Supercrystalline nanocomposites are a burgeoning class of hybrid inorganic-organic materials. Studies showed that self-assembly of iron oxide particles surface-functionalized with organic (e.g. oleic acid) ligands produces a supercrystalline nanocomposite with exceptional mechanical properties. Consequently, significant research has been conducted on these materials to experimentally characterize the mechanical properties of such materials. However, so far all modeling studies used time and rate independent elastoplastic material models. In the light of new experimental results, we propose to extent this view and use time-dependent models to capture viscoelastic behavior. To this end, we quantified this behavior using nanoindentation creep experiments and modelled it using a rheological network model with several parallel Maxwell branches and an additional elasto-plastic branch. We demonstrate how the parameters of such a model can be found using inverse analysis. With the calibrated material model, a good agreement of the time dependent behavior between simulation and experimental results is achieved. Thus, a method is provided to model time dependent behavior using complex non-classical experiments like nanoindentation.

Molecular dynamics (MD) simulations of creep generally face the problem that the creep most often evolves on time scales hard to capture with MD due to their typically short time step size. Consequently, MD studies of creep often use unrealistically high temperatures and stresses and simplified atomistic models to make creep-like processes happen on computationally accessible time scales. Apparently, this compromises the physical reliability of such studies. To alleviate this problem, we designed an MD model of titanium aluminide (TiAl) with a microstructure matching at least many of the key parameters of experimentally observed microstructures. We applied this MD model with stresses much lower than the ones used in most previous creep studies (well below yield stress) and in the temperature range 0.55TM-0.7TM, with melting temperature TM. Compared to typical previous MD studies, this much more realistic setup produces creep rates more than three orders of magnitude smaller and thus much closer to reality. We identified the driving mechanisms of primary creep on the nanosecond scale that agree very well with recent experimental observations, thus contributing towards the overarching goal of bridging the gap between atomistic creep simulations and continuum-scale creep simulations for engineering applications.

Supercrystalline nanocomposites are a new class of hybrid and nanostructured materials that can reach exceptional mechanical strength and can be fabricated at low temperatures. Hierarchically arranged, they bridge the gap from the nano- to the macro-scale. Even though their mechanical properties are starting to be characterized, their constitutive behavior is still largely unexplored. Here, the mechanical behavior of supercrystalline nanocomposites of iron oxide nanoparticles, surface-functionalized with oleic acid and oleyl phosphate ligands, is investigated in both bending and compression, with loading–unloading tests. A new bar geometry is implemented to better detect deformation prior to unstable crack propagation, and notched bending bars are tested to evaluate fracture toughness. Micro-mechanical tests result in the values of strength and elastic modulus that are extremely high for supercrystals, reaching record-high numbers in the oleic acid-based nanocomposites, which also show a significant tension–compression asymmetry. The constitutive behavior of both materials is predominantly linear elastic, with some more marked nonlinearities arising in the oleyl phosphate-based nanocomposites. The fracture toughness of both types of nanocomposites, ∼0.3 MPa√m, suggests that extrinsic toughening, associated with both material composition and nanostructure, plays an important role. Fractographic observations reveal analogies with shear and cleavage in atomic crystals. The influence of material composition, nanostructure, and processing method on the mechanical behavior of the nanocomposites is analyzed.

With the ever-expanding functional applications of supercrystalline nanocomposites (a relatively new category of materials consisting of organically functionalized nanoparticles arranged into periodic structures), it becomes necessary to ensure their structural stability and understand their deformation and failure mechanisms. Inducing the cross-linking of the functionalizing organic ligands, for instance, leads to a remarkable enhancement of the nanocomposites' mechanical properties. It is however still unknown how the cross-linked organic phase redistributes applied loads, how the supercrystalline lattice accommodates the imposed deformations, and thus in general what phenomena govern the overall material's mechanical response. This work elucidates these aspects for cross-linked supercrystalline nanocomposites through an in situ small- and wide-angle X-ray scattering study combined with uniaxial pressing. Because of this loading condition, it emerges that the cross-linked ligands effectively carry and distribute loads homogeneously throughout the nanocomposites, while the superlattice deforms via rotation, slip, and local defects generation.

Supercrystalline nanocomposites are nanoarchitected materials with a growing range of applications but unexplored in their structural behavior. They typically consist of organically functionalized inorganic nanoparticles arranged into periodic structures analogous to crystalline lattices, including superlattice imperfections induced by processing or mechanical loading. Although featuring a variety of promising functional properties, their lack of mechanical robustness and unknown deformation mechanisms hamper their implementation into devices. We show that supercrystalline materials react to indentation with the same deformation patterns encountered in single crystals. Supercrystals accommodate plastic deformation in the form of pile-ups, dislocations, and slip bands. These phenomena occur, at least partially, also after cross-linking of the organic ligands, which leads to a multifold strengthening of the nanocomposites. The classic shear theories of crystalline materials are found to describe well the behavior of supercrystalline nanocomposites, which result to feature an elastoplastic behavior, accompanied by compaction.

A crystal plasticity model of the creep behavior of alloys with lamellar microstructures is presented. The model is based on the additive decomposition of the plastic strain into a part that describes the instantaneous (i.e., high strain rate) plastic response due to loading above the yield point, and a part that captures the viscoplastic deformation at elevated temperatures. In order to reproduce the transition from the primary to the secondary creep stage in a physically meaningful way, the competition between work hardening and recovery is modeled in terms of the evolving dislocation density. The evolution model for the dislocation density is designed to account for the significantly different free path lengths of slip systems in lamellar microstructures depending on their orientation with respect to the lamella interface. The established model is applied to reproduce and critically discuss experimental findings on the creep behavior of polysynthetically twinned TiAl crystals. Although the presented crystal plasticity model is designed with the creep behavior of fully lamellar TiAl in mind, it is by no means limited to these specific alloys. The constitutive model and many of the discussed assumptions also apply to the creep behavior of other crystalline materials with lamellar microstructures.

γ-titanium aluminide (TiAl) alloys with fully lamellar microstructure possess excellent properties for high-temperature applications. Such fully lamellar microstructure has interfaces at different length scales. The separation behavior of the lamellae at these interfaces is crucial for the mechanical properties of the whole material. Unfortunately, quantifying it by experiments is difficult. Therefore, we use molecular dynamics (MD) simulations to this end. Specifically, we study the high-temperature separation behavior under tensile loading of the four different kinds of lamellar interfaces appearing in TiAl, namely, the γ / α 2 , γ / γ PT , γ / γ TT , and γ / γ RB interfaces. In our simulations, we use two different atomistic interface models, a defect-free (Type-1) model and a model with preexisting voids (Type-2). Clearly, the latter is more physical but studying the former also helps to understand the role of defects. Our simulation results show that among the four interfaces studied, the γ / α 2 interface possesses the highest yield strength, followed by the γ / γ PT , γ / γ TT , and γ / γ RB interfaces. For Type-1 models, our simulations reveal failure at the interface for all γ/γ interfaces but not for the γ / α 2 interface. By contrast, for Type-2 models, we observe for all the four interfaces failure at the interface. Our atomistic simulations provide important data to define the parameters of traction–separation laws and cohesive zone models, which can be used in the framework of continuum mechanical modeling of TiAl. Temperature-dependent model parameters were identified, and the complete traction–separation behavior was established, in which interface elasticity, interface plasticity, and interface damage could be distinguished. By carefully eliminating the contribution of bulk deformation from the interface behavior, we were able to quantify the contribution of interface plasticity and interface damage, which can also be related to the dislocation evolution and void nucleation in the atomistic simulations.

The residual strength of a structure made of dissimilar Aluminium panels joined by a stationary shoulder friction stir welding (SSFSW) process is predicted by numerical simulation using finite elements including cohesive elements for crack propagation. The yield strength and strain hardening parameters within the stirred zone and adjacent thermo-mechanically affected and heat affected zones are derived from a tensile specimen cut out from the panel perpendicular to the weld seam. The identification is conducted by a hybrid numerical/experimental procedure with an inverse search by help of digital image correlation in order to obtain the strain field at the welded surface and to compare them to the numerical calculation. The crack propagation parameters are retrieved from specimens with crack in the stir zone and heat affected zone on either side. After this identification procedure, the fracture behaviour of a coupon specimen with a crack crossing the weld is predicted.

A key challenge in the development of inorganic-organic nanocomposites is the mechanical behavior identification of the organic phase. For supercrystalline materials, in which the organic phase ranges down to sub-nm areas, the identification of the organic materials' mechanical properties is however experimentally inaccessible. The supercrystalline nanocomposites investigated here are 3D superlattices of self-assembled iron oxide nanoparticles, surface-functionalized with crosslinked oleic acid ligands. They exhibit the highest reported values of Young's modulus, nanohardness and strength for inorganic-organic nanocomposites. A multiscale numerical modeling approach is developed to identify these properties using supercrystalline representative volume elements, in which the nanoparticles are arranged in a face-centered cubic superlattice and the organic phase is modeled as a thin layer interfacing each particle. A Drucker-Prager-type elastoplastic constitutive law with perfectly plastic yielding is identified as being able to describe the supercrystals' response in nanoindentation accurately. As the nanoparticles behave in a purely elastic manner with very high stiffness, the underlying constitutive law of the organic phase is also identified to be Drucker-Prager-type elastoplastic, with a Young's modulus of 13 GPa and a uniaxial tensile yield stress of 900 MPa, remarkably high values for an organic material, and matching well with experimental and DFT-based estimations. Furthermore, a sensitivity study indicates that small configurational changes within the supercrystalline lattice do not significantly alter the overall stiffness behavior. Multiscale numerical modeling is thus proven to be able to identify the nanomechanical properties of supercrystals, and can ultimately be used to tailor these materials' mechanical behavior starting from superlattice considerations.

Cohesive zone models are efficient tools for describing the material degradation behaviour in engineering structures, mainly used for crack propagation of ductile and brittle materials under monotonous loading. A new formulation for the traction-separation behaviour of a cohesive zone has been set-up and implemented for crack propagation under various thermo-mechanical loading conditions, not only for increasing load, but also for cyclic (fatigue) or constant (creep) load. For the model presented, the separation vector is additively split into an elastic, a plastic and a creep part: . The traction vector, t, is then calculated based on the elastic separation by a simple elastic law, reduced by a damage variable, d: Plasticity is implemented by a yield function and potential; the plastic separation rate is thus defined by the derivative of the potential with respect to the traction: . Notice that the term plasticity used here must not be confused with metal plasticity, which represents the dislocation motion within a material. In contrast, the term is just a mathematical construct to incorporate an inelastic and irreversible separation, which does not affect the elastic behaviour, if unloading occurs. Creep is defined as by a relation between the traction and the creep separation rate, incorporating also the temperature . In order to simulate the degradation of the interface, several damage mechanisms are considered, each with a separate evolution law; one for monotonous loading, one for fatigue loading and one for creep. The total damage is simply the sum of the three damage variables . The evolution law for the monotonous damage variable is based on the plastic deformation and uses a damage potential, the evolution for cyclic damage is based on the energy release rate, , and the creep damage depends on the effective creep separation. Results will be shown for monotonic as well as cyclic loading conditions in order to demonstrate the capabilities of the model for the prediction of crack propagation in precracked specimens.

The focus of this work is on matrix-inclusion nanocomposites and their mechanical behavior, particularly taking into account inelasticity and damage. We propose a nonlocal damage model based on a micropolar continuum theory which captures the heterogeneous interphases in the nanostructure. The model is valid for a large range of matrix-inclusion nanocomposites. The effects of the interaction between nanoparticles, the thickness of the interphase and the size of nanoparticles on the overall mechanical properties of the nanocomposite are analyzed to optimize the microstructure of the nanocomposites. 3D micromechanical simulations are conducted for the particular example of a tailored, ultrastrong nanocomposite. It has extraordinary mechanical properties, and to date, is the strongest synthetic inorganic-organic nanocomposite. The simulation results are compared to experimental data from microcantilever beams for different process temperatures.

Nanocomposites exhibit excellent fracture toughness due to adding nanoparticles into the polymer matrix. The present work aims at developing a multiscale modelling approach to investigate fracture behaviour of nanocomposites with core‐shell nanostructures. In this context, a nonlocal damage model based on the micropolar theory is proposed to describe the damage behaviour of graded shell layers of nanoparticles. The simulation results show the capability of the present model to study the effect of shell morphology and shell material on the fracture toughness of nanocomposites within this multiscale simulation framework. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dental enamel possesses extraordinary mechanical properties due to a complex hierarchical and graded microstructure. In this study, multiscale experimental and computational approaches are employed and combined to study nature’s design principle of the hierarchical structure of bovine enamel for developing bio-inspired advanced ceramics with hierarchical microstructure. Micro-cantilever beam tests are carried out to characterize the mechanical properties from nano- to meso-scale experimentally. In order to understand the relationship between the hierarchical structure and the flaw-tolerance behavior of enamel, a 3D representative volume element (RVE) is used in a numerical analysis to study the deformation and damage process at two hierarchical levels. A continuum damage mechanics model coupled to hyperelasticity is developed for modeling the initiation and evolution of damage in the mineral fibers as well as protein matrix. Moreover, debonding of the interface between mineral fiber and protein is captured by a cohesive zone model. The effect of an initial flaw on the overall mechanical properties is analyzed at different hierarchical levels to understand the superior damage tolerance of dental enamel. Based on the experimental and computational investigation, the role of hierarchical levels on the multiscale design of structure in dental enamel is revealed for optimizing bio-inspired composites.

An anisotropic constitutive model is proposed in the framework of finite deformation to capture several damage mechanisms occurring in the microstructure of dental enamel, a hierarchical bio-composite. It provides the basis for a homogenization approach for an efficient multiscale (in this case: multiple hierarchy levels) investigation of the deformation and damage behavior. The influence of tension–compression asymmetry and fiber–matrix interaction on the nonlinear deformation behavior of dental enamel is studied by 3D micromechanical simulations under different loading conditions and fiber lengths. The complex deformation behavior and the characteristics and interaction of three damage mechanisms in the damage process of enamel are well captured. The proposed constitutive model incorporating anisotropic damage is applied to the first hierarchical level of dental enamel and validated by experimental results. The effect of the fiber orientation on the damage behavior and compressive strength is studied by comparing micro-pillar experiments of dental enamel at the first hierarchical level in multiple directions of fiber orientation. A very good agreement between computational and experimental results is found for the damage evolution process of dental enamel.

Dental enamel exhibits high fracture toughness and stiffness due to a complex hierarchical and graded microstructure, optimally organized from nano- to macro-scale. In this study, a 3D representative volume element (RVE) model is adopted to study the deformation and damage behavior of the fibrous microstructure. A continuum damage mechanics model coupled to hyperelasticity is developed for modeling the initiation and evolution of damage in the mineral fibers as well as protein matrix. Moreover, debonding of the interface between mineral fiber and protein is captured by employing a cohesive zone model. The dependence of the failure mechanism on the aspect ratio of the mineral fibers is investigated. In addition, the effect of the interface strength on the damage behavior is studied with respect to geometric features of enamel. Further, the effect of an initial flaw on the overall mechanical properties is analyzed to understand the superior damage tolerance of dental enamel. The simulation results are validated by comparison to experimental data from micro-cantilever beam testing at two hierarchical levels. The transition of the failure mechanism at different hierarchical levels is also well reproduced in the simulations.

Dental enamel possesses extraordinary mechanical properties due to a complex hierarchical and graded microstructure. Understanding the relationship between the hierarchical structure and the flaw-tolerance behavior can be helpful for developing a new high-performance fiber reinforced composite with the desired mechanical properties. In this study, a representative volume element (RVE) is adopted to study the deformation and damage evolution process of the microstructure. A continuum damage mechanic model coupled to hyperelasticity is developed for modeling the initiation and evolution of damage in mineral fibers as well as protein matrix. In addition, debonding of the interface between fiber and matrix is captured by employing the cohesive zone model. The effect of the aspect ratio on the failure mechanisms of the composite is studied with the proposed damage model.

Dental enamel is a highly anisotropic and heterogeneous material, which exhibits an optimal reliability with respect to the various loads occurring over years. In this work, enamel’s microstructure of parallel aligned rods of mineral fibers is modeled and mechanical properties are evaluated in terms of strength and toughness with the help of a multiscale modeling method. The established model is validated by comparing it with the stress–strain curves identified by microcantilever beam experiments extracted from these rods. Moreover, in order to gain further insight in the damage-tolerant behavior of enamel, the size of crystallites below which the structure becomes insensitive to flaws is studied by a microstructural finite element model. The assumption regarding the fiber strength is verified by a numerical study leading to accordance of fiber size and flaw tolerance size, and the debonding strength is estimated by optimizing the failure behavior of the microstructure on the hierarchical level above the individual fibers. Based on these well-grounded properties, the material behavior is predicted well by homogenization of a representative unit cell including damage, taking imperfections (like microcracks in the present case) into account.