R. A. Brockman

Finite element simulation of laser shock peening

Abstract Laser shock peening is a technique similar to shot peening that imparts compressive residual stresses in materials for improved fatigue resistance. During a laser shock peening event, pressures well above the dynamic yield strength of the material are imparted on the target in a fraction of a microsecond. The severity of the loading causes local plastic deformation which ultimately results in the development of the favorable residual stresses. Finite element analysis techniques have been applied to predict the residual stress induced from laser shock peening. The analytical development, including the loading history and the elastic–plastic constitutive model, is discussed. Analysis results are presented and correlated with experimental data.

A viscoelastic–viscoplastic constitutive model for glassy polymers

A constitutive model is presented which combines nonlinear viscoelasticity and viscoplasticity into a unified set of equations suitable for multi-axial isotropic deformation. The model includes the effects of hydrostatic pressure, strain rate, and strain hardening which have been observed for thermoplastics in the glassy regime. The constitutive model is implemented into a finite element analysis program and appropriate parameters are identified for a polycarbonate. Capabilities of the model are demonstrated through the evaluation of a hard-body impact problem.

Dynamic characterization of compliant materials using an all-polymeric split Hopkinson bar

The split Hopkinson bar is a reliable experimental technique for measuring high strain rate properties of high-strength materials. Attempts to apply the split Hopkinson bar in measurement on more compliant materials, such as plastics, rubbers and foams, suffer from limitations on the maximum achievable strain and from high noise-to-signal ratios. The present work introduces and all-polymeric split Hopkinson bar (APSHB) experiment, which overcomes these limitations. The proposed method uses polymeric pressure bars to achieve a closer impedance match between the pressure bars and the specimen materials, thus providing both a low noise-to-signal ratio data and a longer input pulse for higher maximum strain. The APSHB requires very careful data reduction procedures because of the viscoelastic behavior of the incident and transmitter pressure bars. High-quality stress-strain data for a variety of compliant materials, such as polycarbonate, polyurethane foam and styrofoam, are presented.

Analysis of elastic-plastic deformation in TiAl polycrystals

Abstract A computational model is described for analyzing stress variations within polycrystals of γ-TiAl, including the effect of anisotropic yielding and small-scale plastic flow. Interlamellar (soft mode) slip behavior is controlled by a separate collection of slip systems whose properties are derived from measurements on polysynthetically twinned (PST) specimens. When used to represent several hundred randomly oriented material grains, the model provides distributions and statistical data about the local stress, strain, and plastic deformation resulting from a prescribed macroscopic loading.

Strength Prediction in Open Hole Composite Laminates by Using Discrete Damage Modeling

The present paper addresses the issue of direct simulation of complex local failure patterns in laminated composites. A model capable of discrete modeling of matrix cracking, delamination, and the interaction of these two damage modes is proposed. The analytical technique uses the eXtended Finite Element Method (X-FEM) for the simulation of matrix crack initiation and propagation at initially unknown locations, as well as a cohesive interface model for delamination. The model is capable of representing the complex kinematics of crack networks in composite laminates without previous knowledge of the crack locations or user intervention. An important feature of the technique is that it uses independently measured standard ply-level mechanical properties of the unidirectional composite (stiffness, strength, fracture toughness). Failure simulations of composites containing open holes are presented. Although the process of crack initiation is impossible to capture precisely due to local material variations, the proposed method exhibits excellent agreement with experimental data for matrix crack growth in unidirectional graphite-epoxy composites.

Relaxation of Shot-Peened Residual Stresses Under Creep Loading

Abstract : Shot peening is a commonly used surface treatment process that imparts compressive residual stresses into the surface of metal components. Compressive residual stresses retard initiation and growth of fatigue cracks. During the component loading history, loading, or during elevated temperature static loading, such as thermal exposure and creep. In these instances, taking full credit for compressive residual stresses would result in a methodical approach for characterizing and modeling residual stress relaxation under elevated temperature loading, near and above the monotonic yield strength of IN100. The model incorporates the dominant creep deformation mechanism, coupling between the creep and plasticity models, and effects of prior plastic strain. The initial room temperature residual stress and plastic strain profiles provide the initial conditions for relaxation predictions using the coupled creep-plasticity model. Model predictions correlate well with experimental results on shot-peened dogbone specimens subject to single cycle and creep loading conditions at elevated temperature.

On the use of the Blatz-Ko constitutive model in nonlinear finite element analysis

Abstract The nearly-incompressible material model proposed by Blatz and Ko (Trans. Soc. Rheol., 6, 223–251, 1962) is attractive for its simplicity, and is used currently in several finite element wave propagation codes. A form of the Blatz-Ko model suitable for use within static and implicit dynamic solutions is developed in this paper. Stress point equations for both stress and tangent modulus computations are given, and a typical implementation in FORTRAN is presented. The determination of material properties for the model from laboratory test data is also discussed.

Numerical models of orthotropic and lamellar grain structures

Abstract In this paper, a method for numerically estimating localized stress concentrations that arise in materials with anisotropic crystalline grains is described. This method is used to quantify stress variations within polycrystals of γ-TiAl, a material system composed of two phases of orthotropic material—lamellar colonies of TiAl/Ti 3 Al interspersed with small grains of pure TiAl. Effective elastic properties for the lamellar colonies are calculated from the constituent properties using a procedure developed for laminated orthotropic materials. It is postulated that the local anisotropy and differing orientations of adjacent grains of material can lead to microyielding at stresses below the mean yield strength of the material. The effects of local elastic anisotropy on stresses are presented as statistical variations in the stress distributions under simple states of loading. Three-dimensional (3D) and two-dimensional (2D) models are investigated.

High strain rate characterization of low-density low-strength materials

The Conventional Split Hopkinson Bar (CSHB) is a reliable experimental technique for measuring high strain rate properties of high-strength materials. Attempts to use the CSHB for similar measurements in more compliant materials, such as plastics and foams, are limited by the maximum achievable strain and high noise-to-signal ratios. This work introduces an all-polymeric split Hopkinson bar (APSHB) experiment, which overcomes these limitations. The proposed method uses polymeric pressure bars to achieve a closer impedance match between the pressure bars and the specimen materials, thus providing both low noise-to-signal ratio data and a longer input pulse for higher maximum strain. Data reduction procedures for APSHB that account for the viscoelastic behavior of the pressure bars are presented. Comparing the high strain rate response of 1100 Al obtained from CSHB and APSHB validates these procedures. Stress-strain data at strain rates of 500–2000/s for polycarbonate, polyurethane foam, and styrofoam are p...

Economical stiffness formulations for nonlinear finite elements

Abstract Element-level calculations often represent a significant part of the computing effort in a nonlinear finite element solution, especially when three-dimensional, higher-order elements are used. This paper explores some possibilities for increasing the efficiency of element computations within the general framework of a Newton-Raphson solution technique. A modified tangent stiffness formulation is introduced which provides relatively fast convergence without the extreme computational effort sometimes associated with the usual Newton-Raphson interaction. Numerical examples are used to illustrate the behavior of the method. The use of different types of element formulations within a single finite element mesh, according to the expected or observed degree of nonlinearity, is also identified as a means of reducing solution cost.