Anisotropic Plastic Material Research Articles

A new texture descriptor for data-driven constitutive modeling of anisotropic plasticity

Constitutive modeling of anisotropic plastic material behavior traditionally follows a deductive scheme, relying on empirical observations that are cast into analytic equations, the so-called phenomenological yield functions. Recently, data-driven constitutive modeling has emerged as an alternative to phenomenological models as it offers a more general way to describe the material behavior with no or fewer assumptions. In data-driven constitutive modeling, methods of statistical learning are applied to infer the yield function directly from a data set generated by experiments or numerical simulations. Currently these data sets solely consist of stresses and strains, considering the microstructure only implicitly. Similar to the phenomenological approach, this limits the generality of the inferred material model, as it is only valid for the specific material employed in the virtual or physical experiments. In this work, we present a new generic descriptor for crystallographic texture that allows an explicit consideration of the microstructure in data-driven constitutive modeling. This descriptor compromises between generality and complexity and is based on an approximately equidistant discretization of the orientation space. We prove its ability to capture the structure–property relationships between a variety of cubic–orthorhombic textures and their anisotropic plastic behavior expressed by the yield function Yld2004-18p. Three different machine learning models trained with the descriptor can predict yield loci as well as r-values of unseen microstructures with sufficient accuracy. The descriptor allows an explicit consideration of crystallographic texture, providing a pathway to microstructure-sensitive data-driven constitutive modeling.

A new hybrid phase-field model for modeling mixed-mode cracking process in anisotropic plastic rock-like materials

Mixed-mode cracking is widely encountered in rock-like geomaterials under compression-controlled loadings. Some pending issues still need to be addressed. This work focuses on a new hybrid phase-field fracture method for cracking behavior of anisotropic plastic materials. Several new approaches are introduced. Firstly, a unified decomposition method of elastic strain energy driving crack growth is proposed by combining the advantages of classical spectral and volumetric–deviatoric decomposition algorithms. Then a new damage field evolution criterion is established, allowing to considering a nonlinear interaction between two basic crack propagation modes. The contribution of plastic strain energy to cracking process is investigated by considering an anisotropic yield criterion and combined isotropic-kinematic hardening laws. The validation of the established phase-field model is assessed by a series of representative examples, showing different types of cracking patterns. Sensitivity analysis of some key parameters involved in the model is also carried out to clarify the respective impacts on the progressive cracking patterns. Finally, the effectiveness of the proposed approach is validated by comparison with experimental results.

Data-oriented description of texture-dependent anisotropic material behavior

In metallurgical processes, as for example cold rolling or deep drawing of sheet metal, it is frequently observed that the crystallographic texture, and with it the anisotropic mechanical properties of a material, evolve dynamically. Hence, to describe such processes, it is necessary to model the functional dependence of anisotropic material parameters on the texture, which itself can vary locally with the different plastic strain histories. In this work, we present a new data-oriented approach to parametrize the anisotropic yield function Barlat Yld2004-18p from micromechanical simulations for different textures. This is accomplished by applying supervised machine learning (ML) methods to express the relationship between different crystallographic textures and the material parameters of the yield function. The crystallographic textures are chosen to vary continuously between a random texture on the one hand side, and a unimodal Goss or Copper texture the other. These crystallographic textures are rather common in sheet metal forming. In this way, furthermore, the transition from isotropic plasticity to a rather severe case of anisotropy can be modeled, which is thought to mimic the dynamical evolution of the texture in a metallurgical process. It is found that a regularization strategy is necessary to circumvent the known non-uniqueness between Yld2004-18p parameters and the resulting plastic yield behavior. After this regularization, a unique relationship between the material parameters and the yield onset is established, making it possible to train different ML models with excellent accuracy and generalization properties to anisotropic plastic material behavior. The trained ML models are able to reliably predict the coefficients of unknown textures even with a small amount of training data and, thus, to correctly represent the yield behavior resulting from the various textures. The proposed method represents an efficient extension of the description of anisotropic plastic yielding as it establishes a data-oriented way to explicitly consider microstructural parameters in the material description, which opens new pathways to formulate material models that include the process history.

Developing an anisotropic material for Engineered Material Arresting System (EMAS) usage

ABSTRACT An Engineered Material Arresting System (EMAS) is a bed of crushable material located at the end of an airfield runway within the runway safety area (RSA). An EMAS promotes aircraft stoppage during an aircraft overrun event. Typically, EMAS installations consist of isotropic cementitious material blocks. In contrast, this article explores the potential for using a light-weight anisotropic plastic material composed of unidirectional tubes (honeycomb configuration) as an alternative EMAS material. During this study, a number of laboratory tests were conducted to characterise the stress–strain behaviour of the proposed material. The material testing considered multiple force incidence angles with respect to the material tube orientation. These anisotropic material characterisation results were used as input to a numerical model for determining aircraft performance within an EMAS. The calculated performance results were then compared with the aircraft performance within the EMAS considering other potential EMAS isotropic materials. The results suggest that the compressive strength of the proposed anisotropic material needs to be reduced in order to compare well with those of other potential isotropic materials. The present article analyzes overrun events with the anisotropic material internal tubes oriented parallel to the aircraft motion direction.

Chip formation in machining of anisotropic plastic materials—a finite element modeling strategy applied to wood

This paper presents an FEA modeling strategy for predicting the cutting forces generated during linear wood machining. The objective is to determine both the forces and paths of cracks propagating in elastoplastic and anisotropic materials. The model combines a bilinear representation of the material strain-stress relation and the Hill yield function. The proposed procedure also integrates the displacement extrapolation method to evaluate the stress intensity factors. It establishes the cutting forces from the contact pressures between the tool and the chip. These pressures are determined using the penalty method. The validation phase compares the model predictions with average experimental forces and shows correspondence levels higher than 91% and 92% for low (0.085e10−3 m/s) and high (6.8 m/s) wood-feeding speeds, respectively. The developed model maintains a high precision degree over a large range of feeding-velocity. This study demonstrates that the resistive force between the chip and the tool surface is a function of both the rake angle φ and the coefficient of friction (COF). The friction force prompts a self-energizing effect, which increases the resistive force. On the other hand, larger φ amplitudes reduce this effect. Furthermore, the rake angle φ defines the crack propagation mode. Larger φ amplitudes favor the opening mode, whereas smaller values promote the shear mode. The COF amplitude also influences the surface quality, with larger COFs producing more profound cutting dimples. Thus, reducing the COF should result not only in lower cutting forces but also in a better surface quality of machined parts.

Key factors towards a high-quality additive manufacturing process with ABS material

Additive Manufacturing technologies have gained a lot of popularity during the past years. The current challenge being the transition of this manufacturing technology from prototype oriented towards mass production. In order to achieve this, fabrication times and mechanical parameters must be improved. This paper aims to identify which are the parameters that have the highest influence on parts obtained with fused deposition modeling (FDM) technology from ABS material. In addition, this study identifies which are the most accurate methods to test the mechanical properties of FDM parts while still respecting ASTM standard for testing the tensile properties of plastics. It was found that ASTM D638-02a type I samples are the most suitable to perform tests on high anisotropic plastic materials. The experiment also demonstrates that the build orientation and the wall thickness of FDM fabricated parts has the highest influence on the mechanical properties.

Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements

The focus of this paper is on consistent and accurate adjoint sensitivity analyses for structural topology optimization with anisotropic plastic materials under plane strain conditions. In order to avoid the locking issue, the Enhanced Assumed Strain (EAS) elements are adopted in the finite element discretization, and the anisotropic Hoffman plasticity model, which can simulate the strength differences in tension and compression, is incorporated within the framework of density-based topology optimization. The path-dependent sensitivity analysis is presented wherein the enhanced element parameters are consistently incorporated in the constraints. The objective of topology optimization is to maximize the plastic work. Several numerical examples are presented to show the effectiveness of the proposed framework. The results illustrate that the optimized topologies are highly dependent on the plastic anisotropic material properties.

Texture Based Finite Element Simulation of a Two-Step Can Forming Process

Aluminum sheets used for beverage cans show a significant anisotropic plastic material behavior in sheet metal forming operations. In a deep drawing process of cups this anisotropy leads to a non-uniform height, i.e., an earing profile. The prediction of this earing profiles is important for the optimization of the forming process. In most cases the earing behavior cannot be predicted precisely based on phenomenological material models. In the presented work a micromechanical, texture-based model is used to simulate the first two steps (cupping and redrawing) of a can forming process. The predictions of the earing profile after each step are compared to experimental data. The mechanical modeling is done with a large strain elastic visco-plastic crystal plasticity material model with Norton type flow rule for each crystal. The response of the polycrystal is approximated by a Taylor type homogenization scheme. The simulations are carried out in the framework of the finite element method. The shape of the earing profile from the finite element simulation is compared to experimental profiles.

A Formulation of Additive Finite Anisotropic Thermo‐Plasticity in Logarithmic Lagrangean Strain‐Entropy Space

AbstractA phenomenological model of rate‐independent thermo‐plasticity at finite strains is discussed. The formulation is based on an additive decomposition of the strain measure into an elastic and plastic part as proposed by Green and Naghdi. A constitutive model in the logarithmic Lagrangean strain‐entropy space is developed capable of modelling isotropic elastic and anisotropic plastic material behaviour. The staggered solution scheme for coupled thermo‐mechanical problems employs an isentropic phase for the deformation and an iso‐geometrical phase for the thermal field. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Estimation of the anisotropic plastic property using single spherical indentation—An FEM study

Abstract In this study, a method to evaluate the in-plane anisotropic plastic properties of engineering steels by single spherical indentation is proposed. This method deals with materials that obey the work hardening law and have in-plane anisotropy of the yield stress in orthogonal directions. The method thus estimates the yield stress σ Y , the work hardening exponent n , and the ratio of the yield stresses m . Computations were first carried out by the finite element method (FEM) in order to quantitatively study the deformation surrounding the impression, when the spherical indenter was pressed against the anisotropic plastic materials. The permanent impression that remained after fully unloading the indenter was found to be non-uniform. The pile-up height in the direction of lower yield stress becomes higher than that in the direction of high yield stress. Such differences in height were found to become larger when m is higher. Based on this characteristic, extensive FEM calculations were carried out in order to propose the method to identify the anisotropic plastic properties for various materials whose mechanical properties are available for many engineering steels. The method involves several functions that relate the indentation response (indentation curve and geometry of impression) to the anisotropic plastic property of the material. Numerical experiments were conducted in order to verify the effectiveness of the proposed method.

A Green–Naghdi approach to finite anisotropic rate-independent and rate-dependent thermo-plasticity in logarithmic Lagrangean strain–entropy space

The paper presents a phenomenological model of rate-independent and rate-dependent thermo-plasticity in the logarithmic Lagrangean strain–entropy space at finite strains. The formulation and computational implementation are based on an additive decomposition of the strain measure into an elastic and plastic part as proposed by Green and Naghdi. A rate-independent and rate-dependent constitutive model in the logarithmic Lagrangean strain–entropy space is developed for the modelling of isotropic elastic and anisotropic plastic material behaviour. Furthermore, the notion of a plastic metric as proposed by Miehe, an isotropic hardening variable and the notion of a plastic entropy as proposed by Simo and Miehe dominate the internal variable description. The model keeps the classical general return-mapping scheme in the implicit integration algorithm of the internal variables of associative thermo-plasticity. The resulting coupled thermo-mechanical problem is solved staggeredly via an isentropic phase for the deformation and an iso-geometrical phase for the thermal field. Representative numerical simulations demonstrate the performance of the proposed model.

Numerical modeling of the development of kink-bands in anisotropic plastic materials

Numerical modeling of the development of kink-bands in anisotropic plastic materials

Determination of Constitutive Equation Parameter Using Finite Element Polycrystalline Model.

A plastic constitutive theory incorporating the directional dependence of the plastic strain increment dep on the stress increment dσ' was proposed by Goya and Ito. The expression was given in terms of two transition parameters μ(α) and β(α) which denote the magnitude and the direction angle of the plastic increment, where α denotes the direction angle of the stress increment measured from a particular direction nN, named direction, in which the direction of the stress increment coincide with that of the plastic strain increment. In this report, a computer code for a finite element polycrystalline model is used for the numerical investigation of the variation of the two constitutive parameters μ(α) and β(α) of anisotropic plastic materials. The results show that the approximate functions for the two transition parameters are numerically determined and the direction dependence rule can be naturally extended for anisotropic plastic materials. It is also suggested that several quadratic functions used for classical plastic potential may be introduced for the natural direction potential whose normal is identical to the natural direction.

Recent advances in the numerical modeling of constitutive relations

In this paper we present an overview of the recent developments in the area of numerical and finite element modeling of nonlinear constitutive relations. The paper discusses elastic, hyperelastic, elastoplastic and anisotropic plastic material models. In the hyperelastic model an emphasis is given to the method by which the incompressibility constraint is applied. A systematic and general procedure for the numerical treatment of hyperelastic model is presented. In the elastoplastic model both infinitesimal and large strain cases are discussed. Various concerns and implications in extending infinitesimal theories into large strain case are pointed out. In the anisotropic elastoplastic case, emphasis is given to the practicality of proposed theories and its feasible and economical use in the finite element environment.

An application of the Tsaï criterion as a plastic flow law for timber bolted joint modelling

This paper describes a modelling approach to predict the behaviour of an elementary thin timber bolted joint. The application concerns principally joints with steel side members; bolts have a constant 12 mm diameter with two ratios of end distance to bolt diameter and two bolt clearances. The behaviour of the bolted joints is characterized by a double non linearity; the first one is due to the contact area evolution between the bolt and the hole of the jointed elements. The second one is owing to the evolution of plasticity on the wood. A spring element compatible with isoparametric plane finite elements represents the contact evolution. The elastic-plastic wood is provided with a plastic flow rule according to the Tsai criterion. This study allows an investigation on the parameters characterizing the Tsai criterion, particularly F12 which represents the interaction between the principal axis of orthotropy. A two-dimensional model is used. It permits the assessment of the clearance bolt, joint dimensions, wood plasticity and wood grain angle effect on the joint behaviour. The wood grain angle has a non negligible effect on the plastic strains distribution and it can create a parasite loading because the joint tends to rotate even for an axial loading. The results showed a good agreement between experimental values given by some authors and numerically-predicted stresses on the joint. So, the applications concern a two-dimensional joint with anisotropic plastic material. The generalization in the three-dimensional modelling is desirable to take into account the interaction between the wood and a metallic fastener in thick joints with different geometric characteristics.

立方異方性弾・塑性体の単純伸び

The constitutive equations of the cubic anisotropic plastic materials are generalized to satisfy the principle of material frame-indifference. The constitutive equations obtained in accordance with the requirement for the plastic flow state are assumed to hold in all states, i.e., the natural unstrained state and the plastic flow state. As an example, the simple extension of the materials is analyzed, and the stress-extension relation is obtained. The result shows a gradual transition from the elastic state to the plastic flow state. The comparison between cubic anisotropic and isotropic materials is discussed briefly.

Plastic Analysis of Fiber-Reinforced Shells of Revolution

The yield surface for a shell of revolution which is loaded axisymmetrically and made of an anisotropic plastic material which obeys the maximum shear stress theory of Lance and Robinson is developed in this paper. The material is a model of a ductile matrix reinforced unidirectionally with ductile fibers. The principal axes of the material are assumed to be aligned with the principal axes of stress in the shell. Using the developed yield surface, the complete solution for the problem of plastic analysis of a shallow conical shell with circumferential reinforcement loaded by an axismmetric lateral force applied to a rigid central boss is obtained.

Plastic analysis of filled, reinforced, circular cylindrical shells

Circular cylindrical shells made of anisotropic plastic material and filled with an incompressible fluid are subjected to a ring of load which is centrally located. The anisotropic material is a model of a composite material consisting of a ductile matrix reinforced either circumferentially or longitudinally with ductile fibers. Limit loads for all sizes of shell are obtained and their dependence on the degree of reinforcement is determined. The presence of the fluid considerably increases the limit loads over those for unfilled shells. The limitation due to finite transverse shearing stress is considered and is shown to have a significant effect on the strength of such structures.