Failure analysis of FML plates with cutouts: experimental and finite element approaches/Lakstinio metalo kompozito ploksteliu su iskirtimais suirimo analize eksperimentiniu ir baigtiniu elementu metodais.
Yazdani, Saleh ; Rahimi, G.H.
1. Introduction
At the end of decade 1970s, the idea of using two materials for
conquest of defects of both materials was suggested [1]. Metal
structures have high strength and resistance against impact and are
easily repairable, while composite materials possess features such as
high fracture resistance and high stiffness. By mixing the two types of
materials, all of these properties could be achieved [2]. In 1978, metal
laminate materials known as ARALL in institute of aerospace engineering
in Delft University were introduced. These materials were composed of
thin layers of aluminum alloys and unidirectional and bidirectional
fibers of curing aramid with resin (prepreg) [3]. GLARE laminate
materials are also from family of FML materials which is made of glass
fibers room-temperature-curing epoxy resin and sheets of aluminum
alloys. The great difference between GLARE and ARALL is that, GLARE is
made of glass fibers rather than aramid [4]. FML plates are from family
of hybrid materials which usually composed of thin metal layers and
fibers curing with epoxy resin. Because of employing metal in the
structures of these materials, they show plastic behaviors [5].
Therefore, the elastic/plastic analyses of them are important. These
materials have good properties against impact, fracture, and corrosion.
Moreover, other physical advantages such as high strength, resistance
against fire, and weight-saving compared with metal alloys, lead to
widespread use of them in aerospace and military industries.
Manufactured materials which are composed of metals and composites have
complicated mechanical properties and unpredicted behaviors, therefore,
there have been many studies on this subject, of which we can mention to
researches on the mechanical properties of a special kind of FMLs known
as steel/aluminum/GRP laminate, which was carried out by Khalili et al
[6]. Tensional and fatigue properties of fiber metal laminates with
different fiber materials were studied and compared by G. Reyes and H.
Kang [7]. The effect of angle of fibers arrangement and existence of
fibers of glass and Kevlar on tensional properties of FMLs were
investigated by S. Ebrahim Mousavi-Torshizi [8].
In the field of investigating the tensional behavior of FMLs, some
articles are available in the literatures. P. Soltani et al [9] studied
finite element nonlinear tensional behavior of in-plane loaded GLARE
plates and compared with experimental results which had been presented
by Wu G. and Yang [10]. In both papers, the behaviors of in-plane loaded
sheets of FML have been presented. Numerical and experimental fatigue
analyses in FML panels with cutouts have been performed by E. Armentani.
In this research, a metal barrel of trunk of Airbus A330/300 was
considered as reference structure for designing, and panels with cutout
have been manufactured on this basis and subjected to multi-directional
loading [11]. The effect of geometry on behavior of FML plates in
linking joints has been numerically studied by R. M. Frizzell [12]. In
this analysis effect of delamination between layers, plastic behavior of
Aluminum layers and damage in fibers cured by resin in FML plates with
cutouts while subjecting to shear and tensional loading was
investigated. The results of this research have been compared with
previous experimental paper of the author [13]. Modeling of delamination
and damage in joints made by FML's has been studied by R. M.
Frizell et al. [14]. The thermoplastic behavior of FMLs under tension,
bending and impact loading has been performed by J. G. Carrillo et al.
[15]. The effect of the existence of cutouts and type of them on stress
concentration factor in FML plates has been carried out by Yazdani and
Rahimi [16].
In the load-displacement diagram two important points can be
observed. First point is relevant to plastic collapse load which is not
the necessary load for physical collapse of the structure. In fact,
plastic strains take place significantly at this point. Second point is
relevant to the maximum load which could be tolerated by the structure,
which is named by plastic instability load. Both the points are shown in
Fig. 1. To find plastic collapse load, two commonly methods,
Twice-elastic-slope (TES) method and Tangent-intersection (TI) method,
were suggested in papers. [17, 19]
[FIGURE 1 OMITTED]
The present paper describes the results of experimental and
numerical investigation into the failure and large deflection of FML
plates with different types of cutout. The study is included finite
element models and elastic compensation method to determine the effect
of types of cutouts and increment of their size on strength of the
structures. In addition, results of experimental and finite element
methods are compared with the results of elastic compensation method.
2. Experimental procedures
2.1. Manufacturing procedure
The plates were composed of 5 layers, including 3 aluminum alloy
sheets with thicknesses of 0.4 mm and 0.3 mm (to consider the effect of
thickness on structural behavior) and two woven E-glass layers with
approximate thickness of 0.25 mm for each layer. Aluminum sheets and
woven plies with length a = 104 mm and width b = 100 mm were cured with
epoxy resin, and for manufacturing them the lay-up method was applied.
The properties of aluminum sheets and composite layers which were used
for producing samples have been represented in Table 1.
The samples were pressured in room temperature during 24 hours.
Therefore, FML plates with approximate thicknesses of 1.4 mm and 1.7 mm
were obtained. Schematic view of plates' lay-up is shown in Fig. 2.
[FIGURE 2 OMITTED]
To create cutout in FML plates, the waterjet machine was used, in
order to prevent the delamination and damages in layers. Circular and
elliptical cutouts were created at the center of the plates. Circular
cutouts had two different radii. Radius of first type of circular cutout
was 7 mm, and of the second type was 14 mm. Moreover, for creating
elliptical cutouts, major and minor diameters of ellipse considered
being 28 and 14 mm, respectively. In one type of the samples the major
diameter, and in the other ones minor diameter was aligned in the load
direction. In Table 2, the samples which were tested are introduced with
numbers 1 to 8, and in this paper these names are used in reporting the
results.
Fig. 3 shows the specimens.
FML plates have complicated mechanical properties; the global
mechanical properties of plates obtained by Yazdani [16] are used in the
FEM analysis.
[FIGURE 3 OMITTED]
2.2. Testing procedure
Plates with different cutouts were subjected to static tensional
in-plane loading. The loading was performed by Instron 5500 machine with
capacity of 200 kN and a constant cross head speed of 1.3 mm/sec. In
order to prevent plates to be exposed to shear, special fixtures were
designed and were used in the testing procedure and are shown in Fig. 4.
[FIGURE 4 OMITTED]
3. Finite element simulation
3.1. Finite element model of FMLs
In FEM analysis, ABAQUS commercial software was used. One quarter
of the laminates were modeled because of the symmetry of the geometry,
loading, and boundary conditions. Dimensions which were used in the
simulation had the same sizes in the experimental work to compare
results of the two methods. The size of plates and type of cutouts are
presented in section 2.1. Global mechanical properties obtained by
Yazdani and Rahimi [16] were used in finite element analysis and the
plates were considered being homogenous.
Global mechanical properties of plates are presented in Table 3.
For elastic/plastic analysis of the samples, the measurements of
yield stress and plastic strain obtained from experimental work were
used in FEM analysis.
3.2. Mesh, loading, and boundary conditions
The element (S8R) was used which is an 8-node element and has the
capability of distributing stress in thickness direction. The
arrangement of elements was changed several times to achieve precise
results. In addition, finite element mesh was refined near the cutouts.
In all the simulations points along the x axis were constrained in
the y direction and points along the y axis are constrained along x
direction. Moreover, in the edge which plates are subjected to loading,
all degrees of freedom were removed from them, except displacement in x
direction.
An incremental load-displacement analysis is performed by using the
arc-length RIKS method in the ABAQUS software. Moreover, Von-Mises yield
criterion and non-linear analysis were performed. The RIKS method uses
in geometrically nonlinear static problems, where the load-displacement
response shows a negative stiffness and the structure must release
strain energy to remain in equilibrium. The RIKS method uses the load
magnitude as an additional unknown; it solves simultaneously for loads
and displacements [20].
4. Elastic compensation method
Elastic Compensation Method is a continuum finite element based
method for evaluation of lower bound limit load of the structure. By
using the iterative elastic analysis, considering [E.sup.e.sub.i] as the
module of elasticity in the previous step of loading; [E.sup.e.sub.i+1]
as the modulus of elasticity in the current step; [[sigma].sup.e.sub.i]
as the maximum stress in each element (Von-Mises stresses which were
obtained in FE was used in this paper); and [[sigma].sub.n] as nominal
or average value of stress the elastic modulus is modified after each
iteration according to Eq. (1) [21]:
[E.sup.e.sub.i+1] = [E.sup.e.sub.i]
[[sigma].sub.n]/[[sigma].sup.e.sub.i]. (1)
Where subscript i is the present iteration number. Eq. (1) is
continued until the convergence in results, and for the convergence
criteria, following equation is assumed [22]:
[[[[sigma].sup.e.sub.i+1]- [[sigma].sup.e.sub.i]]/
[[[sigma].sup.e.sub.i+1]]] [less than or equal to ] k, k [approximately
equal to] [10.sup.-4]. (2)
Above linear method mentioned, was used for calculating the lower
bound limit load which is enough for yielding. By considering Eq. (2),
at the end of the analysis, maximum value of [[sigma].sup.e.sub.i] was
calculated and used to obtain the limit load [P.sub.Li] based on the Eq.
(3):
[P.sub.Li]/[[sigma].sub.Y] =
[P.sub.n]/[max.sub.e][[sigma].sup.e.sub.i] [right arrow] [P.sub.Li] =
[P.sub.n] [[sigma].sub.Y]/ [max.sub.e][[sigma].sup.e.sub.i] (3)
In this method global mechanical properties which had been obtained
by Yazdani and Rahimi [16] were used. By the method mentioned, limit
load of each specimen was calculated and is presented in the next
section.
5. Results and discussion
The behavior of FML plates with cutouts under tensional in-plane
loading was considered. Results are expressed as load-displacement
curves which were resulted from experimental work and finite element
analysis. The load-displacement diagrams of samples 1 to 8 are shown in
Figs. 5-12, respectively.
Based on the results of above study, some important points were
concluded. First, the effect of using aluminum sheets on the behavior of
FMLs while subjecting to in-plane loadings. By comparing Figs. 5-8 with
Figs. 9-12 it is observed that the thinner plates have more displacement
in elastic region than the thicker ones under the same applied loadings.
Moreover, due to the more ratio of composite to metal in the plates with
1.4 mm thickness, more applied load was supported by these specimens in
almost all the cases and more displacement was achieved.
Metals have better behaviors in elastic region than composites.
Therefore, increment in the thickness which is related to aluminums
sheets causes more volume ratio of metal to composite in plates with
thickness of 1.7 mm. By doing so, their behavior was improved by
notifying the slope of load displacement diagrams in the elastic
regions.
The second is related to the effect of existence of the inevitable
cutout and the type of it on the strength of the plates. It is obvious
that the strength of all kinds of specimens with cutouts is less than
complete ones. Therefore, four types of cutout were created on the
center of plates to investigate the effect of types of cutout on
plate's failure. By comparing load-displacement diagrams in plates
with 1.4 mm and 1.7 mm thicknesses, it is observed that the maximum
loads were attained in plates with small circular cutout. Moreover, by
comparing Fig. 6 with Fig. 8 and Fig. 10 with Fig. 12, the big circular
cutout supports more load than the elliptical cutout which minor
diameter aligned to the load direction.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
As can be observed, the curves in finite element analysis follow
the same behavior and lead to almost close results to the experiments.
However, the differences can be attributed to neglecting the
delamination effects and approximations of using the global mechanical
properties in both the finite element simulations and elastic
compensation methods.
By using two methods TES and TI, plastic collapse load of the
structures were calculated for experimental and finite element analysis,
and the results are presented in Table 4.
As it is shown in Table 4, the plastic collapse load of the samples
with more thicknesses has been increased, except in the sample 8, and
the values calculated of both methods have close results. In addition,
in average, the minimum plastic collapse load is attributed to the
sample 8, and the maximum is related to the sample 5. Plastic
instability load which is the maximum load that could be attained for
both experimental and finite element methods are obtained and are
presented in Table 5.
The results obtained in Table 5 shows that the maximum plastic
instability load is related to plate with thickness 1.4 mm and circular
cutout with radius 7 mm, and the minimum is corresponding to the plate
with thickness 1.7 mm and elliptical cutout which minor diameter is
aligned in the load direction. Elastic compensation method results are
expressed in Table 6.
As it was observed in Table 6, limit loads which are obtained in
this method are closer to plastic instability loads of the experiment.
6. Conclusion
The failure analysis of FML plates with different types of cutout
have been studied and discussed. For this purpose, experimental, finite
element and elastic compensation methods were used. It shows that the
results in both numerical methods follow the same behaviors as
experiments. In numerical analysis, the delamination of layers was
neglected but in the experiment it is observed that the layers in
plastic region of loading started to show negligible delamination. It
was concluded that in small circular cutout the value of maximum plastic
instability load was more than the plates with elliptical cutouts. The
thinner plates with 1.4 mm carried out more load than the thicker ones;
it can be attributed to the higher ratio of the composite to the metal.
Moreover, due to the higher ratio of the metal in the layers of thicker
plates, they have been shown a better plastic collapse loads and less
displacements under the applied load.
crossref http://dx.doi.org/10.5755/j01 .mech.20.1.3530
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Received February 19, 2013
Accepted January 21, 2014
Saleh Yazdani *, G. H. Rahimi **
* Mechanical Engineering Department, Tarbiat Modares University,
Tehran, Iran, E-mail: yazdani.saleh@yahoo.com
** Mechanical Engineering Department, Tarbiat Modares University,
Tehran, Iran, E-mail: rahimi_gh@modares.ac.ir
Table 1
Material properties of the layers [18]
Material E, GPa v [E.sub.T], [E.sub.L],
GPa GPa
AL 71 0.33 -
Woven/glass epoxy - 15.8 15.8
Material [v.sub.LT] [G.sub.LT],
GPa
AL
Woven/glass epoxy 0.25 2.8
Table 2
Sample's specification
Sample's name Thickness, mm Cutout type
Sample 1 1.4 Circular--7 mm radius
Sample 2 1.4 Circular--14 mm radius
Sample 3 1.4 Elliptical--major diameter
aligned in load direction
Sample 4 1.4 Elliptical--minor diameter
aligned in load direction
Sample 5 1.7 Circular--7 mm radius
Sample 6 1.7 Circular--14 mm radius
Sample 7 1.7 Elliptical--major diameter
aligned in load line
Sample 8 1.7 Elliptical--minor diameter
aligned in load line
Table 3
Global mechanical properties of FML plates [16]
Plate thickness E, GPa v
1.4 mm 49.905 0.25
1.7 mm 54.622 0.25
Table 4
Plastic collapse load using TI and TES method
Plastic Collapse Load, N
Specimens TES Method TI Method
EXP FEM EXP FEM
Specimen 1 12761.5 13901.23 13002.73 13723.81
Specimen 2 13148.58 13121.2 12737.875 12953.136
Specimen 3 11751.02 12166.5 12053.588 11918.089
Specimen 4 13174.59 12541.4 12390.633 11861.093
Specimen 5 13173.54 13826.3 12965.382 14043.169
Specimen 6 13128.26 12495.5 12144.268 11943.542
Specimen 7 13115.62 12369.2 11865.676 11911.054
Specimen 8 10594.03 10417.1 10866.134 10075.453
Table 5
Plastic instability load in experimental and FE analysis
Specimens Plastic Instability Load, N
EXP FEM
Specimen 1 13752 14100
Specimen 2 13659.23 13390.5
Specimen 3 12623.48 12521
Specimen 4 13699.76 12791.1
Specimen 5 13718.13 14006.3
Specimen 6 13195.63 13014.3
Specimen 7 13504.97 12734.7
Specimen 8 10761.84 10563.1
Table 6
Limit load in elastic compensation method
Specimen Limit Load, KN
Specimen 1 13.32
Specimen 2 13.18
Specimen 3 12.26
Specimen 4 12.73
Specimen 5 13.83
Specimen 6 13.07
Specimen 7 13.11
Specimen 8 10.14
