Evan J. Pineda

Numerical Implementation of a Multiple-ISV Thermodynamically-Based Work Potential Theory for Modeling Progressive Damage and Failure in Fiber-Reinforced Laminates

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, referred to as enhanced Schapery theory, utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening, resulting in a negative tangent stiffness. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening characterized through a negative tangent stiffness) results in pathologically mesh dependent solutions within a finite element (FE) framework. Therefore, consistent characteristic lengths are introduced into the formulation to govern the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs are derived. The theory is implemented in association with the commercial FE software, Abaqus. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FE mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared against the experimental results.

Multiscale Modeling of Ceramic Matrix Composites

Results of multiscale modeling simulations of the nonlinear response of SiC/SiC ceramic matrix composites are reported, wherein the microstructure of the ceramic matrix is captured. This micro scale architecture, which contains free Si material as well as the SiC ceramic, is responsible for residual stresses that play an important role in the subsequent thermo-mechanical behavior of the SiC/SiC composite. Using the novel Multiscale Generalized Method of Cells recursive micromechanics theory, the microstructure of the matrix, as well as the microstructure of the composite (fiber and matrix) can be captured.

Combining material and model pedigree is foundational to making ICME a reality

With the increased emphasis on reducing the cost and time to market of new materials, the need for analytical tools that enable the virtual design and optimization of materials throughout their processing-internal structure-property-performance envelope, along with the capturing and storing of the associated material and model information across its life cycle, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality, and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. Fortunately, materials information management systems and physics-based multiscale modeling methods have kept pace with the growing user demands. Herein, recent efforts to identify best practices associated with these user demands and key principles for the development of a robust materials information management system will be discussed. The goals are to enable the connections at various length scales to be made between experimental data and corresponding multiscale modeling toolsets and, ultimately, to enable ICME to become a reality. In particular, the NASA Glenn Research Center efforts towards establishing such a database (for combining material and model pedigree) associated with both monolithic and composite materials as well as a multiscale, micromechanics-based analysis toolset for such materials will be discussed.

A Novel Multiscale Physics Based Progressive Failure Methodology for Laminated Composite Structures

A variable fldelity, multiscale, physics based flnite element procedure for predicting progressive damage and failure of laminated continuous flber reinforced composites is introduced. At every integration point in a flnite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the micro-scale in two difierent FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.

Progressive Damage and Failure Prediction of Open Hole Tension and Open Hole Compression Specimens

Progressive damage and failure in open hole composite laminate coupons under tensile and compressive loading conditions is modeled using Enhanced Schapery Theory (EST). The input parameters required for EST are obtained using standard coupon level test data and are interpreted in conjunction with finite element (FE) based simulations. The capability of EST to perform the open hole strength prediction accurately is demonstrated using three different layups of IM7/8552 carbon fiber composite. A homogenized approach uses a single composite shell element to represent the entire laminate in the thickness direction and this requires the fiber direction fracture toughness to be modeled as a laminate property. The results obtained using the EST method agree quite well with experimental results.

Computational Implementation of a Thermodynamically Based Work Potential Model for Progressive Microdamage and Transverse Cracking in Fiber-reinforced Laminates

A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.

Multiscale Model for Progressive Damage and Failure of Laminated Composites Using an Explicit Finite Element Method

Initial development of a multiscale progressive damage and failure analysis tool for laminated composite structures is presented. The method models microdamage at the lamina level with the thermodynamically based Schapery Theory. Transverse cracking and ber breakage, considered failure mechanisms in this work, are modeled with failure criteria evaluate at the micro-constituent level using the Generalized Method of Cells. This model is implemented using ABAQUS/Explicit nite element software and MAC/GMC Suite of Micromechanics Codes. Load versus displacement and local strain gage results for two center-notched laminates are compared against results using ABAQUS/Standard and experimental data. Furthermore, damage and failure paths are compared to C-scans and photographs of failed specimens.

Simulation of Lightning-Induced Delamination in Un-protected CFRP Laminates

Lightning is a major cause of damage in laminated composite aerospace structures during flight. The most significant failure mode induced by lightning is delamination, which might extend well beyond the visible damage zone, and requires sophisticated techniques and equipment to detect. Therefore, it is crucial to develop a numerical tool capable of predicting the damage zone induced from a lightning strike to minimize costly repair acreage and supplement extremely expensive lightning experiments. Herein, a detailed numerical study consisting of a multidirectional composite with user-defined, temperature-dependent, interlaminar elements subjected to a lightning strike is designed, and delamination/damage expansion is studied under specified conditions. It is observed both the size and shape of the delamination zone are strongly dependent on the assumed temperature-dependent fracture toughness; the primary parameter controlling lightning-induced delamination propagation. An accurate estimation of the fracture toughness profile is crucial in order to have a reliable prediction of the delamination zone and avoid sub-critical structural failures.

A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals

A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, the stand-alone GMC is applied for studying simple material microstructures such as a repeating unit cell (RUC) containing single grain or two grains under uniaxial loading conditions. For verification, the results obtained by the stand-alone GMC are compared to those from an analogous FEA model incorporating the same single crystal plasticity constitutive model. This verification is then extended to samples containing tens to hundreds of grains. The results demonstrate that the GMC homogenization combined with the crystal plasticity constitutive framework is a promising approach for failure analysis of structures as it allows for properly predicting the von Mises stress in the entire RUC, in an average sense, as well as in the local microstructural level, i.e., each individual grain. Two–three orders of saving in computational cost, at the expense of some accuracy in prediction, especially in the prediction of the components of local tensor field quantities and the quantities near the grain boundaries, was obtained with GMC. Finally, the capability of the developed multiscale model linking FEA and GMC to solve real-life-sized structures is demonstrated by successfully analyzing an engine disc component and determining the microstructural scale details of the field quantities.

Microstructural Influence on Deformation and Fatigue Life of Composites Using the Generalized Method of Cells

:Afully!coupleddeformationanddamage!approachtomodeling!the!response!of!composite!materials!and!composite!laminates!is!presented.!!It!is!based!on!the!semi9analytical!generalized!method!of!cells!(GMC)!micromechanics!model!as!well!as!its!higher!fidelity!counterpart,!HFGMC,!bothof!which!provide!closed9form!constitutive!equations!forcomposite!materials!as!well!as!the!micro!scale!stress!and!strain!fieldsin!the!composite!phases.!!The!provided!constitutive!equationsallow!GMC!and!HFGMC!to!function!within!a!higherscale!structural!analysis!(e.g.,!finite!elementanalysis!or!laminationtheory)!torepresenta!composite!material!point,!while!the!availability!ofthe!micro!fields!allow!the!incorporation!oflower! scale! sub9models! to! represent! local! phenomena! in! the! fiber! and! matrix.! !Further,! GMC’s!formulation!performs!averaging!when!applying!certain!governing!equations!such!that!some!degree!of!microscale!field!accuracy!issurrendered!in!favor!of!extreme!computational!efficiency,!rendering!the!method!quite!attractive!as!the!centerpiece!in!a!integrated!computationalmaterialengineering!(ICME)!structural! analysis;! whereas HFGMC!retains!this! microscale! field! accuracy,!but! at! the! price! of!significantly!slower!computational!speed.!Herein,!the!sensitivity!of!deformationandthe!fatigue!life!of!graphite/epoxy!PMC! composites, with! both! ordered! and! disordered! microstructures,!has! beeninvestigated!using!this!coupled!deformation!and!damage!micromechanics!based!approach.!!Thelocal!effects!of!fiberbreakage!and!fatiguedamage!areincluded!as!sub9models!that!operate!onthe!microscale!forthe!individual!composite!phases.!!Foranalysis!of!laminates,!classical!lamination!theory!is!employed!as!theglobal!or!structural!scalemodel,!whileGMC/HFGMC!is!embedded!to!operateon!themicroscale!to!simulate!the!behavior!of!the!composite!material!withineachlaminate!layer.!!Akey!outcome!of!this!study!isthe!statistical!influence!of!microstructure!and!micromechanics!idealization!(GMC!or!HFGMC)!on!the!overall!accuracy!of!unidirectional!andlaminatedcomposite!deformation!and!fatigue!response.!!