Amit G. Salvi

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.

In-Plane fracture of laminated fiber reinforced composites with varying fracture resistance: experimental observations and numerical crack propagation simulations

A series of experimental results on the in-plane fracture of a laminated composite panel is analyzed using the variational multi-scale cohesive method (VMCM). The VMCM results demonstrate the influence of specimen geometry and load distribution on the propagation of large scale bridging cracks in laminated fiber reinforced composites. Experimentally observed variation in fracture resistance is substantiated numerically by comparing the experimental and VMCM load-displacement responses of geometrically scaled single edgenotch three point bend (SETB) specimens. The results elucidate the size dependence of the traction-separation relationship for this class of materials even in moderately large specimens, contrary to the conventional understanding of it being a material property. The existence of a “free bridging zone” (different from the conventional “full bridging zone”) is recognized, and its influence on the evolving fracture resistance is discussed. The numerical simulations and ensuing bridging zone evolution analysis demonstrates the versatility of VMCM in objectively simulating progressive crack propagation, compared against conventional numerical schemes like traditional cohesive zone modeling, which require a priori knowledge of the crack path.

Specimen size effects in the off-axis compression test of unidirectional carbon fiber tow composites

Specimen size effects in the off-axis compression test for unidirectional carbon fiber tow composites were studied by subjecting coupon specimens of different lengths and widths to off-axis compression under static and low velocity impact loading. Specimens were cut such that the fibers are at angles of 15, 30, 45 and 60° to the direction of loading. A modified compression fixture with anti-buckling side supports was used to carry out the tests. Static tests were carried out on a hydraulically activated MTS loading frame, where specimens were subjected to displacement controlled loading. Low velocity impact tests were conducted on a drop tower facility. A three strain gage rosette was used to measure global strains. Load was measured using a load cell. Due to the unique microstructure of the specimens, a modified three parameter orthotropic plasticity characterization of the plastic response was used and the constants associated with this characterization were determined uniquely. It is shown that the orthotropic plastic response of the material is affected by specimen size primarily due to the mechanism of load introduction in the off-axis test and load transfer through the fiber tow/matrix interface that is prevalent in the material.

Strain-Rate Effects on Unidirectional Carbon-Fiber Composites

Strain-rate effects on mode I fracture of unidirectional carbon-e ber tow composites corresponding to crack propagation parallel to the e ber tow direction was investigated. Precracked unidirectional stitched carbon-e ber specimensweresubjected to a staticandlow-velocity-impactthree-pointbend test.Thecrack position asa function oftime and hencethecrack-propagation velocity were measured with thehelp ofspecial crack-propagation gauges and a high-resolution digital camera. Load vs load point displacement was measured for every test. The effect of strain rate on fracture energy was characterized. The Iosipescu shear test under static and low-velocity-impact loading conditions wasused to characterizetherate-dependent shearresponse ofthematerial. In addition, tension and compression responses were characterized using American Society for Testing and Materials standard test cone gurations. It is found that the mode I fracture energy decreases with an increase in the rate of loading. with the failure event. The resin used for the tubes is slightly rate sensitive; however,thisindicatesthat theresin isstiffer and stronger under dynamic conditions. Yet, the dynamically crushed tubes con- sistently absorblessenergythan thestatically crushedtubes,always atalowermeanplateauload.Thus,itappearsthattheratesensitivity of the fracture events warrant a careful examination. The basic building block of braided composite plaques are e ber tows that are braided into different microstructural architectures prior to being infused with resin. Different types of braided archi- tectures are summarized in the text. 1 Prior to studying the fracture propertiesofthebraidedplaques (thebraidedplaquescontainacom- plex internal microstructure ), it is prudent to understand the various fracturemechanisms andfractureproperties of thetows themselves. Fundamental issues related to mode I, mode II, and mixed mode fracture of stitched tow-reinforced composites need investigation. The mode I, mode II, and mixed mode fracture energies are fun- damental properties of a e ber-reinforced composite. Consequently, measurement of these fracture energies is necessary for properly characterizing the response and failure of structures made of these composites. In this paper we present the results of an experimental study that examined the mode I fracture of unidirectional carbon- e ber tow composites with crack propagation along the e ber tow direction. The present investigation of crack growth is limited to low ve- locity impact (LVI) conditions. Under these conditions the dy- namic stress e eld produced by the impact loading subsides, and this transient e eld occurs at the very early stages of loading. In the present experiments the maximum impactor velocity is 4.6 m/s, re- sulting in maximum crack-propagation velocities on the order of 350 m/s. These velocities are a small fraction of the shear wave speed (1540 m/s) and Rayleigh wave speed of the material. Con- sequently, dynamic effects can be neglected. Researchers 7i11 have conducted an extensive experimental and numerical investigation of dynamic crack propagation in unidirectional continuous e ber (prepreg)-laminated composites. The present study examines con- tinuous e ber (e ber tows) unidirectional composites under LVI con- ditions.

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.

Mixed mode in-plane fracture analysis of laminated fiber reinforced composites using the variational multiscale cohesive method

Extending our earlier work on Mode-I crack propagation presented in earlier SDM conferences, this manuscript details the research work currently underway in our group to objectively simulate mixed-mode crack propagation in laminated fiber reinforced composite materials. The analytical framework and numerical implementation using the variational multi-scale cohesive method (VMCM) is discussed. Further, mixed-mode curved crack propagation simulations and their qualitative comparison with experimental observations is presented.

Computational Engineering of Mixed-mode, In-plane Crack Propagation in Laminated Fiber Reinforced Composites

Integrated Computational Engineering (ICE) is a valuable and cost effective resource for ensuring structural integrity and damage tolerance of future aerospace vehicles that are made with laminated fiber reinforced composite laminates. Towards that end, the variational multiscale cohesive method (VMCM) reported by the authors in previous AIAA SDM conferences, 23–26 is extended further to address problems of mixed mode in-plane crack propagation in fiber reinforced laminates. A set of experimental results obtained using a single edge notch eccentric three point bend test is used for validating the VMCM predictions. Further the applicability of VMCM is demonstrated through simulation of mixed mode in-plane crack propagation for different specimen geometries and different loading conditions. I. Introduction A large number of tests, which can contribute to a substantial portion of the total design and manufacturing cost of an aerospace vehicle, are required to ensure the structural integrity and damage tolerance of vehicle structures. These costs can be reduced by developing validated and physics based computational models that can exploit the power of advanced simulation techniques and the increasing computational power of digital computers. High fidelity computational models can provide valuable information regarding the performance of a structure upto and including failure, provided the modeling is based on correct physics, and is validated using laboratory tests that are designed to be discriminatory. The field of integrated computational engineering (ICE), that encompasses this activity, and also includes, in the case of composites, the modeling of the manufacturing process 14 is a rapidly growing and indispensable field which will continue to provide new insights into the performance of advanced composite structures. The finite element method (FEM), is a key enabler of ICE. It has become the mainstay of problems involving any of the broad phenomena of material deformation - elasticity, plasticity and damage. However, its utility for problems of crack propagation has met with mixed success. The distinguishing characteristic of crack problems, in general, is the formation and propagation of sharp boundaries, which are not part of the original boundary value problem. This is not an obstacle, if the resulting crack path is known a priori, and the mesh is ensured to have elemental surfaces align along possible crack surfaces; but often in practice, neither conditions are feasible. For all but trivial crack propagation problems, the crack path is not known beforehand and has to be determined as part of the solution process, and in structural level problems adaptive mesh generation/realignment is prohibitively costly. The traditional Galerkin FEM implementation is not suitable for problems that encounter crack propagation and also involve strain localization, as it leads to mesh subjective schemes, and the related limitations have been well documented in the context of spurious mesh related length scales 1,4,9 and requirements of mesh alignment relative to the localization

Fracture of 2D Triaxially Braided Carbon Fiber Composites and Resin Effects on the Energy Absorption

Results from an experimental program to investigate the propagation of damage in 2D triaxially braided carbon fiber textile composites (2DTBC) under static conditions are reported. A methodology is presented in which classical concepts from fracture mechanics are generalized to address damage growth in an orthotropic and heterogeneous structural material. Along with results from the experimental program, a novel numerical technique that employs ideas from cohesive zone modeling and implemented through the use of finite element analysis is also presented. The inputs that are required to implement such a discrete cohesive zone model (DCZM) are identified. Compact tension specimen (CTS) fracture tests were carried out by loading 2DTBC coupons cyclically and monotonically. Load and load point displacement were measured. The crack initiation, propagation and crack path history was recorded using high resolution digital photography. The measurements were used to extract the fracture energy (GIC) as a function of crack tip position. Notched Tension tests were carried out to measure the maximum stress in the composites, which provides the cohesive strength (σ c ) of these composites. The material constants so obtained and the DCZM modeling strategy were independently verified by conducting single edge notched bend (SENB) fracture tests using a modified three-point bend test fixture. The experimental and numerical analyses were carried out for two different types of 2DTBC made from two different resin systems to confirm the usefulness of the proposed methodology.

Strain Rate Effects on Mode I Fracture of Unidirectional Carbon Fiber Composites

Unidirectional carbon fiber composites were subjected to the Iosipescu shear test under static and low velocity impact conditions (LVI). Specimens were cut for 00 and 900 test configurations. Static tests were carried out on a hydraulically activated MTS loading frame, where specimens were subjected to uniform straining. LVI tests were conducted on a drop tower facility. The shear response of the specimen was measured for both 00 and 900 specimen configurations. Strain rate effects on interfacial crack toughness were also measured. Pre-notched unidirectional stitched carbon fiber specimens were subjected to a static and LVI three point bend test. The crack propagation velocity was measured with the help of special crack propagation gages and a high resolution digital camera. Load vs. load point displacement was measured for every test. The effect of strain rate on fracture toughness was characterized.