Particle-matrix debonding with Strength-Differential effects

Shear-dominated deformation (SHDD) is pivotal in sheet metal forming; however, comprehensive modeling of plastic anisotropy in SHDD, specifically shear anisotropy considering both yield stress and plastic flow, has been inadequately addressed in existing literature. In this work, a generalized constitutive framework is introduced on the basis of stress triaxiality-dependent state variable to accurately emulate plastic anisotropy and the physics-based shear constraint in SHDD. The framework is capable to seamlessly integrate with existing yield criteria, preserving computational efficiency and versatility. Notably, the yield function, anisotropic parameters, and their optimization or analytical determination for the non-shear deformation state remain unaltered. When integrated with the Hill48 yield function, featuring either one or two anisotropic parameters within the generalized constitutive framework, precise characterization of yield strength and plastic flow in SHDD is achieved. The applicability of the framework extends to various anisotropic yield functions such as the widely employed Yld2k-2d and the sixth-order polynomial (Poly6) function as a class of associated flow rule-based yield functions, and one non-quadratic yield function for non-associated flow rule scenarios. Experimental validation with two engineering sheet metals, high-strength dual-phase steel DP980 and high-strength aluminum alloy AA7075-T6, was conducted. Comparative analyses with several recently proposed yield criteria, especially Poly6–18p, highlighted the efficiency of the proposed constitutive framework. Furthermore, this study explores intrinsic shear constraints, particularly the absence of through-thickness strains under in-plane shear stress. Additionally, it offers an enhanced description of plastic anisotropy in shear yield stress within the general framework, providing valuable insights into the complexities of SHDD.

Effect of anisotropic yield functions on the accuracy of hole expansion simulations

Currently available models describing superplastic deformation are mostly based on uniaxial tensile test data and assume isotropic behavior, thus leading to limited predictive capabilities of material deformation and failure. In this work we present a multi-axial microstructure-based constitutive model that describes the anisotropic superplastic deformation within the continuum theory of viscoplasticity with internal variables. The model accounts for microstructural evolution and employs a generalized anisotropic dynamic yield function. The anisotropic yield function can describe the evolution of the initial state of anisotropy through the evolution of unit vectors defining the direction of anisotropy during deformation. The generalized model is then reduced to the plane stress condition to simulate sheet metal stretching in superplastic blow forming using pressurized gas. Different ratios of biaxial stretching were investigated, including the case simulating the uniaxial loading condition, where the model successfully captured the uniaxial experimental data. The model is also used to develop a new forming pressure profile that accounts for anisotropy and microstructural evolution.

On the implementation of rate-independent standard dissipative solids at finite strain – Variational constitutive updates

Nonquadratic anisotropic yield functions have been developed in recent years for many lightweight automotive sheet metals. Realization of the improved performance of these advanced anisotropic yield functions depends in part on a careful calibration of their material constants via simple mechanical tests. This paper describes a novel approach on the parameter identification of plane–stress polynomial anisotropic yield functions by recasting them in a special form in terms of two principal stresses and one loading orientation angle. Independent mechanical tests for the parameter identification can thus be classified according to the plane stress state and the in-plane loading orientation, respectively. Parameter identification options have been examined in detail for a fourth-order homogeneous polynomial anisotropic yield function using the proposed approach. Some new insights have been gained on the permissible types and the number of independent mechanical test measurements per type that are needed for fully calibrating the material constants of the fourth-order yield function. The use of equal biaxial plastic strain ratio instead of equal biaxial yield stress makes the experimental calibration of the yield function more feasible as only simple in-plane uniaxial tension and out-of-plane compression tests of sheet metal samples are required.

Deformations of a planar doubly periodic array of square elasticinclusions in an isotropically hardening elastic-viscoplastic matrixare analysed. The arrays considered have multiple inclusions per unitcell, but in each array all inclusions have the same size. Overallplane strain tension with a superposed tensile biaxial stress isimposed. A finite deformation formulation is used with a cohesivesurface constitutive relation describing the bonding between theinclusion and the matrix. A characteristic length is introduced fromdimensional considerations since the cohesive properties include thework of separation and the cohesive strength. The system analysed isused to study inclusion distribution effects on void nucleation, withthe aim of providing background for incorporating the effect ofclustering on void nucleation into phenomenological constitutiverelations for progressively cavitating plastic solids. For low valuesof the triaxiality of the imposed stress state, void nucleation occursafter extensive overall plastic straining and regular distributionshave a higher value of the void nucleation strain than randomdistributions. For larger values of stress triaxiality, where void nucleation occurs at relatively small overall plastic strains, theeffect of inclusion size dominates the effect of inclusiondistribution and smaller inclusions give rise to higher void nucleation strains. The ability of various scalar measures ofclustering to characterize the computed dependence of void nucleationon inclusion distribution is explored. Within the context of aphenomenological description of void nucleation, it is found that theeffective void nucleation stress is approximately a linear function ofthe overall hydrostatic tension with a coefficient 0.40-0.44 forregular distributions and 0.25-0.35 for random distributions.The results also suggest a possible dependence of the effective voidnucleation stress on a simple scalar measure of clustering.

A new macroscopically anisotropic pressure dependent yield function for metal matrix composite based on strain gradient plasticity for the microstructure

The deformation behavior of high-strength steel sheet during hole expansion is investigated both experimentally and analytically to clarify the effects of the material model (anisotropic yield function) on the finite element simulation of a hole expansion. The test material used in the hole expansion test is a dual-phase steel alloy with a tensile strength of 780 MPa. The elastic-plastic deformation behavior of the test material is precisely measured using biaxial tensile tests with cruciform specimens to determine the appropriate anisotropic yield function for the test material. Moreover, forming simulations of the hole expansion using selected yield functions are carried out. The Yld2000-2d function [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H., and Chu, E., Int. J. Plasticity, 19 (2003), 1297-1319.] with an exponent of 4 has given the closest agreement with the experimentally measured contours of plastic work and the directions of the plastic strain rates. It was also found that the Yld2000-2d function with an exponent of 4 has given the closest agreement with the observed thickness distribution along the expanded hole edge. Consequently, anisotropic yield functions significantly affect the predictive accuracy of the deformation behavior of a sheet during a hole expansion

For finite strain plasticity with both anisotropic yield functions and anisotropic hyperelasticity, we use the Kröner‐Lee decomposition of the deformation gradient to obtain a differential‐algebraic system (DAE) in the semi‐implicit form and solve it by an implicit Richardson‐extrapolated method based on intermediate substeps. The source is here the right Cauchy‐Green tensor and the consistent Jacobian of the second Piola‐Kirchhoff stress is determined with respect to this source. The system is composed by a smooth nonlinear first‐order differential equation and a non‐smooth algebraic equation. The development of a Richardson‐extrapolated implicit integrator for any hyperelastic case and any yield function is the goal of this work. The integration makes use of a backward‐Euler method for the flow law complemented by the solution of a yield constraint. The resulting system is solved by the Newton‐Raphson method to obtain the plastic multiplier and the elastic right Cauchy‐Green tensor . To ensure power consistency, we make use of the elastic Mandel stress construction. Iso‐error maps for three yield functions and three numerical examples are presented.

Modeling of aluminum alloy sheets based on new anisotropic yield functions

Many metallic sheets exhibit a certain initially plastic anisotropy that influences considerably the mechanical behaviour of the sheet material in forming operations. Nowadays, computer modelling based on the finite element method (FEM) in conjunction with the concept of anisotropic yield functions is successfully utilized to design sheet forming processes. The yield function applied in the FEM analysis affects very strongly the computed results such as material flow, springback, wrinkling and limiting strains. Consequently, in order to increase the accuracy of the FEM simulations the yield function used should be as accurate as possible in order to capture all the important anisotropy effects.In this paper, the new plane stress yield function for orthotropic sheet metals recently introduced by the author (Aretz H 2003 J. Mater. Process. Technol. submitted) is applied to orthotropic steel and aluminium sheet metals. The yield function contains eight anisotropy parameters that may be fitted by means of a Newton solver or a least square solver to selected experimental input data. The main attractiveness of the new yield function lies in its very simple mathematical form, which makes it very effective and thus quite interesting for implementation in finite element codes. The capabilities of the new yield function are demonstrated by applications to selected orthotropic sheet materials.

The mechanical properties of thermomechanical rolled low alloyed (TM) steels highly depend on their microstructure, which is formed during the production processes of the metal plate. Additionally, an elastic‐plastic anisotropy is encountered in these materials due to the texture of the ferritic grains. Hence, the material exhibits different stress‐strain curves in rolling direction (RD), normal direction (ND) and transverse direction (TD).The aim of the present work is to include plastic anisotropy of the body‐centered cubic, ferritic phase in an already existing microstructure‐based model for the elasto‐plastic deformation of TM steels and thereby, to widen the scope of such a model to a broader range of materials. The following contribution discusses the results of simulations on single crystals and bicrystals by using an analytical yield function in order to accomplish a deeper understanding of the behaviour and applicability of an analytical, anisotropic yield function on grain level to describe anisotropically deforming metals.

An elastic-plastic analysis of anisotropic laminated composite plate with a hole is carried out using a two dimensional finite element model based on higher order shear deformation theory (HSDT) of anisotropic laminated composite plates. The variation in material properties through thickness is made possible by discrete layer approach. The generalized Huber-Mises yield criterion, developed by Hill, for anisotropic material, is used to determine the onset of plastic flow. The inclusion of anisotropic parameters of plasticity generalizes the plastic yield function. These anisotropic parameters of plasticity are updated during the work hardening history of anisotropic laminated composite plate. The plastic potential, which is an anisotropic yield function, is used to determine an associated flow rule. Finally, an elastic-plastic incremental constitutive relation is obtained using finite element method. By means of an incremental and iterative procedure, the numerical solution of deformation problems in nonlinear anisotropic laminated plates is achieved based on first order shear deformation theory and higher order shear deformation theory. The transverse shear effects on the load deformation characteristics and on the spread of plastic zones around the circular hole are discussed. This method yields accurate values for transverse shear stresses as compared to other shear deformation theories and hence the growth of plastic zones.

The present paper is devoted to the investigation of the prediction capabilities of the forming limit diagrams via frequently used instability criteria, Marciniak–Kuczynski (M–K) theory and Swift–Hill model. Both models consist of a core algorithm which can be modified by using different yield and hardening functions. In the study, the forming limit characteristics of advanced high strength transformation induced plasticity (TRIP) steel are investigated experimentally and numerically. In the instability criteria, Barlat-89 and YLD2000 anisotropic yield functions are implemented and results are compared. Results reveal that the M–K model is acceptable using the YLD2000-2d anisotropic yield function.

Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models