A Fatigue Damage Model for FRP Composite Laminate Systems Based on Stiffness Reduction

This paper introduces a stiffness reduction based model developed by the authors to characterize accumulative fatigue damage in unidirectional plies and(0/θ/0)composite laminates in fiber reinforced polymer(FRP)composite laminates.The proposed damage detection model is developed based on a damage evolution mechanism,including crack initiation and crack damage progress in matrix,matrix-fiber interface and fibers.Research result demonstrates that the corresponding stiffness of unidirectional composite laminates is reduced as the number of loading cycles progresses.First,three common models in literatures are presented and compared.Tensile viscosity,Young’s modulus and ultimate tensile stress of composites are incorporated as key factors in this model and are modified in accordance with temperature.Four types of FRP composite property parameters,including Carbon Fiber Reinforced Polymer(CFRP),Aramid Fiber Reinforced Polymer(AFRP),Glass Fiber Reinforced Polymer(GFRP),and Basalt Fiber Reinforced Polymer(BFRP),are considered in this research,and a comparative parameter study of FRP unidirectional composite laminates with different off-angle plies using control variate method are discussed.It is concluded that the relationship between the drop in stiffness and the number of cycles also shows three different regions,following the mechanism of damage of FRP composites and the matrix is the dominant factor determined by temperature,while fiber strength is the dominant factor that determine the reliability of composite.

A Virtual Work Approach to Modeling the Nonlinear Behavior of Steel Frames

The stiffness reduction is studied in detail of compact W-Shapes （wide-flange steel shapes） that results from yielding of the cross-section due to uniaxial bending and axial compression. Three-dimensional m-p-τ surface plots developed from detailed fiber element models of a W8x31 are used to develop a generalized material model for direct implementation in the virtual work method. A portal steel frame is used to illustrate the virtual work method with the nonlinear material model in a first-order, inelastic analysis implementation and in a second-order, inelastic analysis condition. The nonlinear modeling capabilities of MASTAN2 are used to verify the accuracy of the virtual work results and are found to be in very close agreement.

Beam Element Material Model for Rotary-Straightened Steel W-Shapes

An inelastic material model that was previously developed by the author for standard W-Shapes was adapted for use to model the behavior and strength of rotary-straightened hot rolled W-Shape sections.Using a published residual stress model for these W-Shapes,limit load analyses were conducted using the material model in MASTAN2 and were compared with published finite element results.The material model required an adjustment to the initial yield moment conditions and residual stress ratios.Comparisons with published results indicate that these minor modifications were sufficient to provide very good modeling agreement.The previously developed material model can be used effectively to model the limit load conditions of rotary-straightened hot rolled W-Shape beams and beam-columns in steel frames.The effect of rotary-straightening W-Shapes is more significant for minor axis bending conditions and this becomes more pronounced as the floor load magnitudes increase.

An Inelastic Material Model for Lateral Torsional Buckling and Biaxial Bending of Steel W-Shapes

A new material model for beam elements was developed for use as normalized tangent modulus expressions when performing 3-dimensional second-order inelastic analyses of steel I-section beams.The stiffness matrix of a 14 degree-of-freedom beam element was updated to include the effects of yielding on St.Venant’s torsion and bimoment stiffness at the initial and terminal nodes.A validation study compared the new model’s results with those from published detailed finite element analyses and was found to be in very close agreement.A biaxial end-moment study with two different depth-to-flange-width ratios provided expected and consistent results over a range of moment conditions.