Plastic Work Research Articles

Process Design for Superalloys Sheet Rotary Forming

Inconel 625 is a nickel superalloy, characterized by high fatigue strength. The alloy is resistant to a wide range of corrosive environments, including high-temperature oxidation. For this reason, it is an attractive material for the chemical, shipbuilding and aviation industries. Inconel 625 alloy is designed for plastic working. However, the significant difficulty is the appropriate process design, due to the high deformation resistance. In order to improve the plastic properties of the alloy, processing at elevated temperatures is practiced. In this work, attempts were made to implement rotary forming process of Inconel 625 superalloy. For this purpose, an experiment was designed, investigating the impact of three variables on the process – feed rate, spinning rate and heating. For the tests were used Inconel 625 metal plates in the shape of discs. Axial-symmetrical products were formed, using a spinning machine. The geometry of the products according to selected quality factors was investigated. Optimal process parameters were chosen using multivariate statistical optimization. These parameters will be used to set up processes to obtain product that meets quality requirements.

Using neural networks to represent von Mises plasticity with isotropic hardening

Neural networks are universal function approximators that form the backbone of most modern machine learning based models. Starting from a conventional return-mapping scheme, the algorithmic description of von Mises plasticity with isotropic hardening is mathematically reformulated such that the relationship between the strain and stress histories may be modeled through a neural network function. In essence, the neural network provides an estimate of the instantaneous elasto-plastic tangent matrix as a function of the current stress and plastic work density. For plane stress conditions, it thus describes a non-linear mapping from ℝ4 to ℝ6. The neural network function is first developed for uniaxial stress conditions including loading histories with tension-compression reversal. Special attention is paid to the identification of the network architecture and artifacts related to overfitting. Furthermore, the performance of networks featuring the same number of total parameters, but different levels of non-linearity, is compared. It is found that a fully-connected feedforward network with five hidden layers and 15 neurons per layer can describe the plane stress plasticity problem with good accuracy. The results also show that a high density of training data (of the order of ten to hundred thousand points) is needed to obtain reasonable estimates for arbitrary loading paths with strains of up to 0.2. The final neural network model is implemented into finite element software through the user material subroutine interface. A simulation of a notched tension experiment is performed to demonstrate that the neural network model yields the same (heterogeneous) mechanical fields as a conventional J2 plasticity model. The present work demonstrates that it is feasible to describe the stress-strain response of a von Mises material through a neural network model without any explicit representation of the yield function, flow rule, hardening law or evolution constraints. It is emphasized that the demonstration of feasibility is the focus of the present work, while the assessment of potential computational advantages is deferred to future research.

Ultra-high strain-rate strengthening in ductile refractory high entropy alloys upon dynamic loading

The mechanical properties and strain-rate strengthening mechanism of single-phase TiZrHfNbTaMox (x = 0.25, 0.5, and 0.75) refractory high entropy alloys (RHEAs) upon dynamic loading are investigated. Dynamic compression with varying strain rates of 2100–6000 s−1 at room temperature are performed by the split-Hopkinson pressure bar (SHPB), and the dynamic yielding strength is about 1.3 times of the quasi-static one. Positive strain-rate sensitivity (SRS) on the yielding strength is available, and the work-hardening is weakened but the yielding strength is improved with increasing strain rates due to the adiabatic heating upon dynamic loadings and the dislocation movement resistance, respectively. Considering the adiabatic temperature rise converted by plastic deformation work at high strain rates, the flow behavior is characterized by employing the modified Johnson-Cook model. A semi-empirical Zerilli-Armstrong constitutive model is proposed to predict yielding strengths at various strain rate.

Proposal and application of a new yield criterion for metal plastic deformation

A new linear yield criterion in terms of principal stresses is developed for the purpose of overcoming the analytical difficulty of mechanical parameters when using the nonlinear Mises yield criterion. This developed yield criterion is established through the parabola interpolation method and the mathematical averaging method, which can be called as the mean influence factor yield criterion, or called MIF yield criterion for short. The yield locus of the criterion on the $$\pi $$-plane is an equilateral and non-equiangular dodecagon, lies between the Tresca and TSS loci, and is very close to the locus of the Mises yield criterion. By comparing with the classical yield criteria, the MIF yield criterion varies linearly with the Lode parameter and has a good accuracy with experimental data. Moreover, based on the flow rule and the geometric projection of the principle stress components, the specific plastic work rate of the yield criterion is also derived. The criterion and its specific plastic work rate are used to solve the limit load of a simply supported circular plate and the forging of a rectangular bar, and both the corresponding analytical solutions are obtained. The theoretical results for the limit load and the forging force are in good agreement with the simulation and experimental data, respectively, and are more accurate than the results calculated from other yield criteria.

Effects of stress triaxiality ratio on the heat build-up of polyamide 11 under loading

Adiabatic heat build-up in polymers attributed to the conversion of plastic work into dissipative heat is a well known phenomenon. The temperature in the vicinity of a crack tip due to heat build-up may be exceptionally high so that it can locally reach the glass transition temperature Tg, even though the ambient testing temperature is lower than Tg. A significant alteration of the local material response and damage mechanisms is then induced. By simultaneous measurement of temperature during experimental tests under quasi-static loading and for a wide range of stress triaxiality ratios, a Gurson-Tvergaard-Needleman based thermo-mechanical constitutive model, integrating temperature-dependent coefficients, has been developed. Predictive capabilities of the proposed thermo-mechanical model to simulate the isothermal behaviour of PolyAmide 11 (PA11) have led to adiabatic simulations, to account for the heat build-up highlighted experimentally, of ductile crack extension. The model parameters were identified using experimental data obtained from PA11 samples with a given stress triaxiality ratio. Predicted evolutions given by the proposed constitutive model for other stress triaxiality ratios and geometries are found to be in good agreement with experimental data.

Study on Plastic Response Under Biaxial Tension and Its Correlation with Formability for Wrought Magnesium Alloys

The mechanical response and microstructural changes under biaxial tension of two magnesium alloy sheets, ZE10 and AZ31, have been investigated. The forming limit diagram (FLD) of the two alloys was further assessed using the Marciniak–Kuczynski (M–K) model combined with two constitutive models: (a) crystal plasticity finite element (CPFE), and (b) phenomenological yield. The FLDs predicted by the combined CPFE and M–K model were in excellent agreement with the experimental data. The phenomenological yield models using the mechanical data at small plastic work led to poor prediction results. However, these could well reproduce the experimental FLDs when the mechanical data at larger plastic work were used for parameter identification. In-depth analyses revealed that the evolution of the anisotropic strain hardening during biaxial tension and significant evolution of the r-value during uniaxial tension were the main sources of the error in the predictions by the phenomenological models using the material data at smaller plastic work.

Elastoplastic 3D analyses of plastic zone size dependencies on load-to-yield strength and on crack size-to-width ratios under mixed mode I/II

A pure mode-I approach cannot properly analyze many important practical problems that involve combined mode I and II loadings, which in particular may not be sufficient to estimate crack paths and fracture toughness in such cases. Multiaxial crack tip conditions characterized by a crack inclination angle β in a modified mixed-mode single edge tension SE(T) specimen are used to consider mixed-mode effects on the shapes and volumes of the plastic zones (pz) that form ahead of crack tips, as well as on the plastic work Upl dissipated inside them. A methodology is proposed to evaluate pz volumes Vpz based on a sub-modeling FE analysis that uses the influence volume around a plastified Gauss integration point. For a given Equivalent Stress Intensity Factor Keq, both Vpz and Upl are evaluated for different nominal stress to yield strength ratios σn/SY and several combinations of geometric parameters β, W/B and a/W, where a is the crack size, W is the cracked specimen width, and B is its thickness. Before performing all these analyses, compatibility and convergence studies are carried out to validate the submodels used in such analyses.

A modified yield function for modeling of the evolving yielding behavior and micro-mechanism in biaxial deformation of sheet metals

In-depth understanding of the evolving plastic yielding behaviors and insight into their micro-scaled mechanisms are critical for fully exploiting of the formability of sheet metals, accurately forming of the needed shape and geometries, and precisely tailoring of the needed quality and property of the deformed parts. In this research, the in-plane yielding behaviors of dual-phase steel and aluminum alloy sheets were extensively investigated by biaxial tension experiments with the original and pre-strained specimens. It is found that the profile of the experimental plastic work contours changes with the increase of plastic deformation, no matter what the proportional or complex loading condition is. This indicates that the evolving yield behavior cannot be neglected. Based on the Yld2000-2d yield function, a modified yield function with introducing a variable exponent to represent the evolving yield behavior was proposed and then employed to model the evolving yielding of the given metallic sheets. To investigate the yielding micro-mechanisms, the simulated biaxial tension tests were conducted by using the established representative volume elements (RVEs) with a crystal plasticity model. The simulation results showed that the texture of the given sheet metals has a significant effect on the profile of the yield loci. Moreover, when the hard secondary phase is added into the polycrystalline aggregate, the optimum exponent of yield function for the given RVEs is increased, instead of decrease within a certain range of the plastic strain. The micro-mechanism of the evolving yielding behavior could be attributed to the ‘pinning’ effect of hard inclusions to the polycrystalline grains, i.e. the hardly-deformable particles strengthening the kinetic constraints to the polycrystalline matrix and further obstructing the rotation and plastic deformation of the neighboring grains. This research thus provides a comprehensive understanding of the effect of microscopic structure (crystal structure, texture and secondary hard phase) on the macroscopic plastic yielding behavior of metallic materials as well as a new high-fidelity modelling technique to describe the evolving yielding behavior phenomenologically, in such a way to support the application of FE simulation in sheet metal forming processes.

Optimized bi-material layouts for energy dissipating composites under finite deformations

This study investigates the use of topology optimization as a method for discovering novel layouts of material phases which enhance the energy dissipation capacity of bi-material polymeric composites. Motivated by the experimental and numerical results in Wang et al. (2011), a multi-material topology optimization approach is developed to design composites consisting of a hard glassy polymer phase and soft elastomer phase undergoing large deformations. Computational homogenization is carried out to simulate the composite behavior and the energy dissipated as plastic work in the glassy polymer phase is maximized. The topology optimization examples investigated herein show the ability of the developed framework to exploit the physical phenomena reported in Wang et al. (2011) to improve energy dissipation capacity. Different deformation modes are considered and the influence of symmetry, phase volume fraction, and material rate effects on optimized composites is investigated. Additionally, the design of composites with a soft phase providing energy dissipation capacity and hard phase providing stiffness is carried out to show how vastly different phenomena are exploited to dissipate energy in optimized composites of this type.

Explicit and accurate characterization of hardening- softening behavior of metals up to failure

Full and accurate characterization of metal hardening-softening effects till failure is carried out with a new explicit approach. To this purpose, a new expression for the plastic work is presented explicitly in terms of the uniaxial stress-strain function of any given form. Accordingly, the yield strength as function of the plastic work can be determined jointly from the above functions with the axial logarithmic strain as parametric variable. Using the proposed approach, any test data obtained within the entire stress-strain range with hardening and softening portions up to failure can be fitted by directly treating a suitable form of the uniaxial stress-strain function. This allows one to bypass usual tedious trial-and-error numerical procedures in dealing with nonlinear elastoplastic rate equations for identifying numerous unknown parameters. Accurate simulation results are shown with numerical examples.

A unified and explicit approach for accurately characterizing the hardening-softening behavior of metals with a tension-compression strength asymmetry

A unified and explicit approach is proposed for accurately characterizing a complex hardening-softening behavior of metals with a tension-compression strength asymmetry. The proposed approach provides an explicit determining of the yield strength as plastic work function and contains the following three procedures: (i) a mode invariant is introduced to express the yield strength as a sum of two uncoupled parts for the tension and the compression case; (ii) a new expression for the plastic work is derived explicitly in terms of the uniaxial stress-strain function and, then, the yield strength function can be determined jointly from the just-mentioned two functions with the axial strain as parametric variable; and, finally, (iii) the axial stress-strain function is presented for representing the hardening-softening features. With these procedures, test data over the entire hardening-softening range can be fitted independently for the tension and the compression cases by directly treating the uniaxial stress-strain function. As such, tedious trial-and-error procedures are bypassed in identifying numerous unknown parameters. Numerical examples show that accurate simulations may be achieved with the proposed approach.

The Interface Microstructure and Mechanical Properties of Niobium-316L Stainless Steel Explosively Welded Composite Plate

In order to manufacture stainless steel helium vessels for the superconducting radio frequency (SRF) cavities, niobium-316L stainless steel composite plates were fabricated by explosive welding technique. The microstructure and mechanical properties of the composite plates were investigated both right after explosive welding and after annealing. The microstructure measurement results demonstrated that there was not any brittle intermetallic layer formed nor any diffusion phenomenon observed after heat treatment processes. Due to the plastic deformation and work hardening near the interface, the hardness of the composite plates was higher near the bonding interface than inside the bulk metal regions. Meanwhile, ultimate tensile strength and shear strength of the composite plate reached their maximum values when the sample was annealed at 873 K for 10 h at room temperature. Charpy impact test results at liquid helium results showed that the toughness of composite plate meets the requirements from the SRF cavities’ helium vessels fabrication.

A unified simulation of low-to-high cycle fatigue failure effects for metals with efficient algorithm

Within the framework of a recently established elastoplasticity model incorporating fatigue failure effects into inherent response features, a new and efficient algorithm is proposed to simultaneously treat fatigue failure effects from low to high cycle cases. From the new model it is possible to derive an explicit algorithm with which the accumulated plastic work is directly calculated by means of a recursive scheme, thus bypassing very time-consuming procedures in carrying out numerical integrations of the elastoplastic rate equations for a large number of loading-unloading cycles. Comparisons of simulation results with fatigue failure data from low to high cycle cases are presented to demonstrate the efficacy of the new algorithm.

Thermomechanical modelling for the linear friction welding process of Ni-based superalloy and verification

This paper presents a fully coupled thermomechanical model for the linear friction welding process of Inconel-718 nickel-based superalloy by using the finite element method. Friction heat, plastic work, and contact formulation were taken into account for two deformable plastic bodies oscillating relative to each other under large compressive force. The modelling results of the thermal history at the weldline interface and thermal field at a distance away from the rubbing surfaces were compared to instrumented data sourced from related publications for model verification. Optimal linear friction welding process parameters were identified via comparison of weld temperature to the liquidus temperature of Inconel-718 alloy. Comparison of interface temperature showed a consistent range of values above the solidus melting temperature (1250 ℃) and below the liquidus melting temperature (1360 ℃) of Inconel-718 alloy. For the first time, a visible linear friction welding process window is identified using a thermomechanical computational modelling method. Through computational modelling, the influence of welding process parameters on the heat transfer and deformation of weld was systematically investigated.

Dynamic Strength of AZ31B-4E and AMX602 Magnesium Alloys Under Shock Loading

Free surface velocity histories for two magnesium (Mg) alloys are obtained from planar shock compression experiments. Symmetric plate impacts at velocities of approximately 400, 600, 800, and 1000 m/s are reported, where axisymmetric cylindrical specimens (flat-faced discs) are launched in single stage light gas guns. The studied specimens have been produced from an equal channel angular extrusion process for Mg AZ31B-4E and from a hot extrusion of consolidated powder prepared via a spinning water atomization process for Mg AMX602. The present studies focus on the region of the velocity profiles spanning the Hugoniot elastic limit through the plastic rise up to the Hugoniot state, as opposed to wave reflection, release and spall studied previously in these materials. A semi-analytical method is invoked to extract inelastic constitutive response information from particle velocity histories. The only parameters entering the procedure are fundamental thermoelastic properties—notably including elastic constants up to order three—and the ratio of plastic work to energy storage of defects generated in the crystal lattice. Plastic shock velocities are not available from the present data; these are estimated from the initial bulk modulus, its pressure derivative, and known shock velocities in conventional Mg AZ31B. Shear stress, plastic strain, plastic strain rate, temperature, and dislocation density are computed outcomes. Results demonstrate similar trends in extracted behaviors for the two alloys, whereby maximum strength in the plastic shock front increases with increasing impact velocity in each material. Strain rate sensitivity appears to be greater in AZ31B-4E than AMX602. Flow stress on the Hugoniot is calculated as 295 to 336 MPa for AZ31B-4E and 163 to 293 MPa for AMX602. Maximum flow stress in the plastic rise, as extracted from tests with maximum impact velocity, is on the order of 700 MPa for each alloy.

Comparative Modeling of Power Hardening Micro-scale Metallic Plates Based on Lower and Higher-Order Strain Gradient Plasticity Theories

Present study investigates a comparative study of lower and higher-order strain gradient plasticity (SGP) theories involving the size-dependent micromechanically flexural behaviors of crystalline thin plates. The investigation includes the Mechanism-Based and the Chen–Wang SGP models established on the Taylor dislocation hardening by evoking the statistically stored dislocations and geometrically necessary dislocations. In addition, these models are conjugated with a multiple plastic work-hardening law proposed for the microstructural applications of the SGP. An analytical approach based on energy minimizing method is used for obtaining deflection values in terms of the length scale, exponent of the work-hardening and the tangential module. The obtained results indicate a meaningful dependence of the deflections to the length scale, plastic work hardening and other parameters as well.

Studies on applying hot-rolled coil to hull superstructure

Application of the hot-rolled steel sheet for the members of superstructure, where the strength requirement of these parts in ships is not severe, is expected as a solution to reduce the hull construction cost. Because the hot-rolled steel sheet is applied after recoiling by cold working to return it to a flat plate, the material properties is deteriorated due to excessive plastic working and the residual stress induced by the plastic work might affect for the thermal cutting and welding. There is a possibility that the hot-rolled steel sheet has poor properties comparing with the flat rolled steels applied for hull parts where the structural integrities are required by the classification societies’ rules. The difference of properties between the hot-rolled steel sheet and the flat rolled steel are investigated in this research.

Some principles of generating seismic input for calculating structures

In this paper different models of seismic input are analyzed. The most essential characteristics of seismic effects are peak ground acceleration, peak ground velocity, peak ground displacement, Arias intensity, cumulative absolute velocity, seismic energy density, harmonic coefficient κ, pseudo spectral kinematic characteristics, root-mean-square peak kinematic characteristics, plastic forces work and damage spectrum. The influence of seismic impulse on characteristics of seismic input is studied. A.A. Dolgaya’s and L.N. Dmitrovskaya’s models with seismic impulse are compared. L.N. Dmitrovskaya’s model allows to reach estimated values of energy characteristics of seismic input with the smallest deviation. When generating such processes, it is important to take into account both the properties of real actions and the limiting state of the calculated structure. The considered models of seismic inputs should be applied in the following cases: a) in case of designing mass construction projects when it is not possible to get a package of design accelerograms, b) in typical designing when the design object can be located on sites with different seismic and geological conditions, c) at early stages of designing important objects when the package of design accelerograms is not available yet but it is necessary to make technical solutions.

Application of 2XXX and 7XXX series alloys as input material for the new casting-forging hybrid process

The aim of the work has been to analyze the aluminum alloys for plastic working from the point of view of their usefulnessin the new hybrid manufacturing process which includes gravity casting and forging. The tests have been carried out onpopular aluminum alloys from the 2xxx and 7xxx series: 2017A, 2024, 7022, and 7075, respectively. The authors have focusedon the problem of using these materials at the casting stage. The analyses have included verification of the technologicalproperties of alloys, including fluidity and the tendency to create porosities. Next, the influence of the solidification rate(associated with the use of various molds) on the casting microstructure has been determined. Based on the conducted analyzes, thealloys with the best casting behavior have been indicated. At the same time, possible problems that may occur at the forging stagehave been discussed.

Hybrid Model of Mathematical and Neural Network Formulations for Rolling Force and Temperature Prediction in Hot Rolling Processes

Steelmaking requires precise calculation at several steps of the manufacturing processes. We focus on the hot rolling process using Steckel mills, almost the end step in steel coil manufacturing. The rolling process is a type of plastic working in which a slab passes between two rolls and is stretched to reach the target thickness. It is necessary to predetermine the exact rolling force to obtain a coil with an accurate thickness after the rolling process. First, we introduced a machine learning model for calculating the rolling force, which can be used in-line in real plants. However, a direct calculation of the rolling force can cause stability problems, because the model output directly affects the process. In order to avoid such a problem, we determined a special temperature of the coil by inverse calculation of the classical mechanical model of hot rolling and set it as the model output value. As learning models, deep neural networks (DNN) and gradient boosting-based decision tree models were used. We preprocessed the collected process history data and added artificial features to the model input by creating physical variables used in the classical models. Moreover, to supplement the black-box nature of DNN, feature importance was analyzed from the decision tree model, and utilization and interpretation of each feature in the process are presented. Thus, our methods take advantage of both the classical mathematical model and the deep neural network model.