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Development of a Continuum Damage Mechanics Material Model of a Graphite-Kevlar(Registered Trademark) Hybrid Fabric for Simulating the Impact Response of Energy Absorbing Kevlar(Registered Trademark) Hybrid Fabric for Simulating the Impact Response of Energy Absorbing

This paper describes the development of input properties for a continuum damage mechanics based material model, Mat 58, within LS-DYNA(Registered Trademark) to simulate the response of a graphite-Kevlar(Registered Trademark) hybrid plain weave fabric. A limited set of material characterization tests were performed on the hybrid graphite-Kevlar(Registered Trademark) fabric. Simple finite element models were executed in LS-DYNA(Registered Trademark) to simulate the material characterization tests and to verify the Mat 58 material model. Once verified, the Mat 58 model was used in finite element models of two composite energy absorbers: a conical-shaped design, designated the "conusoid," fabricated of four layers of hybrid graphite-Kevlar(Registered Trademark) fabric; and, a sinusoidal-shaped foam sandwich design, designated the "sinusoid," fabricated of the same hybrid fabric face sheets with a foam core. Dynamic crush tests were performed on components of the two energy absorbers, which were designed to limit average vertical accelerations to 25- to 40-g, to minimize peak crush loads, and to generate relatively long crush stroke values under dynamic loading conditions. Finite element models of the two energy absorbers utilized the Mat 58 model that had been verified through material characterization testing. Excellent predictions of the dynamic crushing response were obtained.

Jackson, Karen E.

Multiscale Fiber Kinking: Computational Micromechanics and a Mesoscale Continuum Damage Mechanics Models

In this work, the fiber kinking phenomenon, which is known as the failure mechanism that takes place when a fiber reinforced polymer is loaded under longitudinal compression, is studied. A computational micromechanics model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking based on the deformation gradient decomposition (DGD) and the LaRC04 failure criteria.

Herraez, Miguel

Quantification of Error Associated with Using Misaligned Meshes in Continuum Damage Mechanics Material Models for Matrix Crack Growth Predictions in Composites

The ability of a material model to capture in-plane matrix mode I and mode II crack growth is an essential component for modeling ply level damage evolution in composite structures. Previous studies using a continuum damage mechanics (CDM) approach have shown success in satisfying benchmark solutions for mode I and II crack growth. However, success was shown using a fiber-aligned meshing strategy, which encourages matrix cracks to propagate in a single band of elements, along the fiber direction. Generating a fiber-aligned mesh becomes a highly involved process for laminates including off-axis (non 0° or 90°) plies. The objective of this study is to quantify the effect of non-fiber aligned mesh discretization on predictions of in-plane matrix crack propagation. The approach taken incrementally varies the mesh orientation angle relative to the fiber orientation; more specifically, misaligned meshes are used to quantify the effect of element angle orientation relative to the initial crack orientation on the energy released during matrix crack propagation simulations using a CDM method. CDM solutions obtained with the misaligned meshes are evaluated against known benchmarks for mode I and II matrix crack growth. The CDM solutions reveal a near-polynomial trend of increased predicted failure stress with increased mesh misalignment angle; hence implying a potential relationship between element orientation angle and apparent fracture toughness.

Justusson, Brian

Time dependent reliability model incorporating continuum damage mechanics for high-temperature ceramics

Presently there are many opportunities for the application of ceramic materials at elevated temperatures. In the near future ceramic materials are expected to supplant high temperature metal alloys in a number of applications. It thus becomes essential to develop a capability to predict the time-dependent response of these materials. The creep rupture phenomenon is discussed, and a time-dependent reliability model is outlined that integrates continuum damage mechanics principles and Weibull analysis. Several features of the model are presented in a qualitative fashion, including predictions of both reliability and hazard rate. In addition, a comparison of the continuum and the microstructural kinetic equations highlights a strong resemblance in the two approaches.

Duffy, Stephen F.

Deterministic and Probabilistic Creep and Creep Rupture Enhancement to CARES/Creep: Multiaxial Creep Life Prediction of Ceramic Structures Using Continuum Damage Mechanics and the Finite Element Method

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep ripture criterion However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of stress, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions This creep life prediction methodology was preliminarily added to the integrated design code CARES/Creep (Ceramics Analysis and Reliability Evaluation of Structures/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of this methodology and the CARES/Creep program.

Jadaan, Osama M.

Crack layer theory

A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.

Chudnovsky, A.

Crack layer theory

A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.

Chudnovsky, A.

Application of a novel finite difference method to dynamic crack problems

A versatile finite difference method (HEMP and HEMP 3D computer programs) was developed originally for solving dynamic problems in continuum mechanics. It was extended to analyze the stress field around cracks in a solid with finite geometry subjected to dynamic loads and to simulate numerically the dynamic fracture phenomena with success. This method is an explicit finite difference method applied to the Lagrangian formulation of the equations of continuum mechanics in two and three space dimensions and time. The calculational grid moves with the material and in this way it gives a more detailed description of the physics of the problem than the Eulerian formulation.

Chen, Y. M.

Space-Time Conservation Element and Solution Element Method Being Developed

The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically reacting flows.

Chang, Sin-Chung

Continuum Damage Mechanics Used to Predict the Creep Life of Monolithic Ceramics

Significant improvements in propulsion and power generation for the next century will require revolutionary advances in high-temperature materials and structural design. Advanced ceramics are candidate materials for these elevated temperature applications. High-temperature and long-duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. An analytical methodology in the form of the integrated design program-Ceramics Analysis and Reliability Evaluation of Structures/Creep (CARES/Creep) has been developed by the NASA Lewis Research Center to predict the life of ceramic structural components subjected to creep rupture conditions. This program utilizes commercially available finite element packages and takes into account the transient state of stress and creep strain distributions (stress relaxation as well as the asymmetric response to tension and compression). The creep life of a component is discretized into short time steps, during which the stress distribution is assumed constant. Then, the damage is calculated for each time step on the basis of a modified Monkman-Grant (MMG) creep rupture criterion. The cumulative damage is subsequently calculated as time elapses in a manner similar to Miner's rule for cyclic fatigue loading. Failure is assumed to occur when the normalized cumulative damage at any point in the component reaches unity. The corresponding time is the creep rupture life for that component.

Powers, Lynn M.

Low-Velocity Impact Analyses of Composite Panels Using Cohesive Zone Modeling and Continuum Damage Mechanics

A parametric study was conducted to gage the sensitivity of simulations of low-velocity impacts on laminated composite panels to various finite element model and material model features. The material model used in this parametric study was previously verified and validated for conducting progressive damage analyses of post-buckled composite structures subjected to quasi-static loading conditions. Based on the results of this parametric study, updates have been made to a progressive damage analysis material model and the best practices for its application. Experimental results are compared to computational results obtained with and without the updates to the models. Both thermoset and thermoplastic fiber-reinforced materials are considered. The resulting enhancements to the material model are presented in detail.

Frank A Leone

Low-Velocity Impact Analyses of Composite Panels Using Cohesive Zone Modeling and Continuum Damage Mechanics

A parametric study was conducted to gage the sensitivity of simulations of low-velocity impacts on laminated composite panels to various finite element model and material model features. The material model used in this parametric study was previously verified and validated for conducting progressive damage analyses of post-buckled composite structures subjected to quasi-static loading conditions. Based on the results of this parametric study, updates have been made to a progressive damage analysis material model and the best practices for its application. Experimental results are compared to computational results obtained with and without the updates to the models. Both thermoset and thermoplastic fiber-reinforced materials are considered. The resulting enhancements to the material model are presented in detail.

Frank Leone