Nonlinear Mixed Hardening Research Articles

Research on welding simulation for vacuum chamber test specimens

The vacuum chamber is an important component of nuclear fusion devices, and the deformation control of the welding process is relatively strict. In this paper, the isothermal multi-level cyclic loading tests have been conducted to explore a nonlinear mixed hardening mode, which can be used as the material input for the welding simulation. Then, welding simulation has been performed for test specimens of the vacuum chamber, and the deformation of test specimens has been obtained under different welding paths. After the first welding simulation is completed, the clamp and limiting plates have been designed based on the deformation of the test specimens. The welding simulation has been performed again with the clamp and limiting plates, in order to evaluate the rationality of the welding process and the design for the clamp and limiting plates. Finally, according to the determined welding process and design for the clamp and limiting plates, welding tests have been conducted, and the welding deformation has been measured. It is found that the difference between the measurement values of the tests and the simulation results is small, which implies that the welding simulation is reasonable.

Characterization and modeling of the hardening and softening behaviors for 7XXX aluminum alloy subjected to welding thermal cycle

The evolution of thermo-elasto-plastic stress-strain during welding process plays a key role in determining the welding residual stresses and mechanical properties of welded joints for age-hardening 7XXX aluminum alloy, which is influenced by the softening and hardening behaviors. In this study, a Gleeble 3800 thermo-mechanical testing machine was employed to simulate the welding thermal cycle process of 7XXX aluminum alloy, and dynamic yield strengths under different temperatures were measured to elucidate the softening behavior. An isothermal multi-level cyclic loading tests at various temperatures were conducted to characterize the cyclic hardening feature. The calculation formulas for the proportion of kinematic and isotropic hardening model were deduced, and the cyclic hardening behavior was quantitatively described. A softening model and a nonlinear mixed hardening model were explored to simulate the evolution of dynamic yield strength and the cyclic hardening behavior, and excellent agreements were obtained between predicted and measured dynamic yield strengths and cyclic stress-strain curves.

Discontinuous plastic flow coupled with strain induced fcc–bcc phase transformation at extremely low temperatures

A popular class of materials massively used at cryogenic temperatures comprises the stainless steels of different grades, such as 304, 304L, 316, 316Ti, 316L, 316LN etc. Such materials are metastable at extremely low temperatures, and usually undergo plastic strain induced phase transformation. In addition, these materials applied in the proximity of absolute zero exhibit the so-called discontinuous (intermittent, serrated) plastic flow (DPF). It consists in frequent, abrupt drops of stress against strain, characterized by increasing amplitude of the stress oscillations. Strong coupling between both phenomena: DPF and phase transformation is observed. Recent experiments performed by means of stainless steel samples tested in liquid helium (4.2 K) clearly indicate strong strain localization during DPF, in the form of shear bands propagating along the sample. However, as soon as the phase transformation process takes place, the motion of shear bands is hindered by formation of secondary phase. A physically based constitutive model developed in the present paper reflects coupling between the discontinuous plastic flow and the plastic strain induced phase transformation in the temperature range 0–T1. The model involves nonlinear mixed hardening, that occurs during the 2nd stage of each serration (stress–strain oscillation). The hardening is based on two mechanisms: interaction of dislocations with the inclusions of secondary phase, evolution of tangent stiffness operator due to changing proportions between the primary and the secondary phases. Nonlinear hardening strongly increases the stress level during each serration, which affects production of the internal lattice barriers, and the amount of the accumulated plastic strain. This, in turn, affects intensity of the phase transformation (full coupling). The constitutive model and its numerical version allow to reproduce the observed serrations, which is crucial for its application in the design of components operating at extremely low temperatures.

Comparison of residual stress induced by TIG and LBW in girth weld of AISI 304 stainless steel pipes

A combined heat source model involving two-part conical models and a cylindrical model was dramatically developed to predict the thermal process of laser beam welding, and a double ellipsoid heat source model was employed to simulate the tungsten inert gas welding process. A nonlinear mixed hardening model and an annealing temperature were considered to character the thermo-elastic-plastic stress-strain behaviour. The developed numerical simulation methods were validated by the experimental measurements. In both cases, excellent agreement was obtained between predicted and measured weld bead macrographs and temperature histories, as well as the welding residual stresses. In terms of the welding residual stress, deformation and production efficiency, the LBW is more advantageous than the TIG on the welding of AISI 304 stainless steel pipes.

On the numerical implementation of the Closest Point Projection algorithm in anisotropic elasto-plasticity with nonlinear mixed hardening

In finite element analysis, among the possible frameworks for stress-point integration algorithms in computational elastoplasticity, the implicit Closest Point Projection (CPP) algorithm is probably the most used one. The idea behind this algorithm is that all necessary variables, including the flow and hardening directions, are iteratively updated and enforced at the final solution. Therefore the algorithm is fully implicit and the final solution is independent of previous iterations. However, there are several possible implementations of the ideas behind the CPP algorithm. Even though asymptotic quadratic convergence may be obtained in all implementations if the algorithm is properly linearized, these different possibilities result in a different number of local iterations and in a different computational effort. Small stress-integration algorithms are frequently the only iterative core of large strain elastoplastic formulations. At the same time they are responsible for a large share of the overall computational time in finite element simulations and key in the overall robustness. In this work we present a new algorithm based on the ideas of the Closest Point Projection algorithm for anisotropic elastoplasticity with mixed hardening. We also compare our proposal with other possible implementations of the CPP algorithm for the same problem, namely the General CPP implementation and the Governing Parameter Method. We show that our proposal is in general more efficient.

Two new hybrid methods in integrating constitutive equations

It is crucial that more powerful integrations be developed as the plasticity models become more sophisticated. Here, two new robust integrating tactics are suggested based on the Exponential map and Euler's algorithms. The integrations are developed for the Drucker–Prager plasticity with nonlinear mixed hardening. Moreover, two different types of exponential strategies are advanced for the plasticity to be compared to the proposed techniques. Dealing with the apex of the yield surface is generally discussed for the integrations as well. Eventually, the proposed algorithms are thoroughly examined in a broad set of numerical tests comprising accuracy, efficiency, and convergence rate investigations. The results demonstrate the supremacy of the suggested schemes amid the six diverse techniques under discussion.

Research on the Reverse Loading Hardening Model of the X80 Pipeline Steel

Based on the reverse uniaxial loading test, the influences of the plastic deformation on the strength properties are studied. The softening of the X80 pipeline steel is observed which reveals the hardening type is mixed hardening. The expression of mixed hardening factor M and the material parameters of the nonlinear mixed hardening model under different M can be obtained. The results show that, if the pre-strain increases and ranges from 0.55% to 2.5%, the mixed hardening characteristics of the X80 pipeline steel will be more obvious and its M will also increase.

Influence of the Number of Tensile/Compression Cycles on the Fitting of a Mixed Hardening Material Model: Roll Levelling Process Case Study

After roll forming processes, metallic coils show several flatness imperfections and residual stresses that must be minimized when high quality components are manufactured by means of sheet metal forming processes. The equipments typically used for this purpose are roll leveling facilities. In the present work, a uniaxial cyclic tension-compression test has been used to determine the mechanical response of steel sheet under the different loading modes. After this, the Chaboche and Lemaitre nonlinear mixed hardening model has been fitted to the material behavior. This hardening model is able to reproduce some phenomena which occur during low cyclic deformation such as Bauschinger effect and workhardening. During the fitting of the model, the number of tension-compression cycles performed in the material characterization and the number of backstresses used for the model definition have been analyzed. Finally the influence of the material model in the roll leveling process results has been numerically analyzed. Different simulations have been performed by introducing initial defects with the objective of predicting residual stresses, residual curvatures, leveling force and torque force at the end of the process.

Seismic behaviour of steel beam to circular CFST column assemblies with external diaphragms

This paper presents experimental and analytical studies on the seismic behaviour of steel I-beam to circular CFST column assemblies with external diaphragms. In the experimental study, four specimens, i.e. two exterior joints and two interior joints in a frame structure, are tested under constant axial loads on columns and cyclic vertical loads on beam ends. The specimens are designed to be strong column-weak beam for exterior joints and strong beam-weak panel zone for interior joints. The failure modes of local buckling on beams and shear deformation of the panel zone are observed in the test. The seismic performance of the beam to column assemblies is assessed by analysing the load–displacement hysteretic curves, the energy dissipation ability and the ductility of the load–displacement skeleton curves. In the analytical study, finite element models of the four test specimens are developed to predict the hysteretic behaviour and the stress distribution. The nonlinear mixed hardening model and the concrete damaged plasticity model are used to define the material properties of steel and concrete, respectively. The steel to concrete interfaces are modelled by hard contact with friction. The fidelity of the model is verified by comparing the prediction with the experimental data. The stress distribution of model components, including steel beams, steel tubes, and concrete cores are illustrated. The results indicate that failure modes have significant effects on the characteristic of stress distribution.

Integration of nonlinear mixed hardening models

PurposeThe purpose of this paper is to present a new effective integration method for cyclic plasticity models.Design/methodology/approachBy defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.FindingsThe numerical tests show the robustness and high efficiency of the proposed integration scheme.Research limitations/implicationsThe von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.Practical implicationsIntegrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.Originality/valueThe paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

Time Integration Algorithm for a Cyclic Damage Coupled Thermo-Viscoplasticity Model for 63Sn-37Pb Solder Applications

In this paper, a semi-implicit time integration scheme has been developed for a damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. The scheme is developed to provide an efficient numerical procedure of integration and iteration for calculating stress and other associated state variables within a strain-driven format. In particular, a novel Newton-Raphson iteration algorithm for the damage coupled constitutive material model involving von Mises viscoplastic potential function with nonlinear mixed hardening is formulated. An algorithmic tangent stiffness tensor is derived and the model is implemented numerically into a commercial finite element (FE) code ABAQUS through its user-defined material subroutine. Several numerical simulations are conducted for validation of the proposed algorithm.

Variational principles for a class of finite step elastoplastic problems with non-linear mixed hardening

A class of elastoplastic relations with non-linear mixed hardening is addressed in the framework of an internal variable theory. The relevant finite step structural problem, resulting from the time integration of the constitutive laws according to a backward difference scheme, is then formulated in a geometrically linear range. Convex analysis and potential theory for monotone multi-valued operators are shown to provide the rationale for the development of a consistent variational theory. As a special result, a convex minimum principle in the final values of displacements, plastic strains and plastic parameters is formulated and a critical comparison with an analogous result proposed in the literature is presented.

Extremum properties of finite-step solutions in elastoplasticity with nonlinear mixed hardening

The class of elastic-plastic constitutive laws assumed herein can be described as follows. We envisage y ⩾ 1 yield criteria (or “modes”) which define the current yield surface; each yield function φα consists of two addends: an effective stress Φα and a yield limit Yα (α = 1,…, y). The former is an order-one, positively homogeneous function of the difference between the stresses σii and reference stresses αii, which are generally nonlinear functional of the plastic strain history, so that kinematic hardening is accounted for. The yield limit Yα is generally a nonlinear function of y nondecreasing internal variables λβ, so that another hardening mechanism (which may reduce to isotropic hardening) is accommodated in the model. The rates of these variables play the role of plastic multipliers in the flow rule.A finite step in the geometrically linear evolutive analysis of such solids is defined according to the backward-difference (or “stepwise holonomic”) strategy for approximate time integration. For the “finite-step” boundary value problem thus arising, various extremum characterizations of solutions are established and the underlying constitutive restrictions are pointed out and discussed.