Showing papers on "Viscoplasticity published in 2021"

Peridynamic modelling of blasting induced rock fractures

Abstract: This paper presents a peridynamics-based computational approach for modelling blasting induced rock fractures. A new non-ordinary state-based peridynamics approach is proposed in conjunction with a Johnson-Holmquist (JH2) constitutive model to consider the pressure dependency, strain rate effect, and viscoplasticity of rocks under blasting loads. The fracturing process in a rock is assessed based on both the JH2 damage model and a tension failure model. The former evaluates the material response pertaining to excessive plastic strain and the latter is used to gauge failure based on tensile stress in consideration of strain rate effect. Detonation in the explosives is simulated using updated Lagrangian peridynamics in conjunction with Jones-Wilkins-Lee (JWL) equation of state. Simulations of single-hole blasting in granite rock are presented and compared with experimental records. The proposed approach is shown to capture reasonably well the plastic material failure surrounding the borehole as well as the tensile cracks on both radial and circumferential directions. Further sensitivity studies indicate that the intact strength parameters in the JH2 model and the tensile strength of material play a vital role in producing the obtained fracture patterns and should hereby be selected with care. The presented computational approach offers a rigorous basis for future development of versatile, multi-physics-integrated computational framework on rock blasting simulations.

Unification of the Rheological Physics of Yield Stress Fluids.

Abstract: The physics above and below the yield stress is unified by a simple model for viscoplasticity that accounts for the nonlinear rheology of multiple yield stress fluids. The model has a rate-dependent relaxation time, allows for plastic deformation below the yield stress, and indicates that rapid elastic deformation aids yielding. A range of commonly observed rheological behaviors are predicted, including the smooth overshoot in the loss modulus and the recently discovered contributions from recoverable and unrecoverable strains in amplitude sweeps.

Modified Johnson-Cook model of aluminum alloy 6016-T6 sheets at low dynamic strain rates

Abstract: The use of a dynamical constitutive model is essential for the numerical analysis of dynamic impact. In this study, uniaxial tension tests were conducted on aluminum alloy (AA) 6016-T6 sheets under different strain rates (0.001–100/s). The results show that the flow properties of AA 6016-T6 is slightly sensitive to strain rate. A modified Johnson-Cook (J-C) model based on the archetype of the J-C equation was developed by integrating the strain rate hardening coefficient with the strain rate. Compared to the original J-C model, the modified J-C model could describe the flow behavior of AA 6016-T6 under different strain rates with an acceptable prediction error of 0.0415%. Moreover, finite element simulations were performed by implementing the modified J-C model into Abaqus/Explicit through the VUMAT subroutine, resulting in a modified J-C equation could accurately predict the plastic deformation of AA 6016-T6.

A fractional elasto-viscoplastic model for describing creep behavior of soft soil

Abstract: In order to solve the analytical solution of the general rate-dependent model and make the theoretical model better reflect the creep behavior of soil, the fractional calculus theory is applied to the EVP (elastic–viscoplastic) model based on the overstress theory. A fractional strain rate model is proposed to construct a constitutive equation of fractional strain rate. The analytical solution of the fractional creep model is solved by applying Laplace integral transformation, and the fractional creep equation under undrained conditions is discussed. Then, the undrained shear creep test results of isotropic consolidated Fukakusa clay and K0 consolidated Sackville clay are used to verify the validity of the time-based fractional creep equation and the sensitivity analysis of the analytical solution. The effectiveness of the fractional creep model for predicting the creep behavior of soil such as soft clay is revealed. The results show that the fractional EVP creep model is obviously better than the traditional integer EVP model. Moreover, when the fractional order is 1, the fractional strain rate model can be reduced to an integer strain rate model, but the fractional creep equation degenerates into a linear creep equation.

A unified viscoplastic model and strain rate–temperature equivalence of frozen soil under impact loading

Abstract: Based on the double-pulse shaping technology, a method for obtaining long rising edge loading pulse by using the structural response of a pulse shaper is proposed. The traditional split Hopkinson pressure bar (SHPB) was improved to be suitable for testing the dynamic mechanical properties of low wave impedance materials. The dynamic mechanical properties of frozen soil at different temperatures and strain rates were tested using the improved SHPB equipment. The increase in the strength of frozen soil was associated with a decrease in temperature and increase in strain rate. The strain rate–temperature equivalence of frozen soil is proposed by regression analysis of the experimental data. The relationship between the temperature and strain rate of frozen soil satisfied the Arrhenius equation and could be explained by the thermal activation mechanism. The thermal softening characteristics of frozen soil caused by the adiabatic heating under impact loading were analyzed, and described by the damage variable driven by the adiabatic heating. The damage dynamic constitutive model is proposed based on the unified viscoplastic theory. The comparison between the model and experimental results indicate the applicability of the model.

An improved unified viscoplastic model for modelling low cycle fatigue and creep fatigue interaction loadings of 9-12%Cr steel

Abstract: An accurate constitutive model is one of the basic aspects to ensure a precise simulation. This study presents an improved unified viscoplastic model to simulate the various behavior of P92 steel under low cycle fatigue (LCF) and creep fatigue interaction (CFI) loadings. In the proposed model, an accumulated inelastic strain dependent parameter is introduced into the nonlinear kinematic hardening rule to represent the evolutionary behavior of strain-stress hysteresis loops and the varied relaxation behavior during CFI loadings. The traditional isotropic hardening rule is modified as well to capture the accelerated cyclic softening phenomena observed in the prolonged hold time of CFI tests. To validate the accuracy and the predictive capability of the proposed model, LCF tests at various strain amplitudes and CFI tests at different hold time are conducted at elevated temperature of 650 °C. Good agreement between the experimental and simulated results verifies the robustness of the proposed model. In addition, the proposed model is distinguished from published models by few determined material parameters.

The strain characteristics and corresponding model of rock materials under uniaxial cyclic load/unload compression and their deformation and fatigue damage analysis

Abstract: The fatigue characteristics of rock materials are usually studied by cyclic load–unload tests, and the deformation and damage development reflect their weakening characteristics. In this paper, according to the mechanical characteristics of rock materials during load/unload cycles, the total strain can be separated into three types, that is, elastic strain, viscoelastic strain, and viscoplastic strain. The elastic strain is linear with stress, and viscoelastic strain exhibits a special behavior after unloading, the viscoplastic strain also displays its own unique features and reflects the damage in rocks. Based on their unique characteristics, we establish elastic, viscoelastic, and viscoplastic submodels, then an elastic-visco-plastic model can be obtained by connecting three submodels in series, which can reflect the development of the law of different strains. In order to verify the reliability of the model, red sandstone samples are selected for cyclic load/unload tests. The results show that the collected strain–time data are well fitted by the model. In addition, the characteristics of strain–time curves imply the deformation and damage development of rocks during load/unload cycles.

A combined viscoelasticity-viscoplasticity-anisotropic damage model with evolving internal state variables applied to fiber reinforced polymer composites

Abstract: A thermodynamically-consistent large strain viscoelasticity-viscoplasticity-damage Internal State Variable (ISV) constitutive material model integrated with a mixture theory combining each individu...

Creep-damage constitutive model based on fractional derivatives and its application in salt cavern gas storage

Abstract: The long-term stability of oil / gas salt cavern storage is still considered as a puzzle, which leads to enormous challenges in its construction and operation. To describe the creep behavior of salt rock more accurately, a new fractional derivative creep-damage (FDCD) constitutive model, based on a modified Mohr-Coulomb criterion, is established by coupling the Hooke body, Abel dashpot and viscoplastic damage body. Previous creep models, especially those coupled with creep and damage, are rarely verified by very long-term creep experimental data. By fitting the creep experimental data of salt rock lasting 21,000 and 15,876 h (875 and 661.5 days), it is found that the proposed model can well characterize the experimental data, especially in the accelerated creep stage. Compared with the classic Nishihara and Burgers models, the FDCD constitutive model has significant advantages, with fewer parameters and higher accuracy. Then the FDCD constitutive model is implemented in FLAC3D with C++ language and applied to the deformation analysis of salt cavern gas storage. The deformation and volume shrinkage of salt caverns obtained by the numerical simulation are in good agreement with those measured by sonar. The FDCD constitutive model can be successfully applied to a numerical program for evaluating the long-term deformation of salt cavern gas storage.

Thermomechanical behaviors of polyether ether ketone (PEEK) with stretch-induced anisotropy

Abstract: Polyether ether ketone (PEEK) is a semi-crystalline thermoplastic polymer with excellent thermo-mechanical properties, bio-compatibility, corrosion resistance, and 3D printability. Due to these merits, it has wide applications in aeronautics and biomedical devices. However, PEEK's excellent thermo-mechanical properties come from its complicated crystalline domains, making it hard to predict and to design PEEK structures under complex service conditions. In this paper, we studied the thermomechanical behaviors of PEEK with stretch-induced anisotropy and developed a constitutive model to incorporate the influence of the complex loading history along different loading axes. From the experiments, it was found that when it is stretched, PEEK demonstrates viscoplastic behaviors with reduced transversal modulus and yield stress in the subsequent loading, due to the initiation and growth of voids during stretching. The tensile sample also shows a necking behavior at relatively low temperature. To capture these behaviors, the constitutive model consists of two main parts. The undamaged part has three branches, one hyperelastic branch for the nonlinear elastic behavior, one viscoelastic branch for glass transition and relaxation in the amorphous domains, and one plastic branch for yielding and hardening in the crystalline domains. The damaged loose-chain part with history-dependent reduced relaxation time is used to capture the microscopic interface debonding between the crystallites and the amorphous domains. Compared with the experimental results, this model captures the stretch-induced volume expansion and the anisotropic evolution of material properties. This developed model is also able to capture the temperature-dependent necking phenomenon and the corresponding nominal stress-strain behaviors in the uniaxial tensile tests at different strain rates and temperatures. The developed model can be used to facilitate the design of PEEK-based structures under complicated loading conditions.

A viscoelastic-viscoplastic mechanical model of time-dependent materials based on variable-order fractional derivative

Abstract: A fractional viscoelastic-viscoplastic model is developed for time-dependent materials, by considering the reference stress in the fractional viscoelastic body. Using this model, the creep, stress relaxation and strain rate behavior is numerically analyzed for frozen soil and zeonex results, with the consideration of continuous order functions that conform to the order interval limits. Subsequently, a variable-order viscoelastic-viscoplastic creep model and also a variable-order viscoelastic-viscoplastic strain rate model are established by the developed variable-order viscoplastic and fractional viscoelastic models, respectively. Finally, the rheological behavior of frozen soil and Zeonex is simulated using the variable-order viscoelastic-viscoplastic creep model and variable-order viscoelastic-viscoplastic strain rate model, and the model parameters are analyzed. The results show that the proposed order function equation is continuous and conforms to the interval effect of the definition. The variable-order viscoelastic-viscoplastic rheological model takes into account the elastic-visco-plastic behavior of the material in the rheological process, and has high accuracy.

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.

Modified Johnson-Cook constitutive model of metallic materials under a wide range of temperatures and strain rates

Abstract: This study concentrated on presenting the classical Johnson-Cook model by introducing a new temperature term, under the framework of an equivalence between heat energy and distortional strain energy. Importantly, the inner relationship among temperature, elastic modulus, the specific heat capacity at constant pressure, and Poisson's ratio was established quantitatively. What the nicest character this term had was that there were no fitting parameters, which made the model be applicable when the temperature was lower than the reference temperature. Thus, the improved Johnson-Cook model could effectively predict the mechanical behavior over a wide range of strain rates and temperatures. Using sets of experimental data with varying temperatures and strain rates, a multi-objective approach combined with the Latin hypercube sampling method, Spearman rank correlation analysis, and an advanced genetic algorithm, was applied for the constitutive model parameter identification and optimization. Consequently, the stress-strain responses of several metallic materials under various complex conditions were reproduced by the proposed model. It was shown that there was a good agreement between the prediction and experiment results, even though the temperature was lower than the reference temperature.

Stability and deformations of deposited layers in material extrusion additive manufacturing

Abstract: This paper presents computational fluid dynamics simulations of the deposition flow during printing of multiple layers in material extrusion additive manufacturing. The developed model predicts the morphology of the deposited layers and captures the layer deformations during the printing of viscoplastic materials. The physics is governed by the continuity and momentum equations with the Bingham constitutive model, formulated as a generalized Newtonian fluid. The cross-sectional shapes of the deposited layers are predicted, and the deformation of layers is studied for different constitutive parameters of the material. It is shown that the deformation of layers is due to the hydrostatic pressure of the printed material, as well as the extrusion pressure during the extrusion. The simulations show that a higher yield stress results in prints with less deformations, while a higher plastic viscosity leads to larger deformations in the deposited layers. Moreover, the influence of the printing speed, extrusion speed, layer height, and nozzle diameter on the deformation of the printed layers is investigated. Finally, the model provides a conservative estimate of the required increase in yield stress that a viscoplastic material demands after deposition in order to support the hydrostatic and extrusion pressure of the subsequently printed layers.