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NASA NTRS2015

3D Progressive Damage Modeling for Laminated Composite Based on Crack Band Theory and Continuum Damage Mechanics

A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.

Wang, John T.↗

NASA NTRS2018

Implementation of a Matrix Crack Spacing Parameter in a Continuum Damage Mechanics Finite Element Model

Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.

Hyder, Imran↗

NASA NTRS1982

Pre- and post-annealing of mechanical damage in silicon wafers

Basic properties of mechanical damage in silicon consisting of cracks and abrasion were studied using transmission electron microscopy. The crystallographic structure of mechanical damage was determined before and after high temperature annealing. The main findings include that stresses in silicon around crack tips are not plastically relieved at room temperature and that abrasion at room temperature introduces shear loops into the silicon. It was also found that cracks of micron size can be annealed out, specifically, if cleavage occurs on 111 planes. The healing products of such cracks are 60 deg and 90 deg dislocations. Submicron cracks transform into stacking faults during annealing. Likewise high concentrations of shear loops due abrasion were found to anneal into stacking faults. A one to one correlation between surface areas containing small cracks and stacking faults was made. Measurements of damage removal on silicon surfaces through chemical-mechanical etching techniques are presented. It is shown that silicon dioxide repolishes damaged silicon surfaces most effectively.

Schwottke, G. H.↗

NASA NTRS1996

Recent Advances in Composite Damage Mechanics

The state of the art and recent developments in the field of composite material damage mechanics are reviewed, with emphasis on damage accumulation. The kinetics of damage accumulation are considered with emphasis on the general accumulation of discrete local damage events such as single or multiple fiber fractures or microcrack formation. The issues addressed include: how to define strength in the presence of widely distributed damage, and how to combine mechanical representations in order to predict the damage tolerance and life of engineering components. It is shown that a damage mechanics approach can be related to the thermodynamics of the damage accumulation processes in composite laminates subjected to mechanical loading and environmental conditions over long periods of time.

Reifsnider, Ken↗

NASA NTRS2011

Continuum Damage Mechanics Models for the Analysis of Progressive Failure in Open-Hole Tension Laminates

The performance of a state-of-the-art continuum damage mechanics model for interlaminar damage, coupled with a cohesive zone model for delamination is examined for failure prediction of quasi-isotropic open-hole tension laminates. Limitations of continuum representations of intra-ply damage and the effect of mesh orientation on the analysis predictions are discussed. It is shown that accurate prediction of matrix crack paths and stress redistribution after cracking requires a mesh aligned with the fiber orientation. Based on these results, an aligned mesh is proposed for analysis of the open-hole tension specimens consisting of different meshes within the individual plies, such that the element edges are aligned with the ply fiber direction. The modeling approach is assessed by comparison of analysis predictions to experimental data for specimen configurations in which failure is dominated by complex interactions between matrix cracks and delaminations. It is shown that the different failure mechanisms observed in the tests are well predicted. In addition, the modeling approach is demonstrated to predict proper trends in the effect of scaling on strength and failure mechanisms of quasi-isotropic open-hole tension laminates.

Song, Kyonchan↗

NASA NTRS1994

Experimental verification of a progressive damage model for composite laminates based on continuum damage mechanics

Progressive failure is a crucial concern when using laminated composites in structural design. Therefore the ability to model damage and predict the life of laminated composites is vital. The purpose of this research was to experimentally verify the application of the continuum damage model, a progressive failure theory utilizing continuum damage mechanics, to a toughened material system. Damage due to tension-tension fatigue was documented for the IM7/5260 composite laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables, respectively, to predict stiffness loss. A damage dependent finite element code qualitatively predicted trends in transverse matrix cracking, axial splits and local stress-strain distributions for notched quasi-isotropic laminates. The predictions were similar to the experimental data and it was concluded that the continuum damage model provided a good prediction of stiffness loss while qualitatively predicting damage growth in notched laminates.

Coats, Timothy William↗

NASA NTRS2020

Analysis of Open Hole Compression Specimens Using the CompDam Continuum Damage Mechanics Model

This report documents a validation study on the standard Open Hole Compression (OHC) laminate test specimen conducted as part of the NASA Advanced Composites Project (ACP). Tests were conducted on OHC specimens with hard, quasi-isotropic, and soft layups using digital image correlation and X-Ray computed tomography to capture the structural response and damage evolution. Progressive damage models were constructed for use with the CompDam continuum damage mechanics code following the best practices established during the ACP. Detailed interrogation of the analysis results and comparison with experimental measurements provide a basis for assessing the capability of the modeling approach for OHC. The structural response is found to be captured well, with strengths predicted within 3\% of the experimental values for hard and quasi-isotropic laminates. In the soft laminate, the model predicts failure to be more brittle than the nonlinear, ductile response that was measured. Damage states extracted from the models at the same load level as test measurements are overlaid to show directly the similarities and differences between test and analysis results. Studying the damage evolution predicted by the analysis reveals that the failure process is a competition between fiber damage and delamination/sub-laminate buckling, with fiber damage dominating the collapse in the hard laminate and sub-laminate buckling governing in the soft laminate. Finally, a series of parametric studies varying numerical solution parameters (mesh size, mass scaling) and physical properties (fiber direction compressive strength and toughness) reveal sensitivities and deficiencies of the model. To the authors' knowledge, this study is the first for OHC specimens to include detailed evaluation of damage mode interactions, direct overlay of predicted and measured damage states, and sensitivity of the predicted results to difficult-to-measure fiber direction material properties.

Continuum damage mechanics↗

NASA NTRS1991

Differential continuum damage mechanics models for creep and fatigue of unidirectional metal matrix composites

Three multiaxial isothermal continuum damage mechanics models for creep, fatigue, and creep/fatigue interaction of a unidirectional metal matrix composite volume element are presented, only one of which will be discussed in depth. Each model is phenomenological and stress based, with varying degrees of complexity to accurately predict the initiation and propagation of intergranular and transgranular defects over a wide range of loading conditions. The development of these models is founded on the definition of an initially transversely isotropic fatigue limit surface, static fracture surface, normalized stress amplitude function and isochronous creep damage failure surface, from which both fatigue and creep damage evolutionary laws can be obtained. The anisotropy of each model is defined through physically meaningful invariants reflecting the local stress and material orientation. All three transversely isotropic models have been shown, when taken to their isotropic limit, to directly simplify to previously developed and validated creep and fatigue continuum damage theories. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation when attempting to characterize a large class of composite materials, and (2) its ability to predict anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Additionally, the potential for the inclusion of various micromechanical effects (e.g., fiber/matrix bond strength, fiber volume fraction, etc.), into the phenomenological anisotropic parameters is noted, as well as a detailed discussion regarding the necessary exploratory and characterization experiments needed to utilize the featured damage theories.

Arnold, S. M.↗

NASA NTRS2016

Model-Based Fatigue Prognosis of Fiber-Reinforced Laminates Exhibiting Concurrent Damage Mechanisms

Prognostics of large composite structures is a topic of increasing interest in the field of structural health monitoring for aerospace, civil, and mechanical systems. Along with recent advancements in real-time structural health data acquisition and processing for damage detection and characterization, model-based stochastic methods for life prediction are showing promising results in the literature. Among various model-based approaches, particle-filtering algorithms are particularly capable in coping with uncertainties associated with the process. These include uncertainties about information on the damage extent and the inherent uncertainties of the damage propagation process. Some efforts have shown successful applications of particle filtering-based frameworks for predicting the matrix crack evolution and structural stiffness degradation caused by repetitive fatigue loads. Effects of other damage modes such as delamination, however, are not incorporated in these works. It is well established that delamination and matrix cracks not only co-exist in most laminate structures during the fatigue degradation process but also affect each other's progression. Furthermore, delamination significantly alters the stress-state in the laminates and accelerates the material degradation leading to catastrophic failure. Therefore, the work presented herein proposes a particle filtering-based framework for predicting a structure's remaining useful life with consideration of multiple co-existing damage-mechanisms. The framework uses an energy-based model from the composite modeling literature. The multiple damage-mode model has been shown to suitably estimate the energy release rate of cross-ply laminates as affected by matrix cracks and delamination modes. The model is also able to estimate the reduction in stiffness of the damaged laminate. This information is then used in the algorithms for life prediction capabilities. First, a brief summary of the energy-based damage model is provided. Then, the paper describes how the model is embedded within the prognostic framework and how the prognostics performance is assessed using observations from run-to-failure experiments

Prognostics↗

NASA NTRS2015

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Leone, Frank A., Jr.↗

NASA NTRS1995

Tension Strength, Failure Prediction and Damage Mechanisms in 2D Triaxial Braided Composites with Notch

The unnotched and notched (open hole) tensile strength and failure mechanisms of two-dimensional (2D) triaxial braided composites were examined. The effect of notch size and notch position were investigated. Damage initiation and propagation in notched and unnotched coupons were also examined. Theory developed to predict the normal stress distribution near an open hole and failure for tape laminated composites was evaluated for its applicability to 2D triaxial braided textile composite materials. Four different fiber architectures were considered; braid angle, yarn and braider size, percentage of longitudinal yarns and braider angle varied. Tape laminates equivalent to textile composites were also constructed for comparison. Unnotched tape equivalents were stronger than braided textiles but exhibited greater notch sensitivity. Notched textiles and tape equivalents have roughly the same strength at large notch sizes. Two common damage mechanisms were found: braider yarn cracking and near notch longitudinal yarn splitting. Cracking was found to initiate in braider yarns in unnotched and notched coupons, and propagate in the direction of the braider yarns until failure. Damage initiation stress decreased with increasing braid angle. No significant differences in prediction of near notch strain between textile and tape equivalents could be detected for small braid angle, but the correlations were weak for textiles with large braid angle. Notch strength could not be predicted using existing anisotropic theory for braided textiles due to their insensitivity to notch.

Norman, Timothy L.↗

NASA NTRS2016

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

Bergan, Andrew C.↗

NASA NTRS2017

Fracture-Based Mesh Size Requirements for Matrix Cracks in Continuum Damage Mechanics Models

This paper evaluates the ability of progressive damage analysis (PDA) finite element (FE) models to predict transverse matrix cracks in unidirectional composites. The results of the analyses are compared to closed-form linear elastic fracture mechanics (LEFM) solutions. Matrix cracks in fiber-reinforced composite materials subjected to mode I and mode II loading are studied using continuum damage mechanics and zero-thickness cohesive zone modeling approaches. The FE models used in this study are built parametrically so as to investigate several model input variables and the limits associated with matching the upper-bound LEFM solutions. Specifically, the sensitivity of the PDA FE model results to changes in strength and element size are investigated.

Leone, Frank A.↗

NASA NTRS2018

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↗

NASA NTRS1979

Hygrothermal damage mechanisms in graphite-epoxy composites

T300/5209 and T300/5208 graphite epoxy laminates were studied experimentally and analytically in order to: (1) determine the coupling between applied stress, internal residual stress, and moisture sorption kinetics; (2) examine the microscopic damage mechanisms due to hygrothermal cycling; (3) evaluate the effect of absorbed moisture and hygrothermal cycling on inplane shear response; (4) determine the permanent loss of interfacial bond strength after moisture absorption and drying; and (5) evaluate the three dimensional stress state in laminates under a combination of hygroscopic, thermal, and mechanical loads. Specimens were conditioned to equilibrium moisture content under steady exposure to 55% or 95% RH at 70 C or 93 C. Some specimens were tested subsequent to moisture conditioning and 100 cycles between -54 C and either 70 C or 93 C.

Crossman, F. W.↗

NASA NTRS1998

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.↗

NASA NTRS2017

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.↗

NASA NTRS2017

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↗