User-defined Material Research Articles

Ballistic performance of polyurea-coated thin aluminium plates: numerical study

Polyurea elastomer exhibits desirable characteristics for impact mitigation, with varying stoichiometric-dependent properties that can be tailored for specific applications and applied to reinforce existing and new structural components. This numerical study aims to investigate the ballistic performance of polyurea-aluminium laminate targets, employing a user-defined material model for polyurea elastomer developed in a finite-element (FE) framework. The model consists of a rigid spherical projectile impacting the considered target plate. A linear increase in the ballistic performance with a growing thickness of polymer coating was observed and is consistent with previously conducted experimental work. The ballistic limit is increased by some 5% per millimetre of polymer coating thickness, when compared to the monolithic metallic plate. The presence of the polymer layer significantly affects the dynamic response mechanisms of the component during bending due to impact. The result is a more localised deformation compared to global bending of the target.

Comprehensive implementations of phase-field damage models in Abaqus

Despite the versatility in modeling complex crack configurations, phase-field damage models for fracture usually count only on in-house codes, greatly restricting their potential applications. It is thus of vital importance to implement them in those commonly used commercial software packages like Abaqus. However, so far only the less robust Newton’s monolithic algorithm or the inefficient staggered solver has been considered. In this work, taking the unified phase-field damage theory (Wu, 2017) as the particular example, we present three distinct strategies of implementing phase-field damage models into Abaqus: (i) UMAT-Newton-M: a thermo-mechanically coupled user-defined material (UMAT) implementation of the modified Newton monolithic solver; (ii) UEL-Staggered: a novel user-defined element (UEL) implementation of the iterative staggered (alternate minimization) algorithm with dummy dofs; (iii) UEL-BFGS: a UEL implementation of the recently advocated BFGS quasi-Newton monolithic algorithm. The aforesaid implementation strategies are then validated against several representative benchmark problems of brittle fracture and quasi-brittle failure. It is found that, the UMAT-Newton-M implementation is the simplest but not robust enough, while the UEL-Staggered implementation is robust but extremely inefficient. Comparatively, in all cases the UEL-BFGS scheme is of the best numerical performance with lest iterations and sufficient robustness. For the sake of reproducibility of the presented numerical results and the promotion of phase-field damage models, the source codes (programmed in the free format syntax of FORTRAN90) are also provided and interested users can download them at https://github.com/jianyingwu/pfczm-abaqus.

Micromechanical modelling of edge failure in 800 MPa advanced high strength steels

Sheared edge failure is one of the major problems associated with the forming of advanced high strength steels (AHSS) such as dual-phase (DP) steels. To improve the performance of AHSS in industrial forming operations, ferritic-bainitic complex-phase (CP) steels have been developed and are gaining attention in academia as well as industry. The present work aims to investigate the influence of microstructure on micro-void (damage) evolution during the edge stretching of CP800 and DP780 steels and develop a micromechanics-based fracture model to predict edge failure for both reamed and sheared holes. Three-dimensional damage histories were obtained using x-ray microtomography on a series of hole tension specimens interrupted at different strain levels. These experiments considered a tensile specimen with a sheared hole at the center of specimen (sheared edge condition) or reamed (ideal edge condition). Void damage measurements, such as void area fraction, number of voids, void diameter, and void aspect ratio, were conducted and the results are compared to the reamed specimens to isolate the sheared edge effect on damage. The void measurements were used to implement a stress-state dependent model for nucleation, and coupled with the Ragab (2004) model for void growth and the Benzerga and Leblond (2014) model for void coalescence to develop a damage-based material model. Higher damage accumulation was observed behind the sheared edge in comparison the reamed edge at a given strain for both materials considered. An uncoupled anisotropic damage-based fracture model was formulated in a LS-DYNA user-defined material subroutine. As an alternative to computationally expensive multi-stage sheared edge stretching simulations, the measured strain-distribution of the sheared edge was mapped into a finite-element model to predict sheared edge failure. The proposed model was validated for the hole tension testing simulations and found to predict failure accurately for both the CP800 and DP780 for both the edge conditions.

A constitutive model for concrete subjected to extreme dynamic loadings

A good physical-based constitutive model should not only properly reproduce the macroscopic dynamic response of concrete, but also capture the meso-damage behavior that actually occurs. This paper presents a constitutive model for concrete subjected to extreme dynamic loadings with the help of the meso-damage mechanics, Duvaut–Lions formulation and elasto-plastic theory. In the present model, a two-step homogenization scheme of concrete is proposed, where compressive damage and tensile damage are treated dividually. The tensile damage is controlled by the nucleation and growth of micro-cracks, while the compressive damage is related to the collapse of micro-voids. Mori-Tanka method is introduced to establish the relationship between the meso-structural parameters and the macro-physical quantities. What is more, a new cap model coupled to the compressive damage is presented to capture the irreversible deformation induced by the micro-void collapse. The present model, containing the erosion algorithm, was successfully implemented into finite element code LS-DYNA through user-defined material model. In order to validate the present model, dynamic tensile tests, quasi-static triaxial compressive tests, planar impact tests and projectile penetration tests were simulated in sequence. The results show that the present model has good consistency between the predicted results and the experimental data, thus verifying its rationality and practicability. Sensitivity analyses of two erosion criteria and mesh dependency were also carried out to understand the influence of these empirical parameters on the compressive damage and tensile damage predicted by the present model.

Development and Evaluation of Crack Band Model Implemented Progressive Failure Analysis Method for Notched Composite Laminate

Progressive failure analysis (PFA) is widely used to predict the failure behavior of composite materials. As a structure becomes more complex with discontinuities, prediction of failure becomes more difficult and mesh dependence must be taken into account. In this study, a PFA model was developed using the Hashin failure criterion and crack band model. The failure initiation was evaluated using the Hashin failure criterion. If failure initiation occurred, the damage variables at each failure mode (fiber tension and compression; matrix tension and compression) were calculated according to linear softening degradation and they were then used to derive the damaged stiffness matrix. This matrix reflected a degraded material, and PFA was continued until the damage variables became “1,” implying complete material failure. A series of processes were performed using the finite element method program ABAQUS with a user-defined material subroutine. To evaluate the proposed PFA model, experimental results of open-hole composite laminate tests were compared with the obtained numerical results. The strain behaviors were compared using a digital image correlation system. The obtained numerical results were in good agreement with the experimental ones.

Numerical Modeling and Experimental Verification for High-Speed Forming of Al5052 with Single Current Pulse

Application of electric current pulses during plastic deformation changes the mechanical behavior owing to the electro-plastic effect. The effect of electric current pulses on the Al5052 alloy is investigated in this study. In order to demonstrate the advantages of passing electric current pulses through a metal sheet during the forming process, a uniaxial tensile test with an electric current pulse was carried out using a self-designed device; this device can apply a 2-kA electric current pulse to the specimen for a short period (>100ms). The electric current increases the temperature of the specimen due to Joule heating. It is, therefore, necessary to decouple the thermal effect from the overall behavior to understand only the contribution of electric current in the mechanical behavior. Firstly, an electro-thermo-mechanical finite element study of an electrically assisted uniaxial tensile test of Al5052 alloy is performed to isolate the thermal effect. The simulated results yielded the thermal effect due to the electric current. By comparing the experimental and simulated results, the contribution of electric current is decoupled from that of thermal effect. The electric current-dependent material model is implemented into the commercial FEM code LS-DYNA using user-defined material(UMAT) subroutine. The electric current-dependent material model was used to simulate the electro-mechanical finite element analysis of the high-speed forming of an aluminum sheet with electric current pulse. Simulation results were compared with experimental results at several applied electric currents to evaluate the accuracy of the UMAT. The present work can be utilized to develop simpler constitutive models for the mechanical behavior of metals subjected to a pulsed electric current.

Modeling the hysteretic responses of RC shear walls under cyclic loading by an energy-based plastic-damage model for concrete

This paper addresses application of an energy-based plastic-damage model for concrete to the modeling of hysteretic responses of reinforced concrete (RC) shear walls. Both damage evolution and plastic flows are accounted for within the framework of thermodynamics, resulting in consistent energy-based damage evolution laws. The model is implemented in the commercial software package ABAQUS via the user-defined material subroutine and applied to two representative benchmark tests of RC shear walls under cyclic loading. It is shown that with the steel reinforcement properly accounted for, the energy-based plastic-damage model can capture realistically the failure modes, load capacities, and overall load–deformation responses of RC shear walls.

A constitutive model for fiber kinking: Formulation, finite element implementation, and verification

A new mesoscale material model is proposed to analyze structures that fail by the fiber kinking damage mode. The model is formulated following the fiber kinking theory such that the interaction of shear nonlinearity and fiber rotation are tracked throughout the loading history. The model is implemented as a user-defined material in a commercial finite element code. A decomposition algorithm is introduced in the finite element implementation to decouple the mesh size and kink band width. To evaluate the assumptions of the mesoscale model, the results were compared with those of a high-fidelity micromechanical model. A direct comparison between the two models shows remarkable correlation, providing evidence that the key features of the fiber kinking phenomenon are appropriately accounted for in the mesoscale model. The model is demonstrated for a simple unnotched compression configuration. The results show that the model is successful at representing the kinematics of fiber kinking.

An enhanced distortional-hardening-based constitutive model for hexagonal close-packed metals: Application to AZ31B magnesium alloy sheets at elevated temperatures

In this study, a new material model for hexagonal close-packed (HCP) metals for predicting their flow responses under monotonic/cyclic loadings at various temperatures is proposed. The temperature-dependent constitutive model is re-formulated using a continuum-based distortional hardening law, which affects the shape of the yield surface depending on the loading direction, and also uses the concept of the dominant deformation modes in magnesium alloys: twin, untwin, and slip-dominate modes, considering the role of the twins in plastic deformation. In terms of the material asymmetry in yield strength, the Cazacu–Barlat–Plunkett (CPB) ’06 yield criterion is extended to include thermal effects. A numerical formulation of the material model has also been developed to allow its implementation into finite element analysis software via a user-defined material subroutine (UMAT). The predicted results of stress–strain response for monotonic and cyclic loadings are excellent agreement with the experimental data. Moreover, the simulated results show the strength differential (SD) effect and unusual flow responses of AZ31B magnesium alloy sheets at room temperature, as well as the variation in the SD effect and anisotropic hardening behavior at elevated temperatures.

Dislocation density based modeling of three-stage work hardening behaviour of type 316LN SS with varying nitrogen content and its finite element implementation for different notch radii

Dislocation density based modified Kocks-Mecking approach has been employed to understand the influence of nitrogen on kinetics of dislocation storage and annihilation processes during tensile deformation of type 316LN stainless steel at 300 K. As compared to original Kocks-Mecking approach, the modified version based on the evolution of forest dislocation density and mean free path of dislocations provides better description of three-stage hardening behaviour of the steel at all the nitrogen content. The effect of increase in nitrogen on work hardening behaviour is clearly reflected in systematic increase in flow stress, mobile and forest dislocation densities and decrease in mean free path at a given plastic strain. The predicted decrease in mean free path with increasing nitrogen has not only influenced the enhancement of dislocation-dislocation interactions leading to higher storage of dislocation but also provides a large driving force for higher dynamic recovery in the steel. The material model is implemented into finite element code via user-defined material subroutine using implicit algorithm to study the influence of notch radius on tensile properties of type 316LN stainless steel for different nitrogen content. Detailed analysis showed that notch-strengthening effect increases with increase in nitrogen and decrease in notch radius in the steel.

Critical Void Volume Fraction Identification Based on Mesoscopic Damage Model for NVA Shipbuilding Steel

NVA mild steel is a commonly used material in the shipbuilding industry. An accurate model for description of this material’s ductile fracture behaviour in numerical simulation is still a challenging task. In this paper, a new method for predicting the critical void volume fraction fc in the Guson-Tvergaard-Needleman (GTN) model is introduced to describe the ductile fracture behaviour of NVA shipbuilding mild steel during ship collision and grounding scenarios. Most of the previous methods for determination of the parameter fc use a converse method, which determines the values of the parameters through comparisons between experimental results and numerical simulation results but with high uncertainty. A new method is proposed based on the Hill, Bressan, and Williams hypothesis, which reduces the uncertainty to a satisfying extent. To accurately describe the stress-strain relationship of materials before and after necking, a combination of the Voce and Swift models is used to describe the material properties of NVA mild steel. A user-defined material subroutine has been developed to enable the application of the new parameter determination method and its implementation in the finite element software LS-DYNA. It is observed that the model can accurately describe structural damage by comparing the numerical simulation results with those of experiments; thus, the results demonstrate the model’s capacity for structural response prediction in ship collision and grounding scenario simulations

A dynamic constitutive model for fiber-reinforced composite under impact loading

A constitutive model was proposed to predict the deformation and characterize the failure features of fiber-reinforced composite structures under dynamic loading. Primarily, quasi-static and dynamic mechanical tests were carried out on composite laminates with designed plying sequences. The material modulus was found rising as the increase of strain rate, while the ultimate strain exhibits no strain rate dependency. Nonlinear behavior was observed under transverse compression and in-plane shear, and was attributed to the progressive damage of material. Based on the results of uniaxial tests, constitutive relations were established for plane stress case and three-dimensional case respectively. Two damage factors were introduced to describe the nonlinear behavior, and failure criteria based on transversely isotropic invariants were proposed. Additionally, the constitutive model was implemented in Abaqus through user-defined material subroutine and validated by the simulation of uniaxial tests and bird impact tests. Comparing to the traditional model, the constitutive relations presented in this paper was proved to have better accuracy and efficiency in predicting dynamic response and ultimate failure patterns of composite structures under dynamic loading.

A CONSTITUTIVE MODEL FOR BOTH LOW AND HIGH STRAIN NONLINEARITIES IN HIGHLY FILLED ELASTOMERS AND IMPLEMENTATION WITH USER-DEFINED MATERIAL SUBROUTINES IN ABAQUS

ABSTRACT Strain energy functions (SEFs) are used to model the hyperelastic behavior of rubberlike materials. In tension, the stress–strain response of these materials often exhibits three characteristics: (i) a decreasing modulus at low strains (<20%), (ii) a constant modulus at intermediate strains, and (iii) an increasing modulus at high strains (>200%). Fitting an SEF that works in each regime is challenging when multiple or nonhomogeneous deformation modes are considered. The difficulty increases with highly filled elastomers because the small strain nonlinearity increases and finite-extensibility occurs at lower strains. One can compromise by fitting an SEF to a limited range of strain, but this is not always appropriate. For example, rubber seals in oilfield packers can exhibit low global strains but high localized strains. The Davies–De–Thomas (DDT) SEF is a good candidate for modeling such materials. Additional improvements will be shown by combining concepts from the DDT and Yeoh SEFs to construct a more versatile SEF. The SEF is implemented with user-defined material subroutines in Abaqus/Standard (UHYPER) and Abaqus/Explicit (VUMAT) for a three-dimensional general strain problem, and an approach to overcome a mathematically indeterminate stress condition in the unstrained state is derived. The complete UHYPER and VUMAT subroutines are also presented.

Two-process constitutive model for semicrystalline polymers across a wide range of strain rates

The presence of crystalline and amorphous phases in semicrystalline polymers presents interesting constitutive modelling challenges. In this study, a physically based, three-dimensional constitutive model has been developed for simulating a wide range of features observed in deformation and processing of semicrystalline polymers. The proposed model combines into one constitutive model such features as: multiple viscoelastic relaxation processes, very wide strain-rate range, temperature-dependence, adiabatic heating, structural rejuvenation; in addition to it being applied to a semicrystalline polymer. The constitutive mathematics is based on a one-process glass-rubber model for amorphous polymers. It adapts that model to semicrystalline polymers by extending it to two relaxation processes: one associated with the glass transition of the mobile amorphous phase; the other associated with relaxation of the crystalline fraction and its associated rigid amorphous phase. In particular, two dominant processes were identified: the α-process and the β-process. The model has been implemented numerically into a commercial finite element code through a user-defined material subroutine (UMAT). The model has been validated against compression test results carried out on polypropylene. Also, the model predicts very well the experimentally observed nonlinear rate-dependent response and post-yield de-ageing of polypropylene.

High-temperature fatigue behavior of a steam turbine rotor under flexible operating conditions with variable loading amplitudes

This study investigated the high-temperature fatigue behavior of a steam turbine rotor under long-term operation with multiple startup types including one cold, three warm and 16 hot-startups at intervals of 45 days. To better describe the mechanical behavior of the rotor material, a unified viscoplastic constitutive model was experimentally validated then implemented with a user-defined material. Analysis initially focused on the inlet region, where thermal loads dominated. Next, the stress and damage at three selected positions with differences in temperature and load were compared and analyzed in detail. The effect of different startup types on the fatigue damage was statistically assessed. The equivalent hot startup (EHS) ratio was calculated to compare the risk level of each position under each startup type in flexible operation mode. Investigation of the inlet region showed that the warm startup conditions adopted here were more damaging than cold startup due to the higher warmup rate. The analysis of fatigue damage showed a temperature-dependent characteristic of the thermo-mechanical load-dominated positions. The EHS ratio of Groove-1 was larger than that of Groove-4, indicating a higher risk level in Groove-1 under flexible operating conditions. For the inlet region, the accumulation of viscoplastic strain made this region a fatigue-damageable position.

Experimental and Numerical Investigations of High-Speed Projectile Impacts on 7075-T651 Aluminum Plates

Simulation of the material failure under high strain rate conditions is one of the most difficult problems in the finite element analyses, and many researchers have tried to understand and reproduce dynamic material fracture. In this study, we investigate a failure criterion that minimizes the mesh dependency at high strain rates and incorporates the criterion into the Johnson-Cook constitutive relationship by developing a user-defined material model. Impact tests were performed using a gas-gun system in order to investigate the response of the 7075-T651 aluminum plate in high-speed collision. On the other hand, numerical simulations are carried out by considering various element sizes and the relationship between element size and failure strain is inversely obtained using numerical results. By accommodating the relationship into the damage model and implementing in the user-defined material model, mesh dependency is significantly reduced, and sufficient accuracy is achieved with alleviated computational cost than the existing damage model. This study suggests an element size-dependent damage criterion that is applicable for impact simulation and it is expected that the criterion is useful to obtain accurate impact responses with a small computational cost.

Computational analysis of tensile damage and failure of mineralized tissue assisted with experimental observations

In this study, deformation and failure mechanisms of mineralized tissue (bone) were investigated both experimentally and computationally by performing diametral compression tests on millimetric disk specimens and conducting finite element analysis in which a granular micromechanics-based nonlinear user-defined material model is implemented. The force-displacement relationship obtained in the simulation agreed well with the experimental results. The simulation was also able to capture location of the failure initiation observed in the experiment, which is inside out from the hole along the loading axis. Furthermore, propagation of micro-sized cracks into failure was observed both in the experiment using simultaneous slow-motion microscopy imaging and in the simulation analyzing the local distortion and local volume change within the specimen. The anisotropy evolution was found to be significant around the hole along the loading axis by evaluating the anisotropy index computed using finite element results. In conclusion, this work revealed that the prediction capability of granular micromechanics-based user-defined nonlinear material model (UMAT) is promising considering the match between the results and observations from the physical experiment and finite element analysis such as force-displacement relationship and failure initiation/pattern. This work has also shown that the tensile damage and failure of mineralized tissues can be characterized using diametral compression (split tension) test.

Fully coupled thermomechanical modeling of shape memory alloys under multiaxial loadings and implementation by finite element method

Different constitutive models along with various numerical implementation approaches have been proposed for shape memory alloys (SMAs) in the last decades. Since 1-D models are only suitable for particular geometries and loading types, due to the broad variety of SMA components in smart structures, 3-D rate-dependent modeling of SMAs is a necessity. In the present research, a fully coupled rate-dependent model to study thermomechanical response of shape memory alloys under multiaxial loadings is presented. The model is implemented into ABAQUS commercial finite element package by developing a user-defined material subroutine. Most of the available works are limited to just mechanical loadings and/or simple geometries, but the current model is able to simulate both shape memory effect and pseudoelasticity. Furthermore, it is capable of being applied to any geometry undergoing thermal/mechanical cycling under a wide range of strain rates spanning quasi-static to high-rate conditions. The obtained numerical results by the model are validated by experimental, analytical, and numerical findings of available three-dimensional case studies in the literature. The predicted results by the current model are shown to be in good agreement with the findings of previous investigations.

Modeling and simulation of carbon composite ballistic and blast behavior

The design of the next generation of aeronautical vehicles is driven by the vastly increased cost of fuel and the resultant imperative for greater fuel efficiency. Carbon fiber composites have been used in aeronautical structures to lower weight due to their superior stiffness and strength-to-weight properties. However, carbon composite material behavior under dynamic ballistic impact and blast loading conditions is relatively unknown. For aviation safety consideration, a computational constitutive model has been used to characterize the progressive failure behavior of carbon laminated composite plates subjected to ballistic impact and blast loading conditions. Using a meso-mechanics approach, a laminated composite is represented by a collection of selected numbers of representative unidirectional layers with proper layup configurations. The damage progression in a unidirectional layer is assumed to be governed by the strain-rate-dependent layer progressive failure model using the continuum damage mechanics approach. The composite failure model has been successfully implemented within LS-DYNA® as a user-defined material subroutine. In this paper, the ballistic limit velocity (V50) was first established for a series of laminates by ballistic impact testing. Correlation of the predicted and measured V50 values has been conducted to validate the accuracy of the ballistic modeling approach for the selected carbon composite material. A series of close-in shock hole blast tests on carbon composite panels were then tested and simulated using the LS-DYNA® Arbitrary-Lagrangian-Eulerian (ALE) method integrated with the Army Research Laboratory (ARL) progressive failure composite model. The computational constitutive model has been validated to characterize the progressive failure behavior in carbon laminates subjected to close-in blast loading conditions with reasonable accuracy. The availability of this modeling tool will greatly facilitate the development of carbon composite structures with enhanced ballistic impact and blast survivability.

Research on the Damage Evolution Process of Steel Wire with Pre-Corroded Defects in Cable-Stayed Bridges

A numerical simulation method is presented in this paper to study the damage evolution and failure process of high-strength steel wires with pre-corrosion defects in cable-stayed bridges under fatigue loads. This method was based on the mechanism of crack nucleation accelerated by corrosion pits, in which cellular automata (CA) and finite element (FE) simulation methods were used. First, based on the continuum damage mechanics (CDM) theory, a fatigue damage model suitable for steel wire with pre-corroded defects was established to describe the evolution process of the microscopic damage of steel wires, and a user-defined material subroutine (UMAT) was written using formula translator (FORTRAN) language. Then, in MATLAB, the shape and position of random pitting defects on the steel wire surface were generated using 3D CA technology. Afterwards, a pitting defect model was successively inputted into AutoCAD, Rhino and ABAQUS software to obtain the FE model of steel wire with initial pitting defects or initial damage. Finally, the life-and-death element method and the UMAT program were used to simulate the fatigue damage evolution process of the steel wire with initial defects in ABAQUS software, and the fatigue life of the steel wire was obtained. The results show that the proposed strategy and algorithm can effectively describe the fatigue damage evolution process of the steel wire with initial pitting defects under the action of a fatigue load, and the simulated fatigue life is in good agreement with the experimental results. The obtained stress-life (S-N) curves of the steel wire with different corrosion degrees show that the influence of pit corrosion on fatigue life is much greater than that of the mass loss caused by corrosion. By comparing the irregular pit model with regular pit models, it can be found that the irregular shape angle is the main reason for the smaller fatigue life and the larger stress concentration in the irregular pit model than in the regular pit model.