Advances in the Bonded Composite Repair o f Metallic Aircraft Structure phần 6 pptx

262 Advances in the bonded composiie repair of metallic aircraft structure

~~~~ ~

+ 1.2 mm skin, 0.52 mm patch

- 3mm skin, 0.889 mm patch

K

8

I

‘I

”’

0 1 2

l/R

3

Fig. 9.34. Composite repairs to cracked holes.

9.12. Findings relevant to thick section repair

As a result of this chapter we find that the major design considerations are, viz:

The maximum stress intensity factor, allowing for the visco-plastic nature of the

adhesive, should be as low as possible and preferably below the critical value

Kth for fatigue crack growth in the material. For cracks at holes or notches, or

repairs to corrosion damage load bi-axiality should be accounted for in the

design process.

L. The maximum adhesive stresses/energy should be below the value at which

fatigue damage accumulates in the adhesive, see [8,16,21]. For FM73 this

2

NORMALIZED

STRESS

INTENSITY

FACTOR, WK.

1

0

0

0

0 UNREPAIRED CRACK /

#

0

#

/

SEMI-INRNITE HART-SMITH’S SOLUTION

TRANSITION FROM

SHORTTOLONGCRACK

.-..-..-.. -..-.*--

ROSES SOLUTION

ROSES CHARACTERISTIC LENGTH

I I I I I

1 2 3 4 5 6

*

NORMALIZED HALF-CRACK LENGTH, a/ll

Fig. 9.35. Crack-tip stress-intensity factors for “short” and “long” cracks, from [29],

Chapter 9. Numerical analysi.7 and design 263

3.

value is -25 MPa. However, to minimise errors in measuring and computing

the adhesive stresses and allowables, see [20], it is best to compute and

measure the energy in the adhesive W = 1 /20gsg = 1 ogdsg. These measure￾ments are best performed using the ASTM thick adherend test, ASTM D

1002, see [16].

The composite patch must not experience failure by interply delamination. This

can be checked by ensuring that the polynomial failure criteria is not greater

than one. The commonly used failure criteria are: Tsai-Hill, Hoffman and Tsai￾Wu. These failure criteria are generally written in the form:

Tsai-Hill criterion: Failure is assumed to occur when

(9.72)

Here the material is assumed to have equal strengths in tension and

compression, i.e. X, = X, = X and Y, = Y, = Y

Hoffman criterion: Failure is assumed to occur when

Tsai-Wu criterion: Failure is assumed to occur when

The coefficient Fl2 is experimentally determined from test specimens under

biaxial loading and F12 must satisfy a stability criterion of the form

(9.75)

creates some complication in the use of this theory. It has been suggested that

F12 be set to zero.

The symbols used in Eqs. (9.76) to (9.79) are defined as:

X, Allowable tensile stress in the principal x (or 1)-direction of the material

X, Allowable compressive stress in the principal x (or 1)-direction of the

material

Y, Allowable tensile stress in the principal y (or 2)-direction of the material

Y, Allowable compressive stress in the principal y (or 2)-direction of the

material

S Allowable shear stress in the principal material system

At the moment one shortcoming in the certification process for composite joints/

repairs and rib stiffened panels is the lack of understanding of the matrix

dominated failures. The vast majority of the analysis tools assume that the

composite is behaving in the linear elastic regime. However, there are instances, see

[22-241 when material nonlinearities, in the composite adherends, play a significant

264 Advances in the bonded composite repair of metallic aircraft structure

role in these failures. Unfortunately, it is currently uncertain as to when these

effects need to be considered, for more details see [22-241.

4. The average stress, over any one ply through the thickness of the boron patch,

should not exceed 1000 MPa.

It must be stressed that for repairs to primary structures a full 3D finite

element analysis must be performed. (Even for repairs to thin skins the stresses

and strain fields are dependent on the mesh density and element type used in the

analysis, see Section 9.9.1 and [20] for a more detailed summary of this

phenomena.) This analysis should include a damage tolerant assessment of both

the structure and the composite repair performed in accordance with the current

FAA procedures for damage tolerant assessment, as given in [25]. As discussed in

[26] this analysis should be supported by test evidence in the appropriate

environment, unless (as stated in [25]) “it has been determined that the normal

operating stresses are of such a low order that serious damage growth is

extremely improbable”, that:

(a) The repaired structure, with the extent of damage established for residual

strength evaluation, can withstand the specified design limit loads (considered

as ultimate loads); and

(b) The damage growth rate both in the structure, the adhesive and the composite

repair, allowing for impact damage, interply delamination and adhesive

debonding under the repeated loads expected in service (between the time the

damage becomes initially detectable and the time the extent of damage reaches

the value for residual strength evaluation) provides a practical basis for

development of the inspection program.

The analysis/testing program should allow for impact damage, interply

delamination and adhesive debonding under the repeated loads expected in service

(between the time the damage becomes initially detectable and the time the extent

of damage reaches the value for residual strength evaluation) provides a practical

basis for development of the inspection program.

9.12.1. Comparison of commercial finite element programs for the 30 analysis of

repairs

A variety of commercial finite element programs can now be used to design

composite repairs. The most widely used programs are: MSC-Nastran, NE￾Nastran, ABAQUS, PAFEC, and ANSYS. To obtain the necessary accuracy, and

to assess all possible failure modes, the finite element analysis of most composite

repairs needs to be 3D. Since the adhesive bond line is typically 0.2mm thick this

means that it is often necessary to work with elements with large aspect ratios. As a

result any analysis should use elements with at least one mid-side node. With this in

mind the relative advantages and disadvantages of these programs are presented

below.

Chapter 9. Numerical analysis and design 265

Program

Name Advantages Disadvantages

ANSYS

ABAQUS

PAFEC

MSC-Nastran

NE-Nastran

Widely used for mechanical design.

ABAQUS is recognised as being an

excellent non-linear program.

Can automatically link 2D and 3D

models.

Can use cubic as well as parabolic elements.

The Nastran data structure is very widely

used and many structural

models are MSC-Nastran based.

The data structure is compatable with

MSC-Nastran.

Has the ability to use enriched 3D

elements. i.e. 21 noded bricks efc.

As such it can tolerate very large aspect

ratio elements.

Can model both material and geometric

non-linearities using both 20 and 21

noded elements.

Cannot cope with very large aspect

ratio elements.

Cannot cope with very large aspect

ratio elements.

If the aspect ratio is large it can

yield poor results when the adhesive

yields.

Requires the use of the PAFEC

graphics pre and post processor.

Cannot cope with very large aspect

ratio elements.

When using 3D parabolic elements.

i.e. 20 noded bricks erc. the analysis

options are quite severely reduced.

Limited number of pre and post

processors available. On PC’s it

uses the same pre and post processor,

it. FEMAP (SDRC). as MSC￾Nastran.

Essentially limited to mechanical

and aeronautical structural analysis.

In 3D elasticity the displacements u, v and w must satisfy the differential

Eq. (9.34)

V4tl=0 ~ V4v=O , and V4w=0 (9.76)

The use of P-element based finite element analysis can violate this fundamental

requirement, if the order is greater than three, and as such the use of P-element

based analysis is not recommended for 3D problems. As pointed out by Liebowitz,

et al. [35] this means that “the basic equilibrium conditions of the basic f.e.

equations is violated”. Furthermore, the use of high order P elements can result in

localised oscillations in the solution, see Zenkiewicz, et al. [36] for more details. As

such the use P-element formulations for fracture and composite repair analysis

should be avoided.

When performing a 2D analysis of a joint the best results are obtained using nine

noded elements, which have a node at the centroid, or the CQUADR element, or

the equivalent element with drilling degrees of freedom. The advantage of these

elements is that they can accommodate large aspect ratio’s and extensive mesh

distortion.

266 Advances in the bonded composite repair of metallic aircraft structure

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Chapter 9. Numerical analysis and design 267

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