Progressive damage modeling of open cut out CFRP laminate

under transverse bending using finite element analysis Yagnik Kalariya (ME13M1009), Dr. M Ramji

Engineering Optics Lab, Department of Mechanical and Aerospace Engineering, IIT Hyderabad

Introduction and objective Carbon fiber reinforced polymer (CFRP) laminates are widely used in aerospace, automotive and

civil structures due to their high specific strength, high stiffness, corrosion resistant and longer fatigue

life. These structures experience tensile or/and compressive load in actual service conditions and their

failure behavior changes accordingly. Since the structures like wing of an aircraft and hull of a marine

ship have multiple cut out for assembly purpose or electrical wiring purposes, their behavior and

failure mechanism is very different from the one without cut outs. CFRP laminates possess superior

tensile properties, but their compressive strengths are often less satisfactory. In addition, pure

compression of structures in real loading scenarios is less frequent than bending-induced compression.

Also, the damage evolution in CFRP laminate with interacting failure modes like matrix cracking,

fiber breakage, debonding and delamination is a very complex phenomenon. Most often the damaged

structures get repaired for extending their service life. Repair of a cracked structure by an adhesively

bonded composite patch has gained lot of importance.

Experimental stress analysis of open cut out CFRP panel under four point bending is carried out

using digital image correlation (DIC) technique. The zones of higher strain level are identified and

they are carefully studied. Further, through thickness normal and shear strain field is obtained. Also

the damage initiation and propagation in notched laminate is carefully studied. Later, a finite element

based progressive damage modeling (PDM) is implemented to exactly capture the experimental

damage mechanism. Both failure initiation and ultimate failure load for the cut out laminate will be

predicted. The accuracy of PDM model will be assessed by comparing the numerical prediction with

experimental results.

Motivation Composite materials are being increasingly used in many industrial applications thanks to their

excellent mechanical properties and low specific weight. Some of these composite structures, such as

robot arms, drive shafts, and helicopter blades, may be modelled, at least in a preliminary design, as

beams subjected to loads that undergo mainly bending moments. Also, as stated above, many aircraft

and marine structures are subjected to bending loading.

This bending load produces delamination opening due to induced interlaminar shear stress. The

interlaminar strength of CFRP laminates is very poor. Propagation of damage owing to buckling of

delaminated part is one of the critical causes of failure in composite laminates. The interlaminar

strength is further influenced by layup configurations. This delamination may arise under various

circumstances, such as in the case of transverse concentrated loads caused by low velocity impacts.

This damage mode is particularly important for the structural integrity of composite structures

because it is difficult to detect during inspection. Furthermore, delamination causes a drastic reduction

of the bending stiffness of a composite structure and, when compressive loads are present, promotes

local buckling. So it is very important to know the behaviour of CFRP laminates under bending loads.

Also, it is very interesting to investigate the repaired panel under the same load to get the restored

properties of the damaged laminate after the repair.

Previous work The failure analysis of composite laminates subjected to out-of-plane load causing bending has

not received as much attention as in-plane loading. Kim carried out buckling analyses of the

laminated plates and shells under axial compression using the finite element method. The formulation

of a geometrically non-linear composite shell element is based on the updated Lagrangian method is

presented to study the buckling behaviour. Bosia et al. studied the through thickness deformation of

laminated composite plates subjected to out-of-plane line and concentrated loads experimentally and

numerically using different span to depth ratios. They used both laminated-shell and solid elements

for finite-element simulations. Echaabi et al. analysed damage progression and failure modes of

graphite-epoxy laminates in three points bending tests. They determined the effect of geometrical

parameters on the successive failures and its failure modes.

From previous experimental and analytical work on unidirectional carbon–epoxy, Wisnom

showed that changing the support span over thickness (s/t) ratio has dramatic effects on the measured

short beam and four-point bend shear strengths. The actual stress-state in a given beam specimen was

three dimensional, with stresses varying through the thickness and along the length and therefore

could not be adequately interpreted by means of classical beam theory. Early in theoretical work,

Kedward also predicted a variation of shear stresses across the width, with peaks at the edge of the

coupon. He also compared the theoretical model with experimental one by conducting short beam

tests. Post showed an interesting discontinuous distribution of the shear strain through the thickness of

the specimen using Moire´ fringe interferometry, with peaks at the ply interfaces where compliant

resin-rich regions are formed and delamination tends to originate. Reddy and Reddy used generalized

layer wise plate theory and a progressive failure model to determine first ply and ultimate failure

loads of a three point bend specimen. Stiffness reduction was carried out at the reduced integration

Gauss points of the finite element mesh depending on the mode of failure. Geometric non-linearity

was taken into account in the Von Karman sense. Tolson and Zabaras studied the first and last ply

failure loads of a laminated composite plate subjected to both inplane and sinusoidal transverse loads.

However, no comparison was made to test results for the transverse load case. Kam and Sher studied

progressive failure of centrally loaded laminated composite plates. The Ritz method, with geometric

nonlinearity, in the Von Karman sense, was used to construct the load displacement behaviour.

Mullea et al. used FBGs and DIC technique to analyze the mechanical behavior of a composite

structure submitted to bending tests. This was carried out by considering a beam type specimen which

presents design singularities such as important thicknesses, ply drop off zones and a reinforced zone.

This study concerned the central reinforced zone of the specimen. In order to estimate the strain

distribution during a series of 3 and 4-point bending tests. Gerald et al. presented a finite element

multiscale analysis that is able to predict material behavior of textile composites via virtual tests,

solely from the (nonlinear) material behavior of epoxy resin and glass fibers, as well as the textile

fiber architecture. They made predictions for a single layer within a textile preform or for multiple

textile layers at once. Turon et al. proposed a thermodynamically consistent damage model for the

simulation of progressive delamination in composite materials under variable-mode ratio. They

developed a novel constitutive equation to model the initiation and propagation of delamination.

Experimental work

Specimen and experimental setup The experimental study involves testing of CFRP panels under pure bending to provide

fundamental insights into its damage mechanism and provides validation for numerical

prediction under the same. The whole field surface strain and displacement of CFRP panels having

single hole and two holes of different configurations will be obtained using digital image correlation

(DIC) technique. It will be helpful in real time monitoring of the damage progression of CFRP panels

with and without cutout under pure bending.

The specimen geometry and the test method used in this study to determine the flexural

properties in CFRP composite laminates are from the recommendations from ASTM D 7264. The

standard span to thickness ratio is 32:1. The standard width and thickness are 13mm and 4mm

respectively. The load span should be half of support span as shown in fig. 1.Composite laminates

will be fabricated by the hand layup technique with unidirectional (UD) carbon fiber mat. The matrix

is made from epoxy resin LY-556 mixed with hardener HY-951 (both Huntsman grade) in the ratio of

10:1 by weight. The average thickness of each layer of laminate after casting is found to be 0.35 mm.

Specimens are cut from fabricated laminates using abrasive cutter mounted on hand-held saw and

then machined to the required dimensions with special diamond-coated end mill supplied by SECO

Tools. A four-point bending fixture is used to investigate the deformation behaviour of CFRP

laminates to produce pure bending condition. All tests will be conducted on MTS servo hydraulic

cyclic test machine under displacement control loading. System of cameras for DIC image acquisition

will be used for monitoring the through thickness strain field of side face. Tests will be taken upto

final failure.

Fig. 1 Four-point loading configuration for pure bending condition

Damage assessment and whole field strain measurement using DIC Digital image correlation (DIC) is an optical-numerical full-field surface displacement

measurement method. It is based on a comparison between two images of the specimen coated by a

random speckle pattern in the undeformed and in the deformed state [Sutton et al. 2009]. Its special

merits encompass non-contact measurement, simple optical setup, no special preparation of specimens

and no special illumination. The basic principle of the DIC method is to search for the maximum

correlation between small zones (sub windows) of the specimen in the undeformed and deformed

states, as illustrated in fig. 2. From a given image-matching rule, the displacement field at different

positions in the analysis region can be computed. The simplest image-matching procedure is the

cross-correlation, which provides the in-plane displacement fields u(x,y) and v(x,y) by matching

different zones of the two images.

Fig.2 Schematic diagram of the deformation relation

Numerical study A finite element-based 3D PDM will be developed for notched and repaired panel under pure

bending load. Both single- and double-sided patch repairs on notched CFRP panels will be

considered. The study will be conducted for panels having different layup configuration. Initiation and

propagation of damage as well as failure mechanism in notched and repaired panels will be

investigated. Both failure initiation and ultimate failure load before and after the repair will be

predicted. Failure of adhesive layer leading to patch debonding will also be studied. The accuracy of

developed model will be assessed by comparing the numerical prediction with experimental results

obtained using DIC technique.

Fig. 3 FEA analysis of CFRP panel under four point bending loading condtion

PDM mainly comprises three steps: stress analysis, damage prediction and damage modeling.

Initially, finite element model of an open cutout and repaired panels are developed. The FE model is

then analyzed under given loading and boundary conditions to obtain the elemental stresses in

principal material directions of the laminate. In second step, the obtained elemental stress values from

FE analysis along with material strength parameters (obtained from experiments) are substituted into a

set of failure criterions to predict the failure of element and its respective failure mode. In the third

step, once the damage is detected by a failure theory, a damage modeling technique is then

incorporated to take into account the effect of damage on load-bearing capacity of the laminate and

further post-damage analysis is performed. The degradation is achieved by material property

degradation method (MPDM) which assumes that the damaged element can be replaced by an

equivalent element with degraded material properties. So, once the failure is identified in any element,

the material properties of the failed elements either that of the composite or adhesive are degraded to

5% of their original value.