Viscoplastic Constitutive Model Research Articles

Manipulating deformation mechanisms with Y alloying of Mg

The effect of Y concentration on the slip and twinning mechanisms in binary Mg–Y alloys are investigated using transmission electron microscopy, electron backscattered diffraction, and visco-plastic self-consistent polycrystal constitutive modeling. Four concentrations of Y are studied in hot-rolled and recrystallized sheet material. The materials were deformed in tension and compression in the rolling direction and compression in the normal direction in order to invoke distinct proportions of slip and twin mechanisms with each test. Within the single crystal hardening model used in polycrystal modeling, a slip-twin interaction law is introduced to account for dislocation density reductions due to dislocation absorption during twin boundary migration. We show that increasing Y concentration reduces the intensities of both the initial and deformation textures. During deformation, the plastic anisotropy in yield stress, the tension-compression asymmetry, and amount of 101‾2⟨1‾011⟩ twinning is shown to decrease with increasing Y. For each alloy, the model identifies a single set of material parameters that successfully reproduced all measured stress-strain curves and achieved agreement with measured deformation textures and twin area fractions. Transcending texture effects, the model interpretation of the flow responses suggests that increased concentrations of Y increase the critical resolved shear stress for basal slip but have negligible effects on the other slip modes. The reduced plastic anisotropy with increases in Y is explained by a concomitant decrease in the prismatic-to-pyramidal slip critical resolved shear stress ratio. The model suggests that their nearly equivalent critical resolved shear stress values lead to the enhanced non-basal activity of Mg–Y alloys, which was confirmed by transmission electron microscopy. The calculations suggest that beyond any texture differences, this reduction in twinning can be attributed to a slightly increased resistance for 101‾2⟨1‾011⟩ twin propagation, particularly in the binary with the highest Y content.

An Experimental and Numerical Study of Quenching-Induced Residual Stresses Under the Effect of Dynamic Strain Aging in an IN718 Superalloy Disc

Abstract The effects of dynamic strain aging (DSA) on residual stresses generated in Ni-base superalloys during heat treatments are not well understood. In this study, the residual stress field induced by water quenching an IN718 disc while undergoing DSA is studied using coupled thermo-mechanical finite element (FE) analyses in conjunction with neutron diffraction (ND) measurements. A visco-plastic constitutive model that incorporates the effect of DSA is proposed to describe the experimentally observed negative strain rate sensitivity and abnormal temperature dependence phenomena in the stress–strain response of solid solution treated IN718. The predicted quenching residual stresses in the disc agree well with the ND measurements. Due to the DSA, a propagating high plastic strain rate region can be identified in the disc during the early stages of the quenching process. Due to the negative strain rate sensitivity and abnormal temperature dependence effects caused by DSA, the predicted residual stresses are approximately 10% greater than when those two effects are not accounted for. The effects of different convection heat transfer conditions in the FE model are examined and discussed. It is found that the convection heat transfer coefficients have a great influence both on the disc residual stresses and DSA-related plastic strain rate field predictions.

Viscoplastic constitutive modeling of boron steel under large strain conditions and its application in hot semi-cutting

Abstract To overcome the long process time of laser cutting and the high costs for repairing cold blanking tools of ultra-high strength hot stamping components, the hot semi-cutting process was proposed. The reliable testing and parameter identification method of the constitutive behavior under large strain conditions are essential for an accurate simulation of hot stamping and hot semi-cutting process. In the present work, a new testing and parameter identification method for the viscoplastic constitutive behavior of boron steel is proposed based on the Gleeble system, which includes a new grip design, shear specimen selection, and its relevant high-temperature and high-speed digital image correlation (DIC) technology. To obtain the stress-strain curves under large deformation, the FEM-based optimization method is also proposed to identify the hardening parameters. To cover a greater strain range, a new viscoplastic hardening model is proposed based on the dislocation density evolution under elevated temperature deformation conditions. The reliability of the proposed testing method and hardening model is verified by the analysis of uniformity of temperature and strain rate, and the comparison of predicted stress-strain curves with parameters identified from shear and tensile testing. The thermomechanical tension of the center-hole and notched specimen, and the hot semi-cutting process are carried out to verify the proposed testing method and hardening model. The results show that the shear specimen has a more uniform temperature and strain rate distribution in the deformation zone than the tensile specimen. Shear specimens can be used to test the hardening behavior under various process conditions until failure at the large strain. The insensitivity to phase transformations of shear testing is another advantage for identifying the constitutive behavior of the product phase formed during continuous cooling. The constitutive behavior of the boron steel under a large strain range can be accurately identified by using the FEM-based optimization method proposed in this paper. Besides, the mechanical response of the center-hole specimen, notched specimen, and the hot semi-cutting deformation predicted by the proposed hardening model shows accurate results.

Viscoplastic constitutive model of a nickel-based superalloy under multiaxial loading conditions

Based on Chaboche constitutive model, a viscoplastic constitutive model of nickel-based alloy under multiaxial loading is proposed by introducing Lemaitre damage model and non-proportional hardening factor. Lemaitre damage model can characterize the effect of microscopic defects on the fatigue behavior and non-proportional hardening factor is used to describe non-proportional hardening phenomenon. Subsequently, the stress–strain hysteresis loops at room and high temperatures under different loading conditions are simulated by the proposed constitutive model. Comparison between experiments and simulations confirms that the proposed model can reasonably predict the fatigue behavior of nickel-based alloy under different multiaxial loadings. At last, the fatigue life predictions under different multiaxial loadings are investigated, and comparison between experiments and simulations verifies the accuracy of the proposed model.

Constitutive modeling of softening mechanism and damage for Ti–6Al–4V alloy and its application in hot tensile simulation process

In this paper, a unified viscoplastic constitutive model for Ti–6Al–4V alloy coupling with damage and softening mechanisms was established to predict the flow behaviors and damage evolution in hot tensile process. To obtain the flow behaviors of Ti–6Al–4V alloy, the hot tensile tests were performed at temperatures between 750 °C and 850 °C and strain rates of 0.01–1 s−1. Then the evolution of microstructure was investigated by scanning electron microscope (SEM) under hot tensile conditions. Otherwise, the macro-fracture morphology of the tensile specimen was observed by SEM. The flow stress and microstructure evolution were predicted based on the set of constitutive model. The constitutive model was embed in ABAQUS by coding a user-defined material subroutine. The results show that the flow stress increases with the temperature decreasing and the strain rate increasing. By comparing the experimental and calculated results, the flow stress and damage evolution can be accurately predicted by the constitutive model. The fracture due to damage can be well predicted by the simulation model, indicating the good predictability of the constitutive model.

A novel phenomenological constitutive model for Ti-6Al-4V at high temperature conditions and quasi-static strain rates

Phenomenological constitutive modeling of Ti-6Al-4V at temperatures between 923 and 1023 K under 0.0005–0.05 s−1 quasi-static rates is studied based on a phenomenological approach. For this purpose, the Johnson–Cook constitutive model is revisited. At low temperature conditions under moderate to high strain rates, the material’s stress–strain curves are the most similar to power-law function. Contrary to this, at high temperature conditions under low to moderate strain rates, the saturation-type function well describes the stress–strain curves. On the other hand, it is illustrated that the Johnson–Cook constitutive model is feeble to predict the material’s behavior correctly. Accordingly, in this study, a viscoplastic temperature-dependent constitutive model is developed. The strain rate hardening as well as thermal softening of the developed model is the same as the Johnson–Cook model. But a temperature-dependent strain hardening function is proposed in which both the saturation-type and power-law hardening behaviors of the material are implemented. In comparison with the Johnson–Cook model, the new constitutive model’s fidelity in capturing the titanium behavior is depicted. At last, by considering an Arrhenius-type phenomenological constitutive model, it is noted that the developed constitutive model has the best correctness in predicting the Ti-6Al-4V stress–strain behavior at high temperature conditions under quasi-static rates.

Experimental and Numerical Investigation of High-Temperature Low-Cycle Fatigue and Creep-Fatigue Life of Bellows

SS316Ti is one of the widely used materials for bellows in sodium cooled fast reactor systems. Conventional design codes for bellows do not address the high-temperature failure modes. In this investigation, a methodology has been proposed for the high-temperature design of the bellows. The bellows were preliminarily designed by standards of EJMA for room temperature application. Subsequently, the detailed visco-plastic finite element analysis of the bellows has been carried out to estimate the high-temperature low-cycle fatigue (LCF) and creep-fatigue (CFI) life. The material parameters required for the visco-plastic constitutive model were generated and validated for fatigue specimens. The LCF and CFI life of the bellows based on analysis were 83 and 74 cycles, respectively. The proposed methodology has been validated by high-temperature testing of the bellows. The LCF and CFI lives of the bellows obtained experimentally were found to be 281 and 237 cycles, respectively. The life arrived based on analysis was found to be conservative compared to corresponding life by testing. The safety margin available over failure based on testing of the bellows is 3.4 under LCF and 3.2 for CFI loading.

Local Stress–Strain Estimation for Tenon Joint Structure under Multiaxial Cyclic Loading at Non-isothermal High Temperature

In this paper, a method based on the improved effective stress concentration factor is proposed to estimate the local stress–strain for tenon joint structure under multiaxial cyclic loading at non-isothermal high temperature. In order to consider the effect of changing temperature on material properties, the impact caused by temperature on the stress–strain response needs to be introduced to the parameters of material constitutive model. So that, each material parameter in viscoplastic constitutive model is expressed as a function of temperature. In addition, the computing method of the effective stress concentration factor is improved so as to solve the problem of the overestimation for local stress–strain of tenon joint structure in the Neuber rule. Moreover, the proposed notch correction method is coupled with the Chaboche unified viscoplastic constitutive model to estimate the local stress–strain of tenon joint structure at non-isothermal high-temperature condition. To verify the reliability of the proposed method, the calculation results are compared with the nonlinear finite element analysis results under various loading paths at non-isothermal high-temperature condition. The results showed that the proposed method can accurately estimate the notch stress and strain under multiaxial thermo-mechanical cyclic loading.

Scratching aluminium alloys – Modelling and experimental assessment of damage as function of the strain rate

State-of-the-art forming applications, machining, and wear processes generally involve large deformations under high speeds which are often limited to surface near zones. Hence, knowledge about a material's behaviour under such conditions is essential to understand wear or deformation. In this work, two techniques are combined to study the behaviour of two aluminium alloys in the high deformation regime: numerical simulations of a fundamental wear event (scratching) of the surface parametrized with data from high-speed compression test; and experimental scratch tests for comparison. Uniaxial compression tests until 200/s were used to identify the material parameters and revealed a high strain-rate dependence of AA1050, while it was negligible for AA7075. The strain rate behaviour was implemented in the numerical simulations using a viscoplastic constitutive model according to Johnson-Cook during high velocity scratch. The numerical simulations allow to get insight in the stress-distributions during scratching at high velocities. The low velocity scratch regime was covered via experimental scratch tests. The combination of scratch experiments and numerical simulations is a promising tool for capturing the behaviour and get detailed insight into material deformation at velocities not covered by conventional scratch testers.

Elastic/viscoplastic characterization of additively manufactured composite based on continuous carbon fibers

Additive manufacturing (AM) of continuous carbon fiber thermoplastic matrix composites (CFRPs) allows for producing bowtie geometries that are more appropriate to probe the mechanical behavior of these composites. The quasistatic thermomechanical behaviors of different 3D printed composites laminae and laminate were investigated at temperatures below the glass transition of the thermoplastic matrix. The influence of the fiber orientation revealed weak performance of off-axis samples compared to the on-axis lamina and multidirectional laminate. Fractography attributed this degradation to the low fiber volume fraction of carbon fibers; 20-21%, and the inherent defects of the fused filament fabrication (FFF) process. The degradation was most significant along the direction transverse to the loading direction where the stiffness and strength dropped by 44% and 35%, respectively at 90°C compared to the room temperature values. The viscoplastic behavior of the 3D printed composites were probed via series of load relaxation and creep tests at different thermal environments. The results of the experimental tests were utilized to both construct and validate a phenomenological viscoplastic constitutive model of the 3D printed FRPs. The experiments and the model predictions established that 3D printed composites with off-axis fiber orientation exhibit significant stress relaxation and creep deformation. The results also emphasized that the prediction of the viscoplastic model is less accurate for the off-axis AM composite configuration.

Construction of elastic viscoplastic constitutive model and settlement control of over-consolidated soil using finite element software ABAQUS

To study the settlement process of high-filled embankment before and after construction, an elastic viscoplastic constitutive model of over-consolidated soil is designed based on finite element analysis. The model is used to predict the settlement of subgrade before and after construction. First, the lower load surface is used as the reference yield surface of strain rate. Based on the principle of relative over stress, two rate sensitive parameters are established through the measurement of triaxial compression test with different strain rates. Second, the relative over stress function, stress function, and dynamic yield criterion function are established. Finally, two kinds of over-consolidated soils with over-consolidation ratios of 16 and 8 are tested for triaxial shear creep, and the finite element software is used for simulation analysis. The results show that the ultimate axial strain decreases with the decrease of deviatoric stress. When the creep time exceeds 3000min, the model has good prediction effect. The finite element calculation results of different backfill layers in inversion parameters show that the maximum settlement layer of high-filled embankment may not occur at the top or bottom, so attention should be paid in the construction process of high-filled embankment. This exploration provides a reference for the study of long-term deformation and strength of high-filled embankment.

Unified constitutive modeling of Haynes 230 including cyclic hardening/softening and dynamic strain aging under isothermal low-cycle fatigue and fatigue-creep loads

A unified viscoplastic constitutive model with wide temperature adaptability is developed based on the basic framework of the Chaboche type model to capture the intricate cyclic viscoplastic behaviors of Haynes 230 subjected to isothermal low-cycle fatigue and fatigue-creep loads. By introducing effective aging time into drag stress in the hyperbolic sine viscosity function, the critical value of back stress and the additional hardening model, a rate-dependent model based on the dimensionless concentration of solute atoms or precipitates is further improved to realize simulation of dynamic strain aging effects. A multistage evolutionary approach to determining asymptotic value of back stress influenced by strain range and cumulative plastic strain is proposed to respond to cyclic hardening or softening evolved differently with the variation of temperature. For the fatigue-creep interaction, a rate or time dependent directional hardening cumulative model combined with the existing mean stress model is established. After the multi-step material parameter determination method is given, the capabilities of the proposed model are fully validated to accurately depict the mechanical behaviors of Haynes 230 for five representative temperatures.

Three-Dimensional Mechanical–Thermal–Chemical Coupled Mesoscopic Simulation of the Collapse of an Air Bubble in an HMX Crystal

Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) is extensively employed in military weapons as the main constituent of HMX-based polymer-bonded explosives (PBXs). It is known that the safety of PBXs is closely related to their microstructures. Discontinuities in PBXs, such as micron-sized pores, air bubbles, and interfaces between the explosive crystal and polymer bonds, may transform into hot spots when subjected to impact. Herein, a three-dimensional mechanical–thermal–chemical coupled mesoscopic model is proposed to study the collapse of an air bubble in an HMX crystal under impact. A viscoplastic constitutive model and the Birch–Murnaghan equation of state are employed for the HMX crystal to predict its mechanical response. Thermal decomposition of HMX is taken into account by using multistep thermal decomposition equations. The viscoplastic model yields results that reasonably agree with data obtained in the plane shock experiment. The influence of the edge length of the mesh elements on simulation results is analyzed. Then more simulations are conducted for studying the feasibility of using the viscoplastic model for different orientations of the HMX lattice. Afterwards, the coupled model is applied to study the collapse of an air-bubble/pore in the HMX crystal for different impact velocities.

Strain rate and temperature dependent strain localization of dynamically stretched lightweight bars: from metal to polymer

This work studies the dynamic strain localization and constitutive relationship of a Ti3Al2.5V alloy in jet engine containment system and a transparent polycarbonate conceived for aircraft canopy application by Digital Image Correlation (DIC) technique from quasi-static condition to high strain rates at different temperatures. The responses of two materials show significant strain rate and temperature sensitivities. Observations of Ti3Al2.5V alloy show that the dynamic local strain rate can reach values up to 1000 % of the nominal strain rate in the necking zone. However, dynamic local strain rate of polycarbonate soars up during strain softening then decreases rapidly with necking propagation, and eventually becomes 20 % of the nominal strain rate until fracture. Appropriate viscoplastic constitutive models are determined for both materials, which are incorporated in finite element simulations to reveal the trend of dynamic local strain rate evolution in dynamic tensile tests. The present work shows two different kinds of strain localization in typical lightweight materials, which should be addressed carefully from Split Hopkinson Tension Bar (SHTB) tests.

Fatigue Crack Growth in Plastically Compressible Solids: Role of Negative Stress Ratio, Plastic Compressibility and Strain Softening

The effect of cyclic loading on fatigue crack growth in plastically compressible solids is investigated at negative stress ratio under plane strain and small scale yielding conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The plastic crack growth, crack tip opening displacement (CTOD) and near crack tip stress fields are presented using finite element method. Material hardening/ softening has a major relevance on crack growth, CTOD and the evolution of stress distribution. It is revealed here that the negative stress ratio can significantly influence the loading conditions at the crack tip and thereby increase the crack growth for tension–compression loading for hardening material whereas the fatigue crack growth of plastically compressible hardening-softening-hardening material is only slightly affected by the negative stress ratio albeit it is accepted in literature that compressive loads contribute to fatigue crack growth significantly. In the present studies, the CTOD variation with applied load and the near stress distribution are also very unusual in nature.

Fatigue life prediction of 316L stainless steel weld joint including the role of residual stress and its evolution: Experimental and modelling

Weld residual stresses have a great effect on the fatigue strength of welding structures. As an internal stress, the residual stress is unfounded to be treated as the conventional mechanical load during the fatigue safety assessment due to its relaxation and redistribution under cyclic loading. Thus, establishing an accurate model considering the effects of residual stress is critical for fatigue strength design. Therefore, this paper develops a sequential coupling residual stress analysis and a cyclic viscoplastic constitutive model to predict the residual stress evolution and its role on the fatigue life, which has been validated by an experimental measurement of residual stress and a SEM-based observation fatigue fracture morphology. The results show that the role of residual stress on fatigue life is mainly reflected by the increase of mean stress, and its increased magnitudes depends on the stress redistribution. The redistribution of residual stresses is closely correlated to the fatigue fracture behavior of weld joints. And a fatigue life prediction model of weld joints is proposed based on the experimental data of base metal by further considering the residual stress and its redistribution. Finally, the experimental results verify the proposed model on predicting both the fatigue failure location and lives of weld joints, and the predicted lives are within the 1.5 error band.

DISLOCATION-BASED CONSTITUTIVE DESCRIPTION FOR MODELING OF THE 6008 ALUMINUM ALLOY BEHAVIOR

The behavior of the 6008 aluminum alloy under impact loading with different strain rates is experimentally studied. Quasi-static compressive stress–strain curves of these materials are obtained in this study by using an RPL100 material testing machine and a split Hopkinson pressure bar. As the strain rate increases, the yield stress and the peak stress of the materials are found to increase significantly. The adiabatic temperature rise generated during the impact process makes the materials soften, so that the rate of the increase in the flow stress gradually decreases with an increase in the strain rate. Based on the dislocation dynamics theory, a viscoplastic dynamic constitutive model for the 6008 aluminum alloy is constructed. The model accurately describes and predicts the mechanical behavior of this material under impact compression at room temperature.

Finite Difference Modeling of the Interstand Evolutions of Profile and Residual Stress during Hot Strip Rolling

Elastic recovery and viscoplastic stress relaxation occur in the interstand of hot rolling, impacting the evolutions of strip profile and residual stress, which are major concerns for obtaining high-quality flat products. A better understanding of the evolutionary mechanisms would help develop shape control strategies. Therefore, a quasi-3D steady-state elasto-viscoplastic rolling model is developed based on the finite difference method. Predictions of spread, profile, and residual stress are validated through comparisons with a two-stand finite element model. The new model is also complemented with a roll stack model and with a viscoplastic constitutive model calibrated by hot compression tests to simulate a seven-stand hot rolling industrial experiment with low carbon steel. Comparisons between the predicted and measured profiles show a satisfactory accuracy. The simulation costs approximately a minute of CPU time, enabling the new model to run massive parametric campaigns for process optimization. It is found that during the interstand elastic recovery, the transverse compressive stress releases and the strip velocity tends to be uniform, revealing residual stress after a significant change of stress pattern. The stress relaxation mainly occurs at the edge near the roll bite and therefore increases the edge drop of the profile; it also decreases the center crown by changing the distribution of the rolling pressure in the roll bite.

Warm forming simulations of Al-Mg alloy sheet using a viscoplastic model and advanced yield functions

Al-Mg alloys have the properties of anisotropy, temperature softening and strain rate hardening in warm forming conditions. The former could be modeled by an advanced non-quadratic yield function. The rate-dependent characteristic could be modeled by viscoplastic constitutive models. Up to now, few investigations have combined a viscoplastic model with advanced yield functions for warm forming simulation, especially by an implicit finite element (FE) program. In this investigation, the warm forming simulation of AA5182-O alloy was presented via Abaqus/Standard, considering the viscoplasticity and anisotropy. The established viscoplastic model could well reflect the nearly rate-independent initial yield stress of the selected material, and its parameters could be easily calibrated. The numerical implementation of the viscoplastic model associated with Yld2000 and Yld2004 yield functions was carried out using an implicit integration algorithm, and the algorithmic tangent was deduced. Results accordance between the simulation and experiment, including warm uniaxial tension test and warm deep drawing test of AA5182-O, showed the rationality of the established material model and the corresponding implicit implementation scheme.

Uniaxial ratcheting deformation of 316LN stainless steel with dynamic strain aging: Experiments and simulation

Dynamic strain aging (DSA) widely exists in austenitic stainless steel at elevated temperature. The materials will be drastically strengthened by this phenomenon. A series of symmetric strain-controlled and asymmetric stress-controlled cyclic experiments were conducted at different temperatures from 293 K to 823 K for 316LN stainless steel. The DSA phenomenon was observed in all the tests under elevated temperatures and it became more significant with the increase of temperature until reached the maximum at 823 K. There were a series of manifestations of DSA such as the anomalous cyclic hardening with temperature increasing in the strain-controlled tests and the quick-shakedown of ratcheting strain in the stress-controlled tests. An appropriate constitutive model to describe the cyclic behavior at different temperatures is necessary. The proposed kinematic hardening model is based on Ohno-Wang model and modified by introducing a hardening index into dynamic recovery term. The index accounts for DSA hardening degree of material under high temperature, therefore the performance mentioned above can be simulated well by this proposed model. By relating the parameters with temperature and plastic strain amplitude, a unified visco-plastic constitutive model was proposed. Simulation results of the proposed model agree much better with experimental values.