Engineering topics

Robert K Goldberg

Publications and source records attributed to Robert K Goldberg.

10 records

NASA NTRS2024

Analytical Simulation of Effects of Local Mechanisms and Microstructure on Creep Response of Unidirectional Ceramic Matrix Composites

A micromechanics-based method has been developed to analyze the creep response of uncoated ceramic matrix minicomposites. Although the global stress level at which the creep response is analyzed is lower than the composite proportional limit, local stresses are assumed to be high enough that localized damage is present in the composite in the form of matrix microcracks. To model the composite creep response, including the effects of matrix cracking, a fiber shear lag-based methodology is employed. In this approach, stresses are assumed to vary in the fiber as a function of time and distance from the crack plane. The varying stresses are then used to compute the overall creep strain for the composite. Various assumptions regarding the level of matrix microcracking in the composite and the level of creep in the fiber and matrix in various portions of the composite unit cell are also examined. The creep response of the fiber is modeled using a linear Burgers model. The model is applied to a SiCf/SiC unidirectional minicomposite system. The computed creep results are compared to experimentally obtained values. The effects of the local fiber volume fraction on the overall creep response of the composite are also studied. This work will allow increased understanding of the key material damage mechanisms and load sharing that take place during creep conditions and can be expanded to provide improved analysis methods for full macrocomposites.

Micromechanics↗

NASA NTRS2021

Application of a Developmental Composite Material Model to Predict the Crush Response of Two Energy Absorbers

In 2012, a consortium was formed with the goal of creating a new composite material model capable of predicting the wide range of properties, accumulated damage behavior, and the many different types of failure in composites under impact loading. The material model was developed for execution in the commercially available nonlinear, explicit transient dynamic finite element code, LS-DYNA®. This material model incorporates three sub-models: deformation, damage, and failure. In addition, the model accounts for strain rate and temperature effects and relies heavily on the input of tabulated material response data. The model is designated *MAT_COMPOSITE_TABULATED_PLASTICITY_DAMAGE, or *MAT_213. Initially, *MAT_213 was developed for use with solid elements only; however, a thin shell element formulation for *MAT_213 has been adapted recently. The objective of this project was to find a suitable modeling example to investigate the capabilities and performance of *MAT_213. In 2012, two composite energy absorbers were designed and evaluated at NASA Langley Research Center through multi-level testing and simulation. The first was a conical-shaped energy absorber, designated the conusoid, which consisted of four layers of hybrid carbon-Kevlar® plain-weave fabric oriented at [+45°/-45°/-45°/+45°] with respect to the vertical direction. The second was a sinusoidal-shaped energy absorber, designated the sinusoid, which consisted of hybrid carbon-Kevlar® plain-weave fabric face sheets, two layers for each face sheet oriented at ±45° with respect to the vertical direction, and a closed-cell ELFOAM® P200 polyisocyanurate foam core. Finite element models were developed of the energy absorbers and simulations were performed using LS-DYNA®. In this paper, the development of a *MAT_213 model of a hybrid carbon-Kevlar® plain-weave fabric is presented. Next, comparisons with material characterization tests are presented. Then, test-analysis results are documented for each energy absorber as comparisons of time-history responses, as well as predicted and experimental structural deformations and progressive damage under impact loading using the *MAT_213 material model. Since a prior *MAT_58, or *MAT_LAMINATED_COMPOSITE_FABRIC material model was used in previous simulations of the energy absorbers, comparisons are made between *MAT_58 and *MAT_213 model predictions with test data. Finally, the paper includes a comprehensive list of “lessons learned,” in which a series of parametric studies are documented that were performed to investigate specific issues related to the material model. These “lessons learned” are included in hopes that they may help future *MAT_213 users.

crashworthiness, LS-DYNA transient dynamic simulat↗

NASA NTRS2021

Analytical Simulation of Effects of Local Mechanisms on Tensile Response of Ceramic Matrix Minicomposites

A micromechanics-based method based on a fiber shear lag analysis was developed to analyze the fast fracture response of uncoated ceramic matrix minicomposites. The model was applied to two SiCf/SiC minicomposite systems that were fabricated by Rolls-Royce and the University of Connecticut. The analysis approach accounts in an average sense for the fact that the cracks in an actual minicomposite often have an irregular geometry. The effects of local variations in the fiber volume ratio on the composite response was also investigated. Parametric studies were performed to investigate the effect of the interfacial shear stress, global fiber volume fraction and percentage of the composite that remains uncracked on the proportional limit stress and the composite secondary modulus. This work will facilitate an increased understanding of the key material mechanisms that take place during fast fracture loading.

Micromechanics Ceramic Matrix Composites Damage↗

NASA NTRS2020

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗

NASA NTRSDate not supplied

Analytical Simulation of the Effects of Local Mechanisms on the Tensile Response of CMC Minicomposites

A micromechanics-based method based on a fiber shear lag analysis was developed to analyze the fast fracture response of uncoated ceramic matrix minicomposites under room temperature conditions. The model was applied to two SiCf/SiC minicomposite systems that were fabricated by Rolls-Royce and the University of Connecticut. The analysis approach does not require the assumption that matrix cracks propagate along the entire width of the minicomposite. The ratio of the fiber slip length to the crack spacing was found to be a key parameter driving the stress level at which the proportional limit takes place and the secondary modulus. Parametric studies were performed to investigate the effect of interfacial shear stress, fiber volume fraction and percentage of the composite that remains uncracked on the proportional limit stress and the composite secondary modulus. This work will allow increased understanding of the key material mechanisms that take place during the fast fracture loading and can be expanded to provide improved analysis methods for full macro composites. simulations to simulations of a flat panel impact test, have been performed to fully exercise and evaluate the capabilities of the developed model.

Micromechanics↗

NASA NTRSDate not supplied

Lessons Learned and Best Practices for Utilizing a Generalized Composite Impact Model

A material model which incorporates several key capabilities which have been identified as lacking in currently available composite impact models has been developed. 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). It has been implemented into the commercially available transient dynamic finite element code LS-DYNA® as MAT_213. The model can simulate the nonlinear deformation, damage and failure that take place in a composite under dynamic loading conditions. As MAT_213 is now being used by a general user community that did not participate in the model development process, a number of issues have been identified that caused uncertainty in assembling a MAT_213 input deck and conducting a MAT_213 analysis. The overall goal of this effort is to develop a quantified set of lessons learned and best practices which will permit a new user to conduct useful MAT_213 simulations without needing to have detailed expert knowledge of the material model and its theoretical underpinnings.

Micromechanics↗

NASA NTRSDate not supplied

Experimental Characterization of Non-Associative Plasticity Flow Rule Coefficients and Post-Peak Stress Degradation for the LS-DYNA MAT213 Model

This project is focused on developing an experimental framework for characterizing non-associative plasticity flow rule coefficients through coupon-scale tests for the LS-DYNA MAT213 model. The main objective is to characterize these coefficients based on the multi-scale (i.e., both microscopic and macroscopic) full-field measurement of the evolution of strain and stress fields. This paper focuses on presenting the experimental work on characterizing the full-scale stress-strain curves of T700/LM-PAEK composites under tension, compression, and shear loads. The experimental data set was intended to build a deformation sub-model in the MAT213 model for the material. The strain data were collected using both microscopic and macroscopic digital image correlation techniques. The microscopic technique was particularly useful for fracture cases under small strains. A preliminary simulation result obtained from the MAT213 model is also presented in the paper. The experimental framework herein will be extended to characterize post-peak stress degradation in the composite material and to develop a damage sub-model for the material. This project will contribute to developing a simulation tool based on the MAT213 model for simulating the rate-dependent impact damage in composites under multi-axial loading.

MAT213↗

NASA NTRSDate not supplied

Application of the MAT 213 Composite Impact Model to NASA Problems of Interest

As composite materials are gaining increased use in aircraft components where impact resistance under high-energy impact conditions is important (such as the turbine engine fan case), the need for accurate material models to simulate the deformation, damage, and failure response of polymer matrix composites under impact conditions is becoming more critical.

Polymer Matrix Composites↗

NASA NTRSDate not supplied

Experimental Calibration of Flow Rule Coefficients for LS-Dyna Mat_213

Composite materials have become a popular choice in aerospace engineering applications due to their low weight, high specific stiffness, high specific energy absorption, and economic synthesis. As use of composite materials has proliferated, the need for accurate simulation under extreme loading conditions is of increasing importance. *MAT_213 is a tabulated plasticity and damage material model in LS-DYNA designed for such use cases. To account for the nonlinear material response, a plasticity algorithm is used, which employs a non-associative flow rule with coefficients requiring experimental calibration. This work outlines an experimental methodology for calibrating these coefficients using the macroscopic stress-strain response and microscopic in-plane strain measurements from coupon scale experiments. The model material used for the development and demonstration of this methodology is a plain weave woven fabric with T300 carbon fiber tows in the warp direction and Kevlar© 49 fiber tows in the weft direction, and an Epon© 828/Epikure© 3223 thermoset epoxy matrix. Coupon-scale tensile testing performed at multiple fiber angles (carbon fibers oriented 0º, 22.5º, 45º, 67.5º, and 90º relative to the loading axis) provides data for multiple calibration processes. The measured plastic strain increments in the principal material coordinate are used to set limits for ratios between flow rule coefficients. The identified ranges are used to bound the search for a set of coefficients, leading to convergence of different coupon responses in the effective stress – effective plastic strain space. Flow rule coefficients found by this methodology are then used as (i) input for LS-DYNA simulations of uniaxial tension coupon tests at varying fiber angles, and (ii) comparison of predicted values for the plastic Poisson’s ratio in global coordinates with the experimentally measured one for all off-axis orientations. These results are quantitatively and qualitatively compared to macroscopic stress-strain curves and experimental strain components. The conformity of the experimentally measured quantities with those derived from the simulations provide a means for assessing the quality of calibrated coefficients.

Polymer Matrix Composites↗

NASA NTRSDate not supplied

Practical Tips for Setting Up an LS-DYNA MAT_213 Analysis

Since 2012, NASA has actively contributed to the development and application of the LS-DYNA MAT_213 material model to predict responses under dynamic loading events. This presentation provides a high-level overview of MAT_213 and captures practical tips and suggestions for using it.

MAT_213↗