ADCS

micro-cracks (residual tensile stresses in the

matrix caused by different thermal expansion

factors of fiber and matrix, the matrix shrinkage

during polymerization)

Locally increased strain in the matrix, which

reduces the strength of the composite compared to

the strength of the neat resin

Adhesive failure of the fiber-matrix interface

Cohesive failure of the matrix

Fiber Failure in compression can be caused by fiber fracture, micro buckling of

the fibers or fiber kinking

• Initial Fiber misalignment introduces shear stresses which promote a fiber

rotation, resulting in a further increase of the shear stresses

• Due to the instability Kinking is initiated, which can be defined as the

localized shear deformation (failure) of the matrix along a band

• Typically, the fibers break at the edges of the band

Fiber failure (FF) in tension is the (final) simultaneous fracture of many fiber bundles

• Due to the brittle behavior of fiber composites, the fiber

fracture occurs suddenly without previous non-linearity

o No stress redistribution possible

o Fiber failure = ultimate failure

• Fiber failure is the only “desired” failure of the laminate

o The fibers are the load-carrying elements, therefore the structure should be

dimensioned for this failure mode

• Two failure modes are generally present at fiber failure

o Failure of the fiber itself

o Failure of the fiber/matrix interface

Fracture plane is not equal to action plane of the loading

o Transverse compressive stresses cannot cause failure in the

action plane of the stresses

• Transverse compressive failure occurs on a plane inclined by ≈ 50° to

the action plane of the transverse compressive stress

o Transverse compressive failure is therefore a shear induced

failure mode

• Compressive failure can lead to dangerous

wedge fracture of the lamina

o Induce a force in thickness direction leading

to major delamination

o Resulting in total failure of the laminate

For shear loading there are always pairwise connected stresses with

perpendicular action planes

o Two possible fracture planes

o Fracture occurs in the plane with the lower fracture resistance

o Experiments show, that the fracture generally appears in a plane parallel to

the fibers

• At first, micro-cracks appear under 45° as principle stress cracks between the

fibers.

Eventually these cracks form a macro-crack parallel to the fiber direction

o In this case the fibers act as crack arrestor

Fracture occurs in a plane inclined by 45° as a result of the equivalent

normal stress in the 45° direction

• None of the shear forces’ action planes are identical with the fracture plane

• Despite the obvious shear loading the induced fracture is a transversal tension fracture

F < 1 no failure

F = 0 failure point

F > 1 failure

Generally the failure index is a non-linear function to the applied load

→ Cannot be used for direct judgment of risk of failure.

Delamination describes the fracture between two adjacent layers of a laminate

Common reasons are impact, buckling, bending

Design rule: maximum two plies with same orientation next to each other

An even distribution of ply angles over the laminate thickness should be accomplishedInter-fiber failure may however lead to catastrophic failure of the laminate for the case of wedge fracture under

transverse compression dominated loading

Gives the “risk of fracture” on Lamina level!

One has to distinguish between “risk of failure” on lamina and laminate level!

Prediction of failure mode

Typical failure modes of the material should be reproduced

The mathematical formulations should be relatively easy to handle

Reliable test methods for all input values should be available

Gives the “risk of fracture” on Laminate level!

Difference between RF and fE

• Laminate level vs. lamina level

• Load defined vs. stress defined

o Non-linear material behavior

o Load can be mechanical / thermal etc.

Pros:

o Easy to use and to implement

o Single equation for the fracture body

Cons:

o Pure mathematical interpolation equation - physically questionable dependencies

o No prediction of failure mode

o Interaction term 1 is difficult to determine

• Independent criteria (e.g. Maximum Stress, Maximum Strain)

o No interaction between different stress/strain components. The failure mode can be predicted. Failure analysis is

often not conservative.

• Fully interactive criteria (e.g. Tsai-Wu, Hoffman)

o All the different stresses are combined in a single equation. The failure mode cannot be predicted.

• Partly interactive criteria (e.g. Hashin, Puck)

o The Failure Function is represented by different equations. Hence, these criteria allow a distinction between different

failure modes (e.g. fiber or matrix failure / tension or compression) and a physically plausible interaction of different

stresses.

• UD lamina show brittle material behavior for Fiber fracture as well as

for Inter-Fiber-Fracture

• Fiber Fracture is mainly caused by normal stresses virtually parallel to

the fiber direction

• Inter Fiber Fracture is mainly caused by a combination of stresses

acting not parallel to the fiber direction

• The strength relating to fiber fracture is higher for tensile loading

compared to compressive loading

• The strength relating to inter-fiber fracture is higher for compressive

loading compared to tensional loading

“The strength prediction of the distinct modes should not be influenced

by the direction of the considered coordinate system!”

4 distinct failure modes are considered:

• Fiber tensile failure

• Fiber compressive failure

• Matrix tensile failure

• Matrix compressive failure

Based on Mohr circle

Shear failure defined by inner friction

Criterion derived from physical principles

Very accurate especially in shear-compression

Reason 54Degree Failur Plane at IFF Compression is that the Compression stress acting normal to the fracture plane impedes shear fracture

The fracture hypothesis of Mohr is used for the description of the fracture phenomena of Inter Fiber Failure! The fracture

plane where IFF will occur is the action plane where the critical stress combination is applied!

High sigma_1 stresses can reduce the action plane fracture resistances -> weakening factor

Maximum strain criterion

− “damage tolerant” criterion epsilon < 0.4% - aerospace

− “fatigue” criterion epsilon < 0.2% - Wind energy

Thermosets:

Good mechanical properties

Most used

[Epoxy]

Thermoplastics:

Good impact properties

Bad thermo-mechanical

behavior

[PPS, PA]

Metal/Ceramics:

High temperature

applications

[Titanium, SiC]

Provides BOTH Predictive Accuracy and Computational Efficiency

Carbon:

High performance

Expensive

Glass:

Moderate tensile

strength

Cheaper

Aramids:

Excellent tensile

properties and energy

absorption

Bad resistance in

compression

Bad adhesion with

polymer matrix

Ceramics:

Properties stability

wrt temperature

Very expensive

Each structure has requirements regarding the mechanical performance

• Verification of performance is indispensable

• Stiffness / strength etc.

Verification through experimental investigation possible

• Test facility is needed

• Drawback: expensive and low flexibility (hardly any loop-back to the design)

More flexible: mechanical analysis

• Influence of the design is possible

• Different variations (e.g. fiber/matrix material) are easier to realize → Optimization

Analysis of the mechanical response of a structure subjected to a certain loading:

• Analytical approach

• Numerical approach, e.g. Finite Element Analysis

Scale 0 – Microstructure

Scale 1 – Micromechanics

Scale 2 – Macromechanics

Homogenization to higher scales

General: 36 constants needed to define material behavior

Anisotropic Material: 21 independent constants

Orthotropic Material: 9 independent constants

Transversely isotropic Material: 5 independent constants

Isotropic Material: 2 independent constants

Transversely isotropic with “plane stress” assumption: 4 independent constants:

Micro-Scale / Micromechanics

• Properties of fibers and matrix

Macro-Scale / Macromechanics - Lamina

• Lamina: one ply of a laminate

• Assumed homogenous, averaged properties

of constituent materials used for analysis

Macro-Scale / Macromechanics - Laminate

• Laminate with several plies

• Single layer behaves like lamina

Repeating Unit Cell (RUC) (RUC almost always used for analytical and numerical calculations)

• Heterogeneous, microstructure is approximated as periodic

• Building block approach

• Periodic boundary conditions to enforce repeating nature

Representative Volume Element (RVE)

• Must contain large enough volume to capture the random microstructure on a statistical basis

Parallel spring model

Assumption of isostrain

Good applicability! for E1

1. The layers are assumed to be perfectly bonded

2. Straight lines perpendicular to the middle surface remain straight and perpendicular to the middle surface after

deformation

3. The thickness is assumed to stay constant

4. Out of plane deflections (bending) are small compared to laminate thickness

CLT is restricted to thin laminates

CLT requires linear elastic material behavior

Serial spring model

Force equilibrium (iso-stress)

Provides a lower bound for E2

One unconsidered mechanism:

•High stiffness of the fibers in longitudinal direction constrains

transverse contraction of the matrix

•no packing of fibers considered

“With 10° off-axis the stiffness of the ply reduces by about 45%.”

A – Extensional stiffness matrix:

→ connects in-plane normal- and shear-strains with

in-plane normal and shear forces

B – Bending-extension coupling stiffness matrix:

→ coupling-matrix: connects in-plane strains and shear strains

with moments and curvatures with normal and shear forces

D – Bending stiffness matrix:

→ connects curvatures with moments

Mid-plane symmetry:

• B Matrix = 0

→ no extension-bending coupling

Balanced laminate

• For every –alpha oriented ply, there is a ply with

+ alpha orientation

• A16 and A26 have zero entries

→ no extension-shear coupling

Length-plane symmetry:

• Only feasible with 0° and 90° plies

• A16, A26 and D16, D26 have zero entries

→ no extension-shear and bending-twist coupling

ABD-Matrix (stiffness) abd-Matrix (compliance)

Input: deformations – Output: loads Input: loads – Output: deformations

(What load does the structure take?)

(What is the best structure to take the load?)

• Layered shell ( for “thin” structures)

• + fast calculation

• - no stresses in thickness direction

• Continuum elements for “thick” structures (One element per ply)

• + Very accurate

• - Fine meshes are required

  
  

Layered continuum element

Aluminum: Milling “Substracting“ Stringers: crack arrester

Composite: Layup “Additive“ Fibers orthogonal to the crack work as crack arrester

• Reduction of the components

→ Reduction of joints

→ Low assembling costs

• Less manufacturing processes

Robust manufacturing process needed

Combination of different materials

• Exchange of parts / reparability

• Hybrid design: composites/metals

Attention: corrosion

• „Fail Safe Design“

• Minimizing scrap

• Simple tolerance compensation

• Simple and cheap tools

1,2,3: bonding (differential)

4: co-bonding (intergral)

5: co-curing (integral)

Optimized Fiber-Layup

• Rovings are oriented in direction of the load path to provide stiffness and strength where needed

-> yields usually anisotropic behavior.

• Goes in hand with integral design

-> Great potential for lightweight design.

Black Metal Design

• CFRP is used with a quasi-isotropic layup and thereby like a sheet metal structure.

• This approach goes often in hand with a differential design.

-> The superior material properties are not fully used – just the difference in

specific properties (stiffness, strength) between composite and metal.

CFRP:

++ high performance (Strength,

Stiffness, [...])

++ crash

- Impact

Aerospace, Automotive, (wind

industry, civil eng.)

GFRP:

++ Cost efficient

+ Impact

Wind industry, aerospace,

automotive, civil eng.

AFRP:

++ Impact

- Compression loading

Differential → NDI of individual members possible before assembly

Integral → NDI is difficult!

Recommendations for Lay-up with Respect to Damage Tolerance

• First and last layer should be orientated ±45° to the main load path

• Grouping of layers with the same orientation has to be avoided

Rivets Solid/Blind: Smooth cylindrical shaft, Used to transfer loads by shear, not normal stresses

• Solid rivets:

• Are the rivets of choice if joint is accessible from both sides

• Blind rivets:

• Are the rivets of choice if the joint area is accessible from one side only

• Are hollow and thus weaker → need to use stronger material and / or larger diameter and / or higher number of rivets → negative weight impact

Bolts: Designed to provide sufficient preload to transfer the load by friction, loss in preload is much higher for composites than for metallic joint partners due to creep

Aviation industry -> Bolts should only be designed to transfer tension, no shear

Space industry -> Bolts are often used to transfer both, tension and shear

Speciality Fasteners

Procedure:

1. Joint Type – Get it right

in first loop!

2. Iterations of fastener

placement, stress and

failure analysis

3. In worst case also joint

type needs to be included

in iterations

Laminate:

Bearing Failure -> happens at high w/d ratios (influenced by joint geometry, laminate stacking etc.)

Net Section Failure -> happens at low w/d ratios

Shear-out -> happens at

Fastener:

Bolt bending -> happens at high lever arms (laminate thicknesses)

Shank shear -> happens at

Tension shear -> happens at

Local thickening

Incorporation of glass softening strips (reducing peak stress)

For high loading above the limits of rivets, bearings and bushing can be utilized.

1. Design the joints first and fill in gaps afterwards – optimizing the basic structure first compromises the joint design and results in low overall structural efficiency

2. The best bolted joints can barely exceed half the strength of un-notched laminates

3. Optimum single-row joints have approximately three-quarters of the strength of optimum four-row joints

4. Rated shear strength of fasteners should not be a factor in design – bolts need to be sized to restrict bearing stresses in laminates

5. Bolt-bearing strength, in particular, is sensitive to through-the-thickness clamp-up (preload in thickness direction) of laminates. Creep may be an issue

6. Bolt bending is much more significant for composites than for metals, because composite members are thicker (for a given load) and more sensitive to non- uniform bearing stresses (because of brittle failure mechanisms)

7. w/d ratio for single-row bolted joints as about 3 to 1

8. w/d ratio for multi-row bolted joints must be varied along the overlap length to distribute loads more evenly and thereby enhance joint efficiency

9. Good fiber patterns are fully interspersed (parallel plies not bunched together) and have at least 10% of the plies in each of the four main directions: 0º, +45º, -45º and 90º. → local thickening to increase laminate thickness

• Liquid shim (gap should be small – e.g. ≤ 0.5mm)

• Metal/solid shim (for thicker gaps e.g. 0.5 mm ≤ x ≤ 2mm)

• Sacrificial plies (for Al fittings GFRP has to be used) – machined to tight tolerances after cure

• The additional gap needs to be considered for joint sizing → e.g. bolt bending.

Chicken rivet:

Primarily used if load path redundancy is required

Bad design

Load path to bonded joint is stiffer → the fasteners/rivets do not receive load until the bond slips → no increase in failure load

• The fasteners/rivets take some load after the bond breaks → may be beneficial in some cases e.g. total energy

consumption

Cohesion = “internal strength” (Cohesion is a characteristic of the adhesive itself (almost))

Adhesion = “ability to stick to a substrate” (Adhesion is a characteristic of the adhesive, the substrate material and its actual surface condition)

Tension Very low

Compression Low

Shear potentially very high

Peel Minimum

Adherend fracture outside the joint

• Generally assessed as a positive type of fracture → „part fails first“

Cohesive Shear

• If this mode of failure occurs in service it is most likely that it can be assigned to incorrect design and analysis

Cohesive peel

• Inappropriate joint design: predominant peel loads

Adhesive shear / Adhesive peel

• Mainly a process related issue

Continuum mechanics / Strength of materials(SoM)

• Stress / strain based failure

prediction

(linear elastic) Fracture mechanics (LEFM)

• Failure prediction based on critical

energy release rate

• Using similarity in between crack

growth (metals) and delamination

growth (composites, bonded

structures)

▪ Only shear stresses within adhesive, only normal (tensile) stresses within adherends

▪ Linear-elastic material behavior

▪ Bending moments and peel stresses due to load eccentricity neglected

▪ Constant adhesive thickness

▪ Ideal adhesion

rho >= 5

• widen the bonding

• stiffen the adherend (higher modulus material or increasing the thickness)

• using adhesives with lower shear modulus

• thicker adhesive layer

Non-linear material behavior

Three zones in the overlap need to be defined:

a central zone which potentially is in the linear-elastic range and

the two outer zones which are potentially in the perfectly plastic regime.

“Straight forward”, “well proven” and “easy to understand” approach

• Failure to occur if allowable is reached

− Allowables: stress, strain

• Identical to SoM-analytical methods without need for massive simplifications

− “any” geometry, “any” boundary condition, “any” load condition

Material data acquisition is an issue → Test data

Numerical issues at singularities

Bond thickness is very small compared to all other geometries

• Need for small elements!

LEFM well capable to deal with singularities

• “Invented” to deal with crack growth / fatigue problems in metal

• Widely used in Aerospace

• Results for a given adhesive are highly dependent on

− Adhesive thickness

− Thickness and modulus of the adherends

− (environments)

→ data only true for very defined configurations

Not suitable for ductile materials

Only suitable for already existing cracks or “calibrated singularities”

• from damage initiation

• via propagation

• to final failure

(1) Bonded joints must always be stronger than the adjacent structure

(2) Load in shear, minimize peel

− Bonding works best for thin structures

− Thick structures require complex geometries to minimize peel

(3) Provide sufficient bond area to resist creep and ensure durability

(4) Use „correct“ design allowables from suitable test methods including temperature and humidity effects

(5) Careful design and analysis are worthless unless processing of the adhesive joint – especially surface preparation is done properly

Positive aspects:

• the likelihood of bond induced failures of the structure is reduced

• the analysis of the entire part / assembly is simplified → adhesive bond may be ignored except for detail analysis of the bond itself

Critiques:

• The rule may not be achieved for all substrate-adhesive combinations, e.g . for very high strength materials like advanced high strength steels

• The application of the rule generally reduces freedom of design, adds weight and increases manufacturing costs – especially with thicker adherends – which seems unnecessary if analysis can show sufficient joint strength (though being lower than the adherend strength)

Remove eccentricity e.g. single lap → double lap

Minimize stiffness change by tapering edges

The “best” configuration from a purely mechanical point of view is the scarf joint.

Both peel and shear stresses are dependent on geometry !only!

By lowering the scarf angle  both peel and shear stresses may be lowered “theoretically” without limitation

The purely geometrical formulation is only valid if its assumptions can be met:

In-plane tension only (=no eccentricity)

Adherends do not yield under load

Identical adherends

Wetting / „Intimate contact“

Chemically active surface

Absence of contamination & prebond-moisture

Mechanically/ Physically/ Chemically

Sanding/ Low pressure plasma/ Anodizing

Non-Crimp-Fabrics NCF

• Laminas are stitched together

• CLT is applicable

Woven Fabrics

• Two fiber directions (0°/90°)

• CLT is not applicable

Braided Fabrics

• Two or three fiber directions

• CLT approach can be tailored for braids

Smeared

• Warp and weft properties are smeared into one lamina

• Only one set of orthotropic material properties is needed for definition

Input is easy to determine (coupon tests)

Existing failure theories can hardly be applied

Cross Ply

• One weave layer is split into different laminas

− 0° lamina for warp

− 90° lamina for weft

• Two sets (warp & weft) of material properties are needed

No testing of isolated 0° or 90° lamina with woven geometry can be performed

Classical approach: analysis can be performed as usual

No big difference in stiffness, but in failure behaviour!

Interlaminar shear stresses caused by transversal forces

1. Determine stiffnesses in x/y

2. Introduction of an equivalent body: b_eq = Ek/Eref *b

3. 
   

1. Determination of the equivalent second moment area I_eq

2. Determination of the equivalent static moment S_eq

3. Setup of shear stress equation

at radius details

at free edges

at ply drop offs

Typical loading conditions:

1. radius opening

2. ~ closing

3. ~ tension

4. ~ compression

Failure modes due to loading conditions

− interlaminar fracture:

occurring for loadings 1, 3 and 4

− failure outside of radius:

occurring for loading 2

• CLT does not take into account stresses such as sigma_z, tau_xz, tau_zy, called interlaminar stresses

• Free-edge delamination (a failure mechanisms uniquely characteristic of composite laminates) is induced by interlaminar stresses

• CLT often implies values of sigma_y, tau_xz where they cannot exist, e.g. at the free edge of a laminate

Termination of one or more plies exposed to load (e.g. out-of-plane bending) leads to both:

• interlaminar shear stress

• interlaminar tensile stresses

similar to the stress state at a free edge

Dropping the top layer of a laminate will end up in higher peel stresses than dropping a layer within the laminate.

„An ending layer should always be covered by another layer.“

-> Stagger distance

Any change in geometric contour or change in material properties that leads to a disruption of the load path results”

− Holes

− Edge notches

− Soft material inclusion

− Laminate layup, fiber orientation

− Notch size and shape

Because peak stresses cannot be flattened due to plastic deformation.

Stress concentration factor

• only dependent on material

• independent on geometry

Assumptions based on Lekhnitskii

• infinite large plate

• thin orthotropic plate

• linear elastic behaviour

• Uniaxial in-plane loading in fiber (1-) direction

• No temperature or moisture induced loads

K = 7.5 0degree plies

K = 3 isotropic material / quasi-isotropic

K = 1.8 +-45degree plies

-> Quasi-isotropic layup in regions with highly loaded holes

Peterson [13] introduces a correction factor to determine the stress concentration at the edge of a hole in a finite plate out of isotropic material

• Determine the physical composition of the composite

• Characterize the composite material in the elastic regime

• Determine the composite material strength for different loading conditions

• Determine the fracture toughness of the material for different failure modes

• Determine the influence of holes, in-service damage and fasteners on the elastic

properties and strength

• Determine the influence of temperature and moisture on the elastic properties and

strength of the composite material

It is like a pyramid where you start off with a lot of coupon test (low level) to ensure a good foundation to move further up. Bigger scales and more complexity arises:

test of sub components

of components

and eventually the whole structure

These are more complex and more expensive therefore gradually less tests

Universal Test Machine:

Electromechanical actuation

Robust and easy to use

Ideal for static and quasi-static tests

Servohydraulic Test Machine:

Servohydraulic actuation

More complex setup due to hydraulic system

For static, quasi-static and medium rate tests

Used also for fatigue testing

• Material heterogeneity

• Material fabrication

• Specimen manufacture and preparation

• Testing

A-basis: At least 99% of the population survives

used for critical parts

B-basis: At least 90% of the population survives

used for redundant structures

Physical properties of the lamina such as density, void content and fiber volume fraction

Fracture toughness for delamination and progressive damage modeling

Mode 1 <-> Mode 2

Testing on coupon level II is performed to determine the mechanical properties of the laminate

− Deformations

− Load – displacement curve

− Strains (strain gauges shall be applied at regions of rather uniform strains).

− Location and type of failure for tests up to rupture.

Bending Stiffness can be increased by a lot basically through steiner part. High lever arm to mid plane, core material in between

Advantages:

• Weight efficient for bending and compression loading

• Acoustic and thermal insulator

• Less buckling prone

Disadvantages:

• Moisture ingression

• Edge closure usually necessary

• Problematic local load introduction

• Corrugated cores

• Honeycomb,

• Balsa wood (susceptible to moisture)

• Foams

The fundamental properties of cores are:

• Low density

• High shear modulus and shear strength

• Stiffness and Strength perpendicular to the face sheets

• Thermal and acoustic insulation

Ribbon direction

Lower stiffness: expansion direction

Facing Failure

Initial failure may occur in either compression or tension face.

Caused by insufficient panel thickness, facing thickness or facing strength

Transverse Shear Failure

Caused by insufficient core shear strength or panel thickness

General Buckling

Caused by insufficient panel thickness or insufficient core shear rigidity

One Layered Shell

• includes all the information of the sandwich

Hybrid Modeling

• Layered shell elements for face sheets

• Volume elements for the core

Local Crushing of Core

• This is caused by low core compression strength

Shear Crimping

• Sometimes occurs following and as a consequence of general buckling. Caused

  by low core shear modulus or low adhesive shear strength.

Face Wrinkling

• Facing buckles as a “plate on an elastic foundation”. It may buckle inward or

  outward, depending on relative strength of core in compression and adhesive in

  flatwise tension.

Intracell Buckling (Dimpling)

• Applicable to cellular cores only. Occurs with very thin facings and large core cells. This effect may cause failure by propagating across adjacent cells thus inducing face wrinkling.

Core chamfers key feature for the risk of core crush during the curing process.

Factors of influence:

• Angle of core chamfers (small angles lower than 20°-25° decreases the risk of core crush)

• Autoclave pressure and temperature

• Core material

• Material, orientation and thickness of the plies are symmetric to the mid-plane

• Short notation with subscript s or sym: (+45,-60)s

• Number of plies can be uneven, example: (+45, 0, +45)

-> Extension-Bending Matrix B = 0

• Orientations of the plies are antisymmetric to the mid-plane (same material and thickness)

→ 𝐴16 = 𝐴26 = 0

→ 𝐵11 = 𝐵22 = 𝐵12 = 𝐵66 = 0

→ 𝐷16 = 𝐷26 = 0

• Only plies with orientations in 0° and 90°

→ 𝐴16 = 𝐴26 = 0

→ 𝐵12 = 𝐵16 = 𝐵26 = 𝐵66 = 0 (only 𝐵11 ≠ 0 and 𝐵22 ≠ 0 )

→ 𝐷16 = 𝐷26 = 0

• Laminate has the same amount of plies with orientation +𝜃 and −𝜃 (same material and same

thickness) but does not contain any ply in 0° or 90°

-> 𝐴16 = 𝐴26 = 0

• Laminate has the same amount of plies with orientation +𝜃 and −𝜃 (same material and same

thickness)

• Can also contain plies in 0° or 90°

• Angle-Ply and Cross-ply are always balanced

-> 𝐴16 = 𝐴26 = 0