Impact Toughness of Ultrafine‐Grained Commercially Pure Titanium for Medical Application

This study aims at achieving the best combination of strength, ductility, and impact toughness in ultrafine‐grained (UFG) Ti Grade 4 produced by equal‐channel angular pressing via Conform scheme (ECAP‐C) with subsequent cold drawing. UFG structures with various parameters (e.g., size and shape of grains, dislocation density, conditions of boundaries) are formed by varying the treatment procedures (deformation temperature and speed at drawing, annealing temperature). The tensile and impact toughness tests were performed on samples with a V‐shaped notch and different structures of commercially pure Ti Grade 4 in the coarse‐grained and UFG states. The results demonstrated that grain refinement, higher dislocation density, and their elongated shape were obtained as a result of drawing at 200 °С, which led to a decrease in both the uniform elongation at tension and the impact toughness of Ti Grade 4. Short‐term annealing at 400–450 °C could improve the impact toughness of UFG Ti with a non‐significant decrease in strength. This short‐term annealing contributes to the dislocation density decrease without considerable grain growth as a result of the recovery and redistribution of dislocations. The dependence of impact toughness on the strain hardening ability of UFG Ti was discussed.

     

Elastic deformation behavior and microstructure evolution of single crystal nickel nanowire in tensile test along [0 0 1] orientation

Elastic deformation behavior and microstructure evolution of single crystal nickel nanowire in tensile test have been investigated using molecular dynamics simulations. When the temperature is above 300 K, the deformation of nanowire is inhomogeneous in the elastic stage. It can generate a kind of (body‐centered cubic)‐like structure within the material to guide the elastic deformation, rather than the uniform deformation of all the atoms. The (body‐centered cubic)‐like structure will transform to be a body‐centered cubic structure gradually with the increasing of strain and will revert to be a face‐centered cubic structure when the twin crystal appears. The formation of (body‐centered cubic)‐like structure could reduce the density of the material to resist deformation. Besides, the (body‐centered cubic)‐like structure increase with increasing of strain or temperature, and they will gather together to reduce the interface energy. Our conclusion also can be proved by the radial distribution functions g(r).     

C0 solid elements for materials with strain gradient effects

Experiments conducted by various researchers in the past few decades have shown that materials display strong size effects when the material and characteristic length scales associated with non‐uniform plastic deformation are of the same order at micron and submicron levels. The state of stress under such a condition was observed to be a function of both strain and strain gradient. The meso‐scale constitutive relation taking into account Taylor dislocation theory is briefly described. The conventional theory of mechanism‐based strain‐gradient (CMSG) plasticity incorporating the intrinsic material length scale is adopted in the formulation of a series of C⁰ solid elements of 20–27 nodes. The model is implemented in ABAQUS, a finite element package via a user subroutine. Convergent studies have been carried for the series of elements with classical as well as CMSG plasticity theories. Numerical results on a bar under constant body force and indentation at submicron level reinforce the observation that materials are significantly strengthened for deformation at micron and submicron levels and the effects of strain gradient cannot be ignored without significant loss of the accuracy of the results. Copyright © 2005 John Wiley & Sons, Ltd.     

Mechanical characterization of hollow ceramic nanolattices

In the analysis of complex, hierarchical structural meta-materials, it is critical to understand the mechanical behavior at each level of hierarchy in order to understand the bulk material response. We report the fabrication and mechanical deformation of hierarchical hollow tube lattice structures with features ranging from 10 nm to 100 μm, hereby referred to as nanolattices. Titanium nitride (TiN) nanolattices were fabricated using a combination of two-photon lithography, direct laser writing, and atomic layer deposition. The structure was composed of a series of tessellated regular octahedra attached at their vertices. In situ uniaxial compression experiments performed in combination with finite element analysis on individual unit cells revealed that the TiN was able to withstand tensile stresses of 1.75 GPa under monotonic loading and of up to 1.7 GPa under cyclic loading without failure. During the compression of the unit cell, the beams bifurcated via lateral-torsional buckling, which gave rise to a hyperelastic behavior in the load–displacement data. During the compression of the full nanolattice, the structure collapsed catastrophically at a high strength and modulus that agreed well with classical cellular solid scaling laws given the low relative density of 1.36 %. We discuss the compressive behavior and mechanical analysis of the unit cell of these hollow TiN nanolattices in the context of finite element analysis in combination with classical buckling laws, and the behavior of the full structure in the context of classical scaling laws of cellular solids coupled with enhanced nanoscale material properties.     

An incremental 2D constitutive model accounting for linear viscoelasticity and damage development in short fibre composites

A model accounting for linear viscoelasticity and microdamage evolution in short fibre composites is described. An incremental 2D formulation suitable for FE‐simulation is derived and implemented in FE‐solver ABAQUS. The implemented subroutine allows for simulation close to the final failure of the material. The formulation and subroutine is validated with analytical results and experimental data in a tensile test with constant strain rate using sheet moulding compound composites. FE‐simulation of a four‐point bending test is performed using shell elements. The result is compared with linear elastic solution and test data using a plot of maximum surface strain in compression and tension versus applied force. The model accounts for damage evolution due to tensile loading and neglects any damage evolution in compression, where the material has higher strength. Simulation and test results are in very good agreement regarding the slope of the load–strain curve and the slope change. Copyright © 2005 John Wiley & Sons, Ltd.     

A study of the mechanical and fatigue properties of metallic microwires

There is an increasing necessity to record the deformation characteristics of microelements containing freestanding bond wires. The data required are either mechanical or thermal such as Young's moduli, stress–strain values, fatigue‐ and thermal‐strain data, but the nominal strength of a structure changes by scaling its size. Due to this size effect, material data cannot be taken from macrospecimens, thus special testing procedures were introduced. Laser optical sensors based on the speckle correlation technique were applied to determine non‐contacting strain values with high strain resolution. For the mechanical properties tensile tests were used. A special ultrasonic resonance fatigue system is described for testing freestanding microwires. In this study the stress–strain and fatigue response of microwires of Cu with a purity of 99.99+% with diameters between 10 and 125 μm with a typical bamboo structure have been investigated. A size dependence of the yield strength which increased with decreasing diameter was observed, while the fracture elongation showed contrary behaviour. Fatigue life also decreased with reduced diameters. An explanation is presented based on formed oxide layers, strengthening effects by dislocation pile‐ups and a pronounced localization of formed slip steps acting as notches being most dominant in the very thin microwires.     

Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model

Dynamic crushing responses of three-dimensional cellular foams are investigated using the Voronoi tessellation technique and the finite element (FE) method. FE models are constructed for such closed-cell foam structures based on Voronoi diagrams. The plateau stress and the densification strain energy are determined using the FE models. The effects of the cell shape irregularity, impact loading, relative density and strain hardening on the deformation mode and the plateau stress are studied. The results indicate that both the plateau stress and the densification strain energy can be improved by increasing the degree of cell shape irregularity. It is also found that the plastic deformation bands appear firstly in the middle of the model based on tetrakaidecahedron at low impact velocities. However, the crushing bands are seen to be randomly distributed in the model based on Voronoi tessellation. At high impact velocities, the “I” shaped deformation mode is clearly observed in all foam structures. Finally, the capacity of foams absorbing energy can be improved by increasing appropriately the degree of cell shape irregularity.     

Formulation and computation of geometrically non‐linear gradient damage

The aim of this contribution is the extension of a small strain and small deformation formulation of gradient enhanced damage to the geometrically non‐linear case. To this end, Non‐local Stored Energy densities, (NSE) are introduced as primary variables. Fluxes conjugated to the gradients of the NSE are then computed from balance laws which in the small strain limit correspond to the averaging equation well known in the literature [1–3]. The principal task is then to establish constitutive laws for these newly introduced NSE‐fluxes. Thereby, four different options are investigated which are motivated from Lagrange and Euler averaging procedures together with changes of the metric tensors. Issues of the corresponding FE‐formulation and its linearization within a Newton–Raphson procedure are addressed in detail. Finally, the four different formulations are compared for the example of a bar in tension whereby large strains are truly envisioned. Copyright © 1999 John Wiley & Sons, Ltd.     

Modeling of creep and stress relaxation of the nickel‐base alloy NiCr20TiAl at isothermal and non‐isothermal loading conditions

The design and dimensioning of new as well as the assessment of operating high‐temperature components in service require a precise prediction of creep and stress relaxation. The increasing share of renewable energies forces fossil‐fired power plants for increasing numbers of start‐ups and shut‐downs. Consequently, transient loading conditions need to be taken into account. In order to meet this demand, non‐isothermal creep equations are necessary, which enables a consistent prediction of creep strain and stress relaxation in a wide range of temperatures and stresses. In this paper, an approach for the visco‐plastic modeling of creep and stress relaxation for non‐isothermal loading conditions is presented. The strain portions creep, “negative creep” and initial plasticity, occurring at elevated temperatures are described by temperature‐dependent phenomenological equations. Within this paper, the adjustment of the parameters is based on a wide database of hot tensile tests, creep and annealing experiments. The nickel‐base alloy NiCr20TiAl has been examined in a temperature range from 450 °C to 650 °C. The developed material models have been successfully validated with isothermal and non‐isothermal relaxation experiments. Further, the recalculation of a staged relaxation test demonstrates the capability of the defined material laws in a wide stress range under isothermal and non‐isothermal loading conditions.     

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.     

Electronic Speckle‐Pattern Interferometry Measurements of Structural Ratcheting Strain

Abstract: Several tensile specimens with a central hole were subjected to a cyclic loading for which the Von Mises stress was beyond the initial yield stress in the vicinity of the hole. The tensile machine was fixed together with a phase‐shifting electronic speckle‐pattern interferometry measurement bench that makes it possible to perform strain measurement along the tensile axis. The plastic strain map corresponding to the 30th cycle was obtained. For the considered measurement field, the resolution of the strain measurement is close to 10^?5. By varying the loading, it was possible to detect and observe the deformation corresponding to an early stage of the ratcheting phenomenon. The non‐ratcheting cyclic plasticity behaviour was not observed during the 30th cycle. In the Discussion section, the experimental results were interpreted using Melans’s theorem, which allowed us to determine an upper bound for the yield stress. Eventually, it is shown that the procedure followed in this work could be a way to obtain some interesting data related to the material behaviour laws.     

Finite element implementation of a kinetic model of dynamic strain aging in aluminum–magnesium alloys

Soare and Curtin (Acta Mater. 2008; 56 :4091–4101, 4046–4061) have recently developed a model of dynamic strain aging in solute‐strengthened alloys. Their constitutive law describes time‐dependent solute strengthening using rate equations that can be calibrated using atomistic simulations. In this paper, their material model is incorporated into a continuum finite element simulation, with a view to completing a multi‐scale method for predicting the formability of solute‐strengthened alloys. The Soare–Curtin model is first re‐formulated as a state‐variable constitutive law, which is suitable for finite element computations. An efficient numerical procedure is then developed to track the strength distribution of aging mobile and forest dislocations in the solid during deformation. The method is tested by simulating the behavior of a 3D aluminum–magnesium alloy tensile specimen subjected to uniaxial loading at constant nominal strain rate. The model predicts the influence of strain rate on the steady‐state flow stress of Al–Mg alloys, but no Portevin–Le Châtelier bands or serrated flow were observed in any of our simulations, and the influence of strain rate on tensile ductility is not predicted correctly. The reasons for this behavior and possible resolutions are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.     

Bracing systems in masonry buildings. Part 1: Simple application of FE programs / Aussteifungssysteme im Mauerwerksbau. Teil 1: Einfache Anwendung von FE‐Programmen

Due to the low tensile strength of masonry perpendicular to the bed joint, masonry wall panels have non‐linear material properties. Assuming simple elastic constitutive laws, this article presents two modelling variants, which consider the lack of tensile strength in a simple manner. Both variants are investigated for their advantages and disadvantages. In a second part of the article, the application of the methods will be illustrated through the example of a four‐storey building.     

A fractal approach to indentation size effect

In this paper, we propose an original interpretation of indentation size effect (ISE) in both single crystal and polycrystalline metals, which is based on the experimental evidence of the formation of fractal cellular dislocation patterns during the later stages of plastic deformation, in strain hardening metals, both under tensile loading and in compression. The proposed approach is a generalization of the arguments already proposed by the senior author in order to derive multifractal scaling laws (MFSL), which apply to tensile strength, fracture energy and the critical strain of brittle and quasi-brittle materials.This approach is thus in the mainstream of the geometrical interpretation of size-scale effects on the strength of solids, which has been counterposed, in recent years, to the mechanical interpretation. The proposed fractal approach aims at strengthening this view, which provides ease of interpretation, and at stimulating discussion on the central key role of dislocation evolution in the plastic deformation of metals, the fractal characteristics of which have not been adequately considered in literature.The obtained equation for ISE, based on the fractal approach, very closely resembles MFSL for tensile strength in quasi-brittle materials and the scaling equation already proposed by other authors, but it is based on a very different underlying physical model. Some experimental hardness data, obtained from microindentation on copper, have been fitted with MFSL, and show a very good agreement.     

Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals

This work reviews and critically discusses the current understanding of two scaling laws, which are ubiquitous in the modeling of monotonic plastic deformation in face-centered cubic metals. A compilation of the available data allows extending the domain of application of these scaling laws to cyclic deformation. The strengthening relation tells that the flow stress is proportional to the square root of the average dislocation density, whereas the similitude relation assumes that the flow stress is inversely proportional to the characteristic wavelength of dislocation patterns. The strengthening relation arises from short-range reactions of non-coplanar segments and applies all through the first three stages of the monotonic stress vs. strain curves. The value of the proportionality coefficient is calculated and simulated in good agreement with the bulk of experimental measurements published since the beginning of the 1960s. The physical origin of what is called similitude is not understood and the related coefficient is not predictable. Its value is determined from a review of the experimental literature. The generalization of these scaling laws to cyclic deformation is carried out on the base of a large collection of experimental results on single and polycrystals of various materials and on different microstructures. Surprisingly, for persistent slip bands (PSBs), both the strengthening and similitude coefficients appear to be more than two times smaller than the corresponding monotonic values, whereas their ratio is the same as in monotonic deformation. The similitude relation is also checked in cell structures and in labyrinth structures. Under low cyclic stresses, the strengthening coefficient is found even lower than in PSBs. A tentative explanation is proposed for the differences observed between cyclic and monotonic deformation. Finally, the influence of cross-slip on the temperature dependence of the saturation stress of PSBs is discussed in some detail. This works takes into account current discussions on the microstructural aspects of cyclic deformation and highlights further work that is required for fully understanding the physical origin of the two scaling laws.     

Mechanical properties of grafold: a demonstration of strengthened graphene

Morphological patterns and structural features play crucial roles in the physical properties of functional materials. In this paper, the mechanical properties of grafold, an architecture of folded graphene nanoribbon, are investigated via molecular dynamics simulations and intriguing features are discovered. In contrast to graphene, grafold is found to develop large deformations upon both tensile and compressive loading along the longitudinal direction. The tensile deformation is plastic, whereas the compressive deformation is elastic and reversible within the strain range investigated. The calculated Young's modulus, tensile strength, and fracture strain are comparable to those of graphene, while the compressive strength and strain are much higher than those of graphene. The length, width, and folding number of grafold have distinctive impacts on the mechanical performance. These unique behaviors render grafold a promising material for advanced mechanical applications.     

Masonry infilled reinforced concrete frames under horizontal loading / Stahlbetonrahmen mit Ausfachungen aus Mauerwerk unter horizontalen Belastungen

The behaviour of infilled reinforced concrete frames under horizontal load has been widely investigated, both experimentally and numerically. Since experimental tests represent large investments, numerical simulations offer an efficient approach for a more comprehensive analysis. When RC frames with masonry infill walls are subjected to horizontal loading, their behaviour is highly non‐linear after a certain limit, which makes their analysis quite difficult. The non‐linear behaviour results from the complex inelastic material properties of the concrete, infill wall and conditions at the wall‐frame interface. In order to investigate this non‐linear behaviour in detail, a finite element model using a micro modelling approach is developed, which is able to predict the complex non‐linear behaviour resulting from the different materials and their interaction. Concrete and bricks are represented by a non‐linear material model, while each reinforcement bar is represented as an individual part installed in the concrete part and behaving elasto‐plastically. Each brick is modelled individually and connected taking into account the non‐linearity of a brick mortar interface. The same approach is followed using two finite element software packages and the results are compared with the experimental results. The numerical models show a good agreement with the experiments in predicting the overall behaviour, but also very good matching for strength capacity and drift. The results emphasize the quality and the valuable contribution of the numerical models for use in parametric studies, which are needed for the derivation of design recommendations for infilled frame structures.