Design for axial crushing

The Macro Element Method is derived from the kinematic method of plasticity and energy method of classic elasticity.

Macro Element Method

The Macro Element Method was worked out (among others) by T. Wierzbicki , W. Abramowicz and N. Jones in late eighties of the last century.

The leading idea - to assume the kinematics of deformed continua rather then calculate it from classic equations of equilibrium

The kinematic approach - the assumed deformation of a structure is defined in terms of space-time shape functions postulated on the basis of experimental observations.

The Super Folding Element - The basic building block of macro elements that describe crushing response of prismatic thin walled members is the Super Folding Element

Effective Crushing Distance – the estimation of height of completely squeezed plastic lobe in axially compressed prismatic elements.

Energy Equivalent stress measure – allows for reliable estimation of a representative stress level in crushed shells.

Crashworthiness analysis at the level of individual members

The design of a structural member at the cross - sectional level is especially important at the pre - design and early design stages when the proper shape and optimal dimensions of a member are sought and the design concept undergoes frequent modifications.

The Macro Element approach advantages:

calculation routines require as input only overall dimensions of the cross –section, and tensile characteristic of the material

the calculation process takes only few seconds on a standard PC

designer can examine a wide range of cross -sectional topologies and run several parametric studies within only few hours of work

Super Folding Element – energy dissipation mechanisms

Super Folding Element

The Super Folding Element describes crushing behavior of a segment of corner line of the prismatic section subjected to arbitrary crash loading.

The core of the theoretical background of CCC is the conceptof Super Folding Element defined as a fragment of a beam which creates a single plastic fold

1. total length, C, of two arms of a SE, C = a + b,

2. central angle, Φ

3. wall thickness ta of the arm of the length a

4. wall thickness tb of the arm of the length b

The initial geometry of a Super Folding Element is defined by four parameters:

Super Folding Element (SFE)

The Super Folding Element represents the segment of a corner line of a prismatic column. Discretization into Super Folding Elements is illustrated below.

SFE is cut by set of two horizontal, parallel planes

The distance between the horizontal planes equals the length of the plastic folding wave of a column

The vertical boundaries –planes equally distanced

from the neighboring corners

Deformable cell –A set of SFE located

between two horizontal planes

Design of Cross Sections for AXIAL CRUSH How basic calculations are used to predict crushing response

of a single prismatic member

One of the most sensitive parts of the design at the level of a single prismatic section is concerned with progressive folding during a head - on collision.

Development of progressive folding requires simultaneous completion of several conditions. These are:

The cross - section geometry

Spot welds

The section must be properly “triggered”

The boundary and loading conditions

conditions, pertinent to the level of a single member, must be met at the design stage of a given member

last condition must be checked at the level of full crash simulation of a construction.

Design of Cross Sections for AXIAL CRUSH

The Cross - Section geometry - local deformation of a section in each plastic lobe can be accommodated without internal contacts and penetrations. In addition, the deformation of each plastic lobe must be compatible with the deformation of it's closest neighbor

Spot welds (rivets or laser weld - line) - must not interfere with the local plastic deformation of a section,

Trigger - introduction of correctly designed hoop dents which guarantee the development of a proper folding mode and reduce the peak load to such a level that the potentially unstable plastic deformations are induced only in the region of triggering dents

Example of design loop – TrainsDesign of front absorbers

Cross Section Editor

The Cross Section Editor is used to design, calculate and optimize Thin Walled Cross-Sections for best crash performances.

In the Solution Explorer window the User can find each element of the designed Cross-Section

• Points

• Plates

• Segments

• Connections

• Super Foldng Elements

Cross Section Editor - results – AXIAL RESPONSE

Axial response – summarizes axial crushing response of the Cross Section and facilitates basic design procedures.

The simple numeric entries like Peak Force, Squash Load or specific energy absorption (SEA) provide basic information on the strength and energy absorption capacity of the cross section.

The expanded Selected Folding Mode container shows data pertinent to the currently selected folding mode. This mode is marked in red on the Axial Crushing characteristic of the cross section.

• Axial Compression

• Energy Absorption

• Peak Force

• SEA (specific energy absorption)

• Squash Load

In the Selected Folding Mode field you will find a drop down list of folding modes For a folding mode you will find results for:

Mean Crushing Force

Plastic Folding Wave

Rolling Radius

Transition Angle

In the Properties window you will find results for:

optimization for AXIAL CRUSH

Typically cross section optimization is done iteratively in several optimization steps. At each step CCC provides the user with information on the design errors at the level of single Super Folding Element and at the level of the whole cross section.

CCC’s Cross Section Editor provides Design Recommendations - list of necessary corrections to the cross sectional geometry up to the point when the section can collapse progressively without internal contacts and/or penetrations.

The cross section stage of design requires fine-tuning of central angles, widths of side faces and appropriate geometry of cross section and of spot welding.

Initial Cross Section Optimized Cross Section

Design Recommendations

The Design Recommendations section guides the User through the optimization process of the cross section for effective axial crushing.

Step 1 – Folding mode – Cross Section Level

Step 2 – Central Angle

Step 3 – Eliminations of narrow and wide faces

Step 4 – Fracture flaw

Step 5 – Contact events

Design for Axial crush - example

An example of initial, bad design of a corrugated panel and final, correct design.

Initial “bad” topology

Final “correct” topology

OPTIMIZATION FOR AXIAL CRUSH

proper selection of central angles

and widths of side faces

Note that both cross sectionsare quite similar and the decision on the correctness of the design is impossiblewithout a detailed numerical simulation.!

Cross Section Editor – edition tools

In the Cross Section Editor you can edit the created Cross Section. A number of edit tools are available which will enable you to:

Move Elements of a Cross Section Rotate Segment

Merge PointsShow Lenght of Plates

STEP 1 - Folding Mode

For the above reasons the inverted folding modes must be eliminated from cross-sections designed for axial crushing (when such a mode is detected it is marked as rejected in the properties window). This is done by corrections to the central angle and/or by reducing/increasing number of corners in the cross-section.

There are three basic folding modes of a corner line:

Asymmetric folding mode Symmetric folding mode “Inverted” folding mode

The asymmetric folding modes are the most wanted folding patterns as they maintain progressive folding of the column.

The symmetric modes involve large membrane stretching of the material and have good Specific Energy Absorption (SEA).On the other hand, however, they frequently induce the so called inverted mode(s)

Inverted folding mode has a very high axial stiffness in early stages of the folding process and therefore notoriously induces global bending of the entire column

Recommended Acceptable Rejected

Asymmetric modes onlyMixture of symmetric and symmetric modes

At least one inverted mode

STEP 1 - Folding Modes

Recommended, accepted & rejected Folding Modes

a

m

a

m

s

m

P

PPq

q qcr

Prediction of natural folding mdoes in an isolated Super Folding Element

Prediction of leading folding mode based onthe level of mean crushing force

The „energy barrier” concept accounts for initial imperfections and spontaneous changeof folding modes

)12090( 00 )12090( 00

Natural folding modes of a Cross Section And Leading Corner Concept

Leading Corner

Direction of information

transfer

Leading Corner Concept – divercity of folding modes

Different folding modes initialize in leading SFE

Incorrect Central Angle

It follows form the mechanics of the SuperFolding Element that the central angle is a primary geometrical factor responsible for energy absorption in a single SFE.

The impact of central angle onto the crushing response concerns also global column geometry

Elements with too small central angle (acute elements) or too large angle (obtuse elements) do not develop progressive pattern.

For the above reasons, according to the CCC’s Design Recommendations, the Central Angle of a Super Folding Element should fit within the range from 80 to 120 deg.

Initial Cross Section Optimized Cross Section

Elimination of Narrow Faces

Irregular folding followed by overall bending induced by internal contact of neighboring walls

When a side face of a cross section is too narrow to accommodate propagating plastic lobes the lobes may collide before plastic fold is completed

“Narrow face” phenomenon is closely related to the magnitude of central angle(s) in neighboring corner(s).

This phenomenon is responsible for local axial stiffeningof the column, which together with drastically reduced bending stiffness of the cross-section leads to the overall bending

On the left: Visualization of lobe collision in Cross Section view.The narrow faces can be eliminated relatively easy with the usage of edit tools available in the Cross Section Editor

Lobe collision

Narrow faces

Elimination of Wide Faces

Irregular folding mode of column with wide side

faces (large width, C, to thickness, t, ratio C/t).

Irregular/non compact folding is typical for elements with large C/t ratio, C/t>>50.

The side face can not be too narrow as shown in preceding section. It can not be too wide either!

When the plate is too wide (thickness too small) the folding of “wide” corner elements becomes irregular.

This may lead to irregular, non progressive folding or non compact folding when consecutive plastic folds are separated by unfolded segments of the column

Non compact folding

In both cases the efficiency of energy absorption is dramatically decreased

Fracture Flaw

Folding of thin walled structures involves large tensile and membrane deformations. Therefore, crashworthy components must be made of sufficiently ductile material that will not rupture during folding process.

Fracture of material decreases energy absorption capacity of an active plastic fold.

Moreover, fracture flaw can completely destroy folding pattern and drastically reduce energy absorption

In the SFE Properties window in the Step 3 –Fracture Indicator field (DesignRecommendationssection) you will find the information about the ductility of the Material (Fracture Indicator D)

In the case of fracture flaw at this stage the only remedy is the change of material to more ductile or reduction of thickness. Modification of the cross section geometry, in general, has a weak influence on induced plastic strains.

Note that Fracture indicator D is calculated for selected Material fracture model. D larger than 1 indicates fracture of Material.

Re-bending

Bending

Re-bending

Bending

Most of the experimentally observed material fractures in crushed specimens is due to bending and re-bending deformations

Material models - Fracture criteria

Fracture Flaw - examples

Surface Cracks –due to large bending straining

The surface cracks are formed outside toroidal surface where compressive strains prevail.The presence of these cracks significantly reduces the energy absorption but in general they do not destroy the folding pattern.

In the first phase of fold formation the corner area is re-bend to almost flat surface. This induces high tensile straining of the material inside the column. The presence of fracture results in significant reduction of energy absorption

Through-thickness fracture of the

corner line due to reverse loading

Mild steel specimen. The surface cracks are

present inside the column. The through

thickness cracks show up when the column

is subjected to tensile loading, which

corresponds to unloading-reloading cycle

in real-life

Through – thickness fracture of the corner line – due to reversed loading

Mild steel specimen. The surface cracks are present inside the column. The through-thickness cracks show up when the column is subjected to tensile loading which corresponds to unloading – reloading cycle in real life

Through – thickness fracture of the corner line

“Safe” cracks

Crack generated during bottoming

deformation in the last phase of the

folding process. This type of fracture has

negligible influence on the overall energy

absorption and folding pattern of an

absorber.

Crack generated during bottoming deformation in the last phase of the folding process. This type of fracture has negligible influence on the overall energy absorption and folding pattern of an absorber.

“Safe” cracks

Connections force connected element to fold in compatible manner regardless of the type of physical connection

Unconnected Super Folding Elements fold freely and do not create compatible folding

Deformation Transfer – Connection Concept

Spot Welds

A spot weld is defined by clicking in turn on two Plates to be connected.

Create Connection tool

There is no limitation as to the number of spot weld connections per one Plate.

By default the connection is created in the middle of the master Plate.

When connecting three Plates, the User must define two Master Plates and one Slave Plate (middle plate)

When more then two flanges are connected in the cross-section the User must use one of the flange as a “leading” flange

Leading Flange

Master Plate

Slave Plate

Master Plate

Optimal position of Spot Welds

Undeformed configuration Deformed configuration

Position of Spot WeldsOn Master and Slave Plates

The final stage of cross-section design is concerned with appropriate triggering mechanism.

A triggering of columns is especially important for complex cross -sections that develop a large number of natural folding modes.

Usually only few of these modes are likely to converge to the desired progressive folding pattern while other modes lead to a premature bending of a column.

Trigger design

Paper model shows triggering dents in

hexagonal column with flanges designed on

the basis of CCC calculations.

Triggering mechanism is designed in order to promote a desired progressive folding pattern and reduce the peak force below the level, which is likely to induce global, Euler - type buckling of a column.

Progressive collapse of a properly triggered long square column, top, and

global bending or irregular folding of untriggered

columns, bottom

CSE – Results – Trigger design

Trigger is a local dent that initiates the desired progressive folding mode and reduces the peak load.

Trigger is designed by specifying either the depth of the triggering dent (in millimeters) or by defining the level of quasi static peak load (in Newtons). Once either of these parameters is defined program shows a coupled parameter: i.e. depth of dent corresponding to defined axial force or vice versa.

Note that design of a trigger makes sense only for Recommended or Accepted folding mode

Thank you

for your kind attention

Impact Design Europeul. 3 Maja 1805-816 MichalowicePOLANDwww.impactdesign.pl

Contact:Agata Abramowicz SokollCEOmail: as@impactdesign.pl