Thermo-viscoplastic Constitutive Model Research Articles

Dynamic response and vibration modes of multi-layer wound cylindrical shell for hydrogen storage under external blast loading

Multi-layer wound cylindrical shells are the preferred structures for storage vessels working in high pressure and hydrogen atmosphere. However, they are susceptible to external blast loads from accidental hydrogen explosions. In order to study the response of such structures under external blast loading, a numerical model was developed, which combined a thermo-viscoplastic constitutive model and a fluid-structure coupling approach, and was subjected to external blast loads of different TNT equivalency weights. The strain responses and initial velocity fields of the structure were analyzed. A rigid-plastic theoretical model was also developed to calculate the maximum displacement of the inner shell and was compared with the simulation results. Moreover, the axial velocity vibration histories and dominant frequencies at different locations of the steel belts were numerically obtained. In addition, four vibration modes of the steel belts were presented in this paper. Furthermore, strain growth was observed in the high-frequency vibration area, and the possible reasons for the strain growth were analyzed and discussed in detail. The results will be useful for predicting the deformation modes of such multi-layer wound cylindrical shell structures under the risk of external hydrogen explosions.

Induction of deformation twinning by dynamic strain aging effect: Rate-temperature coupling effect and constitutive modeling

This study focuses on the rate-temperature dependence analysis and constitutive modeling of the DSA-induced deformation twinning, which is a new plastic deformation mechanism discovered in several low-stacking-fault-energy metallic materials. Two types of deformation twinning, namely primary deformation twinning and DSA-induced deformation twinning, were noticed during the plastic deformation of the commercially pure titanium (CP–Ti). The strain, temperature, and strain rate ranges of the DSA-induced deformation twinning, as well as its rate-temperature coupling dependence, were systematically analyzed. The DSA-induced deformation twinning becomes more pronounced with the increasing strain rate and thereby plays a more significant role in enhancing the strain hardening rate than the primary deformation twinning. According to the dynamic Hall-Petch effect of the deformation twinning, a thermo-viscoplastic constitutive model based on the microstructural evolution and the thermal activation theory was developed. The volume fraction of the deformation twins during plastic deformation was expressed as a function of strain, temperature, and strain rate. The developed model was shown to be able to describe the S-shaped true stress vs. true strain curves over the wide ranges of temperature (77–998 K) and strain rate (0.001–8000/s). Finally, considering the interaction between the DSA and deformation twinning, the authors proposed the synergistic strengthening & toughening effect of DSA and deformation twinning, which was believed as a promising mechanism to achieve the simultaneous strengthening and toughing of the metallic materials.

Deformation and Dynamic Response of Steel Belt Staggered Multilayer Cylindrical Shell Under External Blast Loading

Abstract The deformation and dynamic response of a multilayer cylindrical shell composed of an inner shell and fourteen outer layers under external blast loads of different trinitro-toluene equivalency weights were studied. A numerical model using the thermo-viscoplastic constitutive model and considering fluid–structure coupling between explosion wave and structure was developed. The displacement in axial direction and cross section, as well as the effective strain responses, were analyzed to demonstrate the potential deformation of the shell structure. Results demonstrate that different materials cause inconsistent displacement and separation to develop in the inner and outer shells. In order to address the problem that the displacement of the inner shell is hard to measure due to the shielding and covering of the outer shell, a theoretical formula for calculating the maximum displacement of the inner shell was developed. The deflection process and stress triaxiality histories of the inner shell were investigated, and the results showed that compressive stress is the primary cause of plastic deformation. Additionally, the delamination that appeared in the outer shell was discussed, and it was revealed that there are two factors of delamination: (1) Stress waves spread across adjacent layers in the opposite direction because steel belts were wound in the opposite direction between the two adjacent layers; (2) Outer layers experienced uneven compressive loads. The results will be helpful to provide a reference for the intrinsic safety design of such multilayer cylindrical structures for hydrogen storage, etc.

Mechanistic Study of Rail Gouging during Hypersonic Rocket Sled Tests

Gouging—an obstacle to the development of hypersonic rocket sled test techniques—was mechanistically investigated through experimental and theoretical analyses. Typical gouges were analyzed using macroscopic and microscopic experiments to investigate the evolution of gouging. Quasistatic compression and Hopkinson bar experiments were performed to systematically study the thermoviscoplastic properties of U71Mn rail steel under wide ranges of the strain rate and temperature. The critical condition for gouging was derived based on a thermoviscoplastic constitutive model supplemented by a three-variable criterion for an adiabatic shear instability. The results showed the following. (1) Adiabatic shear bands (ASBs) form when stress reduction under the combined action of frictional heating and high-speed deformation exceeds the strain-hardening effect of the rail material. (2) The nonuniform deformation of the edges of ASBs leads to the generation of cracks that split the rail surface. As the ASBs expand, the cracks grow and coalesce, eventually causing the material to peel off, forming gouges. (3) The relationships among the temperature, strain rate, and strain at the onset of gouging can be determined based on the critical condition for the formation of ASBs in rail steel.

Mechanism of rippling deformation of pipe due to internal reflected detonation

The unique rippling deformation of pipe due to internal detonation and reflected shock was studied. Numerical model incorporating thermo-viscoplastic constitutive model and considering the fluid-structure coupling between detonation wave and pipe was developed. Two pipes made of 304 L steel and 6061-T6 aluminum with different diameter-to-thickness ratios were analyzed. The computed pressure histories, strain response and residual plastic strain patterns were in reasonably good agreements with experiments. Through detailed analysis of wave-pipe interaction and the propagation of incident and reflected flexural waves along the pipe, it is revealed that the rippling deformation is caused by two factors: 1) Plastic bugling deformation near the end wall due to reflected maximum peak pressure; 2) Interference between incident and reflected flexural waves. An analytical solution predicting the axial locations of the ripples was also derived. The ripple closest the reflecting end can be caused by only the reflected maximum pressure or together with the interference effect, which depends on the specific material parameter and diameter-to-thickness ratio of the pipe. The resulting plastic deformation was severer if the above two factors act together. The conclusions provide insights to this unique phenomenon.

Dynamic behavior of CrMnFeCoNi high-entropy alloy in impact tension

High-entropy alloys (HEAs), recently emerging alloy materials with numerous excellent performances, may have a wide application prospect in impact engineering. However, previous research regarding the mechanical behavior of HEAs has primarily focused on quasi-static testing, whereas the dynamic mechanical behavior of HEAs at high strain rates remains elusive. In this paper, the unusual simultaneous strength-plasticity enhancement and the inhibition of the high strain rate embrittlement of CrMnFeCoNi HEA in impact tension were revealed via split Hopkinson tensile bar (SHTB) with high-speed photography. Quantitative microstructural analysis indicates that the cooperation of twins and dislocations is the crucial mechanism for the synchronous enhancement of strength-plasticity in this alloy under impact tension. A thermo-viscoplastic constitutive model based on dislocations and twins evolution was developed to describe dynamic mechanical behavior. The high plastic hardening under dynamic tension was revealed to be induced by high dislocation forest hardening and strong resistance of twins to dislocation motion. The excellent combination of dynamic strength-plasticity of CrMnFeCoNi HEA makes it becoming a promising candidate for impact engineering applications.

Proposition and research progress of the third-type strain aging

The traditional knowledge of plastic flow behavior of metal, dislocation activation theory, and thermoviscoplastic constitutive model of metal needs a further perfection due to the occurrence of third-type strain aging. Third-type strain aging leads to a bell-shaped flow stress-temperature curve, that is, the flow stress first increases as temperature increases, and after a peak value is reached, it decreases with further increase of temperature. Third-type strain aging occurs at both low and high strain rates. The bell-shaped segment induced by third-type strain aging on the flow stress-temperature curve shifts to higher temperature region as strain rate increases. In order to develop a systematic understanding of the third-type strain aging, firstly, macro characteristics of third-type stain aging effect that was distinguished from static strain aging effect and Portevin-Le Chatelier dynamic strain aging effect were introduced. Then, the micro mechanism of third-type strain aging and correlation of third-type strain aging, Portevin-Le Chatelier dynamic strain aging, blue brittleness phenomenon, and internal friction were systematically concluded. Third-type strain aging, Portevin-Le Chatelier dynamic strain aging, blue brittleness phenomenon, and mechanical spectroscopy are all resulted from the interaction of mobile dislocations with diffusion atoms. Third-type strain aging, Portevin-Le Chatelier dynamic strain aging, and blue brittleness phenomenon are different manifestations of dynamic strain aging. Third-type strain aging can be considered as another mode of mechanical spectroscopy. The common constitutive models are able to capture the plastic behavior of many metals under the coupling influence of strain rate and temperature in some cases. However, these thermoviscoplastic constitutive models do not take the effect of third-type strain aging into consideration, and they cannot describe the thermoviscoplastic behavior including the third-type strain aging effect. To accurately describe the plastic behavior of metals, some constitutive models including the effect of third type strain aging were proposed. The development of the thermoviscoplastic constitutive model of metal considering the effect of third type strain aging was finally introduced.

Heat treatment simulation of Ti-6Al-4V parts produced by selective laser melting

Abstract The present work focuses on the simulation of the heat treatment applied after printing of Ti-6Al-4V parts. The numerical tool aims at predicting the influence of heat treatment conditions (e.g. holding time, temperature) on the residual stress field and the distortions for SLM produced parts. The numerical model relies on a thermo-viscoplastic constitutive model. To determine the corresponding material parameters, different creep tests have been performed at temperatures ranging from 723 K to 1173 K. According to the results, the stationary creep strain rate is independent of the hydrostatic pressure, which indicates that the high temperature behavior is not impacted by the initial porosity. Also, the material parameters are observed to change significantly from 873 K, which is due to the progressive transformation of the initial martensitic α ′ microstructure into the α + β lamellar microstructure. To validate the proposed approach, some numerical simulations have been performed for two different parts, for which distortions have been measured. The numerical and experimental distortions have then been compared to each other. For both parts, the agreement between experimental and numerical data is correct.

Experimental and numerical study on warm single-point incremental sheet forming (WSPIF) of titanium alloy Ti–6Al–4V, using cartridge heaters

The single-point incremental forming process is an emerging process, which presents an alternative to the conventional sheet metal forming processes like hydroforming and drawing. It is known to be perfectly suited for prototyping and small series. For example, the incremental forming process offers the possibility of manufacturing medical prosthesis or implants specific to each patient, which are more comfortable and guarantee better performance. The customization of this type of product brings better efficiency and better comfort. However, the manufacture of customized titanium prosthesis is not yet industrialized, mainly due to the geometrical inaccuracy of the parts and inability to form parts with a high wall angle. In fact, considerable forces and damage occur during the process limiting the formability. Several studies have already shown that increasing the working temperature allows improving the formability. A reverse engineering approach associated with warm single-point incremental forming process, in order to produce a customized titanium prosthesis, can make the ability to be exploited in the industry to manufacture titanium alloys medical shapes. In this paper, an experimental and numerical study of the warm incremental process based on the use of heat cartridges is performed. The objective is to demonstrate that our low-cost heating system can be used in forming limit angle similar to that obtained with expensive laser heating. The effects of the wall angle at 450 °C on the forming force, thickness distribution and displacement are investigated by producing a truncated cone with Ti–6Al–4V thin sheets. Results show that the formability is significantly improved with the heating. In addition, a thermo-viscoplastic constitutive model is used to simulate the warm incremental forming process. A comparison of the numerical and experimental results shows that the finite element model gives accurate predictions.

Modeling the combined effect of time and temperature on normally consolidated and overconsolidated clays

Clay is under the coupling influence of both time and temperature in some innovative geomechanical problems. Previous experimental researches have confirmed that time and temperature affect the overconsolidation degree of clay and induce overconsolidated characteristics. However, the experimental findings have not been included in constitutive models so far. This paper presents an innovative thermo-viscoplastic constitutive model based on the unified hardening model for overconsolidated clay. The new model combines the effect of time and temperature on overconsolidation by incorporating a temperature variable and a time variable into the hardening law and simultaneously considers the overconsolidated characteristics of clay by using the unified hardening parameter. The simulated results for laboratory tests show that the proposed model can not only reflect the influence of temperature and strain rate on the preconsolidation pressure, the undrained shear strength and the flow rule, but also describe the failure after undrained heating and creeping.

ACMEG-TVP: A thermoviscoplastic constitutive model for geomaterials

In this paper, a thermoviscoplastic constitutive model for geomaterials is presented. The model is formulated based on two aspects: (i) the nonstationary flow surface theory, which is used to describe the viscous behaviour of geomaterials, and (ii) the thermoplasticity concept, which is adopted to introduce the effect of temperature on geomaterials. In the model, the yield surface evolves with the viscoplastic strain, viscoplastic strain rate and temperature. Thus, it allows the description of combined effects of strain rate and temperature on the mechanical behaviour of geomaterials. The model has been used to simulate various tests involving different thermomechanical loading paths, including non-isothermal constant rate of strain tests, cyclic heating and cooling tests, creep tests with temperature changes and stress relaxation tests. The simulation results agree well with measurements, demonstrating the capacity of the proposed model to reproduce the various thermoviscoplastic behaviour of geomaterials.

Challenges in Thermo-mechanical Analysis of Friction Stir Welding Processes

This paper deals with the numerical simulation of friction stir welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic and aerospace industries, where the quality of the joining is of essential importance. The analysis is focused either at global level, considering the full component to be jointed, or locally, studying more in detail the heat affected zone (HAZ). The analysis at global (structural component) level is performed defining the problem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an efficient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the different computational sub-domains is introduced for the numerical modeling. As a result, the analysis can deal with complex (non-cylindrical) pin-shapes and the extremely large deformation of the material at the HAZ without requiring any remeshing or remapping tools. A fully coupled thermo-mechanical framework is proposed for the computational modeling of the FSW processes proposed both at local and global level. A staggered algorithm based on an isothermal fractional step method is introduced. To account for the isochoric behavior of the material when the temperature range is close to the melting point or due to the predominant deviatoric deformations induced by the visco-plastic response, a mixed finite element technology is introduced. The Variational Multi Scale method is used to circumvent the LBB stability condition allowing the use of linear/linear P1/P1 interpolations for displacement (or velocity, ALE/Eulerian formulation) and pressure fields, respectively. The same stabilization strategy is adopted to tackle the instabilities of the temperature field, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework). At global level, the material behavior is characterized by a thermo–elasto–viscoplastic constitutive model. The analysis at local level is characterized by a rigid thermo–visco-plastic constitutive model. Different thermally coupled (non-Newtonian) fluid-like models as Norton–Hoff, Carreau or Sheppard–Wright, among others are tested. To better understand the material flow pattern in the stirring zone, a (Lagrangian based) particle tracing is carried out while post-processing FSW results. A coupling strategy between the analysis of the process zone nearby the pin-tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW.

Constitutive flow behavior of IFAC-1 austenitic stainless steel depicting strain saturation over a wide range of strain rates and temperatures

In this work, model D8A, a thermo-viscoplastic constitutive model is proposed to describe the flow saturation at higher level of strain over a wide range of strain rates and temperatures. Towards this end, isothermal constant true strain rate compression tests were carried out in a temperature range of 1173–1473K and strain rate range of 0.01–100s−1 on IFAC-1 austenitic stainless steel (SS). Effect of strain, strain rate and temperature on compressive flow behavior of IFAC-1 SS was studied, and IFAC-I SS exhibited flow saturation after strain hardening. Modified Zerilli–Armstrong (MZA) model was employed to describe the flow behavior of this steel in the above mentioned strain rate and temperature domain. However, MZA model was inadequate to provide good description of saturating flow behavior of the alloy IFAC-1. Therefore, model D8A was proposed by improvising the MZA model. D8A contains eight material constants and could describe the flow behavior of IFAC-1 in the entire domain with an average absolute error of 4.5%.

Thermo-viscoplastic modeling incorporating dynamic strain aging effect on the uniaxial behavior of Z2CND18.12N stainless steel

Monotonic tension, isothermal/anisothermal fully reversed strain cycling and zero-to-tension cyclic tests were conducted within the temperature domain from room temperature to 823K to investigate the mechanical behavior of Z2CND18.12N austenitic stainless steel under various uniaxial loading conditions. Interesting results were observed from these tests, including obvious rate-dependence at room temperature but lack of rate-dependence at elevated temperatures with the occurrence of serrated flow stress in tensile tests, more cyclic hardening at higher temperature in strain cycling tests, and tendency to reach shakedown condition at elevated temperatures in zero-to-tension cyclic tests. Dynamic strain aging (DSA) effect was presumably believed to contribute to these characteristics of the material. A thermo-viscoplastic constitutive model was proposed to describe the mechanical behavior of the material under uniaxial loading conditions at small strains. Kinematic hardening rule with two components of back stress and isotropic hardening rule incorporating DSA effect are the novel features of the proposed model. The simulated and predicted results show reasonable agreement with the experimental data.

Adiabatic Shear Fractures and Fragments of Cylindrical Structures under Internal Explosive Loading

Adiabatic shear band (ASB) is a typical response of materials under high strain rate loading. Based on the instability analysis of the thermo-viscoplastic constitutive model, a new rate-dependent failure criteria is proposed, which links dynamical evolution of ASB with macro mechanical critical conditions, and is successfully applied to account for the shear fracture mode of cylindrical structures subjected to explosive loading. Using finite element method, the transient failure procedure and shearing fragments induced by ASB is simulated, and the calculated fracture profile shows a good agreement with the experimental results. The failure analysis indicates that the rate-dependent failure criteria, as well as impulsive loading, govern the shear damage mode of the structures.

Instability Analysis and Rate-Dependent Failure Criteria for Adiabatic Shear Band Propagation of Ti-6Al-4V

Adiabatic shearing is a typical response of materials under high strain rate loading. Based on the instability analysis for the thermo-viscoplastic constitutive model, a new rate-dependent failure criterion is proposed, where the failure strain decreases with the increment in strain rate. Using the finite element simulation of the Mode-II impact problem for the titanium alloy Ti-6Al-4V, we verified the damage mechanism induced by adiabatic shear band (ASB) under this rate-dependent failure criterion. Also the ASB propagation path and the width of localized shear band are predicted, which is in a good agreement with experimental observation.

Thermo-viscoplastic behaviour of 2024-T3 aluminium sheets subjected to low velocity perforation at different temperatures

This paper deals with the mechanical behaviour of the aluminium alloy 2024-T3. This alloy has particular relevance since it is widely used in the aeronautical industry for building aircraft structures. The deformation behaviour of this material has been characterised in tension under wide ranges of strain rate and temperature. Among the aluminium alloys, the AA 2024-T3 highlights due to its high flow stress and strain hardening. Moreover, the material temperature sensitivity has been found dependent on plastic strain. The Modified Rusinek– Klepaczko constitutive description [Rusinek A, Rodríguez-Martínez JA, Arias A. A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper. Int. J. Mech. Sci. 52 (2010) 120–135], which takes into account such dependence of the temperature sensitivity on plastic strain, has been applied for modelling the thermo-viscoplastic response of the material. Satisfactory agreement between experiments and analytical predictions provided by the Modified Rusinek– Klepaczko model has been found. In order to study the material behaviour under impact loading, low velocity perforation tests on AA 2024-T3 sheets have been performed at different initial temperatures using a drop weight tower. Plastic instabilities formation and progression are identified as the cause behind the target collapse for all the impact tests conducted. The results from these perforation tests are compared with those reported in [Rodríguez-Martínez JA, Pesci R, Rusinek A, Arias A, Zaera R, Pedroche DA. Thermo-mechanical behaviour of TRIP 1000 steel sheets subjected to low velocity perforation by conical projectiles at different temperatures. Int. J. Solids Struct. 47 (2010) 1268–1284.] for TRIP 1000 steel sheets. The comparison reveals that the amount of specific energy absorbed by the aluminium targets is much lower than that corresponding to the steel targets. The role played by inertia on delaying plastic instabilities formation is determined as potential responsible for such behaviour.

Creep, plasticity, and fatigue of single crystal superalloy

Single crystal components in gas turbine engines are subject to such extreme temperatures and stresses that life prediction becomes highly inaccurate resulting in components that can only be shown to meet their requirements through experience. Reliable life prediction methodologies are required both for design and life management. In order to address this issue we have developed a thermo-viscoplastic constitutive model for single crystal materials. Our incremental large strain formulation additively decomposes the inelastic strain rate into components along the octahedral and cubic slip planes. We have developed a crystallographic-based creep constitutive model able to predict sigmoidal creep behavior of Ni base superalloys. Inelastic shear rate along each slip system is expressed as a sum of a time dependent creep component and a rate independent plastic component. We develop a new robust, computationally efficient rate-independent crystal plasticity approach and combined it with creep flow rule calibrated for Ni-based superalloys. The transient variation of each of the inelastic components includes a back stress for kinematic hardening and latent hardening parameters to account for the stress evolution with inelastic strain as well as the evolution for dislocation densities. The complete formulation accurately predicts both monotonic and cyclic tests at different crystallographic orientations for constant and variable temperature conditions (low cycle fatigue (LCF) and thermo-mechanical fatigue (TMF) tests). Based on the test and modeling results we formulate a new life prediction criterion suitable for both LCF and TMF conditions.

Failure criteria with unilateral conditions for simulation of plate perforation

Abstract Finite element analysis of plate perforation is performed using a thermoelastic–thermoviscoplastic constitutive model and two uncoupled damage criteria with unilateral conditions. The first criterion is based on continuum damage mechanics, while the second is the Cockcroft–Latham criterion. Fracture is assumed to occur at a critical damage, and crack propagation is modelled with element erosion. The identification of the material parameters is based on inverse modelling of a uniaxial tension test. The constitutive model and damage criteria are applied in explicit finite element analysis of the perforation of a 12 mm thick steel plate struck by a blunt projectile in the sub-ordinance velocity regime. The results show the importance of the unilateral conditions in obtaining accurate prediction of the adiabatic shear banding process. The two fracture criteria have comparable dependence on the stress triaxiality and the Lode parameter when the microcrack-closure parameter is set to zero in the criterion based on continuum damage mechanics, and give similar failure mode and ballistic limit in the plate perforation problem.

Thermomechanical behavior of thermoset shape memory polymer programmed by cold-compression: Testing and constitutive modeling

Programming is a key process for thermally activated stress or strain recovery of shape memory polymers (SMPs). Typically, programming requires an initial heating above the glass transition temperature ( T g ), subsequent cooling below T g and removal of the applied load, in order to fix a temporary shape. This work adopted a new approach to program thermoset SMPs directly at temperatures well below T g , which effectively simplified the shape fixing process. 1-D compression programming below T g and free shape recovery of a thermoset SMP were experimentally investigated. Functional stability of the shape fixity under various environmental attacks was also experimentally evaluated. A mechanism-based thermoviscoelastic–thermoviscoplastic constitutive model incorporating structural and stress relaxation was then developed to predict the nonlinear shape memory behavior of the SMP trained below T g . Comparison between the prediction and the experiment showed good agreement. The structure dependence of the thermomechanical behavior of the SMP was further discussed through a parametric study per the validated constitutive model. This study validates that programming by cold-compression is a viable alternative for thermally responsive thermoset SMPs.