Marco Salviato

Stress Distributions Around Rigid Nanoparticles

A closed form solution for the stress fields around a rigid nanoparticle under uniaxial tensile load is provided. The work explicitly accounts for the presence, around the nanoparticle, of an interphase of thickness comparable to the particle size and different elastic properties from those of the matrix. The solution allows one to determine, in closed form, the stress concentration around nanoparticles relevant for fracture and strength assessments of polymer nanocomposites.

Microplane triad model for simple and accurate prediction of orthotropic elastic constants of woven fabric composites

An accurate prediction of the orthotropic elastic constants of woven composites from the constituent properties can be achieved if the representative unit cell is subdivided into a large number of finite elements. But this would be prohibitive for microplane analysis of structures consisting of many representative unit cells when material damage alters the elastic constants in each time step in every element. This study shows that predictions almost as accurate and sufficient for practical purposes can be achieved in a much simpler and more efficient manner by adapting to woven composites the well-established microplane model, in a partly similar way as recently shown for braided composites. The undulating fill and warp yarns are subdivided into segments of different inclinations and, in the center of each segment, one microplane is placed normal to the yarn. As a new idea, a microplane triad is formed by adding two orthogonal microplanes parallel to the yarn, one of which is normal to the plane of the laminate. The benefit of the microplane approach is that it is easily extendable to damage and fracture. The model is shown to give realistic predictions of the full range of the orthotropic elastic constants for plain, twill, and satin weaves and is extendable to hybrid weaves and braids.

Microplane-Triad Model for Elastic and Fracturing Behavior of Woven Composites

A multiscale model based on the framework of microplane theory is developed to predict the elastic and fracturing behavior of woven composites from the mesoscale properties of the constituents and the weave architecture. The effective yarn properties are obtained by means of a simplified mesomechanical model of the yarn, based on a mixed series and parallel coupling of the fibers and of the polymer within the yarns. As a novel concept, each of the several inclined or aligned segments of an undulating fill and warp yarn is represented by a triad of orthogonal microplanes, one of which is normal to the yarn segment while another is normal to the plane of the laminate. The constitutive law is defined in terms of the microplane stress and strain vectors. The elastic and inelastic constitutive behavior is defined using the microplane strain vectors which are the projections of the continuum strain tensor. Analogous to the principle of virtual work used in previous microplane models, a strain energy density equivalence principle is employed here to obtain the continuum level elastic and inelastic stiffness tensors, which in turn yield the continuum level stress tensor. The use of strain vectors rather than tensors makes the modeling conceptually clearer as it allows capturing the orientation of fiber failures, yarn cracking, matrix microcracking, and interface slip. Application of the new microplane-triad model for a twill woven composite shows that it can realistically predict all the orthotropic elastic constants and the strength limits for various layups. In contrast with the previous (nonmicroplane) models, the formulation can capture the size effect of quasi-brittle fracture with a finite fracture process zone (FPZ). Explicit finite-element analysis gives a realistic picture of progressive axial crushing of a composite tubular crush can initiated by a divergent plug. The formulation is applicable to widely different weaves, including plain, twill, and satin weaves, and is easily extensible to more complex architectures such as hybrid weaves as well as twoand three-dimensional braids. [DOI: 10.1115/1.4032275]

Notch effect in clay-modified epoxy: a new perspective on nanocomposite properties

In this work, an experimental investigation of the notch effect on clay-modified epoxy resins is carried out, discussing the results from Single Edge Notch Bending tests and Double Edge Notch Tension tests on notched components. It is found that when the notch root radius is greater than a limit value, which depends on the clay content, the brittle failure of notched nanomodified specimens is controlled by the material strength. Under this circumstance nanomodification, while enhancing the polymer fracture toughness, might have a detrimental effect on the strength of notched components. This study brings to light a new feature of nanomodification according to which particular care should be used when using nanomodified resins for structural applications in the presence of notches or holes.

Elastic Microplane Formulation for Transversely Isotropic Materials

This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: 1) the spectral decomposition of the stiffness tensor to define the microplane constitutive laws in terms of energetically orthogonal eigenstrains and eigenstresses; and 2) the definition of orientation-dependent microplane elastic moduli. It is shown that the first approach provides a rigorous way to tackle anisotropy within the microplane framework whereas the second approach represents an approximation which, however, makes the formulation of nonlinear constitutive equations much simpler. The efficacy of the second approach in modeling the macroscopic elastic behavior is compared to the thermodynamic restrictions of the anisotropic parameters showing that a significant range of elastic properties can be modeled with excellent accuracy. Further, it is shown that it provides a very good approximation of the microplane stresses provided by the first approach, with the advantage of a simpler formulation. It is concluded that the spectral stiffness decomposition represents the best approach in such cases as for modeling unidirectional composites, in which accurately capturing the elastic behavior is important. The introduction of orientation-dependent microplane elastic moduli provides a simpler framework for the modeling of transversely isotropic materials with remarked inelastic behavior, as in the case, for example, of shale rock.

Viscous energy dissipation of kinetic energy of particles comminuted by high-rate shearing in projectile penetration, with potential ramification to gas shale

While dynamic comminution is of interest to many processes and situations, this work is focused on the projectile impact onto concrete walls, in which predictions have been hampered by the problem of the so-called ‘dynamic overstress’. Recently, in analogy with turbulence, Bažant and Caner modeled the overstress as an additional viscous stress generated by apparent viscosity that accounts for the energy dissipation due to kinetic comminution of concrete into small particles at very high shear strain rate. Their viscosity estimation, however, was approximate since it did not satisfy the energy balance exactly. Here their model is extended and refined by ensuring that the drop of local kinetic energy of high shear strain rate of forming particles must be exactly equal to the energy dissipated by interface fracture of these particles. The basic hypothesis is that the interface fracture occurs instantly, as soon as the energy balance is satisfied. Like in the preceding work, this additional apparent viscosity is a power function of the rate of the deviatoric strain invariant. But here the power exponent is different, equal to

Toughening mechanisms in nanoparticle polymer composites: experimental evidences and modeling

-7/3

Nanomechanics based theory of size effect on strength, lifetime and residual strength distributions of quasibrittle failure: A review

-7/3, and the apparent viscosity is found to be proportional also to the time derivative of the rate of that invariant, i.e., to the second derivative of the shear strain. It is assumed that the interface fracture that comminutes the material into small particles occurs instantly, as soon as the local kinetic energy of shear strain rate in the forming particles becomes equal to the energy required to form interface fractures. The post-comminution behavior, including subsequent further comminution and clustering into bigger particle groups to release the kinetic energy that is being dissipated by inter-group friction, is discussed and modeled. The present formulation makes it possible to eliminate the artificial damping of all types, which is normally embedded in commercial finite element codes but is not predictive since it is not justified physically. With the aforementioned improvements, and after implementation into the new microplane model M7 for fracturing damage in concrete (which includes the quasi-static rate effects), the finite element predictions give superior agreement with the measured exit velocities of steel projectiles penetrating concrete walls of different thicknesses and with the measured depths of penetration into concrete blocks by projectiles of different velocities. Finally it is pointed out that the theory presented may also be used to predict proximate fragmentation and permeability enhancement of gas shale by powerful electric pulsed-arc explosions in the borehole.