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Dynamic failure and crash simulation of carbon fiber sheet moulding compound (CF-SMC)

Dynamic failure and crash simulation of carbon fiber sheet moulding compound (CF-SMC) Carbon fiber sheet moulding compounds (CF-SMC) are a promising class of materials with the potential to replace alu- minium and steel in many structural automotive applications. In this paper, we investigate the use of CF-SMC materials for the realization of a lightweight battery case for electric cars. A limiting factor for a wider structural adoption of CF-SMC has been a difficulty in modelling its mechanical behaviour with a computational effective methodology. In this paper, a novel simulation methodology has been developed, with the aim of enabling the use of FE methods based on shell elements. This is practical for the car industry since they can retain a good fidelity and can also represent damage phenomena. A hybrid material modelling approach has been implemented using phenomenological and simulation-based principles. Data from computer tomography scans were used for micro mechanical simulations to determine stiffness and failure behaviour of the material. Data from static three-point bending tests were then used to determine crack energy values needed for the applica- tion of hashing damage criteria. The whole simulation methodology was then evaluated against data coming from both static and dynamic (crash) tests. The simulation results were in good accordance with the experimental data. Graphic abstract Keywords Numerical analysis · Compression moulding · Mechanical testing · Carbon fiber composites * Federico Coren 1 Introduction federico.coren@tugraz.at This paper focuses on the use of lightweight material for Institute of Automotive Engineering, Graz University the construction of a battery cases for electric vehicles of Technology, Inffeldgasse 11/II, 8010 Graz, Austria (Fig. 1). Battery cases can be large components, up to 1.5 Institute of Polymer Product Engineering, Johannes Kepler × 2.5 m, and are usually placed low in the car between the University Linz, Altenberger Strasse 69, 4040 Linz, Austria front and rear axles. A good battery case has to provide Institute of Vehicle Safety, Graz University of Technology, a secure positioning of all the components inside. At the Inffeldgasse 23/I, 8010 Graz, Austria Vol.:(0123456789) 1 3 64 Automotive and Engine Technology (2021) 6:63–77 In addition, old components can be recycled to new raw material with similar mechanical properties [10]. Currently, the material is applied, for example, to the window frames of the Boeing 787 Dreamliner [11], for structural parts of the Lamborghini Sesto Elemento [12], for Audi R-8 components [6, 13], for Dodge Viper Con- vertible [14] and bicycle drive train components of Cam- pagnolo [15]. Common industrial simulation practise is to represent the properties of this material class with an elastic modulus and a static Yield strength only [6]. However experimental and numerical studies have shown that the mechanical character- istics are also determined by the chip dimensions and their mutual interactions [16–18]. Several studies have been per- Fig. 1 Battery case concept showing the outer shell made of CF-SMC and the inner components such as the battery cells and auxiliaries formed to characterise the failure mechanism of such materi- als [5, 19–21]. Results indicate that the damage mechanism depends both on the nature of fibers and matrix as well as same time, it has to protect the electrical components in on the loading conditions. Compared to unidirectional ply case of an external accident and a battery malfunction or based composites, CF-SMC exhibits similar stiffness values run-off [1 –3]. Generally traction battery systems comprise but with reduced strength [22, 23]. The material is tolerant a multitude of cells or cell modules that are housed inside to manufacturing defects and notches [8, 22–24]. Failure a battery case together with the auxiliaries for power dis- is a matrix-dominated phenomena based on intralaminar tribution, cooling and control. The overall weight for the chip fracture and interlaminar chip delamination, with lit- whole battery system can easily overcome 400 kg in case tle to none fiber breakage [17, 22, 22]. The stress transfer of a medium sized 50 kW/h system, given a typical ratio of and interaction between the chips makes the failure model- 6,7 kg/kWh, with the battery case alone weighting over 80 ling for this material class difficult. Further influence fac- kg [4]. The most widely adopted construction materials for tors are the energy of the loading event, the strain rate and battery cases are steel and aluminium, held together with the impactor geometry [21, 25]. Some phenomena, as for welds and bolted connections [4]. These materials present instance the strain rate dependency, might disappear if a a lower stiffness to weight ratio compared to unidirectional particular fiber is used, with carbon fiber exhibiting almost carbon fiber but at the advantage of being price competi- no dependency [21]. Since many automotive components tive and easier to manufacture. have to be designed to absorb energy in the event of a crash, Carbon fiber sheet molding compounds (CF-SMC) are a it is of great importance to have a good understanding of the class of materials composed of pre-preg chips or bundles of dynamical mechanical properties and failure mechanisms. chopped carbon fibers dispersed in a matrix material. The This paper aims to develop a modelling procedure for most common matrix materials are epoxy and vinyl-ester industrial simulation practices. In detail, the material model resins [5, 6]. CF-SMC material possess a unique combina- and damage model should be able to capture the complex tion of properties being lightweight, having high strength dynamic mechanical properties [19, 20, 26], while at the values, crack resistance and a competitive price. Using this same time being applicable to shell elements with a dimen- material to replace the aluminium for a battery case, can sion greater than 1 mm. lead up to 30% weight reduction, while maintaining excel- lent mechanical properties [6]. The CF-SMC raw material possesses a certain viscosity level, thus allowing complex geometry to be moulded by using a pressing and curing 2 Experimental work process. In order for the resin to polymerize and solidify, the pressed parts need to be exposed to heat. The heat is 2.1 Material and specimen manufacture generally provided within the press tool. Curing time is in the order of minutes, [6] allowing for high-output industrial The material used is HexMC®-i [6] manufactured by Hex- applications. In comparison with traditional carbon fiber cel®. It comes from the producer as a rolled pre-preg mat products, CF-SMC allows for the decoupling of the product of 460 mm width and 4 mm thickness, that is composed of quality from the operator ability. This is due to the quasi- randomly oriented 50 × 8 mm pre-preg chips. These mats isotropic nature of the material, as well as the adoption of can be cut, transferred into a mould and then compression pressing techniques [5–9]. moulded and cured. 1 3 Automotive and Engine Technology (2021) 6:63–77 65 Fiber Matrix Nominal fiber volume HS Carbon M77 Hexel Epoxy 57% Cure time Material density Curing temperature 3 ◦ 3 min 1.55 g/cm 150 C Yield strength Elastic modulus 300 Mpa 38 Gpa Fig. 3 CF-SMC test specimen dimensions of the profile The specimens tested in this work were hat-profiles pro- duced by SGL CARBON GmbH [27] (Fig. 2). In detail, the mould was filled with a preformed charge pole test 8.88 m/s ( 32.0 ± 0.5 km/h ) [28] and 8.94 m/s with a coverage of 82 percent of the die surface. The mould ( 32.20 ± 0.80 km/h ) for the American counterpart [29]. temperature was 150 C with curing times of 3 min and a To obtain dynamic loading and failure data, a horizontal pressure of 690 kN/m . The specimen geometry (Fig. 3) was sled rig was used (Fig. 5). This consists of an instrumented chosen due to the complex local stress and failure modes support, a rail structure and an impactor element. of a 3-point bending test. Ease of production allowed for a The rail structure is 6 m long, and its function is to large number of samples. The radii and inclined surfaces cre- support and guide a cart structure. The cart consists of ate general tension and compression states of the specimen a base, mounted on the rail via bearings, and an instru- while complex stress configurations are locally generated mented striker Fig.  5a, that is free to move longitudi- under the impactor. The hat profile test was preferred upon nally. The whole cart assembly is accelerated via a steel a classic cut-out rectangular “coupon test” because the lat- cable passing through a pulley system. At the beginning ter would have not allowed for a complex loading scenario. the striker element is located on the farthest end of the cart. The movement of the cable is provided by a fall- 2.2 Quasi‑static testing ing mass situated on a remote location, behind the rigid crash wall. Once the cart approaches the end of the rail Quasi-static monotonic three-point bending tests (Fig. 4) of system, a hydraulic shock absorber paired with a coil the hat profiles were performed on a servo-hydraulic MTS spring, decelerate suddenly the cart. The striker is free 852 test system. The steel fixture had a length of 360 mm to continue its longitudinal trajectory until impact with with half cylinder supports and a striker with a diameter the specimen (Fig. 5c). Teflon and a thin layer of grease of 20 mm. Displacement signals were recorded from the ensure minimal friction between the cart surface and position of the actuator piston. Force signals were recoded the striker bottom. The specimen is supported by an U from a MTS load cell mounted on the striker. This was shaped steel support, that is anchored to the steel wall via secured underneath the non-movable crosshead. All tests were performed at room temperature ( 23 ± 1 C ) and at a constant actuator speed of 2 mm/min until complete failure of a specimen. 2.3 Sled impact tests The test velocities were between 6.9 and 9.38 m/s. These velocities are determined by the Euro NCAP side Fig. 4 Static test rig the hat profile specimen (a), is supported by two half cylinders (b). The lateral movement of the hat profile is restricted by two lateral lobes (c) positioned on both sides of the supports (b). Fig. 2 Production process the mats of randomly oriented chips are Four hand-tighten screws placed on the lobes (d) allow for a secure loaded into the press dies. The pressure allows the material to flow positioning. The impactor (e) applies force in the middle of the speci- and the imposed temperature cures the specimen within the press tool men 1 3 66 Automotive and Engine Technology (2021) 6:63–77 Table 1 Test conditions for all the dynamic experiment conducted on the HexMC hat profile Test name Mass of Sled Test name Mass of Sled impactor velocity impactor velocity (kg) (m/s) (kg) (m/s) HexMc #1 2.85 8.71 HexMc #9 5.03 9.18 HexMc #2 2.85 8.71 HexMc 5.03 9.18 #10 HexMc #3 2.85 9.38 HexMc 2.85 9.28 #11 HexMc #4 3.99 9.38 HexMc 2.85 9.28 #12 HexMc #5 3.99 9.38 HexMc 2.85 6.90 #13 HexMc #6 3.99 9.38 HexMc 2.85 6.90 Fig. 5 Dynamic test rig two aluminium rails support the cart struc- #14 ture. Over it lays the striker (d). The striker can move horizontally on HexMc #7 5.03 9.18 HexMc 2.85 6.90 the cart structure. The specimen (c) is supported by a steel structure #15 identical to the static test, and that is anchored to the wall through the force sensor (b). A position sensor is present as well (a). The Hat HexMc #8 5.03 9.18 HexMc 2.85 8.26 specimen is held into position by four screws present on the lobes of #16 the supports. The impact is recorded by high-speed cameras a three component quartz force link (Kistler Type 9367C) (Fig. 5b). To have an accurate trigger for the data acquisi- tion system, a physical copper switch is located on the top Δt ⩽ min L (1) of the specimen. The switch is composed of two thin strips 𝜆 + 2 of copper divided by a small air gap. As the striker makes L is a characteristic length associated with an element,  is contact with the specimen, the two copper elements touch the density of the material in the element, and 𝜆 and are the together, closing the trigger circuit. This trigger is used to effective Lamé’s constants for the material in the element. start the flash lightning as well as for selecting the correct Lamé constant are defined in terms of Young’s modulus E start time for the data acquisition procedure. On top of the and Poisson’s ratio  with the following equations: structure a high speed and high accuracy laser displace- ment sensor (Keyence LK-H152) is placed, that records E𝜈 𝜆 = (2) the position of the striker via a target on top of the striker (1 + 𝜈 )(1 − 2𝜈 ) structure. In addition, the striker is also instrumented with an accelerometer that is placed on the non-striker side. (3) 2(1 + 𝜈 ) 2.4 Experimental conditions For this reason, we target on element and material formula- tion that enables the use of shell elements between approxi- Testing conditions are described in Table 1. mately 1 and 5 mm. At any given location in the test specimen, an aver- age of 12 layers of carbon fibres are present. These layers consist of carbon chips that are randomly oriented during 3 Model development the manufacture process (Fig.  11). For this reason, the fiber lay up differs from place to place in the specimen. For the development of CF-SMC applications an advanced From a macroscopic perspective, it has been measured that industrially usable modelling and simulation method has to the properties of CF-SMC materials are quasi-isotropic be devised. For vehicle development purposes, it is common [6, 16, 22, 31]. The level of fiber randomness guarantees practice to limit the size and number of the elements in a a homogeneous plane response. The elastic response of simulation. Specifically for explicit simulations, element size straight-sided rectangular specimens (305 × 38 × 3 mm) has a direct impact on computational time. The maximum during bending tests is well captured using a simplified time increment is related to the element size and speed of quasi-isotropic approach [32]. Quasi isotropic material sound in the material with the following relation [30]: properties are commonly used in industry [6, 31]. 1 3 ̂𝜇 ̂𝜇 ̂𝜇 Automotive and Engine Technology (2021) 6:63–77 67 However, failure initiation and damage progression depend (6) on local fiber orientation. The very nature of the fibers cre- ates a modelling challenge for dynamic events [33]. The yield The simplest loading scenario consist in an uniform uniaxial strength of the fiber is almost an order of magnitude higher stress applied in the x direction. Expressing the stress state compared to the matrix. During crash events, the crack propa- in the material system results in: gation exhibits a preferred direction along the fiber chips as = cos (7) f 11 can bee seen in Fig. 12. Generally the crack front travels along the path of least resistance even if this means an increase of the crack length. = sin (8) m 11 4 Material modelling = sin  cos (9) f 11 To simulate the damage behaviour two aspects have to be con- The failure indicator is expressed by the function F. sidered: damage initiation and damage evolution. The Hashin For F = 1 the material has failed. f stands for fiber, criterion was adopted as a criterion for damage initiation [34]. m stands for matrix, + indicates tensile, − indicates Damage evolution was modelled with a continuum mechanics compressive. linear-damage model [30]. For each mode (fiber and matrix) two possible scenario are possible: compressive and tensile. The choice of a par- 4.1 Hashin damage initiation criterion ticular failure mode, depends from the sign of the diago- nal components of the stress tensor. The two-dimensional Lets consider a generic laminar shell element. The element failure criteria are: is referred to a fixed coordinate system x x and a material Tensile fiber mode ( ⩾ 0) 1 2 coordinate system x x rotated by an angle  . Fibers are ori- 1 2 ented along the axle x and the transverse direction is the one 1 11 12 F = + (10) f + on x (Fig. 6). A generic plane state of stress    is transformed 11 22 12 into    with respect to the material system. Fiber compressive mode (𝜎 < 0) 11 22 12 The following notation is adopted, where f stands for fiber mode and m for matrix mode failure. F = (11) f − (4) Tensile matrix mode ( ⩾ 0) (5) 22 2 2 22 12 F = + (12) Compressive matrix mode (𝜎 < 0) 2 2 2 − 22 m 22 12 F = + − 1 + (13) 2 2 m m f where Tensile failure stress in fiber mode Compressing failure stress in fiber mode Tensile failure stress in matrix mode Compressing failure stress in matrix mode Failure shear stress in fiber mode Failure shear stress in matrix mode Strain Shear component contribution Poisson ratio in direction 1 2 Fig. 6 Generic element x x are the fixed reference system, x x are 1 2 1 2  Poisson ratio in direction 1 3 the material reference system 1 3 68 Automotive and Engine Technology (2021) 6:63–77 ⟨ ⟩⟨ ⟩ + L Characteristic length 22 22 12 12 c + = , (19) m_eq + c ∕L m_eq Matrix compression (𝜎 < 0) G Tensile failure energy in fiber mode − c − 2 G Compressing failure energy in fiber mode  = L ⟨− ⟩ + (20) f 22 m_eq 12 G Tensile failure energy in matrix mode G Compressing failure energy in matrix mode ⟨− ⟩⟨− ⟩ + 22 22 12 12 Viscous damping = , (21) m_eq − c ∕L E Young’s modulus fiber m_eq E Young’s modulus matrix 4.2.2 Damage evolution 4.2 Continuum damage mechanics As the damage starts, a damage variable d is assigned to the element material. 4.2.1 Equivalent formulation of constitutive equation The damage variable will evolve such that the stress–dis- placement behaves as shown in Fig.  7 in each of the four fail- A quantity called characteristic length L is introduced into ure modes (fiber and matrix in compression and tension). The the formulation of the stress–displacement constitutive equa- positive slope of the stress–displacement curve prior to dam- tion. This number is based on the element geometry and age initiation (point (1), corresponding to  in Fig. 7) corre- eq element formulation. In the case of a first-order element such sponds to linear elastic material behaviour. At this point, the as the shell elements used, it is the typical lengths of a line failure value F has reached value 1. The negative slope after across the element itself [30, 35]. damage initiation is achieved by evolution of the respective This allows for the material constitutive equation to be damage variables according to the Eq. 22 until point (2) in expressed as equivalent_stress (  ) vs equivalent_ dis- _eq failure Fig. 7 denoted by  . placement (  ) instead of stress (  ) vs strain ( ). eq _eq The damage index d for a particular failure mode is given Both equivalent_stresses and equivalent_displacement by the expression can be expressed as function of the characteristic length L as follows. failure 0 is the xy component of the strain tensor. The ⟨⟩ rep- eq eq eq xy d = (22) resents the Maculay bracket operator, which is defined as � � failure 0 eq ⟨ ⟩ =  + � � ∕2. eq eq 11 11 11 Fiber tension ( ⩾ 0) where  represents the initial equivalent displacement at eq + c 2 2 which the initial criterion for that failure mode was met and = L ⟨ ⟩ +  (14) f _eq 12 failure is the displacement at which the material is completely eq ⟨ ⟩⟨ ⟩ + 11 11 12 12 = , (15) f _eq + ∕L f_eq Fiber compression (𝜎 < 0) − c = L ⟨− ⟩ 11 (16) f _eq ⟨ ⟩⟨ ⟩ 11 11 = , (17) f _eq − ∕L f_eq Matrix tension ( ⩾ 0) + c 2 = L ⟨ ⟩ +  (18) m_eq 12 Fig. 7 Equivalent stress vs equivalent displacement  corresponds to eq failure the damage initiation, F = 1.  corresponds to the displacement eq after which the element does not offer any more mechanical resist- ance Source [30] 1 3 Automotive and Engine Technology (2021) 6:63–77 69 4.2.3 Dissipated energy For each failure mode a specific dissipated energy G due to failure must be defined. This consists of the area of the triangle OAC in Fig. 9. The  for the various modes thus eq depend on the respective energy parameter G. 4.3 Viscous regularization In Explicit simulations, the viscous regularization is a parameter used for taking into account possible mate- Fig. 8 Damage variable until the failure initiation is reached (point rial behaviour that is strain rate dependent. No need to (1) in Fig. 7), the damage variable value remains zero. As the equiva- change the viscous damping during the simulations has lent displacement increases, the damage values rises up to 1 (point (2) been observed. The viscous damping value is kept constant in Fig. 7), when the element does not offer any resistance to deforma- at 0.00001 throughout the whole simulation series. The tion absence of strain rate dependency for the various dynamics of our tests is in accordance with existing literature [21]. damaged. Graphical representation of damage evolution is shown in Fig. 8. The damage value d is zero until reaching the damage criterion. After the critical equivalent displace- 5 FEM calculation ment, the d value increases up to 1. The damage coefficient D is defined as 5.1 Finite element model description D = 1 −(1 − d )(1 − d ) (23) f m 12 21 The model is represented in Fig.  10. It consists of three main parts: a roughly meshed steel support, the CF-SMC with  and  Poisson ratios. 12 21 finely meshed part and the rigid impactor. The test speci- To chose the proper damage index for a specific load men consists of S4 elements with 4 integration points, with case, the first and second diagonal stress components are orthotropic material. Average element size is 5 × 5 mm. observed. Based on these values, the damage indexes defined The boundary conditions consist in a rigid support of the in 22 are chosen such that: steel base, created by a multi-point constraint (COUPLING d if 𝜎 ⩾ 0 KINEMATIC) in the same location and size of the actual d = (24) f − d if 𝜎 < 0 d if 𝜎 ⩾ 0 d = (25) d if 𝜎 < 0 + − + − d =1 −(1 − d )(1 − d )(1 − d )(1 − d ) (26) f f m m After the damage initiation (point (1) in Fig. 7), the material response is computed by the following equation: (27) where  is the strain tensor and the term  is the damaged elasticity matrix, having the form : = Fig. 9 Loading–unloading path a loading cycle with complete dam- age follows the 0-A-C path. In case of unloading at a partially damage ⎡ (1 − d )E (1 − d )(1 − d ) E 0 ⎤ f f f m 21 f state (point B) the elastic modulus will be represented by the steep- ⎢ ⎥ (1 − d )(1 − d ) E (1 − d )E 0 f m 12 m m m ness of the line 0-B. In case of further loading, the line 0-B, instead ⎢ ⎥ 00 (1 − d )GD ⎣ ⎦ of the line 0-A, will be followed (28) 1 3 70 Automotive and Engine Technology (2021) 6:63–77 Fig. 11 X-ray tomography images of a CF-SMC tensile test speci- men. Top image is taken from above the press-plane. Bottom image is a slice in the thickness of the specime. Resolution is respectively 3 3 (30 μm) voxel size (top) and (5 μm) voxel size (bottom). A voxel corresponds to a pixel for a given slice thickness in the magnetic res- onance imaging Fig. 10 FEM modell total number of elements is ca 19,000 force sensor. The CF-SMC piece is in contact with the steel 5.2.1 Material fitting base with a friction coefficient of 0.1. The rigid impactor is commanded a specific initial velocity with direction towards The parameters for the material fitting were determined in the CF-SMC piece. The solver used is ABAQUS v2019 two stages. Initially, the rough values were calculated based on data from with CT-scans (computerized tomography 5.2 Random element orientation approach scan) and the material modelling software Digimat [36]. In the second step, force displacement data coming from The CF-SMC material is composed of a high number of a three-point bending static test were used to validate the carbon fiber chips, held together by resin (Fig.  11). In the initially estimated material values. uncured mats, the chips are horizontally laid. During the pressing process, the chips can move relative to one other 5.2.2 Simulation: equivalent volume method and flow into the tool’s form. The complex spatial disposition of the chips and their The elastic, yield and shear moduli are derived from a tech- high number pose a great modelling challenge. It is theoreti- nique called representative volume element. Material data cally possible to map all the chip positions in every speci- for the individual fibers and resin came from the producer men and to model every individual one with solid elements. (elastic modulus and strengths of fiber and resin). Ct-scans Nevertheless, this would require an enormous amount of (as in Fig. 11) were used to determine the fiber location, elements. Also with simple mechanical simulations of such orientation and stacking in a CF-SMC sample. models, the calculation time would become enormous. Shell elements are the workhorse of the car industry for thin walled structures. Thus we developed a model based on them. In order to predict the complex failure behaviour dur- ing crack propagation (as seen in Figs. 12, 13) a randomized direction approach was used. In this approach each shell element is assigned an in-plane random material orientation ◦ ◦ with a value from 0 to 180 respective to the local element coordinate system (Fig. 14). This allows for the damage to travel along a complex path along the hat profile, thus recreating a stochastic crack propagation dynamics that was observed during the tests. To cope with the high number of elements, we used a Fig. 12 Crack through CF-SMC close up of a typical failed specimen. script to modify the FEM input file and to assign to every The crack has run along with the chips where the resin has failed. The element a random orientation angle. fiber are almost undamaged 1 3 Automotive and Engine Technology (2021) 6:63–77 71 Fig. 15 Force displacement for 3 point bending static test Table 2 Material data values Property Unit Value E (Mpa) 40,000 Fig. 13 Damage process of the specimen the three stages of the E (Mpa) 36,000 dynamic test: contact (1), crack initiation (2) and crack propagation – 0.3 (3). Note the material fails along the edges of the fiber chips. The – 0.087 nature of the crack is quite complex due to the local anisotropy of the (Mpa) 600 material f (Mpa) 600 (Mpa) 130 (Mpa) 130 G (J/m ) G 180 (J/m ) + 2 G (J/m ) 140 − 2 G (J/m ) 140 (N s/m) 1E−6 5.2.3 Validation: 3 point bending static test A three-point bending test was performed (Fig. 4) to vali- date the material parameters derived from the simulation in Sect. 5.2.2. This test was also used to empirically deter- mine the breaking energies (specific dissipated energies G) of the material (Table 2, Fig. 15). Fig. 14 FEM model close up of hat profile FEM model. The green lines represent the normal to the principal direction of each element 6 Results for dynamic simulations A material modelling software (digimat) [36] combined FEM simulations of the 3 point bending dynamic loading all this informations and computed the equivalent properties were performed matching all the test conditions of Table 1. for a certain volume. The volume considered corresponds The tests were grouped in test sets based on the common to the size of the element used in the simulation of the hat impactor velocity and mass (Table 3). profile. In this way, we determined the equivalent material parameter for a representative element. 1 3 72 Automotive and Engine Technology (2021) 6:63–77 Table 3 Results analysis data from the test-set-up Name of test group Sled Vel. (m/s) Mass (kg) n. of tests Test-set #4 9.18 5.03 4 Test-set #3 9.38 3.994 3 Test-set #2 9.38 2.851 1 Test-set #5 9.28 2.851 2 Test-set #1 8.71 2.851 1 Test-set #7 8.26 2.851 1 Test-set #6 6.9 2.851 3 Test performed under the same conditions are grouped into test-sets. Test-sets ordered by decreasing impact energy Fig. 17 Test-FEM test-set # N1. Around 8 mm the impactor has rebounced away from the hat profile Fig. 16 Hashin fiber damage top view of the simulated dynamic impact for test-set # 4. Bottom figures represent the early interaction phase. Second figure is taken at half contact time. Third figure repre- sents the maximum penetration. In red the elements that have failed under the Hashin criteria 6.1 Damage distribution in FEM model Fig. 18 Test-FEM test-set # N2 The simulated damage evolution and distribution (Fig. 16) is in accordance with the observed damage in the hat-profiles during dynamic testing (Fig. 13). 6.2 Force displacement results The following images compare the force–displacement curve from explicit FEM simulations to measured ones. The force is measured on the back of the support structure, where the force sensor is placed. The displacement refers to the move- ment of the impactor. By the simulations the viscous damp- −6 ing parameter was adjusted. A constant value of 10 led to satisfactory forces vs displacement prediction. This is a very small number, thus excluding a strain-rate material response (Figs. 17, 18, 19, 20, 21, 22, 23). Fig. 19 Test-FEM test-set # N3 1 3 Automotive and Engine Technology (2021) 6:63–77 73 Fig. 20 Test-FEM test-set # N4 Fig. 23 Test-FEM test-set # N7 Table 4 Results analysis data from the test-sets ordered from the interaction with the highest energy Max force measured Force pre- Percent error (averaged on all test) dicted (kN) (kN) Test-set #4 33.28 34.456 3.5 Test-set #3 36.78 36.689 0.2 Test-set #2 36.09 35.057 2.9 Test-set #5 33.805 33.478 1.0 Test-set #1 35.05 30.948 11.7 Test-set #7 29.83 34.460 15.5 Test-set #6 27.24 29.457 8.1 Errors are defined in respect to the measured maximum force. If the test-set consist of more than one measurement, an average of the value is used Fig. 21 Test-FEM test-set # N5 6.2.1 Maximum predicted force The maximum deviation of the maximum computed force was between 0.2 and 15% depending on the crash series. The spread in some of the measurements is attributed to manufacturing process and the random chip distribution of the hat profile (Table  4). 6.2.2 Correlation of force curves To estimate the difference between the measured and simu- lated values, the correlation and R were calculated. The values refer to the correlation between force and displace- ment. Both values are calculated on an interval starting at 0 mm and going until data from measurement are present or at the first zero crossing of the computed force. The correla- tion, averaged on all the data is 0.78 and R is 0.62 (Table 5). Fig. 22 Test-FEM test-set # N6 1 3 74 Automotive and Engine Technology (2021) 6:63–77 Table 5 Correlation and Test N Correlation R R values of force data vs displacement Test-set #1 0.63 0.40 Test-set #2 0.82 0.67 Test-set #3 0.78 0.62 Test-set #4 0.82 0.68 Test-set #5 0.76 0.59 Test-set #6 0.89 0.79 Test-set #7 0.76 0.57 Average 0.78 0.62 Fig. 25 Mesh dependency analysis FEM simulated forces for differ - ent element size: 0.5, 1 and 5 mm. Performed for test-set #2 condi- tions Fig. 24 Data comparison result comparison of the FEM and meas- ured forces for dynamic 3 point bending for test serie # 4. Different FEM lines correspond to different initial random orientation of the element material direction 6.3 Influence of initial element orientation Fig. 26 FFT analysis frequency content of the force vs time for the measured and simulated signal. The force was measured under crash_ To exclude a possible influence on the initial orientation of test_n10 conditions the elements principal direction, a series of the simulation were performed with different initial element orientation (Fig. 24). We observed little variation related to the initial element orientation. 6.4 Mesh size sensitivity Mesh-size sensitivity was analysed running simulations where the model’s element size was varied. Elements of 0.5, 1 and 5 mm were considered. From the analysis, a scat- ter band of the force–displacement results can be observed. Fig. 27 3280 Hz mode shape the movement of the lobes that follow The smoothed response curves show a small element size the red lines around the black dashed lines are responsible for the sensitivity (Fig. 25). amplification of the signal around 3000 Hz. A constraint of the lateral movement of the lobes along the red lines, subdues the spikes in the force vs displacement curve 1 3 Automotive and Engine Technology (2021) 6:63–77 75 Fig. 28 Force curve smoothing comparison of the same test condi- tions with different supports. In yellow a support structure with artifi- Fig. 29 35 g z acceleration complete battery FEM simulation. Hashin cially stiffer support lobes. The force was measured under crash_test_ damage n10 conditions going to be used to extend the validity of the simulation 6.5 Fluctuation the force–displacement curves methodology to big components (Fig. 29). An Eigenfrequency analysis was performed on the sup- port and we found a strong component at ca 3000 Hz, 8 Conclusion corresponding to the outward-inward movement of the supports lobes (Fig.  27). This frequency is responsible The material modelling was successfully verified by static for the crests present in the computed force displacement and dynamic experiments. The value for viscous regulari- curves (Fig. 26). The surface interaction between the steel zation throughout all simulations is small (0.000001) and support and the carbon hat profile limits the lateral swings constant. This means, that a strain rate dependency is not of the steel support lobes (Fig. 27). To recreate this effect present for this material within testing conditions typical in the simulation, it is possible to constraint the inward- for automotive engineering. Specifically this means that a outward movement of the lobes of the steel support. This static test is sufficient to capture the mechanical behaviour has the effect of smoothing the force vs displacement needed to simulate automotive test impact speeds. This work curve (Fig. 28). demonstrates an efficient and accurate simulation method for The analysis of the frequency content of the simulated CF-SMC materials based on shell elements. The simulation and measured force in time, reveals a reasonable frequency procedure adopts a random orientation of the elements prin- matching of the basic peaks. cipal direction and an orthotropic continuum-based material definition. This modelling procedure leads to a satisfactory represen- 7 Complete battery simulation tation of damage and crack behaviour, including stochastic effects. The battery is modelled with shell elements, whose mini- Prediction of maximal force, force displacement curves mum size is 1 mm. The simulation is performed with 35 and energy absorption are found to be sufficiently accurate, g acceleration in z direction. The vertical acceleration is a and within the scatter of experimental testing. demanding requirement for a battery case, given the high This approach is suitable for simulating large components weight of the modules inside. In our particular case, the such as battery cases for electric vehicles. Considering the side crushing is of less importance, given the presence of material damage in the design phase, allows for a reduction protective structures coming from the car body. The battery of weight. This is an important step for evaluating further case geometry derives from an ongoing industrial project introduction of CF-SMC components in the automotive representing therefore a real case. industry. We observed a highly damage tolerant material The simulation methods developed during this work are behaviour, with a large amount of energy absorbed before currently used to simulate the mechanical behaviour of the complete material failure. Crack growth was also hampered aforementioned battery case. Mechanical crash tests are by the presence of randomly oriented carbon chips, that 1 3 76 Automotive and Engine Technology (2021) 6:63–77 Technol. 71(12), 1471–1477 (2011). https:// doi. org/ 10. 1016/j. resulted in segmented cracks. 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Martulli, L.M., Creemers, T., Schöberl, E., Hale, N., Kerschbaum, M., Lomov, S.V., Swolfs, Y.: A thick-walled sheet moulding com- directly on the sled, would generate a force signal with a pound automotive component: manufacturing and performance. stronger emphasis from the carbon hat-profile and reduced Compos. Part A Appl. Sci. Manuf. 128, 105688 (2020). https:// effect from the steel support. doi. org/ 10. 1016/j. compo sitesa. 2019. 105688 9. Wan, Y., Straumit, I., Takahashi, J., Lomov, S.V.: Micro-CT anal- Acknowledgements XCT scans shown in Fig. 11 were performed by ysis of the orientation unevenness in randomly chopped strand B. Plank from University of Applied Sciences Upper Austria. Part of composites in relation to the strand length. Compos. 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Euro NCAP: Euro NCAP Oblique Pole Side Impact Testing jurisdictional claims in published maps and institutional affiliations. Protocol Version7.0.4. (2018). URL https:// www. cdn. euron cap. com/media/ 41753/ eur o-ncap- pole- pr otocol- obliq ue- im pact-v704. 20181 10615 20208 151. pdf 29. US Department of Transportation National Highway Traffic Safety Administration Office of Crashworthiness Standards. 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automotive and Engine Technology Springer Journals

Dynamic failure and crash simulation of carbon fiber sheet moulding compound (CF-SMC)

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10.1007/s41104-021-00078-1
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Abstract

Carbon fiber sheet moulding compounds (CF-SMC) are a promising class of materials with the potential to replace alu- minium and steel in many structural automotive applications. In this paper, we investigate the use of CF-SMC materials for the realization of a lightweight battery case for electric cars. A limiting factor for a wider structural adoption of CF-SMC has been a difficulty in modelling its mechanical behaviour with a computational effective methodology. In this paper, a novel simulation methodology has been developed, with the aim of enabling the use of FE methods based on shell elements. This is practical for the car industry since they can retain a good fidelity and can also represent damage phenomena. A hybrid material modelling approach has been implemented using phenomenological and simulation-based principles. Data from computer tomography scans were used for micro mechanical simulations to determine stiffness and failure behaviour of the material. Data from static three-point bending tests were then used to determine crack energy values needed for the applica- tion of hashing damage criteria. The whole simulation methodology was then evaluated against data coming from both static and dynamic (crash) tests. The simulation results were in good accordance with the experimental data. Graphic abstract Keywords Numerical analysis · Compression moulding · Mechanical testing · Carbon fiber composites * Federico Coren 1 Introduction federico.coren@tugraz.at This paper focuses on the use of lightweight material for Institute of Automotive Engineering, Graz University the construction of a battery cases for electric vehicles of Technology, Inffeldgasse 11/II, 8010 Graz, Austria (Fig. 1). Battery cases can be large components, up to 1.5 Institute of Polymer Product Engineering, Johannes Kepler × 2.5 m, and are usually placed low in the car between the University Linz, Altenberger Strasse 69, 4040 Linz, Austria front and rear axles. A good battery case has to provide Institute of Vehicle Safety, Graz University of Technology, a secure positioning of all the components inside. At the Inffeldgasse 23/I, 8010 Graz, Austria Vol.:(0123456789) 1 3 64 Automotive and Engine Technology (2021) 6:63–77 In addition, old components can be recycled to new raw material with similar mechanical properties [10]. Currently, the material is applied, for example, to the window frames of the Boeing 787 Dreamliner [11], for structural parts of the Lamborghini Sesto Elemento [12], for Audi R-8 components [6, 13], for Dodge Viper Con- vertible [14] and bicycle drive train components of Cam- pagnolo [15]. Common industrial simulation practise is to represent the properties of this material class with an elastic modulus and a static Yield strength only [6]. However experimental and numerical studies have shown that the mechanical character- istics are also determined by the chip dimensions and their mutual interactions [16–18]. Several studies have been per- Fig. 1 Battery case concept showing the outer shell made of CF-SMC and the inner components such as the battery cells and auxiliaries formed to characterise the failure mechanism of such materi- als [5, 19–21]. Results indicate that the damage mechanism depends both on the nature of fibers and matrix as well as same time, it has to protect the electrical components in on the loading conditions. Compared to unidirectional ply case of an external accident and a battery malfunction or based composites, CF-SMC exhibits similar stiffness values run-off [1 –3]. Generally traction battery systems comprise but with reduced strength [22, 23]. The material is tolerant a multitude of cells or cell modules that are housed inside to manufacturing defects and notches [8, 22–24]. Failure a battery case together with the auxiliaries for power dis- is a matrix-dominated phenomena based on intralaminar tribution, cooling and control. The overall weight for the chip fracture and interlaminar chip delamination, with lit- whole battery system can easily overcome 400 kg in case tle to none fiber breakage [17, 22, 22]. The stress transfer of a medium sized 50 kW/h system, given a typical ratio of and interaction between the chips makes the failure model- 6,7 kg/kWh, with the battery case alone weighting over 80 ling for this material class difficult. Further influence fac- kg [4]. The most widely adopted construction materials for tors are the energy of the loading event, the strain rate and battery cases are steel and aluminium, held together with the impactor geometry [21, 25]. Some phenomena, as for welds and bolted connections [4]. These materials present instance the strain rate dependency, might disappear if a a lower stiffness to weight ratio compared to unidirectional particular fiber is used, with carbon fiber exhibiting almost carbon fiber but at the advantage of being price competi- no dependency [21]. Since many automotive components tive and easier to manufacture. have to be designed to absorb energy in the event of a crash, Carbon fiber sheet molding compounds (CF-SMC) are a it is of great importance to have a good understanding of the class of materials composed of pre-preg chips or bundles of dynamical mechanical properties and failure mechanisms. chopped carbon fibers dispersed in a matrix material. The This paper aims to develop a modelling procedure for most common matrix materials are epoxy and vinyl-ester industrial simulation practices. In detail, the material model resins [5, 6]. CF-SMC material possess a unique combina- and damage model should be able to capture the complex tion of properties being lightweight, having high strength dynamic mechanical properties [19, 20, 26], while at the values, crack resistance and a competitive price. Using this same time being applicable to shell elements with a dimen- material to replace the aluminium for a battery case, can sion greater than 1 mm. lead up to 30% weight reduction, while maintaining excel- lent mechanical properties [6]. The CF-SMC raw material possesses a certain viscosity level, thus allowing complex geometry to be moulded by using a pressing and curing 2 Experimental work process. In order for the resin to polymerize and solidify, the pressed parts need to be exposed to heat. The heat is 2.1 Material and specimen manufacture generally provided within the press tool. Curing time is in the order of minutes, [6] allowing for high-output industrial The material used is HexMC®-i [6] manufactured by Hex- applications. In comparison with traditional carbon fiber cel®. It comes from the producer as a rolled pre-preg mat products, CF-SMC allows for the decoupling of the product of 460 mm width and 4 mm thickness, that is composed of quality from the operator ability. This is due to the quasi- randomly oriented 50 × 8 mm pre-preg chips. These mats isotropic nature of the material, as well as the adoption of can be cut, transferred into a mould and then compression pressing techniques [5–9]. moulded and cured. 1 3 Automotive and Engine Technology (2021) 6:63–77 65 Fiber Matrix Nominal fiber volume HS Carbon M77 Hexel Epoxy 57% Cure time Material density Curing temperature 3 ◦ 3 min 1.55 g/cm 150 C Yield strength Elastic modulus 300 Mpa 38 Gpa Fig. 3 CF-SMC test specimen dimensions of the profile The specimens tested in this work were hat-profiles pro- duced by SGL CARBON GmbH [27] (Fig. 2). In detail, the mould was filled with a preformed charge pole test 8.88 m/s ( 32.0 ± 0.5 km/h ) [28] and 8.94 m/s with a coverage of 82 percent of the die surface. The mould ( 32.20 ± 0.80 km/h ) for the American counterpart [29]. temperature was 150 C with curing times of 3 min and a To obtain dynamic loading and failure data, a horizontal pressure of 690 kN/m . The specimen geometry (Fig. 3) was sled rig was used (Fig. 5). This consists of an instrumented chosen due to the complex local stress and failure modes support, a rail structure and an impactor element. of a 3-point bending test. Ease of production allowed for a The rail structure is 6 m long, and its function is to large number of samples. The radii and inclined surfaces cre- support and guide a cart structure. The cart consists of ate general tension and compression states of the specimen a base, mounted on the rail via bearings, and an instru- while complex stress configurations are locally generated mented striker Fig.  5a, that is free to move longitudi- under the impactor. The hat profile test was preferred upon nally. The whole cart assembly is accelerated via a steel a classic cut-out rectangular “coupon test” because the lat- cable passing through a pulley system. At the beginning ter would have not allowed for a complex loading scenario. the striker element is located on the farthest end of the cart. The movement of the cable is provided by a fall- 2.2 Quasi‑static testing ing mass situated on a remote location, behind the rigid crash wall. Once the cart approaches the end of the rail Quasi-static monotonic three-point bending tests (Fig. 4) of system, a hydraulic shock absorber paired with a coil the hat profiles were performed on a servo-hydraulic MTS spring, decelerate suddenly the cart. The striker is free 852 test system. The steel fixture had a length of 360 mm to continue its longitudinal trajectory until impact with with half cylinder supports and a striker with a diameter the specimen (Fig. 5c). Teflon and a thin layer of grease of 20 mm. Displacement signals were recorded from the ensure minimal friction between the cart surface and position of the actuator piston. Force signals were recoded the striker bottom. The specimen is supported by an U from a MTS load cell mounted on the striker. This was shaped steel support, that is anchored to the steel wall via secured underneath the non-movable crosshead. All tests were performed at room temperature ( 23 ± 1 C ) and at a constant actuator speed of 2 mm/min until complete failure of a specimen. 2.3 Sled impact tests The test velocities were between 6.9 and 9.38 m/s. These velocities are determined by the Euro NCAP side Fig. 4 Static test rig the hat profile specimen (a), is supported by two half cylinders (b). The lateral movement of the hat profile is restricted by two lateral lobes (c) positioned on both sides of the supports (b). Fig. 2 Production process the mats of randomly oriented chips are Four hand-tighten screws placed on the lobes (d) allow for a secure loaded into the press dies. The pressure allows the material to flow positioning. The impactor (e) applies force in the middle of the speci- and the imposed temperature cures the specimen within the press tool men 1 3 66 Automotive and Engine Technology (2021) 6:63–77 Table 1 Test conditions for all the dynamic experiment conducted on the HexMC hat profile Test name Mass of Sled Test name Mass of Sled impactor velocity impactor velocity (kg) (m/s) (kg) (m/s) HexMc #1 2.85 8.71 HexMc #9 5.03 9.18 HexMc #2 2.85 8.71 HexMc 5.03 9.18 #10 HexMc #3 2.85 9.38 HexMc 2.85 9.28 #11 HexMc #4 3.99 9.38 HexMc 2.85 9.28 #12 HexMc #5 3.99 9.38 HexMc 2.85 6.90 #13 HexMc #6 3.99 9.38 HexMc 2.85 6.90 Fig. 5 Dynamic test rig two aluminium rails support the cart struc- #14 ture. Over it lays the striker (d). The striker can move horizontally on HexMc #7 5.03 9.18 HexMc 2.85 6.90 the cart structure. The specimen (c) is supported by a steel structure #15 identical to the static test, and that is anchored to the wall through the force sensor (b). A position sensor is present as well (a). The Hat HexMc #8 5.03 9.18 HexMc 2.85 8.26 specimen is held into position by four screws present on the lobes of #16 the supports. The impact is recorded by high-speed cameras a three component quartz force link (Kistler Type 9367C) (Fig. 5b). To have an accurate trigger for the data acquisi- tion system, a physical copper switch is located on the top Δt ⩽ min L (1) of the specimen. The switch is composed of two thin strips 𝜆 + 2 of copper divided by a small air gap. As the striker makes L is a characteristic length associated with an element,  is contact with the specimen, the two copper elements touch the density of the material in the element, and 𝜆 and are the together, closing the trigger circuit. This trigger is used to effective Lamé’s constants for the material in the element. start the flash lightning as well as for selecting the correct Lamé constant are defined in terms of Young’s modulus E start time for the data acquisition procedure. On top of the and Poisson’s ratio  with the following equations: structure a high speed and high accuracy laser displace- ment sensor (Keyence LK-H152) is placed, that records E𝜈 𝜆 = (2) the position of the striker via a target on top of the striker (1 + 𝜈 )(1 − 2𝜈 ) structure. In addition, the striker is also instrumented with an accelerometer that is placed on the non-striker side. (3) 2(1 + 𝜈 ) 2.4 Experimental conditions For this reason, we target on element and material formula- tion that enables the use of shell elements between approxi- Testing conditions are described in Table 1. mately 1 and 5 mm. At any given location in the test specimen, an aver- age of 12 layers of carbon fibres are present. These layers consist of carbon chips that are randomly oriented during 3 Model development the manufacture process (Fig.  11). For this reason, the fiber lay up differs from place to place in the specimen. For the development of CF-SMC applications an advanced From a macroscopic perspective, it has been measured that industrially usable modelling and simulation method has to the properties of CF-SMC materials are quasi-isotropic be devised. For vehicle development purposes, it is common [6, 16, 22, 31]. The level of fiber randomness guarantees practice to limit the size and number of the elements in a a homogeneous plane response. The elastic response of simulation. Specifically for explicit simulations, element size straight-sided rectangular specimens (305 × 38 × 3 mm) has a direct impact on computational time. The maximum during bending tests is well captured using a simplified time increment is related to the element size and speed of quasi-isotropic approach [32]. Quasi isotropic material sound in the material with the following relation [30]: properties are commonly used in industry [6, 31]. 1 3 ̂𝜇 ̂𝜇 ̂𝜇 Automotive and Engine Technology (2021) 6:63–77 67 However, failure initiation and damage progression depend (6) on local fiber orientation. The very nature of the fibers cre- ates a modelling challenge for dynamic events [33]. The yield The simplest loading scenario consist in an uniform uniaxial strength of the fiber is almost an order of magnitude higher stress applied in the x direction. Expressing the stress state compared to the matrix. During crash events, the crack propa- in the material system results in: gation exhibits a preferred direction along the fiber chips as = cos (7) f 11 can bee seen in Fig. 12. Generally the crack front travels along the path of least resistance even if this means an increase of the crack length. = sin (8) m 11 4 Material modelling = sin  cos (9) f 11 To simulate the damage behaviour two aspects have to be con- The failure indicator is expressed by the function F. sidered: damage initiation and damage evolution. The Hashin For F = 1 the material has failed. f stands for fiber, criterion was adopted as a criterion for damage initiation [34]. m stands for matrix, + indicates tensile, − indicates Damage evolution was modelled with a continuum mechanics compressive. linear-damage model [30]. For each mode (fiber and matrix) two possible scenario are possible: compressive and tensile. The choice of a par- 4.1 Hashin damage initiation criterion ticular failure mode, depends from the sign of the diago- nal components of the stress tensor. The two-dimensional Lets consider a generic laminar shell element. The element failure criteria are: is referred to a fixed coordinate system x x and a material Tensile fiber mode ( ⩾ 0) 1 2 coordinate system x x rotated by an angle  . Fibers are ori- 1 2 ented along the axle x and the transverse direction is the one 1 11 12 F = + (10) f + on x (Fig. 6). A generic plane state of stress    is transformed 11 22 12 into    with respect to the material system. Fiber compressive mode (𝜎 < 0) 11 22 12 The following notation is adopted, where f stands for fiber mode and m for matrix mode failure. F = (11) f − (4) Tensile matrix mode ( ⩾ 0) (5) 22 2 2 22 12 F = + (12) Compressive matrix mode (𝜎 < 0) 2 2 2 − 22 m 22 12 F = + − 1 + (13) 2 2 m m f where Tensile failure stress in fiber mode Compressing failure stress in fiber mode Tensile failure stress in matrix mode Compressing failure stress in matrix mode Failure shear stress in fiber mode Failure shear stress in matrix mode Strain Shear component contribution Poisson ratio in direction 1 2 Fig. 6 Generic element x x are the fixed reference system, x x are 1 2 1 2  Poisson ratio in direction 1 3 the material reference system 1 3 68 Automotive and Engine Technology (2021) 6:63–77 ⟨ ⟩⟨ ⟩ + L Characteristic length 22 22 12 12 c + = , (19) m_eq + c ∕L m_eq Matrix compression (𝜎 < 0) G Tensile failure energy in fiber mode − c − 2 G Compressing failure energy in fiber mode  = L ⟨− ⟩ + (20) f 22 m_eq 12 G Tensile failure energy in matrix mode G Compressing failure energy in matrix mode ⟨− ⟩⟨− ⟩ + 22 22 12 12 Viscous damping = , (21) m_eq − c ∕L E Young’s modulus fiber m_eq E Young’s modulus matrix 4.2.2 Damage evolution 4.2 Continuum damage mechanics As the damage starts, a damage variable d is assigned to the element material. 4.2.1 Equivalent formulation of constitutive equation The damage variable will evolve such that the stress–dis- placement behaves as shown in Fig.  7 in each of the four fail- A quantity called characteristic length L is introduced into ure modes (fiber and matrix in compression and tension). The the formulation of the stress–displacement constitutive equa- positive slope of the stress–displacement curve prior to dam- tion. This number is based on the element geometry and age initiation (point (1), corresponding to  in Fig. 7) corre- eq element formulation. In the case of a first-order element such sponds to linear elastic material behaviour. At this point, the as the shell elements used, it is the typical lengths of a line failure value F has reached value 1. The negative slope after across the element itself [30, 35]. damage initiation is achieved by evolution of the respective This allows for the material constitutive equation to be damage variables according to the Eq. 22 until point (2) in expressed as equivalent_stress (  ) vs equivalent_ dis- _eq failure Fig. 7 denoted by  . placement (  ) instead of stress (  ) vs strain ( ). eq _eq The damage index d for a particular failure mode is given Both equivalent_stresses and equivalent_displacement by the expression can be expressed as function of the characteristic length L as follows. failure 0 is the xy component of the strain tensor. The ⟨⟩ rep- eq eq eq xy d = (22) resents the Maculay bracket operator, which is defined as � � failure 0 eq ⟨ ⟩ =  + � � ∕2. eq eq 11 11 11 Fiber tension ( ⩾ 0) where  represents the initial equivalent displacement at eq + c 2 2 which the initial criterion for that failure mode was met and = L ⟨ ⟩ +  (14) f _eq 12 failure is the displacement at which the material is completely eq ⟨ ⟩⟨ ⟩ + 11 11 12 12 = , (15) f _eq + ∕L f_eq Fiber compression (𝜎 < 0) − c = L ⟨− ⟩ 11 (16) f _eq ⟨ ⟩⟨ ⟩ 11 11 = , (17) f _eq − ∕L f_eq Matrix tension ( ⩾ 0) + c 2 = L ⟨ ⟩ +  (18) m_eq 12 Fig. 7 Equivalent stress vs equivalent displacement  corresponds to eq failure the damage initiation, F = 1.  corresponds to the displacement eq after which the element does not offer any more mechanical resist- ance Source [30] 1 3 Automotive and Engine Technology (2021) 6:63–77 69 4.2.3 Dissipated energy For each failure mode a specific dissipated energy G due to failure must be defined. This consists of the area of the triangle OAC in Fig. 9. The  for the various modes thus eq depend on the respective energy parameter G. 4.3 Viscous regularization In Explicit simulations, the viscous regularization is a parameter used for taking into account possible mate- Fig. 8 Damage variable until the failure initiation is reached (point rial behaviour that is strain rate dependent. No need to (1) in Fig. 7), the damage variable value remains zero. As the equiva- change the viscous damping during the simulations has lent displacement increases, the damage values rises up to 1 (point (2) been observed. The viscous damping value is kept constant in Fig. 7), when the element does not offer any resistance to deforma- at 0.00001 throughout the whole simulation series. The tion absence of strain rate dependency for the various dynamics of our tests is in accordance with existing literature [21]. damaged. Graphical representation of damage evolution is shown in Fig. 8. The damage value d is zero until reaching the damage criterion. After the critical equivalent displace- 5 FEM calculation ment, the d value increases up to 1. The damage coefficient D is defined as 5.1 Finite element model description D = 1 −(1 − d )(1 − d ) (23) f m 12 21 The model is represented in Fig.  10. It consists of three main parts: a roughly meshed steel support, the CF-SMC with  and  Poisson ratios. 12 21 finely meshed part and the rigid impactor. The test speci- To chose the proper damage index for a specific load men consists of S4 elements with 4 integration points, with case, the first and second diagonal stress components are orthotropic material. Average element size is 5 × 5 mm. observed. Based on these values, the damage indexes defined The boundary conditions consist in a rigid support of the in 22 are chosen such that: steel base, created by a multi-point constraint (COUPLING d if 𝜎 ⩾ 0 KINEMATIC) in the same location and size of the actual d = (24) f − d if 𝜎 < 0 d if 𝜎 ⩾ 0 d = (25) d if 𝜎 < 0 + − + − d =1 −(1 − d )(1 − d )(1 − d )(1 − d ) (26) f f m m After the damage initiation (point (1) in Fig. 7), the material response is computed by the following equation: (27) where  is the strain tensor and the term  is the damaged elasticity matrix, having the form : = Fig. 9 Loading–unloading path a loading cycle with complete dam- age follows the 0-A-C path. In case of unloading at a partially damage ⎡ (1 − d )E (1 − d )(1 − d ) E 0 ⎤ f f f m 21 f state (point B) the elastic modulus will be represented by the steep- ⎢ ⎥ (1 − d )(1 − d ) E (1 − d )E 0 f m 12 m m m ness of the line 0-B. In case of further loading, the line 0-B, instead ⎢ ⎥ 00 (1 − d )GD ⎣ ⎦ of the line 0-A, will be followed (28) 1 3 70 Automotive and Engine Technology (2021) 6:63–77 Fig. 11 X-ray tomography images of a CF-SMC tensile test speci- men. Top image is taken from above the press-plane. Bottom image is a slice in the thickness of the specime. Resolution is respectively 3 3 (30 μm) voxel size (top) and (5 μm) voxel size (bottom). A voxel corresponds to a pixel for a given slice thickness in the magnetic res- onance imaging Fig. 10 FEM modell total number of elements is ca 19,000 force sensor. The CF-SMC piece is in contact with the steel 5.2.1 Material fitting base with a friction coefficient of 0.1. The rigid impactor is commanded a specific initial velocity with direction towards The parameters for the material fitting were determined in the CF-SMC piece. The solver used is ABAQUS v2019 two stages. Initially, the rough values were calculated based on data from with CT-scans (computerized tomography 5.2 Random element orientation approach scan) and the material modelling software Digimat [36]. In the second step, force displacement data coming from The CF-SMC material is composed of a high number of a three-point bending static test were used to validate the carbon fiber chips, held together by resin (Fig.  11). In the initially estimated material values. uncured mats, the chips are horizontally laid. During the pressing process, the chips can move relative to one other 5.2.2 Simulation: equivalent volume method and flow into the tool’s form. The complex spatial disposition of the chips and their The elastic, yield and shear moduli are derived from a tech- high number pose a great modelling challenge. It is theoreti- nique called representative volume element. Material data cally possible to map all the chip positions in every speci- for the individual fibers and resin came from the producer men and to model every individual one with solid elements. (elastic modulus and strengths of fiber and resin). Ct-scans Nevertheless, this would require an enormous amount of (as in Fig. 11) were used to determine the fiber location, elements. Also with simple mechanical simulations of such orientation and stacking in a CF-SMC sample. models, the calculation time would become enormous. Shell elements are the workhorse of the car industry for thin walled structures. Thus we developed a model based on them. In order to predict the complex failure behaviour dur- ing crack propagation (as seen in Figs. 12, 13) a randomized direction approach was used. In this approach each shell element is assigned an in-plane random material orientation ◦ ◦ with a value from 0 to 180 respective to the local element coordinate system (Fig. 14). This allows for the damage to travel along a complex path along the hat profile, thus recreating a stochastic crack propagation dynamics that was observed during the tests. To cope with the high number of elements, we used a Fig. 12 Crack through CF-SMC close up of a typical failed specimen. script to modify the FEM input file and to assign to every The crack has run along with the chips where the resin has failed. The element a random orientation angle. fiber are almost undamaged 1 3 Automotive and Engine Technology (2021) 6:63–77 71 Fig. 15 Force displacement for 3 point bending static test Table 2 Material data values Property Unit Value E (Mpa) 40,000 Fig. 13 Damage process of the specimen the three stages of the E (Mpa) 36,000 dynamic test: contact (1), crack initiation (2) and crack propagation – 0.3 (3). Note the material fails along the edges of the fiber chips. The – 0.087 nature of the crack is quite complex due to the local anisotropy of the (Mpa) 600 material f (Mpa) 600 (Mpa) 130 (Mpa) 130 G (J/m ) G 180 (J/m ) + 2 G (J/m ) 140 − 2 G (J/m ) 140 (N s/m) 1E−6 5.2.3 Validation: 3 point bending static test A three-point bending test was performed (Fig. 4) to vali- date the material parameters derived from the simulation in Sect. 5.2.2. This test was also used to empirically deter- mine the breaking energies (specific dissipated energies G) of the material (Table 2, Fig. 15). Fig. 14 FEM model close up of hat profile FEM model. The green lines represent the normal to the principal direction of each element 6 Results for dynamic simulations A material modelling software (digimat) [36] combined FEM simulations of the 3 point bending dynamic loading all this informations and computed the equivalent properties were performed matching all the test conditions of Table 1. for a certain volume. The volume considered corresponds The tests were grouped in test sets based on the common to the size of the element used in the simulation of the hat impactor velocity and mass (Table 3). profile. In this way, we determined the equivalent material parameter for a representative element. 1 3 72 Automotive and Engine Technology (2021) 6:63–77 Table 3 Results analysis data from the test-set-up Name of test group Sled Vel. (m/s) Mass (kg) n. of tests Test-set #4 9.18 5.03 4 Test-set #3 9.38 3.994 3 Test-set #2 9.38 2.851 1 Test-set #5 9.28 2.851 2 Test-set #1 8.71 2.851 1 Test-set #7 8.26 2.851 1 Test-set #6 6.9 2.851 3 Test performed under the same conditions are grouped into test-sets. Test-sets ordered by decreasing impact energy Fig. 17 Test-FEM test-set # N1. Around 8 mm the impactor has rebounced away from the hat profile Fig. 16 Hashin fiber damage top view of the simulated dynamic impact for test-set # 4. Bottom figures represent the early interaction phase. Second figure is taken at half contact time. Third figure repre- sents the maximum penetration. In red the elements that have failed under the Hashin criteria 6.1 Damage distribution in FEM model Fig. 18 Test-FEM test-set # N2 The simulated damage evolution and distribution (Fig. 16) is in accordance with the observed damage in the hat-profiles during dynamic testing (Fig. 13). 6.2 Force displacement results The following images compare the force–displacement curve from explicit FEM simulations to measured ones. The force is measured on the back of the support structure, where the force sensor is placed. The displacement refers to the move- ment of the impactor. By the simulations the viscous damp- −6 ing parameter was adjusted. A constant value of 10 led to satisfactory forces vs displacement prediction. This is a very small number, thus excluding a strain-rate material response (Figs. 17, 18, 19, 20, 21, 22, 23). Fig. 19 Test-FEM test-set # N3 1 3 Automotive and Engine Technology (2021) 6:63–77 73 Fig. 20 Test-FEM test-set # N4 Fig. 23 Test-FEM test-set # N7 Table 4 Results analysis data from the test-sets ordered from the interaction with the highest energy Max force measured Force pre- Percent error (averaged on all test) dicted (kN) (kN) Test-set #4 33.28 34.456 3.5 Test-set #3 36.78 36.689 0.2 Test-set #2 36.09 35.057 2.9 Test-set #5 33.805 33.478 1.0 Test-set #1 35.05 30.948 11.7 Test-set #7 29.83 34.460 15.5 Test-set #6 27.24 29.457 8.1 Errors are defined in respect to the measured maximum force. If the test-set consist of more than one measurement, an average of the value is used Fig. 21 Test-FEM test-set # N5 6.2.1 Maximum predicted force The maximum deviation of the maximum computed force was between 0.2 and 15% depending on the crash series. The spread in some of the measurements is attributed to manufacturing process and the random chip distribution of the hat profile (Table  4). 6.2.2 Correlation of force curves To estimate the difference between the measured and simu- lated values, the correlation and R were calculated. The values refer to the correlation between force and displace- ment. Both values are calculated on an interval starting at 0 mm and going until data from measurement are present or at the first zero crossing of the computed force. The correla- tion, averaged on all the data is 0.78 and R is 0.62 (Table 5). Fig. 22 Test-FEM test-set # N6 1 3 74 Automotive and Engine Technology (2021) 6:63–77 Table 5 Correlation and Test N Correlation R R values of force data vs displacement Test-set #1 0.63 0.40 Test-set #2 0.82 0.67 Test-set #3 0.78 0.62 Test-set #4 0.82 0.68 Test-set #5 0.76 0.59 Test-set #6 0.89 0.79 Test-set #7 0.76 0.57 Average 0.78 0.62 Fig. 25 Mesh dependency analysis FEM simulated forces for differ - ent element size: 0.5, 1 and 5 mm. Performed for test-set #2 condi- tions Fig. 24 Data comparison result comparison of the FEM and meas- ured forces for dynamic 3 point bending for test serie # 4. Different FEM lines correspond to different initial random orientation of the element material direction 6.3 Influence of initial element orientation Fig. 26 FFT analysis frequency content of the force vs time for the measured and simulated signal. The force was measured under crash_ To exclude a possible influence on the initial orientation of test_n10 conditions the elements principal direction, a series of the simulation were performed with different initial element orientation (Fig. 24). We observed little variation related to the initial element orientation. 6.4 Mesh size sensitivity Mesh-size sensitivity was analysed running simulations where the model’s element size was varied. Elements of 0.5, 1 and 5 mm were considered. From the analysis, a scat- ter band of the force–displacement results can be observed. Fig. 27 3280 Hz mode shape the movement of the lobes that follow The smoothed response curves show a small element size the red lines around the black dashed lines are responsible for the sensitivity (Fig. 25). amplification of the signal around 3000 Hz. A constraint of the lateral movement of the lobes along the red lines, subdues the spikes in the force vs displacement curve 1 3 Automotive and Engine Technology (2021) 6:63–77 75 Fig. 28 Force curve smoothing comparison of the same test condi- tions with different supports. In yellow a support structure with artifi- Fig. 29 35 g z acceleration complete battery FEM simulation. Hashin cially stiffer support lobes. The force was measured under crash_test_ damage n10 conditions going to be used to extend the validity of the simulation 6.5 Fluctuation the force–displacement curves methodology to big components (Fig. 29). An Eigenfrequency analysis was performed on the sup- port and we found a strong component at ca 3000 Hz, 8 Conclusion corresponding to the outward-inward movement of the supports lobes (Fig.  27). This frequency is responsible The material modelling was successfully verified by static for the crests present in the computed force displacement and dynamic experiments. The value for viscous regulari- curves (Fig. 26). The surface interaction between the steel zation throughout all simulations is small (0.000001) and support and the carbon hat profile limits the lateral swings constant. This means, that a strain rate dependency is not of the steel support lobes (Fig. 27). To recreate this effect present for this material within testing conditions typical in the simulation, it is possible to constraint the inward- for automotive engineering. Specifically this means that a outward movement of the lobes of the steel support. This static test is sufficient to capture the mechanical behaviour has the effect of smoothing the force vs displacement needed to simulate automotive test impact speeds. This work curve (Fig. 28). demonstrates an efficient and accurate simulation method for The analysis of the frequency content of the simulated CF-SMC materials based on shell elements. The simulation and measured force in time, reveals a reasonable frequency procedure adopts a random orientation of the elements prin- matching of the basic peaks. cipal direction and an orthotropic continuum-based material definition. This modelling procedure leads to a satisfactory represen- 7 Complete battery simulation tation of damage and crack behaviour, including stochastic effects. The battery is modelled with shell elements, whose mini- Prediction of maximal force, force displacement curves mum size is 1 mm. The simulation is performed with 35 and energy absorption are found to be sufficiently accurate, g acceleration in z direction. The vertical acceleration is a and within the scatter of experimental testing. demanding requirement for a battery case, given the high This approach is suitable for simulating large components weight of the modules inside. In our particular case, the such as battery cases for electric vehicles. Considering the side crushing is of less importance, given the presence of material damage in the design phase, allows for a reduction protective structures coming from the car body. The battery of weight. This is an important step for evaluating further case geometry derives from an ongoing industrial project introduction of CF-SMC components in the automotive representing therefore a real case. industry. We observed a highly damage tolerant material The simulation methods developed during this work are behaviour, with a large amount of energy absorbed before currently used to simulate the mechanical behaviour of the complete material failure. Crack growth was also hampered aforementioned battery case. Mechanical crash tests are by the presence of randomly oriented carbon chips, that 1 3 76 Automotive and Engine Technology (2021) 6:63–77 Technol. 71(12), 1471–1477 (2011). https:// doi. org/ 10. 1016/j. resulted in segmented cracks. All of these properties make comps citech. 2011. 06. 004 the CF-SMC an advantageous material for safety critical 6. HexMC®-i Moulding Compound Carbon Epoxy HexMC®-i / C car components. / 2000 / M77. ., (Sept 2019). https:// www. hexcel. com/ user_ area/ Some potential improvement that could be implemented conte nt_ media/ raw/ HexMCi_ C_ 2000_ M77_ DataS heet. pdf 7. Palmer, J., Savage, L., Ghita, O.R., Evans, K.E.: Sheet moulding in future are: a stiffer support structure and a better position- compound (SMC) from carbon fibre recyclate. Compos. Part A ing of the force sensor for the dynamic test of hat profiles. Appl. Sci. Manuf. 41(9), 1232–1237 (2010). https:// doi. org/ 10. The first would result in the reduction of spurious frequen- 1016/j. compo sitesa. 2010. 05. 005 cies in the force signal. The second, by placing the sensor 8. Martulli, L.M., Creemers, T., Schöberl, E., Hale, N., Kerschbaum, M., Lomov, S.V., Swolfs, Y.: A thick-walled sheet moulding com- directly on the sled, would generate a force signal with a pound automotive component: manufacturing and performance. stronger emphasis from the carbon hat-profile and reduced Compos. Part A Appl. Sci. Manuf. 128, 105688 (2020). https:// effect from the steel support. doi. org/ 10. 1016/j. compo sitesa. 2019. 105688 9. Wan, Y., Straumit, I., Takahashi, J., Lomov, S.V.: Micro-CT anal- Acknowledgements XCT scans shown in Fig. 11 were performed by ysis of the orientation unevenness in randomly chopped strand B. Plank from University of Applied Sciences Upper Austria. Part of composites in relation to the strand length. Compos. Struct. 206, the research was performed within the framework of the ‘CAR e-Bo’ 865–875 (2018). https:// doi. org/ 10. 1016/j. comps truct. 2018. 09. project with contributions by SGL Composites GmbH (Ried im Innk- reis, AUT) and Alpex Technologies GmbH (Mils, AUT). The project 10. Turner, T.A., Pickering, S.J., Warrior, N.A.: Development of recy- was funded by the Austrian Research Promotion Agency (FFG) and cled carbon fibre moulding compounds—preparation of waste the Austrian Federal Ministry of Transport, Innovation and Technol- composites. Compos. B Eng. 42(3), 517–525 (2011). https:// doi. ogy under the program ‘Mobility of the Future’ with the Grant number org/ 10. 1016/j. compo sitesb. 2010. 11. 010 11. Boeing 787 features composite window frames. Reinforced Plastics (2007). ISSN 00343617. https:// doi. org/ 10. 1016/ s0034- 3617(07) 70095-4 Funding Open access funding provided by Graz University of 12. Wade, B., Feraboli, P., Gasco, F.: Lamborghini forged composite Technology. technology for the suspension arms of the sesto elemento. Mon- treal. In: Montreal, Quebec, Canada, 26–28 September 2011. 26th Open Access This article is licensed under a Creative Commons Attri- Annual Technical Conference of the American Society for Com- bution 4.0 International License, which permits use, sharing, adapta- posites 2011: The 2nd Joint US–Canada Conference on Compos- tion, distribution and reproduction in any medium or format, as long ites (2011) as you give appropriate credit to the original author(s) and the source, 13. Hexel Corporation. Hexcel Case Study: Audi R8 Carbon Fiber provide a link to the Creative Commons licence, and indicate if changes X-Brace (2019). https:// www . hexcel. com/ user_ ar ea/ conte nt_ were made. 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Chen, Z., Tang, H., Shao, Y., Sun, Q., Zhou, G., Li, Y., Hongyi, can be Fitted and/or be Used on Wheeled Vehicles and the Con- X., Zeng, D., Xuming, S.: Failure of chopped carbon fiber sheet ditions for Reciprocal Recognition of Approvals Granted on the molding compound (SMC) composites under uniaxial tensile Basis of these Prescriptions1 loading: computational prediction and experimental analysis. 4. Jaguar Land Rover Automotive PLC, January 2020 (2020) Compos. Part A Appl. Sci. Manuf. 118, 117–130 (2019). https:// 5. Scott, A.E., Mavrogordato, M., Wright, P., Sinclair, I., Spearing, doi. org/ 10. 1016/j. compo sitesa. 2018. 12. 021 S.M.: In situ fibre fracture measurement in carbon-epoxy lami- 21. Trauth, A., Weidenmann, K.A., Altenhof, W.: Puncture properties nates using high resolution computed tomography. Compos. Sci. of a hybrid continuous-discontinuous sheet moulding compound 1 3 Automotive and Engine Technology (2021) 6:63–77 77 for structural applications. Compos. 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Journal

Automotive and Engine Technology – Springer Journals

Published: Mar 25, 2021

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