Elastoplastic Properties Research Articles

Bayesian optimization of 7-component (AlVCrFeCoNiMo) single crystal alloy’s compositional space to optimize elasto-plastic properties from molecular dynamics simulations

Abstract Exploring the vast compositional space of high-entropy alloys (HEAs) promises materials with superior mechanical properties much needed in industrial applications. We demonstrate on the 7-component alloy AlVCrFeCoNiMo system with randomly ordered atoms that this exploration of the compositional space can be accelerated by combining molecular dynamics simulations with Bayesian optimization. Our algorithm is tested on maximizing the shear modulus, resulting in pure Mo, an unsurprising result based on Mo’s large density. Maximizing the yield stress results in Co-, Cr- and Ni-based alloys with the optimal composition varying depending on the presence of defects within the crystal. Finally, we optimize the plastic behaviour by aiming for high stresses while minimizing the deformation fluctuations, and find that a predominantly NiMo alloy’s high lattice distortions ensure a smooth stress response. The results suggest that mechanical properties of 2- to 4-component alloys with optimized composition may be superior to those of equiatomic HEAs without short-range order.

Multiscale model for bottom-up prediction of failure parameters of unidirectional carbon-fiber-reinforced composite lamina from the atomic to filament-scales, and its application to failure modeling of open-hole quasi-isotropic composite laminates

A multiscale model is developed to comprehensively predict the failure parameters associated with the elasto-plasticity of a unidirectional carbon-fiber-reinforced composite lamina; the prediction is performed according to the resin-matrix design. The developed model involves quantum-chemical reaction-path calculations, molecular-dynamics simulations, and micromechanical analyses at the filament scale. The presented model is further combined with an advanced numerical approach developed based on an extended finite-element method, to analyze composites at the laminate scale. Using the established four-scale model, the open-hole tension and compression of a quasi-isotropic laminate are simulated, starting from the composition of an epoxy resin. The predicted elasto-plastic properties and strengths of a unidirectional lamina are in good agreement with the previously reported experimental results. Furthermore, the strengths predicted for the open-hole tests are also plausible, as they are similar to the experimental values reported in literature. The established multiscale model is expected to be useful in composite-material development as it facilitates rapid and exhaustive analysis.

Additively-manufactured lattice-grid sandwich cylinders and elastoplastic multi-failure analyses

Aluminum alloy lattice-grid sandwich cylinders, comprising a symmetric pyramidal truss core and open grid face-sheets, are additively manufactured using the selective laser melting method. The compression behaviors of these sandwich cylinders are investigated. Failure is controlled by three competing mechanisms: global buckling, core shear instability and grid buckling, with the active failure mode determined by the cylinder geometry and the material yield stress. Failure criteria are defined in terms of the effective elastoplastic properties of the grid-skins and core, which agree well with the measured and simulated failure responses, and are applied to generate multi-failure maps with cylinder geometrical parameters as axes. The maps help with failure load prediction and design optimization. For these cylinders, grid buckling is proposed as the dominant failure mode.

Deep learning coupled Bayesian inference method for measuring the elastoplastic properties of SS400 steel welds by nanoindentation experiment

Nanoindentation experiment has shown broad application prospects due to its ability to measure the mechanical properties of various materials at multiple scales. In this paper, a deep learning coupled Bayesian inverse approach is proposed for measuring the elastoplastic parameters of SS400 steel welds by nanoindentation experiment. The nanoindentation experiments were performed on the SS400 steel welds, including base metal (BM), weld zone (WZ), and heat affected zone (HAZ), and the experiment load–displacement (P-h) curves were obtained. The hyper-parameters tunable artificial neural network (ANN) was established to correlate elastoplastic parameters with indentation P-h curves. Based on Bayesian inference theory, the posterior density function for estimating the unknown material parameters was established. Transitional Markov chain Monte Carlo was used for sampling from the posterior density function, and the elastoplastic properties in different regions of SS400 steel welds were identified. The advantage of the established measuring method is that the hyper-parameters optimized ANN model can provide the very accurate forward relationship between material properties and indentation P-h curves. Besides, the inverse Bayesian framework can quantify the potential uncertainty of the identified elastoplastic parameters. The measured elastoplastic properties of the base metal of SS400 steel show good agreement with tensile experiment data, of which the maximum measuring error is less than 12%. The measured elastoplastic properties in WZ and HAZ are also proved to be effective. The uncertainty of the identified elastoplastic parameters of SS400 steel welds can be quantified by posterior marginal distribution, using Mean and Variance values. The results proved that the proposed inverse measuring method is reliable and effective.

Thermal Annealing Effect on Elastoplastic Behaviour of Al/Cu Bimetal during Three-Point Bending.

This paper presents the results of experimental studies on the effects of temperature and time of annealing on the elastoplastic properties of bimetallic aluminium-copper sheets. Mechanical tests were carried out on flat samples previously heated to temperatures of 250, 350, 450, and 500 °C for 40, 90, and 150 min. At the beginning of the tests, the elastic constants and internal friction energy were determined after thermal exposure using the impulse vibration exposure method. Further tests were carried out on the same samples using the three-point bending test. Based on the tests, the following quantities were determined and analysed: elasticity angles, translocations of the neutral axes of the cross-sections of samples, and changes in the values of bending moments plasticizing the extreme layers of bimetallic Al/Cu samples resulting from thermal interactions. The final part of this paper presents the results of measurements of the thickness of diffusion zones at the interface and their effect on the stability of the joint after annealing. The studies that were conducted indicate the dominant influence of the thermal factor on the properties of the Al/Cu bimetal above the temperature of 350 °C, which leads to the weakening of its strength and the degradation of the structure at the metallic phase boundary.

Fracture failure analysis of plastic fiber based on thermodynamic strength theory and experiment

In order to analyze the mechanical behavior of plastic fiber bundle, a theoretical model considering elastic and plastic behavior of single fiber is established. Based on uniaxial tensile tests of polythene single fiber, elastoplastic mechanical properties, such as elastic modulus and plastic modulus, are obtained. Moreover, distributions of yield strength and breaking strength of single fiber are determined. The stress–strain curve of polythene fiber bundle is predicted by theoretical model. The correctness of this theoretical model is verified by uniaxial tensile test of polythene fiber bundle. All experimental data points are within the range predicted by theoretical model. Some key parameters which regulate mechanical behavior of single fiber are investigated theoretically. Results show that Weibull parameters of yield strength and breaking strength of single fiber have great effect on mechanical performance of fiber bundle. The concentration of distribution area of breaking strength can improve the overall fracture strength of fiber bundle. Results and conclusions in this investigation can extend and perfect fiber bundle model in terms of plastic behavior.

A multifaceted approach using RVE homogenization methodology for identification of elastoplastic behavior of steel matrix composite: Application to deep-drawing process

The integration of cutting-edge materials and computational methods is now essential in contemporary engineering, especially in sectors where a deep comprehension of the mechanical behavior of reinforced composite materials is crucial. In this context, steel matrix composites, enhanced with reinforcing elements like TiB2, have garnered attention due to their potential for superior mechanical properties and wide-ranging applications. This article explores an innovative computational framework based on the Representative Volume Element (RVE) concept to examine the elastoplastic properties of a ferritic steel matrix reinforced with ceramic particles (TiB2). The finite element analysis (FEA) is performed with periodic boundary conditions (PBCs) to apply the specified loading to the RVE. As a first endeavor, the developed multi-faceted approach provides a broader perspective on shear behavior and the elastoplastic composite’s properties of Fe-TiB2 for various reinforcement volume fractions. Then, the focus of this study lies in its application to the deep-drawing process, a critical manufacturing operation with significant implications in industries such as automotive and aerospace. The established approach for homogenizing elasto-plastic Fe-TiB2 composites is applied to analyze the influence of reinforcement variation on several critical aspects during the deep-drawing process, including formability, forming force, Von Mises stress distribution, and logarithmic strain.

Elastoplastic and Electrochemical Characterization of xTiB2 Strengthened Ti Porous Composites for Their Potential Biomedical Applications

The microstructure, elastoplastic properties, and corrosive response of induced porous Ti-TiH2 materials reinforced with TiB2 particles were investigated. Samples were fabricated using CP-Ti Grade1, Titanium Hydride (TiH2), TiB2 powders (0, 3, 10, and 30 vol.%), and ammonium bicarbonate salt (40 vol.%) as a space holder. Composites were fabricated using the Powder Metallurgy technique under high-vacuum conditions (HVS) at 1100 °C. Scanning electron microscopy, X-ray diffraction, nanoindentation tests, and electrochemical assays were used to investigate the pore formation, pore distribution, phase formation, elastoplastic properties, and electrochemical behavior of the compounds, respectively. With a mean pore diameter of 50–900 µm and Young’s modulus of less than 100 GPa, which is close to the properties of human bone, the pore structures of the compounds processed here are shown to be a potential biomaterial for osseointegration. In addition, their H/Er and H3/Er2 ratios for the reinforced samples are higher than those of the unreinforced sample (1.5 and 4 times higher than the unreinforced sample, respectively), suggesting a better wear resistance of the Ti-TiH2/xTiB2 composites. Electrochemical experiments demonstrated that the Ti-TiH2/xTiB2 composites exhibited superior passivation properties compared to the Ti-TiH2 sample. Additionally, the corrosion rates exhibited by the 3 and 10 vol.% of TiB2 samples were found to be within an acceptable range for potential biomedical applications (29.26 and 185.82 E-3 mm·y−1). The elastoplastic properties combined with the electrochemical behavior place the Ti-TiH2/3-10TiB2 composites as potential candidates for the biomedical application of CP-Ti.

Influence of fibril aspect ratio, chemical functionality, and volume fraction on the mechanical properties of cellulose nanofibril materials

Nanocellulose has emerged as a widely utilized building block in nanostructured materials due to its availability, sustainability, large surface area, and high stiffness and aspect ratio. The wet or dry elastoplastic properties of these materials are determined by the fibrils' stiffness, chemical properties, hemicellulose content, and the number of fibril contacts. However, the specific contributions and relative importance of each factor remain unclear. Therefore, this work was devoted to systematically comparing the material properties of gels, aerogels, and wet and dry sheets prepared from CNFs with different aspect ratios, chemical functionality, and hemicellulose content. The fibrils were prepared by chemical and mechanical processing of different pulps. By preserving the native structure as much as possible, higher aspect ratio fibrils can be obtained, which allows for the development of more mechanically robust materials. The results demonstrate that higher aspect ratios lead to more interconnected networks at a lower solids concentration, resulting in a more evenly distributed stress and longer-range stress transfer, yielding stiffer and more ductile materials. The most important finding was that the aspect ratio influences the network formation, resulting in different network topologies. The results were also compared to earlier published data and integrated into a theoretical beam-bending model for a complete elastoplastic description of the network properties, including the influence of fibril aspect ratio and chemical functionality. This information improves our understanding and description of nanofibril networks for which general models have been missing. It can be used to optimize nanofibril preparation and, hence, the resulting eco-friendly materials.

Three-dimensional elastoplastic post-buckling analysis of functionally graded plates using a novel meshfree Tchebychev-radial point interpolation approach

This paper presents a three-dimensional (3D) analysis of the post-buckling behavior of functionally graded (FG) plates for the first time using an elastoplasticity-based meshfree formulation. A novel 3D Tchebychev-radial point interpolation approach, which combines radial basis functions with Tchebychev polynomials, is developed to solve the nonlinear post-buckling problem. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The governing equations are derived using the principle of virtual work by considering the 3D full Green–Lagrange strain components. The Newton–Raphson technique along with the arc-length method is used to determine post-buckling equilibrium paths of FG plates. The effective elastoplastic properties of the functionally graded material are assessed by exploiting the homogenization method, named Tamura–Tomota–Ozawa (TTO) model. It has been demonstrated that the accuracy of the solution is improved by incorporating Tchebychev polynomials into the radial point interpolation method (RPIM) shape function, and the stability and robustness of the results are independent of variations in the shape parameter. Furthermore, it is confirmed that TRPIM, with a slightly higher CPU time compared to RPIM, exhibits a higher convergence rate. The excellent agreement of the results with those existing in the literature shows that the proposed meshfree method can be used as a robust and accurate numerical tool to predict the elastoplastic post-buckling behavior of FG plates. Further numerical assessments indicate that post-buckling paths are significantly affected by factors such as geometric parameters, material gradient, loading ratio, and boundary conditions (BCs).

An algorithm based on B-differentiable equations method for solving problems involving frictional contact coupled with concrete plastic damage

In this paper, an algorithm is proposed to solve the frictional contact problems while considering elasto-plastic material properties. The static and dynamic solution procedures are derived in incremental form, respectively. The proposed method employs a two-layer iteration strategy. In the outer iteration layer, the equilibrium equations are solved, with the stress and stiffness matrix updated at each iteration. Within the inner iteration layer, the contact force is calculated, where the contact equations, expressed as B-differentiable equations, incorporate only contact conditions in normal and tangential directions, and the contact flexibility matrix, obtained by applying unit force pair to all contact node pairs in turn, is introduced. Consequently, the solution for nonlinear equilibrium equations and contact equations is decoupled, requiring only one decomposition of the stiffness matrix for each calculation of the contact flexibility matrix, as it remains constant within the contact iteration layer. In addition, the constitutive model of concrete developed by Lee and Fenves is utilized. This model adopts two independent variables to describe tensile and compressive damage, together considering the strength recovery of the concrete. Numerical examples demonstrate the accuracy of the proposed method by comparing the results from Abaqus. Furthermore, the present algorithm is applied to static and dynamic analyses of a concrete arch dam with several transverse joints, where the effects of gravity, water level, the number of contact surfaces, and seismic load are considered, and some conclusions are obtained.

Phase-field ductile fracture simulations of thermal cracking in additive manufacturing

We present a multiphysics phase-field fracture model for thermo-elasto-plastic solids in the context of finite deformation and apply it to simulate the hot cracking phenomenon during metal additive manufacturing. The model is derived in a thermodynamically consistent manner, with the intercoupling mechanisms among elastoplasticity, phase-field crack and heat transfer comprehensively considered. It involves particularly coupled parameters among these materials physics, e.g. plasticity-dependent degradation function and fracture toughness, damage-dependent yield surface and thermal properties, and temperature-dependent elastoplastic properties and fracture strength. The finite element implementation of the coupled phase-field model is benchmarked with simulation results of a tensile test of an I-shape specimen, encompassing elastoplasticity, hardening, necking, crack initiation and propagation, in contrast to the related experimental results. The validated model is further employed to simulate the multiphysics hot cracking phenomenon in additive manufacturing in the context of both the effective powder-bed model and the powder-resolved model thanks to prior non-isothermal phase-field powder-bed-fusion simulations. Simulation results reveal certain key features of the hot crack and its dependency on process parameters like beam power and scan speed, which are helpful for the fundamental understanding of crack formation mechanisms and process optimization.

Elastoplastic Mechanical Properties and Kinematic Hardening Model of 35CrNi3MoVR.

The existing tensile-compression elastoplastic models are not suitable for varies of materials. An accurate constitutive model of the elastoplastic mechanical properties more suitable for 35CrNi3MoVR was produced by optimizing the existing fitting equations based on uniaxial tensile-compression tests, which are able to describe the elastoplastic stress-strain relation and Bauschinger effect varying with the maximum tensile plastic strain. A UMAT subroutine of the constitutive model in ABAQUS was proposed and conducted for FEM calculation. Hydraulic autofrettage tests were carried out under different pressures on thick-walled 35CrNi3MoVR tubes, and the results were compared with those of FEM calculations to further validate the accuracy of the fitting model. The results show that the constructed power function kinematic hardening model can effectively describe the elastoplastic mechanical properties of 35CrNi3MoVR and can be applied to the autofrettage calculation of this material. The comparison among the calculation results of different models proved that the model proposed in this research has better performance compared to other existing models. Taking the Mises stress at the inner surface of the thick-walled tubes as the evaluation criterion, the error of the power function kinematic hardening model reaches less than 3%, decreasing the error by at least 50%.

Experimental study on dynamic characteristics of frozen saline silty clay under cyclic loading

In order to investigate the dynamic characteristics of frozen saline silty clay (studied saline soil) under reciprocating loading, a series of cyclic tri-axial experiments have been conducted for studied saline soil with 0.0, 0.5, 1.5, and 2.5 % of Na2SO4 contents under confining pressures 0 MPa–18 MPa at −6 °C, respectively. The test results show that as the increase of number of cycle N, the accumulated axial strain εaN continuously increases, and the relationship between εaN and N can be described by an exponential function: εaN=aNb; As the number of cycle N increasing, dynamic shear modulus GdN and dynamic bulk modulus KdN increase firstly and then decrease slightly; Salt content and confining pressure have great influences on the εaN, GdN and KdN. Within the same loading cycle, GdN and KdN decrease until reaching their minimums when the salt content is 0.5 %, and then GdN and KdN increase as the increase of salt content. With the change of salt content, εaN presents an opposite change law to GdN and KdN. For the studied saline soil with same salt content, during the same loading cycle, εaN and GdN increase until reaching their minimums, and then decrease as the increase of confining pressure, KdN increases with the increase of confining pressure. This study can be applied to evaluate the elasto-plastic properties of frozen soils and saline soils subjected to cyclic dynamic loading.

Spatial distribution of local elastic moduli in nanocrystalline metals

Elastoplastic properties of nanocrystalline metals are nonuniform on the scale of the grain size, and this nonuniformity affects macroscopic quantities as, in these systems, a significant part of the material is at or adjacent to a grain boundary. We use molecular dynamics simulations to study the spatial distributions of local elastic moduli in nanograined pure metals and analyze their dependence on grain size. Calculations are performed for copper and tantalum with grain sizes ranging from 5 to 20 nm. Shear-modulus distributions for grain and grain-boundary atoms were calculated. It is shown that the noncrystalline grain boundary has a wide shear-modulus distribution, which is grain-size independent, while grains have a peaked distribution, which becomes sharper with increasing grain size. Average elastic moduli of the bulk, grains, and grain boundary are calculated as a function of grain size. The atomistic simulations show that the reduction of total elastic moduli with decreasing grain size is mainly due to a resulting larger grain-boundary atoms fraction, and that the total elastic moduli can be approximated by a simple weighted average of larger grain elastic moduli and a lower grain-boundary elastic moduli. Published by the American Physical Society 2024

Elastoplastic properties of ion exchangers based on cross-linked polyelectrolytes

In this paper, we dilatometrically studied the elastoplastic properties of spherical grains of industrial weakly acidic and strongly acidic ion-exchanger in experiments with constant uniaxial compression and a subsequent unload at room temperature, depending on the ionic form and concentration of the electrolyte solution. It was found that the ionic form of polyacrylate and polymethacrylate cross-linked with triethylene glycol dimethacrylate and divinylbenzene, respectively, and the concentration of the external solution affects their elastoplastic properties. In dilute solutions of sodium chloride and calcium chloride, the gels exhibited elastic properties with close relative amplitudes of deformation. The amplitude of deformation of the grain of polymethacrylate crosslinked with divinylbenzene, in the Ni form, in a dilute nickel chloride solution was significantly lower than that of the Ca form, with significant plastic deformation. With an increasing concentration of the external solution of calcium and nickel chlorides under mechanical load on the grain of polymethacrylate cross-linked with divinylbenzene, the total deformation of the granule and the magnitude of elastic deformation decreased, while the residual (plastic) deformations increased. In concentrated solutions of CaCl2 and NiCl2, such an ion-exchanger became an inelastic rigid material. Even under increased mechanical load, the magnitude of its elastic compressive deformation was very small. The K-form of a swollen in water strongly acidic polystyrene cation-exchanger with grafted sulpho groups cross-linked with divinylbenzene is also characterized by elastic deformations, i.e. the polymer is in a highly elastic state. However, the polystyrene matrix is more rigid compared to polyacrylic and polymethacrylic cation-exchangers in the alkali metal ion form, so the amplitude of deformation is significantly smaller. For such a cation-exchanger in Ca- and Ni- forms, elastic deformations prevail even in concentrated solutions.

The effects of polycrystalline 3 C-SiC with different roughness coefficients on the crystal structure of nano-grin ding based on molecular dynamics

To investigate the effect of different roughness subsurface on the crystal structure and grain boundary changes during polycrystalline 3 C-SiC nanocrystalline grinding. Polycrystalline 3 C-SiC with different roughness subsurface is constructed by Voronoi method, the stress, crystal structure change and grain boundary crossing mechanism of polycrystalline 3 C-SiC are analyzed by molecular dynamics method. Three different roughness surfaces (Ry=0.02 um, Ry=0.04 um and Ry=0.045 um) are selected for analysis, before the nano-grinding process, the polycrystalline 3 C-SiC is first annealed to make the atoms closely arranged and eliminate the vacancy defects inside the grains. Different roughness affects the friction force of polycrystalline 3 C-SiC and changes the deformation of its subsurface. Consequently, affecting the elastoplastic properties of polycrystalline 3 C-SiC. Different roughness will affect the shear force on the polycrystalline 3 C-SiC subsurface, the smaller the roughness, the greater the shear stress on the subsurface. The polycrystalline 3 C-SiC crystal structure with a roughness of Ry=0.04um is most obviously affected, the length of the dislocations it produces is relatively small, and the situation is more obvious at the boundary, fewer internal dislocations indicating internal dislocation slip phenomenon is less and more favorable for processing.

Plastic collapse behavior of plate to CHS connection under biaxially symmetric load

This study investigates the plastic collapse behavior of a non-diaphragm type connection with flange plates connected to a circular hollow section (CHS) column, where four flanges were joined from two orthogonal directions. The analysis was conducted using the finite element method (FEM). The focus was on determining the collapse load of the flange joint under a biaxially symmetric load from the four flanges. In an initial numerical analysis, the fundamental collapse behavior of the cylindrical wall was explored. Finite element models of CHS tubes with perfectly elasto-plastic material properties were employed. The analysis revealed that the plastic collapse mechanism of the cylindrical wall was influenced by the axial force in the transverse flanges. Prediction equations for the collapse load of the joint were formulated, assuming four representative collapse mechanisms and employing the principle of virtual work based on the numerical analysis results. Additionally, the ultimate strength of the joint, determined by the plastic collapse of the cylindrical wall, was computed using finite element models of CHS tubes with realistic hardening properties. A comparison between predictions from the equations based on perfectly elasto-plastic CHS tubes and numerical solutions through finite element analysis (FEA) of CHS tubes with realistic hardening properties validates the accuracy of the proposed prediction equations, even when applied to realistic steel tubes.

Indentation stress–strain analysis and finite element simulation to determine elastoplastic properties of thin films decreasing the substrate contribution

AbstractThe mechanical performance of protective coatings is crucial in daily industrial environments, with transition metal nitrides being among the most commonly used hard coatings for machining tool protection. However, determining their elastoplastic properties via conventional methods can be challenging due to the thickness‐dependent response of film/substrate systems. In this study, we utilised two sputtering Ti‐Al‐N films as a model hard thin film/soft substrate system to showcase an alternative methodology to the Oliver and Pharr method. This alternative approach involves determining Young's modulus, yield stress and hardness through indentation stress–strain curves obtained from nanoindentation tests, effectively decreasing the substrate's contribution. This decrease was corroborated by finite element simulations conducted on films with thickness below 1.0 μm. The elastoplastic properties determined using our methodology fell within the range reported for typical Ti‐Al‐N films. Furthermore, by applying our methodology, we were able to correlate and discuss the observed differences in mechanical behaviour between the two films based solely on their microstructural, compositional and morphological properties. Thus, we have demonstrated a viable alternative methodology to address substrate contribution challenges in the mechanical characterisation of thin film/substrate systems when employing an indenter with a large radius of curvature (~650 nm). This research holds potential implications for the design of protective submicrometric films with industrial applications.

Micromechanical prediction of the elastic and plastic properties of sintered steels

One of the characteristic features of sintered steels is the porosity in their microstructure resulting from the compaction and sintering process. This porosity strongly influences the mechanical properties. To enhance the understanding for the structure–property relationship of sintered Astaloy®85Mo with 0.4 wt.%C, a micromechanical modelling approach based on face-centred cubic (fcc) representative volume elements (RVE) is proposed. The fcc-like periodic arrangement of the sintered particles in the RVE enables the consideration of a realistic non-spherical pore morphology. To compare the predictions with experimental results, accompanying uniaxial tensile tests are considered at different pore volume fractions after initial microstructure characterisation. In addition to the effect of pore volume fraction, the influence of sinter necks on the predicted overall strength is also systematically investigated. Despite the fairly simple nature of the underlying fcc structure, the RVE simulations are perfectly capable of reproducing the experimental trend, showing that the elasto-plastic properties decrease with increasing porosity. This is in contrast to analytical predictions, which underestimate the decrease in properties due to spherical pore assumptions. Moreover, the finite element-based simulations reveal a less pronounced influence of the sinter neck shape on the macroscopic behaviour, even though substantial differences in plastic strain localisation are discernible at the microscopic scale.