Search

This work presents a comprehensive investigation of the elastic and fracture behavior of ply-to-ply angle interlock three-dimensional woven composites. The research investigated novel splitting and wedge-driven out-of-plane fracture tests to shed light on the tensile fracture behavior in the thickness direction and to provide estimates of the out-of-plane tensile strength and fracture energy. In addition, size effect tests on geometrically-scaled Single Edge Notch Tension (SENT) specimens were performed to fully characterize the intra-laminar fracture energy of the material and to study the scaling of structural strength in this type of three-dimensional composites. The results confirmed that size effect in the structural strength of these materials is significant. In fact, even if the range of sizes investigated was broader than in any previous size effect study on traditional laminated composites and two-dimensional textile composites, all the experimental data fell in the transition zone between quasi-ductile and brittle behavior. This implies strong damage tolerance of the investigated three-dimensional composites. The analysis of the data via Bazant's Type II Size Effect Law (SEL) enabled the objective characterization of the intra-laminar fracture energy of three-dimensional composites for the first time. Finally, Arcan rig tests combined with X-ray micro-computed tomography allowed unprecedented insights on the different damage mechanisms under multi-axial nominal loading conditions, particularly tension-dominated and shear-dominated conditions.

This work investigates the mode I and II interlaminar fracturing behavior of laminated composites and the related size effects. Fracture tests on geometrically scaled Double Cantilever Beam (DCB) and End Notch Flexure (ENF) specimens were conducted to understand the nonlinear effects of the cohesive stresses in the Fracture Process Zone (FPZ). The results show a significant difference between the mode I and mode II fracturing behaviors. It is shown that, while the strength of the DCB specimens scales according to the Linear Elastic Fracture Mechanics (LEFM), this is not the case for the ENF specimens. Small specimens exhibit a pronounced pseudo-ductility with limited size effect and a significant deviation from LEFM, whereas larger specimens behave in a more brittle way, with the size effect on nominal strength closer to that predicted by LEFM. This behavior, due to the significant size of the Fracture Process Zone (FPZ) compared to the specimen size, needs to be taken into serious consideration. It is shown that, for the specimen sizes investigated in this work, neglecting the non-linear effects of the FPZ can lead to an underestimation of the fracture energy by as much as 55%, with an error decreasing for increasing specimen sizes. Both the mode I and II test data can be captured very accurately by Ba\v{z}ant's type II Size Effect Law (SEL).

Hindered adsorbed layers completely filling the nanopores must cause significant deviations from the classical BET isotherms for multimolecular adsorption of vapor in porous solids. Since the point of transition from free to hindered adsorption moves into narrower nanopores as the pore vapor pressure (or humidity) decreases, the area of the surface of multimolecular adsorption layer exposed to vapor gets modified by an area reduction factor that decreases with increasing thickness of the layer, and thus also with increasing vapor pressure. The area reduction factor does not affect the rates of direct adsorption or condensation from the vapor, which represent a local process, but imposes a lateral constraint on the total area and volume of the free portion of the adsorption layer in direct contact with vapor. Assuming a power-law for the dependence of the area reduction factor on the number of molecular layers, one can express the modified isotherm in terms of logarithmic or polylogarithmic (a.k.a Jonqui\`ere) functions. Comparisons with some published experimentally obtained isotherms show that the present modification of the BET theory for hindered adsorption goes in the right direction. Detailed calibration of the theory and an extension for indirect communication of vapor molecules with the molecules adsorbed in nanopores less than a few nm wide will require further research., Comment: 15 pages, 4 figures

While the hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as the current commercial softwares, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000$\times$. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. But their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nano- or micro-cracking damage. It is numerically demonstrated that a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings.

The reporting and evaluation of creep tests of concrete is complicated by the fact that creep is significant even for the shortest observable load durations. Compared to the strain after 0.1 s load duration, the strain at 2 hour duration is typically 53% greater. Most experimenters have for decades been unaware of this fact. Consequently, the reported creep curves require correction by a time shift, which ranges from 0 to 2 hours. This further implies a vertical shift of entire creep curve, important for all times up to structure lifetime. To filter out the errors, it is argued that, within an initial period during which the advance of hydration is negligible, which is normally about 1 day, the initial basic creep must follow a power law of the time. Creep test data from the literature are used to prove it. Corrections by time and deformation shifts are determined by minimization of the sum of squared deviations of the power law from the creep test data. For a fixed exponent n and time shift s, the optimization is reduced to linear regressions of two kinds, depending on whether the data are given in terms of either the compliance function or the creep coefficient. For both, the linear regression parameters depend nonlinearly on the chosen values of n and s. To avoid nonlinear optimization, which need not converge to the correct result, a set of many discrete values of n and s within their realistic ranges is selected and the (n,s) combination minimizing the objective function is obtained by a search. Enforcing a power law form of the initial creep curve is found to lead to better data fits. The optimum exponent n for the entire database is around 0.3, applicable to the time period cca (10 s, 1 day). After that, the exponent transits to about 0.1, and prior to that it is about 0.08., Comment: Pre-Print (Materials and Structures), 20 pages, 11 figures

The size effect of Muttoni et al.'s CSCT is shown to be very close and asymptotically identical to the energetic size effect law (SEL) extensively verified experimentally and theoretically (due to appear in the 2019 ACI Code for both beam shear and punching). However, the CSCT derivation and calculation procedure obfuscates the mechanics of failure. It is shown to rest on six scientifically untenable hypotheses, which makes CSCT untrustworthy outside the testing range. It would have to be taught to students as a dogma. These conclusions are supported by experimentally calibrated finite element simulations of crack path and width, stress distributions and localizations during failure, and strain energy release. The simulations also show the CSCT to be incompatible with the 'strut-and-tie' model modernized to include the size effect in the compression strut. Finally, further deficiencies are pointed out for the Modified Compression Field Theory (MCFT), currently embedded in the Model Code., Comment: 16 pages, 4 figures

The staggered (or imbricated) lamellar "brick-and-mortar" nanostructure of nacre endows nacre with strength and fracture toughness values exceeding by an order of magnitude those of the constituents, and inspires the advent of new robust biomimetic materials. While many deterministic studies clarified these advantageous features in the mean sense, a closed-form statistical model is indispensable for determining the tail probability of failure in the range of 1 in a million, which is what is demanded for most engineering applications. In the authors' preceding study, the so-called `fishnet' statistics, exemplified by a diagonally pulled fishnet, was conceived to describe the probability distribution. The fishnet links, representing interlaminar bonds, were considered to be elastic perfectly-brittle. However, the links may be quasibrittle or almost ductile, exhibiting gradual postpeak softening in their stress-strain relation. This paper extends the fishnet statistics to links with post-peak softening slope of arbitrary steepness. Probabilistic analysis is enabled by assuming the postpeak softening of a link to occur as a series of finite drops of stress and stiffness. The maximum load of the structure is approximated by the strength of the k-th weakest link (k >= 1), and the distribution of structure strength is expressed as a weighted sum of the distributions of order statistics. The analytically obtained probabilities are compared and verified by histograms of strength data obtained by millions of Monte Carlo simulations for each of many nacreous bodies with different link softening steepness and with various overall shapes.

The solidification theory has been accepted as a thermodynamically sound way to describe the creep reduction due to deposition of hydrated material in the pores of concrete. The concept of self-equilibrated nanoscale microprestress has been accepted as a viable model for marked multi-decade decline of creep viscosity after the hydration effect became too feeble, and for increase of creep viscosity after any sudden change of pore humidity or temperature. Recently, though, it appeared that the original microprestress-solidification theory (MPS) predicts incorrectly the diffusion size effect on drying creep and the delay of drying creep behind drying shrinkage. Presented here is an extension (XMPS) that overcomes both problems and also improves a few other features of the model response. To this end, different nano- and macro-scale viscosities are distinguished. The aforementioned incorrect predictions are overcome by a dependence of the macro-scale viscosity on the rate of pore humidity change, which is a new feature inspired by previous molecular dynamics (MD) simulations of a molecular layer of water moving between two parallel sliding C-S-H sheets. The aging is based on calculating the hydration degree, and the temperature change effect on pore relative humidity is taken into account. Empirical formula for estimating the parameters of permeability dependence on pore humidity from concrete mix composition are also developed. Extensive validations by pertinent test data from the literature are demonstrated.

Similar to nacre or brick-and-mortar structures, imbricated lamellar structures are widely found in natural and man-made materials and are of interest for biomimetics. These structures are known to be rather insensitive to defects and to have a very high fracture toughness. Their deterministic behavior has been intensely studied, but statistical studies have been rare and is so far there is no undisputed theoretical basis for the probability distribution of strength of nacre. This paper presents a numerical and theoretical study of the PDF of strength and of the corresponding statistical size effect. After a reasonable simplifications of the shear bonds, an axially loaded lamellar shell is statistically modelled as a square fishnet pulled diagonally. A finite element (FE) model is developed and used in Monte Carlo simulations of strength. An analytical model for failure probability of the fishnet is developed and matched to the computed statistical histograms of strength for various sizes. It appears that, with increasing size, the pdf of strength slowly transits from Gaussian to Weilbull distribution but the transition is different from that previously obtained at Northwestern for quasibrittle materials of random heterogeneous mesostructure.

Static and dynamic analysis of the fracture tests of fiber composites in hydraulically servo-controlled testing machines currently in use shows that their grips are much too soft and light for observing the postpeak softening. Based on static and dynamic analysis of the test setup, far stiffer and heavier grips are proposed. Tests of compact-tension fracture specimens of woven carbon-epoxy laminates prove this theoretical conclusion. Sufficiently stiff grips allow observation of a stable postpeak, even under load-point displacement control. Dynamic stability analysis further indicates that stable postpeak can be observed under CMOD control provided that a large mass is rigidly attached to the current soft grips. The fracture energy deduced from the area under the measured complete load-deflection curve with stable postpeak agrees closely with the fracture energy deduced from the size effect tests of the same composite. Previous suspicions of dynamic snapback in the testing of composites are dispelled. So is the previous view that fracture mechanics was inapplicable to the fiber-polymer composites.

Design of large composite structures requires understanding the scaling of their mechanical properties, an aspect often overlooked in the literature on composites. This contribution analyzes, experimentally and numerically, the intra-laminar size effect of textile composite structures. Test results of geometrically similar Single Edge Notched specimens made of 8 layers of 0 degree epoxy/carbon twill 2 by 2 laminates are reported. Results show that the nominal strength decreases with increasing specimen size and that the experimental data can be fitted well by Bazant's size effect law, allowing an accurate identification of the intra-laminar fracture energy of the material. The importance of an accurate estimation of Gf in situations where intra-laminar fracturing is the main energy dissipation mechanism is clarified by studying numerically its effect on crashworthiness of composite tubes. Simulations demonstrate that, for the analyzed geometry, a decrease of the fracture energy to 50% of the measured value corresponds to an almost 42% decrease in plateau crushing load. Further, assuming a vertical stress drop after the peak, a typical assumption of strength-based constitutive laws implemented in most commercial Finite Element codes, results in an strength underestimation of the order of 70%. The main conclusion of this study is that measuring accurately fracture energy and modeling correctly the fracturing behavior of textile composites, including their quasi-brittleness, is key. This can be accomplished neither by strength- or strain-based approaches, which neglect size effect, nor by LEFM which does not account for the finiteness of the Fracture Process Zone.

The modeling of high velocity impact into brittle or quasibrittle solids is hampered by the unavailability of a constitutive model capturing the effects of material comminution into very fine particles. The present objective is to develop such a model, usable in finite element programs. The comminution at very high strain rates can dissipate a large portion of the kinetic energy of an impacting missile. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate is enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a high-rate shear strain of forming particles. For simplicity, the shape of these particles in the plane of maximum shear rate is considered to be regular hexagons. The rate of release of free energy density consisting of the sum of this energy and the fracture energy of the interface between the forming particle is minimized. The particle sizes are assumed to be distributed according to Schuhmann's power law. It is concluded that the minimum particle size is inversely proportional to the (2/3)-power of the shear strain rate, that the kinetic energy release is to proportional to the (2/3)-power, and that the dynamic comminution creates an apparent material viscosity inversely proportional to the (1/3)-power of the shear strain rate., Comment: 13 pages, 2 figures

Motivated by the puzzle of sorption hysteresis in Portland cement concrete or cement paste, we develop in Part II of this study a general theory of vapor sorption and desorption from nanoporous solids, which attributes hysteresis to hindered molecular condensation with attractive lateral interactions. The classical mean-field theory of van der Waals is applied to predict the dependence of hysteresis on temperature and pore size, using the regular solution model and gradient energy of Cahn and Hilliard. A simple "hierarchical wetting" model for thin nanopores is developed to describe the case of strong wetting by the first monolayer, followed by condensation of nanodroplets and nanobubbles in the bulk. The model predicts a larger hysteresis critical temperature and enhanced hysteresis for molecular condensation across nanopores at high vapor pressure than within monolayers at low vapor pressure. For heterogeneous pores, the theory predicts sorption/desorption sequences similar to those seen in molecular dynamics simulations, where the interfacial energy (or gradient penalty) at nanopore junctions acts as a free energy barrier for snap-through instabilities. The model helps to quantitatively understand recent experimental data for concrete or cement paste wetting and drying cycles and suggests new experiments at different temperatures and humidity sweep rates., Comment: 26 pages, 10 figs

The sorption-desorption hysteresis observed in many nanoporous solids, at vapor pressures low enough for the the liquid (capillary) phase of the adsorbate to be absent, has long been vaguely attributed to changes in the nanopore structure, but no mathematically consistent explanation has been presented. The present work takes an analytical approach to account for discrete molecular forces in the nanopore fluid and proposes two related mechanisms that can explain the hysteresis at low vapor pressure without assuming any change in the nanopore structure. The first mechanism, presented in Part I, consists of a series of snap-through instabilities during the filling or emptying of non-uniform nanopores or nanoscale asperities. The instabilities are caused by non-uniqueness in the misfit disjoining pressures engendered by a difference between the nanopore width and an integer multiple of the thickness of a monomolecular adsorption layer. The second mechanism, presented in Part II, consists of molecular coalescence within a partially filled surface, nanopore or nanopore network. This general thermodynamic instability is driven by attractive intermolecular forces within the adsorbate and forms the basis to develop a unified theory of both mechanisms. The ultimate goals of the theory are to predict the fluid transport in nanoporous solids from microscopic first principles, and to determine the pore size distribution and internal surface area from sorption tests., Comment: Infrastructure Science (Northwestern University)