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NASA NTRS1991

Progressive failure methodologies for predicting residual strength and life of laminated composites

Two progressive failure methodologies currently under development by the Mechanics of Materials Branch at NASA Langley Research Center are discussed. The damage tolerance/fail safety methodology developed by O'Brien is an engineering approach to ensuring adequate durability and damage tolerance by treating only delamination onset and the subsequent delamination accumulation through the laminate thickness. The continuum damage model developed by Allen and Harris employs continuum damage laws to predict laminate strength and life. The philosophy, mechanics framework, and current implementation status of each methodology are presented.

Harris, Charles E.↗

NASA NTRS1995

Experimental Verification of a Progressive Damage Model for IM7/5260 Laminates Subjected to Tension-Tension Fatigue

The durability and damage tolerance of laminated composites are critical design considerations for airframe composite structures. Therefore, the ability to model damage initiation and growth and predict the life of laminated composites is necessary to achieve structurally efficient and economical designs. The purpose of this research is to experimentally verify the application of a continuum damage model to predict progressive damage development in a toughened material system. Damage due to monotonic and tension-tension fatigue was documented for IM7/5260 graphite/bismaleimide laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables to predict stiffness loss in unnotched laminates. A damage dependent finite element code predicted the stiffness loss for notched laminates with good agreement to experimental data. It was concluded that the continuum damage model can adequately predict matrix damage progression in notched and unnotched laminates as a function of loading history and laminate stacking sequence.

Coats, Timothy W.↗

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 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.↗

NASA NTRS2006

A Thermodynamically Consistent Damage Model for Advanced Composites

A continuum damage model for the prediction of damage onset and structural collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The principal damage mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a damage tensor that is fixed in space. Crack closure under load reversal effects are taken into account using damage variables established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different damage mechanisms occurring at the ply level. The constitutive damage model is implemented in a finite element code. The objectivity of the numerical model is assured by regularizing the dissipated energy at a material point using Bazant's Crack Band Model. To verify the accuracy of the approach, analyses of coupon specimens were performed, and the numerical predictions were compared with experimental data.

Maimi, Pere↗

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.↗

DOE OSTI2021

A predictive modeling tool for damage analysis and design of hydrogen storage composite pressure vessels

In this study, a predictive modeling tool is developed for damage analysis and design of hydrogen (H 2 ) storage composite pressure vessels. It integrates micromechanics of matrix cracking into a continuum damage mechanics (CDM) description for damage evolution, and three-dimensional (3D) finite element (FE) modeling of the vessel structural response. At the scale of the composite layer (mesoscale), the temperature-dependent stiffness reduction law in terms of the damage variable for transverse matrix cracking is computed using an Eshelby-Mori-Tanaka approach for the initial composite thermoelastic properties and a self-consistent model for the stiffness reduction as a function of the damage variable. While transverse matrix cracking obeying a damage evolution relation can progressively evolve from an initiation to a saturation state, fiber failure is predicted by a micromechanical fiber rupture criterion that accounts for the fiber strength and matrix stress. The implementation of this integrated multiscale modeling model into a 3D FE formulation enables damage analysis and design of H 2 storage composite pressure vessels. The developed tool is illustrated through 3D damage analyses of a cryogenically compressed H 2 storage vessel model subjected to thermomechanical loadings to investigate effects of the helical layer fiber orientation and loading scenario on damage development, vessel integrity and burst pressure.

08 HYDROGEN↗

DOE OSTI2021

A mechanistic damage model for solid oxide fuel cell ceramic materials - Part I: Constitutive modeling

A multiscale mechanistic damage model for solid oxide fuel cell (SOFC) ceramics that combines micromechanics of stiffness reduction due to material porosity change and microcracking with a continuum damage mechanics (CDM) description for the evolution of microcracks up to fracture is developed in this work. The model also accounts for volumetric swelling of the anode due to redox cycling. Porosity change and swelling during redox combined with normal operating thermomechanical loads could increase the stress, strain and damage distributions in SOFC stacks leading them to failure. The proposed model involves three governing parameters: (i) the porosity in terms of the pore or void volume fraction, (ii) material swelling magnitude prescribed at a given loading step, and (iii) the damage variable that describes microcracking caused by thermomechanical loads and swelling. Pores and microcracks in the ceramics are modeled as randomly distributed ellipsoidal inclusions with negligible stiffness by an Eshelby-Mori-Tanaka formulation combined with an inclusion orientation distribution method. Microcracking damage evolution is described by a CDM formulation. Volumetric swelling is treated in a similar way to thermal expansion in the constitutive relations. After validation and numerical checks, the damage model is used to analyze a simplified SOFC positive-electrode/electrolyte/negative-electrode (PEN) structure subjected a redox cycle in addition to thermomechanical loads experienced during normal operation of a SOFC stack.

30 DIRECT ENERGY CONVERSION↗

NASA NTRS2003

Optimal Battery Charging for Damage Mitigation

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

Hartley, Tom T.↗

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 NTRS2014

Simulating the Impact Response of Composite Airframe Components

In 2010, NASA Langley Research Center obtained residual hardware from the US Army's Survivable Affordable Repairable Airframe Program (SARAP). The hardware consisted of a composite fuselage section that was representative of the center section of a Black Hawk helicopter. The section was fabricated by Sikorsky Aircraft Corporation and designated the Test Validation Article (TVA). The TVA was subjected to a vertical drop test in 2008 to evaluate a tilting roof concept to limit the intrusion of overhead mass items, such as the rotor transmission, into the fuselage cabin. As a result of the 2008 test, damage to the hardware was limited primarily to the roof. Consequently, when the post-test article was obtained in 2010, the roof area was removed and the remaining structure was cut into six different types of test specimens including: (1) tension and compression coupons for material property characterization, (2) I-beam sections, (3) T-sections, (4) cruciform sections, (5) a large subfloor section, and (6) a forward framed fuselage section. In 2011, NASA and Sikorsky entered into a cooperative research agreement to study the impact responses of composite airframe structures and to evaluate the capabilities of the explicit transient dynamic finite element code, LS-DYNA®, to simulate these responses including damage initiation and progressive failure. Finite element models of the composite specimens were developed and impact simulations were performed. The properties of the composite material were represented using both a progressive in-plane damage model (Mat 54) and a continuum damage mechanics model (Mat 58) in LS-DYNA. This paper provides test-analysis comparisons of time history responses and the location and type of damage for representative I-beam, T-section, and cruciform section components.

Jackson, Karen E.↗

NASA NTRS2024

Impact Response of Thermoplastic Composites – Experiments and Modeling

This study investigates the impact response of thermoplastic composite materials. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK reinforced with T700G (T700/LMPAEK ). Several High Energy Dynamic Impact (HEDI) tests were performed wherein an aluminum projectile impacted T700/LMPAEK panels at different velocities. In the impact experiment studied herein, the projectile impacted the T700/LMAPEK panel at 73.2 m/s and rebounded. The ensuing damage to the T700/LMPAEK panel was characterized via ultrasonic C-scans, visualizing damage modes including matrix cracking and delaminations. Since the projectile rebounded, the fiber breakage damage mode was not evident. The impact event was modeled using a combined continuum damage mechanics and cohesive zone analysis approach with the commercially available hydrocode LS-DYNA®. The dynamic deformation and damage of the continuum, i.e., the plies in the T700/LMPAEK laminate, was modeled using a Deformation Gradient Decomposition (DGD) material model, i.e., MAT299 available within LS-DYNA. The interlaminar regions were treated as zero-thickness cohesive zones, wherein the dynamic delamination mechanics was modeled using a traction-separation formulation. Mixed-mode delamination growth was captured using the Benzegaggh-Kenane (B-K) traction-separation interpolation law. Strain-rate sensitivity of interlaminar fracture toughness was included using approximations based on published literature. The outcomes of the modeling effort are discussed herein which demonstrate good correlations with test data regarding panel deflection, panel-projectile interactions, damage modes and damage extent.

Impact modeling↗

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.↗

DOE OSTI2023

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

36 MATERIALS SCIENCE↗

NASA NTRS2018

Analysis of the Influence of Layer Shifting on the Elastic Response and Damage Nucleation and Growth in Woven Composite Laminates

The influence of relative layer shifting on the elastic and damage response of plain weave composite laminates is analyzed using a continuum damage mechanics approach in combination with the finite element method. First, the homogenized properties of the woven composite as a function of the number of layers and of layer shifting are presented. Next, the damage development in various shifting configurations is studied using different damage constitutive models for the matrix and the fiber bundles. It is shown that the impact of layer shifting on both the elastic response and the nonlinear damage response is significant. Most notably, the model captures changes in the damage mechanisms within the woven composite that occur due to layer shifting, resulting in stiffer, more brittle behavior, which has been shown experimentally in the literature. Model results in the linear and nonlinear regimes are shown to be consistent with both an independent analytical model and reported experiments.

layer shifting↗

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 NTRS2016

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

GMC↗

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.↗