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NASA NTRS1992

A differential CDM model for fatigue of unidirectional metal matrix composites

A multiaxial, isothermal, continuum damage mechanics (CDM) model for fatigue of a unidirectional metal matrix composite volume element is presented. The model is phenomenological, stress based, and assumes a single scalar internal damage variable, the evolution of which is anisotropic. The development of the fatigue damage model, (i.e., evolutionary law) is based on the definition of an initially transversely isotropic fatigue limit surface, a static fracture surface, and a normalized stress amplitude function. The anisotropy of these surfaces and function, and therefore the model, is defined through physically meaningful invariants reflecting the local stress and material orientation. This transversely isotropic model is shown, when taken to it's isotropic limit, to directly simplify to a previously developed and validated isotropic fatigue continuum damage model. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation in attempting to characterize a class of composite materials, and (2) the capability of the formulation in predicting anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Also, specific material parameters representing an initial characterization of the composite system SiC/Ti 15-3 and the matrix material (Ti 15-3) are reported.

Arnold, S. M.↗

DOE OSTI2025

Comparison of interlaminar damage modeling strategies for hybrid composite/aluminum laminates subjected to low-velocity impact

Low-velocity impact of hybrid metal-composite structures was investigated experimentally and computationally. Composite laminates consisting of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) were joined with a 6061-T6 aluminum plate using an epoxy adhesive. Two variations of the structure were studied; one consisting of all plies oriented at 0° and one consisting of all plies oriented at 45°. A drop tower was used to impact structures at a range of energies, including energies above and below the threshold at which the aluminum layer was perforated. Numerical simulations were implemented using Sierra/SM, an in-house transient dynamics finite element code developed at Sandia National Laboratories. A Hosford plasticity model was used to describe the response of the aluminum layer. A newly implemented orthotropic continuum damage mechanics (CDM) constitutive model was used to represent the composite laminate. This 3D-CDM model was compared to a cohesive zone model (2D-CDM/CZM) to investigate efficacy of aluminum perforation energy prediction, delamination prediction, and computational cost. Accuracy of each model was evaluated using the experimental results. Each showed good agreement with the tests for both the force and velocity histories, as well as the observed damage mechanisms. The 2D-CDM/CZM model was marginally more accurate in capturing both the composite and aluminum behavior — this model averaged error percentages of -11.2% and 10.8% for residual velocity and peak force, respectively. Meanwhile, the 3D-CDM model predictions yielded average error percentages of -35.5% (velocity) and 22.6% (force). However, the 3D-CDM model generally resulted in a decreased computational cost; the average run time was 14% shorter than the 2D-CDM/CZM model and 3x as many timesteps per hour were computed using the same computational resources. In conclusion, new experimental data on the impact and perforation resistance of metal-composite laminates is presented in addition to numerical predictions of the impact behavior.

Carbon fiber↗

DOE OSTI2021

A probabilistic creep model incorporating test condition, initial damage, and material property uncertainty

Uncertainty is prevalent in the creep resistance of alloys, where at elevated temperature and low pressure, rupture can range across logarithmic decades. In this study, a probabilistic continuum-damage-mechanics (CDM)-based model is derived to capture the uncertainty of creep resistance. To meet this objective, creep data for alloy 304 Stainless Steel is gathered. A constitutive model, “Sinh”, is calibrated deterministically to determine the statistical variability of the material properties. Three sources of uncertainty are injected into the model: test condition (stress and temperature), initial damage, and material properties. Probabilistic simulations are carried out by (a) calibrating probability distribution functions (pdfs) for each source of uncertainty (b) randomly sampling the pdfs using Monte Carlo methods and (c) executing simulations to replicate the uncertain creep behavior. A sensitivity analysis is performed to evaluate the relative effect of each source of uncertainty. In full probabilistic simulations, the cumulative uncertainty of creep behavior is evaluated. The probabilistic model accurately predicts the creep deformation and rupture of the available experiments. The probabilistic model is validated for interpolation but lacks extrapolation ability. Several future works are proposed to further improve the model.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A new woven composite constitutive model validated by shock wave experiments

In this paper, we present results of plate impact simulations of shock compressed woven glass fiber-reinforced plastic (GRP) performed using the Arbitrary Lagrangian–Eulerian three-dimensional finite element code. A hyperelastic large-strain-based empirical Continuum Damage Mechanics (CDM) formulation is employed to describe damage initiation and growth in the shock-compressed GRP. The model parameters calibration scheme utilizes the Velocity Interferometer System for Any Reflector normal particle velocity measurements at the free surface of the GRP target plates. The impact velocity in the experiments ranged from 8.5 to 418 m/s. The finite element model considered planar 0°/90° bidirectional plies with an individual ply thickness of 0.68 mm, stacked to reach a total laminate thickness of 6.8 mm. The anisotropic elastic strains were estimated from the experimentally determined tetragonal symmetry stiffness matrix for the GRP. The strain-based damage model captures several salient features observed in the measured free surface particle wave profiles, including the shock rise time, onset of Elastic—Elastic Cracking, and the shape of the nonlinear portion of the experimental particle velocity profiles. Furthermore, the CDM model predicts the dominant damage mode to be matrix microcracking due to shear and the associated bulk expansion (bulking) under the global compressive loading in the plate impact configuration.

42 ENGINEERING↗

DOE OSTI2022

Turn Your Half-Cut Cells for a Stronger Module

Here, we employ an existing model of crystalline silicon photovoltaic module cell fracture to explore the effect of cell size and orientation on their probability of fracture under module uniform loading. In addition, we also apply continuum damage mechanics to modify this model to consider the effect of cell fracture on the probability of subsequent cell fracture. We elucidate that cell fracture increases the probability of subsequent cell fracture and that rectangular modules containing half-cells aligned with the module's long orientation are much more robust against cell fracture than full-cell and half-cell short orientation modules.

14 SOLAR ENERGY↗

DOE OSTI2021

Damage Modeling of Solid Oxide Fuel Cells Accounting for Redox Effects

This work applies a multiscale mechanistic damage model developed for brittle ceramics and implemented in commercial finite element (FE) packages via user subroutines to study progressive damage in solid oxide fuel cells (SOFC) subjected to thermomechanical loading under normal operating and shutdown conditions including redox effects. The damage model captures the micromechanics of stiffness reduction due to material porosity change and microcracking and integrates the as-obtained stiffness reduction law into a continuum damage mechanics (CDM) formulation for the evolution of microcracks up to fracture. The volumetric “swelling” that occurs during redox is treated in constitutive modeling similarly to thermal expansion, but swelling strains are irreversible. Furthermore, this damage model was first validated through predictions of strength and stress-strain response for the SOFC electrode materials. Next, it has been applied to predict the potential for degradation in a generic planar SOFC stack with large active area cells. Multicell stack models were simulated in both co-flow and counter-flow configurations. In addition, a constant temperature redox cycle was also simulated to capture overall cell electrode damage due to volumetric swelling of the nickel (Ni)-based anode in the anode-supported cells.

25 ENERGY STORAGE↗

DOE OSTI2024

Numerical modeling and experimental validation of low velocity impact of woven GFRP/CFRP composites

Low-velocity impact of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composite laminates was studied experimentally and numerically. Hybrid laminates containing blocked layers of GFRP/CFRP/GFRP with all plies oriented at 0° were investigated. Relatively high impact energies were used to obtain full perforation of the laminate in a low-velocity impact setup. Numerical simulations were carried out using the in-house transient dynamics finite element code, Sierra/SM, developed at Sandia National Laboratories. A three-dimensional continuum damage model was used to describe the response of a woven composite ply. Two methods for handling delamination were considered and compared: (1) cohesive zone modeling and (2) continuum damage mechanics. The reduced model size achieved by omission of the cohesive zone elements produced acceptable results at reduced computational cost. Further, the comparison between different modeling techniques can be used to inform modeling decisions relevant to low velocity impact scenarios. The modeling was validated by comparing with the experimental results and showed good agreement in terms of predicted damage mechanisms and impactor velocity and force histories.

36 MATERIALS SCIENCE↗

NASA NTRS1988

A continuum damage model of fatigue-induced damage in laminated composites

A model is presented which predicts the stress-strain behavior of continuous fiber reinforced laminated composites in the presence of microstructural damage. The model is based on the concept of continuum damage mechanics and uses internal state variables to characterize the various damage modes. The associated internal state variable growth laws are mathematical models of the loading history induced development of microstructural damage. The model is demonstrated by using it to predict the response of damaged AS-4/3502 graphite/epoxy laminate panels.

Harris, Charles E.↗

NASA NTRS1989

Predictions of Poisson's ratio in cross-ply laminates containing matrix cracks and delaminations

A damage-dependent constitutive model for laminated composites has been developed for the combined damage modes of matrix cracks and delaminations. The model is based on the concept of continuum damage mechanics and uses second-order tensor valued internal state variables to represent each mode of damage. The internal state variables are defined as the local volume average of the relative crack face displacements. Since the local volume for delaminations is specified at the laminate level, the constitutive model takes the form of laminate analysis equations modified by the internal state variables. Model implementation is demonstrated for the laminate engineering modulus E(x) and Poisson's ratio nu(xy) of quasi-isotropic and cross-ply laminates. The model predictions are in close agreement to experimental results obtained for graphite/epoxy laminates.

Harris, Charles E.↗

NASA NTRS1990

Creep and creep rupture of strongly reinforced metallic composites

A creep and creep damage theory is presented for metallic composites with strong fibers. Application is to reinforced structures in which the fiber orientation may vary throughout but a distinct fiber direction can be identified locally (local transverse isotropy). The creep deformation model follows earlier work and is based on a flow potential function that depends on invariants reflecting stress and the material symmetry. As the focus is on the interaction of creep and damage, primary creep is ignored. The creep rupture model is an extension of continuum damage mechanics and includes an isochronous damage function that depends on invariants specifying the local maximum transverse tension and the maximum longitudinal shear stress. It is posited that at high temperature and low stress, appropriate to engineering practice, these stress components damage the fiber/matrix interface through diffusion controlled void growth, eventually causing creep rupture. Experiments are outlined for characterizing a composite through creep rupture tests under transverse tension and longitudinal shear. Application is made to a thin-walled pressure vessel with reinforcing fibers at an arbitrary helical angle. The results illustrate the usefulness of the model as a means of achieving optimal designs of composite structures where creep and creep rupture are life limiting.

Robinson, D. N.↗

NASA NTRS1990

A model for predicting damage induced fatigue life of laminated composite structural components

This paper presents a model for predicting the life of laminated composite structural components subjected to fatigue induced microstructural damage. The model uses the concept of continuum damage mechanics, wherein the effects of microcracks are incorporated into a damage dependent lamination theory instead of treating each crack as an internal boundary. Internal variables are formulated to account for the effects of both matrix cracks and internal delaminations. Evolution laws for determining the damage variables as functions of ply stresses are proposed, and comparisons of predicted damage evolution are made to experiment. In addition, predicted stiffness losses, as well as ply stresses are shown as functions of damage state for a variety of stacking sequences.

Allen, David H.↗

NASA NTRS1991

A continuum model for damage evolution in laminated composites

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

Lo, D. C.↗

NASA NTRS1998

Deterministic Multiaxial Creep and Creep Rupture Enhancements for CARES/Creep Integrated Design Code

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 rupture 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 sum, 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 Ns methodology and the CARES/Creep program.

Jadaan, Osama M.↗

NASA NTRS2003

Interface Finite Elements for the Analysis of Fracture Initiation and Progression

Progressive failure analyses (PFA) are important for the prediction of residual strength and damage tolerance of vehicle structures, and to predict the energy absorbing capability of vehicle structures under crash-type loads. Typically continuum damage mechanics (CDM) and fracture mechanics (FM) are the methods used for PFA. The method of interfacial damage mechanics (IDM) is used for PFA in this research. IDM has capabilities intermediate between CDM and FM, and is used to numerically model the initiation, growth, and arrest of cracks. IDM smooths the stress singularity at the crack tip, and is easily adaptable with other nonlinearties such as plasticity and material damage. IDM is implemented by user-defined interface elements in the ABAQUS/ Standard structural analysis software package. The structural components selected to demonstrate the effectiveness PFA using interface elements are, for the most part, those with published test data. These structural components were subjected to quasi-static loading in the tests. Thus, the ABAQUS analyses are used to predict geometrically and materially nonlinear equilibrium states. Impact loading, dynamic fracture, reflected stress waves, inertia, and time dependent material behavior are not considered.

Ambur, Damodar R.↗

NASA NTRS1998

A Damage-Dependent Finite Element Analysis for Fiber-Reinforced Composite Laminates

A progressive damage methodology has been developed to predict damage growth and residual strength of fiber-reinforced composite structure with through penetrations such as a slit. The methodology consists of a damage-dependent constitutive relationship based on continuum damage mechanics. Damage is modeled using volume averaged strain-like quantities known as internal state variables and is represented in the equilibrium equations as damage induced force vectors instead of the usual degradation and modification of the global stiffness matrix.

Coats, Timothy W.↗

NASA NTRS2012

Simulating the Response of a Composite Honeycomb Energy Absorber: Dynamic Crushing of Components and Multi-Terrain Impacts - Part 1

This paper describes the experimental and analytical evaluation of an externally deployable composite honeycomb structure that is designed to attenuate impact energy during helicopter crashes. The concept, designated the Deployable Energy Absorber (DEA), utilizes an expandable Kevlar (Registered Trademark) honeycomb to dissipate kinetic energy through crushing. The DEA incorporates a unique flexible hinge design that allows the honeycomb to be packaged and stowed until needed for deployment. Experimental evaluation of the DEA included dynamic crush tests of multi-cell components and vertical drop tests of a composite fuselage section, retrofitted with DEA blocks, onto multi-terrain. Finite element models of the test articles were developed and simulations were performed using the transient dynamic code, LSDYNA (Registered Trademark). In each simulation, the DEA was represented using shell elements assigned two different material properties: Mat 24, an isotropic piecewise linear plasticity model, and Mat 58, a continuum damage mechanics model used to represent laminated composite fabrics. DEA model development and test-analysis comparisons are presented.

Jackson, Karen E.↗

NASA NTRS2012

Macro Scale Independently Homogenized Subcells for Modeling Braided Composites

An analytical method has been developed to analyze the impact response of triaxially braided carbon fiber composites, including the penetration velocity and impact damage patterns. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. Currently, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. To determine the stiffness and strength properties required for the constitutive model, a top-down approach for determining the strength properties is merged with a bottom-up approach for determining the stiffness properties. The top-down portion uses global strengths obtained from macro-scale coupon level testing to characterize the material strengths for each subcell. The bottom-up portion uses micro-scale fiber and matrix stiffness properties to characterize the material stiffness for each subcell. Simulations of quasi-static coupon level tests for several representative composites are conducted along with impact simulations.

Blinzler, Brina J.↗

NASA NTRS2014

Adhesive Characterization and Progressive Damage Analysis of Bonded Composite Joints

The results of an experimental/numerical campaign aimed to develop progressive damage analysis (PDA) tools for predicting the strength of a composite bonded joint under tensile loads are presented. The PDA is based on continuum damage mechanics (CDM) to account for intralaminar damage, and cohesive laws to account for interlaminar and adhesive damage. The adhesive response is characterized using standard fracture specimens and digital image correlation (DIC). The displacement fields measured by DIC are used to calculate the J-integrals, from which the associated cohesive laws of the structural adhesive can be derived. A finite element model of a sandwich conventional splice joint (CSJ) under tensile loads was developed. The simulations indicate that the model is capable of predicting the interactions of damage modes that lead to the failure of the joint.

Girolamo, Donato↗