Influence of Crystal Plasticity Parameters on the Strain Hardening Behavior of Polycrystals

The effective mechanical properties of a polycrystal depend directly on the single-crystal properties of each grain and its crystallographic orientation with respect to the load axis. While the micromechanical approach has been used quite extensively to study the influence of grain shape and crystallographic texture on the resulting mechanical behavior of a polycrystal, the influence of the crystal plasticity parameters, which describe the constitutive behavior of the single crystal, requires to be investigated systemically because, typically, these parameters are fitted to describe a given material behavior. In the current research, this gap is filled by systemically studying the effect of changes in crystal plasticity parameters on the effective mechanical properties of polycrystals. The numerical model employed here consists of a representative volume element of 100 grains, and the material properties are described by using a non-local crystal plasticity model. A proper homogenization technique was used to homogenize the micromechanical results to an effective macroscopic material response. The equivalent stress versus equivalent plastic strain curve was obtained numerically by introducing the Voce-type hardening law, mimicking the material behavior in uniaxial tensile tests. The four parameters of the Voce-type hardening law were fitted to the macroscopic stress-strain curves, and the correlation between the crystal plasticity parameters and the Voce parameters has been studied, which is an efficient way to study the influence of microscopic material descriptions on the macroscopic behavior of polycrystals.

Characterisation of the plane anisotropy and its effect on interstitial free steel thin sheet metal forming simulation

The main purpose of this paper is to study the orthotropic plastic behaviour of the cold-rolled interstitial free steel HC260Y when it is submitted to various loading directions under monotonic tests. The experimental database included tensile tests carried out on specimens (in the as-received condition and after undergoing an annealing heat treatment) cut in different orientations according to the rolling direction. A model was proposed, depending on a plasticity criterion, a hardening law and an evolution law, which takes into account the anisotropy of the material. To validate the proposed identification strategy, a comparison with the experimental results of the planar tension tests, carried out on specimens cut parallel to the rolling direction, was considered. The obtained results allowed the prediction of the behaviour of this material when it is subjected to other solicitations whether simple or compound.

THE EFFECT OF MATERIAL MODELS IN THE FEM SIMULATION ON THE SPRINGBACK PREDICTION OF THE TRIP STEEL

In this work, the influence of material models used in the FEM simulation on the springback prediction is investigated. The interest of this paper is to extend the knowledge base regarding springback predictions in numerical simulation. The springback effect of a V-shaped sheet metal part made of TRIP steel, with a thickness of 0.75 mm was investigated. The bending angle was set to 90°. In the numerical simulation, Hill48 and Barlat yield criteria were used in combination with Ludwik's and Swift's hardening models. Achieved data from the numerical simulations were compared and evaluated with experimental test results. The experimental results showed the relation between springback and calibration force. The effect of specimen cut direction on the springback was smaller in comparison with the calibration force. The numerical results of the springback were not identical with the experimentally achieved springback values in most cases. Particularly, when a calibration force of 1 800 N was used in the simulation. The simulation results showed a good correlation between experimental and numerical results, when Hill48 and Barlat yield criteria were used in combination with Ludwik hardening law and calibration force F with the value 900 N was applied.

Description of the Expansion of a Two-Layer Tube: An Analytic Plane-Strain Solution for Arbitrary Pressure-Independent Yield Criterion and Hardening Law

The main objective of the present paper is to provide a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions for its subsequent use in the preliminary design of hydroforming processes. Each layer’s constitutive equations are an arbitrary pressure-independent yield criterion, its associated plastic flow rule, and an arbitrary hardening law. The elastic portion of strain is neglected. The method of solution is based on two transformations of space variables. Firstly, a Lagrangian coordinate is introduced instead of the Eulerian radial coordinate. Then, the Lagrangian coordinate is replaced with the equivalent strain. The solution reduces to ordinary integrals that, in general, should be evaluated numerically. However, for two hardening laws of practical importance, these integrals are expressed in terms of special functions. Three geometric parameters for the initial configuration, a constitutive parameter, and two arbitrary functions classify the boundary value problem. Therefore, a detailed parametric analysis of the solution is not feasible. The illustrative example demonstrates the effect of the outer layer’s thickness on the pressure applied to the inner radius of the tube.

Localized Necking Model for Punching Fracture Simulation in Unstiffened and Stiffened Panels

The ductile fracture of thin-shell structures was studied here using a localized necking model. The punching experiments for unstiffened and stiffened panels were compared with numerical predictions using a combined ductile fracture and localized necking model using shell elements. The plasticity and fracture model parameters of JIS G3131 SPHC steel were identified by performing calibration experiments on standard flat bars, notched tension, central hole tension, plane strain tension, and shear specimens. The plasticity beyond the onset of necking was modeled using the Swift hardening law. The damage indicator framework with a combined Hosford–Coulomb fracture model and the domain of shell-to-solid equivalence (DSSE) were adopted to characterize the fracture initiation. The model parameters were calibrated based on the loading paths to fracture initiation, which were extracted from a non-linear finite element (FE) analysis. The presented HC–DSSE model was validated using punch tests and was able to predict fracture initiation with good accuracy.

Numerical study of the square cup stamping process: a stochastic analysis

The industrial demand for products with better quality and lower production costs have encouraged the widespread application of the finite element analysis (FEA) in the development and optimization of sheet metal forming processes. To ensure that the FEA solutions are reliable and robust it is important to take into account the uncertainties that inevitably arise in a real industrial environment. In this context, a numerical study on the influence of the material and process uncertainty in the stamping results of a square cup is presented. In this analysis, it is assumed uncertainty in the elasticity properties, hardening law parameters, anisotropy coefficients, blank thickness, friction coefficient and in the blank holder force. The effect of the uncertainty in these input parameters is evaluated in the punch force, equivalent plastic strain, thickness and cup geometry. Firstly, quasi-Monte Carlo method was used to evaluate the variability in the simulation outputs, considering the uncertainty of the input parameters. This analysis shows that the geometry is the output most sensitive to the uncertainty of the input parameters. Afterwards, a variance-based sensitivity analysis was carried out to identify the input parameters that most influence the output variability. It was concluded that the hardening law parameters and the anisotropy coefficients have the most influence in the stamping results variability of a square cup.

The model of plastic deformation and failure of solids

The new model is proposed to explain localized plasticity and failure development in solids. This is based on the idea about the interaction of plasticity acts with acoustic emission pulses. They are generated in the course of the elementary plasticity acts. It is shown experimentally that plastic flow is always localized on the macroscopic scale level. The distribution of localization in the volume has the form of different autowave processes and depends on the work hardening law.