SIMULATION OF THE MECHANICAL PROPERTIES OF FERROCEMENT PLATES

Abstract

Ferrocement is a composite material in which rich cement sand mortar is reinforced with layers of continuous and small diameter steel wire meshes. The confidence in the material has been building up with time resulting in its wider applications. Even though structural and architectural potentials of ferrocement were realized earlier, systematic experimental studies into its mechanical behaviour started in late sixties. Theoretically ferrocement elements have been analysed using either the conventional reinforced concrete theory or composite material theory. Some researchers neglect the contribution of mortar in tension while others incorporate the same in the analysis. The finite element method has been used to a limited extent by some investigators to simulate the behaviour of ferrocement elements numerically. The aim of the study is to conduct extensive experimental tests to evaluate the mechanical properties of ferrocement plates and then to simulate their mechanical behaviour using anisotropic elastoplasticity. The latter is done using the Mindlin plate theory employing alayered approach in conjunction with the finite element method. In this regard the objectives ofthe thesis are outlined as follows • To review the literature related to the mechanical properties of ferrocement with emphasis on tension, compression, flexure, fatigue and impact. • To review the methods of analysis used for the theoretical treatment of ferrocement plates. • To assess the validity of empirical relationships used for the determination of moduli of elasticity ofmortar for subsequent evaluation of the composite modulus. • To conduct a parametric study of free vibration characteristics on ferrocement plates using different solution approaches, configurations and material properties. • To undertake convexity studies for the anisotropic Hoffman and Sun yield criteria in principal stress space for subsequent application in the nonlinear analysis of ferrocement plates. • To carry out a detailed experimental investigation under inplane tension and compression to evaluate the behaviour and mechanical properties in elastic and inelastic regimes. • To numerically simulate the load-deflection behaviour of ferrocement plates under inplane loading using the properties derived from experiment. • To carry out an experimental investigation under flexure and to simulate the experimental results using the mechanical properties derived from inplane tests. • To experimentally analyse the behaviour of ferrocement plates under fatigue and impact. Current literature in the area of mechanical properties of ferrocement and its use in simulating nonlinear material behaviour is reviewed. Methods based on thin plate assumptions and Mindlin-Reissner thick plate theory are discussed. The anisotropic Hoffman yield criterion, which is pressure sensitive and smooth and which can be used in the mathematical modelling of the mechanical behaviour of ferrocement plates in the postelastic range, is also discussed. The analysis of ferrocement slabs has been undertaken by various investigators, wherein these slabs are treated as multilayered laminated plates composed of anisotropic laminae. While the methodology of mathematical modelling of laminated plates is well accepted, considerable ambiguity remains with regard to the assessment of elastic properties of ferrocement. In order to estimate these for the composite, the properties of its constituents need to be assessed first. In the elastic range the properties of interest are the moduli and the Poisson's ratios of the matrix and the mesh. In the present study the validity of empirical relations used for the determination of modulus of elasticity of mortar is assessed. Several empirical relationships have been proposed for the evaluation ofthe mortar modulus. These include those recommended by several codes ofpractice. Elastic analysis of simply supported ferrocement slabs that have been experimentally tested by various investigators, is carried out. The analytical deflections are compared with the experimental deflections for different recommended values of the mortar modulus E Finally Em values that give analytical deflection similar to the experimentally obtained deflection are computed. On the basis of the analytical study undertaken, it is observed that the empirical relations based on mortar crushing strength predict too large a value ofmortar modulus and hence cannot be relied upon in the macromechanics based structural analysis of ferrocement slabs. Accurate determination of elastic moduli through appropriate experimental methods is essential so that analysis of ferrocement structural system can be conducted with confidence. VI Although ferrocement has a high degree of ductility and energy absorption, its use as an alternative and cost effective material under dynamic conditions is yet to be established. In this regard an accurate free vibration analysis forms an essential first step towards obtaining asolution under forced vibration. For the free vibration analysis the ferrocement plate has been idealised as amultidirectional, multilayered laminate consisting of a series of laminae put on top ofeach other at the same or different orientations. The closed form solutions are compared with the numerical solutions obtained using the finite element method employing nine noded Lagrangian Mindlin plate element with enhanced shear interpolation. Simply supported ferrocement slabs in regular plies were analysed using five different approaches viz. (A) Closed form solution using Mindlin plate theory with rotatory inertia. (B) Closed form solution using Mindlin plate theory without rotatory inertia. (C) Closed form solution using classical lamination theory without shear rigidity and without rotatory inertia. (D) Numerical solution using finite element method with 9noded Lagrangian Mindlin plate element employing consistent mass matrix. (E) Numerical solution using finite element method with 9noded Lagrangian Mindlin plate element employing lumped mass matrix. The effect of orientation, moduli ratio, number of layers and aspect ratio on the fundamental frequency is also studied. For the slabs analysed it appears that neglecting the rotatory inertia and adoption of lumped mass matrix (in the finite element solution) does not alter the vibrational characteristics. The mesh orientation and the ratio of the mesh moduli in their two principal directions affects the free vibration frequencies. The experimentally determined natural frequency reported for aferrocement slab compares well with analytically obtained value which reinforces the validity of the macromechanics approach. Convexity is an essential condition for any plasticity model. Moreover, experimental findings confirm that failures of ductile as well as quasi-brittle materials exhibit convexity mboth volumetric and deviatoric planes. Hoffman suggested a nine parameter model which incorporated volumetric stress dependence, by including linear stress terms. Sun and his coworkers also proposed anine parameter model with only quadratic stress terms 17/ It would appear that either of these criteria could be employed with ferrocement as they are smooth and pressure sensitive. For this reason they were selected for further investigation. In order to ensure convexity the choice of the parameters to be used cannot be arbitrary and certain interrelationships among the parameters needs to be satisfied. Mathematical investigations indicate that satisfaction of simple relationships among parameters ensures convexity of the Hill and Hoffman yield criteria. For the Sun criterion convexity can be ensured for the simple plane stress case when five ofthe nine parameters are set to zero. However for the general three dimensional case, the interrelationships are far more stringent and it is not obvious how convexity conditions can be satisfied. Hoffman yield criterion is, therefore, adopted for further analytical work in this study. Inplane tension and compression experiments were conducted on plain mortar (12 tests) and ferrocement (45 tests) with woven and welded meshes. Tension tests were also conducted on the meshes (6 tests). The objective of the experiment was to study the behaviour of the specimen under inplane loading and to evolve a set of elastic and inelastic material properties. The number of wire mesh layers were varied from three to five. The wire meshes were laid in varying orientations viz. 0°, 15° ,30° ,45° ,60° ,75° and 90°. From the tests on mortar plates it is observed that empirical relations predict too large avalue of mortar modulus. The inplane compression tests result in a higher modulus than that obtained under tension. Aweighted average is suggested for general loading conditions. For the prediction of composite (ferrocement) modulus, it is found that the effectiveness factor for the meshes needs to be incorporated in the rule of mixtures as reported by earlier investigators. For ferrocement both in woven and welded mesh weakest configuration results from 45° orientation due to the lowest volume fraction of wire mesh in the direction ofloading at this orientation. Two different mathematical models viz. homogeneous layered model and mortarferrocement layered model are proposed for analytical simulation. Both the models use the properties derived from the experiments. Ferrocement and its constituents are modelled mechanically using elastoplasticity. In both cases the plate is assumed to constitute of a suitable number of layers. The homogeneous layered model assumes all the layers to be of identical material. The anisotropic Hoffman yield criterion is used to simulate the material behaviour. The mortar-ferrocement layered model uses isotropic Hoffman yield criterion vm for mortar layers. For ferrocement layers both transversely isotropic (transtropic) and orthotropic material idealisations are used along with the Hill criterion. Due consideration is made for ensuring the convexity ofthe ensuing yield surfaces. The analytical predictions compare well with the experimental results in the elastic range. In the post-elastic range fairly reasonable match is observed. The mortarferrocement layered orthotropic model is found to perform the best. Experimental tests were conducted under flexure on 15 plain mortar and 36 ferrocement simply supported specimens under three point bending. Woven and welded wire meshes were used and the number of wire meshes layers were varied from three to five. The wire meshes were laid in varying orientations viz. 0°,30°,45°,60° and 90°. From the tests on mortar specimens, the mortar modulus was evaluated using bending theory and found to be close to the average moduli obtained from inplane tension and compression tests. Anumerical analysis, once again, using homogeneous layered model and mortarferrocement layered model in conjunction with mechanical properties derived from inplane experiments was conducted to simulate the flexural behaviour. It is found that the mortarferrocement layered model performs well as compared to the homogeneous model. For a majority of the situations the mortar-ferrocement layered model with orthotropic material idealisation performs best. The development of plastic strain with increased loading is also considered. From the analysis conducted it appears that asingle set of properties evaluated from inplane tests can be employed in the simulation of mechanical behaviour under different loading conditions. Tests were also conducted to ascertain the flexural fatigue response of ferrocement specimens in 3, 4and 5layers of woven mesh and 3layers of welded mesh. Well defined failure plane is observed in all the specimens. With increasing mesh layers fatigue life is found to increase appreciably. S-N relationships are proposed. The impact response of ferrocement specimens under varying impact loads and durations was studied. It was found that the dynamic amplification was dependent on both the duration and the amplitude of the square pulse. The dynamic amplification factor varies from 0.7 to 1.7 up to 60% ofultimate static load and 1.2 to 4beyond