X X Zhang

G Ruiz

R C Yu

M Tarifa

Fracture behaviour of high-strength concrete at a wide range of loading rates

Keywords: high-strength concrete, loading rates, drop-weight impact machine, fracture energy, dynamic increase factor

Three-point bending tests on notched beams of a high-strength concrete have been conducted using both a servo-hydraulic machine and a self-designed drop-weight impact device. The fracture energy and the peak load were measured over a wide range of loading point displacement rates, spanning eight orders of magnitude. Under low displacement rates, from 10 -4 mm/s to 10 mm/s, the tests were performed with the servo-hydraulic machine; from 10 2 mm/s to 10 3 mm/s we used the drop-weight impact machine. The results show that the fracture energy and the peak load increase as the loading rate increases.

Nevertheless, such a trend is relatively slight under low rates and can be attributed to viscous effects mainly originating from the presence of water in the pore structure. Under high rates the increases in the fracture energy and in the peak load are dramatic due to the effect of inertia.

Introduction

Nowadays high strength concrete (HSC) is very often used in modern complicated structures of considerable height and span, such as skyscrapers, high towers and large bridges. These are more vulnerable to damages caused by earthquakes, wind and blast loading owing to the fact that HSC is more brittle than normal strength concrete (NSC). As a result, the dynamic fracture properties of HSC are more important than those of NSC with regard to safety assessment and the design of modern structures.

Over the past few decades, compared with the extensive research into the static fracture behaviour of HSC [START_REF] Yan | Effect of fracture path on the fracture energy of high-strength concrete[END_REF][START_REF] Einsfeld | Fracture parameters for high-performance concrete[END_REF][START_REF] Zhang | Effect of coarse aggregate size on relationship between stress and crack opening in normal and high strength concretes[END_REF][START_REF] Sagar | Fracture energy of normal and hsc beams[END_REF][START_REF] Bharatkumar | Effect of fly ash and slag on the fracture characteristics of high performance concrete[END_REF][START_REF] Chen | Effect of aggregate on the fracture behavior of high strength concrete[END_REF][START_REF] Rao | Strength and fracture toughness of interface in high strength concrete[END_REF][START_REF] Wittmann | Crack formation and fracture energy of normal and high strength concrete[END_REF][START_REF] Rao | Fracture energy and softening behavior of high-strength concrete[END_REF][START_REF] Wu | Effect of coarse aggregate type on mechanical properties of high-performance concrete[END_REF][START_REF] Dong | Fracture properties of high-strength concrete[END_REF][START_REF] Darwin | Fracture energy of high-strength concrete[END_REF][START_REF] Li | High-strength concrete in uniaxial tension[END_REF][START_REF] Gettu | Effect of aging on the fracture characteristics and brittleness of a high-strength concrete[END_REF][START_REF] Marzouk | Fracture energy and tension properties of high-strength concrete[END_REF][START_REF] Gettu | Fracture properties and brittleness of high-strength concrete[END_REF], much less information is available on its dynamic fracture behaviour [START_REF] Müeller | Constitutive modelling of high strength / high performance concretestate of the art report[END_REF][START_REF] Schuler | Fracture behaviour of high performance concrete (hpc) investigated with a hopkinson-bar[END_REF][START_REF] Mindess | Fracture toughness of concrete under impact loading[END_REF]. Schuler et al. [START_REF] Schuler | Fracture behaviour of high performance concrete (hpc) investigated with a hopkinson-bar[END_REF] measured the tensile strength and the fracture energy of high performance concrete (HPC) with spalling tests, and Mindess et al. [START_REF] Mindess | Fracture toughness of concrete under impact loading[END_REF] obtained dynamic mechanical properties of HSC and NSC using a drop weight impact machine. More detailed information about these results will be given later, in the section comparing our results with data already published. Nevertheless, experimental data on the rate sensitivity of the fracture properties of HSC are very scarce, as evidenced by Müeller in a recently published state-of-the-art report on constitutive modelling of HSC [START_REF] Müeller | Constitutive modelling of high strength / high performance concretestate of the art report[END_REF].

Thus, in order to get additional insights into the loading rate effect on the fracture properties of HSC, in this paper we present three-point bending tests conducted at a wide range of loading point displacement rates (for simplicity, it is substituted by loading rates), from 10 -4 mm/s to 10 3 mm/s, using both a hydraulic servo-controlled testing machine and a drop-weight impact instrument. The results show that both the fracture energy and the peak load increase with increases in loading rates. Under low loading rates, such tendency is slight, while under high loading rates it is significant. This paper also provides formulations

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for the rate-dependency of the fracture energy and of the peak load, these will be helpful when simulating such rate dependency numerically. This paper is structured as follows: the experimental procedure is given in section 2, in section 3 the results are presented and discussed. Finally, in section 4 some conclusions are drawn.

Experimental procedure

Material characterization

A single high strength concrete was used throughout the experiments, made with a Porphyry aggregate of 12 mm maximum size and ASTM type I cement, I 52.5R.

Microsilica fume slurry and super plasticizer (Glenium ACE 325, B225) were used in the concrete composition. The mixing proportions by weight were 1:0.187:2.12:0.445:0.30:0.065 (cement: water: coarse aggregate: sand: microsilica fume slurry: super plasticizer).

There was a strict control of the specimen-making process, to minimize scattering in test results. All of the specimens were cast in steel molds, vibrated by a vibrating table, wrap-cured for 24 hours, demolded, and stored for 4 weeks in a moist chamber at 20℃ and 98% relative humidity until they were tested.

Compressive tests were conducted according to ASTM C39 and C469 (which are analogous to EN 12390-3 and EN 13412) on 75 mm×150 mm (diameter × height) cylinders.

Brazilian tests were also carried out using cylinders of the same dimensions and following the procedures recommended by ASTM C496 (which is analogous to EN 12390-6). We made 8 cylinders, 4 for compression tests and 4 for splitting tests.

Three-point bending fracture tests

In order to study the loading rate effect on the fracture behaviour of the HSC, threepoint bending tests were conducted on notched beams over a wide loading rate range, from 10 -4 mm/s to 10 3 mm/s. Two testing machines were adopted to carry out the tests, one was a hydraulic servo-controlled testing machine, the other was a self-designed drop-weight impact instrument.

The dimensions of the test beams were 100×100 mm 2 (B×D) in cross section, and 400 mm (L) in total length. The initial notch-depth ratio (a/D) was approximately 0.5, and the span (S) was fixed at 300 mm during the tests.

Tests under loading rates from 10 -4 mm/s to 10 1 mm/s

In this low loading rate range, the tests were performed using the hydraulic servocontrolled testing machine as shown in Fig. 1.

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In regard to the measuring method applied to obtain the fracture energy (G F ), we followed the procedures devised by Elices, Guinea and Planas [START_REF] Guinea | Measurement of the fracture energy using 3-point bend tests .1. Influence of experimental procedures[END_REF][START_REF] Planas | Measurement of the fracture energy using 3-point bend tests .2. Influence of bulk energy-dissipation[END_REF][START_REF] Elices | Measurement of the fracture energy using 3-point bend tests .3. Influence of cutting the p-delta tail[END_REF][START_REF] Elices | On the measurement of concrete fracture energy using three-point bend tests[END_REF]. G F is obtained as:

) a ( exp - + = D B W W G um F (1)
where W exp is the area under the experimental load-displacement curve (P exp -δ exp ), and W um is the unmeasured energy that corresponds to the portion of the ligament that is still unbroken when we stop the test. We calculate this by assuming that the crack propagation obeys a cohesive model, which leads to a hyperbolic tail in the P-δ curve when the displacement is very large and the ligament is very short [START_REF] Elices | Measurement of the fracture energy using 3-point bend tests .3. Influence of cutting the p-delta tail[END_REF][START_REF] Elices | On the measurement of concrete fracture energy using three-point bend tests[END_REF]. Fig. 2 illustrates the process followed to obtain the complete fracture energy. δ u and P u correspond to the termination of the bending test. It should be noted that the kinetic energy of the specimen is very small and insignificant compared with the fracture energy in our tests. Moreover, the unmeasured energy is approximately 10% of that of the measured one.

In order to get the complete failure information from the specimen, the weight compensation technique was adopted during the test. i.e., springs were used to hold the specimen all the time as shown in Fig. 1. The beam rests on two rigid-steel cylinders laid on two supports permitting rotation out of the plane of the beam and rolling along the beam´s longitudinal axis with negligible friction. These supports roll on the upper surface of a very stiff beam fastened to the machine actuator. The load-point displacement is measured in relation to points over the supports on the upper surface of the beam.

Two LVDTs (linear variable differential transducers) fixed to the steel beam are used to measure the displacement between the loading rod and the steel beam. To load, a hydraulic servo-controlled test system was employed. The tests were performed in positioncontrol. Three loading rates were applied during the test from quasi-static level (5.50×10 -4

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mm/s) to rate dependent levels (5.50×10 -1 mm/s and 1.74×10 1 mm/s). Three specimens were tested at each loading rate.

Tests under loading rates from 10 2 mm/s to 10 3 mm/s

In this high loading rates range, all impact tests were conducted using the instrumented, drop-weight impact apparatus designed and constructed in the Laboratory of Materials and Structures of the Universidad de Castilla -La Mancha, as shown in Fig. 3. It has the capacity to drop a 316 kg mass from heights of up to 2.6 m, and can accommodate flexural specimens with spans of up to approximately 1.6 m. In this study, an impact hammer weighing 120.6 kg was used and three drop heights adopted were 40, 160 and 360 mm.

Three specimens were tested at each drop height.

A detailed description of the instrument is given in reference [START_REF] Zhang | A new drop-weight impact machine for studying fracture processes in structural concrete[END_REF]. The impact force between the hammer tup and the specimen is measured by a piezoelectric force sensor. In addition, the reaction force between the support and the specimen is determined by another two force sensors.

An accelerometer attached to the impact hammer was used to measure acceleration and displacement during the impact process. Assuming that the hammer displacement was essentially equal to the displacement of the specimen at the loading point, the velocity and the loading point displacement could be evaluated using the following equations [START_REF] Sukontasukkul | Effect of loading rate on damage of concrete[END_REF].

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The initial impact velocity of the hammer, is

) 0 ( h u & aH u h 2 ) 0 ( = & (2)
where a is the corrected gravitational acceleration ( ), H stands for the hammer drop height. During the impact process, the velocity of the hammer can be obtained using Eq. 3.

2 / 14 . 0 71 . 9 s m ± (3) dt t u u t u t h h h ∫ + = 0 ) ( ) 0 ( ) (
where is the acceleration recorded by the accelerometer attached to the hammer. Then, the displacement of the hammer, and also the loading point displacement of the specimen is calculated by Eq. 4.

) (t u h & & ) (t u h ∫ ∫ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = t t h h h dt dt t u u t u 0 0 ) ( ) 0 ( ) ( & & & (4)

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In reference [START_REF] Zhang | A new drop-weight impact machine for studying fracture processes in structural concrete[END_REF], for measuring the loading point displacement of the specimen during impact process, three accelerometers were mounted along the length of the beam. Thus, the displacement of each location of the accelerometer attached can be obtained by double integration of the acceleration and, then, the loading point displacement can be determined by linear extrapolation.

It is very easy to damage the cables and accelerometers when using a heavy hammer during the tests, thus, in this work we used an accelerometer bonded on the hammer to get the loading point displacement instead assuming that the loading point displacement of the specimen is identical to that of the hammer.

In order to verify this assumption, we performed tests using both methods to capture the loading point displacement. For protecting cables and accelerometers, steel yokes were used to fix the specimen, so that the specimen can not bound from the support, the hammer drop height was 100 mm. Fig. 4 shows the comparison of results using the two methods to measure the loading point displacement. It is clear that their tendency versus time and the order in magnitude are the same. When the specimen is broken, the loss of contact between the hammer and the specimen makes that the differences between experimental results obtained by the two methods are bigger. So, we think that the assumption that the loading point displacement of the specimen is identical to that of the hammer is reasonable.

under dynamic loading conditions, there is neither a standard nor any generally accepted procedure for measuring fracture energy. In this case, it is not that clear that the fracture energy is not fully measured, since the ligament in the dynamic tests ends up completely broken. So, we decide to give the measured value, not accounting for any type of unmeasured energy. The measured energy is calculated by the area under the reaction

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force-displacement (load-displacement) curves, where the reaction force is evaluated by adding the values from both support data points [START_REF] Zhang | A new drop-weight impact machine for studying fracture processes in structural concrete[END_REF][START_REF] Banthia | Impact testing of concrete using a drop-weight impact machine[END_REF].

Furthermore, we did not use any kind of damping materials during the tests, nor did we observe any compressive damage in the impact area.

Results and discussion

Experimental results

Fig. 5 shows the comparison of the typical load-displacement curves at different loading rates. It is clear that the peak load increases in line with increases in loading rates.

However, the stiffness of the beam does not show a similar tendency, which is due to the sensitivity of the elastic flexibility of the beam to the boundary conditions during the application of the concentrated load [START_REF] Planas | Stiffness associated with quasi-concentrated loads[END_REF]. Table 2 provides detailed information about the experimental results. The data in the parenthesis are the standard deviation. The dynamic increase factor (DIF), is defined by the ratios of peak load (P max ) and of the fracture energy to their corresponding quasi-static values. Here, the lowest loading rate ( mm/s) is taken as the quasi-static loading condition. H stands for the drop height of the hammer under impact loading conditions.

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Fig. 6 shows the loading rate effect on the fracture energy. It is clear that the fracture energy increases with increases in loading rates, it should also be noted that beyond a certain threshold (7.04×10 2 mm/s) the rate effect becomes more pronounced and a significant increase is observed. A prediction equation for the loading rate effect on the fracture energy is derived from the test data.

[

] [ ] ⎪ ⎩ ⎪ ⎨ ⎧ × ≥ + - = × < + = + = mm/
δ δ δ δ δ log G m G G F r S F F (5)
where is the static fracture energy. Exponents m and r are adjusting parameters, is the loading rate given in mm/s. Eq. 5 can be used to efficiently predict the loading rate effect on the fracture energy and could also be helpful when performing numerical simulations. It is worth noting that 147.5 N/m obtained by fitting the experimental data is the static value of the fracture energy, and that this could only be obtained by a strictly static test [START_REF] Ruiz | Influence of the loading rate on the measurement of the fracture energy of a high strength concrete[END_REF].

S F G δ &
Under low loading rates, those less than the threshold, the rate effect is slight, and it can be attributed to viscous effects mainly originated by the presence of free water in voids and porous structures. The fact that dry concrete exhibits very little rate sensitivity, except at very high strain rates, provides further justification for our explanation of this tendency [START_REF] Mindess | Concrete. United States of America[END_REF].

However, under impact loading rates, greater than the threshold, the rate effect is remarkable due to the inertia effect [START_REF] Brara | Fracture energy of concrete at high loading rates in tension[END_REF][START_REF] Weerheijm | Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests[END_REF][START_REF] Rossi | Effect of loading rate on the tensile behaviour of concrete : Description of the physical mechanisms[END_REF]. Furthermore, the high increase in the fracture energy is caused by many micro-cracks that develop under impact loading [START_REF] Brara | Fracture energy of concrete at high loading rates in tension[END_REF][START_REF] Bischoff | Compressive behaviour of concrete at high strain rates[END_REF][START_REF] Vegt | Failure mechanisms of conrete under impact loading[END_REF].

Namely, at high loading rates the mechanism of failure is characterized by the propagation

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of many micro-cracks at the same time, these micro-cracks do not have sufficient time to search for paths of minimum energy or lowest resistance. Thus, they are forced to propagate along the shortest path with higher resistances, this leads us straight to the conclusion that the fracture energy should increase as a function of the loading rate. .

Fig. 6. Loading-rate dependence of the fracture energy Fig. 7 shows the loading rate effect on the peak load, the trend is similar to that of the fracture energy. i.e., under low loading rates, the tendency is moderate, while under high loading rates it is dramatic. The maximum DIF for the peak load is 7.14, compared with 38.23 for the fracture energy. It could be that the fracture energy is more sensitive to microcracks than the peak load under high loading rates. This also makes it possible to use only one exponential function to describe the behavior of peak load versus loading rates. Fig. 6 presents the function as well, namely, Fig. 7. Loading rate dependence of the peak load

Comparison with data already published

As mentioned before, compared with the extensive research into the quasi-static fracture behaviour of HSC, much less information is available on its rate-sensitivity behaviour. Table 3 provides a comparison of some impact experimental results from Mindess et al. [START_REF] Mindess | Fracture toughness of concrete under impact loading[END_REF] and the results presented in this paper. The definition of high-strength concrete continues to change as advances in concrete technology make it easier to achieve increasingly higher strengths using conventional construction practices, thus, the compressive strength of the HSC in the paper is around two times bigger than that used in reference [START_REF] Mindess | Fracture toughness of concrete under impact loading[END_REF].

From this table it is clear that the trend of the loading rate effect on the mechanical properties of both high strength concretes is similar, however a big difference is found in the DIF for the peak load. It could be that this is more relevant due to the differences in the span/width ratio during the tests. In general, the weight of the hammer, the impact energy

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and the dimensions of the beams do affect the experimental results. Nevertheless, the results from different drop-weight impact machines are comparable.

Schuler et al. [START_REF] Schuler | Fracture behaviour of high performance concrete (hpc) investigated with a hopkinson-bar[END_REF] measured the tensile strength and the fracture energy of High Performance Concrete (HPC) at high strain rates between 10 /s and 100 /s with spalling tests. A DIF of 3 was observed at a crack opening velocity of 1.7 m/s for the fracture energy. This does not concur with the experimental results obtained by drop-weight impact tests, which can partly be attributed to the inconsistency among the methods of loading and associated errors.

Furthermore, under low loading rates, the rate sensitivity of the fracture energy is slight compared with the fracture energy variation at high loading rates. This leads some authors to conclude that the fracture energy is constant and rate independent at low loading rates [START_REF] Birkimer | Dynamic tensile test of concrete materials[END_REF][START_REF] Weerheijm | Concrete under impact tensile loading and lateral compression[END_REF][START_REF] Schuler | Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates[END_REF].

Conclusions

The fracture behaviour of a high strength concrete under dynamic loading conditions was investigated in this study. The loading rates varied considerably from a quasi-static

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level to a dynamic level, the order of magnitude changed from 10 -4 mm/s to 10 3 mm/s. As a result of the study, the following conclusions can be drawn.

(1) The fracture energy is sensitive to the loading rate. Under low loading rates, below 7.04×10 2 mm/s, the rate effect is slight, and can be attributed to viscous effects mainly originated by the presence of free water in voids and porous structures. However, the rate effect is pronounced when the loading rate goes beyond the threshold of 7.04×10 2 mm/s.

(2) The peak load and the fracture energy both increase with increases in loading rates, however, under high loading rates the effect on the energy is even more pronounced than that on the peak load.

(3) Finally, two prediction-equations for the rate sensitivity of the fracture energy and the peak load are proposed. These formulas are helpful in numerical simulations that evaluate the rate dependence of fracture behaviour.

Fig. 1 .Fig. 2 .

 12 Fig. 2. Determination of the fracture energy.

Fig. 3 .

 3 Fig. 3. (a) Schematic diagram and (b) photo of the drop-weight impact machine.

Fig. 4

 4 Fig. 4 Comparison of the loading point displacement

Fig. 5 .

 5 Fig. 5. Load-displacement curves at different loading rates.

  is the static peak load, exponents k and n are adjusting parameters. It is noteworthy that the fitting also gives the static value of the peak load, 5.88 kN.

Table 1

 1

	shows the

Table 2

 2 Experimental results at different loading rates.

	Testing	H	δ &	P max	DIF	W F	DIF
	machine	(mm)	(mm/s)	(kN)	for P max	(N/m)	for W F
	Hydraulic	-	5.50×10 -4	5.33 (0.33)	1	148 (9)	1
	servo-controlled	-	5.50×10 -1	7.20 (0.30)	1.35	205 (12)	1.39
	device	-	1.74×10 1	8.22 (0.37)	1.54	226 (19)	1.53
	Drop-	40	8.81×10 2	23.87 (3.10)	4.48	1205 (24)	8.14
	weight impact	160	1.76×10 3	34.34 (2.73)	6.44	3968 (653)	26.81
	instrument 360	2.64×10 3	38.07 (7.65)	7.14	5658 (885)	38.23

Table 3

 3 Comparison of experimental results

		Experimental results from	Experimental results
		Mindess et al. [19]	in this paper
	Compressive strength (MPa)	62	127
	Dimensions of the beam	100×125×1400	100×100×400
	(width × depth × length) (mm)
	Span (mm)	960	300
	Drop height of the hammer (mm)	150	160
	Weight of the hammer (kg)	345	120.6
	DIF for the peak load	2.96	6.44
	DIF for the fracture energy	21.38	26.74

& & & &

& & & & &

Acknowledgements

Funding from the Ministerio de Ciencia e Innovación, Spain, under grant MAT2006-09105 and from the Consejería de Educación y Ciencia, JCCM, Spain, under grant PAI08-0196, is gratefully acknowledged.


Dr Sebastian Heimbs
email: sebastian.heimbs@eads.net

S Heller

P Middendorf

F Hähnel

J Weiße

Low velocity impact on CFRP plates with compressive preload: Test and modelling

Keywords: Low velocity impact, composite laminates, preloading, finite element modelling, delamination

When laminated composite materials in modern aircraft structures are subject to impact loads, they are typically not unloaded but under a certain state of prestress. Therefore, in this study the effect of a compressive preload on the low velocity impact behaviour of three different carbon fibre-reinforced plastic (CFRP) materials is investigated. An experimental test programme is documented first, including the design of a preload test device, the specimen manufacture and the results description. An increased deflection and energy absorption for composite plates with a preload of 80% of the buckling load could be observed. Non-destructive inspections showed a large extent of delaminations occurring between individual plies, being an important energy absorption mechanism. The development of numerical simulation methods for this impact scenario using the commercial explicit finite element code LS-DYNA is described in detail. The focus is on the composite material, delamination and preload modelling. The final simulation results showed a good correlation to the experimental data in terms of force and energy plots or the evaluated interlaminar and intralaminar damage, although these numerical results proved to be strongly influenced by simulation parameters like mesh size or the number of shell element layers.

Introduction

Fibre-reinforced composite materials are known for their high weight-specific mechanical properties and are therefore used in numerous lightweight engineering applications, in particular in aircraft design. However, a constant concern for such laminates -much more than for similar metallic structures -are impact loads of foreign objects, which can cause internal material damage. This damage can significantly reduce the strength and it can grow under load and may be difficult to detect. Typical impact scenarios in aircraft design range from a tool dropped on the laminate surface (high mass, low velocity), over runway debris thrown up by the tires or hail (low mass, high velocity) to bird strike during flight (high mass, high velocity).

The impact behaviour of composite laminates has been treated extensively in the technical literature. A comprehensive overview on this topic is given by Abrate [START_REF] Abrate | Impact on composite structures[END_REF]. However, nearly all studies are concerned with

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2 impact loads on unloaded composite materials. But with regard to aircraft structures, it is rather unlikely that the impacted surface is unloaded. The composite structure may be subject to compressive, tensile or shear loads in the operational environment. Therefore, knowledge of the effect of preloading on the impact behaviour of composite laminates is of significance, since the damage development can be drastically different. Only very few studies in the literature cover this topic.

Analytical investigations were performed by Sun and Chattopadhyay [START_REF] Sun | Dynamic response of anisotropic laminated plates under initial stress to impact of a mass[END_REF], Malekzadeh et al. [START_REF] Malekzadeh | Response of in-plane linearly prestressed composite sandwich panels with transversely flexible core to low-velocity impact[END_REF], Khalili et al. [START_REF] Khalili | Analysis of fiber reinforced composite plates subjected to transverse impact in the presence of initial stresses[END_REF] and Choi [START_REF] Choi | Low-velocity impact analysis of composite laminates under initial in-plane load[END_REF]. They all come to the conform results that under tensile preloading the contact force is increased and the contact time as well as the deflection are reduced compared to the impacted unloaded plate. These results were confirmed by the experimental tests of Mitrevski et al. [START_REF] Mitrevski | Low-velocity impacts on preloaded GFRP specimens with various impactor shapes[END_REF] on glass fibre-reinforced (GFRP) composites.

Besides these GFRP laminates, most papers deal with experimental investigations of the influence of preloading on the low velocity impact behaviour of carbon fibre-reinforced composites (CFRP). And here, in particular, uniaxial and biaxial tensile preloading is investigated, as by Butcher [START_REF] Butcher | The impact resistance of unidirectional CFRP under tensile stress[END_REF], Butcher and Fernback [START_REF] Butcher | Impact resistance of unidirectional CFRP under tensile stress: further experimental variables[END_REF], Sankar and Sun [START_REF] Sankar | Low-velocity impact damage in graphite-epoxy laminates subjected to tensile initial stresses[END_REF], Avva et al. [START_REF] Avva | Effect of impact and fatigue loads on the strength of graphite/epoxy composites[END_REF], Phillips et al. [START_REF] Phillips | The impact behaviour of high performance, ceramic matrix fibre composites[END_REF], Park [START_REF] Park | The impact response of composites under stress[END_REF], Nettles et al. [START_REF] Nettles | The effects of tensile preloads on the impact response of carbon/epoxy laminates[END_REF], Herszberg et al. [START_REF] Herszberg | The residual tensile strength of stitched and unstitched carbon/epoxy laminates impacted under tensile load[END_REF], Kelkar et al. [START_REF] Kelkar | Behavior of tensile preloaded composites subjected to low-velocity impact loads[END_REF], Mines et al. [START_REF] Mines | Static behaviour of transversely loaded CFRP laminate panels subject to inplane tension[END_REF] and Whittingham et al. [START_REF] Whittingham | The response of composite structures with pre-stress subject to low velocity impact damage[END_REF]. The result of these studies is the tensile preload affecting the failure behaviour and failure modes. Garcia-Castillo et al. [START_REF] Garcia-Castillo | Response of pre-loaded laminate composite plates subject to high velocity impact[END_REF] performed a comparable investigation for high velocity impact loads. Sharma [START_REF] Sharma | Low-velocity impact tests on fibrous composite sandwich structures[END_REF], Mines et al. [START_REF] Mines | Static behaviour of pre-stressed polymer composite sandwich beams[END_REF] and Malekzadeh et al. [START_REF] Malekzadeh | Response of in-plane linearly prestressed composite sandwich panels with transversely flexible core to low-velocity impact[END_REF] also included composite sandwich structures with foam or honeycomb cores in their studies.

The stress situation in the lower aircraft fuselage during take-off, when it is likely to be exposed to impacting stones propelled by the tires, is a compressive stress state. The impact behaviour under such compressive preloads is addressed in even fewer papers. This preloading condition is yet more complex because plate buckling becomes an issue for relatively thin composite structures. The investigations of Starnes et al. [START_REF] Starnes | Effect of impact damage and holes on the compressive strength of a graphite/epoxy laminate[END_REF],

Nettles and Lance [START_REF] Nettles | The effects of compressive preloads on the compression-after-impact strength of carbon/epoxy[END_REF], Robb et al. [START_REF] Robb | The damage tolerance of GRP laminates under biaxial prestress[END_REF], Tweed et al. [START_REF] Tweed | Impact performance of stressed composites[END_REF], Chiu et al. [START_REF] Chiu | Low velocity impact behavior of prestressed composite laminates[END_REF] and Zhang et al. [START_REF] Zhang | Impact damage with compressive preload and post-impact compression of carbon composite plates[END_REF] include such compressive preloads.

Besides pure experimental investigations on the impact behaviour of composite laminates, numerical finite element (FE) simulations play an increasingly relevant role in engineering development. Validated simulations not only allow for a detailed analysis of stress distributions and damage progression in the laminate during the impact event but also enable efficient parameter studies with respect to geometries, loading conditions or laminate configurations. For impact simulations as a transient loading, FE codes based on an explicit time integration scheme are typically used, which are characterised by small time step intervals. On the other side, the preloading happens on a static basis, making implicit calculations more appropriate. Therefore, the combination of preloading and impact loading requires special numerical strategies. FE simulations of low velocity impacts on preloaded composite structures have first been addressed by Sun and Chen [START_REF] Sun | On the impact of initially stressed composite laminates[END_REF]. However, just like in the work of Tweed et al. [START_REF] Tweed | Impact performance of stressed composites[END_REF] and Mines et al. [START_REF] Mines | Static behaviour of pre-stressed polymer composite sandwich beams[END_REF], who used the commercial explicit code LS-DYNA, no detailed information on the preload modelling are given. Kelkar et al. [START_REF] Kelkar | Analysis of tensile preloaded composites subjected to low-velocity impact loads[END_REF] bring forward the argument that their static and dynamic tests led to the same results. As a consequence, they considered the impact as a static loading and combined the preloading and impact simulation in an entirely implicit calculation with the commercial software ANSYS. Zhang et al. [START_REF] Zhang | Impact damage with compressive preload and post-impact compression of carbon composite plates[END_REF] used the in-house FE package FE77 and performed a completely explicit simulation utilising dynamic relaxation for the preloading. Mikkor et al. [START_REF] Mikkor | Finite element modelling of impact on preloaded composite panels[END_REF] as well as Pickett et al. [START_REF] Pickett | Test and modelling of impact on pre-loaded composite panels[END_REF] used the commercial explicit code PAM-CRASH. Especially in the latter paper a detailed description of the preloading modelling is given, which is performed as a part of the explicit simulation by stretching the composite plate directly before the impact load.

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The aim of the current paper is to get a deeper insight into the influence of compressive preloads on the low velocity impact behaviour of CFRP plates. On the one hand, this is done by experimental impact test series on unloaded and preloaded specimens, which involves the design of a special specimen fixture allowing for compressive preloads. On the other hand, numerical techniques are evaluated to adequately simulate the preloading and impact event in the commercial FE code LS-DYNA, with the focus on the composite material, delamination and preload modelling.

Materials & manufacturing

In this study three different carbon fibre-reinforced epoxy (CF/EP) materials were investigated with a difference in their manufacturing process and laminate stacking sequence. Within this paper they are referred to as material type A, B and C and are specified as follows:

• Type A: Non-crimp fabric (NCF) in a symmetric, quasi-isotropic lay-up with 24 plies: [-45°/0°/45°/90°] 3s , Fig. 1a • Type B: Prepreg tape in a symmetric, quasi-isotropic lay-up with 24 plies: [-45°/0°/45°/90°] 3s , Fig. 1b • Type C: Prepreg tape in a symmetric lay-up with preferred 0°-direction and 24 plies (50/33/17 lay-up: 50% 0° plies, 33% ±45° plies and 17% 90° plies): [0°/45°/0°/-45°/0°2/45°/0°/-45°/90°2/0°] s .

The quadraxial NCF (type A) from the manufacturer Saertex, made from 12K HTS carbon fibres, was used with Hexcel's RTM6 epoxy resin in a vacuum assisted process (VAP) to fabricate the CFRP plates in an autoclave at a curing temperature of 180°C. The cured plates had a mean thickness of 3.2 mm with a standard deviation of 0.08 mm and a fibre volume fraction of 51%.

In contrast to this liquid resin infusion process, in the prepreg material (type B, type C) from the manufacturer Cytec the unidirectional 12K HTS carbon fibres were already pre-impregnated with a 977-2 epoxy matrix. The prepreg tape plies were stacked according to the target fibre orientation angles and were cured in an autoclave at 180°C and 7 bar. The resulting average cured plate thickness was 2.7 mm with a standard deviation of 0.11 mm.

The fibre volume fraction was 65%. An overview of the mechanical properties of the NCF and prepreg material , based on technical data sheet values of the manufacturer and adapted to the actual fibre volume contents, is given in Tab. 1 and Tab. 2. Any strain rate dependency of those properties is neglected due to the relatively low deformation speeds occurring in this low velocity impact study.

A diamond saw was used to cut out the final test specimens with a size of 400 mm x 150 mm. 2 mm thick tapered GFRP tabs with a width of 50 mm were bonded onto both sides of these specimens, reducing the free specimen length to 300 mm (Fig. 2). Both specimen ends were ground parallel to ensure a uniform lengthwise compressive load distribution. These specimen dimensions are much smaller and thicker compared to a commercial aircraft skin panel within the frames and stringers. However, the boundary conditions in this generic study were not chosen to represent a real aircraft impact scenario but to limit the complexity of testing and modelling and to achieve higher in-plane compressive loads without the occurrence of plate buckling.

A total of six strain gauges were applied on each preloaded specimen, five on the upper and one on the lower surface, see Fig. 2. The locations of these strain gauges were selected to give valuable information with respect to the following topics: if the target preloading is met, if a uniform load distribution in length and width direction of the plate is achieved and if plate buckling occurs under the compressive preload. The low velocity impact testing was conducted on a Dynatup 8250 drop tower facility. The CFRP plate had to be positioned under this drop tower and should also be preloaded in compression. Therefore, a special specimen fixture was designed and fabricated that allows for a specific uniaxial compressive preloading.

3.1

Specimen fixture and pre-loading device

For the lengthwise compressive preload introduction two parallel steel plates with ground surfaces were used. To achieve a fixed support of both ends of the CFRP plates, two clamping jaws were mounted on each end. The lateral sides of the plate were only simply supported with a special support inhibiting translational movements in vertical direction but allowing for horizontal translations during the preloading and rotations during the impact load. The final specimen fixture is shown in Fig. 3.

One end of this fixture was mounted to the base of the drop tower, while the other end was connected to a compression device with two hydraulic cylinders. With these cylinders the preloading force was applied to the specimen. To control the preloading both the compression force and the strain values from the specimen's strain gauges were recorded.

Low velocity impact test conditions

For all impact tests in this study a hemispherical steel impactor with a diameter of 1 in. (25.4 mm) and a mass of 1.85 kg was used (Fig. 4). The clamping conditions of the CFRP plates include a fixed support of the longitudinal ends and a simple support of the lateral sides, as illustrated before.

All three materials were tested with and without preloading. To limit the complexity of this study, a reference energy level of 40 J was chosen. Since the impactor mass was constant, this corresponds to an impact velocity of 6.5 m/s. Few additional tests with material type B were conducted with 30 J.

Compressive preloading conditions

The difficulty of compressive preloading is the risk of initial plate buckling as a stability failure of the relatively thin specimens under in-plane compression. The aim of this study was to avoid initial buckling and only to impact plates, which show no initial deflections. On the one hand this limits the amount of prestrain to a moderate level and affects the evaluation of the preload effect, but on the other hand the complexity of this investigation is reduced, especially with respect to the numerical modelling. The buckling loads of the respective specimen plates of type A, B, and C were first estimated by an analytical buckling analysis and implicit FE buckling analyses. But finally the real buckling load was determined experimentally by compressing calibration plates and evaluating the strain gauge data. The occurrence of plate buckling could be detected by a change in the strain values with respect to the first or second buckling mode. Afterwards, the in-plane compression was reduced to 80% of the detected buckling load. This corresponds to a prestrain of 1800 με for material type A, 1100 με for material type B and 670 με for material type C. However, these are the mean values of the maximum prestrain of the individual specimens' strain gauge data. The prestrain distribution was not ideally uniform over the whole specimen as a result of unavoidable imperfections in the plate thickness and the parallelism of the compression supports. An overview of the impact test conditions is given in Tab. 3. Shown are mean values from three specimens for each load case.

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Damage evaluation by non-destructive inspection

Ultrasonic inspections are a well-established method for non-destructive evaluations of composite material damage and delaminations and were also adopted in this study. A Hillger USPC 3000 device was used, which is based on the impulse echo principle with the scanning head being both transmitter and receiver of the ultrasonic signal. If cracks or defects are present inside the specimen, a reflection is generated that is detected and visualised in a B-scan (sectional view) or C-scan (top view) image.

Test results

The results of the impact tests on unloaded and preloaded CFRP plates are summarised in Tab. 3 and in Fig. 5 and Fig. 6 in terms of time-dependent plots of impact force F(t), energy E(t) and plate deflection s(t). The energy is computed here from the initial kinetic energy E kin (t 0 ) of the impactor, its mass m imp and velocity v(t). A photoelectric sensor was used to measure the initial velocity v(t 0 ) before impact.

( ) ( ) ( ) ( ) [ ] 2 0 0 2 1 t v t v m t E t E imp kin Δ + - = (1)
with

( ) ( ) ∫ - ⋅ = Δ t imp dt t F m t g t v 0 1 . (2)
The deflection s(t) is calculated by double integration of the impact force

( ) ( ) ( ) ∫ ∫ - ⋅ + ⋅ = t t imp dt t F m t t v t g t s 0 0 0 2 1 2 1 . (3)
In general, the force level increases slowly in the beginning, which is the result of an oscillation of the plate after first contact with the impactor. When the plate swings back upwards the contact force increases steeply. After the point of maximum deflection, the force level decreases to zero again. The energy curves increase continuously to a maximum and fall to a certain level. This residual value is an indicator for the absorbed energy, which is not transferred to the impactor as elastic springback. If the plate behaved completely elastic without failure and neglect of friction losses, the energy curve would return to zero again. The deflection curve has a parabolic shape and is shown here in the positive quadrant.

The test results of all three materials indicate that the compressive preloading leads to an increased deflection of the CFRP plates and therewith to a higher extent of material damage. More energy is absorbed and less energy is returned as elastic springback compared to the unloaded plates. The increased damage can especially be seen in the ultrasonic C-scan images in Fig. 6. In general, the propagation of delaminations is higher for the preloaded specimens. Delaminations occur between several plies across the thickness, each having a dumbbell shape and orientation depending on the respective fibre orientation angle. From the top view this leads to a nearly circular shape for the quasi-isotropic prepreg specimens of material type B and a rather oval shape for type A and C. The marginal difference in the delaminated area between 30 J and 40 J for type B is in correlation with experimental findings by Avery and Grande [START_REF] Avery | Influence of materials and layup parameters on impact damage mechanisms[END_REF]. They also impacted 24-ply CF/EP plates and found the total damage area detected by ultrasonic inspection to increase almost linearly for energies up to 30 J. No further increase was detectable until approximately 40 J, then it increased again. This was attributed to the introduction of fibre breakage as an additional damage mode between 30 and 40 J. Also in the current study the appearance of fibre cracking and blow-out of 45° plies on the back side of the plate was observed only for the 40 J specimens, which The comparison of the test results in Tab. 3 for the prepreg material types B and C, which only differ in the stacking sequence, shows that the maximum plate deflection is slightly lower for the quasi-isotropic specimens of type B. Also the shape of the delaminated area in Fig. 6 is different. This results from the fact that delaminations do not arise between layers of similar fibre orientation. In material type B with the lay-up [-45°/0°/45°/90°] 3s a doubling of two similar layers occurs only in the midplane, leaving 22 ply interfaces for possible delaminations. The stacking sequence of type C [0°/45°/0°/-45°/0°2/45°/0°/-45°/90°2/0°] s has five doublings and only 18 potential delamination interfaces. It is known from [START_REF] Avery | Influence of materials and layup parameters on impact damage mechanisms[END_REF] that if the creation of a delamination at a particular interface is not favourable then larger delaminations tend to occur at those interfaces, where the creation is favourable, absorbing the impact energy. This may explain the larger extent of delaminations in material type C, which reduce the plate's stiffness more significantly and lead to a higher deflection compared to type B.

The results in Tab. 3 also indicate that the NCF material type A absorbs considerably more energy than the prepreg material. This phenomenon may be ascribed to the lower strength properties in Tab. 2, which result from the lower fibre volume fraction, more ondulations (see Fig. 1) and lower matrix properties of RTM6 resin compared to 977-2 (the fibres are the same). Because the polyester yarn, which is used to fixate the carbon fibre non-crimp fabric, can be the origin of failure or distorts the fibre orientation and leads to resin nests, the properties of NCF material are in general lower than for unidirectional prepreg. In this material intralaminar failure occurs earlier at a lower internal stress state, which is proved by the lower impact force level in Fig. 5 compared to the prepreg material. A higher amount of impact energy is therefore absorbed by internal material damage. The specimens of type A showed the highest amount of fibre cracking and fibre blow-out on the back side of the plates in this study. The delamination failure for the NCF plates is limited to the five interfaces between the fixed quadraxial ply packages, because the fixating polyester yarn acts as a reinforcement in thickness direction and impedes delaminations. This can be seen in the ultrasonic B-scan images in Fig. 8. In these cross-sectional views through the impacted plates the depths of the delaminations from the upper surface can be visualised. However, only the first delaminations from the top are visible, the ones below are in the shadow and cannot be detected. But still a large difference between material type A and B is obvious in Fig. 8.

While in the prepreg material type B delaminations can occur between any ply, they are limited to the few quadraxial package interfaces in material type A. As a consequence, larger delaminations are created here.

The variation of the in-plane loading during the impact can be evaluated from the strain gauge data. In general, the strain level varies during the impact with respect to the strain gauge position, e.g. the strain gauges close to the impact location on the top surface, which is the compression side under bending, show increased compression strains. After the impact, the strain gauges indicate a remaining buckling deformation for types A and C, while the plates of type B return to their initial state.

Summarising the experimental results of the low velocity impact tests on CF/EP plates with energies of 40 J, it can be stated that both intralaminar (fibre breakage and matrix failure) and interlaminar (delamination) failure occur in the composite material with the compressive preload increasing the amount of damage and energy absorption. Therefore, the emphasis in the development of impact simulation models must be placed on intralaminar and interlaminar failure and preload modelling. In order to investigate if the experimentally determined failure behaviour of CFRP plates with compressive preload under low velocity impact loads can be represented in a numerical simulation, modelling methodologies of the composite material failure, delaminations and preload have been investigated. For this purpose the commercial explicit finite element software LS-DYNA was used.

Model development

The development of the FE model for the low velocity impact simulations in LS-DYNA involves the modelling of the composite material including intralaminar failure and delamination failure, the modelling of the preload and the modelling of the impactor with adequate contact definitions. These topics are addressed as follows.

Composite material modelling

The composite plates consist of 24 plies of unidirectional CF/EP. As the plates' length and width dimensions are large compared to the thickness, a 2D modelling approach with shell elements is appropriate. In aircraft engineering shell models are standard because almost all structures in aircraft design are thin-walled, although in this transverse impact load case stresses in thickness direction may exist. However, it would not be adequate to investigate a 3D modelling approach in this study, which might increase accuracy, but is of minor relevance for the engineering practice due to the high computational cost and inefficiency. The linear-elastic composite material model Mat54 for shell elements in LS-DYNA, based on the failure criteria by Chang and Chang [START_REF] Chang | A progressive damage model for laminated composites containing stress concentrations[END_REF] was adopted. The elastic material behaviour of the individual ply is calculated based on the input of the Young's modulus, shear modulus and Poisson's ratio (see Tab. 1). Damage occurs as soon as one of the four criteria by Chang/Chang is met. Four criteria are distinguished, representing tensile and compressive failure in the fibre and matrix direction of the unidirectional ply (Fig. 9). A special criterion for shear failure is not implemented. The interaction of shear stresses is included in the failure criteria instead.

Tensile failure, fibre direction:

⎩ ⎨ ⎧ < ≥ - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = elastic failure SC XT e t f 0 0 1 2 12 2 1 2 , τ β σ (4)
Compressive failure, fibre direction:

⎩ ⎨ ⎧ < ≥ - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = elastic failure XC e c f 0 0 1 2 1 2 , σ (5)
Tensile failure, matrix direction:

⎩ ⎨ ⎧ < ≥ - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = elastic failure SC YT e t m 0 0 1 2 12 2 2 2 , τ σ (6)
Compressive failure, matrix direction:

⎩ ⎨ ⎧ < ≥ - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = elastic failure SC SC YC YC SC e c m 0 0 1 1 4 2 2 12 2 2 2 2 2 2 , τ σ σ (7)
Here XT and XC are the strength values for tension and compression in fibre direction, YT and YC in matrix direction. SC is the shear strength. The strength values were taken from Tab. 2. The parameter β can be used to scale the shear stress interaction in the fibre tensile failure criterion. β=1 yields the Hashin criterion, which overestimates the shear stress interaction as stated by Schweizerhof et al. [START_REF] Schweizerhof | Energy absorption with composite crash elements in frontal crash -an analysis with LS-DYNA3D[END_REF]. β=0, on the other hand, yields the

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8 simple maximum stress criterion without interaction. In this study a value of β=0.04 was used. As known from other impact studies, the matrix tensile and fibre tensile failure criteria play the most significant role for the low velocity impact behaviour of composite laminates.

In addition to these stress-based criteria, failure strains can be defined as well. When these failure strain parameters in Mat54 are used, the stress level after meeting the Chang/Chang criteria is kept at a constant level until the failure strains are reached. Then the respective layer is assigned with zero stiffness properties. This post-damage behaviour is based on the theory of Hahn and Tsai [START_REF] Hahn | On the behavior of composite laminates after initial failures[END_REF], who found a better correlation of the model with experimental data, if the post-damage stress level of the unidirectional ply is kept constant until the whole laminate fails, instead of setting it to zero immediately.

Inside one shell element a number of sub-layers can be defined in thickness direction, representing the laminate lay-up, which is referred to as a 'layered shell' modelling approach. In this study, each single ply was defined by one integration point with the respective ply thickness and fibre orientation angle. Once all single layers of the shell element have failed, the whole element is eroded, i.e. deleted from the calculation. Underintegrated fournode shell elements of the type Belytschko-Tsay [START_REF]LS-DYNA Keyword User's Manual, Version 971[END_REF] with a stiffness-based hourglass control were used for the modelling of the composite plate. This was justified since the hourglass energy in the final impact simulations was negligible with less that 1% of the total energy, which makes the utilisation of more expensive elements with a selectively reduced or full integration unnecessary.

Delamination modelling

Interlaminar delamination failure as the separation of two laminate layers plays a significant role in low velocity impacts on composite plates as an energy absorption mechanism and a degradation factor of the plate's stiffness and should therefore be implemented in the simulation model. In this study, the LS-DYNA contact formulation Contact_automatic_one_way_surface_to_surface_tiebreak with the failure law option 8 [START_REF]LS-DYNA Keyword User's Manual, Version 971[END_REF] was used between separate shell elements. This modelling approach is referred to as a 'stacked shell' model. The contact allows for the simulation of crack propagation based on the cohesive zone model, implemented in LS-DYNA as a delamination contact by Borg [START_REF] Borg | Simulation of delamination initiation and growth in fiber composite laminates[END_REF]. After defined normal and shear failure stresses (NFLS, SFLS) are met, damage is a linear function of the distance of two points initially in contact. As soon as a defined critical crack opening (CCRIT) is reached, the contact is released and converted into a regular surface-to-surface contact preventing penetrations. The energy release rates G IC and G IIC for normal and shear interface failure are approximated by

CCRIT NFLS G IC ⋅ ⋅ = 2 1 ( 8
)
CCRIT SFLS G IIC ⋅ ⋅ = 2 1 . ( 9
)
The value NFLS was determined in a numerical analysis of a double cantilever beam (DCB) test. First the critical force F crit and the critical crack opening displacement d crit , which are necessary for the crack propagation, were calculated analytically based on the known value of G IC =225 J/m² as a material constant and the following equations:

EI a b G F IC crit 2 = ( 1 0 ) M A N U S C R I P T A C C E P T E D ARTICLE IN PRESS 9 EI a F d crit crit 3 3 2 = ( 1 1 )
with a as the initial crack opening length, b as the specimen width and EI as the bending stiffness. This crack opening was applied to a corresponding FE model of the DCB specimen in LS-DYNA and the resulting normal interface stress at the crack tip was evaluated under this crack opening load case, which is the value NFLS. The value CCRIT can be obtained subsequently by solving equation [START_REF] Butcher | Impact resistance of unidirectional CFRP under tensile stress: further experimental variables[END_REF]. Finally, equation ( 9) was used to calculate SFLS with the known value of CCRIT and G IIC =640 J/m².

This study covers 24-ply CFRP laminates. If each ply is modelled as a separate layer of shell elements with 23 delamination contact formulations in-between, the model would be very expensive to calculate. Moreover, a certain minimum contact thickness has to be assured in order to avoid contact breakdown [START_REF] Bala | Contact Modelling in LS-DYNA, Part 2 -Contact Parameters: Default and Recommended Values[END_REF]. As an alternative, different models with two, three, four and six separate layers of shell elements were generated, each shell element covering a certain number of different plies as different internal integration points. For comparison reasons, a model with just one shell element and without delamination was also generated. Identical parameters NFLS, SFLS and CCRIT of the delamination contact were used for the models with two to six layers of shell elements. In this case, the latter model with five contact interfaces corresponds to the NCF material type A,

where delaminations occurred only between the six quadraxial ply packages. Although this modelling approach is not able to cover reality by enabling delamination between each single ply of the prepreg material, it is, however, an approach to evaluate if interlaminar failure occurs at all and an additional energy absorption mechanism. An alternative delamination modelling method in a shell element model is the utilisation of cohesive elements, which was not adopted in this study.

Preload modelling

While the low velocity impact is a transient load case with material damage occurring in a short time period, the compressive preloading of the composite plate, on the other hand, happens on a rather static basis. To combine these two loadings in a single model, different numerical approaches have been investigated.

One way is to use the implicit LS-DYNA solver for the preloading and the explicit solver for the transient impact loading. The implicit-explicit switching functionality in LS-DYNA is straightforward and can be performed within one single input deck. With this technique, the implicit preloading calculation takes only a few seconds, making this method very efficient. However, neither the delamination contact nor the cohesive elements are implemented in the implicit solver version used in this study, making this technique inapplicable.

The other way is to use solely the explicit LS-DYNA solver, also for the preloading. To avoid oscillations, the displacement-controlled preloading should be applied within a sufficiently long time interval or by using the dynamic relaxation feature to damp nodal velocities. This method is less computationally efficient -though more stable.

In this study, the explicit solver without dynamic relaxation was used for both preloading and impact loading due to stability reasons. The displacement-controlled compressive prestress was applied in a period of 10 ms without provoking any noticeable oscillations, with the impact event lasting approx. 6 ms until springback. With respect to a slightly decreasing time step size, this corresponds to half of the total computational time ascribed to the preloading and the other half to the impact load. A further benefit in computational time might be achievable with the Initial_strain_shell and Initial_stress_shell options in LS-DYNA, which were not investigated in this

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study. The other boundary conditions in the model were defined corresponding to the impact test rig, with fully constrained nodes at the longitudinal ends of the specimen and simply supported nodes at the lateral ends.

The impactor was modelled as a spherical rigid body with conventional shell elements and the rigid LS-DYNA material model Mat20 as well as a defined initial velocity. Another alternative would be the modelling of the impactor as an idealised spherical contact entity without a user-defined mesh. However, in this study this led to a significantly higher computational cost, and was therefore not applied.

Simulation results

Comparison between experiment and simulation

In this section the simulation results are presented and compared with the experimental data. To limit the amount of result data in this paper, only material type B is treated in the following sections. The general findings have been verified to be similar for the other two types A and C. Since numerous simulation parameters have a significant influence on the numerical results, one reference model is treated first. The influence of the single parameters (mesh size, number of shell element layers etc.) is discussed later. This reference model consists of three layers of shell elements with two delamination tiebreak contacts in-between and an element length of 3 mm (Fig. 10). For a comparison between experimental and numerical results, the following data were evaluated:

• Impact contact force:

While the contact force in the experiment was recorded directly by the strain gauge-based load cell, the numerical force curve was obtained by recalculating the impactor's rigid body acceleration. The results for the unloaded and preloaded case are shown in Fig. 11. The correlation between experiment and simulation is acceptable in both cases. In the beginning, the behaviour is characterised by an oscillation of the plate after first contact with the impactor, which is represented correctly by the simulation model. When the plate swings back upwards the contact force increases steeply. The further drops in the force plot result from oscillations and material damage. Despite some deviations in the curve peak values, the overall contact time matches again very satisfactorily.

• Energy plot:

The results of the energy plot are shown in Fig. 12. For the unloaded and preloaded case the experimental and numerical curves match with a high degree of accuracy. Also the final values of the absorbed energy are in good correlation.

• Interlaminar failure (delamination):

In the experiment, the delaminated area is slightly higher for the plate with compressive preload compared to the unloaded plate (Fig. 6). The diameter measures approx. 25 mm. In the simulation model an additional interface force file was written out for the visualisation of the delamination contact. Once the contact fails completely and CCRIT is reached, the respective nodal value of a failure variable changes from 1 to 0, which can be visualised in a two-coloured fringe plot in Fig. 13. Shown are the two contact interfaces with black shading around each released node. In the reference simulation model with two tiebreak contact interfaces the visualisation of the delaminated area as described above also leads to a diameter of 25-30 mm. However, is has to be kept in mind

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that the comparability of the illustration in Fig. 13 and the C-scan image in Fig. 6 is limited, because the model only consists of two interfaces with possible interlaminar failure. Although the area might be similar from the top view, the real delaminations in the C-scan image are built up from numerous delaminations between more than just two interfaces. The simulation results just indicate that interlaminar failure occurs and give a rough estimation of the propagation.

• Intralaminar failure (fibre/matrix failure):

The intralaminar fibre and matrix damage could not be evaluated precisely in the test specimens but could only be analysed in the LS-DYNA simulation results by plotting the Mat54 failure variables. These variables are set from 1 to 0 if failure occurs in fibre tensile mode, fibre compressive mode, matrix tensile mode or matrix compressive mode. The simulation results of the reference model showed that the only intralaminar failure mode occurring is matrix tensile failure. The two-coloured fringe plot of this failure variable for the individual integration points across the thickness of the 24-ply laminate is shown in Fig. 14. Three stacks with eight layers can be seen, each stack representing one shell element and each layer representing one integration point across the shell's thickness. Damage starts from the bottom plies on the opposite side of the impact. This is the tensile side under plate bending and since the matrix tensile strength has the lowest value (see Tab. 2), failure occurs in matrix tensile mode. This phenomenon with higher damage in the bottom plies can both be observed for the global structure as well as for each single shell element. The extent of intralaminar damage for the preloaded model is slightly higher than for the unloaded plate.

Influence of element size

Since the element size is known to have an influence on simulation results, a parameter study was carried out, investigating element lengths of 1.5 mm, 2 mm, 3 mm, 4.7 mm, 6 mm and 8 mm. This study covered both models with and without a delamination contact. The results of this study showed a strong mesh dependency. This is because both the composite material failure behaviour of Mat54 and also the delamination contact are influenced by the element size, and therefore the absorbed energy varies with the element length (Fig. 15). A convergence for small elements is visible. Since the impact of the sphere is a very local load introduction, very fine meshes are necessary to cover the mechanical behaviour adequately. The parameters of the delamination contact need to be adjusted for each mesh size to obtain consistent results.

Influence of number of shell element layers

To evaluate the influence of the number of shell element layers in the stacked shell model, or in other words the number of delamination contact interfaces in-between, models with two, three, four and six layers of shell elements across the thickness were generated with delamination contact definitions in-between. A model with just one layer of shell elements without delamination was also compared (Fig. 16).

The corresponding energy plots from the impact simulations in Fig. 17 show a strong influence of the number of shell layers. In the model without delamination contact, the absorbed energy has the lowest value. This is because no interlaminar failure can occur in this model. Instead of that, intralaminar failure in fibre tension mode occurs in this model, which does not happen in the other models with delamination contact definitions.

In general, the more delamination contact interfaces are used, the more the bending stiffness of the plate is reduced even if no delamination occurs. In other words, the bending stiffness of a stacked shell model is lower

M A N U S C R I P T A C C E P T E D ARTICLE IN PRESS 12
than the one of a layered shell model. This relation could be verified for different mesh sizes by means of bending simulations of a cantilever beam and is presumably caused by transverse shear deformations in the contact interface. The less the bending stiffness, the higher is the deflection and the material damage. In this context, the one-shell-model without delamination contact showed the highest stiffness and the lowest deflection.

Therefore, an increase of the number of shell elements and delamination contacts does not necessarily bring the model closer to reality, when its stiffness behaviour is degraded in such a way.

Conclusions

In this study the low velocity impact behaviour of laminated carbon fibre/epoxy plates with and without compressive preloading was investigated. The experimental test series showed an increased deflection for the preloaded composite plates, which lead to a higher extent of material damage compared to the unloaded plates with delaminations as one important energy absorption mechanism. Therefore, the total absorbed energy was higher for the preloaded plates. The intralaminar and interlaminar damage was higher for the NCF material compared to the prepreg material resulting from lower stiffness and strength properties. Delaminations occurred only between the few quadraxial package interfaces, while they may occur between any ply in the prepreg material.

A further aim of this paper was to develop a model in the explicit finite element software LS-DYNA to simulate the low velocity impact behaviour of the composite plates and to investigate, if the effect of the compressive preloading can be covered adequately by the numerical model. The emphasis was on the composite material modelling, delamination modelling and preloading modelling. In this study, the composite material model Mat54 and the delamination tiebreak contact were adopted. The preloading was performed on an explicit basis, which may not be the most efficient but in this case the most stable technique. The implicit solver, which is able to reduce the computational time significantly, did not work properly with the delamination contact or alternatively with cohesive elements.

The final simulation results showed a good correlation to the experimental data in terms of force and energy plots or the evaluated interlaminar and intralaminar damage. The effect of the compressive preloading with increased energy absorption could be observed in the simulation as well. However, these numerical results proved to be strongly influenced by simulation parameters, in particular the element size and the number of shell element layers. This study showed that delamination modelling is crucial for impact simulations and delamination contacts should be included in a shell model, leading to a stacked shell modelling approach.

Neglecting delaminations in a one-shell-model leads to unrealistically increased intralaminar fibre/matrix damage behaviour.

  M A N U S C R I P T A C C E P T E D ARTICLE IN PRESS 6 is most clearly visible in the ultrasonic runtime images in Fig. 7. Here the different shades of grey indicate the different depths of the delaminations.

Fig. 1 .

 1 Figure Captions:

Fig. 2 .

 2 Fig. 2. Dimensions of impact test specimens (in mm).

Fig. 3 .

 3 Fig. 3. Specimen fixture for compressive preloading.

Fig. 4 .

 4 Fig. 4. Top view of preloaded specimen in test fixture and impactor.

Fig. 5 .

 5 Fig. 5. Experimental results: Force, energy and deflection plots during low velocity impact.

Fig. 6 .

 6 Fig. 6. Experimental results: Ultrasonic C-scan images (flaw echo images) showing delaminated areas.

Fig. 7 .

 7 Fig. 7. Ultrasonic C-scan images (runtime images) of 30 J and 40 J impact.

Fig. 8 .

 8 Fig. 8. Ultrasonic B-scan images showing the distribution of delaminations in the NCF and prepreg material.

Fig. 9 .

 9 Fig. 9. Illustration of failure modes covered by the material model.

Fig. 10 .

 10 Fig. 10. Reference model for low velocity impact simulations on preloaded composite plate.

Fig. 11 .

 11 Fig. 11. Contact force plot in experiment and simulation for unloaded and preloaded prepreg plates type B.

Fig. 12 .

 12 Fig. 12. Energy plot in experiment and simulation for unloaded and preloaded prepreg plates type B.

Fig. 13 .

 13 Fig. 13. Extent of delaminations in impact simulation of preloaded plate.

Fig. 14 .

 14 Fig.14. Extent of matrix tensile failure in impact simulation of preloaded plate.

Fig. 15 .

 15 Fig. 15. Influence of element size on energy plot (here: stacked shell model with one delamination contact).

Fig. 16 .

 16 Fig. 16. Overview of different numbers of shell element layers for the composite laminate modelling.

Fig. 17 .

 17 Fig. 17. Influence of number of shell layers on energy plot (here: element size 3 mm).

16 Table 1

 161 Overview of lamina elastic material properties

	Material:	ρ [g/cm³] E11 [GPa] E22 [GPa] G12 [GPa] ν12
	Type A (NCF)	1.46	124	10.5	4.2	0.3
	Type B, C (prepreg)	1.62	153	10.3	5.2	0.3

Table 2

 2 Overview of lamina elastic strength properties

	Material:	σ11 +	σ11 -	σ22 +	σ22 -	τ12
		[MPa]	[MPa]	[MPa]	[MPa]	[MPa]
	Type A (NCF)	1953	1378	67	240	61
	Type B, C (prepreg)	2540	1500	82	236	90

Table 3

 3 Overview of impact test conditions and resultsSpecimen name: Material: Thickness [mm]: Prestrain [με]: Preload [kN]: Impact energy [J]: Absorbed energy [J]: Max. deflection [mm]:

	A1	Type A (NCF)	3.2	0	0	40	22.4	12.2
	A2	Type A (NCF)	3.2	1800	36	40	25.9	13.3
	B1	Type B (prepreg)	2.7	0	0	40	14.0	12.2
	B2	Type B (prepreg)	2.7	1100	23	40	17.9	13.3
	B3	Type B (prepreg)	2.7	0	0	30	6.7	10.7
	B4	Type B (prepreg)	2.7	1100	23	30	10.1	12.1
	C1	Type C (prepreg)	2.7	0	0	40	12.4	13.0
	C2	Type C (prepreg)	2.7	670	21	40	18.2	14.0