Kedar Kirane

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]

Strain-rate-dependent microplane model for high-rate comminution of concrete under impact based on kinetic energy release theory

The apparent increase of strength of concrete at very high strain rates experienced in projectile impact (10 s−1 to 106 s−1), called ‘dynamic overstress’, has recently been explained by the theory of release of local kinetic energy of shear strain rate in finite size particles about to form. This theory gives the particle size and the additional kinetic energy density that must be dissipated in finite-element codes. In previous research, it was dissipated by additional viscosity, in a model partly analogous to turbulence theory. Here it is dissipated by scaling up the material strength. Microplane model M7 is used and its stress–strain boundaries are scaled up by factors proportional to the −4/3rd power of the effective deviatoric strain rate and its time derivative. The crack band model with a random tetrahedral mesh is used and all the artificial damping is eliminated. The scaled M7 model is seen to predict the crater shapes and exit velocities of projectiles penetrating concrete walls of different thicknesses as closely as the previous models. The choice of the finite strain threshold for element deletion criterion, which can have a big effect, is also studied. It is proposed to use the highest threshold above which a further increase has a negligible effect.

Fracture and Size Effect on Strength of Plain Concrete Disks under Biaxial Flexure Analyzed by Microplane Model M7

The biaxial tensile strength of concrete (and ceramics) can be easily tested by flexure of unreinforced circular disks. A recent experimental study demonstrated that, similar to plain concrete beams, the flexural strength of disks suffers from a significant size effect. However, the experiments did not suffice to determine the size effect type conclusively. The purpose of this study is to use three-dimensional stochastic finite-element analysis to determine the size effect type and shed more light on the fracture behavior. A finite-element code using the microplane constitutive Model M7 is verified and calibrated by fitting the previously measured load-deflections curves and fracture patterns of disks of thicknesses 30, 48, and 75 mm, similar in three dimensions, and on flexure tests on four-point loaded beams. It is found that the deformability of the supports and their lifting and sliding has a large effect on the simulations, especially on the fracture pattern, and the strength and Young’s modulus of concrete must be treated as autocorrelated random fields. The calibrated model is then used to analyze the size effect over a much broader range of disk thicknesses ranging from 20 to 192 mm. The disks are shown to exhibit the typical energetic size effect of Type I, that is, the disks fail (under load control) as soon as the macrofracture initiates from the smooth bottom surface. The curve of nominal strength versus size has a positive curvature and its deterministic part terminates with a horizontal asymptote. The fact that material randomness had to be introduced to fit the fracture patterns confirms that the Type 1 size effect must terminate at very large sizes with a Weibull statistical asymptote, although the disks analyzed are not large enough to discern it.

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

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

-7/3

Size effect in Paris law and fatigue lifetimes for quasibrittle materials: Modified theory, experiments and micro-modeling

-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.

Microplane damage model for fatigue of quasibrittle materials: Sub-critical crack growth, lifetime and residual strength

As shown long ago, plain and longitudinally reinforced concrete beams without stirrups exhibit a significant size effect on torsional strength, which was thought to be of a type occurring after long, stable crack growth (called Type II). This paper shows, by experimentally calibrated finite element simulations, that: 1) longitudinally reinforced concrete beams with stirrups also exhibit a significant size effect; and 2) the size effect in beams both with and without stirrups is not of Type II but Type I, characterizing failure at macrocrack initiation. In the practical size range, Type I is deterministic and terminates with a horizontal, rather than inclined, asymptote. The simulations are based on microplane model M7, which was shown to match well all the types of uniaxial, biaxial, and triaxial tests with post-peak softening in tension and compression. The model is calibrated by simulating previous torsional size effect tests of plain concrete beams and of longitudinally reinforced beams without stirrups, as well as the tests of beams with stirrups having different reinforcement ratios and different aspect ratios. The fact that all these tests are fitted closely, in terms of not only the maximum loads but also the crack patterns, lends credence to the predictions of size effect in beams with stirrups.