Design for axial crushing - Impact Design Europe
Transcript of Design for axial crushing - Impact Design Europe
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
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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: [email protected]