Transformation Field Analysis Method Research Articles

Multiscale modelling and simulation of polymer nanocomposites using transformation field analysis (TFA)

High performance fibre-reinforced polymers (FRP) have successfully been established in the aerospace industry. The performance of epoxy resins used for carbon fibre reinforced plastics can be significantly improved by the incorporation of nanoparticles.A Transformation field analysis (TFA) proposed by Dvorak and co-workers is utilized to predict the properties of a representative volume of inelastic heterogeneous materials consisting of polymers and nanoparticles.Thus, the TFA method at the nanoscale can be implemented as a user routine integrated into RVE micro scale model, where the modified matrix is reinforced by a certain volume fraction of aligned fibres. This yields to save computational resources and time in combination with good efficiency compared to todays established multiscale approaches.To the author’s knowledge, this is the first implementation of the TFA method for three-dimensional nanocomposites problems.Finally, a single nano level application based TFA approach and numerical multi-scale (micro/FEA-nano/TFA) application are implemented to verify the behaviour of elastic-plastic epoxy nanocomposite consisting of agglomerating fillers in nano-scale and reinforced by aligned fibres in micro-scale under different external loads. To validate this multiscale approach, a multiscale approach based TFA micro scale and TFA nano scale is processed.

Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities

The present work is devoted to the estimate of linear effective poroelastic properties of isotropic porous rocks characterized by an assemblage of porous grains (oolites), mesopores and solid grains. Examples of such type of microstructure may be found in oolitic limestones. Two distinct classes of pores are taken into account, micropores or intra oolitic pores and mesopores or inter oolitic pores. In the framework of Hashin Composite Sphere Assemblage (CSA, Hashin, 1962) and self-consistent models, a two step homogenization model is developed. At the first step, micropores are homogenized inside the oolites. At the second step, oolites, mesopores and solid grains are assembled by using the self consistent scheme. Levin’s theorem and transformation field analysis method are used to derive poroelastic coefficients (Biot coefficient and solid Biot modulus). Simple explicit formula are presented for effective poroelastic coefficients in the general case of double porosity media, under the assumption of spherical shape for all constituent particles and isotropic distribution. Finally comparisons between model and experimental data are presented for an oolitic limestone which includes micro-indentation results obtained at mesoscale and poromechanical results obtained at macroscale. Comparisons show that in the case of low macro stiffness, a degraded interfacial transition zone (ITZ) surrounding oolites, need to be introduced to fit the data

Stress Relaxation in Prestressed Composite Laminates

Viscoelastic deformation caused in symmetric laminated plates by release of fiber prestress and by uniform thermomechanical loads is analyzed on the constituent, ply and overall laminate scales with the Transformation Field Analysis (TFA) method (G. J. Dvorak, Proc. R. Soc. Lond., 1992, A437, pp. 311–327). Fiber prestress is applied in individual plies prior to matrix cure and released after matrix consolidation. Linear or nonlinear viscoelastic constitutive relations are used to evaluate the inelastic deformation rates in terms of current constituent stress averages. The TFA method regards both thermal and inelastic strains as piecewise uniform eigenstrains acting in superposition with mechanical loads and fiber prestress release on an elastic laminate. Interactions between the eigenstrains at the three different size scales are described by certain influence functions derived from micromechanical analysis of the plies and laminates. Applications describe stress relaxation in two carbon/epoxy laminates after cooling from the curing temperature and release of optimized fiber prestress, that allows maximum tensile load application while keeping both interior and free-edge stresses within prescribed strength limits. Subsequent viscoelastic deformation under constant rate loading, and stress relaxation caused by a sustained application of an elevated temperature to a laminate without prestress are also analyzed. Results are presented in the form of initial failure maps that identify overall stress states which may or may not initiate a specific damage mode in the laminate.

Transformation field analysis of damage evolution in composite materials

Evolution of distributed damage in heterogeneous solids is modeled using the transformation field analysis method (Proc. Roy. Soc. Lond. A (1992) 437, 311) and selected models of interface debonding in fibrous or particulate composites. In this approach, stress changes caused by local debonding under increasing overall loads are represented by residual stresses generated by damage-equivalent eigenstrains that act together with the applied mechanical loading program and physically based local transformation strains on an undamaged elastic aggregate. Interaction of the actual and equivalent eigenstrains with the mechanical loads at any state of damage is described by certain transformation influence functions; this provides explicit expressions for the local stress averages and the damage-induced enhancement of the overall compliance at any current damage state. Damage rates are then derived from a prescribed probability distribution of interface strength and local potential energy released by debonding. Numerical simulations of damage evolution in a glass/elastomer composite indicate which of these two conditions controls the process at different reinforcement densities and overall stress states. In general, the energy released by a single particle at a given overall stress decreases with increasing reinforcement density, and in proportion to particle size. Therefore, dense reinforcement by small-diameter particles or fibers should enhance resistance to inclusion debonding in composite systems.

ISOTHERMAL FATIGUE BEHAVIOR OF SIGMA/TIMETAL 21S LAMINATES, PART II: MODELING AND NUMERICAL ANALYSIS

Micromechanical modeling is employed to evaluate the stresses and strains in Sigma/ Timetal 2IS liminates under the isothermal fatigue conditions described in Part I [1], The effects of temperature and time variations on the constitutive response of the matrix and fiber are considered. Loading is limited to uniform in-plane stresses and to uniform changes in temperature. The local fields and macroscopic response of the plies are estimated with the finite-element method in conjunction with the transformation field analysis method, which utilizes overall elastic properties and transformation influence coefficients derived from the Mori-Tanaka model. Fiber debonding and sliding are modeled by modifying certain fiber elastic moduli. The results show that the inelastic deformation of the titanium matrix, assisted by extensive fiber debonding in the off-axis plies, promotes stress transfer to the fibers in the 0° plies. Under repeated loads, the fiber strain increase gradually at a certain rate, which depends on the applied load frequency. Regardless of lay up and hading frequency, the laminates fait when the overall axial strain reaches the critical value of (1 ± 0.1)%.

ASME 1992 Nadai Lecture—Micromechanics of Inelastic Composite Materials: Theory and Experiment

Some recent theoretical and experimental results on modeling of the inelastic behavior of composite materials are reviewed. The transformation field analysis method (G. J. Dvorak, Proc. R. Soc. London, Series A437, 1992, pp. 311–327) is a general procedure for evaluation of local fields and overall response in representative volumes of multiphase materials subjected to external thermomechanical loads and transformations in the phases. Applications are presented for systems with elastic-plastic and viscoelastic constituents. The Kroner-Budiansky-Wu and the Hill self-consistent models are corrected to conform with the generalized Levin formula. Recent experimental measurements of yield surfaces and plastic strains on thin-walled boron-aluminum composite tubes are interpreted with several micromechanical models. The comparisons show that unit cell models can provide reasonably accurate predictions of the observed plastic strains, while models relying on normality of the plastic strain increment vector to a single overall yield surface may not capture the essential features of the inelastic deformation process.