Fracture Analysis of FRP Composites Subjected To Static and Dynamic Loading

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Fracture Analysis of FRP Composites Subjected To Static and Dynamic Loading

Fazal Mohammed1, MD Nasir Ali2, S.A.Quadri 3

1M.Tech Student, Dept. of PG studies, VTU Regional office Gulbarga, Karnataka

2 Asst. Professor, Dept. of Mechanical Engineering, KBN College of engineering, Gulbarga, Karnataka

3 Asst. Professor, Dept. of Mechanical Engineering, KBN College of engineering, Gulbarga, Karnataka

Abstract The objective of this paper is to investigate the Stress Intensity Factor (SIF) for benchmark problems for static and dynamic loading in composite plates having center, edge. Further the analysis is extended to CT specimen, plate with 3-point bend, v-notch. In the static analysis SIFs are found for an isotropic material using singular and j-integral approach and it is inferred that the deviation is minimal. For the orthotropic material SIF is found out for the above specimens with Carbon /Epoxy, R Glass /epoxy, S2 glass fabric/epoxy material properties. The Transient Dynamic analysis on the above specimens is carried out. Full method is employed to perform loading and the J-integral approach is used to find the SIFs. The detail analysis using FEA is carried out for calculating SIF for the above specimens.

Keywords Crack tip, J-integral, Stress Intensity Factor (SIF), Singularity, longitudinal and transverse modulus

  1. INTRODUCTION

    The fundamental goal in production and application of composite materials is to achieve performance from the composite that is not available from the separate constituents or from other materials. The need for high performance to weight ratio structure coming from the most advanced engineering fields is the main driver of the increasing usage of composite materials for crucial application. Recent developments in industries such as aerospace industry require lightweight and stiff materials fit the bill perfectly. The materials such as fibre-reinforced plastics are widely being used as a replacement for steel in many industries.

    Unlike conventional isotropic materials of steel and concrete there are no readily available design charts and guidelines to help the structural engineer when it comes to working with composites. Analytical solutions for cracked plates are very limited.

    Among the available methods for calculating fracture parameters, the interaction energy integral method has emerged as a useful technique for the extraction of mixed- mode stress intensity factors. The contour integrals where derived directly from the J-integral by considering an additive composition of the existing fields with a judicious choice of known auxiliary fields. For the purpose of post processing finite element solutions, the contour integrals

    were typically recast as equivalent domain integrals over a finite region surrounding the crack tip [1].

    The work of B.K.Thakkar and P.C.Pandey [2] reviews the progressive failure analysis of fiber-reinforced polymer composites. According to the work, various modes of failure of FRP laminae are fiber micro cracking, fiber kinking, fiber matrix debonding and matrix cracking. Matrix cracking: if the state of stress results in a pre dominant tensile stress in the direction perpendicular to the fibers, the matrix may separate out from the surface of the fibers and create a void. These voids nucleate to create a crack running parallel to the fibers. Matrix cracking affects the transfer of loads between fiber and matrix. Delamination is a mode of structural failure, which can be said to be material failure at laminate level. Delamination initiates a separation of layers in a localized manner and further propagation to peeling off of one ply from another. A continuum damage model describes mathematically the nucleation and evolution of a localized material failure zone

    The need for testing such specimens is often dictated by the characteristic dimensions of the end product. A new methodology which combines experimentally determined loads and fracture time, together with a numerical model of the specimen is presented in paper [3]. Calculations are kept to a minimum by virtue of the linearity of the problem. The evolution of the stress intensity factor (SIF) is obtained by convolving the applied load with the calculated specimen response to unit impulse force. The fracture toughness is defined as the value of the SIF at fracture time. The numerical model is first tested by comparing numerical and analytical solutions of the impact-loaded beam. One point impact experiments were carried out on of commercial tungsten base heavy alloy specimens.

    Aim of this paper is to provide the structural engineer with data regarding SIF and variation of stress at the crack tip using Finite Element Analysis. FEA addressing plate problem fall under two categories-one involving singularity formulations and other involving paths independent integrals approach [4].

    ANSYS allows us to model orthotropic materials with specialize elements called Layered Elements. After building a model with a layered element structural analysis can be

    carried out. Steel and glass polymer are taken as an orthotropic materials in our present study.

  2. ELEMENT DESCRIPTION USED IN ANALYSIS

    1. PLANE82-2D, 8-node structural solid: It provides more accurate results for mixed (quadrilateral-triangular) meshes and can tolerate irregular shapes without as much loss of accuracy. The 8-node elements id defined by eight nodes having two degrees of freedom at each node: translations in the nodal x and y directions. The element may be used as a plane element or as an axisymmetry element. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.

      Figure 1: PLANE82 Geometry

    2. SHELL99-Linear layered structural shell:

      This is an 8-node, 3-D shell element can be used for layered applications of a structural shell model. It is designed to model thin to moderately thick plate and shell structures with aside-to-thickness ratio of roughly 10 or more . it allows up to 250 layers. The element has six degrees of freedom at each node; translations in the nodal x,y and z directions and rotations about the nodal x,y, and z-axes.

      Figure 2: SHELL99 Geometry

      LN= Layer number NL= Total number of layers

  3. FRACTURE ANALYSIS OF CRACKS USING FEA

    For case study-I, Plane 82 element is used for modelling of plate under plane stress conditions as per given dimensions. For case study II, SHELL 99 element is used varying the number of layers. The element near crack tip were meshed with crack tip elements by shifting mid side node to 1/4th distance. The meshed models are solved by applying tensile load and symmetric boundary conditions. Then the J- integrals are completed.

    Material properties

    For isotropic plate E=48.3 GPa, =0.3. For orthotropic plates:

    Table 1: Orthotropic Plates

    Properties

    R-glass

    S-glass

    Carbon/epoxy

    Ex

    48GPa

    22.925GPa

    70 GPa

    Ey

    12.4 GPa

    22.925GPa

    25 GPa

    Ez

    12.4 GPa

    12.4 GPa

    25 GPa

    xy

    0.32

    0.12

    0.32

    yz

    0.28

    0.2

    0.25

    zx

    0.28

    0.2

    0.25

    Gxy

    <>6.6 GPa

    4.7 GPa

    15 GPa

    Gyz

    4.14 GPa

    4.2 GPa

    12 GPa

    Gzx

    4.14 GPa

    4.2 GPa

    15 GPa

    Density

    2 gm/cm3

    1.8gm/cm3

    2 gm/cm3

  4. CALCULATION OF FRACTURE PARAMETERS

    For finding SIF first define a crack tip and crack path around the tip. The first node on the path should be the crack-tip node. For a half-crack model, two additional nodes are required, both along the crack face. For a full-crack model, where both crack faces are included, four additional nodes are requires: two along one crack face and two along the other path along crack face.

    Figure 3: path along the crack face

    J-Integral is one of the most widely accepted parameters for elastic-plastic fracture mechanics. The J-Integral is defined as follows:

    Where W is the strain energy density, T is the kinematic energy density, represents the stresses, u is the displacement vector, and is the contour over which the integration is carried out. For a crack in a linear elastic material, the J-Integral represents the energy-release rate

  5. RESULTS & DISCUSSIONS Case-1: Isotrophic Material

    Static analysis:

    Table 2: SIFs for isotropic plate under static loading

    Table 4: SIFS for different layers by varying a/b ratios of S-glass material

    Approach

    J Integral

    Singular

    SIF

    `26.29

    37.528

    Layers

    a/b ratio

    SIF, N-mm

    0.2

    0.4

    0.6

    0.8

    2

    7.0892

    12.8333

    20.1301

    30.8745

    4

    4.8577

    9.6751

    14.5123

    22.2153

    6

    5.12

    10.1272

    15.4309

    23.4259

    8

    4.8577

    9.6751

    14.5123

    22.2153

    Case-2 composite material: Static analysis:

    SIF, N-mm-3/2

    Layers

    a/b ratio

    SIF , N-mm

    0.2

    0.4

    0.6

    0.8

    2

    4.4728

    9.0672

    13.6758

    22.1776

    4

    4.4728

    9.0672

    13.6758

    22.1776

    6

    4.4730

    9.0675

    13.6764

    22.1785

    8

    4.4728

    9.0672

    13.6758

    22.1776

    25

    20

    15

    10

    5

    0

    0 5 10

    No of layers

    a/b ratio=0.2

    a/b ratio=0.4

    a/b ratio=0.6

    a/b ratio=0.8

    Evaluation of stress intensity factor (SIF) in composite plate with centre line crack.

    Table 3: SIFS for different layers by varying a/b ratios of R-glass material

    40

    SIF, N-mm-3/2

    a/b

    Figure 5: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    From table 4 it is observed that by increasing the (a/b) ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release is high as the crack grows. However the variation of SIF with respect to number of layers is almost constant because the transverse modulus

    30

    20

    10

    0

    0 5 10

    No of layers

    ratio=0.2

    a/b ratio=0.4

    a/b ratio=0.6

    a/b ratio=0.8

    effect is neglected.

    Table 5: SIFS for different layers by varying a/b ratios of carbon /epoxy material

    Layers

    a/b ratio

    SIF , N-mm

    0.2

    0.4

    0.6

    0.8

    2

    6.6811

    11.4237

    17.5825

    26.7372

    4

    5.38

    9.4828

    14.0852

    22.1491

    6

    5.5616

    9.8354

    14.7751

    23.016

    8

    5.38

    9.4828

    14.0852

    22.1491

    Figure 4: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    From table 3 it is observed that by increasing the (a/b) ratio, the SIF is increasing. This is due to the crack propagation; material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same and for plate with 2 layers SIF is very high as compared to all other layers. Due to symmetry lay up and when the crack is parallel to fibre direction the SIF is more and when it is in transverse direction the SIF is less.

    Figure 6: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    From table 5 It is observed that by increasing the a/b ratio, the SIF is increasing. This is due to the crack propagation; material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same and for plate with 2 layers SIF is very high as compared to all other layers. Due to symmetry lay up and when the crack is parallel to fiber direction the SIF is more and when it is in transverse direction the SIF is less.

    The SIF is high in R-glass as compared to S-glass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez , Hence its SIF is less than R-glass.

    Evaluation of stress intensity factor (SIF) in composite plate with edge crack

    Table 6: SIFS for different layers by varying a/b ratios of R-glass material

    Layers a/b ratio

    SIF , N-mm

    0.2

    0.4

    0.6

    0.8

    2

    12.9616

    27.7766

    62.9939

    206.5355

    4

    10.3766

    22.7027

    53.4329

    176.0265

    6

    10.8965

    24.4534

    56.889

    187.9538

    8

    10.3766

    22.7027

    53.4329

    176.0265

    Figure 7: Variation of Stress Intensity Factor (SIF) with increasing number

    From table 6 It is observed that by increasing the (a/b) ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same due to the symmetry lay up of even distribution. The SIF is higher at less number of layers and gradually decreases while increasing the number of layers symmetrically in odd numbers.

    Table 7: SIFS for different layers by varying a/b ratios of S-glass material

    Layers

    a/b ratio

    SIF , N-mm

    0.2

    0.4

    0.6

    0.8

    /td>

    2

    9.7147

    21.2567

    50.6355

    166.2591

    4

    9.7147

    21.2567

    50.6355

    166.2591

    6

    9.7151

    21.2576

    50.6375

    166.2658

    8

    9.7147

    21.2567

    50.6355

    166.2591

    Figure 8: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    From table-7 It is observed that by increasing the a/b ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is almost constant because the transverse modulus effect is neglected.

    Layers

    a/b ratio

    SIF , N-mm

    0.2

    0.4

    0.6

    0.8

    2

    13.1761

    30.6753

    66.0074

    219.79

    4

    10.8237

    23.5611

    52.7597

    174.364

    6

    11.2033

    24.895

    55.3584

    183.4079

    8

    10.8237

    23.5611

    52.7597

    174.364

    Table 8: SIFS for different layers by varying a/b ratios of carbon /epoxy material

    of layers

    Figure 9: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    From table-8 It is observed that by increasing the a/b ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same due to the symmetry lay up of even distribution. The SIF is higher at less number of layers and gradually decreases while increasing the number of layers symmetrically in odd numbers.

    From table-9 it is observed that the variation of SIF with respect to number of layers is not linear for the plates with R-glass and Carbon /Epoxy materials. It is also observed that the SIF for these plates with 4 and 8 layers is same. The variation of SIF with respect to the number of layers for the S-Glass plate is almost minimal.

    The SIF is high in R-glass as compared to S-glass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez ,hence its SIF is less than R-glass.

    S.NO

    SIF , N-mm

    Layers

    R-Glass

    S-Glass

    Carbon

    1

    2

    14.3631

    4.8929

    12.6748

    2

    4

    3.5936

    4.8929

    6.2458

    3

    6

    5.8188

    4.8893

    7.663

    4

    8

    3.5936

    4.8929

    6.2458

    Evaluation of stress intensity factor (SIF) in CT specimen Table 10: SIF for different layers and different materials

    SIF, N-mm-3/2

    The SIF is high in R-glass as compared to S-glass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez, hence its SIF is less than R-glass.

    Evaluation of stress intensity factor (SIF) in composite plate with 3-point bend.

    Table 9: SIF for different layers and different materials

    20

    15

    10

    5

    0

    0 5 10

    No of layers

    R-Glass S-Glass Carbon

    S.NO

    SIF , N-mm

    Layers

    R-Glass

    S-Glass

    Carbon

    1

    2

    196.7223

    94.8953

    153.4209

    2

    4

    183.8553

    94.8953

    154.4226

    3

    6

    170.1841

    94.8983

    143.1733

    4

    8

    183.8553

    94.8953

    154.4226

    Figure 10: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    Figure 11: Variation of Stress Intensity Factor (SIF) with increasing number of layers

    From table-10 it is observed that the variation of SIF with respect to number of layers is not linear for the plates with R-glass and Carbon /Epoxy materials. It is also observed that the SIF for these plates with 4 and 8 layers is same. The variation of SIF with respect to the number of layers for the S-Glass UD/Epoxy plate is almost minimal.

    The SIF is high in R-glass as compared to S-glass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez ,hence its SIF is less than R-glass.

    Evaluation of stress intensity factor (SIF) in composite plate with V-notch

    Table 11: SIF for different layers and different materials

    S.NO

    SIF , N-mm

    Layers

    R-Glass

    S-Glass

    Carbon

    1

    2

    15.5864

    8.7347

    6.9341

    2

    4

    16.5136

    8.7347

    4.8469

    3

    6

    17.5849

    8.7350

    4.2871

    4

    8

    16.5136

    8.7347

    4.8469

    SIF, N-mm-3/2

    20

    15

  6. CONCLUSIONS

Singular finite element approach is used for calculating SIFs for plate made up of isotropic material and J-Integral approach is used for calculating SIF for both the plates made up of isotropic and orthotropic materials. Stress induced in the composite material plates are found to be much lesser than isotropic material plates due to fibre reinforcements at different angles. Further the crack growth is obstructed by the fibre orientation. The SIF in R-glass plates is high as compared to S-glass fabric/epoxy and Carbon /epoxy is due to longitudinal and transverse modulus influence. The SIF in S-glass is almost constant because the transverse modulus effect is being neglected. The SIF for all specimens subjected to dynamic loading is found to be nearly double when compared to static loading.

10

5

0

0 5 10

No of layers

    1. lass S-Glass Carbon

      REFERENCES

      1. J.Ahmad and F.T.Loo, Solution of plate bending problems in fracture mechanics using specialized FEA,engng fracture mechanics 661-672.

      2. B.K.Thakkar and P.C.Pandey, 2006, Continuum damage mechanics applied to progressive failure analysis of FRP

        Figure 12: Variation of Stress Intensity Factor (SIF) with increasing number of layers

        From table-11 It is observed that the variation of SIF with respect to number of layers is not linear for the plates with R-glass and Carbon /Epoxy materials. It is also observed that the SIF for these plates with 4 and 8 layers is same. The variation of SIF with respect to the number of layers for the S-Glass plate is almost minimal.

        The SIF is high in R-glass as compared to S-glass and Carbon composite due to longitudinal and transverse modlus influence. In carbon composite, Ey=Ez ,hence its SIF is less than R-glass.

        composites- A review Journal of Structural Engineering, Vol.33, No , pp 267-285.

      3. R.Kumutha, R.Vaidyanathan and M.S.Palanichamy, Dec 2006-Jan 2007, Behaviour of concrete compression and specimens strengthened using glass fibre-reinforced plastics Journal of Structural Engineering, Vol. 33, No.5, pp 01-405.

      4. Barna.A.Szabo and Glenn J.Sharmann, 1988, International journal for numerical methods,Vol.26, 1855-1881.

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