User Material Subroutine Research Articles

Implementation of a Phase Mixture Model for Rate‐Dependent Inelasticity

AbstractPower plant components have to withstand complex thermo‐mechanical loads, i.e. frequent start‐ups and shut‐downs in combination with long holding times at high temperatures induce creep‐fatigue loads. Tempered martensitic steels with high chromium content feature high creep strength and corrosion resistance among other properties such that these alloys are often used for power plant components.This contribution focuses on the simulation of the complex mechanical behavior of the alloy X20CrMoV12‐1 based on a multi‐axial phase mixture model. Within this model, we distinguish two phases: a hard and a soft phase. Both phases are connected via an iso‐strain approach, and nonlinear kinematic hardening as well as microstructural softening effects are taken into account by introducing a backstress and a softening variable as internal variables. The model is implemented into the commercial finite element code ABAQUS with a user material subroutine. For this purpose, the stress update algorithm and the consistent tangent operator are implemented based on the backward EULER method in combination with NEWTON‐RAPHSON iteration. Next, a wide range of benchmarks for uni‐axial as well as multi‐axial stress states is taken into account in order to verify the numerical implementation. Furthermore, a thermo‐mechanical fatigue test based on a typical sequence of start‐ups and shut‐downs of power plants is simulated.

Predicting the Biodegradation of Magnesium Alloy Implants: Modeling, Parameter Identification, and Validation.

Magnesium (Mg) and its alloys can degrade gradually up to complete dissolution in the physiological environment. This property makes these biomaterials appealing for different biomedical applications, such as bone implants. In order to qualify Mg and its alloys for bone implant applications, there is a need to precisely model their degradation (corrosion) behavior in the physiological environment. Therefore, the primary objective develop a model that can be used to predict the corrosion behavior of Mg-based alloys in vitro, while capturing the effect of pitting corrosion. To this end, a customized FORTRAN user material subroutine (or VUMAT) that is compatible with the finite element (FE) solver Abaqus/Explicit (Dassault Systèmes, Waltham, MA, USA) was developed. Using the developed subroutine, a continuum damage mechanism (CDM) FE model was developed to phenomenologically estimate the corrosion rate of a biocompatible Mg–Zn–Ca alloy. In addition, the mass loss immersion test was conducted to measure mass loss over time by submerging Mg–Zn–Ca coupons in a glass reactor filled with simulated body fluid (SBF) solution at pH 7.4 and 37 °C. Then, response surface methodology (RSM) was applied to calibrate the corrosion FE model parameters (i.e., Gamma (γ), Psi (ψ), Beta (β), and kinetic parameter (Ku)). The optimum values for γ, ψ, β and Ku were found to be 2.74898, 2.60477, 5.1, and 0.1005, respectively. Finally, given the good fit between FE predictions and experimental data, it was concluded that the numerical framework precisely captures the effect of corrosion on the mass loss over time.

Rutting investigation of asphalt pavement subjected to moving cyclic loads: an implicit viscoelastic–viscoplastic–viscodamage FE framework

ABSTRACT In this study, rutting due to factors such as damage and permanent deformation and different types of moving cyclic loads are investigated. For this purpose, prediction of rutting and life estimation of asphalt pavement life are made possible by 3D simulation of pavement under realistic moving, equivalent and pulsatile loads at high cycle numbers. A thermodynamically consistent viscoelastic–viscoplastic–viscodamage model is implicitly discretised and user material subroutine implemented in the FEM software to predict asphalt pavement behaviour. All the discretised equations in the numerical procedure are obtained and the material consistent tangent matrix is presented. Additionally, the Newton–Raphson method is employed to calculate internal variables including internal variables of damage and viscoplastic strain components. In addition, the discretisation flowchart and respective algorithms are presented. Simulation results indicate the impact of factors such as mean load, applied stress level and loading time on rutting and damage. Furthermore, the rutting due to equivalent and pulsatile loadings have about 40% difference from the value corresponding to the realistic moving load obtained by the simulation of the tire as a hyper-viscoelastic material on the asphalt pavement. This difference leads to the inaccurate estimation of asphalt pavement’s service life by pulsatile and equivalent loading types.

Finite Element Implementation of a Temperature-Dependent Cyclic Plastic Model for SA508-3 Steel

A new temperature-dependent cyclic plastic model, combining the nonlinear cyclic softening and kinematic hardening rules is established for a nuclear material of SA508-3 steel. A modified isotropic hardening rule is proposed to capture the temperature-dependent cyclic softening, and a modified kinematic hardening rule is established to improve the prediction of the ratcheting behavior by introducing an exponential function related to the accumulated plastic strain. The stress is updated by the radial return mapping algorithm based on the backward Euler integration. A new expression of consistent tangent modulus for the equilibrium iteration is derived, and then the proposed model is implemented into the finite element software ABAQUS by using the user material subroutine (UMAT) to simulate the temperature-dependent ratcheting behaviors of SA508-3 steel. Finally, the ratcheting evolutions of notched bars at elevated temperature are obtained by uniaxial stress-controlled cyclic tests, and the nonuniform strain fields on the surface of plates with a center hole is measured by using the digital image correlation (DIC) technology. Comparisons between experimental and simulated results of a material point and structural examples show that the implemented model can provide reasonable predictions for ratcheting behaviors and nonuniform strain fields of structures at different temperatures for SA508-3 steel.

Stress analysis of the TMSR graphite component under irradiation conditions

TMSR uses nuclear graphite as a neutron moderator, a reflector, and the structural material, and utilizes molten salt as a coolant. When running normally, the graphite components are immersed in the molten salt. Thus, the nuclear graphite comes into direct contact with the molten salt, which infiltrates the open pores of the nuclear graphite. This infiltration may influence the stress analysis of the graphite component. In this study, a User Material subroutine was used to analyze the stress distribution of the graphite component, both with and without molten salt infiltration. Many influence factors were taken into consideration, such as the dose gradient, the shape of the permeation zone, and the permeation area. The results show that the dose gradient, shape, and area of the permeation zone all significantly influence the stress distribution. Furthermore, the results of the stress analysis indicate that for a regular graphite component with a square cross section, the peak maximum principal stress value occurs at the center of the cross section, and the symmetry of the maximum principal stress distributions was modified by quarter circle and half ellipse permeation zones.

Comparison of numerical modelling techniques for impact investigation on a wind turbine blade

Wind turbine blades are exposed to numerous impact risks throughout their lifetimes. The impact risks range from bird collisions during operation to impacts with surrounding structures at the time of transportation and installation. Impact loads on the fibre composite blades can induce several complex, simultaneously interacting and visually undetectable damage modes and have a high potential to reduce the local and global blade stiffness. An assessment of such impact-induced damages is therefore necessary and usually involves high computational costs using numerical procedures, especially when analysing large composite components. To minimise this computational expense, different numerical impact modelling techniques are utilised, primarily shell-element-based approaches and multiscale-modelling-based global-local approaches. In this article, a comparison between (1) pure shell, (2) shell-to-solid coupling, and (3) submodelling finite element modelling techniques using Abaqus/Explicit is presented for a case where an impactor hits the leading edge of a blade. A high-fidelity local solid finite element model is developed for the leading edge of a DTU 10 MW blade at the region of impact and its stiffness is compared with baseline. A user material subroutine VUMAT for the intralaminar damage mode based on the Hashin failure criterion is formulated and then validated via an experiment from the literature. Finally, based on different numerical modelling techniques, impact investigations are performed, and the impact responses, damage to the blade and computational analysis durations are compared. It is found that the submodelling-based global-local approach is the most efficient analysis technique for this case, capturing failure modes including delamination, core crushing and local surface indentation in the blade. The findings of this study can be used to develop accurate and computationally efficient tools for modelling impact-induced damage to a blade.

Effects of microstructure on rolling contact fatigue of a wind turbine gear based on crystal plasticity modeling

With the increases of the power densities and loading capacity of heavy duty machines such as wind turbines, rolling contact fatigue (RCF) problems of gears have become key problems limiting the reliabilities of those machines. The RCF analysis of gear has been widely studied from the perspective of the geometrical aspect and working conditions. However, the underlying mechanism of gear RCF remains unclear, especially the influence of material micro-structure on fatigue behavior is to be discovered. In this work, an integrated methodology considering the microstructure and crystal plasticity is proposed to evaluate the RCF performance of a wind turbine gear. The Voronoi tessellations are used to construct the virtual microstructure of the gear material. The crystal plasticity constitutive model considering the kinematic hardening and the isotropic hardening is established. The crystal plasticity constitutive is implemented in ABAQUS/Standard using a user material subroutine (UMAT). The Fatemi-Socie multiaxial fatigue criterion (FS) is applied to study the contact fatigue behavior of this heavy-duty gear considering the normal stress and shear strain of crystallographic slip systems. The influence of the crystal anisotropy of gear material on the RCF performance is investigated. The results indicate that the randomness of grain orientation and the anisotropy of crystal properties lead to the discretization of maximum FIP and the distinction of the failure position. Among the results of fifteen sets of models with randomly distributed grain orientations, compared with the mean value, the maximal fluctuating of magnitude and the depth position of maximum FIP are up to 15.8% and 20%, respectively. The effect of the grain orientation on FIP is explored. The predicted results reveal that the anisotropy and randomness of crystal orientation lead to the discretization of magnitude of FIP and the variation of crack initiation position. The rolling fatigue cracks tend to initiate along the direction having angles between 20° to 45° relative to the rolling direction.

Passive Force–Displacement Behaviour of GRS Bridge Abutments

Many bridge abutments suffered severe damages due to pounding of superstructure elements of the bridge during seismic excitation. Collision of the girder is resisted by passive pressures mobilised in the backfill soils. Seismic load on the bridge structure causes the bridge abutments to undergo lateral translation (Δ) and rotation. The present study focuses on the evaluation of passive force (Pp) developed in the reinforced backfills of the geosynthetic-reinforced soil (GRS) bridge abutments. The GRS abutments of nine configurations with three different geogrid spacing and three different geogrid lengths are modelled using finite element (FE) approach under lateral push. Hypoplastic soil constitutive model with inter-granular strain concept is used to model the soil behaviour. User material subroutine, VUMAT is developed to simulate the soil behaviour in Abaqus. The maximum passive resistance (Pp,ult) increases by 12% in the GRS abutments with closer geogrid spacing.

Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells

A geometrically nonlinear analysis of elastoplastic ceramic/metal functionally graded material (FGM) shells is investigated in this paper based on the first-order shear deformation theory. The elastoplastic behavior of the ceramic particle-reinforced metal matrix FGM shell is assumed to follow Ludwik hardening law. The elastoplastic material properties are assumed to vary smoothly through the thickness of the shells. The Mori–Tanaka model and self-consistent formulas of Suquet are employed to locally evaluate effective elastoplastic parameters of the ceramic/metal FGM composite. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) developed to study the FG shells in large displacements and rotations. With the aim of demonstrating the accuracy of the present method, current numerical results are compared to experimental and numerical ones considering geometrically nonlinear elastoplastic FGMs and show very good agreement. The overall robustness of the new developed solution taking into account both geometric and material nonlinearities is demonstrated through several non-trivial benchmark problems taken from the literature. The effect of the constituent distribution on the deflections is analyzed.

Modeling thermal recovery of the Mullins effect

Many elastomeric materials exhibit the Mullins effect, or stretch-induced stress softening. However, early experiments show that the Mullins effect may be recovered after annealing previously stretched material in a stress-free state. And that both the rate and degree of recovery are affected by the annealing temperature. In this work, we develop a thermo-mechanically-coupled large-deformation constitutive model that quantitatively captures thermal recovery of the Mullins effect. The model is calibrated to experiments from the literature, and is numerically implemented by writing a user material subroutine for the finite element program Abaqus/Standard. Lastly, our simulation results suggest that unanticipated behavior due to recovery of the Mullins effect is possible.

Anisotropic Gurson‐Tvergaard‐Needleman plasticity and damage model for finite element analysis of elastic‐plastic problems

SummaryImplementation and analysis of the anisotropic version of the Gurson‐Tvergaard‐Needleman (GTN) isotropic damage criterion are performed on the basis of Hill's quadratic anisotropic yield theory with the definition of an effective anisotropic coefficient to represent the elastic‐plastic behavior of ductile metals. This study aims to analyze the extension of the GTN model suitable for anisotropic porous metals and to investigate the GTN model extension. An anisotropic damage model is implemented using the user material subroutine in ABAQUS/standard finite element code. The implementation is verified and applied to simulate a uniaxial tensile test on a commercially produced aluminum sheet material for three‐dimensional and plane stress test cases. Spherical and ellipsoidal micro voids are considered in the matrix material, and their effects on the uniaxial stress‐strain response of the material are analyzed. Hill's quadratic anisotropic yield theory predicts substantially large damage evolution and a low stress‐strain curve compared with those predicted by the isotropic model. An approximate model for anisotropic materials is proposed to avoid increased damage evolution. In this approximate model, Hill's anisotropic constants are replaced with an effective anisotropy coefficient. All model‐generated stress‐strain predictions are compared with the experimental stress‐strain curve of AA6016‐T4 alloy.

Finite element calculations of hole expansion in a thin steel sheet with polynomial yield functions of four and six degrees

A three-dimensional finite element simulation was used to study the anisotropic plasticity behavior of sheet metal forming. Both Gotoh’s (fourth order) yield function and the more flexible sixth order polynomial yield functions with an associated flow rule were implemented as user material subroutines in the FE code ABAQUS. Parameter values in the yield functions were decided by fitting the yield stresses and plastic strain ratios along various directions of uniaxial and biaxial tension. To verify the FE implementation and to evaluate the modeling capabilities of the developed yield functions that were certified to be convex, the hole expansion experiment by Kuwabara et al.[1] was considered as the target example. The simulation results using the sixth order yield function showed a better agreement with the experimental results than those of lower order yield functions such as Hill’s second order or Gotoh’s fourth order yield functions.

An elasto-plastic constitutive model of magnesium alloy sheet at warm forming temperature under strain path changes

In the current work, a continuum-based approach is discussed in order to describe the plastic hardening behavior of magnesium alloy sheets under strain path changes at warm forming temperature. The constitutive model is represented to use an anisotropic distortional yield function combining a stable component and a fluctuating component. The stable component includes the yield function that represents the material’s anisotropy or the strength effect between tension and compression. The evolution of the fluctuating component is reformulated based on recently developed HCP metal’s distortional hardening model at room temperature. The modified models were implemented into finite element (FE) software via user-material subroutine. Predicted stress-strain curves of tension-compression-tension (TCT) and compression-tension-compression (CTC) loadings for two pre-strains were compared with experimental results. Overall, the proposed model could give reliable agreement with experimental data.

FE implementation of HAH model using FDM-based stress update algorithm for springback prediction of AHSS sheets

The homogeneous anisotropic hardening (HAH) model was implemented into a finite element (FE) code in order to predict springback for an advanced high strength steel (AHSS) sheet sample after double-stage U-draw bending. The finite difference method (FDM) was utilized as an alternative way to calculate the derivatives of this advanced distortional plasticity model allowing the update of the equivalent plastic strain and stress tensor at each time step in the user-material subroutines (UMAT and VUMAT). The FDM makes it easier to derive the stress gradient of complex yield surfaces. The proposed FDM-based stress update algorithm was verified by comparing the springback profiles after the single- and double-stage U-draw bending tests for a DP980 sheet sample predicted with analytical and numerical approaches. In addition, the springback measurement parameters and computational efficiencies depending on both approaches were also compared. The results indicate that the computational efficiency and accuracy of the FE simulations with the FDM-based stress update algorithm were similar to those of the analytical method.

Experimental characterisation and computational modelling for cyclic elastic-plastic constitutive behaviour and fatigue damage of X100Q for steel catenary risers

New higher strength steels are required for deep and ultra-deepwater steel catenary risers (SCRs). In this work, the cyclic elastic-plastic-damage behaviour of X100Q, a candidate next-generation SCR material is experimentally characterised and modelled. The material is shown to exhibit early life (primary) fatigue damage followed by the more conventional (secondary) fatigue damage; as a result, it is necessary to demarcate the observed cyclic softening into dynamic recovery and damage-induced softening. An automated constitutive parameter optimisation process in combination with a new two-stage cyclic damage evolution model successfully predicts the effect of strain-range on damage evolution. The model is implemented in a user material (UMAT) subroutine for multiaxial application, within a hierarchical global-local modelling methodology for dynamic fatigue analysis of an SCR girth weld geometry. The interdependency between fatigue damage-induced material degradation and cyclic plasticity at the weld is shown for a range of load cases.

Meso-scale progressive damage modeling and life prediction of 3D braided composites under fatigue tension loading

3D braided composites have broad potential applications in the high-tech industries because of their superior mechanical properties. Fatigue is an essential design factor for their use in those engineering applications. The fatigue damage accumulation during cyclic loading should be involved in the numerical models in order to predict the fatigue life accurately. In this paper, a unit-cell based finite element model in conjunction with continuum damage mechanics (CDM) is developed for simulating the fatigue damage evolution process and predicting the fatigue life of 3D braided composites under fatigue tension loading. This meso-scale fatigue modeling, including stress analysis, failure criteria and material property degradation scheme, is implemented via a user-material subroutine UMAT based on ABAQUS/Standard platform with FORTRAN code. The fatigue damage initiation and propagation processes of 3D braided composites with typical braiding angles on the unit-cell model as a function of number of cycles are presented in detail. The fatigue life of 3D braided composites is predicted from the computed S-N curve and the stiffness degradation process is also investigated. The obtained numerical results indicate that the present model can provide a suitable reference to the numerical study of the fatigue issues in other textile composites.

A new temperature-dependent anisotropic constitutive model for predicting deformation and spring-back in warm deep drawing of automotive AA5086-H111 aluminium alloy sheet

A new temperature-dependent anisotropic hardening and yield function based on non-associated flow rule (NAFR) which accurately describes the anisotropic properties of aluminium alloy sheet metal is presented in this paper. This new NAFR coupling yield function has been successfully implemented in commercial FEM software Abaqus via user material subroutine UMAT to model warm forming of AA5086-H111 aluminium alloy and good agreement was found in the predicted earing profiles and spring-back compared with experiments. The new NAFR coupling yield function has been shown be superior to the existing Hill48 (associated flow rule) yield function making it suitable for FEA of warm deep drawing and design of tooling for various automotive panels and components.

Elasto-Plastic Modeling of Low-Velocity Impact on Functionally Graded Circular Plates

Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investigated in this paper based on Mori–Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the particle reinforced metal matrix FGM plate is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) and USDFLD subroutine. The effect of the power-law index on low-velocity impact parameters like contact force, deflection, permanent indentation, velocity distribution and the kinetic energy are examined using the proposed method. With the aim of demonstrating the accuracy and efficiency of the present method, current numerical results are compared to experimental and theoretical results from the literature and show very good agreement.

Study of multi-objective optimization of process parameters in film posting based on outside mold decoration

In order to optimize the process parameters in film posting based on outside mold decoration (OMD), the polymethyl methacrylate (PMMA) plastic sheets were tested in uniaxial tensile tests at high temperature with different temperatures and strain rates. The coefficients of the viscoelastic constitutive model called Duan Saigal Greif Zimmerman (DSGZ) were calculated based on the uniaxial tensile tests, and the predicted curve of DSGZ model and experimental data were compared and analyzed. The user material subroutine in ABAQUS of the DSGZ model was designed and written by adopting elastic prediction-radial consumers algorithm and was integrated into ABAQUS for the simulation of forming process of mouse shell posting film using the OMD process. After solving the model, the film thickness distribution and its deforming distribution in the X- and Y-direction were obtained. The optimization objective was to minimize the standard deviation of film thickness and its deforming distribution in the X- and Y-direction for 50 nodes on the thin film of mouse shell. The process parameters of OMD were sampled based on the method of optimal Latin hypercube design. In addition, the radial basis functions model was built. As the analysis shows, the radial basis functions model is sufficiently accurate. Based on the models, the process parameters of OMD were multi-objective optimized and analyzed by adopting archive-based micro-genetic algorithm. The best process parameters group was obtained after comprehensive analysis.

Study of rolling contact fatigue behavior of a wind turbine gear based on damage-coupled elastic-plastic model

Gear contact fatigue has a significant influence on the reliabilities of heavy-duty gear-driven machines such as wind turbines. In the present work, an elastic-plastic contact fatigue model in conjunction with damage is developed to study the fatigue performance of a megawatt wind turbine gear. In this model, damages caused by both elasticity and plasticity are considered based upon the continuous damage mechanics (CDM) in the frame of ABAQUS using a user material subroutine. Damage accumulation and the evolution of the material mechanical properties are recorded during the fatigue crack initiation life. The contributions of elastic damage and plastic damage are distinguished. The effect of applied load on the contact fatigue life is studied and the stress–life curve is fitted based upon the numerical data. Results show that under a wide range of load conditions, the contact fatigue of the gear is always dominated by the elastic damage.