E. Soppa

Experimental and numerical characterisation of in-plane deformation in two-phase materials

The aim of the present work consists in the comparison of in-plane strain fields with out-of-plane displacements in micro-areas of an Ag/Ni-composite after a macroscopic compressive deformation of 8.6%. The in-plane deformations in an Ag/Ni-composite have been analysed experimentally with a high resolution object grating technique and numerically using the finite element method. The out-of-plane displacements were measured with an atomic force microscope (AFM). The development of local strain fields in micro-areas at the surface of an Ag/Ni-composite was simulated numerically using the FE-method in plane strain condition. A real cut-out of the microstructure served as input for the calculation. The out-of-plane displacements determined by AFM measurements were used further to correct the in-plane values of strains evaluated by the object grating technique. The roughness on the surface of the sample was characterised by fractal dimensions and compared with the in-plane strains in the same micro-region.

Influence of the microstructure on the deformation behaviour of metal-matrix composites

Abstract In this contribution, investigations of the influence of the microstructure on the macro-, meso- and micro-effects in metal–matrix composites are presented by direct combination of experiment and simulation. The aim of the presented work consists in an improved understanding of the mechanical behaviour of heterogeneous materials by combining information of different length scales.

Simulation of elastic–plastic deformation and fracture of materials at micro-, meso- and macrolevels

Abstract Physical Mesomechanics of materials is a new branch of mechanics that focuses attention on a mesovolume of loaded material. It is a macro particle in classical continuum mechanics and its behavior under load is equivalent to the bulk. The structural elements for a particular application requires specific models while the computational techniques have to be developed. These research groups have been studying heterogeneous materials behavior at the mesolevel under different types of loading. Hierarchical models are developed to study deformation and fracture of solids at the micro- meso- and macrolevels. Taken into account are the influence of micro- and mesostructure of loaded material in relation to its macro behavior. This work focuses on unifying the method of approach to be supported by tests and calculations. In particular, deformation and fracture mechanisms at the micro-, meso- and macrolevels are examined for metals and composites.

Computational mechanics of heterogeneous materials––influence of residual stresses ☆

Heterogeneous materials such as Metal Matrix Composites (MMCs) of the type Al/SiC contain significant residual stresses due to different thermal expansion coefficients from the metal and ceramic constituents. They are believed to influence the mechanical properties of these materials to some extent — including some changes in their failure behavior. In this contribution, a physically based micromechanical approach is applied in order to clarify the influence of residual stresses on local as well as global properties of MMCs. A representative microstructural cut-out of an Al/10% SiC-composite is meshed with finite elements in order to take phase boundaries into account. This mesovolume possesses all characteristic features of the material, such as volume fraction, distribution characteristics as well as shape of the particles. The deformation behavior of this microstructure is analyzed under large compressive external loading up to strains of about 10%. In addition, the failure behavior is modeled using Rice&Tracey’s failure criterion which was recently shown to model microstructural failure to a good approximation. It is found that although residual stresses do have some impact on failure initiation in the microstructure, strains due to external loading are much more of importance in this respect. In order to illuminate the influence of particle shape and arrangement, artificial two-dimensional microstructures are analyzed as well. It is found that irregular particle shapes are much more prone to fracture in the matrix as compared to regular shapes and that particle alignments are not beneficial with respect to failure aspects. The distribution and maximum values of the damage parameter are shown. It is found that in all cases analyzed, damage follows the pattern of plastic deformation and is much less influenced by hydrostatic stresses than expected. Nevertheless, damage nucleates between clusters of particles where shear deformation as well as hydrostatic tensile stresses are concentrated in the matrix.

SIMULATION OF INTERPENETRATING MICROSTRUCTURES BY SELF CONSISTENT MATRICITY MODELS

A self consistent matricity model has been developed to simulate the mechanical behaviour of an isotropic two-phase composite with a coarse interpenetrating microstructure. The model is an extension of a recently developed self consistent model for matrices with randomly distributed inclusions (1). In addition to the volume fraction of the phases, the matricity model allows a further parameter of the microstructure, the matricity of each phase, to be included into the simulation of the mechanical behaviour of composites with interpenetrating microstructures. The model is applied to an Fe/Agcomposite and its validity and superiority upon previous models is demonstrated.

Investigation of the strengthening of particulate reinforced composites using different analytical and finite element models

Abstract The limit flow stress of composite materials reinforced with randomly distributed spherical particulate inclusions is investigated using both numerical and finite element (FE) models. Comparison is made between the different models and with experiments. The recently published modified Oldyrod model, an analytical numerical method which predicts the stress–strain response of materials undergoing both elastic and plastic deformation using elastic methods is investigated. It is compared with the classical axisymmetric cell model as well as with a 3D-embedded finite element model. The models are first compared with each other for the ideal case of a rigid inclusion in an elastic–plastic non-hardening matrix. It is found that all models predict much the same strengthening for 50% inclusion but at higher volume fractions differ significantly. The axisymmetric model predicts a very strong composite response due to particles nearly impinging on each other in contrast to the other models considered where more realistic boundary conditions are imposed by surrounding the cell with actual material. Comparison is then made between the different 3D-models and experiment for a 58 vol% martensite–austenite composite. This represents the case of a hard inclusion in a relatively soft matrix. In the elastic regime and during the early stages of plastic deformation all models are seen to give a good estimate of the composite response. However, at higher strains, the response predicted by the 3D-embedded cell model fits closest to the experimental results. It is seen that the much simpler and so computationally much quicker modified Oldroyd model also gives valid results for a wide band of inclusion volume fractions. The exact location of this band is seen to vary with the hardening exponent of the matrix material. A comparison between the modified Oldroyd model, 3D-embedded cell model, the 3D-axisymmetric cell model and the previously published Duva model for rigid inclusions in a variety of elastic–plastic hardening matrices shows significant differences between the models. For materials with high strain hardening exponents the benefit of using the 3D-embedded cell model is increased. Finally, comparison is further made with experiments where both phases are capable of elastic–plastic deformation. Again at higher strains the 3D-embedded cell model is seen to give the best indication of the composite response. However, it is seen that the modified Oldroyd model can also be used to give useful results for the investigated materials.

Localization of strain in metal matrix composites studied by a scanning electron microscope-based grating method.

The deformation characteristics of the metal matrix composites Ag/Ni and Al/Al2O3 are studied at microstructural level by a scanning electron microscopebased grating method and finite element (FE) simulation. The measured strain was found to localize in narrow bands in the ductile matrix of both composites. In the case of the Al/Al2O3 composite, the bands are preferentially initiated in Al regions adjacent to the interface of large Al2O3 particles, leading to local strain maxima. The band positions found in the Ag/Ni composite are also affected by the less deformable Ni phase, but strain localization first occurs by sliding of single Ag grains sometimes located away from the Ni phase. Using a FE model of real phase geometry and measured border displacements as boundary conditions, the simulation agrees reasonably with the experiment. The differences in the case of the Al/Al2O3 composite are due to particle cracks and voids at the particle/matrix interface. This effect was found in the experiment but not considered in modelling. For the Ag/Ni composite the band positions agree fairly well. However, the level and gradient of strain is clearly different as the crystallographic orientation of the Ag grains was not accounted for in modelling.

Influence of geometry factors on the mechanical behavior of particle- and fiber-reinforced composites

By utilizing the finite element method (FEM) combined with cell models, the mechanical behavior of metal matrix composites (MMCs) with stripes consisting of reinforcing particles was investigated numerically. The results show that the mechanical behavior of MMC with aligned particles can be changed by varying the distance between the stripes even if the volume fraction of reinforcing particles is kept constant. It was also found that the shape of reinforcing particles had little effect on the mechanical behavior of material. In the same way, the transverse mechanical behavior of fiber-reinforced material was studied and similar trends with respect to the mechanical behavior were found. It is also found that even if particles are strongly aligned, the particle-reinforced materials behave strongly different compared to topologically similar fiber-reinforced materials.

The influence of second phase and/or grain orientations on deformation patterns in a Ag polycrystal and in Ag/Ni composites

As a consequence of the elastic and plastic anisotropy of the grains in polycrystalline materials, inhomogeneous stress and strain fields develop in the grain structure. In addition, in two-phase materials, different mechanical properties of the phases lead to further localisation of the plastic deformation. Both effects which influence the development and formation of shear bands as well as the damage process during loading are investigated on polycrystalline Ag and two-phase Ag/Ni by means of the finite element method (FEM).

Thermal and Mechanical Fatigue Loading: Mechanisms of Crack Initiation and Crack Growth

The present contribution is focused on the experimental investigations and numerical simulations of the deformation behaviour and crack development in the austenitic stainless steel X6CrNiNb18-10 (AISI–347) under thermal and mechanical cyclic loading in HCF and LCF regimes. The main objective of this research is the understanding of the basic mechanisms of fatigue damage and development of simulation methods, which can be applied further in safety evaluations of nuclear power plant components. In this context the modelling of crack initiation and crack growth inside the material structure induced by varying thermal or mechanical loads are of particular interest. The mechanisms of crack initiation depend among other things on the art of loading, microstructure, material properties and temperature. The Nb-stabilized austenitic stainless steel in the solution-annealed condition was chosen for the investigations. Experiments with two kinds of cyclic loading — pure thermal and pure mechanical — were carried out and simulated.The fatigue behaviour of the steel X6CrNiNb18-10 under thermal loading was studied within the framework of the joint research project [1]. Interrupted thermal cyclic tests in the temperature range of 150 °C to 300 °C combined with non-destructive residual stress measurements (XRD) and various microscopic investigations, e.g. in SEM, were used to study the effects of thermal cyclic loading on the material. This thermal cyclic loading leads to thermal induced stresses and strains. As a result intrusions and extrusions appear inside the grains (at the surface), at which micro-cracks arise and evolve to a dominant crack. Finally, these micro-cracks cause continuous and significant decrease of residual stresses.The fatigue behaviour of the steel X6CrNiNb18-10 under mechanical loading at room temperature was studied in the framework of the research project [2]. With a combination of interrupted LCF tests and EBSD measurements the deformation induced transformation of a fcc austenite into a bcc α′-martensite was observed in different stages of the specimen lifetime. The plastic zones develop at the crack tips, in which stress and strain amplitudes are much higher than the nominal loading, and enable martensitic transformation in the surrounding of the crack tip. The consequence of this is that cracks grow in the “martensitic tunnels”. The short and long crack growth behaviours of the steel X6CrNiNb18-10 under mechanical loading at room temperature and T = 288 °C were studied for different loading parameters. Moreover, the R-ratio was modified in order to study the effect of crack closure at the crack tip for long cracks.Several FE-models of specimens with different geometries and microstructures were created and cyclically loaded according to the experimental boundary conditions. A plastic constitutive law based on a Chaboche type model was implemented as a user subroutine in the FE software ABAQUS. The corresponding material parameters were identified using uniaxial LCF tests of X6CrNiNb18-10 with different strain amplitudes and at different temperatures. These calculations aimed in the estimation of stress and strain distributions in the critical areas in which the crack initiation was expected.Copyright