Phase-field modeling for anisotropic ductile damage of magnesium alloys at finite deformations

The damage anisotropy of an extruded ZK60 Mg alloy is characterized using tensile tests and scanning electronic microscopy.The accumulation of anisotropic deformations leads to the great differences of the dimple evolution and strains at fracture along different loading directions.To introduce the anisotropic deformation information into the damage constitutive relationship,a thermodynamically consistent phase-field model of ductile damage fully coupled with elastoplastic finite deformations is developed in this study.Using the user-defined constitutive relationship and displacement-temperature coupling element,the finite element simulations are conducted.The results show that:(1)ZK60 Mg alloys presents clear R-value difference in 0°,45°,and 90°tests of intact specimens.The 45°test possesses the greatest R-value(1.50)and the greatest strain at fracture,however,the R-value for 0°is less than 1,indicating the thinning is preferential.(2)The higher ultimate stress leads to a larger average dimension of the dimples,whereas the higher density correlates with a larger elongation ratio at the fracture.The disappearance of the stress-bearing area indicates that the phase-field assumption on stress degradation is completely compatible with the dimple analysis on fractography.(3)The simulation results of the stress-strain relationships and damage paths correlate well with the experimental ductile damage of magnesium alloys at 200◦C.Slight errors are basically attributed to the modeling parameters and finite element iteration algorithm.The proposed model presents fine applicability and reliability for the predictions of plastic deformations,ductile damage,and fracture of anisotropic Mg alloys.

Prediction of fracture limits of Ni-Cr based alloy under warm forming condition using ductile damage models and numerical method

The stretch forming and the deep-drawing processes were carried out at 300 and 673 K to determine the safe forming and fracture limits of IN625 alloy.The experimentally obtained strain-based fracture forming limit diagram(FFLD)was transformed into a stress-based(σ-FFLD)and effective plastic strain(EPS)vs triaxiality(η)plot to remove the excess dependency of fracture limits over the strains.For the prediction of fracture limits,seven different damage models were calibrated.The Oh model displayed the best ability to predict the fracture locus with the least absolute error.Though the experimentally obtained fracture limits have only been used for the numerical analysis,none of the considered damage models predicted the fracture strains over the entire considered range of stress triaxiality(0.33<η<0.66).The deep drawing process window helped to determine wrinkling,safe and fracture zones while drawing the cylindrical cups under different temperature and lubricating conditions.Further,the highest drawing ratio of 2 was achieved at 673 K under the lubricating condition.All the numerically predicted results of both stretch forming and deep drawing processes using the Hill 1948 anisotropic yielding function were found to be good within the acceptable range of error.

On Ductile Damage Modelling of Heterogeneous Material Using Second-Order Homogenization Approach

The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework is described.The structure at the macrolevel is discretized by the triangular C^(1) finite elements obeying nonlocal continuum theory,while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable.The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity.The macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent strain.The softening at each material point at the macrolevel is detected by the critical value of the homogenized damage,where homogenization of the damage variable is performed onlywithin softening area.Due to the nonlocal continuumtheory applied,a realistic softening behaviour is demonstrated after the damage initiation,compared to the widely used first-order homogenization approach.All algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark problems.The damage evolution at both microlevel and macrolevel has been demonstrated.

NUMERICAL PREDICTIONS AND EXPERIMENTAL VALIDATIONS OF DUCTILE DAMAGE EVOLUTION IN SHEET METAL FORMING PROCESSES

Prediction of forming limit in sheet metal forming is among the most important challenges confronting researchers. In this paper, a fully coupled elastic-plastic-damage model has been developed and implemented into an explicit code. Due to the adoption of the plane stress and finite strain theories, model can predict deformation and damage of parts quickly and accurately. Also, damage initiation, propagation, and fracture in some operations are predicted and validated with experiments. It is concluded that finite strain combined with continuum damage mechanics can be used as a quick tool to predict ductile damage, fracture, and forming limits in sheet metal forming processes.

Numerical simulation of ductile fracture behavior for aluminum alloy sheet under cyclic plastic deformation

A numerical analysis of mechanical behavior of aluminum alloy sheet under cyclic plastic deformation was investigated.Forming limit at fracture was derived from Cockcroft-Latham ductile damage criterion.The strain path of bending center of incremental roller hemming could be accepted as a kind of plane strain bending deformation process.Incremental rope roller hemming could be used to alleviate ductile fracture behavior by changing the stress state of the hemming-effected area.SEM observation on the fracture surface indicates that cyclic plastic deformation affects ductile fracture mechanism.

Numerical Methodology for Metal Forming Processes Using Elastoplastic Model with Damage Occurrence

Ductile damage often occurs during metal forming processes due to the large thermo-elasto （visco） plastic flow Iocalisation. This paper presents a numerical methodology, which aims to virtually improve any metal forming processes. The methodology is based on elastoplastic constitutive equations accounting for nonlinear mixed isotropic and kinematic hardening strongly coupled with isotropic ductile damage. An adaptive remeshing scheme based on geometrical and physical error estimates including a kill element procedure is used. Some numerical results are presented to show the capability of the model to predict the damage initiation and growth during the metal forming processes.

Numerical simulation and optimization of process parameters in fineblanking process

Fineblanking process is a typical large localized plastic deformation process. Based on its forming characteristics, a numerical model is established and an elasto-plastic simulation is performed using the finite element method （FEM）. The re-meshing method is used when the severe element distortion occurs to facilitate further computation and avoid divergence. The McClintock fracture criterion is adopted to predict and determine the time and site of crack initiation and propagation. Based on this numerical model, the distribution and developing trend of the stress and strain in the shearing zone are predicted. Furthermore, the influence of several process parameters, such as punch-die clearance, edge radius of punch and die, V-ring force, counter force, etc., on the blanked quality is analyzed. The discipline is in accordance with the actual manufacture situation, which can be a guidance to optimization of process parameters.

A LOWER BOUND APPROACH TO THE YIELD LOCI OF POROUS MATERIALS

A lower bound approach is proposed for the first time to solve the macroscopic yield loci of porous materials.The results are then compared with Gurson's upper bound yield loci and those of the experiments.It is shown that the present analysis is much more in accordance with the experimen- tal results than the Gurson's.

Analysis of Sheet Metal Extrusion Process Using Finite Element Method

Sheet bulk metal forming processes have been widely developed to the facilitate manufacture of complicated 3D parts. However, there is still not enough know-how available. In this paper, as one of the typical sheet bulk metal forming processes, the sheet metal extrusion process was studied. A reasonable finite element method （FEM） model of sheet metal extrusion process taking the influence of flow-stress curve with wide range of plastic strain and ductile damage into consideration was established and simulated by an arbitrary Lagrangian-Eulerian （ALE） FEM implemented in MSC.Marc. Validated by comparing the results with experiment, some phenomenological characteristics, such as metal flow behavior, shrinkage cavity, and the influence of different combinations of diameter of punch, diameter of extrusion outlet, and diameter of pre-punched hole were analyzed and concluded, which can be used as theoretical fundamental for the design of the sheet metal extrusion process.

An Improved Ductile Fracture Criterion for Fine-blanking Process

In order to accurately simulate the fine-blanking process, a suitable ductile fracture is significant.So an evaluation strategy based on experimental and corresponding simulation results of tensile, compression, torsion and fine-blanking test is designed to evaluate five typical ductile fracture criteria, which are widely-used in metal forming process.The stress triaxiality and ductile damage of each test specimen are analyzed.The results show that none of these five criteria is sufficient for all tests.Furthermore, an improved fracture criterion based on Rice and Tracey model, taking the influence of both volume change and shape change of voids into account, is proposed.The characterization of this model for fine-blanking process is easily done by the tensile test and the prediction result shows good.

Fracture Prediction for an Advanced High-Strength Steel Sheet Using the Fully Coupled Elastoplastic Damage Model with Stress-State Dependence

In this study,the numerical simulations of sheet metal forming processes are performed based on a fully coupled elastoplastic damage model.The effects of stress triaxiality and Lode angle are introduced into the damage evolution law to capture the loading-path-dependent failure.The proposed constitutive model is implemented into the finite element(FE)code ABAQUS/Explicit via the user-defined subroutine(VUMAT).Next,the identification procedure for DP780 based on the hybrid experimental-numerical method is presented in detail.The numerical results of simple tests are compared with the experiments,and obvious improvement is observed for the proposed model under various loading paths.Finally,the model is applied to predict the edge fracture during sheet blanking process.The predicted global load–displacement responses and crack paths have a good agreement with the experimental results,indicating that the model holds great potentials in simulation of metal forming processes.

Compressive failure analysis of unidirectional carbon/epoxy composite based on micro-mechanical models

A 2D micro-mechanical model was proposed to study the compressive failure of Uni Directional（UD） carbon/epoxy composite. Considering the initial imperfection and strength distribution of the fiber, the plasticity and ductile damage of the matrix, the failure of T300/914 UD composite under longitudinal compression and in-plane combined loads was simulated by this model. Simulation results show that the longitudinal compressive failure of the UD composite is caused by the plastic yielding of the matrix in kink band, and the fiber initial imperfection is the main reason for it. Under in-plane combined loads, the stress state of the matrix in kink band is changed, which affects the longitudinal compressive failure modes and strength of UD composite.The failure envelope of r_1–s_（12） and r_1–r_2 are obtained by the micro-mechanical model. Meanwhile,the compressive failure mechanism of the UD composite is analyzed. Numerical results agree well with the experimental data, which verifies the validity of the micro-mechanical model.

Optimization of Clinching Tools by Integrated Finite Element Model and Genetic Algorithm Approach

Clinching is a convenient and efficient cold forming process that can join two sheets without any additional part. This study establishes an intelligent system for optimizing the clinched joint. Firstly, a mathematical model which introduces the ductile damage constraint to prevent cracking during clinching process is proposed.Meanwhile, an optimization methodology and its corresponding computer program are developed by integrated finite element model(FEM) and genetic algorithm(GA) approach. Secondly, Al6061-T4 alloy sheets with a thickness of 1.4 mm are used to verify this optimization system. The optimization program automatically acquires the largest axial strength which is approximately equal to 872 N. Finally, sensitivity analysis is implemented, in which the influence of geometrical parameters of clinching tools on final joint strength is analyzed. The sensitivity analysis indicates the main parameters to influence joint strength, which is essential from an industrial point of view.