The crash is a situation that can not be avoided, but their effects on the vehicle occupants or race car driver can be mitigated in order to reduce as much as possible the injuries. However, the crash have many aspects that are difficult to test and predict their effects on the structure. In order to have a proper model of crash of any structure, it is necessary a deep knowledge on the parameters involved and the proper test to perform. This article provides a summary of those subjects.

Parameters

Since composite materials have other methods to absorb energy with respect to metals, it is necessary different parameters to quantify their performance. These are the specific energy absorption (SEA), the crush force efficiency (CFE) and the sustained crush stress (SCS).

Specific energy absorption (SEA)

SEA = W/(ρAδ) = (∫₀^δ Fdδ)/(ρAδ)

The specific energy is a parameter defined by the formula above written. Where W is the total absorbed energy, ρ is the density of the material, A is the cross-section area and δ is the total crush displacement and F is the crush force. Similarly in the impact analysis, this parameter can also be obtained by drop down tests. However, in this case, instead of having an unsupported area, there is a stiff steel plate. The impactor is also different, instead of a spherical one, there is a plate impactor. This test also result in a force-displacement (F-δ) plot. However, in the case of crashing, the term used is crush rather than displacement. It is important to keep in mind that, crash and crush have different meaning. The first is the situation, while the crush is the component subjected to a crash. Hence, the main graph of the crash analysis is the force-crush length plot. The crush length is the value of how much the specimen is shortened.

The plot illustrates that, at the beginning there is a rapidly rise of the force, which it reaches the peak force. Then it decreases until a value that it keeps constant along the experiment. This region of the graph is called as progressive crushing, which is a reasonably constant load that is obligatorily lower than the peak. The progressive crushing occurs, because the crashing mechanism is self-repeating while fibers are being broken. Hence, it is possible to consider that, the specific energy and load are approximately constant. The peak force at the beginning occurs due to the lack of a crash initiator. This is a sort of trigger on the component that is weakened section or point. It is usually made by a series of dents or holes that locally vary the stiffness of the impact point. However, the specimens have a perfect shape with no crash initiators. The result is the one seen on the plot. First, it breaks, which is represented by the peak force, then it crashes, which activates the progressive crushing mechanism. Hence, the force decreases until a constant value. The point in which the force becomes constant is where the range of interest begins. The reason is that, it is this one used for the calculation of the specific energy absorption, which is the energy per unit mass of crashed material. Then, the SEA formula becomes:

SEA = [F_mean(δ_e-δ_i)]/[Aρ(δ_e-δ_i)]

Since it is being considered the zone with constant force, the term F becomes the mean force or the average load. However, this is a sort of practical evaluation since the energy is usually calculated through the area below the curve. This is also the sustained crush region. Usually, this approach is valid for quasi-static compression testing and dynamic crush ones. However, its results are different. This might be a consequence of the dependence on the strain rate of the composite materials during crushing.

Sustained crush stress (SCS)

From the average crush load, it is calculated the sustained crush stress by the following definition:

SCS = F_mean/A

SCS is given by the average force divided by the cross-section area. The main objective of this parameter is to establish a comparison of SCS with the compression strength. Hence, it is possible to establish a percentage of the progressive with respect to the compressive strength. This last one is defined by the peak force divided by the cross-section area.

Crush force efficiency (CFE)

Basically, the crush force efficiency is a ratio between the mean and the peak force.

CFE = F_mean/F_peak

The mean force can be obtained from the SEA measurements, while the peak one is a function of the material properties. Closer to 1, better energy absorption, better CFE. This means that, the material reaches its elastic load limit and after that it is crushed at a constant load. The usual value obtained for quasi-static compressive test oscillates around 0.6-0.8, while for dynamic tests the usual value is 0.4. The importance of CFE on the design of crash structures is to absorb the impact energy preserving crush through some length. Then it is provided some millimeter of deceleration. The peak force of crashing requires quite strong structures, which most of the cases mean more weigth. Hence, CFE is useful parameter to define light crash structures, which is normally the case for race cars. The crash force efficiency is sometimes given as the load uniformity index, which simply the inverse of CFE.

Modes of failure

When analysing a failure in composite materials, there are four modes, the folding, the splaying, the fiber breakage (buckling) and the fragmentation. These modes occur according to the material type and geometry. The folding failure mode is very common in metallic structures. Aluminum or steel circular crash structure fails by progressive folding. However, this can also be observed when using aramid fiber composites or aramid-carbon fiber hybrid composites. The folding is defined by a sequence of folding at crush front that is propagated along the structure. Even though those composites have similar behavior as metals, it is necessary a very high strain to failure ratio for this failure mode properly occur. Hence, the specific energy absorption (SEA) only reach intermediate levels folding. The reason is the lack of energy dissipation mechanism.

The other mode is the progressive crushing. This is subdivided into splaying and fragmentation. The splaying is a failure mode that is combined by an inelastic deformation and an interlaminar fracture. Even though the structure exhibits a sort of petals, these are still embraced to it. It can occur in a circular or plate structures. The splaying begins from a wedge, which is in a gap between the structure and the crush plate. This wedge represents the triggers used to initiate the crash of the structures. Hence, as compressive forces are applied, the wedge crashes the material generating longitudinal cracks. These cause the separation of the fibers, which are bent admitting a shape similar to petals. In other words, they splay out. This process generates also a large amount of interlaminar cracks. Frictional forces arise not only due to the wedge, but also regarding the crush plate and the bent layers. These are bent in different radii and this make them to slide relative to each other. The fragmentation failure mode is the most effective one. It is also a mixed mode of inelastic deformation and interlaminar fracture. However, in this case the parts tend to fragmentise in small pieces. In other words, occurs separation. This mode can also be triggered by a wedge. It causes a shear failure that leaves a sharp edge in front of the crush plate. Hence, this will form new wedges that also break the structure leaving a renewed tip. This process occurs until the material is totally consumed. The progressive crushing is the best mode of failure since it develops the highest SEA. It is based in the fracture mechanics that, more energy is dissipated if more surfaces are created.

In the case of fiber breakage or buckling, the failure mode is totally inelastic. Hence, it dissipates a very small amount of energy. For this reason it is not commonly adopted. Therefore, if the lay-up is capable to receive a crash and fragmentize in many members, new surfaces will be created. In addition, if the fragments are very small, then the energy dissipated will be very high. Hence, the fragmentation tends to be the highest energy dissipation mechanism.

Materials

For composite materials, the energy absorption is defined by several factors, one of them is the type of composite material. This is important since the micro-structure features affect the macroscopic characteristics of the composite. Hence, it is analyzed the impact of the fibers and matrices on SEA.

Fibers

Considering the main requirements for the automotive applications, the main fibers are carbon, glass and aramid. These are quite different regarding their failure modes. The first two often fails by splaying, fragmentation or the combination of these, while aramid fibers fail by folding. These have a more ductile deformation since they have a higher strain at failure. Hence, the fibers have a very different values of SEA. Basically, carbon fiber reinforced plastics (CFRP) exhibit higher values of SEA than glass fiber reinforced plastics (GFRP). The general GFRP exhibit SEA values comparable or higher than some CFRP. For instance, considering an unidirectional carbon fiber with a thermoplastic matrix (PEEK), the SEA obtained is very high, about 57-160 kJ/kg. In this case, most of the energy will be absorbed by the matrix. Another case is a squared epoxy carbon fabric, that exhibits only 15 kJ/kg. This aspect also has some influence of the shape. Usually, round and conical impactors can deliver a high SEA. The unidirectional and braided squared epoxies have a SEA of 37 and 30 kJ/kg, respectively. The braided architecture suppresses some failure modes that could be useful for energy dissipation. The glass fibers also have a wide range of SEA with respect to its variations. In general GFRP works better when unidirectional than the mat architecture, in terms of the failure under crash. The mat architecture is composed by randomly oriented fibers, thus reducing a bit the performance in terms of SEA. In the case of GFRP with thermoplastics, the results are better than thermosets, because the first has high failure strain. This is provided by the matrix, which part of the energy is absorbed by its plastic deformation. Therefore, the basic difference between CFRP and GFRP is due to the higher density of GFRP, which limits its SEA. Another possible fiber the aramid. This normally has a low SEA, about kJ/kg, because it deforms by folding, which is a mode that has low absorption. In case of aramid braided fibers, the energy absorption increases, it varies between 14-51 kJ/kg. However, for aramid fibers, this performance is mostly obtained by braided architecture.

Matrix

The matrices are considered with respect two aspects, sizing and fracture toughness. In terms of sizing, studies suggest that SEA can be improved up to 25% with sized components. This occurs, because it is motivated the splaying deformation mode, which improves SEA due to the higher friction losses at the interface. Comparing thermosets with thermoplastics results in a better performance of the second one. Considering a PEEK-carbon and an epoxy-carbon composites, these yield 57 and 127 kJ/kg, respectively. However, PEEK-carbon composite allow some improvements if the fiber orientation is moved to 0°. It is possible to reach a SEA about 160 kJ/kg. Some studies indicate that, the fracture toughness can be a manner to improve SEA, mainly for thermoplastics. Basically, it was observed that, mode 1 and mode 2 fracture toughness are correlated with SEA. If mode 1 is increased, SEA is increased, but this could come at cost of CFE decreasing. In the case of mode 2 fracture toughness increasing, only SEA will increase. These results suggest that, energy absorption may be improved by increasing shear failure events, because the splaying failure mode results on the plies sliding relative to each other.

Fiber volume fraction

The plot of the fiber volume fraction with respect to the specific energy absorption considering many experiments is a scatter of data that exhibit no trend. There is no statistical distinction between CFRP, GFRP, aramid and hybrid composites. Even though there is no trend, it is observed that, an increase on the fiber volume fraction increases SEA, but without logical correlation. Another important point of this graph is that, composite materials have a higher SEA than steel and aluminum for almost all fiber volume fractions. There are two reasons for that, the composites are lighter than metals and the composite materials usually deform by progressive crushing, which absorbs more energy. The metals, due to its ductility, normally have just one failure mode, folding. Therefore, the crash structure made from composite materials are more efficient than similar ones made from metals. Their SEA are higher than the same for metals.

Trigger

The trigger is an impact initiator that concentrates the crush force of the impact in order to begin the permanent deformation at a desired position. As a result, the peak force observed on the graph is removed and the specific energy absorption is removed. Normally, the trigger is based on the variation of the local geometry, but there are also non-geometrical crash initiators. The most common triggers are the bevel, the steeple, the notch and the tulip. Studies suggest that, SEA might be improved by variations on the geometry and the size of the trigger. Between those triggers, the notch and the tulip ones provides the highest SEA, because their failure mode is the fragmentation. The bevel and the steeple are prone to produce delaminations on the crash structure, thus the energy observed is lower since composites naturally parallel delaminates to the faces of the component. Even though there are clear performance differences, the bevel trigger is usually adopted due to its simplicity.

Another trigger is the plug trigger, which is used for crushing square or circular tubes. Basically, the tubes are compressed against the plug trigger, which causes an axial tearing on the tubular coupon. The plug trigger composed by a central fitting that has fillets with a determined radius. When the tube is pressed against the plug trigger, it tears in stripes that are bended due to the plug fillets. Even though the stripes are bended, they still have some residual strength and this reduces SEA of this trigger.

The close-end trigger is another method applied in tubes. It is based in a region of the tube near to its flanges. This has a smaller thickness with respect to the flange, then the chamfer help in motivating the interlaminar failure through bending.

Another parameters

Qualitatively, the geometry, the test speed and the applied load are parameters that may cause SEA variation. Some test specimen are hollow tubes, their thickness is an important parameter for SEA. Usually, it is preferred a thickness to diameter ratio (t/D) between 5 and 10 %. Hence, thin hollow tubes are better than thick ones. For cases which the tube is a squared one, there are proper approximations by an equivalent diameter. In these cases, t/D is more an estimation.

An important aspect should be considered regarding the matrix, that is the strain rate. The reason is that, the thermoset and thermoplastics have different sensitivities with the strain rate. This means that, the test speed should be controlled when the composite is made from a thermoplastics resin. They are more sensitive to strain rate. This means that, the first load to failure increases with the sensitivity to strain rate. Usually, the higher the velocity, the higher the load to first failure.

The load is also an important detail, because there are the peak and the mean ones and they are differently impacting on the results. When the crash begins, the failure mechanism is self-repeating. In addition, the impact load are also affected by geometrical aspects. If the loads are applied with a small slope, it is possible to improve SEA due to a higher impact one. The use of a higher load angles does not increase that effect, instead it reduces SEA. It is better to adopt some attenuator with an anti-intrusion panel.

Test coupons and fixtures

The impact and crash experiments are based in coupons and their fixtures. Actually, this is also a sort of characteristics of the test bench since each coupon require different fixture. The function of these is to avoid as much as possible the coupon buckling. For this reason there are several test methods which are defined by the coupons and their fixtures. Basically, there are three types of coupons, thus three types of tests, the self-supporting, the flat coupon and the tube testing methods. These are the principle of the building block approach.

Self-supporting coupon test method

The self-supporting test method is based on coupons with an out-of-plane curvature. If well designed, these coupons can be exposed to those tests without failing by buckling. However, the shape of the coupon can vary according to what is being analyzed through this experiment. The common geometry are the DLE segment and the sinusoidal coupons. The first is based in a semi-circular cross-section with flanges at its tips. It is bonded in a support plate and crushed without any fixtures. This self-supporting coupon is commonly used to compare the specific energy absorption of different materials when exposed to a quasi-static or dynamic loading tests. The DLR coupon was proposed by the german aerospace center, thus its use is more restricted. The sinusoidal self-supporting coupon, also called corrugated, is the most used one. It is based in a cross-section that is composed by a series of semi-circles with defined radius as in a sine wave signal. There are several geometrical parameters to characterize those coupons as the coupon width, the number of waves, the gross thickness, the width-to-gross thickness ratio and the included angle, they characterize the different variations of the sinusoidal coupon.

Flat coupon test methods

The flat coupon test is simpler than the previous one with respect to the coupon. The flat one is simple and easy to manufacture. Although it has a geometry which is not representative of a structure, for instance, the stresses suffered by the coupon are common at flat sections of a monocoque or any other structure. Hence, the flat coupons are useful to analyze the laminate behavior, to compare different material performances, to evaluate the fiber architecture behavior, to obtain important information for computational model and, in some cases, to predict the structural behavior of a linear section.

There are several kinds of test devices which are proposed in order to, not only test the previously mentioned aspects, but also triggers, chamfers and angles. Usually, those test benches are based on sliders that move driven by guide rods, normally four. The specimen is constrained by fixtures, which also have some variations. Most of them allow tearing of the specimen around the supports. This results in a higher energy absorption than the same test without those types of supports, thus it is not a representative output. In addition, the effect of the interlaminar crack grow is suppressed, which reduced delamination opportunities and, has a significant possibility of contaimination from debris in the fixtures. All those aspects result in an energy absorption higher than the one for unconstrained crush.

Certainly, there are other test benches designed to reduce the tearing phenomena. This is obtained by leaving a small gap in which the coupon can crush without artificial constraint. The value of this gap should be controlled, because if it is to high, the specimen will be exposed to buckling. On the other hand, if the support is excessively constraining the specimen, the crushing will not be properly performed. In any case, the coupon tearing is avoided, but the unsupported gap should be carefully defined.

Tube testing

The tube testing or element-level test methods are very common in automotive field since the specimen (tubes) are very similar to the impact attenuator structures. For instance, the ones at the upper and front rails. There are several variations of tubes with respect to its geometry, but the circular tube is by far more effective in providing the highest SEA. Although the tube testing is not considered a coupon method, they are still part of the first level of the building block approach. The reason is due to its shape, which make it representative of a structure, that are impact absorbers.

Coupon testing overal characteristics

Regarding those tests, it is possible to split then according to their characteristics. The corrugated test does not require test fixtures, its shape ensure a great stability with buckling. However, this test frequently avoid delamination, which produces a result that might be out of the real condition. In addition, this specimen has a more complicated manufacturing.

The flat coupon with supported gage section has the problem of coupon tearing, which makes the result not representative. The specimens are simple and easy to build. The test machine are cylindrical or knife edge supports, which has no significative difference.

The flat coupon with unsupported gage section is similar to the previous one in terms of test benches. However, they have devices to tune the gap of the gage section. For this reason, the fixture are proper for this method. This test is usually adopted for crashworthiness purposes. Hence, if it is being tested the specific energy absorption of a material, this corresponds to the level 1 of building block. This is a basic property of the laminate, thus this test can be adopted for material scrutinising.

The tube testing have larger and more expensive specimens with respect to the previous tests. Another cons are the great influence of the tube shape and geometry on SEA. For this reason, it is common to build specimens very similar to the impact attenuator. The stress state is more complex than in coupon methods. This can be beneficial since to scale-up a complex impact attenuator usually it is not possible to perform several tests. Hence, determining the basic properties of the impact attenuator material allow to model it, thus checking if it will pass or not prior to the real test. This test is used to scale-up by using numerical analysis. In any case, representative specimens of the structure are still necessary to validate the model. Therefore, by the results, it is possible to infer if the model is able to scale-up the real impact attenuator.

Modelling crush: Progressive failure of continuum damage

Some issues in modelling occur due to the fact that it is a dynamic analysis. Considering that there are stress waves into the material, these go back and forth in the impact direction and also propagates along the transversal direction. A crash analysis requires the elimination of the finite elements that have failed in order to simulate the part of the structure that have reached the maximum damage locally. This means that, there is the release of the energy which is connected to that failed finite element. Hence, the simulation may have a situation which is not the real one, but it is influenced by the higher oscillations of the load. In these cases, there is a small oscillation that is due to the stress waves that go back and forth in the structure. In addition, there is also a larger oscillation that is caused by the elimination of some elements. However, there is one common aspect for finite elements, which is based on the physics, it must respect the energy conservation. Hence, what is saw in finite elements, even though it causes such type of behaviour, is that the energy which is released by the deletion of the element must be equal to the energy spent by the external force. Therefore, there will be always an energy conservation. Unfortunately, the solution can be much more unstable than it really is due to the numerical issues.

References

• MIL-HDBK-17-3F, Volume 3, Department of Defence USA (DoD), 2002;
• Busco, A. Comportamento all’impatto dei materiali compositi. Tese di dottorato, Università di Napoli “Federico II”, 2007;
• Borelli, R. Sviluppo di procedure numeriche per la simulazione del danno in strutture in composito. Tese di dottorato, Università di Napoli “Federico II”, 2011;
• This article was also based on the lecture notes written by the author during the Design for Composite Structures of Racing Ca attended at Unimore.