Journal of Composite Materials

The Air Force Research Laboratory led a research effort to benchmark the accuracy of static and fatigue predictions of several emerging composite progressive damage analysis techniques. The static portion of this technical effort is described in detail in a previous special issue of the Journal of Composite Materials. This paper provides the details of the fatigue experiments that were conducted to calibrate and validate the computational models. Initially, in-plane and out-of-plane S–N curves were generated through coupon tests that were performed on unidirectional laminae. The challenges experienced during fatigue testing of in-plane, matrix-dominated unidirectional coupon specimens are presented in detail. The higher fidelity test data from the fiber-dominated and out-of-plane experiments are also included in this paper. Following the calibration experiments, a series of tension–tension fatigue validation tests were conducted on open-hole coupons with three different stacking sequences. Each specimen was cycled to a pre-determined number of fatigue cycles, followed by static residual strength tests in both tension and compression. This paper provides the stress–strain responses of these validation tests as well as high-resolution X-ray computed tomography images of the subsurface damage as a function of cycles. Seven analysis teams used these test results to calibrate their models and to benchmark the accuracy of their predictions of damage and residual mechanical properties.

This manuscript presents the blind prediction of fatigue life performance in three laminated carbon fiber reinforced polymer composite layups using a reduced-order space-time homogenization model. To bridge the spatial scales, the modeling approach relies on the Eigendeformation-based reduced order homogenization method. To bridge the time scales associated with a single load cycle and the overall life of the composite, a homogenization-based accelerated multiple-time-scale integrator with adaptive time stepping capability is employed. The proposed multiscale modeling approach was used to predict the evolution of composite stiffness and progressive damage accumulation as a function of loading cycles, as well as residual strength after fatigue in tension and compression, for three layups ([0,45,90,−45]_2s, [30,60,90,−60,−30]_2s, and [60,0,−60]_3s). Following blind prediction, the experimental data from the blind prediction specimens were employed to better understand the failure mechanisms and recalibrate the model. This study was performed as a part of the Air Force Research Laboratory's “Damage Tolerant Design Principles” Program.

Finite element simulations of three laminates in open-hole configuration subjected to constant amplitude tension–tension fatigue loading are investigated as part of the Damage Tolerant Design Principles program organized by the Air Force Research Laboratory. All coupons were made from unidirectional IM7/977-3 plies, which are composed of intermediate modulus carbon fibers and a toughened epoxy matrix. Government furnished experimental data from an assortment of fatigue loaded unnotched coupons were used to characterize the behavior of the composite material in the simulations. The commercial software Autodesk Helius PFA was used to model the non-linear response of the material. Blind simulations of coupon stiffness and damage at several cycle numbers and residual coupon tensile and compressive strengths are benchmarked against experimental measurements and X-rays. Upon review of the experimental results, a second round of simulations was performed where the modeling strategy was updated to improve correlation to experiment.

Multiscale Designer, developed by Altair, has been studied for its suitability for fatigue life prediction of advanced composite aircraft structures made of polymer matrix composites. The extensive experimental data provided by the Air Force Research Laboratory have been utilized to characterize the linear, non-linear, monotonic, and cyclic loading properties of micro-constituents comprising the polymer matrix composite system. The characterized properties have been then utilized to predict fatigue life and residual strength and stiffness of the aerospace grade polymer matrix composites.

The discrete damage modeling method is extended for progressive failure analysis in laminated composites under fatigue loading. Discrete damage modeling uses the regularized extended finite element method for the simulation of matrix cracking at initially unknown locations and directions independent of the mesh orientation. A material history variable in each integration point is introduced and updated after each loading increment, corresponding to certain load amplitude and number of cycles. The accumulation of the material history variable is governed by Palmgren-Miner’s rule. Cohesive zones associated with mesh-independent cracks are inserted when the material history parameter reaches the value of 1. Cohesive zone model consistently describing crack initiation and propagation under fatigue loading without any assumption of initial crack size is proposed. The fatigue properties required for matrix failure prediction include shear and tensile S-N curves as well as Mode I and II Paris law parameters. Tensile fiber failure is assumed unaffected by fatigue. All input data required for model application are directly measured by ASTM tests except tensile fiber scaling parameter and compression fiber failure fracture toughness, which were taken from literature sources. The model contains no internal calibration parameters. Fatigue damage extent, stiffness degradation and residual tensile and compressive strength of IM7/977-3 laminates have been evaluated. Three different layups, [0/45/90/-45]_2S, [30/60/90/-60/-30]_2S and [60/0/-60]_3S, were modeled and tested. The predictions captured most experimental trends and showed good agreement with X-ray CT damage assessment; however, significant further work is required to develop reliable methodology for quantitative composite durability prediction.

A coupled, transversely isotropic, deformation and damage fatigue model has been implemented within the finite element method and utilized, along with a static progressive damage model, to predict the fatigue life, stiffness degradation as a function of number of cycles, and post-fatigue tension and compression response of notched, multidirectional laminates. The material parameters for the fatigue model were obtained utilizing ply-level classical lamination theory simulations and the provided [0], [90] and [±45] experimental composite laminate S–N data. Within the fatigue damage model, the transverse and shear stiffness properties of the plies were degraded with an isotropic scalar damage variable. The stiffness damage in the longitudinal (fiber) ply direction was suppressed, and instead the strength of the fiber was degraded as a function of fatigue cycles. A maximum strain criterion was used to capture the failure in each element, and once this criterion was satisfied, the longitudinal stiffness of the element was eliminated. The resulting, degraded properties were then used to calculate the new stress state. This procedure was repeated until final failure of the composite laminate was achieved or a specified number of cycles was reached. For post-fatigue tension and compression behavior, four internal state variables were used to control the damage and failure. The predictive capability of the above-mentioned approach was assessed by performing blind predictions of notched multidirectional IM7/977-3 composite laminate response under fatigue and post-fatigue tensile and compressive loading, followed by a recalibration phase. Tabulated data along with detailed results (i.e. stress–strain curves as well as damage evolution states at given number of cycles compared to experimental data) for all laminates are presented.

Virtual testing has lately gained widespread acceptance among scientists as a simple, accurate, and reproducible method to determine the mechanical properties of heterogeneous microstructures, early in the production process. As a result of the rapid expansion of the use of composites in aerospace design, virtual testing techniques are, in fact, deemed extremely useful to eliminate unnecessary tests and to reduce cost and time associated with generating allowables for lengthy lifing analyses of structures. Leveraging on a limited set of experimental data, a Progressive Failure Analysis can accurately predict the life and safety of a component/assembly, simply tapping on the physics of its micro-/macro- mechanics material properties, manufacturing processes, and service environments. The robust methodology is showcased using blind predictions of fatigue stiffness degradation and residual strength in tension and compression after fatigue compared with test data from Lockheed Martin Aeronautics and Air Force Research Laboratory). The multi-scale progressive failure analysis methodology in the GENOA software considers uncertainties and defects and evaluated the damage and fracture evolution of three IM7-977-3 laminated composite layups at room temperature. The onset and growth of composite damage was predicted and compared with X-ray CT. After blind predictions, recalibrations were performed with knowledge of the test data using the same set of inputs for all layups and simulations. Damage and fracture mechanism evolution/tracking throughout the cyclic loading is achieved by an integrated multi-scale progressive failure analysis extended FEM solution: (a) damage tracking predicts percentage contributing translaminar and interlaminar failure type, initiation, propagation, crack growth path, and observed shift in failure modes, and (b) fracture mechanics (VCCT, DCZM) predicts crack growth (Crack Tip Energy Release Rate vs. Crack Length), and delamination. The predictive methodology is verified using a building block validation strategy that uses: (a) composite material characterization and qualification (MCQ) software, and (b) the GENOA multi-scale progressive failure analysis fatigue life, stiffness degradation, and post-fatigue strength predictions for open-hole specimens under tension/compression at RTD. The unidirectional tension, compression, and in-plane shear lamina properties supplied by Lockheed Martin Aeronautics and the Air Force Research Laboratory (based on the D3039, D638, D3518 tests) were used by MCQ to reverse engineer effective fiber and matrix static and fatigue properties for the IM7-977-3 material system. The use of constituent properties identified the root cause problem for composite failure and enabled the detection of damage at the micro-scale of the material where damage is incepted. For all three case studies (namely, layups [0/45/90/−45]_2s, [+60, 0, −60]_3s, and [+30, +60, 90, −60, −30]_2s), the blind predictions on the fatigue stiffness degradation and residual strength of the open-hole coupon in tension/compression under cyclic loading (with R = 0.1) at RTD were evaluated using a FE mesh (made of 2k shell elements), in which only one shell element, containing all plies, was employed through the thickness. The results of all analyses correlated very well with the tests, including the damage micro-graphs generated during the cyclic loading.

This paper presents a combined continuum damage and discrete crack (CDDC) modelling approach for fatigue damage characterization and post-fatigue residual strength prediction of laminated composite components with a hole. In order to capture both the fatigue cycle-driven material degradation and discrete damage-induced stress concentration and redistribution, an overlapped element approach is developed based on a combined user-defined material (UMAT) and user-defined element (UEL). An Abaqus element coupled with UMAT for fatigue damage characterization is used to detect the location of failure initiation, while the discrete crack network-based (DCN) UEL is applied to insert a crack without remeshing. The intensified stress field induced by the newly inserted matrix crack is used for the evaluation of failure initiation and stiffness degradation. The UMAT for the fatigue analysis has incorporated the stress-cycle (S-N) curves for the damage evolution characterization associated with matrix and fiber based on the tested S-N curves for plies at their different orientations. A continuum damage mechanics (CDM) approach is used for the fatigue-driven delamination initiation and propagation by insertion of a finite thickness interface layer at each ply interface. Both the blind and recalibrated predictions are performed for specimens of three different layups under the Air Force Tech Scout 1 program. The predicted fatigue failure progression and the stiffness against cycle curves are compared with the test data provided by the Air Force Research Lab (AFRL). In addition, post-fatigue residual strength predictions are performed for these notched specimens under tension and compression.

This paper provides overall comparisons of the fatigue results of an Air Force Research Laboratory exploration into the state of the art of existing technology in composite progressive damage analysis. This program performed blind and recalibration benchmarking exercises for nine different composite progressive damage analysis codes using unnotched and open-hole composite coupons under both static and fatigue loading. This paper summarizes the results of the fatigue portion of this program in which seven of the codes were evaluated. Comparisons are made herein for all seven participants’ predictions with the test data. Overall percent error data are presented, as well as a long list of observations and lessons learned during this year-long effort.