An experimental and numerical study of the localization behavior of tantalum and stainless steel

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material’s local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length is 870–890 μm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 × 10⁴ s⁻¹ in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the shear section. The numerical results for stainless steel suggest that melting temperature was reached throughout the shear band shortly after peak load. Due to sample geometry, the stress state in the shear zone was not pure shear; a significant normal stress relative to the shear zone basis line was developed.     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

The transmission of turbulent boundary layer unsteady pressure and shear stress through a viscoelastic layer

The transmission of unsteady pressure and shear stress, generated by a turbulent boundary layer in water, through a viscoelastic layer backed by a rigid plate is investigated. Analytical models are used to estimate the unsteady pressure and shear stress from 10 to 1000 Hz for a flat plate boundary layer with zero pressure gradient. Additionally, models for the transfer of the unsteady pressures and shear stress through the viscoelastic layer are developed. The models are used to predict the unsteady pressure fluctuations, or flow noise, which would be seen by a finite size sensor embedded under the elastomer layer. The unsteady pressure levels are found to be 20 dB greater than the unsteady shear stress levels across all frequency ranges computed, in agreement with recent measurements. The unsteady pressure transfer functions have a peak at the shear wavenumber and are larger than the shear stress transfer magnitudes from 10 to 50 Hz. The unsteady shear stress transfer functions have a peak at the acoustic wavenumber and are larger than the pressure transfer magnitudes from 50 to 1000 Hz. Over the frequency range examined, the unsteady pressures were found to be the dominant contributor to the sensor flow noise due to the considerably larger magnitude of the unsteady pressures on the top of the viscoelastic layer.     

Effect of gravity on the mechanical properties of lunar regolith tested using a low gravity simulation device

Simulations of the bearing capacity and shear strength of regolith under Earth’s gravity produce different results from those under low gravity. A low-gravity simulation device was developed in this study, and an internal stress model of regolith simulant was established to correct the errors. The model revealed additional force on both shear plane in the shear test and the press plate area in the pressure–sinkage test. The sinkage and shear test results showed that low gravity decreased the deformable index n, frictional modulus k_φ and cohesion c, whereas there were no obvious changes to the cohesive modulus k_c and internal friction angle φ. The sinkage generally increased as the gravity decreased under a consistent normal load larger than 50 N, but when the wheel load was lower than 50 N, the sinkage of the TYII-1 simulant was larger under 1 G than 1/6 G. Gravity had little effect on the shear strength of the regolith. However, the tractive thrust of the TYII-1 simulant was lower under 1/6 G than 1 G. The smaller difference was due to differences in the way the soils responded to changes in the gravity level for the TYII-2 simulant.     

A 1-D theory for extensional deformation of a viscoelastic filament under exponential stretching

We consider a viscoelastic filament placed between two coaxial discs, with the bottom plate fixed and the top plate pulled at an exponential rate. Using a slender rod approximation, we derive a one-dimensional (1-D) model which describes the deformation of a viscoelastic filament governed by the Oldroyd-B constitutive model. It is assumed that the flow is axisymmetric and that inertia and gravity are negligible. One solution of the model equations corresponds to ideal uniaxial elongation. A linear stability analysis shows that this solution is unstable for a Newtonian fluid and for viscoelastic filaments with small Deborah number (De ≤ 0.5). For Deborah number greater than 0.5, ideal uniaxial elongation is linearly stable. Numerical solution of the nonlinear equations confirms the result of the linear stability analysis. For initial conditions close to ideal uniaxial flow, our results show that if De > 0.5, the central portion of the filament undergoes considerable strain hardening. As a result, the sample remains almost cylindrical and the deformation approaches pure uniaxial extension as the Hencky strain increases. For De ≤ 0.5, the Trouton ratio based on the effective extension rate at the mid-plane radius gives a much better approximation to the true extensional viscosity than that based on the imposed stretch rate.     

Simple constitutive modelling of nonlinear viscoelasticity under general extension

We study the behaviour of a single integral constitutive equation, capable of providing analytic expressions for the viscoelastic stress in extensional flows of a variety of deformation histories and geometries, ranging from uniaxial to equibiaxial. It is based on the use of a stress damping function, with a power-law dependence on the elongation, λ: h(λ) = 1/λⁿ. The parameter n (0 ≤ n ≤ 2) signifies the nonlinear viscoelastic character of the material and, therefore, is an inverse measure of network connectivity strength of the underlying microstructure. This renders the constitutive approach applicable to incompressible polymers of a variable degree of branching, strain hardening and stress thinning behavior. Methods of connecting n with the macromolecular architecture and the alignment strength of the flow are also explored.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

Modeling and measuring visco-elastic properties: From collagen molecules to collagen fibrils

Collagen is the main structural protein in vertebrate biology, determining the mechanical behavior of connective tissues such as tendon, bone and skin. Although extensive efforts in the study of the origin of collagen exceptional mechanical properties, a deep knowledge of the relationship between molecular structure and mechanical properties remains elusive, hindered by the complex hierarchical structure of collagen-based tissues. Understanding the viscoelastic behavior of collagenous tissues requires knowledge of the properties at each structural level. Whole tissues have been studied extensively, but less is known about the mechanical behavior at the submicron, fibrillar and molecular level. Hence, we investigate the viscoelastic properties at the molecular level by using an atomistic modeling approach, performing in silico creep tests of a collagen-like peptide. The results are compared with creep and relaxation tests at the level of isolated collagen fibrils performed previously using a micro-electro-mechanical systems platform. Individual collagen molecules present a non-linear viscoelastic behavior, with a Young's modulus increasing from 6 to 16 GPa (for strains up to 20%), a viscosity of 3.84±0.38 Pa s, and a relaxation time in the range of 0.24–0.64 ns. At the fibrils level, stress–strain–time data indicate that isolated fibrils exhibit viscoelastic behavior that could be fitted using the Maxwell–Weichert model. The fibrils showed an elastic modulus of 123±46 MPa. The time-dependent behavior was well fit using the two-time-constant Maxwell–Weichert model with a fast time response of 7±2 s and a slow time response of 102±5 s.     

Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.     

Non-linear viscoelastic response of magnetic fiber suspensions in oscillatory shear

This paper reports the first study on the large amplitude oscillatory shear flow for magnetic fiber suspensions subject to a magnetic field perpendicular to the flow. The suspensions used in our experiments consisted of cobalt microfibers of the average length of 37 μm and diameter of 4.9 μm, dispersed in a silicon oil. Rheological measurements have been carried out at imposed stress using a controlled stress magnetorheometer. The stress dependence of the shear moduli presented a staircase-like decrease with, at least, two viscoelastic quasi-plateaus corresponding to the onset of microscopic and macroscopic scale rearrangement of the suspension structure, respectively. The frequency behavior of the shear moduli followed a power-law trend at low frequencies and the storage modulus showed a high-frequency plateau, typical for Maxwell behavior. Our simple single relaxation time model fitted reasonably well the rheological data. To explain a relatively high viscous response of the fiber suspension, we supposed a coexistence of percolating and pivoting aggregates. Our simulations revealed that the former became unstable beyond some critical stress and broke in their middle part. At high stresses, the free aggregates were progressively destroyed by shear forces that contributed to a drastic decrease of the moduli. We have also measured and predicted the output strain waveforms and stress–strain hysteresis loops. With the growing stress, the shape of the stress–strain loops changed progressively from near-ellipsoidal one to the rounded-end rectangular one due to a progressive transition from a linear viscoelastic to a viscoplastic Bingham-like behavior.     

Experimental investigation of the transverse mechanical properties of a single Kevlar® KM2 fiber

A new experimental setup is developed to investigate the transverse mechanical properties of Kevlar^® KM2 fibers, which has been widely used in ballistic impact applications. Experimental results for large deformation reveal that the Kevlar^® KM2 fibers possess nonlinear, pseudo-elastic transverse mechanical properties. A phenomenon similar to the Mullins effect (stress softening) in rubbers exists for the Kevlar^® KM2 fibers. Large transverse deformation does not significantly reduce the longitudinal tensile load-bearing capacity of the fibers. In addition, longitudinal tensile loads stiffen the fibers' transverse nominal stress–strain behaviors at large transverse deformation. Loading rates have insignificant effects on their transverse mechanical properties even in the finite deformation range. An analytical relationship between transverse compressive force and displacement is derived at infinitesimal strain level. This relation is used to estimate the transverse elastic modulus of the Kevlar^® KM2 fibers, which is 1.34 ± 0.35 GPa.     

Instantaneous flow field above the free end of finite-height cylinders and prisms

The flow above the free ends of surface-mounted finite-height circular cylinders and square prisms was studied experimentally using particle image velocimetry (PIV). Cylinders and prisms with aspect ratios of AR = 9, 7, 5, and 3 were tested at a Reynolds number of Re = 4.2 × 10⁴. The bodies were mounted normal to a ground plane and were partially immersed in a turbulent zero-pressure-gradient boundary layer, where the boundary layer thickness relative to the body width was δ/D = 1.6. PIV measurements were made above the free ends of the bodies in a vertical plane aligned with the flow centreline. The present PIV results provide insight into the effects of aspect ratio and body shape on the instantaneous flow field. The recirculation zone under the separated shear layer is larger for the square prism of AR = 3 compared to the more slender prism of AR = 9. Also, for a square prism with low aspect ratio (AR = 3), the influence of the reverse flow over the free end surface becomes more significant compared to that for a higher aspect ratio (AR = 9). For the circular cylinder, a cross-stream vortex forms within the recirculation zone. As the aspect ratio of the cylinder decreases, the reattachment point of the separated flow on the free end surface moves closer to the trailing edge. For both the square prism and circular cylinder cases, the instantaneous velocity vector field and associated in-plane vorticity field revealed small-scale structures mostly generated by the separated shear layer.     

Size effects on tensile and compressive strengths in metallic glass nanowires

Shear localization induced brittleness is the main drawback of metallic glasses which restricts their practical applications. Previous experiments have provided insights on how to suppress shear localization by reducing the sample size of metallic glasses to the order of 100 nm. In order to reveal the size effects and associated deformation mechanisms of metallic glasses in an even finer scale, we perform large-scale atomistic simulations for the uniaxial compression and tension of metallic glass nanowires. The simulation results show that, as the diameter of metallic glass samples decreases from 45 nm to 8 nm, the tensile yield strength increases while the compressive yield strength decreases. Homogeneous flow is observed as the governing deformation mechanism in all simulated metallic glass samples, where plastic shearing tends to initiate on the sample surface and propagate into the interior. To rationalize the size dependence of yield strengths, we propose a theoretical model based on the concept of surface stress and Mohr–Coulomb criterion. The theoretical predictions agree well with the simulation results, implying the important role of surface stress on the yielding of MGs below 100 nm. Finally, a discussion about the size effects of strength in metallic glasses at different length scales is provided. Our results suggest that the shear band energy and surface stress might be the two crucial parameters in determining the critical size required for the transition from shear localization to homogeneous deformation in MGs.     

Analysis of an organized turbulent structure using a pattern recognition technique in a drag-reducing surfactant solution flow

This work presents the investigation for an organized turbulent structure in a drag-reducing flow of dilute surfactant solution by utilizing a particle image velocimetry system to perform the pattern recognition technique on a trajectory in four quadrants of streamwise and wall-normal velocity fluctuations. The pattern recognition is added to a new algorithm in order to directly capture the spatial rotation motion. The Reynolds number based on the channel height and bulk mean velocity was set to 1.5 × 10⁴. Surfactant solution with a weight concentration of 150 ppm was employed and the drag reduction rate was 65%. In the drag-reducing flow, we observe increased frequencies of occurrence of the flow events that correspond to a meandering motion in the wall-normal direction of the high-and low-speed regions. Three findings from investigation of the ensemble-averaged Reynolds shear stress and vortex structure are as follows: (i) the Reynolds shear stress in the large fluctuation range occurs in the narrow region; (ii) Size, strength, arrangement and inclination in the spatial vortex structure in the drag-reducing flow differ from those of the water; and (iii) all trajectory contributions for the wall friction coefficient decrease. Finally, we interpreted that the viscoelasticity characterizing the viscoelastic stress and relaxation time in rheological properties of the flow changes specific elementary vortex for the drag-reducing flow, and the trajectories of each flow pattern change drastically.     

Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression

Fractures in natural rocks have an important effect on the strength and failure behavior of rock mass, which are often evaluated in rock engineering practice. The theoretical evaluation of mechanical behavior of fractured rock mass has no satisfactory answer due to the role of confining pressure and crack geometry. Therefore, in this paper, conventional triaxial compression experiments were carried out to study the strength and failure behavior of marble samples with two pre-existing closed cracks in non-overlapping geometry. Based on the experimental results of a number of triaxial compression tests, the effect of crack coalescence on the axial supporting capacity and deformation property were investigated with different confining pressures. The results show that intact samples and flawed samples (marble with pre-existing cracks) have different deformation properties after peak stress, which change from brittleness to plasticity and ductility with the increase of confining pressure. The peak strength and failure mode are found depending not only on the geometry of flaw, but also on the confining pressure. The strength of flawed samples shows distinct non-linear behavior, which is in a better agreement with non-linear Hoek–Brown criterion than linear Mohr–Coulomb criterion. For a kind of rock that has been evaluated as a Hoek–Brown material, a new evaluation criterion is put forward by adopting optimal approximation polynomial theory, which can be used to confirm more precisely the strength parameters (cohesion and internal friction angle) of flawed samples. For intact samples, the marble leads to typical shear failure mode with a single fracture surface under different confining pressures, while for flawed samples, under uniaxial compression and a lower confining pressure (σ₃ = 10 MPa), tests for coarse and medium marble (the coarse and medium refer to the grain size) exhibit three basic failure modes, i.e., tensile mode, shear mode, and mixed mode (tensile and shear). Shear mode is associated with lower strength behavior. However, under higher confining pressures (σ₃ = 30 MPa), for coarse marble, the axial supporting capacity is not related to the geometry of flaw. The friction among crystal grains determines the strength behavior of coarse marble. For medium marble, the failure mode and deformation behavior are dependent on the crack coalescence in the sample. The present research provides increased understanding of the fundamental nature of rock failure under conventional triaxial compression.     

Analytical and numerical techniques to predict carbon nanotubes properties

In this paper, two different approaches for modeling the behaviour of carbon nanotubes are presented. The first method models carbon nanotubes as an inhomogeneous cylindrical network shell using the asymptotic homogenization method. Explicit formulae are derived representing Young’s and shear moduli of single-walled nanotubes in terms of pertinent material and geometric parameters. As an example, assuming certain values for these parameters, the Young’s modulus was found to be 1.71 TPa, while the shear modulus was 0.32 TPa. The second method is based on finite element models. The inter-atomic interactions due to covalent and non-covalent bonds are replaced by beam and spring elements, respectively, in the structural model. Correlations between classical molecular mechanics and structural mechanics are used to effectively model the physics governing the nanotubes. Finite element models are developed for single-, double- and multi-walled carbon nanotubes. The deformations from the finite element simulations are subsequently used to predict the elastic and shear moduli of the nanotubes. The variation of mechanical properties with tube diameter is investigated for both zig-zag and armchair configurations. Furthermore, the dependence of mechanical properties on the number of nanotubules in multi-walled structures is also examined. Based on the finite element model, the value for the elastic modulus varied from 0.9 to 1.05 TPa for single and 1.32 to 1.58 TPa for double/multi-walled nanotubes. The shear modulus was found to vary from 0.14 to 0.47 TPa for single-walled nanotubes and 0.37 to 0.62 for double/multi-walled nanotubes.     

Biomimetic staggered composites with highly enhanced energy dissipation: Modeling, 3D printing,and testing

We investigate the damping enhancement in a class of biomimetic staggered composites via a combination of design, modeling, and experiment. In total, three kinds of staggered composites are designed by mimicking the structure of bone and nacre. These composite designs are realized by 3D printing a rigid plastic and a viscous elastomer simultaneously. Greatly-enhanced energy dissipation in the designed composites is observed from both the experimental results and theoretical prediction. The designed polymer composites have loss modulus up to ~500 MPa, higher than most of the existing polymers. In addition, their specific loss modulus (up to 0.43 km²/s²) is among the highest of damping materials. The damping enhancement is attributed to the large shear deformation of the viscous soft matrix and the large strengthening effect from the rigid inclusion phase.     

Surface characteristics of spruce veneers and shear strength of plywood as a function of log temperature in peeling process

The objective of this study was to determine the effect of temperature of spruce (Picea orientalis L.) logs during peeling process on surface roughness, adhesive wettability, colour variation of veneer, and shear strength of plywood made from these veneer sheets. Veneer samples were manufactured from the logs after they were kept for 3 h and 24 h to reach to average temperatures of 52 °C and 32 °C, respectively. A fine stylus method was used for surface roughness evaluation of the veneer produced from two types of the logs and it was found that the samples peeled from the logs with a temperature of 52 °C had significantly better roughness values than those of manufactured from the logs with 32 °C at a 95% confidence level. Wettability of veneer samples was determined with contact angle measurements according to the sessile drop method. Urea formaldehyde (UF) and phenol formaldehyde (PF) resin drops were used in contact angle measurements. Contact angles of PF resin drops on veneers were similar for each peeling temperature while the contact angles of UF glue resin on veneers produced from the logs with 32 °C were lower than those of produced from the logs with 52 °C. Small colour difference was measured (indicated by a low ΔE value) on veneer samples depending on the log temperature. The highest shear strength value was determined for the plywood manufactured from veneers obtained from the logs with 52 °C by using UF glue.     

An improved atomistic simulation based mixed-mode cohesive zone law considering non-planar crack growth

A novel and improved atomistic simulation based cohesive zone law characterizing interfacial debonding is developed which explicitly accounts for the non-planarity of the crack propagation. Group of atoms in the simulation constituting cohesive zones which are used to obtain local stress and crack opening displacement data are determined dynamically during the non-planar crack growth as they cannot be determined apriori. The methodology is used to study the debonding of Σ5 (2 1 0)/[0 0 1] symmetric tilt grain boundary interface in a Cu bicrystal under several mixed mode loading conditions. Simulations show that such bicrystalline specimen exhibits three types of energy dissipative mechanisms – shear coupled GB migration (SCM) away from the crack-tips, change in spacial orientation of GB structural units rendering highly disordered grain boundary near the crack tips and brittle intergranular fracture. Which combination of these three deformation mechanism will be active influencing the degree of non-planarity of the crack propagation at various stages of loading depends on the loading mode-mixity. As the ratio of shear component of the loading parallel to the GB plane and normal to the tilt axis with respect to the normal loading increases (thereby increasing the mode-mixity), overall strain-to-failure also increases and SCM tends to become the dominant deformation mechanism. Through this framework, analytical functional forms and parameters describing cohesive laws for both normal and shear traction as a function of the mode-mixity of the loading and crack opening displacement are predicted.