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At least 361 records · Page 20

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

Capturing the softening in T91 steel annealed with molten LBE through interfacial gradient plasticity

In order to study the effect of annealing with molten lead–bismuth eutectic alloy (mLBE) on the mechanical properties of T91 steel, micropillar compression tests were analyzed through the consideration of mechanical interface energy terms within gradient plasticity. The stress–strain curves of the micropillars showed significant stochastic effects, characterized by a different elastic and plastic behavior response for each pillar. Among the various pillars, some exhibited a similar trilinear behavior. Scanning electron microscopy (SEM) images of these specimens demonstrated localized slip deformation and slip planes after compression, while transmission electron microscopy (TEM) images showed the presence of a severe slip zone along the random grain boundaries (RGBs), indicating that the GBs played a dominant role in the deformation/slip. By employing interfacial gradient plasticity that can explicitly account for the presence of GBs, the trilinear response was captured, allowing for the determination of the mechanical interface parameter. As anticipated the pillars which underwent severe slip at the GBs had a lower value for the mechanical interface parameter. Finally, annealing with mLBE can, therefore, in some cases result in softening in the overall stress–strain, as it lowers the mechanical interface energy of GBs.

36 MATERIALS SCIENCE↗

Treatment of multiaxial creep-fatigue by strainrange partitioning

Strainrange partitioning is a recently developed method for treating creep-fatigue interaction at elevated temperature. Most of the work to date has been on uniaxially loaded specimens, where as practical applications often involve load multiaxiality. It is shown how the method can be extended to treat multiaxiality through a set of rules for combining the strain components in the three principal directions. Closed hysteresis loops, as well as plastic and creep strain ratcheting are included. An application to hold-time tests in torsion will be used to illustrate the approach.

S S Manson↗

Finite-element formulations for problems of large elastic-plastic deformation

An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.

Mcmeeking, R. M.↗

Dislocation density-based plasticity model from massive discrete dislocation dynamics database

In this work, we present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each slip system, and, equivalently, an exponential dependence of the plastic shear strain rate on the resolved shear stress. Hence the proposed generalized Taylor relation subsumes the Orowan relation for plastic flow. The DDD data also calls for a correction to the Kocks-Mecking model of dislocation multiplication to account for the increase of dislocation density on slip systems with negligible plastic shear strain rate. This is accomplished by allowing the multiplication rate on each slip system to include contributions from the plastic strain rates of the two coplanar slip systems. The resulting constitutive model successfully captures the strain hardening rate dependence on the loading orientation as predicted by the DDD simulations, which is also consistent with existing experiments.

36 MATERIALS SCIENCE↗

ACT University Collaboration Proposal: Role of manufacturing defects on material failure under dynamic loading for developing enhanced failure models and theories (Final Report)

Research on the tensile behavior of additively manufactured 316L stainless steel coupon specimens at increasing strain rates was conducted over the past year at Penn State. Dynamic loading rates into the 1000 1/s loading rates were performed on specimens with nearly 1.32” gage lengths. Stress-strain plots show ductile and plastic behavior well beyond 12% strain with necked specimens, having smaller effective gage lengths showing up to 56% ultimate strain. Additional tests performed on compact tension specimens helped with simulation work to understand the deformation behavior. Using finite elements, it was possible to determine the feasibility of a comprehensive experimental validation study towards an improved model for AM material failure – specifically, the Bai-Wierzbicki approach which accounts for lode angle and triaxiality. A non-significant number of tests are projected for eight specific failure nodes, with additional replicates to provide strain-rate capabilities to the existing formulation. One such correction factor is explored for quasi-static, notched specimens. Finally, stress intensity factor was explored using a set of compact-tension specimens which would also provide useful validation data for any simulation work.

36 MATERIALS SCIENCE↗

Incorporation of Damage and Failure into an Orthotropic Elasto-Plastic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in the composite impact models currently available in LS-DYNA(Registered Trademark) is under development. In particular, the material model, which is being implemented as MAT 213 into a tailored version of LS-DYNA being jointly developed by the FAA and NASA, incorporates both plasticity and damage within the material model, utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength), and is able to analyze the response of composites composed with a variety of fiber architectures. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. The capability to account for the rate and temperature dependent deformation response of composites has also been incorporated into the material model. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, in composites it has been found that loading in one direction can lead to damage in multiple coordinate directions. To account for this phenomena, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. The onset of material failure, and thus element deletion, is being developed to be a function of the stresses and plastic strains in the various coordinate directions. Systematic procedures are being developed to generate the required input parameters based on the results of experimental tests.

Finite Element Method↗

Elastic And Plastic Deformations In Butt Welds

Report presents study of mathematical modeling of stresses and strains, reaching beyond limits of elasticity, in bars and plates. Study oriented toward development of capability to predict stresses and resulting elastic and plastic strains in butt welds.

Verderaime, V.↗

High temperature low-cycle fatigue mechanisms in single crystals of nickel-based superalloy Mar-M 200

Twenty three high temperature low-cycle fatigue tests were conducted on single crystals of the nickel-based superalloy Mar-M 200. Tests were conducted at 760 and 870 C. SEM fractography and transmission electron microscopy were used to determine mechanisms responsible for the observed orientation dependent fatigue behavior. It has been concluded that the plastic characteristics of the alloy lead to orientation-dependent strain hardening and fatigue lives at 760 C. At 870 C, the elastic characteristics of the alloy dominated the behavior, even though the plastic strain ranges were about the same as they were at 760 C. This led to orientation-dependent fatigue lives, but the trends were not the same as they were at 760 C.

Milligan, W. W.↗

Plasticity - Theory and finite element applications.

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

Armen, H., Jr.↗

Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates

Here, this paper presents a novel formulation and its robust numerical implementation of strain-gradient (SG) crystal plasticity within a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. The resulting non-local SG-LS-EVPFFT formulation is used to model and understand the process of kink band formation during layer-parallel compression of nano-metallic laminates (NMLs). NMLs are layered composites with nanoscale thicknesses, thus requiring consideration of the interaction between dislocations and interfaces within the micromechanical model. The length-scale parameter of the SG model is calibrated by simulating a double pile-up and comparing predictions to analytical solution. This required new expressions for the defect energy, resulting in more accurate double pile-up predictions. The calibrated SG-LS-EVPFFT model is then used to simulate layer-parallel compression of copper-niobium NML. Formation of kink bands is predicted, and the model is used to rationalize the microscopic mechanisms enabling the formation process. It is found that accumulation of dislocations at interfaces leads to activation of layer-parallel slip, which in turn leads to kink band formation.

36 MATERIALS SCIENCE↗

Probabilistic analysis of structures involving random stress-strain behavior

The present methodology for analysis of structures with random stress strain behavior characterizes the uniaxial stress-strain curve in terms of (1) elastic modulus, (2) engineering stress at initial yield, (3) initial plastic-hardening slope, (4) engineering stress at point of ultimate load, and (5) engineering strain at point of ultimate load. The methodology is incorporated into the Numerical Evaluation of Stochastic Structures Under Stress code for probabilistic structural analysis. The illustrative problem of a thick cylinder under internal pressure, where both the internal pressure and the stress-strain curve are random, is addressed by means of the code. The response value is the cumulative distribution function of the equivalent plastic strain at the inner radius.

Millwater, H. R.↗

Biaxial load effects in fracture mechanics

It is found that the standard expressions for elastic stress and displacement in the crack-tip region (i.e., the so-called singular solution) cannot be considered to be approximations that are acceptable in a completely general sense. This conclusion is best illustrated by the instance of a biaxially loaded infinite sheet with a flat horizontal central crack, where the effect of load applied parallel to the plane of the crack appears entirely in the second terms of the series representations for local stresses and displacements. An elastoplastic finite-element analysis of the same biaxially loaded finite specimen geometry shows that the global energy release rate, the J-integral, the plastic stress and strain intensity factors (in the sense of Hilton and Hutchinson), and the size of the crack border region plastic yield, all have pronounced biaxial load dependence.

Liebowitz, H.↗

The effects of plasticity in adhesive fracture

An energy-balance analysis is presented for adhesive failure in end loaded cantilever beams. The analysis includes the effects of input work, stored strain energy, dissipated plastic energy, and specific adhesive surface energy. Experimental results obtained with 6061-T6 aluminum are presented as evidence for the validity of the approach.-

Chang, M. D.↗

Elastic-plastic analysis of AS4/PEEK composite laminate using a one-parameter plasticity model

A one-parameter plasticity model was shown to adequately describe the plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The elastic-plastic stress-strain relations of coupon specimens were measured and compared with those predicted by the finite element analysis using the one-parameter plasticity model. The results show that the one-parameter plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.

Sun, C. T.↗