oportunities in composites

8/9/2019 Oportunities in Composites

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Opportunities in CompositesComposites Design Tutorial 3

Stephen W. Tsai

Aeronautics &

AstronauticsStanford University

September 2, 2008

We wish to welcome all participants of this tutorial. This is the 3rd time that we have offered this. Each session has been updated, plus new ones in Steve Huybrechts that

you just

heard

and

in

Ran

Kim

on

test

methods.

We look forward to working with all of you.

In my brief introduction here today, I wish to show some of the motivations of our tutorials. We firmly believe that composites have much to offer. We need to built a solid knowledge and empowered with effective tools to make composites competitive. We will give you some examples of the great opportunities.

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Weight => Fuel => Green

Toyota Prius“2/3 lighter,twice as

fuelefficient”

B-78720 percentlighter now,50 percent

possible

GEnx“66 percent

lighter,100 percent

stronger,Infinite life!”

The driver of our technology is fuel efficiency and durability.

We have the case of Boeing 787 that took a bold action in extending the use of composites from the minor role to a major component of the entire structure. It opens the door for others to follow.

The GEnx engine is another example of a company that pioneered in the use of composites for fan blades. Not only GE90 and its derivative engines have an unrivaled safety and weight advantage, it is the sole engine for Boeing 777 ‐200 and ‐300.

Toyota is another world leader in fuel efficient cars with it Prius that has set a standard

for others to follow with plug ‐in cars and other products. The key performance is derived from the use of composites.

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Test ‐based Blocks vs MMFStrength Paramides

On the left is the traditional test ‐based building block approach. The basic block is a ply of unidirectional, NCF, fabric, or another material. It is an empirical approach that

requires thousands

of

tests

to

characterize

the

basic

material,

and

extensions

to

smooth

laminates, and laminates with open or filled holes. There is no attempt to model or simulate failures of composites.

On the right is our approach, called MMF: Micromechanics of Failures. It goes one level below the basic ply. Fiber, matrix and their interface are the building blocks. The number of variables are significantly reduced to 6: two for fiber, two for mastrix and two for interface. When we go one level lower we can build a system of database for design and manufacturing much simpler and easier to acquire than the test ‐based approach shown on the right.

This tutorial is dedicated to show how MMF can change the mindset of the traditional composites design leading to more competitive composites.

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Decreasing Number/ComplexityAllowable data set: US$20,000,000 and 2 years

$20x10 6

$2x10 6

$10 5

One example of the traditional test ‐based building block approach is the number of specimens, their testing and the time required to accomplish the test. The design

allowable using

this

method

costs

20

million

US

dollars

and

takes

2

years.

Once

such

data set is established it is rigidly followed and makes material and processing changes nearly impossible to be accepted. Notched specimens such as laminates with open and filled hole are used to as part of the database. Such specimens lead to one of the reasons of the cost and time of this design allowable generation.

If we learn to use models and simulation to predict specimens with holes from smooth specimens the cost and time will reduce by an order of magnitude. Thus the first step to change our mind set in data generation is to develop methods for prediction. Then the number of specimens with holes will be limited to those required for validation.

Finally our approach goes one level lower than the plies. We go to the constituents as we mentioned earlier. Then the number of specimens and time required can be reduced by another order of magnitude. Furthermore, we can introduce time and temperature dependent strength, such as creep rupture and fatigue, within the same frame work of simulation. This approach will be explained by several of our lecturers later in this tutorial.

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MMF: Fatigue Life Prediction

MMF

TIME-TEMPERATURE DEPENDENTMATRIX PROPERTIES

FATIGUE LIFE OF LAMINATES

In the upper left is the master curve storage modulus of typical epoxy based on time and temperature dependent behavior of a viscoelastic material.

With MMF it is possible to link the master curve of this matrix material to those of laminated structures. The creep rupture and fatigue of composite laminates can be predicted. Again, corresponding failure envelopes can be easily generated. This is how on the lower right showing successive fatigue failure envelopes of a laminate expressed in life or number of cycles.

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Percent [+/-45]0 10 20 30 40 50 60 70 80 90 100

P e r c e n

t [ 0 ]

0

10

20

30

40

50

60

70

80

90

100

P e r c e

n t [ 9 0 ]

/4 laminate : [0 n1 /(+/-45) n2/2 /90 n3 ]

10 Percent Rule: /4 Laminates

[0 5 /(+/-45) 2/2 /90 4]= [0 5 /(+/-45) 1 /90 4]

[0 4 /(+/-45) 6/2 /90 0]= [0 4 /(+/-45) 3]

n1+n2+n3=100%

[0 8 /(+/-45) 0/2 /90 2]= [0 4 /90 1]

Examples

Balance Laminates

11! - 8! = 66 - 30= 36 Laminates

If our family of laminates is based on 10 percent increments, we will have a total of 11! or 66 laminates with combinations of [0], [90] and [+45/ ‐45] ply angles. This is shown in

the “carpet

plot” above.

There is a design practice by many organizations known as the 10 percent rule: there must be 10 percent ply in each of the four ply angles. That is, none of the four angles can be zero.

If this rule is imposed, the possible laminates in this family are bounded by the red triangle in the carpet plot above. The number of possible laminates reduces from 66 to 36, a loss of 20 possible laminates.

There are additional penalties. The minimum thickness or gage of the laminate goes up for many laminates. If another design rule says that all laminates have to be symmetric, this penalty is doubled; i.e., twice as bad.


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Severe Penalties Imposed by Rules:4 ply angles; 10% rule; symmetric laminate; test ‐

based

The design rules of 4 ply angles, 10 percent rule, symmetric laminates and test ‐based building block approach.

The results of these penalties are shown in this plot of the effective laminate stiffness along the 1‐axis as functions of percentages of [0], [90] and [± 45]. When these percentages are 25 we have a quasi ‐isotropic laminate shown by a hexagon. The value is shown by a horizontal line. We designate it as a Quasi ‐isotropic cut ‐off. It means that composite laminate should not be designed to have a stiffness lower than this value.

It turns out that most carbon/epoxy composites have such value that is about the same as aluminum. Most composites used today have stiffness nearly to this aluminum value. So it is often referred to as the black aluminum. It is much too conservative.

What is worse, anisotropy is essentially ignored. Many design practice of aluminum is carried over. Example is the use of allowable based on strain. We would prefer that stress by used.

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Tri‐Angle: [0/ ± ] Laminate Stiffness

9

E1o

E6o50% [0]

1.5x Al

50% [0]

(50/50/0)

Instead of using 4 ply angles, we show what 3 angles can do. On top of this viewgraph, we have the longitudinal stiffness E1° as a function of the percentage of angle ‐ply

angle [±

]. At

the

bottom

we

show

the

shear

modulus

as

a function

of

the angle

as

it

goes from 0 to 90 degrees. Volume percent of [0] is the parameter.

As also show the quasi ‐isotropic constants as a reference point. It is represented by [0/ ± 60] for both longitudinal stiffness E1° and shear modulus E6° .

Tridirectional laminates can have good stiffness to compete with 4‐angle laminates shown in previous carpet plots. An example of 50 percent [0] and [± 45] is shown. The [02/ ± 45] or (50/50/0) has the same shear modulus as aluminum (at 27 GPa) with much increased longitudinal stiffness, at 104 GPa and 1.5 times that of aluminum.

Fewer ply angles will reduce number of failure modes. It will be simpler to select a sublaminate from which thick laminates can be build. The resulting laminate will be more homogenized and therefore tougher. More will be said later in this session about sublminates and importance of homogenization.

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Angle‐Ply [± ]: a continuous variable

Higher shear Higher stiffness

Aluminum1.5 x Al

22.5 22.5

1.3 x Al

E1 E6

27.5 27.5

In this viewgraph we show the same comparison if 2 ply angles are used. We call this angle ‐ply laminates.

On the left is the longitudinal stiffness of [± 22.5] with a value 1.5 that of aluminum.

On the right is the longitudinal shear modulus of the same [± 27.5] laminate with a value 1.3 that of aluminum.

The 40 percent lighter of CFRP has not been included. Thus on a specific stiffness basis, angle ‐ply laminates can be nearly 200 percent more efficient than aluminum. This phenomenal advantage of composites have not been achieved in most structural

applications. It shows how much more advantage of composites are there to be used.

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First‐ and Last‐Ply Failures

TensileStress

Tensile Strain

Extension of inactnot admissible

Prediction of strength is a very difficult problem. Laminates are assumed to be intact without load. As stress increases micro cracking appears until a saturation level is

reached. It

is

usually

assumed

that

this

saturation

level

is

reached

instantaneously.

We

identify this point as FPF. Most failure criteria including MMF can make such prediction reasonably accurately.

What happens beyond FPF is far more difficult to simulate. It is not admissible to assume that the stiffness of the composite will continue its stiffness after FPF. Presence of micro crack will make laminate softer.

One approximation for this matrix degradation is to assume that all plies in a laminate have two states: the intact and fully degraded. The latter are defined as plies with fully saturated micro cracks. This state can be simulated by reducing the effective stiffness of the matrix to a fraction of the intact matrix. The effective stiffness of the laminate is

thus reduced. The LPF occurs when fiber tensile strength is reached. We call this degradation approximation a simultaneous failure model.

For other combined stresses that include compressive stress components micro cracking is not induced. There will be no stiffness degradation. Then FPF and LPF will be the same. The prediction of ultimate strength of a laminate may appear to be straightforward. But this can be deceiving because the real life, failure modes in laminates are very complicated. They include not only micro cracking but also delamination and micro buckling. These modes interact and occur sequentially. We will offer simple models and will caution participants to be aware of their limitations.


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Laminates with Open or Filled Hole

Laminates with stress concentration is of many practical values, and will be presented. It is important to learn how strength and life can be predicted.

Failure prediction becomes far more complicated than the case of homogenous state of stress; i.e., the state of stress is uniform and does not change from point to point. This is usually the case of test coupons where the variation of stresses away from the grips or tabs is nearly uniform. For the case of stress concentration shown above, the stress varies from point to point. Failure then would initiate from some hot spot and grows as load is increased. So progressive failure will be covered by several lectures later in this tutorial.

It is therefore our approach to start the behavior of the constituents and move on to laminates and components. Once this link from micro to macro is validated, design allowable can be generated with a consistent scheme. More data for strength and life

can be generated with fewer but more revealing tests and specimens. We will gain more confidence in design and have more competitive composites. That is our goal.

Simulation and calculation are the keys to successful design. Philosophy must be quantized. Estimate of bounds must be made before tests are performed. In this tutorial we will show you how to use from simple Mic‐Mac calculators to Simulia/Abaqus 6.7 and beyond. With simulation we will gain confidence and make our composites competitive.


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Unique Sizing of CompositesMultiple laminates

M u l t i p l e l o a d s

Selection and sizing of laminates is fundamentally different from sizing isotropic materials. As shown in the table, we have multiple load sets shown in the column on the left. The number in the curly brackets are three in‐plane loads N1, N2 and N6. N6 is

the in‐plane shear.For aluminum, the required thickness in mm for each load is easily calculated. We used von Mises criterion. The aluminum strength used is 206 MPa. The thickness required to take all the load sets will be 21.1, shown in red. If a higher strength is used, the thickness will reduce proportionally. If a strength of 412 MPa is used, all thicknesses listed in this column will be reduced by 1/2.For composite laminates, the selection of best laminate will required calculation of all possible laminates to be used. So for each laminate and each load, the required thickness will be different. This is shown in the table for 5 common laminates. Under each laminate, the required thickness for each load set based on the ultimate

strength (LPF) is shown. The lightest or thinnest laminate for each load set is found in the last column. For the first uniaxial tensile load of {4,0,0}, the lightest laminate would be (50/33/16) with 4.51 mm. This is shown in blue.If this laminate must take all the load sets, the required thickness is shown in red. For the first laminate (quasi ‐isotropic) is 11.2 mm shown in red for all laminates in the last row. Thus the controlling load for this laminate is pure shear of {0,0,2}. So the best laminates for all the load sets will be the second laminate with (40/40/20); I.e., 40 percent [0], 40 percent [+45/ ‐45], and 20 percent [90]. The total thickness of this laminate for all the loads will be 9.57 mm, shown in blue at the lower right corner. Thus selection of laminate type and thickness is a two step operation, not one step that is needed for isotropic materials. One step is to take are of the ultimate strength and the other is to calculate the strength for each laminate and load set. It is a matrix operation as seen in the table above. Prof. Ha will present a fully automated LamRanksoftware as part of the Super Mic‐Mac in this tutorial.

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Options for Simultaneous Savings: Weight/Damage Tolerance, and Cost

• Use 3 or 2 ply angles instead of 4• Continuous variable (no discrete jump in plies)• Continuous stacking (no symmetric layup)• Homogenization (tougher & less warpage)• Simpler ply drop

• Bonded joints• Lower minimum gage• Simplified Simulia/Abaqus

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STRENGTH & LIFEOF COMPOSITES

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New Goals

• To reach aggressive design – trust MMF• To combat black aluminum – 50 % wt savings• To explore use of fewer ply angles• To increase homogenization ‐ toughness• To reinvest weight savings to increase damage

tolerance• To integrate design with manufacturing• To build the most competitive composites

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