General principles and perspectives Specimen preparation Tension Compression Shear Flexure Through-thickness testing Interlaminar fracture toughness Impact and damage tolerance Fatigue Environmental testing of organic matrix composites Scaling effects in laminated composites Statistical modelling and testing of data variability Development and use of standard test methods.

Mechanical testing of advanced fibre composites

This article attempts to review the progress achieved in the understanding of scaling and size ef­ fect in the failure of structures. Particular emphasis is placed on quasi brittle materials for which the size etTect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, non local finite element models and discrete element models. Extensions to com­ pression failure and to the rate-dependent material behavior are also outlined. The damage con­ stitutive law needed for describing a microcracked material in the fracture process zone is dis­ cussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber compos­ ites, rocks and ceramics are presented. There are 377 references included in this article.

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Scaling of Structural Failure

Size effects in the testing of fibre-composite materials

A paradigm shift has emerged over the last decade pointing to an exciting research area dealing with the harnessing of elastic structural instabilities for ‘smart’ purposes in a variety of venues. Among the different types of unstable responses, buckling is a phenomenon that has been known for centuries, and yet it is generally avoided through special design modifications. Increasing interest in the design of smart devices and mechanical systems has identified buckling and postbuckling response as a favorable behavior. The objective of this topical review is to showcase the recent advances in buckling-induced smart applications and to explain why buckling responses have certain advantages and are especially suitable for these particular applications. Interesting prototypes in terms of structural forms and material uses associated with these applications are summarized. Finally, this review identifies potential research avenues and emerging trends for using buckling and other elastic instabilities for future innovations.

https://iopscience.iop.org/article/10.1088/0964-1726/24/6/063001/pdf

Buckling-induced smart applications: recent advances and trends

Because the uncertainty in current empirical safety factors for structural strength is far larger than the relative errors of structural analysis, improvements in statistics offer great promise. One improvement, proposed here, is that, for quasibrittle structures of positive geometry, the understrength factors for structural safety cannot be constant but must be increased with structures size. The statistics of safety factors has so far been generally regarded as independent of mechanics, but further progress requires the cumulative distribution function (cdf) to be derived from the mechanics and physics of failure. To predict failure loads of extremely low probability (such as 10 - 6 to 10 - 7 ) on which structural design must be based, the cdf of strength of quasibrittle structures of positive geometry is modelled as a chain (or series coupling) of representative volume elements (RVE), each of which is statistically represented by a hierarchical model consisting of bundles (or parallel couplings) of only two long sub-chains, each of them consisting of sub-bundles of two or three long sub-sub-chains of sub-sub-bundles, etc., until the nano-scale of atomic lattice is reached. Based on Maxwell–Boltzmann distribution of thermal energies of atoms, the cdf of strength of a nano-scale connection is deduced from the stress dependence of the interatomic activation energy barriers, and is expressed as a function of absolute temperature T and stress-duration τ (or loading rate 1 / τ ). A salient property of this cdf is a power-law tail of exponent 1. It is shown how the exponent and the length of the power-law tail of cdf of strength is changed by series couplings in chains and by parallel couplings in bundles consisting of elements with either elastic–brittle or elastic–plastic behaviors, bracketing the softening behavior which is more realistic, albeit more difficult to analyze. The power-law tail exponent, which is 1 on the atomistic scale, is raised by the hierarchical statistical model to an exponent of m = 10 to 50, representing the Weibull modulus on the structural scale. Its physical meaning is the minimum number of cuts needed to separate the hierarchical model into two separate parts, which should be equal to the number of dominant cracks needed to break the RVE. Thus, the model indicates the Weibull modulus to be governed by the packing of inhomogeneities within an RVE. On the RVE scale, the model yields a broad core of Gaussian cdf (i.e., error function), onto which a short power-law tail of exponent m is grafted at the failure probability of about 0.0001–0.01. The model predicts how the grafting point moves to higher failure probabilities as structure size increases, and also how the grafted cdf depends on T and τ . The model provides a physical proof that, on a large enough scale (equivalent to at least 500 RVEs), quasibrittle structures must follow Weibull distribution with a zero threshold. The experimental histograms with kinks, which have so far been believed to require the use of a finite threshold, are shown to be fitted much better by the present chain-of-RVEs model. For not too small structures, the model is shown to be essentially a discrete equivalent of the previously developed nonlocal Weibull theory, and to match the Type 1 size effect law previously obtained from this theory by asymptotic matching. The mean stochastic response must agree with the cohesive crack model, crack band model and nonlocal damage models. The chain-of-RVEs model can be verified and calibrated from the mean size effect curve, as well as from the kink locations on experimental strength histograms for sufficiently different specimen sizes.

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/464.pdf

Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture

The feasibility of using scale model testing for predicting the full-scale behavior of flat composite coupons loaded in tension and beam-columns loaded in flexure is examined. Classical laws of similitude are applied to fabricate and test replica model specimens to identify scaling effects in the load response, strength, and mode of failure. Experiments were performed on graphite-epoxy composite specimens having different laminate stacking sequences and a range of scaled sizes. From the experiments it was deduced that the elastic response of scaled composite specimens was independent of size. However, a significant scale effect in strength was observed. In addition, a transition in failure mode was observed among scaled specimens of certain laminate stacking sequences. A Weibull statistical model and a fracture mechanics based model were applied to predict the strength scale effect since standard failure criteria cannot account for the influence of absolute specimen size on strength.

Scale effects in the response and failure of fiber reinforced composite laminates loaded in tension and in flexure

Recent advances in computational speed have made aircraft and spacecraft crash simulations using an explicit, nonlinear, transient-dynamic,e niteelement analysiscodemore feasible.This paperdescribes thedevelopment of a simplelanding-gearmodel, which accurately simulatestheenergy absorbed by thegearwithoutaddingsubstantial complexity to the model. For a crash model the landing gear response is approximated with a spring where the force applied to the fuselage is computed in a user-written subroutine. Helicopter crash simulations using this approach are compared with previously acquired experimental data from a full-scale crash test of a composite helicopter.

/pdf/simulation-of-aircraft-landing-gears-with-a-nonlinear-4feqe9h1un.pdf

Simulation of Aircraft Landing Gears with a Nonlinear Dynamic Finite Element Code

The energy absorption response and crushing characteristics of geometrically scaled graphite-Kevlar epoxy composite plates were investigated. Two different trigger mechanisms including notch, and steeple geometries were incorporated into the plate specimens to initiate crushing. Sustained crushing was achieved with a new test fixture which provided lateral support to prevent global buckling. Values of specific sustained crushing stress (SSCS) were obtained which were lower than values reported for tube specimens from previously published data. Two sizes of hybrid plates were fabricated; a baseline or model plate, and a full-scale plate with inplane dimensions scaled by a factor of two. The thickness dimension of the full-scale plates was increased using two different techniques: the ply-level method in which each ply orientation in the baseline laminate stacking sequence is doubled, and the sublaminate technique in which the baseline laminate stacking sequence is repeated as a group. Results indicated that the SSCS has a small dependence on trigger mechanism geometry. However, a reduction in the SSCS of 10-25% was observed for the full-scale plates as compared with the baseline specimens, indicating a scaling effect in the crushing response.

Scaling of energy absorbing composite plates

An experimental program was conducted in which scale model graphite-epoxy composite beams were loaded in bending until failure to investigate the effects of specimen size on flexural response and strength. Tests were performed on unidirectiona l, angle-ply, cross-ply, and quasi-isotropic beams of eight different scaled sizes ranging from 1/6 scale to full scale. The beams were subjected to an eccentric axial compressive load designed to promote large bending deformations and rotations. Results indicated that, although normalized flexural response was independent of specimen size, a significant scale effect in strength was observed for all laminate types. Typically, failure stresses and strains decreased as the size of the beam specimen increased from subscale to the full-scale prototype. Standard failure criteria for composite materials, such as the maximum stress, maximum strain, and tensor polynomial criteria, cannot predict the strength degradation with increasing specimen size. Consequently, a Weibull statistical model and a fracture mechanics model were used to analyze the strength scale effect.

Karen E. Jackson

Papers

Scale effects in the response and failure of fiber reinforced composite laminates loaded in tension and in flexure

Simulation of Aircraft Landing Gears with a Nonlinear Dynamic Finite Element Code

Scaling of energy absorbing composite plates

Scaling effects in the flexural response and failure of composite beams

Analytical Crash Simulation of Three Composite Fuselage Concepts and Experimental Correlation.