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Delamination micromechanics analysis

A three-dimensional finite element analysis was developed which includes elastoplastic, orthotropic material response, and fracture initiation and propagation. Energy absorption due to physical failure processes characteristic of the heterogeneous and anisotropic nature of composite materials is modeled. A local energy release rate in the presence of plasticity was defined and used as a criterion to predict the onset and growth of cracks in both micromechanics and macromechanics analyses. This crack growth simulation technique is based upon a virtual crack extension method. A three-dimensional finite element micromechanics model is used to study the effects of broken fibers, cracked matrix and fiber-matrix debond on the fracture toughness of the unidirectional composite. The energy release rates at the onset of unstable crack growth in the micromechanics analyses are used as critical energy release rates in the macromechanics analysis. This integrated micromechanical and macromechanical fracture criterion is shown to be very effective in predicting the onset and growth of cracks in general multilayered composite laminates by applying the criterion to a single-edge notched graphite/epoxy laminate subjected to implane tension normal to the notch.

Adams, D. F.↗

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗

J-integral estimates for cracks in infinite bodies

An analysis and discussion is presented of existing estimates of the J-integral for cracks in infinite bodies. Equations are presented which provide convenient estimates for Ramberg-Osgood type elastoplastic materials containing cracks and subjected to multiaxial loading. The relationship between J and the strain normal to the crack is noted to be only weakly dependent on state of stress. But the relationship between J and the stress normal to the crack is strongly dependent on state of stress. A plastic zone correction term often employed is found to be arbitrary, and its magnitude is seldom significant.

Dowling, N. E.↗

Constitutive modeling of cyclic plasticity and creep, using an internal time concept

Using the concept of an internal time as related to plastic strains, a differential stress-strain relation for elastoplasticity is rederived, such that (1) the concept of a yield-surface is retained; (2) the definitions of elastic and plastic processes are analogous to those in classical plasticity theory; and (3) its computational implementation, via a 'tangent-stiffness' finite element method and a 'generalized-midpoint-radial-return' stress-integration algorithm, is simple and efficient. Also, using the concept of an internal time, as related to both the inelastic strains as well as the Newtonian time, a constitutive model for creep-plasticity interaction, is discussed. The problem of modeling experimental data for plasticity and creep, by the present analytical relations, as accurately as desired, is discussed. Numerical examples which illustrate the validity of the present relations are presented for the cases of cyclic plasticity and creep.

Watanabe, O.↗

On the symbolic manipulation and code generation for elasto-plastic material matrices

A computerized procedure for symbolic manipulations and FORTRAN code generation of elastoplastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, the Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

Chang, T. Y.↗

An internal variable constitutive model for the large deformation of metals at high temperatures

The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.

Brown, Stuart↗

Method and models for R-curve instability calculations

This paper presents a simple method for performing elastic R-curve instability calculations. For a single material-structure combination, the calculations can be done on some pocket calculators. On microcomputers and larger, it permits the development of a comprehensive program having libraries of driving force equations for different configurations and R-curve model equations for different materials. The paper also presents several model equations for fitting to experimental R-curve data, both linear elastic and elastoplastic. The models are fit to data from the literature to demonstrate their viability.

Orange, Thomas W.↗

Polymer powder prepregging: Scoping study

Early on, it was found that NEAT LARC-TPI thermoplastic polyimide powder behaved elastoplastically at pressures to 20 ksi and temperatures to 260 degrees celcius (below MP). At high resin assay, resin powder could be continuously cold-flowed around individual carbon fibers in a metal rolling mill. At low resin assay (2:1, C:TPI), fiber breakage was prohibitive. Thus, although processing of TPI below MP would be quite unique, it appears that the polymer must be melted and flowed to produce low resin assay prepreg. Fiber tow was spread to 75 mm using a venturi slot tunnel. This allowed intimate powder/fiber interaction. Two techniques were examined for getting room temperature powder onto the room temperature fiber surface. Electrostatic powder coating allows the charged powder to cling tenaciously to the fiber, even while heated with a hot air gun to above its melt temperature. A variant of the wet slurry coating process was also explored. The carbon fibers are first wetted with water. Then dry powder is sprinkled onto the wet tow and doctor-rolled between the fibers. The wet structure is then taken onto a heated roll, with hot air guns drying and sinter-melting the powder onto the fiber surfaces. In both cases SEM shows individual fibers coated with powder particles that have melted in place and flowed along the fiber surface via surface tension.

Throne, James L.↗

Elastic-plastic crack analysis using a global-local approach on a parallel computer

A global-local finite-element analysis procedure is employed to solve elastoplastic crack problems. This procedure involves a global analysis using a coarse mesh and the subsequent locally refined analysis of a number of subregions. Parallel computation is involved in the local analyses. Numerical examples are performed on a MIMD parallel computer to demonstrate the time-saving capability of the proposed procedure.

Sun, C. T.↗

Numerical fracture simulation of bend specimens using a CTOD criterion

Stable crack growth in 50-mm-thick side-grooved three-point bend specimens of HY-130 steel is modeled numerically. A two-dimensional elastoplastic FEM formulation incorporating a CTOD fracture criterion is developed analytically, and the theoretical predictions are compared with experimental data in graphs. Good general agreement is obtained, except for the crack extension, which was typically overpredicted. The value of the J integral at crack initiation is found to be 83 kJ/sq m.

Shivakumar, K. N.↗

Finite element methods in fracture mechanics

Finite-element methodology specific to the analysis of fracture mechanics problems is reviewed. Primary emphasis is on the important algorithmic developments which have enhanced the numerical modeling of fracture processes. Methodologies to address elastostatic problems in two and three dimensions, elastodynamic problems, elastoplastic problems, special considerations for three-dimensional nonlinear problems, and the modeling of stable crack growth are reviewed. In addition, the future needs of the fracture community are discussed and open questions are identified.

Liebowitz, H.↗

Elasto-plastic finite element analyses of two-dimensional rolling and sliding contact deformation of bearing steel

An elastoplastic finite element analysis of repeated rolling-plus-sliding contact is presented for the elastic-linear-kinematic hardening-plastic properties of hardened bearing steel at room temperature. Contacts in the absence of frictional heating are found to produce peak cyclic strain ranges and residual stresses that are similar to the values obtained for pure rolling. For the cases considered, the energy dissipated as heat by plastic deformation is found to be 3-15 percent of the energy dissipated at the surface by friction.

Kumar, A. M.↗

Symbolic derivation of material property matrices in finite element analysis

The principles and operation of MMAX, a symbolic-computation program which automates the process of generating property matrices for structural materials, are briefly described and illustrated with sample analyses of a rubberlike material and an elastoplastic material. MMAX is written in LISP under the symbolic finite-element generator FINGER and the general symbolic manipulator MACSYMA; it first derives the formulas required by mathematical manipulation, and then translates the formulas into FORTRAN code, adapted to the particular type of machine to be used for the numerical calculations. This approach is shown to combine efficiently the advantages of symbolic and numerical computation for engineering applications.

Tan, H. Q.↗

Three-dimensional aspects of plasticity-induced fatigue crack closure

A three-dimensional elastoplastic finite element analysis of fatigue crack growth and closure in a center-crack tension specimen was performed in order to investigate the crack opening stress as a function of specimen thickness under constant amplitude loading conditions. Elastic-perfectly plastic conditions were assumed and cycle loading was kept at R = 0.1. Firstly, by imposing proper boundary conditions on the three-dimensional model, a plane strain analysis was carried out. The ratio of stabilized opening stress over the maximum applied stress under plane strain conditions was found to be 0.28. Secondly, the model thickness was varied under fully three-dimensional conditions, and crack-opening stresses were determined for each specimen thickness. The crack-opening stress is found to vary through the thickness for the center crack tension specimen. On the specimen surface and in the midplane the crack-opening stress levels tend to two-dimensional solutions for plane stress and plane strain conditions, respectively.

Chermahini, R. G.↗

Surface-crack growth: Models, experiments, and structures; Proceedings of the Symposium, Sparks, NV, Apr. 25, 1988

The present volume on surface-crack growth modeling, experimental methods, and structures, discusses elastoplastic behavior, the fracture analysis of three-dimensional bodies with surface cracks, optical measurements of free-surface effects on natural surfaces and through cracks, an optical and finite-element investigation of a plastically deformed surface flaw under tension, fracture behavior prediction for rapidly loaded surface-cracked specimens, and surface cracks in thick laminated fiber composite plates. Also discussed are a novel study procedure for crack initiation and growth in thermal fatigue testing, the growth of surface cracks under fatigue and monotonically increasing load, the subcritical growth of a surface flaw, surface crack propagation in notched and unnotched rods, and theoretical and experimental analyses of surface cracks in weldments.

Reuter, Walter G.↗

Advanced applications of BEM to inelastic analysis of solids

Newly evolved boundary element solution algorithms are utilized for solving a range of elastoplastic and thermoplastic problems. The first algorithm is the typical iterative procedure in which the unknown boundary solution and the initial stress (or strain) rates are found together in an incremental iterative fashion. The second one is a variable stiffness type approach in which the incremental boundary solution is obtained in a direct (noniterative) manner. The third procedure differs from the two prior algorithms in that volume integration is not needed to incorporate the nonlinear effects in the analysis. Instead, initial stress rates are introduced in the boundary element system by way of particular integrals. The methodology is used in a general purpose, multiregion system that employs quadratic isoparametric shape functions to model the geometry and field variables of the body and can admit up to 15 substructured areas of different material properties.

Banerjee, P. K.↗

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

Banerjee, P. K.↗

Analytical and computational models of shells; Proceedings of the Symposium, ASME Winter Annual Meeting, San Francisco, CA, Dec. 10-15, 1989

Topics presented include asymptotic analysis and computation for shells, the edge effects in the Reissner-Mindlin plate theory, nonlinear problems of geometrically exact shell theories, and developments in variational methods for high performance plate and shell elements. Also presented are an assumed strain solid element model for geometrically nonlinear shell analysis, shell finite elements with six degrees of freedom per node, hierarchic plate and shell models based on p-extension, and a simple shell element formulation for large-scale elastoplastic analysis. Also discussed are the assessment of computational models for multilayered composite cylinders, shell models for impact analysis, analysis of shell structures subjected to contact-impacts, and the application of shell theory to cardiac mechanics.

Noor, Ahmed K.↗