Terms Of Strain Rate Research Articles

Collapse loads for rectangular foundations by three‐dimensional upper bound limit analysis using radial point interpolation method

SummaryA three‐dimensional kinematic limit analysis approach based on the radial point interpolation method (RPIM) has been used to compute collapse loads for rectangular foundations. The analysis is based on the Mohr‐Coulomb yield criterion and the associated flow rule. It is understood that the internal plastic power dissipation function and flow rule constraints can be expressed entirely in terms of plastic strain rates without involving stresses. The optimization problem has been solved on basis of the semidefinite programming (SDP) by using highly efficient primal‐dual interior point solver MOSEK in MATLAB. The results have been presented in terms of the variation of the shape factors with changes in the aspect ratio (L/B) of the footing for different values of soil internal friction angle (ϕ). Computations have revealed that the shape factors, sc and sq, due to effects of cohesion and surcharge increase continuously with (1) decrease in L/B and (2) increase in ϕ. On the other hand, the shape factor sγ, due to the effect of soil unit weight, increases very marginally with an increase in L/B up to (1) ϕ = 25° for a rough footing and (2) ϕ = 35° for a smooth footing. Thereafter, for greater values of ϕ, the variation of sγ with L/B has been found to be quite similar to that of the factors sc and sq. The variations of (1) nodal velocity patterns, (2) plastic power dissipation, and (3) maximum plastic shear strain rates have also been examined to interpret the associated failure mechanism.

Effect of Tool Geometry and Heat Input on the Hardness, Grain Structure, and Crystallographic Texture of Thick-Section Friction Stir-Welded Aluminium

The effect of tool geometries on the microstructure and crystallographic texture of 32-mm-thick friction stir-welded AA6082 has been investigated. The use of a tapered probe tool results in a significant variation in the grain size from the top to the base of the nugget, whereas parallel probe tools produce a uniform grain size throughout the nugget. The grain size in the nugget reflects the amount of deformation experienced and the speed of deformation expressed in terms of strain rate. An approach is proposed to calculate the strain rate during FSW of aluminum for which values between 217 and 362 s−1 were obtained. The strain rate can be either uniform or varied through the joint thickness based on the type of tool used. The tapered tool produces a variation of the strain rate, whilst the parallel tool has a uniform strain rate throughout, which can explain the obtained grain structure in each case. The tool geometries also influenced texture development with the tapered tool producing a tilt of the local shear reference frame by an angle to the normal direction equal to the taper angle.

Strain induced crystallization in biobased Poly(ethylene 2,5-furandicarboxylate) (PEF); conditions for appearance and microstructure analysis

Poly(ethylene 2,5-furandicarboxylate) (PEF) is an emerging biobased thermoplastic polymer that may replace PET for stretching applications such as bottle blowing, thermoforming, or film extrusion. The stretch ability and strain induced microstructure in PEF have not been fully addressed in the literature despite being the key issue for industrial processing. In this study, it is demonstrated that PEF can develop an organized crystalline-like microstructure under uni-axial stretching above its glass transition and can exhibit behavior close to that of PET with drastic strain hardening and coupled sensitivities to strain rate and temperature. The time-temperature superposition principle appeared to make it possible to map stretch ability in terms of strain rate and temperature, and to develop conditions for strain-induced crystallization (SIC). The periodic microstructure of stretched PEF was highlighted by means of wide-angle X-Ray scattering and analyzed with stochastically modulated temperature DSC (TOPEM). Depending on the stretching conditions applied to PEF, different morphologies of crystals are developed. The heat capacity (ΔCP), crystalline fraction (XC), mobile amorphous fraction (XMAF), and rigid amorphous fraction (XRAF) for stretched and non-stretched PEF samples were evaluated.

Effects of Reaction Progress Variable Definition on the Flame Surface Density Transport Statistics and Closure for Different Combustion Regimes

ABSTRACTThe implications of the choice of reaction progress variable on the performances of the flame surface density (FSD) based mean reaction rate closure and the well-established sub-models of the FSD transport have been analysed in context of Reynolds Averaged Navier Stokes simulations. For this purpose, a detailed chemistry direct numerical simulation (DNS) database of freely-propagating statistically planar air flames (with an equivalence ratio of 0.7) spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion has been considered. The FSD and the unclosed terms of its transport equation have been analysed for reaction progress variables defined based on normalised and mass fractions and temperature. The performances of the closures for turbulent flux of FSD, and tangential strain rate term have been found to be mostly unaffected by the choice of reaction progress variable. However, the well-established existing models for the unresolved tangential strain rate term have been found not to perform well for the cases representing the CF and TRZ regimes of premixed combustion. The performance of a well-established existing model for the combined propagation and curvature terms has been found to be significantly dependent on the choice of reaction progress variable. Furthermore, the surface-averaged value of the density-weighted displacement speed cannot be approximated by the corresponding unstretched laminar flame value especially for the flames in the BRZ regime. Detailed explanations have been provided for the observed behaviours of the FSD based reaction rate closure and sub-models for the unclosed terms of the FSD transport equation in different combustion regimes for different choices of reaction progress variable.

Generalized flame surface density transport conditional on flow topologies for turbulent H2-air premixed flames in different regimes of combustion

The generalized flame surface density (FSD) transport conditional on local flow topologies in premixed turbulent flames has been analyzed based on a detailed chemistry direct numerical simulation database of statistically planar turbulent hydrogen-air premixed flames with an equivalence ratio of 0.7 representing the corrugated flamelets, thin reaction zones and broken reaction zones regimes of combustion. The local flow topologies have been categorized by the values of the three invariants of the velocity gradient tensor and the statistical behaviors of the generalized FSD and different terms of its transport equation conditional on these flow topologies have been analyzed in detail for different choices of the reaction progress variable. The qualitative behavior of the different terms of the generalized FSD transport equation has been found to be similar for different choices of reaction progress variable but the statistical behaviors of the tangential strain rate term and its components have been found to be affected by the regime of combustion. The topologies, which exist for all values of dilatation rate, contribute significantly to the generalized FSD transport in premixed turbulent flames for all regimes of combustion. An unstable nodal flow topology, which is representative of a counter-flow configuration, has been found to be a dominant contributor to the FSD transport for all regimes of combustion irrespective of the choice of reaction progress variable. Moreover, a focal topology which is obtained only for positive values of dilatation rate, has been found to contribute significantly, especially to the curvature and propagation terms of the FSD transport equation for all regimes of combustion including the broken reaction zones regime. However, the contributions of the flow topologies to the turbulent transport and tangential strain rate term, which are obtained only for positive dilatation rates, have been found to weaken from the corrugated flamelets to the broken reaction zones regime.

Determination of the instantaneous strain rate during small punch testing of 316 L stainless steel

The Small Punch Test, SPT, has been widely used by scientists for the mechanical characterization of nuclear materials and different applications. This technique is able to provide an approximation of mechanical properties from a very small amount of material. However, the inhomogeneous distributions of local stresses and strains, coupled to the response of the material hinder accurate predictions of the mechanical properties in terms of tensile tests parameters. Additionally, the determination of the instantaneous strain rate, as the test proceeds, remained a pending issue. This article analyses the predictions of SPT on 316 L steels by a FEM model, validated by an additively manufactured 316 L SLM (Selective Laser Melting) stainless steel, in terms of thickness evolution, local deformation and instantaneous strain rate during SPT testing. This alternative analysis shows that the deformation behaviour and, thus, the final form of the sample is affected by the strain hardening behaviour, which it has an influence on the instantaneous local strain rate. The instantaneous local strain rate was calculated for two dissimilar 316 L austenitic stainless steel, one “hardened”, characterized by low ductility but very high yield strength (YS) and ultimate tensile strength UTS, and another “annealed”, characterized by very low YS and large ductility, typical of annealed 316 L steel. The calculated central and minimum thicknesses, strain and instantaneous local strain rate, are not linear as SPT testing proceeds. Therefore, they are fitted to polynomial equations for both annealed and hardened 316 L steels. These functions allow, for instance, LVDT measurement corrections for appropriate SPT curve analysis, and proper true strain rate measurements for creep (SPCT) data analysis.

Fatigue Characteristics of Limestone under Triaxial Compression with Cyclic Loading

This paper presents an experimental investigation of the fatigue properties of limestone subjected to triaxial compression with axial cyclic loading. Tests were conducted on intact limestone samples with a loading frequency of 0.5 Hz and a confining pressure of 10 MPa. The test results show the following five points. (1) Under triaxial conditions, the axial and circumferential deformations at the failure point induced by cyclic loading are slightly larger than the corresponding deformations at the peak stress achieved by conventional compression tests. (2) The first level cyclic loading process has a strong influence on rock deformation in the primary phase during subsequent level cyclic loading. A smaller difference in stress amplitude between the two loading stress levels leads to less deformation during the latter. (3) Circumferential and volumetric changes are more sensitive to fatigue failure in terms of deformation and strain rate than axial changes. (4) The three phases of dissipated energy evolution are consistent with a sample’s deformation such that the energy dissipation characteristics reflect the fatigue damage evolution process. (5) A new damage formula is proposed that can concisely describe a rock’s zero-cycle damage and damage evolution.

Effect of Die Geometry on the Formability of 5052 Aluminum Alloy in Electromagnetic Impaction Deformation.

The formability of aluminum alloy sheet in electromagnetic impaction deformation has attracted the attention of numerous researchers for the past decades. However, the influences of die geometry and high-speed impaction electromagnetic deformation on formability have not been well established, thereby resulting in the formability of the sheet not being developed fully. In this study, the influence of die geometry on the formability of 5052 aluminum alloy in electromagnetic deformation was investigated by comparing the formability of 5052 aluminum alloys formed using a hemispherical die and a cylindrical die. The intriguing finding is that the formability of the 5052 aluminum alloy formed using a cylindrical die is considerably higher than that formed using a hemispherical die. Therefore, die geometry significantly influences the formability of 5052 aluminum alloy. The influence of die geometry on the formability of 5052 aluminum alloy in high-speed impaction electromagnetic deformation was explained in terms of strain rate, pressure stress, and stress state. This investigation enhances insight into the interaction between sheets and dies, and provides a reference for the studying influence of dies on the forming limit of sheets in high-speed impaction deformation.

Upper-Bound Finite-Element Limit Analysis of Axisymmetric Problems for Mohr-Coulomb Materials Using Semidefinite Programming

An upper-bound formulation for performing finite-element limit analysis by using semidefinite programming (SDP) for an axisymmetric stability problem involving the Mohr-Coulomb yield criterion has been presented. The SDP technique has an advantage in that it can deal with the yield criterion directly in its native form in terms of principal stresses and strains without any smoothing of the parent yield surface. The associated flow rule and plastic power dissipation are expressed entirely in terms of principal plastic strain rates. Nodal velocities and element plastic strain rates were framed as basic governing variables without involving stresses. The solution was obtained by using the SDP solver MOSEK in MATLAB. The problem of finding the bearing capacity of a circular footing was dealt with by choosing a planar domain that was discretized with (1)three-noded constant strain finite elements and (2)six-noded linear strain finite elements. The results were obtained with and without the provision of the velocity discontinuities, and were compared with those reported in literature. It was learned that quite accurate solutions can be obtained with the application of six-noded linear strain triangular elements and using velocity discontinuities along all the elements' interfaces.

Constitutive Modeling of the High-Temperature Flow Behavior of α-Ti Alloy Tube

In the hot metal gas forming process, the deformation conditions, such as temperature, strain rate and deformation degree, are often prominently changed. The understanding of the flow behavior of α-Ti seamless tubes over a relatively wide range of temperatures and strain rates is important. In this study, the stress–strain curves in the temperature range of 973-1123 K and the initial strain rate range of 0.0004-0.4 s−1 were measured by isothermal tensile tests to conduct a constitutive analysis and a deformation behavior analysis. The results show that the flow stress decreases with the decrease in the strain rate and the increase of the deformation temperature. The Fields–Backofen model and Fields–Backofen–Zhang model were used to describe the stress–strain curves. The Fields–Backofen–Zhang model shows better predictability on the flow stress than the Fields–Backofen model, but there exists a large deviation in the deformation condition of 0.4 s−1. A modified Fields–Backofen–Zhang model is proposed, in which a strain rate term is introduced. This modified Fields–Backofen–Zhang model gives a more accurate description of the flow stress variation under hot forming conditions with a higher strain rate up to 0.4 s−1. Accordingly, it is reasonable to adopt the modified Fields–Backofen–Zhang model for the hot forming process which is likely to reach a higher strain rate, such as 0.4 s−1.

Integrating the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) in the Biot viscosity extended framework

The viscosity extended Biot theory [Sahay, Geophysics (2008)] incorporates pore fluid viscosity in the constitutive relation of the classical Biot theory. The strain rate term due to pore fluid viscosity turns the zero velocity slow S wave mode into a diffusive process. In this framework, it is claimed that fast P and S waves bleed energy when the slow S wave is generated at an interface or at a discontinuity. On the other hand, the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) [Chotiros and Isakson, JASA (2004)] models the grain to grain contact as compression and shear relaxation processes and obtains a causal poro-elastic frame response. In this work, we incorporated the grain to grain contact physics in the constitutive relation of the Biot theory and integrated it into the viscosity extended Biot framework. With realistic parameters, the fast S wave phase velocity and attenuation in the integrated model show a significant difference over a range of frequencies when compared to BICSQS. Additionally, this integrated model may provide a more accurate match for the measured reflection coefficient.

Assessment of Poliak-Jonas criterion for the onset of dynamic recrystallization in semi-solid deformation

In the present investigation, the application of the Poliak-Jonas criterion in the semi-solid state has been evaluated. The evolution of grains by dynamic recrystallization during semi-solid forming was studied using electron backscatter diffraction (EBSD) analysis. The strain rate in the solid phase for each strain in terms of the overall strain rate, as well as the liquid fraction, was calculated based on the Gurson model. The numerical investigation revealed that the preliminaries of the Poliak-Jonas criterion are almost satisfied in the semi-solid deformation of alloys at low and moderate strain rates. However, there is less reliability regarding the criterion at high values of strain rates, where commonly used in industrial applications.

Temperature, Strain Rate and Pressure Sensitivity of the Polyetheretherketone’s Yield Stress

The polymer yield behavior is affected by temperature, strain rate and pressure. In this work, tensile yield stress of polyetheretherketone (PEEK) is characterized for temperature ranging between [Formula: see text] and [Formula: see text] ([Formula: see text]C and [Formula: see text]C). The tensile yield stress is decreasing in terms of temperature. Two temperature transitions are observed: [Formula: see text] ([Formula: see text]C) and the glass transition temperature. The temperature sensitivity is well captured by the modified-Eyring equation proposed by the authors. This paper completes three previous works where the PEEK’s yield behavior was described under compression on wide ranges of strain rate and temperature and under tension on a wide range of strain rates. Thus, the pressure effect is analyzed in terms of temperature and strain rate. Using either the experimental data or the modified-Eyring equation, the effect of the hydrostatic pressure is increasing with temperature and decreasing with strain rate.

A Viscoplastic Constitutive Equation from Kolsky Bar Data for Two Steels

Kolsky bar data for viscoplastic materials are usually presented as true stress versus true strain curves at nearly constant values of engineering strain rates. However, constitutive models for numerical simulations require the true axial rate of deformation which is true strain rate. We present a procedure that uses existing data with constant engineering strain rate to obtain a constitutive equation in terms of true strain rate for 304 stainless steel and 4340 Rc 45 steel.

Two-dimensional speckle-tracking echocardiography evaluation of left atrial function according to glycemic state in patients with coronary artery disease.

The study population comprised 205 consecutive patients with CAD: 104 diabetic, 51 prediabetic, and 50 euglycemic patients. LA function was evaluated with two-dimensional speckle-tracking echocardiography and the longitudinal deformation indices of the LA were measured. Our results showed that early diastolic strain was lower in the diabetic patients than in the prediabetic and euglycemic patients. The absolute value of early diastolic strain rate was reduced in the diabetic patients compared with the euglycemic patients. Late diastolic strain was increased in the diabetic patients compared with the prediabetic and euglycemic patients. The multivariate analysis showed that diabetes was a determinant of early diastolic strain and strain rate, but not late diastolic strain. LA conduit function, as evaluated in terms of early diastolic strain and strain rate, was impaired in the diabetic CAD patients compared with the prediabetic and euglycemic CAD patients.

Evaluation of the ductile-to-brittle transition temperature of a silicon steel under various strain rate conditions with a servo-hydraulic high speed testing machine

This paper is concerned with the construction of an empirical model of the Ductile-to-Brittle Transition Temperature (DBTT) for 3.4% silicon steel based on tensile test results at strain rates ranging from 0.001 s‒1 to 100 s‒1. Dynamic tensile tests are conducted using an in-house servo hydraulic tensile test machine at strain rates of 1 s‒1, 10 s‒1, and 100 s‒1 and quasi-static tensile tests are conducted using Instron 4206 at strain rates of 0.001 s‒1 and 0.01 s‒1 with an environmental chamber. Fracture elongations are measured by a DIC method during all tests using the high-speed camera for accurate measurement. The DBTT of 3.4% silicon steel is presented in terms of fracture strain with the variation of the temperature and the strain rate. It is demonstrated from the test results that the DBTT increases as the strain rate increases. An empirical model of the DBTT is constructed in terms of strain rate, temperature and fracture elongation. The parameters of the empirical model are calculated from experimental results obtained at various temperatures and strain rates.

Effects of silicon on characteristics of dynamic strain aging in a near-α titanium alloy

AbstractThe effects of temperature and strain rate on the tensile properties of Timetal 834 near-α titanium alloy and alloy 834 without silicon were examined in the temperature range of 250 °C to 600 °C, employing strain rates in the range of 6.67 × 10−6 s−1 to 6.67 × 10−3 s−1. Manifestations of dynamic strain aging such as serrated flow, plateaus in the variations of 0.2 % yield strength and ultimate tensile strength, peak in strain hardening exponent with temperature and negative strain rate sensitivity were observed in both the alloys. Serration maps in terms of strain rate versus temperature are presented for both the alloys. The activation energy for serrated flow was determined in both the alloys by employing various methodologies mentioned in the literature. Analysis of the results suggested that addition of Si leads to increased severity of dynamic strain aging.

High strain rate characterization of shear thickening fluids using Split Hopkinson Pressure Bar technique

Shear thickening fluids (STFs) are a special class of field responsive fluids which exhibit change of phase from liquid to solid when subjected to imposed shear. This remarkable characteristic of STFs has led to their application in soft body armor technologies, leading the development of concept of Liquid Body Armors (LBAs). LBAs extensively rely upon the symbiotic relationship between STF and high strength FRP (Fiber Reinforced Polymer) composites comprising of high tenacity fibers such as Kevlar, UHMWPE (Ultra High Molecular Weight Poly Ethylene) etc. Although in the past, STFs have been widely characterized by rheometers at low strain rates (≤103 s−1), but in actual practical scenarios, body armours encounter much higher strain rates (of the order of 105–107 s−1) under a ballistic impact. The main objective of this study is to capture the dynamics of STFs at such high strain rates by employing Split Hopkinson Pressure Bar (SHPB) technique. The STF sample was synthesized by dispersing 67.5wt.% of 100nm silica powder in Poly Propylene Glycol (PPG) and ethanol, using ultrasonic homogenization method. The mechanical response of STF was studied at high strain rates in terms of the stress-strain behavior and variation of the impact toughness with the loading rate of the fluid specimen. It was observed that the impact toughness of STF increased progressively with the specimen loading rate. The peak stress and peak strain rate attained in the SHPB tests were 147MPa and 22,100 s−1, respectively. The characteristic transition time of STF was found to be in the range of 13–25 µs.

Surface phenomena revealed by in situ imaging: studies from adhesion, wear and cutting

Surface deformation and flow phenomena are ubiquitous in mechanical processes. In this work we present an in situ imaging framework for studying a range of surface mechanical phenomena at high spatial resolution and across a range of time scales. The in situ framework is capable of resolving deformation and flow fields quantitatively in terms of surface displacements, velocities, strains and strain rates. Three case studies are presented demonstrating the power of this framework for studying surface deformation. In the first, the origin of stick-slip motion in adhesive polymer interfaces is investigated, revealing a intimate link between stick-slip and surface wave propagation. Second, the role of flow in mediating formation of surface defects and wear particles in metals is analyzed using a prototypical sliding process. It is shown that conventional post-mortem observation and inference can lead to erroneous conclusions with regard to formation of surface cracks and wear particles. The in situ framework is shown to unambiguously capture delamination wear in sliding. Third, material flow and surface deformation in a typical cutting process is analyzed. It is shown that a long-standing problem in the cutting of annealed metals is resolved by the imaging, with other benefits such as estimation of energy dissipation and power from the flow fields. In closure, guidelines are provided for profitably exploiting in situ observations to study large-strain deformation, flow and friction phenomena at surfaces that display a variety of time-scales.

Comparison of creep strength and intrinsic ductility for serviced and reheat treated T91 steel based on stress relaxation testing

High precision stress relaxation tests (SRT) at four temperatures were conducted on T91 (9%Cr) steel after extended boiler service, and also after re-heat treatment. Relative differences in creep strength, measured over five decades in strain rate were dependent on test temperature. Using an established correlation between strain rate sensitivity and elongation at failure, intrinsic ductility values as a function of stress and test temperature were determined. The general trend of a minimum in ductility in terms of stress or strain rate was consistent with long term creep rupture data on T91, and with literature data on alloy steels. However, the precision and repeatability of the SRT analysis contrasted with the appreciable scatter and heat to heat variation in traditional testing. It is argued that the current creep strength evaluation based on the nearly constant state measurement from the SRT test is superior to the measurement of stress dependence of minimum creep rate in traditional creep rupture testing. The complexity of primary creep in laboratory testing, which may not be significant at operating stresses where loading strains may be fully recoverable (anelastic), does not apply to the SRT. Since very low strain rates are achieved in a one day test, the procedures for setting of design allowables and design analysis based on the SRT data should not be significantly different from current practice. This technique offers accelerated alloy development and optimisation for creep strength and also ductility, and hence resistance to notch sensitivity.