Strain Rate History Research Articles

Influence of Strain Rate and Stress History on Stress–Strain-Strength and Pore Pressure Characteristics of Organic Marine Clay

Influence of Strain Rate and Stress History on Stress–Strain-Strength and Pore Pressure Characteristics of Organic Marine Clay

Smoothed particle hydrodynamics simulations of microstructure induced stress overshoot in structured fluids

Stress overshoot/undershoot is an important phenomenon in structured fluids undergoing dynamic and transient flow. To accurately capture the flow process, it is important to have a better understanding of and include in the numerical modeling the microstructure evolution that leads to the stress overshoot/undershoot phenomenon. We present a procedure for incorporating a microstructure model into a Lagrangian framework based on the smoothed particle hydrodynamics fluid solver. The numerical simulation is performed for a typical structured fluid under an applied strain rate history flow. Good agreement between the numerical results and the experimental data lends credence to and validates the proposed procedure for simulations of complex mixture flows. Additionally, the interaction between a flow of structured fluid and a circular cylinder placed in a channel is investigated. The viscous force is found to overshoot together with the applied gradient pressure and decrease over time as the fluid approaches the equilibrium state.

Linking polymer architecture to bubble shape in LDPE film blowing through multistage modeling

To meet the challenge of efficient modeling of film blowing with realistic constitutive equations for commercial thermoplastic melts, we present a multistage optimization modeling framework that integrates polymerization reaction modeling, rheology modeling, and bubble-shape prediction. A direct link is thereby created between the polymer architecture and the bubble shape of low-density polyethylene (LDPE) through a three-stage modeling protocol. Stage 1 aims to get complete polymer structure information from a limited set of linear and nonlinear rheological data and the measured averaged molecular weight. An optimization loop uses the Tobita algorithm for polymer reaction and the BoB model for rheology to minimize the deviation between experimental data and model predictions. Stage 2 is designed to obtain a representative reduced ensemble of LDPE in the Rolie-double-poly (RDP) model to reduce the computational cost of rheology calculations during processing. The parameters of the reduced molecular components are obtained by fitting the RDP model to a wide range of rheology data predicted by the BoB model applied to the full ensemble of polymer architectures obtained in stage 1. In stage 3, the reduced-ensemble RDP model is coupled to measured temperature profiles using time–temperature superposition, and the bubble shape and strain rate history of a fluid particle in the bubble are obtained by minimizing error in the momentum balance equations. We show that each stage of the process yields successful fitting, and at the end, we obtain an a priori prediction of height-dependent bubble radius and velocity in agreement with experiment. With this multistage optimization strategy, we link the polymer compositions to the bubble properties during the film blowing of LDPE.

Fracture-pattern growth in the deep, chemically reactive subsurface

Arrays of natural opening-mode fractures show systematic patterns in size and spatial arrangement. The controls on these factors are enigmatic, but in many cases the depth of formation appears to be critical. Physical, potentially depth-dependent factors that could account for these variations include confining stress, fluid pressure, and strain rate; these factors are common inputs to existing fracture models. However, temperature-dependent chemical processes likely exert an equally important control on patterns, and such processes have not yet been rigorously incorporated into models of fracture formation. Here we present a spring-lattice model that simulates fracturing in extending sedimentary rock beds, while explicitly accounting for cementation during opening of fractures, and for rock failure via both elastic and time-dependent failure criteria. Results illustrate three distinct fracturing behaviors having documented natural analogs, which we here term fracture facies. “Exclusionary macrofracturing” occurs at shallow levels and produces large, widely spaced, uncemented fractures; “multi-scale fracturing” occurs at moderate depth and produces partially cemented fractures having a wide range of sizes and spacings; and “penetrative microfracturing” occurs at great depth and produces myriad narrow, sealed fractures that are closely and regularly spaced. The effect of depth is primarily to accelerate both dissolution and precipitation reactions via increased temperature and porewater salinity; the specific depth range of each fracture facies will vary by host-rock lithology, grain size, strain rate, and thermal history.

Experimental characterization and prediction of forming limit diagrams of PHS1800 during hot stamping

The use of press-hardening steels (PHSs) in automotive bodies creates the opportunity of producing thinner, higher-strength components. PHS1800, an Al-Si coated PHS grade with ultimate tensile strength of around 1.8 GPa after hot stamping, is a candidate material for vehicle anti-intrusion applications. The current study aims to investigate the formability of this steel during the hot-stamping process. A custom Marciniak punch test and in situ digital image correlation (DIC) techniques were used to determine the in-plane forming limits of this steel during quenching from an austenitic temperature. The carrier blank thickness and geometry were exploited to quench the surrounding material of the specimens while promoting localization in their central regions. Approximately linear strain paths ranging from uniaxial to biaxial stretching were obtained in the tests while avoiding friction and out-of-plane bending. The forming limit curves (FLCs) of the material under various hot-stamping conditions were then predicted using the Marciniak-Kuczyński (MK) model, taking into account the temperature and strain-rate histories. The predicted limit strains were in good accord with the measured data.

Experimental and postprocessing procedures for the response of sheet metals to high strain rate

Metals subjected to high strain rates in Hopkinson bar testing remarkably increase their temperature, so that thermal and dynamic effects are always interleaved. Experimental procedures in such field are not clearly standardized and the most common methods for tensile testing and postprocessing cannot highlight some crucial aspects of the dynamic response of metals. When sheet metal specimens are tested instead of bulk specimens, the accurate derivation of the flow curves are further complicated due to intrinsic strain nonuniformities induced by the specimen geometry and to possible material anisotropy. The local strain peaks calculated by digital image correlation, together with the specimen elongation / shrinking evaluated on the deforming specimen by optical methods, deliver remarkably different estimates of the stress-strain curves and of the strain rate histories for the same given test. Such differences are discussed in this paper together with the assessment of the anisotropic response of the material at static, intermediate and high strain rates.

The strain rate history effect in a selective-laser-melt 316L stainless steel

The strain rate history effect in a selective laser melt 316L (SLM-316L) alloy was investigated through quasi-static (10−3 s−1) and high strain rate (1600-3200 s−1) interrupted and reloading compression tests. The specimens pre-tested until about prescribed strains at quasi-static and high strain rates were reloaded dynamically and quasi-statically, respectively. The results revealed that the flow stress depended on strain and strain rate as well as strain-rate history. Quasi-static reloading the dynamically pre-tested specimens until about prescribed strains induced a higher flow stress than the specimens tested quasi-statically. The strengthening was ∼70 MPa at 0.11 pre-strain and decreased as the dynamic test pre-strain was increased due to adiabatic heating. On the other side, reloading the quasi-statically pre-tested specimens dynamically at 0.11 pre-strain resulted in ∼60 MPa lower flow stress than the specimens tested dynamically. The grains of the quasi-statically tested specimens until 0.11 strain were shown to have a lower Taylor factor for twinning and geometrically necessary dislocation density, indicating more potential for twinning than dynamically tested specimen. Although, quasi-statically and dynamically tested specimens were deformed predominantly by the twinning induced plasticity, a higher fraction of twin boundaries was shown microscopically in the dynamically pre-tested specimens until 0.11 pre-strain. This phenomenon of boundary strengthening could be used as a tool of strengthening of SLM-316L alloy at low strains.

Improved dynamic strength of TRIP steel via pre-straining

The mechanical properties of transformation-induced plasticity (TRIP) steels are attractive in many applications that benefit from high work hardening and high total elongation. Under dynamic loading rates (ε˙>103s−1) TRIP steels lose these beneficial properties and are one of the few known materials whose dynamic response is softer than the quasi-static response (ε˙≈10−3s−1). Here we show that after quasi-static pre-straining a TRIP steel to 10%, the dynamic strength increases three-fold from approximately 500 MPa to 1500 MPa while retaining the high work hardening response. The mechanical response during strain-rate history tests indicates that the yield strength is nearly insensitive to strain rate while strain hardening is extremely sensitive to temperature rise. Micrographs of the microstructural evolution taken from interrupted tests indicate that phase transformation is delayed at dynamic rates and ceases after an adiabatic temperature rise of 100−140∘C, which is consistent with existing thermodynamic theory.

Coupled influence of tectonics, climate, and surface processes on landscape evolution in southwestern North America

The Cenozoic landscape evolution in southwestern North America is ascribed to crustal isostasy, dynamic topography, or lithosphere tectonics, but their relative contributions remain controversial. Here we reconstruct landscape history since the late Eocene by investigating the interplay between mantle convection, lithosphere dynamics, climate, and surface processes using fully coupled four-dimensional numerical models. Our quantified depth-dependent strain rate and stress history within the lithosphere, under the influence of gravitational collapse and sub-lithospheric mantle flow, show that high gravitational potential energy of a mountain chain relative to a lower Colorado Plateau can explain extension directions and stress magnitudes in the belt of metamorphic core complexes during topographic collapse. Profound lithospheric weakening through heating and partial melting, following slab rollback, promoted this extensional collapse. Landscape evolution guided northeast drainage onto the Colorado Plateau during the late Eocene-late Oligocene, south-southwest drainage reversal during the late Oligocene-middle Miocene, and southwest drainage following the late Miocene.

Thermodynamic Restrictions in Linear Viscoelasticity.

The thermodynamic consistency of linear viscoelastic models is investigated. First, the classical Boltzmann law of stress–strain is considered. The kernel (Boltzmann function) is shown to be consistent only if the half-range sine transform is negative definite. The existence of free-energy functionals is shown to place further restrictions. Next, the Boltzmann function is examined in the unbounded power law form. The consistency is found to hold if the stress functional involves the strain history, not the strain–rate history. The stress is next taken to be given by a fractional order derivative of the strain. In addition to the constitutive equations involving strain–rate histories, finding a free-energy functional, consistent with the second law, seems to be an open problem.

Experimental and numerical investigations on the process quality and microstructure during induction heating assisted incremental forming of Ti-6Al-4V sheet

• Development of induction heating SPIF system to provide localized heating to deform Ti-6AI-4V alloy sheet. • A Nickel ball-roller forming tool has been integrated into the SPIF system to improve the surface quality. • The relation between mechanical and microstructural behaviours was investigated by analysing forming force, geometric accuracy, thickness profile and surface roughness with recrystallisation, grain refinement and micro-hardness throughout the process. • A Finite Element (FE) model was established to verify the experimental results. The FE obtained strain and strain rate history was used as input to form a constitutive model to investigate the microstructural evolution. • Arrhenius model has been established by calculating of Zener-Hollomon parameter (Z-parameter) to correlate the grain size and micro-hardness at specific regions. The conventional single point incremental forming (SPIF) process is unable to perform high geometrical accuracy and formability for the Ti-6AI-4V alloy sheet. In response, this article has proposed a reliable high-frequency induction heating-assisted SPIF system. Rapid localised heating (600 ℃ and 700 ℃ ) was integrated with a synchronized Inconel 625 Nickel alloy ball-roller forming tool to achieve high geometric accuracy and surface quality. This article also produced new insights into correlating mechanical and microstructural properties in SPIF at 600 ℃ and 700 ℃ . By investigating the mechanical properties (forming force, geometric accuracy, thickness profile), an explicit finite element (FE) simulation was established to predict the results. The output strain history from the FE simulations was used as input and integrated with electron backscatter diffraction (EBSD) and micro-hardness characterisations, to form a constitutive model (Arrhenius model) to calculate the Zener-Hollomon parameter (Z-parameter). The grain size and micro-hardness experimental results were correlated with Z-parameter calculation to predict the microstructural development at the initial, middle, and final stages of the deformation process. The mechanical results revealed that the 700 ℃ experiment performed enhanced geometric accuracy and thickness profile, with a reduced forming force. However, the surface quality is reduced as the lubricant dissipated rapidly, while the ball-roller tool effectively compensated for this behaviour by reducing the friction. At the microstructural level, 600 ℃ revealed strong strain hardening and grain deformation, and 700 ℃ revealed better grain refinement by dynamic recovery (DRV) and dynamic recrystallisation (DRX). A proportional relationship between Z parameters and grain size and a low-high-low micro-hardness profile was proposed.

Time-Dependent Compression Behavior of Sands under Oedometric Conditions

A set of experimental data on the time-dependent oedometric compression behavior of sands is presented. The investigation focuses on the behavior of a clean quartz sand with respect to creep, strain-rate response, stress relaxation, and strain and strain rate history. The influence of different fine contents up to 25% by weight on creep, strain rate response, and stress relaxation are studied. The tests were conducted under vertical effective stress levels up to 7,500 kPa with specimens of medium dense and very dense relative density. The tests show a stress and density dependent creep behavior regardless of the fine content. Creep of sands with more than 14% by weight fine content can be described by a constant Cα/Cc ratio, whereas clean sand shows varying ratios. The response of the soils upon sudden changes in loading strain rate changes from clean sand, which exhibits only a temporary response of the stress-strain behavior, to the sands with more than 14% by weight fine content, which have a permanent response of the stress-strain behavior with continued straining. Stress relaxation tests show decreasing normalized stress relaxation σ/σ0 with increasing vertical effective stress. The behavior is independent of the density. It is described by the oedometric swelling index κ0. The tests on the influence of strain rate history show that the creep behavior of the sands is not dependent on it in the time scales studied.

Influence on strain-rate history effects on the development of necking instabilities under dynamic loading conditions

The present paper is devoted to the analysis of strain-rate history effects on neck formation under dynamic loading. For materials presenting strain-rate history effects, two different strain-rate sensitivities should be distinguished: the instantaneous strain-rate sensitivity and the work-hardening strain-rate sensitivity. We have analysed the relative contributions of these two kinds of strain-rate sensitivities to neck retardation for two different configurations: a bar under impact tension and a dynamically expanding ring. For this purpose, we have developed finite element models and, for the second configuration, an analytical model based on the linear stability analysis. The obtained results show that strain-rate history effects have a significant influence on the onset and development of necking. The reason of this phenomenon is that, contrary to the instantaneous strain-rate sensitivity, the work-hardening strain-rate sensitivity does not contribute to delay the neck formation.

Temperature Dependent Dynamic Strain Localization and Failure of Ductile Polymeric Rods under Large Deformation

Ductile polymers have been increasingly applied in engineering applications to enhance the structural reliability under impact loading. Due to the limitation of experimental setup to achieve large tensile deformation and the difficulty to achieve dynamic force equilibrium, the localization and post-necking stages up to fracture of ductile polymers at high strain rates have less been investigated. In the present work, the dynamic strain localization of ductile polymeric rods under large tensile deformation up to fracture is studied on the bespoke Hopkinson tension bar synchronized with a high-speed camera. Transparent polycarbonate (PC) is used as a model material in the present study. Likewise, the constitutive response and fracture behaviour of polycarbonate are also characterized with the assistance of Digital Image Correction (DIC) from low to high strain rates under various temperature conditions. The results quantitatively show that the dynamic local strain rate initially increases dramatically to 200 % of the nominal strain rate due to strain localization. This is followed by a rapid drop with necking propagation, and finally tends to stay at strain rate of approximately 20 % of the nominal strain rate until fracture. The elevated temperatures would result in higher local strain rates. Two constitutive models with and without the consideration of constant strain rate condition are constructed for PC and incorporated in finite element simulations. The trend of dynamic local strain rate history with respect to nominal strain rate is successfully reproduced in simulations. The constitutive models particularly the simple dynamic amplification model, are able to reflect the phenomenological key features of the experimentally observed macroscopic and local responses of polycarbonate, and would find their potential applications in impact resistant transparency design.

Development of LSTM networks for predicting viscoplasticity with effects of deformation, strain rate and temperature history

Abstract In this paper, long short-term memory (LSTM) networks are used in an original way to model the behavior of a viscoplastic material solicited under changing loading conditions. The material behavior is dependent on history effects of plasticity which can be visible during strain rate jumps or temperature changes. Due to their architecture and internal state (memory), the LSTM networks have the ability to remember past data to update their current state, unlike the traditional artificial neural networks (ANNs) which fail to capture history effects. Specific LSTM networks are designed and trained to reproduce the complex behavior of a viscoplastic solder alloy subjected to strain rate jumps, temperature changes or loading-unloading cycles. The training datasets are numerically generated using the constitutive viscoplastic law of Anand which is very popular for describing solder alloys. The Anand model serves also as a reference to evaluate the performances of the LSTM networks on new data. It is demonstrated that this class of networks is remarkably well suited for replicating the history plastic effects under all the tested loading conditions.

DEM numerical tests on dry granular specimens: the role of strain rate under evolving/unsteady conditions

In this paper, the mechanical behaviour of an ideal dry granular material under both evolving and steady conditions has been studied. Triaxial loading both constant volume and constant pressure Discrete Element (DEM) tests on periodic cells have been performed. The role played by strain rate, void ratio and imposed pressure has been analysed. The aim of the paper is to obtain a numerical data set, at present totally absent in the literature, useful for the definition of constitutive relationships capable of reproducing phase transitions (from solid-to-fluid and vice versa) taking place in granular materials. The novelty of the data set obtained derives also from the type of loading tests performed, referred as heating, cooling and cyclic, in which different strain rate histories are imposed, inspired to what locally occurs in flowing granular masses, accelerating and decelerating according to the slope inclination. The numerical results are interpreted by considering state variables (granular temperature and fabric) and the energies evolution (elastic and kinetic fluctuating) to put in evidence phase transition processes. Again, this interpretation of the results is fundamental to conceive upscaled constitutive relationships based on thermodynamic theories. The numerical results have allowed to highlight the role of the strain acceleration/deceleration, and the evolution of the directional properties of the microstructure even in the collisional regime (never described up to now). Cooling constant volume tests results provide a description, not available in the literature, of the evolving response of the material under pure collisional conditions.

Mechanical characterization and constitutive modeling of aluminum AA1050 subjected to high strain-rates

This work develops an elastic-viscoplastic constitutive formulation to the mechanical behavior of polycrystalline FCC metals subjected to high-strain-rate cold deformation, with application to aluminum AA1050. Following a phenomenological approach, the model can account for important macroscopic features related to the mechanical response of ductile metals subjected to high-velocity plastic deformations, such as: (i) strain-hardening; (ii) strain-rate-hardening; and (iii) instantaneous flow stress rate-sensitivity. As a novelty of this proposal, memory effects corresponding to past strain-rate history are considered to affect both the level and rate of material hardening. Another new aspect is the phenomenological representation of both the thermal activation and dislocation drag mechanisms influencing the instantaneous flow stress response. The model calibration and its validation are performed based upon experimental data for commercial pure aluminum AA1050 for wide strain and strain-rate ranges. In comparison with experiments, the proposed model provides suitable predictions for both continuous and sequential compression tests. Overall, due to its relative simplicity and constitutive capabilities, the proposed model proves to be a potential constitutive alternative to simulate engineering problems involving dynamic plastic deformations.

Effect of strain rate history on the piezomagnetic field of ferromagnetic steels

The goal of this research is to investigate the effect of strain rate history on the piezomagnetic behavior of ferromagnetic steels. Cyclic tensile tests were carried out to record the magnetic fields on the surfaces of Q345 and X80 steel specimens. The impacts of different strain rate histories on the magnetic signals were investigated and the evolutions of piezomagnetic fields of Q345 and X80 steels are closely related to the strain rate history. The magnetic fields demonstrate a systematic evolution when the strain rate history increases from 0.03 min−1 to 0.3 min−1. When the strain rate history decreases from 0.3 min−1 to 0.03 min−1, the magnetic fields remain relatively stable. The results were explained by the movement of magnetic domains and the strength of pinning sites induced by the external stress. This study shows that strain rate history should be considered as one of the variables that influence the piezomagnetic field of ferromagnetic steels.

How sensitivity of metals to strain, strain rate and temperature affects necking onset and hardening in dynamic tests

The material characterization at high strain rates still has room for improvements, especially regarding the possible interactions between strain, strain rate and temperature effects. Some known approximations are still common practice, such as the use of simplified stress–strain calculations at post-necking strains, based on the specimen length, instead of the formulation based on the specimen cross-section. In this work, the behaviour of A2-70 stainless steel at different strain rates and temperature is analyzed, with particular attention to how strain rate and temperature sensitivities affect necking onset and hardening. At the strain rates of interest for this work, the inertia effect is shown to play a secondary role in anticipating or delaying the necking onset. Therefore, the instability onset is firstly analytically derived by just explicitly accounting for the coupling between strain, strain rate and temperature variables within a general multiplicative hardening function, without the need of recalling bifurcation or perturbation analyses. The strains at necking onset, obtained from experiments at different temperatures and strain rates (by hydraulic machine and by tensile Hopkinson bar – SHTB), allow to check the validity of the proposed relationships expressing the combined effect of the relevant variables on the instability condition. Video recordings and image analysis measurements of the deforming round specimens allow comparing the diameter-based effective true stresses, true strains and true strain rates to their nominal length-based counterparts, enabling to quantify the approximation intrinsic in the simplified calculations. The fracture strains and the shapes of necked specimens at incipient failure finally highlighted that the elongation-based approach spoils the accuracy of stress–strain measurements in remarkably different ways for same material, depending on the temperature – strain rate history at hand, thus preventing the use of the latter approach also for merely comparative purposes.

Effect of Strain Rate on the Formation of Strain-Induced Martensite in AISI 304L Stainless Steel

The effect of strain rate on the stress–strain response and the austenite to strain-induced α′-martensite transformation of austenitic steel 304L was studied. Compression tests were carried out at room temperature in the strain rate range of 10−3 to 103 s−1 and the evolution of martensite was quantified using a ferritoscope. Higher strain rates resulted in lower strain-induced α′-martensite. Strain incremental tests were carried out at 1 s−1 to simulate isothermal tests and to delineate effect of adiabatic heating on the α′-martensite transformation. Strain rate change tests were also carried out to determine the effect of prior strain rate history on the strain-induced α′-martensite content. These experiments showed that apart from the effect of adiabatic heating at high strain rates on the α′-martensite content, there is an additional effect of strain rate. While the adiabatic heating effect could be based on the increase in stacking fault energy (reduction of stacking fault width) with temperature, the additional effect due to strain rate was explained based on the expected reduction in stacking fault width with increasing strain rate.