Numerical and Experimental Studies on Hydro-Forming of a Thin Metallic Disc

This paper deals with the hydro-forming of a flat thin metallic disc to achieve a forward domed disc which will be subsequently adopted to manufacture a rupture disc. The plastic deformation induced by the hydraulic energy is numerically simulated through an isotropic hardening plasticity model using a non-linear explicit finite element analysis (FEA). The variation in disc’s central deformation, thickness, equivalent plastic stress and equivalent plastic strain with respect to the applied hydraulic pressure are determined from FEA simulations. The hydro-forming setup is then designed and manufactured, and the metallic disc is experimented under hydro-forming process. The reduction in thickness due to stretching of the thin disc is evaluated from experiment and simulation and a close agreement is found. This research attempt helped in finalizing the hydro-forming fluid pressure, the feasibility and the accuracy of practically achieving the desired geometry of the metallic disc. The near-fixidity effects on abrupt variation in sheet thickness and plastic strain are well captured through simulations which are very difficult to be studied through hydro-forming experiments.

Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil

In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.

The Refined Model of the Elastic-Plastic Dynamic Behavior of Reinforced Curved Panels Sensitive to Strain Rate

The initial-boundary value problem of dynamic elastic-viscoplastic deformation of flexible curved panels (shallow shells) with plane -cross and spatial reinforcement structures is formulated. The inelastic behavior of the materials of the composition components is described by the constitutive equations of the theory of plastic flow with isotropic hardening, and their sensitivity to strain rate is taken into account. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The used kinematic and dynamic two-dimensional relations and the corresponding boundary conditions make it possible to describe, with varying degrees of accuracy, the mechanical bending behavior of shallow composite shells. This takes into account the possible weak resistance of such reinforced panels to transverse shears. In the first approximation, the used two-dimensional equations, the initial and boundary conditions degenerate into the relations of the traditional non-classical Ambartsumyan theory. For the numerical integration of the formulated nonlinear dynamic problem, an algorithm of time steps is applied, based on the use of an explicit scheme of the cross type. The elastoplastic and elastic-viscoplastic behavior of the reinforced cylindrical shallow shells under transverse dynamic loads generated by an air blast wave is investigated. Metal-composite and fiberglass thin-walled constructions are considered. It is shown that the refusal to take into account the dependence of the plastic properties of the components of the composition on the rate of their deformation does not allow adequately describing the inelastic dynamic behavior of both metal-composite and fiberglass shallow shells. It is shown that in the calculations of even relatively thin reinforced cylindrical panels (with a relative thickness of 1/50), the use of the Ambartsumyan theory leads to completely unacceptable results in comparison with the refined bending theory. It has been demonstrated that even for relatively thin curved fiberglass panels, replacing the traditional flat -cross reinforcement structure with a spatial structure with obliquely laid fiber families can significantly reduce not only the intensity of deformations in the binder, but also the maximum deflection values in modulus. For metal-composite shallow shells with a weakly expressed anisotropy of the composition, the positive effect of the indicated replacement of reinforcement structures is practically not manifested.

On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

In this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Residual stresses in gas tungsten arc welding: a novel phase-field thermo-elastoplasticity modeling and parameter treatment framework

The fusion welding process of metallic components, such as using gas tungsten arc welding (GTAW), is often accompanied by detrimental deformations and residual stresses, which affect the strength and functionality of these components. In this work, a phase-field model, usually used to track the states of phase-change materials, is embedded in a thermo-elastoplastic finite element model to simulate the GTAW process and estimate the residual stresses. This embedment allows to track the moving melting front of the metallic material induced by the welding heat source and, thus, splits the domain into soft and hard solid regions with a diffusive interface between them. Additionally, temperature- and phase-field-dependent material properties are considered. The J2 plasticity model with isotropic hardening is considered. The coupled system of equations is solved in the FE package FEniCS, whereas two- and three-dimensional initial-boundary-value problems are introduced and the results are compared with reference data from the literature.

Anisotropy of a Selective Laser-Melted Ti–6Al–4V Lattice Structure

Selective laser melting (SLM) is a widely adopted additive manufacturing process for the preparation of metallic lattice structures. However, it causes a build-direction-dependent anisotropy of morphologies, microstructures, and mechanical properties, making it difficult to predict the behavior and performance of lattice structures. In this study, tensile samples with different cross-sections and build directions (BDs) were fabricated by SLM. The anisotropic morphology, microstructure, and tensile properties were observed and measured using optical microscopy, scanning electron microscopy, and three-dimensional digital image correlation to determine the effects of the size and BD of SLMed materials. The extracted data were sequentially used to modify the geometric and physical models of the lattice. Body-centered cubic lattice structures were fabricated by SLM, and compression tests were performed to verify the modified compression model. In addition to the BD-related grains, the cross-sectional area of the SLMed sample affects its mechanical properties. The small cross-section makes the microstructure finer because the proportion of the contour path that uses higher power is no longer negligible. The sample with small cross-section has more anisotropy because of the lack of tolerance to heterogeneity and macro defects like roughness. In this study, by analyzing samples with small cross-sections, a model consisting of an isotropic hardening law and Hill’s anisotropic yield function is established to describe the yield and plasticity behavior of the as-built SLMed Ti–6Al–4V lattice. The simulated and experimental data fit very well, verifying the methodology employed in this study.

A Design Optimization Study for the Die Dimensioning Using the Locking Nut Folding Simulation

An inverse analysis based on optimization process is performed to determine die curvatures for a locking nut’s flange folding process which has highly nonlinear material behaviour. The nut material is AISI C1040 steel. The ring material is polyamide 6. The Chaboche’s nonlinear kinematic hardening rule is combined with bilinear isotropic hardening model as a hardening rule for the plasticity model combined with associated flow rule and von Mises yield criterion. The inverse analysis is applied to determine the curvatures by using genetic algorithm optimization method based on dimensional accuracy. The optimum mould curvatures are determined. So a comprehensive methodology is presented for determination of curvatures.

Thermodynamics and Analysis of Predicted Responses of a Phase Field Model for Ductile Fracture

The fundamental idea in phase field theories is to assume the presence of an additional state variable, the so-called phase field, and its gradient in the general functional used for the description of the behaviour of materials. In linear elastic fracture mechanics the phase field is employed to capture the surface energy of the crack, while in damage mechanics it represents the variable of isotropic damage. The present paper is concerned, in the context of plasticity and ductile fracture, with a commonly used phase field model in fracture mechanics. On the one hand, an appropriate framework for thermodynamical consistency is outlined. On the other hand, an analysis of the model responses for cyclic loading conditions and pure kinematic or pure isotropic hardening are shown.

Effect of reverse thermoelastic phase transformation on stress of onset of structural deformation in titanium nickelide

The experimental study results of the dependence in the stress value of the onset of the structural deformation on the degree of the reverse phase transformation occurring after the complete direct martensitic transformation in titanium nickelide are described. It is established that these results are qualitatively and quantitatively correctly described in the framework of the model according to which the maximum value of the intensity of the intrinsic inelastic deformation of the martensitic part of the representative volume of the shape-memory alloy is used as a parameter of isotropic hardening.