Basic features of plastic strains: From micro-mechanics to incrementally nonlinear models

Most rate-independent constitutive relations for granular materials are based on the existence of a regular flow rule. This assumption states that once the mechanical state of a material point belongs to the yield surface, then the direction of the plastic strains is independent of the loading direction. In this paper, the notion of a regular flow rule is shown to exist only for two-dimensional and axisymmetric loading conditions. By considering our incrementally nonlinear constitutive model, it is established that this notion disappears as soon as more general loading conditions are applied, as also predicted from discrete element simulations. Moreover, a sound micro-mechanical interpretation of the vanishing of a regular flow rule in three-dimensional loading conditions is given from a multi-scale perspective using the micro-directional model. This model highlights the great influence of the loading history on the shape of the plastic Gudehus response-envelope.     

Stiffness based technique to probe cyclic damage accumulation in micro-structurally graded bond coats via micro-beam bending tests

This paper highlights a novel technique to delineate the fatigue response of different regions within thin microstructurally graded platinum nickel aluminide bond coats. Notched clamped beam structures fabricated from distinct microstructural zones of these coatings are subjected to programmed cyclic bending using the nano-indentation system. A methodical approach is established herein to quantify the cyclic damage preceding crack pop-in by using the cyclic stiffness of the beam as an indicator to mark failure. Preliminary results from these tests show that there is a characteristic change in the stiffness of the beam before a crack pop-in event occurs and different regions within the coating show different stiffening characteristics. Factors affecting the measured stiffness such as offsets in the loading position and blunting of the notch tip have been estimated using the finite element method. A graded flow stress model has been proposed and implemented in FEM to quantify the local flow stress changes accompanying the measured rise in stiffness. Electron transparent foils lifted off from the notched region of the beam post-testing suggests that the cyclic stiffening of the beams occurs due to dislocation hardening in the plastically deformed region close to the notch tip. Toughening mechanisms active in the crack wake have thus been investigated and correlated to the measured cyclic stiffness.     

Interfacial and wetting properties of carbon fiber reinforced epoxy composites with different hardeners by electrical resistance measurement

In this research, interfacial and wetting properties of N,N,N,N-tetraglycidyl-4,4-diaminodiphenylmethane (TGDDM) epoxy resin with two hardeners with different chemical structure were evaluated by electrical resistance (ER) measurement. The heat of reaction of TGDDM epoxy with the two different hardeners, 33 and 44 di-amino di-phenyl sulphone (DDS), was analyzed by differential scanning calorimetry (DSC). The TGDDM epoxy exhibited different mechanical properties with the two different DDS hardeners. Combined ER, wetting measurements and the microdroplet test were used for evaluating the spreading effect and interfacial shear strength (IFSS) of carbon fiber (CF) reinforced TGDDM epoxy composites with these different hardeners. The heat of reaction and mechanical properties of TGDDM/DDS were influenced by the chemical structure and different free volumes of the epoxy resins. The relationships between the ER-wetting results and the IFSS were internally consistent. Ultimately it was demonstrated that ER measurements makes it possible to estimate the interfacial and wetting properties of CF reinforced epoxy composites.     

Analytical and numerical analysis of frictional damage in quasi brittle materials

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori–Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress–strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.     

Admissible deformation fields for the homogenization of elastoplastic materials with generalized periodicity

In this paper we present the admissible deformation fields and the corresponding functional setting needed for the homogenization of the non-linear equations describing the elastoplastic behavior of structures with generalized periodicity.     

Analytical network-averaging of the tube model:: Rubber elasticity

In this paper, a micromechanical model for rubber elasticity is proposed on the basis of analytical network-averaging of the tube model and by applying a closed-form of the Rayleigh exact distribution function for non-Gaussian chains. This closed-form is derived by considering the polymer chain as a coarse-grained model on the basis of the quantum mechanical solution for finitely extensible dumbbells (Ilg et al., 2000). The proposed model includes very few physically motivated material constants and demonstrates good agreement with experimental data on biaxial tension as well as simple shear tests.     

On the transverse compression response of Kevlar KM2 using fiber-level finite element model

Flexible textile composites like woven Kevlar fabrics are widely used in high velocity impact (HVI) applications. Upon HVI they are subjected to both longitudinal tensile and transverse compressive loads. To understand the role of transverse properties, the single fiber and tow transverse compression response (SFTCR and TTCR) of Kevlar KM2 fibers are numerically analyzed using plane strain finite element (FE) models. A finite strain formulation with a minimum number of 84 finite elements is determined to be required for the fiber cross section to capture the finite strain SFTCR through a mesh convergence study. Comparison of converged numerical solution to the experimental results indicates the dominant role of geometric stiffening at finite strains due to growth in contact width. The TTCR is studied using a fiber length scale FE model of a single tow comprised of 400 fibers transversely loaded between rigid platens. This study along with micrographs of yarn after mechanical compaction illustrates fiber spreading and fiber–fiber contact friction interactions are important deformation mechanisms at finite strains. The TTCR is also studied using homogenized yarn level models with properties from the literature. Comparison of TTCR between fiber length scale and homogenized yarn length scale models indicate the need for a nonlinear material model for homogenized approaches to accurately predict the transverse compression response of the fabrics.     

A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts

In this paper the effects of accidental impacts on polysilicon MEMS sensors are investigated within the framework of a three-scale finite element approach. By allowing for the very small ratio (on the order of 10⁻⁴) between the inertia of the MEMS and the inertia of the whole device, macro-scale analyses at the package length-scale are run to obtain the loading conditions at the sensor anchor points. These loading conditions are successively adopted in meso-scale analyses at the MEMS length-scale to detect where the stress level tends to be amplified by sensor layout. To foresee failure of polysilicon in these domains, as caused by the propagation of inter- as well as trans-granular cracks up to percolation, representative crystal topologies are handled in micro-scale analyses. In case of a uni-axial MEMS accelerometer falling from a reference drop height, results show that the crystal structure within the failing sensor detail can have a remarkable effect on the failure mode and on the time to failure. Conversely, through comparison with simulations where the MEMS is assumed to fall anchored to the naked die, it is assessed that packaging only slightly modifies failure details, without significantly reducing the shock loading on the sensor. F. Fachin is currently with: Technology Laboratory for Advanced Materials and Structures, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 (USA). F. Cacchione is currently with: ABB SACE, Viale dell’Industria 18, Vittuone, 20010 (Italy).     

Effect of particle size distribution on micro- and macromechanical response of granular packings under compression

The role of particle size heterogeneity on micro- and macromechanical properties of assemblies of spherical particles was studied using DEM simulations. The response to an imposed load of a granular material composed of non-uniformly sized spheres subjected to uniaxial confined compression was investigated. A range of geometrical and micro-mechanical properties of granular packings (e.g., void fraction, contact force distribution, average coordination number and degree of mobilisation of friction at contacts between particles) were examined, and provided a more accurate interpretation of the macroscopic behaviour of mixtures than has previously been available. The macromechanical study included stress transmission, stiffness and angle of internal friction of the granular assemblies.The degree of polydispersity showed slight effect on both, the void fraction and the elastic properties of the system. The tendency for increase in the lateral-to-vertical pressure ratios was observed with an increasing degree of particle size heterogeneity; however, the different pressure ratios calculated for samples with various degrees of polydispersity lay within the range of data scatter.