CZone analysis

The crush stress in the composite material can vary as a function of a predefined field variable. This field variable can represent any physical or geometrical quantity that might affect the crush stress, such as curvature of the laminate.

CRUSH STRESS, DEPENDENCIES

CRUSH STRESS, DEPENDENCIES=5
90.0,   0.0, , , 0.0
60.0,  45.0, , , 0.0
90.0,  90.0, , , 0.0
60.0, 135.0, , , 0.0
90.0, 180.0, , , 0.0
99.0,   0.0, , , 1.0
66.0,  45.0, , , 1.0
99.0,  90.0, , , 1.0
66.0, 135.0, , , 1.0
99.0, 180.0, , , 1.0

The crush stress in the composite material can depend on the deformation rate at the crush front. The crush stress velocity factor is used to scale the crush stress based upon velocity. The scaling factor is calculated from a user-supplied table of scaling factor versus relative surface velocity.

The final crush stress is the velocity dependence factor multiplied by the original crush stress. No extrapolation of the supplied data is performed for velocities that lie outside the maximum or minimum value supplied, as shown in Figure 6.

Figure 6. Crush stress is held constant outside of the supplied data range.

CRUSH STRESS VELOCITY FACTOR

CRUSH STRESS VELOCITY FACTOR
1.5, 0.0
1.0, 1.0
1.5, 100.0
1.0, 1E6

In the component testing method a component is manufactured from the candidate material. The component geometry should support crushing, such as a straight box or similar section with a side length to wall thickness ratio that prevents local buckling. This is the most accurate testing method; however, it is also relatively costly. This approach involves the following steps:

1. Crush the component using an impact sled.

2. Measure the acceleration of the sled.

3. Calculate the crush force from the acceleration.

4. Calculate the crush stress by dividing the crush force by the cross-sectional area of the component.

The high cost of this test method has led to the development of lower cost coupon test methods described in the following sections.

Several organizations are developing the flat coupon testing method. Test coupons are typically cut from a flat sheet using a water jet to minimize damage at the cut edges. One end of the coupon is weakened by incorporating a saw-tooth shape or chamfer to initiate crushing. The flat coupon is placed in a fixture that prevents buckling. A drop-tower or servo-hydraulic test apparatus is used to push the coupon through the fixture onto a crushing or target plate. The ongoing crush force is divided by the cross-sectional area of the flat coupon to determine the crush strength.

In the flat coupon testing method, the coupon typically has a region near the crushing end that is free from support or constraint. This region is the unsupported length. Figure 8 shows a coupon crushing fixture installed in a servo-hydraulic dynamic testing apparatus.

Figure 8. Flat coupon test apparatus (courtesy of Engenuity, Ltd.).

Figure 9 shows how the material crushes at the lower end of the fixture as it is forced down through the fixture's low-friction guides. The fixture has adjustments for different coupon thicknesses and for varying the unsupported length.

Figure 9. Crushing a flat coupon (courtesy of Engenuity, Ltd.).

Several organizations are developing the shaped coupon testing method. The test coupons are shaped with corrugations to give them stability when they are crushed on a flat surface. Like the flat coupons, one end of the shaped coupon is weakened with a saw-tooth shape, as shown in Figure 10, or a chamfer to initiate crushing.

Figure 10. A typical shaped coupon used for crush testing (courtesy of Engenuity, Ltd.).

Figure 11 shows the shaped coupon after testing.

Figure 11. The crushed shaped coupon (courtesy of Engenuity, Ltd.).

The shaped coupons are more expensive than the flat coupons but still significantly less expensive than producing custom test components.

Many composites exhibit ongoing delamination in the crush zone as part of the crushing process. Shaped coupons tend to suppress delamination, often leading to a higher value for the crush stress than the flat coupons, which allow delamination more readily. The ratio of the measured crush stresses from the shaped and flat coupon methods varies with the material.

Most composite structures consist of both flat and curved regions. To evaluate a realistic crush performance for these structures, it is recommended to test samples using both coupon methods. You can then assign the flat coupon crush stress values to flat regions and the shaped (suppressed delamination) crush stress values to curved regions. This approach is illustrated in Figure 12.

Figure 12. Identifying regions of higher crush resistance based on curvature.

The top image shows a CZone for Abaqus analysis of a cone made from two components joined at the flanges. The bottom images show the regions of crush stress assignment in the two pieces that make the cone. The corner radius areas, including the flange areas where the two pieces are joined, help to suppress delamination. They are assigned a delamination suppressed crush stress of 122 MPa. The flat areas are assigned a flat coupon crush stress of 50 MPa. The physical test of the component yielded an average crush stress of 77 MPa.

Some materials have a high resistance to delamination, such that the flat and shaped coupon test methods converge toward a common crush stress value. Further research is being conducted into methods of suppressing delamination in the flat coupon test method to determine the elevated crush strength values while using the low cost flat coupons.

CZone for Abaqus uses the contact output variable CRUSHSTATE to report information about the current crushing state of the nodes on the slave surface:

In addition, you should request output of the relevant damage variables in accordance with the composite damage model used in the simulation. For example, for the Tsai-Wu criterion you need output of solution-dependent state variables, and for the Hashin damage model you need output of the damage variables documented in Output. You can use these results to determine the regions that failed due to crushing and those that failed as a result of composite damage and failure.

Highlighting failed regions

Plot the contours of CRUSHSTATE on the undeformed shape to highlight the regions that have failed or are starting to fail as a result of crushing. The regions where CRUSHSTATE is six (colored red in Figure 13) have failed as a result of crushing. Regions where CRUSHSTATE is five (colored yellow) are currently crushing.

Figure 13. Plotting output variable CRUSHSTATE on the undeformed shape.

Removing failed elements from the view

You can use ResultField OutputStatus Variable to remove the failed elements from the view. Select CZASTATE as the output variable, and remove elements with a value greater than 3; select Apply to undeformed state to remove the elements from the undeformed model view. The result is shown in Figure 14.

Figure 14. Fragments that broke away from the model as the surrounding elements failed.

Removing elements that failed due to material damage

If you use the Tsai-Wu damage initiation model, you can remove the elements that have failed as a result of material damage. Select SDV3 to be the status variable, and remove elements whose SDV3 value is greater than 0.99, as shown in Figure 15.

Figure 15. Removing elements that have failed as a result of material damage.

If you are using the Hashin damage model, you can request the damage output variables associated with different damage mechanisms to evaluate the dominant damage mode (see Output).

In this benchmark a rectangular cross-section cone is attached to a rigid wall, as shown in Figure 16, and impacted with a moving sled with a mass of 324 kg and an initial velocity of 10m/s. The input file for this example is cza_bm1-cone-ahv_gc.inp.

Figure 16. The plain cone test setup (courtesy of Engenuity, Ltd.).

The layup of the composite cone includes three different thickness regions. It is thinnest at the front (left) and gets thicker toward the rear (right), as shown in Figure 16. The thickness at the front of the cone is such that local buckling occurs and fragments of material break away due to bending stresses. As crushing progresses, the increased wall thickness allows progressive crushing of the cone without buckling and bending failure. Figure 17 shows the final crushed state of the cone.

Figure 17. The plain cone sample at test completion (courtesy of Engenuity, Ltd.).

Figure 18 shows some material fragments that broke away from the front of the cone.

Figure 18. Fragments taken from the experimental test (courtesy of Engenuity, Ltd.).

The tapered colored markings on the fragments indicate that they came from the front of the cone on the long sides. The fragments that were predicted to break out from the thin part of the cone in the simulation match well with the test fragments, as shown in Figure 19.

Figure 19. Fragments that broke away during the simulation.

The predicted sled acceleration curve also matches well with the test data, as shown in Figure 20.

Figure 20. History of the sled acceleration for the simulation and experiment.

In this benchmark a complex cone is attached to a moving sled, as shown in Figure 21, and impacted against a wall. The input file for this example is cza_bm3-b-cone-ahv_gc.inp. The sled has a mass of 1150 kg and an initial velocity of 9.1 m/s.

Figure 21. Experimental setup for the complex cone (courtesy of Engenuity, Ltd.).

The component geometry is intended to represent some of the typical features and general size of a typical automotive front longitudinal member. The layup of this component was designed to behave in a way that shows an initial period of crushing, followed by catastrophic failure of the backup structure. At the front of the component the layup is relatively thin, and the backup structure is strong enough to support the crushing forces. As crushing progresses, the thickness of the layup progressively increases. At a certain point the back of the cone can no longer support the increased crushing forces from the thicker material, and failure occurs at the curved transition area—this quickly propagates around the section and the cone breaks in two. Figure 22 and Figure 23 show experimental and analysis results, respectively, at the point of failure.

Figure 22. Experimental results for the complex cone (courtesy of Engenuity, Ltd.).

Figure 23. Simulated failure of the complex cone.

Acceleration histories of the experimental and analysis results correlate well, as shown in Figure 24. The acceleration of the analysis approaches a constant value near zero after the crushing event, as shown by the red curve. The acceleration of the experimental results exhibit some experimental noise after passing through zero, as shown by the blue curve.

Figure 24. Time history of the sled acceleration for the complex cone.

This first, simple example tests the failure of elements and the correct calculation of the crushing forces through the CZone for Abaqus interaction. A sled, modeled as a discrete rigid body, impacts a simple composite strip. The composite strip has an encastre boundary condition at one end and is constrained to remain planar. The acceleration versus time history should be constant once the crushing mode is established. The crushing stress for the material is independent of the direction in which it is being crushed.

The results are obtained by running cza_v1_gc.inp. The time history of the sled acceleration (history variable Spatial acceleration: A1 PI: SLED-1 Node 37 in NSET SLED-RP) should be plotted to confirm the constant loading, as shown in Figure 25.

Figure 25. The time history of acceleration for the single strip.

In this test the plate is angled relative to the strip of composite material. The crushing force should gradually increase as the sled makes contact with the strip before the crushing force becomes approximately constant. The crushing stress for the material is independent of the direction in which it is being crushed.

The results are obtained by running cza_v2_gc.inp. The time history of the sled acceleration (history variable Spatial acceleration: A1 PI: SLED-1 Node 37 in NSET SLED-RP) should be plotted to confirm the loading, as shown in Figure 26.

Figure 26. The time history of acceleration for the angled strip.

CZone for Abaqus contact definitions are described in CZone methodology. This example tests an oblique (non-crushing) impact. The input file for this example is cza_v3_gc.inp. A composite strip is moving toward an oblique rigid plate, which is constrained in all degrees of freedom. The composite structure should hit and bounce clear from the plate. The filtered time history of the force on the rigid reference node of the plate is shown in Figure 27.

Figure 27. The time history of the force on the rigid reference node.

A very simple test is performed to check the friction calculations. The input file for this example is cza_v4_gc.inp. Two parts are defined, each containing a single element, but one part larger than the other. The larger part is a rigid surface, encastre at the rigid reference node, and the other is a very simple composite layup with two plies. The two parts are pressed together by a distributed load acting on the composite. Relative motion between the surfaces is induced by boundary conditions acting at the corner points of the composite element. The effective coefficient of friction can be calculated by monitoring the reaction force in the 1- and 2-directions and dividing it by the reaction force in the 3-direction. Figure 28 and Figure 29 show the friction forces in the 1- and 2-directions, respectively. The friction coefficient is shown in Figure 30.

Figure 28. The time history of friction force in the 1-direction.

Figure 29. The time history of friction force in the 2-direction.

Figure 30. Time history of the friction coefficient.

In this test a single composite specimen, with five fingers and a central palm, is completely constrained. The composite has a simple layup composed of 10 layers of orthotropic material. The crush resistance is a function of angle for this material defined for the crush stress. The input file for this example is cza_v5_gc.inp.

Five individual sleds are defined, each paired with a finger on the composite component, as shown in Figure 31.

Figure 31. The initial configuration of the five finger model.

The sleds travel toward and along the length of the fingers with an initial velocity. The progress of the sleds is resisted by the force required to crush the composite fingers. The angular dependence of the crush resistance means that each sled travels a different distance along the fingers. The displacement versus acceleration for each sled is shown in Figure 32.

Note:

Two of the curves—the ones for nodes 1290 and 1292—are identical, so there appear to be only four curves in the graph. This is the result of the angular properties of the second and fourth fingers having identical crushing properties in the test direction.

Figure 32. The displacement versus acceleration for each of the five sleds.

This test uses the same composite geometry and layup of the Five finger test. In this case the crush resistance is a function of crush velocity instead of angle. The crush stress velocity factor defines a scaling factor that is applied to the crush resistance based on velocity. The input file for this example is cza_v6_gc.inp.

Five individual sleds are defined, each paired with a finger on the composite component, as shown in Figure 31. Each sled travels with a different initial velocity defined along the length of the finger. The progress of the sleds is resisted by the force required to crush the composite fingers. The velocity-dependent crush properties and the different initial velocities generate a different crushing resistance and, therefore, a different acceleration, for each sled (see Figure 33).

Figure 33. The time history of acceleration for the five sleds with different initial velocities.

The geometry and layup of the plain cone benchmark is reused in this verification problem. For information about the model, see Plain cone. The cone is rotated relative to the sled, and the sled is constrained to remain stationary. An initial velocity of 10 m/s is applied to the cone and to the 500 kg mass attached to the back of the composite structure. The input file for this example is cza_v7_gc.inp.

A combination of crushing and brittle failure is predicted by the model. As the front face of the cone makes contact with the rigid surface, it exhibits brittle failure, peeling along the edges that join it to the side walls. This exposes new edges to a crushing interaction with the rigid surface. The mixture of brittle failure and crushing produces a noisy reaction force at the rigid reference node.

Here, a simplified airfoil representing the nose cone of a Formula One car makes contact with a rigid pole. The input file for this example is cza_v8_gc.inp. The car is traveling at approximately 140 km/h. The initial impact causes brittle failure on the leading edge as the composite makes contact with the cone. The model setup is shown in Figure 34 and Figure 35.

Figure 34. Airfoil contact, side view.

Figure 35. Airfoil contact, front view.

After initial impact, the failure mode becomes crushing as the impact continues and new composite material is exposed. Eventually the forces become too great, and failure is observed where the airfoil joins the nose (the boundary condition on the edge of the airfoil away from the pole). As this failure occurs, the composite structure rotates and the crushing ceases. This verification problem tests the implementation of the Tsai-Wu failure criteria and the transition from bouncing (hard contact) to crushing.

The difference in the failure modes is shown in Figure 36 and Figure 37. All failed elements from both crushing and brittle failure have been removed from Figure 36. Only elements that failed as a result of crushing have been removed from Figure 37. The removal of failed elements in Abaqus/CAE is discussed in Output.

Figure 36. Airfoil with all failed elements removed.

Figure 37. Airfoil with only crushed elements removed.

A tapered composite sample is crushed against a stationary rigid surface, as shown in Figure 38. The input file for this example is cza_v9_gc.inp.

Figure 38. The composite failure model setup.

The crush force increases as the first tapered element crushes against the rigid surface. The increasing load causes the element behind the tapered element to fail as a result of brittle failure. The first element is free to bounce from the surface as the rest of the structure continues toward it. The reaction force at the rigid reference node is shown in Figure 39.

Figure 39. The reaction force at the rigid reference node.

A coarse representation of a cylindrical component is used to test the damage and failure of elements close to the crush zone interaction. The input file for this example is cza_v10_gc.inp. The component, shown in Figure 40, is pushed against a flat, rigid, encastre surface.

Figure 40. The composite failure model setup.

The first element bounces against the rigid surface and transfers the load through the neighboring elements to the rest of the structure. Eventually the two neighboring elements fail as a result of damage mechanisms. This releases the central element, which bounces from the surface. The component continues to move toward the rigid surface, and eventually the side walls begin to crush. The time history of the reaction forces is shown in Figure 41.

Figure 41. Reaction forces during the composite failure.