Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Soft Impact

  • J. A. Artero-GuerreroEmail author
  • J. Pernas-Sánchez
  • D. Varas
  • J. López-Puente
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_209-1

Synonyms

Definitions

Soft impact refers to high kinetic events in which a collision occurs between an object and a structure, being the mechanical properties of the first quite low compared with the later material. In a “soft impact event,” the projectile is greatly deformed and even damaged during the interaction with the impacted structure, contrary to “rigid impact event” in which the projectile almost remains intact during the impact process. The typical examples of soft impacts are produced in the aerospace sector such as hail or ice impact, bird strike, and tire fragment impact.

Introduction

During its service life, structures can be subjected to a variety of loading cases. Restricted to dynamic loading, impact is one of the most concerning case due to its possible disastrous consequences. Impacts on structures can be produced by the accidental or the deliberate hit of an object into the structure that could be a civil infrastructure or transport structure. Regarding the differences between the material properties of projectile and structure, impacts can be divided in two main categories: rigid impacts and soft impacts. In the first, stiffness and strength of projectile are higher than the structure, and hence the damage is produced only in the structure, while the projectile almost remains unalterable. Soft impacts are those in which the mechanical properties of the projectile are significantly lower than the structure. In those both projectile and structure get deformed and damaged after the impact. If the properties of projectile and structure are similar, the case cannot be considered neither a rigid nor a soft impact event. Nevertheless the type of failures is similar to soft impactor cases, since damage occurred in both elements.

Concerning the relative velocity between projectile and structure, impacts can be divided in two categories: high velocity impact and low velocity. There are many definitions to clarify the border between these two categories, although it is commonly accepted that impacts above 40–50 m/s can be considered as high velocity impacts. The impact of a “rigid” projectile can be studied for low velocity impacts and high velocity impacts (González et al., 2011; Artero-Guerrero et al., 2015; López-Puente et al., 2002). However for soft impact, the study is only restricted to high velocity impacts since the low strength and stiffness of the material cannot affect importantly if the impact is at low velocity. The study of high velocity impact takes on particular importance in the aeronautic sector, and moreover, the impact of soft projectiles is not uncommon (Mines et al., 2007; Johnson et al., 2009). During certain maneuvers, such as takeoff and landing, the structural components can be hit by tire fragments; or during flight birds, hail or ice can hit different parts of the aircraft as the fuselage, wings, stabilizers, radome, or nacelles. In Fig. 1 it can be seen the main impact hazards and the most probable impact location on an aircraft. Nevertheless, of all the different kinds of impacts, those involving hail and ice are the most dangerous due to their probability of occurrence as well as their potential consequences (Pernas-Sánchez et al., 2012). Other occasional debris could act as soft impactor such as foams in the case of the space shuttle accident (Melis et al., 2004; Fasanella et al., 2004; Carney et al., 2004) or other nonstructural parts but because of its low probability are less studied. The rain impact could be classified as a soft impact, considering the damage provoked by the repetitive impacts process (Abrate, 2016).
Fig. 1

Impact hazards in a commercial aircraft

Nowadays it has to be remarked that soft impactors have become even more important due to the use of composite material in aerospace structures. Composite materials are being used more and more in primary structures of aerospace structures because of its excellent specific properties which allow to achieve a reduction in the weight of the structure and hence a less fuel consumption. This main consequence has both economical and environmental advantages that have to be taken into account. Nevertheless it is well known the poor behavior of these types of materials when subjected to perpendicular dynamic loading (López-Puente et al., 2008). These types of impact could promote the delamination failure between each composite plies that could affect the bearing capacity of the structure and even the operability of the aircraft (Pernas-Sánchez et al., 2016a). So the soft impact event, mainly bird, ice, and tire fragment, on composite structures is certainly an area that worth the research. Therefore, vulnerability to impact has become an important issue from a regulatory perspective and aeronautical safety. Both the American and European regulatory certification requirements (FAR and JAR, respectively) include specific cases for preventing severe failure caused by an impact. This thread is also included by the European agency, literally from an EASA 2011 report “A critical safety issue for the design of primary aircraft structures is vulnerability and damage tolerance due to foreign object impact from bird strike, hail, tire rubber and metal fragments” (Toso and Johnson, 2011), highlighting the impact threat as a key factor in the design of aircraft structures.

Bird strikes account for around 90% of all incident related to structural damage due to impact on aircraft (Meguid et al., 2008). Therefore the certification program gives a main importance to the bird impact resistance of aeronautical structures as radomes, wing leading edges, fuselage, tail wing, engines, or window frames. The cost and complexity of this test are very high; full-sized structures with real-like boundary condition should be tested raising the costs. Moreover, there exists an uncertainly in the behavior of the projectile due to the variability between bird species, and therefore it could promote different behaviors increasing the analysis complexity. Numerical methods are also very useful in these problems trying to reduce cost doing virtual testing campaign in which different designs are tried. A proper validation for the model with the experimental test is needed for the successful use of the numerical model. Also the numerical model will help to understand the phenomena occurred in such a complex problem.

The threat of ice has become a subject of aircraft regulation for the aeronautical authorities (JAR-E 970), especially in aircraft with propellers or the ones with open rotor engines belonging to the new generation of aircraft used for medium-range routes (Pernas-Sánchez et al., 2012). Different studies, both experimentally and numerically, have analyzed the damage that this kind of impacts produces in aluminum (Chuzel, 2009; Combescure et al., 2011) and CFRP structures (Kim et al., 2003; Johnson et al., 2006; Park and Kim, 2010). It can be seen that in CFRP structures, these impacts are very concerned since delamination can be extended in all the structure(Pernas-Sánchez et al., 2016a). Researchers have also made an important effort in reproducing adequately its constitutive behavior since many different models can be found.

Regarding to tire fragment impact, these cases reached more importance after the accident of the supersonic Concorde aircraft in Paris (Authors, 2000; Seddon et al., 2004). In that case, the impact of a tire fragment in the wings, where the fuel was allocated, generated some structural damage that added to the fire turned into the catastrophic failure of the aircraft. Moreover this accident ended with the era of the supersonic civil flights. The research effort has been focused also in the determination of constitutive models that reproduce adequately the force produced by the rubber in this impact and the damaged developed into the structure (Mines et al., 2007; Guégan et al., 2010; Neves et al., 2010).

Bird Strike

When a structure, in this case, an aerospace structure, is collided by one or more birds, the impact is known as bird strike. From the beginning of aeronautic history, bird strike has been a problem to concern; in fact it was already described by Wright brothers (MacKinnon, 2004) in 1905, and the first fatal accident occurred in 1912 (Lewis, 1995). Up to 2004, it has been reported 242 fatalities related to bird strike incidents (Stoll and Brockman, 1997). Nevertheless there are many incident per year, some estimation reaches 30000 bird strike (ICAO, 2001, Proposed amendment to annex 14, unpublished), but the majority cause little or even no damage. This number can be increased due to the environmental awareness that has increased the bird population nowadays (Eschenfedler, 2001). Moreover, the fact that airports are far away from cities and therefore closer to natural habitats of birds makes increase the possibility of bird strikes. The impacts are not restricted only to airports, because the possibility of finding a large flock of birds at high altitude is not negligible. In this case, the impact is even more dangerous since the aircraft velocity is higher. Some calculations provide a value of $USD 3 billion per year of economical losses for the aircraft companies (Short et al., 2000).

Bird Strike Experimental Tests

Due to the importance of the problem, both from a safety and economical point of view, bird strike tests have to be carried out to proof the viability of aircraft structure against this menace. Moreover, for certification purposes this impact is compulsory in certain aircraft components where the probability of bird strike is high (such as fuselage, windshield, or rotor blades). For example, Boeing 777 engines are required to produce at least 75% of full-rated thrust after the impact of four 1.125 kg birds (Lewis, 1995). The structural parts are required to maintain its integrity once the impact has taken place. In order to perform the impact test, the bird has to be accelerated to the required velocity (50–200 m/s). Usually this is performed using a pneumatic launcher in which compressed air impels the projectile and accelerates it through the cannon barrel. To adapt the geometry of the bird to the inner diameter of the barrel, it is needed to use a sabot. The design requirement of this component is to maintain the bird integrity during the acceleration process so that the bird could completely impact the structure. In addition, the sabot should be light as well as be easily separated from the projectile once it exits the barrel, hence avoiding to alter the impact on the structural components. Due to the small time of the impact (milliseconds scale), special instrumentation has to be used to register adequately the impact. High-speed cameras have to be used with an adequate frame rate (10–20 kfps), and dynamic sensors (usually piezoelectric) have to be used to register acceleration, forces, pressures, etc.

The literature regarding experimental bird strike against aerospace structure is scarce, because the majority of the research are centered on studying the impact on rigid plates to analyze the force produced and obtain data useful to validate its numerical models. Nevertheless it has to be remarked the work of Liu et al. (2017) in which a tail leading edge is impacted by a 3.6 kg bird. Experimental results are compared with numerical simulation obtaining a good correlation in terms of damage produced. Also in the work of Hu et al. (2016), experimental test is performed to analyze the impact resistance of a composite helicopter cockpit. A numerical simulation is used to improve the design of the cockpit. Aluminum plates impacted against bird are also analyzed in the work of Liu et al. (2014).

Certification tests require the use of real birds to perform the impact. Only the mass of the birds and the impact velocity are the variables defined in the certification program, varying for the different aircraft types. The variability of bird species or even between individuals from the same kind produces changes in the density and in the impactor geometry that could affect to the impact phenomenon and consequences. Therefore many companies use bird substitutes for the pre-certification tests in order to obtain more repeatable and confident results (Budgey, 2000). The design of the bird substitute is focused on reproducing the pressure loading and not the biometric parameters of real birds. It has been tested different materials, such as meat, rubber, silicone, foam, wax, and emulsion, while the best results are obtained for gelatin (Wilbeck, 1978; Nizampatnam, 2007; Baughn and Graham, 1988). Nevertheless it is important to follow the instructions for the gelatin preparation in order to achieve a correct pressure loading. Since the impactor geometry of the artificial bird is not defined, it has been done an intense work, both experimental and numerical, to determine the adequate one (McCallum and Constantinou, 2005; Airoldi and Cacchione, 2006; Zhu and Tong, 2008). Typically, bird substitute has been simplified using cylinder, cylinder with hemispherical ends, ellipsoid, or even sphere. It can be concluded that best results are obtained with the use of cylinders with hemispherical ends. In these cases, the pressure pulse history predicted numerically correlated better with the experimental impacts performed. Apart from the shape of the substitute bird, it is necessary to determine the length/diameter ratio (L/D) of the impactor. Typically the better results are obtained with (LD = 2). Recently, it has been tested more realistic artificial bird geometry, including the neck and even bones. In those tests, it can be seen that the impact of the neck, previously to the impact of the body, can prestress the structure and therefore modify the damage generated (McCallum and Constantinou, 2005). Both experimental and numerical academic studies have appeared in recent years comparing the impact of real and substitute birds in different rigid targets (Allaeys et al., 2017) obtaining useful data that can be used in future research. Nevertheless, it is still needed more experimental test comparing real bird strike and artificial bird strike to define adequately the geometry of the bird substitute.

Numerical Modelling of Bird Strike

Due to the important cost, both on time and economical, that a bird strike carry, numerical modelling could be a useful tool to help study the impact on aircraft structures (Nizampatnam, 2007). Usually an incremental step-by-step methodology is done for this purpose: testing experimentally one or two configurations of the bird strike into the structure, validate the numerical model, and then perform a virtual test campaign in which different impact conditions are studied and analyzed. Nowadays the confidence on numerical methods, and concretely finite element codes, has increased, and even it is discussed if the certification can be done using only numerical methods (“Certification by analysis”). However, the numerical model has to rely on material models that represent adequately the constitutive behavior of the structure material and the bird material in such strain rate conditions.

Nevertheless, before the growth of the finite element codes, there were some more simplified models that predicted pressure contours of bird strike. Willbeck developed a theoretical model of the different stages that occur during an impact (Wilbeck, 1978). The bird strike can be divided into three main stages: shock regime, release regime, and steady flow regime. These three stages can be seen in Fig. 2. During the first moment of the impact, a compressive shock wave is generated at the contact surface and transmitted through the projectile as the impact occurs. The pressure is very high and can be characterized by the Hugoniot relationship:
$$\displaystyle \begin{aligned} P_H=\rho_0 V_0 V_{\mathrm{shock}} \end{aligned} $$
(1)
where ρ0 is the initial density, V0 is the impact velocity, and Vshock is the velocity of the shock wave propagation. The model uses an empirical linear relation between the shock wave velocity and the impact velocity:
$$\displaystyle \begin{aligned} V_{\mathrm{shock}}=c+k V_0 \end{aligned} $$
(2)
where c is the sound velocity of the material and k the empirical constant. The second stage is the release regime in which a release pressure wave is generated in the projectile edges limiting the duration of the shock wave. The last stage is called steady flow regime. In this case the pressure and velocity can be considered constant during this phase. The pressure in the central axis of the projectile is called stagnation pressure, and it is obtained using the Bernoulli equation:
$$\displaystyle \begin{aligned} P_{\mathrm{stg}}=\frac{1}{2}\rho_0 V_0^2 \end{aligned} $$
(3)
As the point is far from the central axis, the pressure can be obtained using the following expression (Banks and Chandrasekhara, 1963):
$$\displaystyle \begin{aligned} P(r)=P_{\mathrm{stg}}\mathrm{exp}[-\frac{1}{2}\left(\frac{r}{a}\right)^2] \end{aligned} $$
(4)
being r the distance from the impact point and a the radius of the projectile. During this phase it can be a radial expansion of the bird particles. In some cases, a phenomenon that can be considered also, is the force and therefore, possible damage on a structure, created by the subsequent impact of this mass diverted from the first impact. As it can be seen in Fig. 3, the characteristic curve shows the high pressure of the shock wave limited on time due to the release wave and the lasting of the steady flow pressure.
Fig. 2

Phases in a bird strike impact according to Wilbeck (1978). (a) Shock regime. (b) Release regime. (c) Steady flow regime

Fig. 3

Schematic representation of a pressure time history in a bird strike

Since the use of finite element codes increases in the solid mechanics, bird strike has been a problem that has been tried to be solved using these codes. In order to rely on the model, it is crucial that material models reproduce accurately the behavior of the bird when subjected to impact. As it is known, birds are mostly composed of water, and in the range of the velocities at which the impact occurs, it can be considered that the bird behaves as a fluid. Therefore it is needed to determine the equation of state of the bird. Using the Hugoniot linear relation, Wilbeck (1978) obtained the following EOS:
$$\displaystyle \begin{aligned} P=\rho_0 c_0^2 \frac{\rho(\rho-\rho_0)}{((1-k)\rho+k\rho_0)^2} \end{aligned} $$
(5)

Other EOS types as polynomial ones have been used showing that in the range of velocities considered for the bird strike (V < 200 m/s), the differences between the EOS are negligible. Usually the forces of bird strike impact on “rigid” structure are used to check the adequacy of the used EOS.

The bird strike problem is a highly nonlinear problem, and the numerical model has to be able to handle with large deformation, contact, and nonlinear behavior of materials. Therefore the most suitable codes correspond to those that are called “hydrocodes” based on explicit solvers. These solvers offer different discretization schemes that can be used: Lagrangian technique, Eulerian, Arbitrary Lagrangian Eulerian (ALE), or smooth particle hydrodynamics (SPH).
  • Lagrangian technique. This approach is not appropriate in the cases in which it is expected large deformation of the impactor because it could lead to severe element distortion since the mesh is fixed to the material displacements. This problem could lead to some numerical instabilities (e.g., time integration instabilities) (Anghileri et al., 2005b; Pernas-Sánchez et al., 2012). Nevertheless there are several techniques that can handle this problem, as the element deletion (Stoll and Brockman, 1997) or the use of a remeshing rule (Nizampatnam, 2007). Element deletion helps to successfully terminates the simulation eroding from it the most deformed elements. However it causes inaccuracy due to the loss of momentum and energy that generates artificial oscillations in the contact force. Remeshing rules are based on modifying the mesh when deformations are high in order to alleviate them, but it increases importantly the computational cost associated with the simulation. There are several references that do not recommend the use of Lagrangian technique for bird strike (Georgiadis et al., 2008).

  • Eulerian technique. Contrary to Lagrangian technique, in which the mesh is coupled with the material displacements, the Eulerian mesh is fixed to the space and the material flow across it. In the Eulerian technique, the solver first computes a Lagrangian step, then mesh moves back to the initial position, and the method introduces the material in its correct positions using an advection scheme. With this methodology element distortion is avoided, but computational cost increases because of the advection step. In addition, boundaries are not well defined, and therefore a fine mesh has to be used. Eulerian technique can handle with accuracy high velocity fluid-structure interactions (FSI) (Varas et al., 2009, 2012; Artero-Guerrero et al., 2013, 2014) or fluid-like structure interaction as the bird strike.

  • Arbitrary Lagrangian Eulerian technique. The ALE technique is a generalization of both previous ones, in such a way that the numerical mesh is not coupled to material deformation but has a particular velocity. There are several methods to define the movement of the mesh to be more efficient in avoiding severe element distortions (Hughes et al., 2013) and, consequently, better handle high deformations.

  • Smooth particle hydrodynamics. The smooth particle hydrodynamics is a meshless method that discretizes the continuum into particles that interacts between them through a smoothing kernel definition. This method is suitable to model soft impact events since no mesh is presented, and therefore it could handle high deformations. This method was used previously giving good correlations with experimental results (Lacome, 2004; Zammit et al., 2010; Anghileri et al., 2005a; Liu et al., 2008; Georgiadis et al., 2008; Wu et al., 2009; Salehi et al., 2010). In Fig. 4 it can be seen as an accurate modelling of the impact process of a bird substitute using the SPH model when comparing with the experimental results.
    Fig. 4

    Different time instants of a substitute bird impacting on a rigid plate in an experimental test and a numerical simulation using a SPH model

There is no clear conclusions about which is the best method in order to reproduce the problem; nevertheless the method has to handle appropriately the fluid-like behavior of the impactor during the impact in the most efficient way.

Ice Impact

Ice could impact against an aircraft during its flight. Due to the differences on the stiffness and strength between both materials, the impact can be considered as a soft impact. An example of this phenomenon is the hail impact that could be very dangerous when aircraft get into some hail storms. The size that could reach a hail (up to 50 mm) could be enough to create important damage on the structure. Not only hail impact has to be considered, because ice can grow in some parts of the aircraft and eventually it can flung from the component impacting into the structure. For example, nowadays the aerospace industry is studying the possibility of introducing the open rotor engines in which several propellers are rotating at high velocity without a casing. It is known that this technology produces a decrease in the fuel consumption and therefore in CO2 emissions. However, in open rotor engines, ice can be accumulated in a propeller, and it can be released at very high velocity. That’s why all the fuselage region near to the engine has to be ice impact resistant. In the space industry, also it has to be taken into consideration ice impacts since it can be accumulated also in fuel pipes and it can eventually hit the structure, in this case, at hypervelocity. Concerning other transport industries (car, naval, etc.) or oil and gas transportation industries, the ice impact could be an important threat to be studied. Nevertheless the range of velocities considered is much lower, and the impact cannot be considered as a soft impact. As it has been shown for bird impact, ice impact has been studied using experimental tests and also numerical models.

Ice Impact Experimental Tests

In order to perform ice impact tests, it is required the use of gas cannons that are able to accelerate the projectile at the impact velocity. The use of sabots is needed to adapt the geometry of the projectile to the inner diameter of the barrel. Moreover, in these cases, it has a second function which is to thermally insulate the ice in order to prevent the melting of the projectile. The brittle nature of the ice produces that frequently it can be broken during the acceleration because of the inertial forces or the vibrations experienced during it. The sabot has to help also to mitigate this undesirable effect because the ice has to reach the structure without losing its integrity. The manufacturing of ice projectile is also an aspect that has to be taken into consideration. Usually it is done following a two-step manufacturing process. In the first step, an ice block in which the air bubbles are concentrated in one side is manufactured; in the second step, the ice is melted into the desired shape by means of two pre-warmed metal blocks and a combination of gravity load and heat conduction. This melting process avoids to use any carving process which can produce cracks inside the ice projectile. It is worth to mention that the microstructure of the ice block obtained is columnar granular which is different from the hailstones formed in nature.

Concerning ice impact experimental test, there are several works in which ice is impacted against rigid plates to study the forces and pressures generated and others where the impact occurs against an aerospace structure in which also the damages produced in the structure are analyzed. Impact on rigid structures has been done using a “rigid” target supported in a system to measure the force, which could be a dynamic load cell or Hopkinson bars-based systems among others (Pernas-Sánchez et al., 2015; Pereira et al., 2006; Kim and Kedward, 1999; Tippmann et al., 2013). In all the experimental results, it is shown that as the impact velocity raises, contact force increases as it can be seen in other soft impactors as birds. It has been detected also the effect of the different crystalline structure is negligible at high impact velocities. In the work of Pernas-Sánchez et al. (2015), it has been tested different ice sphere diameters, and it is concluded that the maximum contact force is only a function of the kinetic energy, and not the mass or velocity separately. Same trends have been observed in other works (Tippmann et al., 2013; Pereira et al., 2006; Kim and Kedward, 1999). The aforementioned dependence on the projectile kinetic energy could be explained by attending to the ratio between the distortion energy density and the kinetic energy density. The first one (Udist) is related to the energy needed to deform the material up to failure and in this case depends on the mechanical properties of the ice (which are very low). The second one (Uk) is the kinetic energy of the ice projectile per unit of mass. This ratio is very small:
$$\displaystyle \begin{aligned} \frac{U_{\mathrm{dist}}}{U_k}=10^{-3}\end{aligned} $$
(6)
which means that the distortion energy density is negligible when compared to the kinetic energy density, and hence the impact is dominated by inertial effects. The impact process of a sphere into a rigid plate can be seen in Fig. 5. At the first instant of the impact, it can be seen a fragmentation front traveling into the ice sphere produced by the shock compressive wave produced in the impact and forming brittle cracks on the ice. It can be seen that the ice sphere becomes opaque after it. As the impact continues, the ice starts to deform radially which converts the ice into a set of small particles behaving as a fluid, similar to what happened on the bird strike. A phenomenon that can be considered also, as in the case of bird strike, is the force and, therefore, possible damage on a structure, created by the subsequent impact of the conglomeration of ice particles diverted from the first impact.
Fig. 5

Different instant point in an ice sphere impact on a rigid target (Pernas-Sánchez et al., 2015)

Ice projectile has been launched also against aerospace structural components to analyze the coupled response of the projectile and target. The behavior of the projectile does not differentiate to the one experienced on rigid target, exhibiting the brittle cracks and then the radial expansion. Different impactor geometries with different nose geometries have been used; nevertheless the sphere is the most used. It is shown that when an ice projectile with flat ends is launched normally, it produces the maximum deformations on aluminum plates (Anghileri et al., 2005c). This result can be predicted by the theory developed by Wilbeck (1978) for the impact of low strength projectiles. Ice impacts have been tested also into composite structure (Pernas-Sánchez et al., 2016a; Kim and Kedward, 1999; Appleby-Thomas et al., 2011). As it is said before, one of the main drawbacks of composite materials is its poor impact performance, and therefore it is expected that ice impact consequence will be more catastrophic than on metal plates. Different composite plate thickness has been tested in the work of Pernas-Sánchez et al. (2016a). It has been observed that the main damage mode is composite delamination; however, fiber failure and debonding can be seen at higher kinetic energy. Contrary to solid projectile impact on composite plates where delamination increases gradually as the velocity increases before the penetration (Pernas-Sánchez et al., 2014), in ice impact delamination increases drastically from no damage to fully delamination in a small range of velocity. In cases where the composite laminates are thinner, penetration can be produced exhibiting a higher range of damages, as fiber failure or matrix cracking.

Experimental tests have been done also to characterize the ice behavior (Schulson, 2001; Jones, 1997; Fasanella and Boitnott, 2006; Shazly et al., 2009). The majority of the tests have been carried out with iceIh, the most common ice on earth. This kind of ice is formed when liquid water is cooled below 0 °C at ambient pressure. IceIh possess a hexagonal crystal structure. Under low strain rate, it has been shown that the mechanical properties of ice depend on the condition of ice formation (single crystal, columnar or granular polycrystalline structure, presence of air bubbles, etc.). Young’s modulus has been reported to be in the range of 9.7 to 11.2 GPa, and Poisson’s ratio varies from 0.29 to 0.32. In tension, ice shows brittle behavior due to crack nucleation and cleavage. Tensile strength varies between 0.7 and 3.1 MPa and depends on the specimen volume, following a Weibull statistical distribution. On the other side, compression increases ductility and strength, like in other brittle materials, the mechanism usually hypothesized being intergranular friction. Compressive strength ranges between 5 and 25 MPa. This property is strongly affected by temperature as well, so experimental results are commonly provided for a given set of pre-defined temperatures (e.g., − 10 °C, − 20 °C, − 30 °C, − 40 °C). However, a change to brittle compressive failure appears at strain rates higher than 10−2 s−1, that is, in the range of strain rates that could appear in a high velocity impact. Therefore it has to be analyzed the mechanical properties under these circumstances. It has been used high-speed universal testing machines (\(\dot {\varepsilon }\sim 10\) s−1), drop-weight tower (\(\dot {\varepsilon } \sim 10^{2}\) s−1), or split Hopkinson pressure bars (\(\dot {\varepsilon } \sim 10^{3}\) s−1). In those tests it has been identified several common aspects: compressive strength increases with strain rates, and microstructure does not play an important role under high strain rates. In Fig. 6 it can be seen the relation between compressive strength and strain rate with data obtained in different works. Additionally, it has been reported that as the peak stress is reached in ice, the residual strength is not negligible during dynamic compression. All these tests have been used to characterize the mechanical behavior of ice.
Fig. 6

Ice compressive strength as function of the strain rate (Pernas-Sánchez et al., 2012)

Numerical Modelling of Ice Impact

Numerical modelling and specially FEM models of ice impact has been used to reproduce the consequences and damages on a structure, helping to understand the problem and also to design structures that could resist to this menace. The main effort on numerical modelling has been done on using an appropriate material model to reproduce the behavior of ice under high velocity impacts and also in using the appropriate technique to reproduce the high deformation experienced on an ice impact.

Material models have been selected as function of the mechanical behavior observed on the characterization tests (Combescure et al., 2011; Tippmann et al., 2013; Carney et al., 2006; Anghileri et al., 2005c; Pernas-Sánchez et al., 2012). The first model appeared on the literature uses a Huber-Mises plastic flow model in combination with a failure criteria based on maximum plastic strain and hydrostatic stress. Once the onset of failure occurs, only hydrostatic pressure can be carried. Nevertheless this model does not take into account the pressure and strain rate dependence of material. These dependencies are firstly taken into account by Carney et al. (2006) who propose a modelling in which also various failure modes are considered: maximum plastic strain and pressure cutoff in compression and in tension. Drucker-Prager yield function has been used also to reproduce ice behavior (Pernas-Sánchez et al., 2012). In this work, also the strain rate dependence has been taken into consideration and the residual strength after the onset of failure. A power law strain rate sensitivity has been proposed. The model uses a nonassociated plastic flow rule in order to do not overestimate the volumetric part of the plastic strain. Finally the failures are defined by a compressive cutoff and a tensile cutoff. After the failure only compressive hydrostatic stress can be carried.

Ice material also exhibits high deformation during the impact process, and therefore it is required the use of an adequate technique to tackle this problem. Solutions are very similar to the ones used for bird strike impact: the use of a Lagrangian technique in combination with an appropriate erosion model, the Eulerian technique, the ALE, or the SPH meshless method. In the work of Pernas-Sánchez et al. (2012), there is an interesting comparison between these different methods. Although the Lagrangian technique is not able to reproduce the fluid-like behavior of the ice after the fracture process, in terms of pressure/load and computational cost, the Lagrangian technique is the most adequate. The previous model can be used also to analyze the damage of composite plates when subjected to high velocity ice sphere impact. It can be seen in Fig. 7 that the numerical model is able to reproduce accurately the delamination area generated in a plate in a velocity range from 50 to 275 m/s.
Fig. 7

Experimental and numerical delaminated area obtained in an ice sphere impact

Tire Fragment Impact

The tire fragment impact has received less attention than the other two previous cases by the aeronautic industry. Nevertheless, since the accident of Concorde in Paris in the year 2000, some research has been done to analyze this problem. In this accident, a metal piece that was in the runaway produced the Concord tire explosion during the takeoff maneuver. Some tire fragments impacted into the aircraft wing where the fuel tanks are allocated. A high pressure wave was produced into the fuel tank that generated important damages on the structure leading to the catastrophic failure of the aircraft. One hundred and thirteen people were dead on the accident causing the end of the supersonic civil flights.

In this case of impact where the difference in stiffness between the impactor and the structure is high, as in the other soft impacts, an important part of the initial kinetic energy is wasted in the deformation of the projectile (Karagiozova and Mines, 2007). In the case of the tire fragment, it is not observed a massive fragmentation process as it can be seen in the ice or bird impact. Nevertheless the complexity of the process of tire impact (large deformation, nonlinear behavior, contact problems, inertial effects) means that experimental methods are needed both in terms of the mechanical characterization of materials in impact conditions and to validate the constitutive and simulation models developed.

Tire Impact Experimental Tests

In order to reproduce the experimental test of a tire fragment impact, it is required the use of an experimental setup similar to the one explained in the previous cases. The tire fragment has to be inserted in a sabot that is accelerated in a gas gun. As it has been said previously, the tire fragment impact is a problem less studied than other soft impact due to its low probability of occurrence. There are only very few experimental tests in which a tire fragment impact test is carried out (Mines et al., 2007; Guégan et al., 2010). It has to be remarked the work of Mines et al. (2007) in which it is analyzed cubic and parallelepiped tire fragment launched at different speeds (75–135 m/s) and angles (0°, 30°, 60°, and 90°) against aluminum plates. The results show that the high velocity normal impacts induce the higher deformations. However, the low velocity impact at an oblique angle produce important bending of the projectile, and a second impact can occur in the aircraft, producing even more damages in the structures than the high-speed case (Guégan et al., 2010).

In combination to the tire impact test, it has been carried out experimental tests to characterize the tire fragment material. Aircraft tires are designed to withstand high loads during short periods and to guarantee stability in adverse conditions such as high pressure gradients due to crosswinds, hydroplaning, as well as high temperatures and brake friction. To guarantee this, aircraft tires are made of a rubber matrix, usually natural rubber, with fabric reinforcements which tend to be nylon. It has been performed uniaxial quasistatic test both in tension and compression that have been useful to demonstrate the nonlinear behavior of tire rubber which experiences high deformation before failure (Mines et al., 2007). The presence of nylon fabric is responsible for the anisotropic behavior of the material. Moreover it is required dynamic experimental tests to fully characterize tire material under impact conditions. Drop-weight tower and gas gun test have been used to perform dynamic compression on the material (Mines et al., 2007). It has been concluded that the material has not shown a significant strain rate sensibility, despite contact force are higher on high velocity impact due to inertial effects.

Numerical Modelling of Tire Impact

As it was said previously, tire material is complex because it contains rubber and nylon fragment reinforcement. Therefore the material has to take into account the anisotropy and the nonlinear behavior. Characterization tests explained previously have been used to correlate the material models. The majority of the models used for the rubber are based on hyperelastic material model in which large deformations takes place without plastic deformations or any dissipation mechanisms (Treloar, 1975; Ogden, 1998; Johnson et al., 2009). In the case of incompressible material model, the constitutive model can be expressed on a strain energy function expressed through a power function of the principal stresses. If the material is compressible, the strain energy function can be expressed in terms of the porosity. In order to model the nylon reinforcement, one common technique is the introduction of one-dimensional bar element (Watanabe and Kaldjian, 1985; Reese et al., 2001). The nodes of these elements are linked to those on the matrix, fulfilling the compatibility conditions.

There are very few simulations in which the impact of a tire fragment has been taken into consideration. In the work of Johnson et al. (2009), it has been analyzed the impacts of tire fragments on composite panels. The numerical results show that the composite failure is mainly delamination, while an important part of the kinetic energy of the impact is absorbed by the projectile deformation. In any case, the problem of impact caused by tire fragment is still an open field of research both from the experimental and numerical point of view.

Other Soft Impacts

Soft impact event can referred also to the high velocity collision of water or another liquid against a structure (Abrate, 2016). The most studied example is the impact of rain into aerospace structures. Certainly the erosion that can provoke the rain in the leading edges of turbine blades made of composite material is an issue that has to be taken into consideration. There are several works in which this problem has been investigated in composites aerospace structures (Matthewson and Gorham, 1981; Hancox, 1973). Another occasional debris that could act as soft impactor is the case of nonstructural parts that could detach and collide to the structure. An example of this was the Columbia space shuttle accident where the impact of foam generates some damage that has important consequences in the final accident of the structure (Melis et al., 2004; Fasanella et al., 2004; Carney et al., 2004). Nevertheless these cases are less studied because of their low probability of occurrence.

Finally, another impact that can be taken into consideration is the impact of composite debris against composites structures. This phenomenon raises its importance since the possible use of open rotor engines. In this case the engine has composite blades that are not enclosed by a casing, and one of them it could detach impacting to the surrounding structure. As it was said previously in these cases, the stiffness of the projectile and impacted structure is similar, and therefore it cannot be considered neither a soft nor a “rigid” impact event. Nevertheless it can be seen in the work of Mata-Díaz et al. (2017) that the behavior of a composite fragment when impacted to a rigid plate presents several similarities with a soft impact (highly deformation on the projectile, massive fragmentation process, etc.). Certainly this is a case in which it has to be done for further research.

Cross-References

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • J. A. Artero-Guerrero
    • 1
    Email author
  • J. Pernas-Sánchez
    • 1
  • D. Varas
    • 1
  • J. López-Puente
    • 1
  1. 1.Department of Continuum Mechanics and Structural AnalysisUniversity Carlos III of MadridMadridSpain

Section editors and affiliations

  • F. Teixeira-Dias
    • 1
  1. 1.Institute for Infrastructure and Environment (IIE), School of EngineeringThe University of EdinburghEdinburghUK