Fatigue crack nucleation: Mechanistic modelling across the length scales

This paper presents an assessment of recent literature on the mechanistic understanding of fatigue crack nucleation and the associated modelling techniques employed. In particular, the important roles of (a) slip localisation and persistent slip band formation, (b) grain boundaries, slip transfer and interfaces, (c) microtexture and twins, and (d) nucleation criteria and microcracks are addressed in the context of the three key modelling techniques of crystal plasticity (CP), discrete dislocation (DD) plasticity and molecular dynamics (MD) where appropriate. In addition, the need for computational fatigue crack nucleation methodologies which incorporate mechanistic understanding is addressed.Key challenges identified include (i) the overall need for multiscale models for fatigue crack nucleation which are continuum-based but mechanistically informed; (ii) full (3D) crystal slip models to capture slip localisation at a DD level; (iii) MD modelling methodologies for slip transfer to inform DD models; and (iv) rigorously validated dislocation structure models at the DD and CP levels.     

Interaction between different internal length scales for strain localisation analysis of single phase materials

 It is well known that both rate dependent and gradient-dependent constitutive models introduce internal length scales in dynamic initial value problems. As a result, numerical solutions of such initial value problems involving strain-softening no longer exhibit excessive mesh dependence. In this paper, the length scales included in a solid model which exhibits both above mentioned constitutive behaviours are discussed. The internal length scales derived from damping effects, which are typical for the viscoplastic models, and the wave length, obtained from the critical wave number for which the wave speed is not imaginary, are used together to give a prediction of the internal length scale of the combined model. The approach proposed here for prediction of the internal length scale is more general than commonly used procedures and permits to explain phenomena observed in viscoplastic and gradient dependent models. A one dimensional example is given to illustrate the theoretical findings. Received: 10 July 2002 / Accepted: 1 November 2002 This work was supported by the EC International Scientific Coorperation Programme. The support of the State Educational Committee, the Scientific Fund for National Outstanding Youth and National Natural Science Foundation (50178016, 19872016) of China is also acknowledged. The work was partially financed by Research Project MIUR ex40% 2000, MM08161945_003.     

Quantitative mapping of surface elastic moduli in silica-reinforced rubbers and rubber blends across the length scales by AFM

The surface elastic moduli of silica-reinforced rubbers and rubber blends were investigated by atomic force microscopy (AFM)-based HarmoniX material mapping. Styrene–butadiene rubbers (SBR) and ethylene–propylene–diene rubbers (EPDM) and SBR/EPDM rubber blends with varying concentrations of silica nanoparticles (0, 5, 10, 20, 50 parts per hundred rubber, phr) were prepared to investigate the effect of different composition on the resulting morphology, filler distribution and elastic moduli of a specific rubber or rubber blend sample. For SBR, the elastic modulus values varied from 0.5 MPa for unfilled SBR to 5 MPa for 50 phr reinforced SBR with the increase in the concentration of filler. For EPDM, the corresponding values increased from 1.4 MPa for unfilled EPDM to 4.5 MPa for 50 phr reinforced EPDM. Local stiff and soft domains in silica-reinforced SBR and EPDM rubbers and rubber blends were identified by HarmoniX AFM imaging. While the stiff silica particles show modulus values as high as 2 GPa, the rubber matrix reveals modulus values in the range of ca. 30 MPa for the rubber blends to ca. 300 MPa for the unfilled rubbers. The lower value of elastic modulus of the EPDM phase in the blend, compared to the blank EPDM compound can be attributed to the presence of Sunpar oil in the compound which has a very good affinity with EPDM and decreases the rubber modulus. The elastic moduli maps revealed an increase of the areal fraction of silica particles showing an intrinsic surface modulus value with rising silica content in the compound preparation mixture. HarmoniX AFM measurements revealed the formation of larger silica aggregates in EPDM in contrast to SBR where isolated silica particles were observed. For silica-reinforced rubber blends a phase separation into a soft (ca. 40 MPa) and a significantly harder phase could be observed (ca. 500 MPa–1.5 GPa) indicating the incorporation of silica particles in the SBR phase. Using HarmoniX AFM imaging significantly higher surface elastic moduli were observed compared to those obtained by bulk tensile testing. Possible reasons for the observed differences between bulk modulus values and those measured by AFM are discussed in detail, including the aspect of different averaging procedures like inherent to surface probing by AFM versus bulk tensile testing, different filler distributions in SBR and EPDM and the AFM modulus calibration procedures.     

Microstructural characterization of transformable Fe–Mn alloys at different length scales

The as-annealed and deformed Microstructure of transformable Fe–Mn alloys were, comprehensively, characterized over a wide range of length scales. Differential interference contrast optical metallography, combined with a tinting etching method, was employed to examine the grain morphology. A new specimen preparation method, involving electro-polishing and electro-etching, was developed for scanning electron microscopy and electron back-scattered diffraction analysis. This method leads to a very good imaging contrast and thus bridges the length scale gap between optical metallography and transmission electron microscopy. Moreover, it enables simultaneous scanning electron microscopy and electron backscatter diffraction analysis which allows correlations among morphology, crystal orientation and phase analysis in the length scale of microns. Transmission electron microscopy investigations were also made to evaluate the thermal and mechanical transformation products as well as defect structures.     

Methodology of materials discovery in complex metal hydrides using experimental and computational tools

We present a review of the experimental and theoretical methods used in the discovery of new metal–hydrogen materials systems for hydrogen storage applications. Rather than a comprehensive review of all new materials and methods used in the metal hydride community, we focus on a specific subset of successful methods utilizing theoretical crystal structure prediction methods, computational approaches for screening large numbers of compound classes, and medium-throughput experimental methods for the preparation of such materials. Monte Carlo techniques paired with a simplified empirical Hamiltonian provide crystal structure candidates that are refined using density functional theory. First-principle methods using high-quality structural candidates are further screened for an estimate of reaction energetics, decomposition enthalpies, and determination of reaction pathways. Experimental synthesis utilizes a compacted-pellet sintering technique under high-pressure hydrogen at elevated temperatures. Crystal structure determination follows from a combination of Rietveld refinements of diffraction patterns and first-principles computation of total energies and dynamical stability of competing structures. The methods presented within are general and applicable to a wide class of materials for energy storage.     

Quantification of structural and material failure mechanisms across different length scales: from instability to brittle-ductile transitions

Structures may fail due to a myriad of different causes. Often, distinction is made between structural and material failure, that means a structure can fail, while the material is still intact (this is the case in so-called stability loss), or the material fails, which, as consequence, may lead to structural failure. The material behavior may turn out difficult to be mathematically guessed at the macro-level. On the other hand, a lot may be known about the chemistry or the microstructure of the material of interest. Herein, we aim at categorizing different scenarios which in the end provoke structural failure, discussing various cases investigated during the last five years, at the Institute for Mechanics of Materials and Structures of Vienna University of Technology: A well-chosen eigenvalue problem shows considerable potential for categorizing stability loss. We then turn to complex composite materials with a hierarchical organization, where a single constituent dominates the overall quasi-brittle failure of the material, such as lignin in wood and wood products, or the cement–water reaction products (shortly called hydrates) in cement-based materials. The picture changes if the first inelastically behaving constituent is related to ductile load carrying, then the loads within the microstructure are re-distributed before the overall material fails: this turns out to be the case in bone. Finally, due to highly confined multiaxial stress states, the elastic portion of the overall energy invested into the material may become negligible—and then yield design analysis employed on material volumes gives an idea of the highly ductile behavior of complex confined materials, such as asphalt. What integrates all the reported cases is the high capacity of mature mathematical and mechanical formulations to reveal the intricate, yet decipherable nature of the (continuum) mechanics of materials and structures.     

Smart computational fracture of materials and structures

The use of the finite element method for complex engineering problems is now common. To ease the burden on the engineer the development of smart or adaptive computational methods is now required to model complex problems. In this paper we investigate the development of an adaptive finite element method for fracture-related problems. The adaptive method involves various stages which include the finite element analysis, error estimation/indication, mesh refinement and fracture/failure analysis in a loop. Some simple error estimators, based on stress projection, are used to investigate the adaptive finite element process. Element refinement is based on three schemes; the first and second are a simple and hierarchical refinement scheme with transitioning which avoids the need for constraint equations between element boundaries. Another scheme based on constraint equations between elements is also examined. The energy norm is used to estimate the element error. The software has the ability to introduce a discrete fracture in the structure according to standard fracture analysis practice. Crack tip parameters are calculated using a least-squares fit of the displacements into the asymptotic crack tip displacement field. Some simple examples are used to investigate the adaptive process, its behavior and some of the practical problems encountered. The convergence and equilibrium of the adaptive process, in terms of global error in the energy norm, are investigated. In the example the same problem is analyzed using both a fine computational grid and a coarse one. The coarse mesh is then adapted using the three different procedures available. The estimated error in the solution and the stress intensity are shown against the number of elements and number of iterations. Some further areas of research in adaptive finite element analysis are discussed.     

Finite element modeling and experimental characterization of crosstalk in 1-D CMUT arrays

Crosstalk is the coupling of energy between the elements of an ultrasonic transducer array. This coupling degrades the performance of transducers in applications such as medical imaging and therapeutics. In this paper, we present an experimental demonstration of guided interface waves in capacitive micromachined ultrasonic transducers (CMUTs). We compare the experimental results to finite element calculations using a commercial package (LS-DYNA) for a 1-D CMUT array operating in the conventional and collapsed modes. An element in the middle of the array was excited with a unipolar voltage pulse, and the displacements were measured using a laser interferometer along the center line of the array elements immersed in soybean oil. We repeated the measurements for an identical CMUT array covered with a 4.5-microm polydimethylsiloxane (PDMS) layer. The main crosstalk mechanism is the dispersive guided modes propagating in the fluid-solid interface. Although the transmitter element had a center frequency of 5.8 MHz with a 130% fractional bandwidth in the conventional operation, the dispersive guided mode was observed with the maximum amplitude at a frequency of 2.1 MHz, and had a cut-off frequency of 4 MHz. In the collapsed operation, the dispersive guided mode was observed with the maximum amplitude at a frequency of 4.0 MHz, and had a cut-off frequency of 10 MHz. Crosstalk level was lower in the collapsed operation (-39 dB) than in the conventional operation (-24.4 dB). The coverage of the PDMS did not significantly affect the crosstalk level, but reduced the phase velocity for both operation modes. Lamb wave modes, A0 and S0, were also observed with crosstalk levels of -40 dB and -65 dB, respectively. We observed excellent agreement between the finite element and the experimental results.     

Heterogeneities at multiple length scales in 2D layered materials: From localized defects and dopants to mesoscopic heterostructures

Nano Research - Two-dimensional (2D) materials hold great promise for applications in optoelectronics, quantum information science, and energy conversion due to their remarkable properties imbued...     

X-ray tomography applied to the characterization of cellular materials. Related finite element modeling problems

The analyses of several materials exhibiting a cellular structure have been carried out using X-ray tomography. This new technique allows the three dimensional and non destructive visualisation of the studied materials at the scale of their cellular microstructure. Qualitative examples are given for metal foams, bread and cellular concrete. The similarity between these materials is striking. It has been measured by quantitative 3D image processing. The different Finite Element Methods available today to produce meshes from these images are presented and discussed in the final part of this paper.     

Review and experimental evaluation of models for drivability simulation with focus on tire modeling

Forschung im Ingenieurwesen - Recent research showed a significant role of the interaction between traction and torsional vibrations on control design in passenger cars. However, there is...     

The computational modeling of nonequilibrium thermodynamics of the martensitic transformations

A mathematical model describing the thermodynamic properties of martensitic crystals is introduced. The thermodynamic model uses the elastic energy derived from the Ericksen-James theory and it incorporates a heat-flux which couples the temperature gradient with the underlying lattice structure. The presented numerical computations simulate thermal effects during the development of the martensitic lamellae from an unstable deformation of the martensitic crystal. The micro-thermal structures are observed to accompany the development of the martensite.     

Dynamic response and damage evolution in composite materials subjected to underwater explosive loading: An experimental and computational study

The effect of underwater shock loading on an E-Glass/Epoxy composite material has been studied. The work consists of experimental testing, utilizing a water filled conical shock tube and computational simulations, utilizing the commercially available LS-DYNA finite element code. Two test series have been performed and simulated: (1) a reduced energy series which allowed for the use of strain gages and (2) a series with increased energy which imparted material damage. The strain gage data and the computational results show a high level of correlation using the Russell error measure. The finite element models are also shown to be able to simulate the onset of material damage by both in-plane and delamination mechanisms.     

Tensile modulus of carbon nanotube/polypropylene composites – A computational study based on experimental characterization

Micromechanical and computational models significantly over-predict the tensile modulus of composites, as they ignore many experimentally observed factors. Computational models that capture the effect of polymer-filler contact, the presence of carbon nanotube (CNT) agglomerates and the alignment of CNTs with respect to the applied load on the tensile modulus of CNT-reinforced polypropylene (PP) are proposed and discussed in detail in this study. The CNT/PP composites are made by melt mixing and injection molding. The CNT/PP contact area is characterized in terms of width and modulus using Atomic Force Microscope (AFM). The presence, including the size and distribution of CNT agglomerates, is characterized using Scanning Electron Microscope (SEM). The tensile modulus of CNT/PP composites, measured as a function of CNT content according to ASTM D638, is compared to predictions made using numerical methods based on Finite Element Analysis (FEA) within the composite’s elastic regime. The model over-predicts the modulus of the CNT/PP composites by 85% for 5 wt.% CNT/PP composites assuming perfect filler–polymer interfacial contact. When imperfect CNT/PP contact, CNT agglomerates and alignment are accounted for in the model the effective composite modulus predicted is in good agreement with the experimental data. The computational design tools proposed in this study by systematically incorporating experimentally observed characteristics, in combination with the manufacturing method used to make the CNT/PP composites, can lead to composites with engineered properties made by a scalable and cost effective method.