kind of end-linked polymer network by employing dual end-functionalized polymer chains that chemically attach to the surface of nanoparticles (NPs), so that the NPs act as large cross-linkers. We examine the effects of the length and flexibility of polymer chains on the dispersion of NPs, and the effect of the chain length on the stress-strain behavior and the segment orientation during the deformation process. We find that the stress upturn becomes more prominent with the decrease of the chain length, attributed to the limited extensibility of the chain strand connecting two neighboring NPs. In addition, this end-linked polymer nanocomposite (PNC) is shown to have a temperature-dependent stress-strain behavior that is contrary to traditional physically mixed PNCs, whose mechanical properties deteriorate with increasing temperature. This is due to the stability of the dispersion of NPs and higher entropic elasticity at higher temperature for the former, while the latter has poorer interfacial interaction at higher temperature, leading to less reinforcing efficiency. By imposing a dynamic oscillatory shear deformation, we obtain a dynamic hysteresis loop for end-linked and physically mixed dispersions. Interestingly, the end-linked system possesses a much smaller hysteresis loss than does the physically mixed system, with the latter exhibiting a more prominent decrease with increasing temperature, due to less interfacial contact. Our results demonstrate that end-linked PNCs combine attractive static and dynamic mechanical properties and exhibit an unusual response to temperature, which could find potential applications in the future.

Comparative study of natural rubber and acrylonitrile rubber reinforced with aligned short aramid fiber

The aims of this paper are three-fold. The first is to determine the reinforcement of high performance short aramid fiber in two representative rubber matrices, namely natural rubber and acrylonitrile rubber. The second is to ascertain the effect of rubber polarity on the reinforcement. The third is to establish a pattern of reinforcement for use with less studied fibers. The rubbers were reinforced either with only aramid fiber or with a hybrid of aramid fiber and carbon black. The fiber contents were varied at 0, 2, 5 and 10 parts (by weight) per hundred rubber (phr) while those of carbon black were 0, 10, 20 and 30 phr. Conventional sulfur vulcanization was used. It was found that aramid fiber can reinforce both rubbers in the low strain region effectively, although to a significantly different degree. The hybrid carbon black provides additional reinforcement at low to medium strains and allows high strain stress upturn to occur in both rubber matrices. The findings enable the preparation of rubber composites having a wide, controllable range of mechanical behavior for specific high-performance engineering applications. Significantly, they also serve as a benchmark for developing reinforced systems from alternative fibers, particularly those from natural sources.