De Xie

Discrete Cohesive Zone Model to Simulate Static Fracture in 2D Triaxially Braided Carbon Fiber Composites

A discrete cohesive zone model (DCZM) is implemented to simulate the mode I fracture of two dimensional triaxially braided carbon (2DTBC) fiber composites. The 2DTBC is modeled as an elastic-one-parameter (a66) plastic continuum. The plastic behavior of the 2DTBC was characterized by measuring a66. Mode I fracture tests are carried out by using a modified single edge notch bend (SENB) configuration. Fracture toughness (GIC) as a function of crack extension is measured by a compliance approach. The fracture tests are then simulated by using the DCZM based interface element in conjunction with the commercial software ABAQUS® through a user subroutine UEL. The simulated results, carried out under conditions of plane stress, are compared with the experimental results and also verified for mesh sensitivity. The results presented provide guidelines and a basic understanding to model structural response of non-homogeneous materials, incorporating fracture as a damage mechanism and using constituent level material properties, geometry, and fracture toughness (GIC) as input.

Postbuckling analysis with progressive damage modeling in tailored laminated plates and shells with a cutout

Abstract An approach to modeling inplane damage progression in postbuckled laminated composite panels is shown to be accurate by comparison to experimental test data from other sources. A simple tailoring concept is shown to be very effective in increasing compressive buckling loads and ultimate loads for flat plates and curved panels with a central cutout. Effects of cutout size, the degree of tailoring, and inplane restraint on the unloaded edges are investigated. Optimal tailoring produces relative improvements in the flat plates ranging from 40% to 175% in buckling load and 190–240% in ultimate load capacity when compared to uniform plates with the same cutout sizes. In the curved panels, tailoring lowers the imperfection sensitivity and in some cases produces ultimate loads greater than the theoretical undamaged buckling loads. To the contrary, the ultimate load for the uniform curved panel is much lower than the undamaged buckling load. Relative improvements in ultimate loads range from a low of about 40% to a high of about 155% compared to uniform curved panels. Large differences in the damage initiation locations and damage progression patterns are shown between the flat and the curved panels. In summary, the tailoring concept investigated here can provide excellent improvements in ultimate load capacity in flat and curved panels with the largest benefits occurring in thin flat panels that are loaded far into the compressive postbuckling regime.

Estimation of Fatigue and Fracture Allowables For Metallic Materials Under Cyclic Loading

In this paper, a new strategy for fatigue (S-N) and fatigue crack growth is proposed. It starts with estimation of the fracture toughness from simple tensile tests and ends up to the prediction of structural fatigue life. The methodology consists of three parts as shown in Figure 1. In Part I the information from a complete stress-strain curve was used to estimate the fracture toughness based on the energy method developed by Farahmand [1, 2]. As the result the GENOA/FTD module was developed for this functionality. The Fracture Toughness Determination code (FTD) is a useful tool that can generate the plane strain and plane stress fracture toughness for metallic alloys by using the material static properties. In addition, it can provide material fracture toughness as a function of part thickness. In Part II, the plane strain and plane stress fracture toughness (KIC & KC) were used to generate the fatigue crack growth rate data (the da/dN versus ∆K curve). The Fatigue Crack Growth module (GENOA/FCG) was established which can generate the whole region of the da/dN versus ∆K curve [3]. In Part III, the da/dN versus ∆K curve was used to predict the fatigue life and residual strength in conjunction with finite element analysis (FEA). When the stress intensity factor solution is not available for the crack geometry in consideration, the virtual crack closure technique (VCCT) was used to compute the strain energy release rates which were then converted to stress intensity factors [4-8]. The GENOA/PFA module, a progressive failure analysis code, has this functionality.

Cohesive Zone Model for Surface Cracks using Finite Element Analysis

A debonding comparative study for accuracy and software convergence among the Finite Element based non-predetermined crack growth strength/strain based Progressive Failure Analysis (PFA) and pre-determined crack growth fracture mechanics based Continuous/Discrete cohesive zone model (CZM) is performed. It is concluded that for typical 2D/3D crack growth or debonding, a combination of PFA and CZM will result in then most accurate predicted load-displacements in comparison with test. PFA requires the fiber/matrix or lamina material input and is mesh sensitive at the crack tip, necessitating a mesh convergence effort. PFA generates an accurate crack path and the load displacement curve (up-to load peak value). Continuous/Discrete CZM requires the fracture toughness, correlation of cohesive strength and predetermined crack path/interfaces. Several comparative studies of these methodologies against test data were performed. In particular the Composite Storage Module (CSM) adhesively bonded joint tests revealed the pre-mature failure of the bonded area as possible combination of both adhesive and cohesive failure. Adhesive joint failure was caused by a) non-clean surface preparation, b) thick bond line, and c) existence of voids in the adhesive bondline. The problem was analyzed using two approaches: a) Progressive failure analysis with complete and partial bond void representation and b) Virtual Crack Closure Technique with complete and partial bonding. Results indicated full load carrying capability of the joint using PFA and VCCT and a complete bondline approach and a significant reduction in the load carrying capability due to improper bonding.

Discrete Cohesive Zone Model to Simulate Static Fracture in Carbon Fiber Composites

A discrete cohesive zone model (DCZM) is developed to simulate the mode I and mixed mode fracture. For the mode I case, experimental results generated using a modified single edge notched bend specimen of a 2D triaxially braided composite (2DTBC) are used to verify the DCZM. The 2DTBC is modeled as an elastic one-parameter (“a66”) plastic continuum. The plastic behavior of the 2DTBC is characterized by measuring a66. Fracture toughness (GIC) as a function of crack extension is measured by a compliance approach in the SENB tests. A previously developed mixed mode bending (MMB) fracture test configuration is a useful method to generate fracture envelopes for delamination failure of composites. The DCZM is used to simulate mixed mode fracture of a unidirectional laminated composite loaded using the MMB. The simulated results are compared with selected experimental results and also verified for mesh sensitivity. It is shown that the present DCZM is a versatile tool to study failure of a wide class of composite materials.

Delamination Growth and Residual Strength of Compressively Loaded Sandwich Panels with Stiffness Tailored Face Sheets

This study shows that a simple approach to stiffness tailoring of composite face sheets can improve the performance of sandwich panels under compressive loading when delaminations are present. The simple stiffness tailoring concept used here is to reposition of all 08 material (aligned with the loading direction) into regions of certain width near the edges of the sandwich panel. This concept has been shown to improve the buckling and postbuckling performance of solid plates and to offer control of delamination growth. To evaluate this tailoring design concept in sandwich panels, numerical simulations of onset and propagation of the delamination growth were conducted with uniform face sheets and tailored face sheets. The delamination front tracing method previously developed by the authors was used to perform the delamination growth analysis. The interfacial elements, which allow the growth of the delamination front to be traced, are placed at the interface between the top face sheet and the core in the undelaminated region. They enable calculation of the strain energy release rates and application of a fracture mechanics delamination growth criterion. Gap elements were used to avoid interfacial overlap. Based on the numerical study, the improvement in the ultimate load provided by the simple stiffness tailoring concept ranges from 80% to 100%, depending on the extent of tailoring. Substantial improvements in the residual strength and stiffness, after significant delamination growth, can also be observed. Therefore, this article provides a potential design concept that can improve the damage tolerance of sandwich panels without adding weight.

Crack Growth Strategy in Composites under Static Loading

*† ‡ § Crack growth in composites can be analyzed by a strategy of two independent steps. The first step, based on the material strength theory, is used to predict the damage mechanism, damage pattern, and the crack growth path. In the second step, fracture mechanics is used to determine the failure loads. The procedure of this strategy is demonstrated by laminated double cantilever beam and fracture coupons (center crack, inclined crack and compact tension) made of stitched warp-knit fabric composites.

Mixed-Mode Fracture Modeled Through a Discrete Cohesive Zone Model-DCZM

The Discrete Cohesive Zone Model (DCZM) is proposed to simulate fracture initiation and subsequent growth when material nonlinear effects are significant using the finite element method. Different from the widely-used Continuum Cohesive Zone Model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses 1D rod type elements and applies the cohesive law as the rod internal force vs. nodal separation. A series of 1D interface elements are placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes are introduced within the DCZM extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations (double cantilever beam -DCB, end notched flexure - ENF and mixed mode bending - MMB) are examined, and results are presented that show mesh independence. Good agreement between the present approach and previously published results is shown.