For a correct representation of ductile fracture, it is crucial to consider triaxiality effects and micromechanical processes in the material. Based on Aldakheel et al. (2018), we propose a phase-field model for ductile fracture in conjunction with porous plasticity according to the Gurson-Tvergaard-Needleman model, where the driving force is modified to include a threshold value composed of the critical and failure porosity. The phase-field is considered as a regularisation of void coalescence and replaces the local effective porosity in the porous plasticity model. The coupled model is applied to 13Cr steel, a realistic material for applications subject to large deformations and ductile fracture. New experimental data for the high-strength stainless steel is obtained from various experimental tests covering different stress states and is used to validate explicit finite element simulations. The implementation offers the possibility of viscous regularisation and adaptation to experimental results, with this work including a study of the viscosity parameter to ensure a good approximation to the quasi-static fracture evolution.

Constitutive models for the Portevin-Le Chatelier (PLC) effect are systematically evaluated and compared to tension tests under both constant strain rates, and abrupt strain rate changes for an AlMg alloy at room temperature, where digital image correlation (DIC) was used to precisely identify the onset of the PLC instability. A recently proposed physically-based modified mechanical threshold strength (MTS) model is compared to the phenomenological Kubin-Estrin-McCormick (KEMC) model and to two versions of the KEMC model, incorporating either a modified aging stress (KEMC-I) or an altered work-hardening evolution (KEMC-II). Key aspects investigated include the stress-strain response under constant and varying strain rates, the evolution of critical strain, and the strain dependence of strain rate sensitivity (SRS). Results indicate that the additive formulation of all KEMC-type models fails to comply with the Cottrell-Stokes law, whereas the modified MTS model, which couples work-hardening and viscosity, effectively captures this behaviour. Furthermore, accurate modelling of the strain dependence of SRS necessitates the inclusion of strain-dependent aging effects, as implemented in KEMC-I and the modified MTS model. Crucially, the onset of the PLC effect is governed by the competition between the stabilizing influence of work hardening and the destabilizing effect introduced by dynamic strain ageing.

In this study, two state-of-the-art implementations of the rate-dependent Crystal Plasticity Finite Element Method (CPFEM) as user material subroutines in the finite element solvers Abaqus/Explicit and Abaqus/Standard (Implicit) are presented. Adaptive substepping in the explicit solver and line-search stabilized implementation in the implicit solver enable fast and stable calculations also for small strain-rate sensitivities. A comparative analysis of simulation results is made and computation times of the two implementations are compared and discussed, including the use of reduced-integration elements and mass scaling for the explicit solver. It is identified under which conditions the explicit or the implicit solver is preferred.

Ductile failure by the onset of strain localisation after non-proportional load paths is investigated herein by using the imperfection version of the strain localisation theory. A computational framework assuming a planar, porous imperfection band inside a homogeneous solid was used to investigate ductile failure as caused by void nucleation, growth, and coalescence. The localisation analysis framework was calibrated based on a single uniaxial tension test and finite element simulations thereof. Despite the somewhat frugal calibration, the localisation analyses successfully reproduced experimentally measured macroscopic fracture strains from notched tension tests and notched compression-tension tests. The method was subsequently applied to a structural problem involving large deformations and complex load paths, and the results show great promise for future work.

Aluminium Whipple shields are commonly used to protect spacecraft against hypervelocity impacts (HVIs) from orbital debris and micrometeoroids. Since numerical models nowadays are vital in the design process of protective shields, experimental studies of HVI are important to ensure that the numerical methods are robust and capable of accurately describing a range of impact conditions and material responses. The shatter regime is the transition velocity range between ballistic impact and hypervelocity impact, typically defined from 3 to 7 km/s. In this region, the debris cloud generated by the impact transitions from a few large, solid fragments at the lower end of the velocity range, to a high number of smaller fragments and partial melting of the projectile at the higher velocities. In this study, an experimental campaign of 22 normal impacts of spherical AA1100 projectiles on AA6061-T6 Whipple shields is performed, where the impact velocity and bumper thickness are systematically varied to study the change in debris cloud characteristics and shield damage. Impact velocities from 2.6 to 5.0 km/s are investigated, combined with bumper thicknesses of 1.0, 1.5 and 2.0 mm. Analysis of the experimental results is conducted using high-speed camera footage of the debris clouds and post-impact analysis of bumpers and rear walls. A numerical model is then established using the Smoothed Particle Hydrodynamics (SPH) method in the IMPETUS Solver, and the numerical results are compared to the experimental data. The simulations are able to capture the main trends found in the experimental study, and show a similar level of damage as the experiments when varying the impact velocity and bumper thickness. The simulations have somewhat smaller fragments generated in the debris cloud than in the experiments, leading to slightly less damage inflicted on the rear wall.

The behavior of various bumper materials subjected to hypervelocity impact is of high interest, as different materials show varying ability to shock and break up an incoming projectile, and can produce varying amounts of ejecta on impact. In this study, an experimental campaign of 10 normal impacts of spherical Al 2017-T4 projectiles on Whipple shields at 3 and 7 km/s is presented, with various bumper configurations of near equal areal density. Five different bumper configurations are studied (aluminum wire mesh, steel wire mesh, Nextel woven fabric, open-cell aluminum foam with a face sheet, and Beta cloth with an aluminum plate) and compared to a traditional thin Al 6061-T6 bumper. The results are evaluated based on high-speed video footage of the debris cloud development over the standoff distance, as well as observed damage on the ejecta catcher, bumper, rear wall, and witness plate, and 3D scans of the rear walls and witness plates. The results are found to be significantly different between the different bumper configurations. At 3 km/s, the bumper configuration with open-cell aluminum foam with a face sheet performed best, while at 7 km/s, the baseline Al 6061-T6 bumper and the bumper with Beta cloth showed the best performance.

The coupled effects of lattice cell geometry and crystallographic texture on the anisotropic mechanical characteristics of additively manufactured (AM) lattice structures are computationally studied in this work. The crystal plasticity finite element method (CPFEM) is used to investigate the elastic and plastic anisotropy induced by crystallographic texture. A Python-based open-source tool is developed within Abaqus/CAE for polycrystal modeling of complex geometries with various grain morphologies, tailored for CPFEM analysis. Simulations reveal that the effective elastic anisotropy and the yield surface of the lattice structures are significantly influenced by AM-induced crystallographic texture. For instance, a simple cubic lattice structure with a density of 50% and a strong cube texture, displays nearly isotropic elastic behavior, despite its strong geometrical anisotropy. Analysis of various unit cell configurations highlights the interaction between crystallographic texture and lattice geometry, emphasizing the role of microstructural factors in optimizing mechanical performance.

In this study, we use micromechanics-based modeling to investigate the effect of a non-uniform void size distribution on the plastic flow and fracture behavior of porous ductile solids. We perform 2D plane strain finite element simulations of statistical volume elements containing between 3 x 3 and 22 x 22 uniformly-spaced voids of varying sizes, using two different modeling approaches: (i) resolving the voids spatially and (ii) using a porous plasticity model and spatially varying the initial porosity. For each sample size, thirty statistical volume elements are generated through random sampling from a log-normal void size distribution to quantify the variation for a given number of voids. The macroscopic behavior and microstructural evolution are analyzed under different imposed stress states. Our findings indicate that non-uniform void sizes have negligible effects on initial yielding and behavior before peak stress, but the strain at which maximum stress is attained varies. Beyond peak stress, there is a significant variation in the macroscopic stress-strain response and void growth between the statistical volume elements. Mean failure strain decreases and scatter diminishes as sample size increases, but even large samples retain scatter in failure strain. We achieve tremendous speed-up using models with porous plasticity while producing results comparable to models with spatially resolved voids. This suggests that a cost-effective modeling approach, where the voided subregions of the model are described using a porous plasticity model and spatially varying initial porosity, facilitates simulations of 3D volume elements with a statistically representative number of voids.

In this study, we investigate the modelling of ductile failure in an aluminium alloy in different temper conditions. We propose using a porous plasticity model with a stress-enhanced nucleation rule to describe the ductile failure process that is assumed to be closely related to the presence of particles. The primary objective is to determine if a single set of failure parameters can be used to describe the ductility of the aluminium alloy in several temper conditions. To support this investigation, tension tests are carried out on smooth and notched samples made from an extruded plate of aluminium alloy AA6110. By varying the heat treatment of the alloy, four materials are considered with different strength, work hardening, and ductility, while the grain structure and the distribution of the constituent particles are unchanged. A secondary objective is to evaluate a cost-efficient calibration procedure for the porous plasticity model. Finite element simulations of the tension tests show that the calibration procedure is accurate and that the same set of failure parameters can be used for all four temper conditions with acceptable accuracy when using the stress-enhanced nucleation rule.

We model ductile fracture for geometrically linear deformations by coupling plasticity and phase-field fracture models in a variationally consistent framework. The main aim of the proposed model is to account for the effect of stress triaxiality, in order to accurately reproduce ductile fracture, in particular, the instant and location of fracture initiation. For this purpose, we couple the modified Cam-Clay plasticity model with a phase-field fracture model. We study the behaviour of the model analytically in terms of homogeneous material responses, and numerically on plane-strain and axisymmetric specimens under tension with different notches.

In this study, we evaluate the use of strain localization analysis based on the imperfection band approach to model the effect of heterogeneous particle distribution on the ductile failure of structural metallic materials. To this end, tensile tests are performed on smooth and notched samples made of aluminium alloy AA6110 with an equiaxed grain structure and an inhomogeneous distribution of the constituent particles. The constituent particles are assumed to be the main contributors to the ductile failure of the alloy. By varying the heat treatment of the alloy, three different materials are considered with different strength, work hardening, and ductility, while the grain structure and constituent particle distribution are unaltered. Finite element simulations of the tension tests are conducted using both metal and porous plasticity models and the stresss-train histories of the elements in the minimum section of the specimen are used in strain localization analyses. In these analyses, ductile failure is assumed to occur when the strain rate inside a thin, planar imperfection band becomes infinite. The imperfection band is modelled with porous plasticity, using either a higher initial porosity than in the bulk material or by adding void nucleation. It is found that the ductility of the materials is most accurately captured by modelling the imperfection band by stress-enhanced nucleation.

Brittle materials are known for their violent and unpredictable cracking behavior. A behavior which is dictated by a combination of microscopical material defects and the competition between the potential energy of the system and the surface energy of the material. In this study, we present the implementation of a dynamic fracture phase-field model with a new crack driving force into a commercial finite element (FE) solver and examine its behavior using three different tension-compression splits. After validating the implementation, we use the model to investigate its predictive capacity on quasi-statically loaded L-shaped soda-lime glass specimens with varying critical load levels. The dynamic fracture phase-field model predicted similar crack propagation to what was found in the literature for quasi-static and dynamic validation cases. By varying the critical load level for the L-shaped soda-lime glass specimens using the new crack driving force, the model predicted a positive correlation between the initial crack propagation speed and the critical load level, similar to what was seen in the experiments. However, the predicted crack propagation speed decreased quicker than the experimental crack propagation speed. The tension-compression splits had an impact on the predicted crack propagation paths. Overall, the proposed crack driving force used in the dynamic fracture phase-field model seems to capture the relation between critical load and initial crack propagation speed and thus enables crack predictions for specimens of varying strength.

Crystal plasticity models enhanced with coupled or uncoupled damage and fracture criteria give an opportunity to account for the role of microstructure in ductile fracture, most directly representing the local variations of stress and strain fields inside and between the grains, voids and particles. Some computationally efficient crystal plasticity, damage and fracture models have recently been developed and applied to some cases of polycrystalline fracture. Such models allow to investigate in a direct way the effects of, e.g., shear bands, larger voids, particles, free surfaces and load direction on the development of damage and fracture. The cast and homogenized Al1.2Mn alloy investigated previously is used here as a basis for simulations. The alloy has an equiaxed grain structure with no texture and contains a population of larger particles and a population of dispersoids. The grain structure and the large particles are modelled directly in the finite element model, while the effect of dispersoids is represented by the damage and fracture part of the single crystal plasticity model. The study investigates the effect of different model parameters and features on the global and local behaviour of the material during localization and fracture, in light of available experimental data.

This article addresses large-scale analyses of welded aluminium connections where the weak zones are to be represented by a few shell elements. A combined experimental and numerical study on the behaviour and modelling of welded aluminium connections is presented, where a shell -element modelling framework applicable in large-scale analyses is proposed, accounting for geometrical instability, thinning, and ductile fracture. The proposed modelling framework is calibrated and validated using cross -weld tension tests. The test campaign involves tension testing of two Al-Mg-Si alloys and two welding techniques widely used in industrial applications. The shell -element simulations represented the response of the tests reasonably well.

This paper presents an experimental and numerical study on quasi-static ductile tearing of thin plates of the aluminium alloy AA6016 in three tempers. Depending on the temper, the main fracture mechanism in the plate tearing tests changes from grain boundary failure to coalescence of voids nucleated at the constituent particles. The experiments are complemented by nonlinear finite element simulations using an enriched Gurson–Tvergaard–Needleman (GTN) model to describe the material response. The onset of accelerated void growth is initiated either by incipient material softening (named the softening model ) or by the occurrence of strain localization (named the localization model ). It was found that strain localization takes place at a critical porosity f_ c , which depends on the current hydrostatic and deviatoric stress states. While the failure strain depends on the stress path, the critical porosity appears to be path independent. A third method is proposed (named the f_ c (T,L) model ), where a critical porosity surface f_ c = f_ c ( T,L) is used to determine when accelerated void growth starts. The surface is generated beforehand by solving for strain localization under proportional stress states defined by the stress triaxiality T and the Lode parameter L . By comparing the simulations to the experiments, it was found that the localization model performed well for a wide range of stress states. The softening model does not portray dependence on the Lode parameter and is therefore less versatile. The localization model and the f_ c (T,L) model gave similar predictions, but some minor differences were observed for two of the three tempers.

Localized deformation bands are often observed in materials exhibiting the Portevin–Le Chatelier (PLC) effect. However, efficient quantitative analysis of PLC bands remains challenging. A novel method is thus proposed in this work, where a multi-strain-jump function is introduced to capture the experimentally obtained staircase-like strain profile from digital image correlation (DIC). This approach is simple to implement and allows for: (i) automatically extracting the band strain throughout the test, which can be used to further evaluate the band velocity, and (ii) linking band characteristics with the corresponding local material properties. The efficiency of the method is demonstrated by analysing the band characteristics for different strain rates and temperatures. The results reveal that the relative band velocity is proportional to the work hardening rate, i.e., vb/vg∝Θ, for the continuously propagating type A bands.

When plastic deformation of metals occurs by dislocation motion, a part of the plastic work is stored in the material while the remainder is dissipated as heat. The fraction of the plastic work dissipated as heat can be observed on a macroscopic scale as infrared radiation. Typically, this fraction of plastic work converted into heat is assumed to be constant and around 90%. In this study, an experimental–numerical approach was used to calculate the Taylor–Quinney coefficient as a function of plastic deformation. The experimental foundation was obtained by performing tension tests at slightly elevated strain rates on notched specimens from two dual-phase steels and an aluminium alloy in three temper conditions. The temperature on the surface of the specimens was obtained using an infrared camera, and these temperature recordings were correlated to displacement measurements from a virtual extensometer enabled by digital image correlation. A user material model was used in combination with the thermo-mechanical solver in Abaqus/Standard to perform numerical simulations of the tension tests. Simulations were carried out with both constant and strain-dependent values of the Taylor–Quinney coefficient to examine the effect on the surface temperature in the centre of the specimen during the deformation process. Furthermore, numerical simulations were conducted to find a numerical expression for the Taylor–Quinney coefficient as a function of equivalent plastic strain, such that the temperature evolution in the simulations matches with the temperature measurements from the experiments.

Non-local models have over the years been established as an effective approach to solve the pathological mesh dependency problem observed in finite element simulation of strain-softening materials. This paper presents the formulation, implementation, and application of a gradient -based non-local Gurson-Tvergaard-Needleman (GTN) model for explicit finite element analysis. The porosity is taken as the non-local variable where the increment in porosity is averaged over the volume using an implicit gradient model. The gradient model is implemented in Abaqus/Explicit by utilising the coupled thermal-mechanical solver, which proves to be both a simple and computationally efficient approach. Due to the use of an explicit integration scheme, a transient term is introduced to the partial differential equation of the gradient formulation. The non-local GTN model is compared to the local counterpart for increasing mesh refinements using a plane strain shear band specimen, a plane strain tension specimen, and a plane strain compact tension specimen. The proposed approach can remedy the pathological mesh dependency problem. For the plane strain tension specimen, it is shown that the non -local GTN model will preserve the fracture mode (slant versus cup-cup fracture mode) when the mesh is refined. The non-local GTN model is also able to predict the same fracture mode as observed in ductile tearing experiments. However, non-local averaging can over-smooth the fields and exclude the slant fracture mode from occurring if the material length Lc is too large.