Mohammadali Shirinbayan
email: mohammadali.shirinbayan@ensam.eu

Hassan Beigi Rizi
email: hassan.beigi_rizi@ensam.eu

Navideh Abbasnezhad
email: navideh.abbasnezhad@ensam.eu

Abbas Tcharkhtchi
email: abbas.tcharkhtchi@ensam.eu

Joseph Fitoussi
email: joseph.fitoussi@ensam.eu

Tension, compression, and shear behavior of advanced sheet molding compound (A-SMC): Multi-scale damage analysis and strain rate effect

Advanced sheet molding compounds (A-SMC) are a new generation of alternative materials to steels for applying in automotive structures. It contains a thermoset matrix involving mineral charge (CaCO 3 ) reinforced with a high fraction of discontinuous bundles of glass fibers (around 50% in mass) compared to the other types of SMC composites. The crashworthiness evaluation and multi-scale mechanical characterizations of this automotive material is essential. In this study, at first, the microstructure of A-SMC composite was investigated by Scanning Electron Microscopy (SEM), ultrasonic analysis, and X-ray micro-tomography. Two configurations' plates of Randomly Oriented (RO) and Highly Oriented (HO) were analyzed under quasi-static tension, compression, and shear loadings. To study the effect of fiber orientation, for HO plate, two fiber directions were chosen: HO-0 • (parallel to the Mold Flow Direction (MFD)) and HO-90 • (perpendicular to the MFD). Strain rate effect (from 0.25 s -1 to 10 s -1 ) on shear properties and visco-damage behavior of A-SMC composite has been studied. For this purpose, a new setup for shear testing was designed after optimization via ABAQUS FE code to achieve constant strain rate. HO-0 • samples represented higher strength in tension and compression loadings, unlike shear loading compared to RO and HO-90 • samples. A multi-scale damage study confirmed that predominant damage mechanism is decohesion at fiber/matrix interface under tension, compression, and shear loadings.

Introduction

Zero-and Low-Emission Vehicles (ZLEV) have been the center of attention of automotive industries. Every few years, European Commission attends a session for setting a target of increasing lifetime service and reducing greenhouse gas emissions of a new generation of cars [1,[START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF]. Consequently, one of the important factors is the type of applied materials. In this issue, Sheet Molding Compounds (SMCs) are an alternative to metallic parts thanks to lightweight, excellent chemical resistance, and long-life service for automotive structural components [START_REF] Shirinbayan | Multi-scale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates[END_REF]. SMC composites are high-strength, cost-effective composites, with the combination of thermosetting resin (vinyl ester, phenolic, modified vinyl urethane and unsaturated polyester), fillers (calcium carbonate, clay, mica, etc.), fiber reinforcement (glass, carbon, or aramid fibers) and other additives for special aims that are manufactured by thermocompression process [START_REF] Yalcin | 5 -hollow glass microspheres in sheet molding compounds[END_REF][START_REF] Shirinbayan | Coupled effect of loading frequency and amplitude on the fatigue behavior of advanced sheet molding compound (A-SMC)[END_REF]. Recently, a new generation of SMC composites called Advanced SMCs (A-SMCs) containing vinyl-ester resins with 50% chopped bundles of glass fibers in mass were introduced that possess impressive mechanical resistance and high energy absorption capacity compared to steels [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF].

In an automobile, crashworthiness of structure is a capability for energy absorption of impact that should be considered in different aspects of damage via tension, compression, and shear loadings [START_REF] Jacob | Energy absorption in polymer composites for automotive crashworthiness[END_REF][START_REF] Abbasnezhad | Influence of loading conditions on the overall mechanical behavior of polyetherether-ketone (PEEK)[END_REF]. Designing the A-SMC composites similar to the other composites are challenging due to the variety of microstructure (i.e. amount of reinforcements and fibers orientation in addition to elastic, visco-elastic/plastic behavior of matrix), anisotropic behavior and multiple coupled damage mechanisms concerning to the condition of loading [START_REF] Baste | Evaluation of anisotropic damage in composite materials[END_REF][START_REF] Jendli | Anisotropic strain rate effects on the fibre-matrix interface decohesion in sheet moulding compound composites[END_REF]. In this regard, a wide variety of studies were focused on their mechanical behavior in tension and compression loadings. Shirinbayan et al. [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF] have developed an experimental procedure to study the mechanical behavior of A-SMC under high strain rate tensile test. The ABAQUS finite element (FE) code was used to simulate the optimal design of sample geometry and experimental damping set-up regarding

Table 1

A comparison between three types of SMC in terms of composition [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF][START_REF] Laribi | Sheet molding compound automotive component reliability using a micromechanical damage approach[END_REF]. Fig. 2. Schematics of (a) high strain-rate tensile test, (b) interrupted tensile device [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF].

the thickness and materials properties. A special attention was given to the multi-scale damage analysis of different fiber orientation of A-SMC under high strain rate loading. The results showed that the mechanical behavior of A-SMC composite was highly strain-rate dependent. However, Young's modulus presented a constant variation. Moreover, it was recognized that two damage mechanisms of fiber-matrix interface debonding and pseudo-delamination among the bundles of fibers were competing, which the latter was affected by strain rate and fiber orientation.

Likewise, in other study [START_REF] Shirinbayan | Multi-scale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates[END_REF], the quasi-static and dynamic behavior of A-SMC composite for two configurations plates using interrupted tensile test method was studied. The outcomes revealed that the main mechanism of damage was fiber-matrix interface decohesion. At high strain rates, matrix micro-cracking that stems from interface micro-cracks propagation into the matrix in bundles of fibers was more obvious. One step before final failure, the mechanism of pseudo-delamination appeared, where it is more sensitive to high strain rates and fiber orientation parallel to the loading direction.

Besides of tensile test, modeling the compression behavior of SMC composites were more considered in the recent decade [START_REF] Asadi | Basalt fibers as a sustainable and cost-effective alternative to glass fibers in sheet molding compound (SMC)[END_REF][START_REF] Dumont | Compression moulding of SMC: in situ experiments, modelling and simulation[END_REF][START_REF] Kim | Optimisation of location and dimension of SMC precharge in compression moulding process[END_REF][START_REF] Kim | Experimental investigation and numerical simulation of SMC in compression molding[END_REF][START_REF] Park | A study on fiber orientation in the compression molding of fiber reinforced polymer composite material [J][END_REF]. For example, Shirinbayan et al. [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF], have studied the multi-scale damage analysis of low-density SMC (LD-SMC) composite for monitoring the consequences of local damage mechanisms in mechanical response of LD-SMCs under quasi-static compression loadings. The results confirmed the effect of fiber orientation on the compression behavior of LD-SMC. However, there is no study on the compression behavior of A-SMC composites.

In addition to tension and compression tests, shear behavior of composites is important [START_REF] Mostafa | Insight into the shear behaviour of composite sandwich panels with foam core[END_REF][START_REF] Dargahi | On the properties of magnetorheological elastomers in shear mode: design, fabrication and characterization[END_REF]. Different shear test methods have been introduced like single lap shear testing (SLST) [START_REF] Kellar | Contributor contact details[END_REF], short beam strength (SBS) shear testing [START_REF] Astm | 3165-07: standard test method for strength properties of adhesives in shear by tension loading of single-lap-joint laminated assemblies[END_REF][START_REF]Luft-und Raumfahrt_-Kohlenstoffaserverstärkte Kunststoffe_-Unidirektionale Laminate; Bestimmung der scheinbaren interlaminaren Scherfestigkeit[END_REF] and compression shear test (CST) based on composite types. However, the mentioned tests contain some limitations. For better understanding, numerous studies were published in terms of shear test optimization [START_REF] Astm D | /D2344M-00 standard test method for short-beam strength of polymer matrix composite materials and their laminates[END_REF][START_REF] Botelho | Mechanical behavior of carbon fiber reinforced polyamide composites[END_REF][START_REF] Sell | Application of the plane simple shear test for determination of the plastic behaviour of solid polymers at large strains[END_REF]. Shokrieh et al. [START_REF] Shokrieh | Investigation of strain rate effects on in-plane shear properties of glass/epoxy composites[END_REF] carried out the investigation of in-plane shear properties dependency to strain rate from static to dynamic criterion via symmetric and balanced ±45 • glass/epoxy composite laminate under uni-axial tensile test using a servo-hydraulic testing apparatus. They proved that shear properties were sensitive to strain rate. Holmes et al. [START_REF] Holmes | Development of an S-specimen geometry for shear testing of woven thermoplastic composites[END_REF] developed shear testing of woven thermoplastic composites through geometry optimization by designing an S-shaped specimen and provided a pure shear deformation mode for failure investigation. Moreover, Jia et al. [START_REF] Jia | Shear properties of polyurethane ductile adhesive at low temperatures under high strain rate conditions[END_REF] investigated the shear properties of polyurethane ductile adhesive in terms of strain rate dependency at a certain temperature. They applied thick adherent shear test (TAST) specimens and concluded that shear strength increased by loading speed. Kolanu et al. [START_REF] Kolanu | Damage assessment studies in CFRP composite laminate with cut-out subjected to in-plane shear loading[END_REF] studied damage assessment of carbon fiber reinforced polymers (CFRP) laminate, including cut-out part via in-plane shear loading for understanding the presence of cut-out and its counter effects. In another research [START_REF] Urapakam Ramakrishnan | Strength and failure characteristics of a glass fiber SMC-R composite under combined tensile and shear stresses[END_REF], failure characteristics of SMC-R composite under combined quasi-static tensile and shear tests were covered. It was summed up that, by increasing shear stress, the degree of non-linearity increased.

Modeling of the global mechanical and damage behavior of composites is necessary in design calculation of structural components [START_REF] Chatzigeorgiou | Effective mechanical properties of "fuzzy fiber" composites[END_REF][START_REF] Tan | A physically-based constitutive model for the shear-dominated response and strain rate effect of carbon fibre reinforced composites[END_REF]. One can note that debonding at fiber/matrix interfaces is the main damage mechanism of SMC composites [START_REF] Cherkaoui | Elastic composites with coated reinforcements: a micromechanical approach for nonhomothetic topology[END_REF][START_REF] Christensen | Mechanics of composite materials[END_REF]. The Mori-Tanaka method (MTM) is a famous model for analyzing multi-phase materials and modeling the effective linear and nonlinear behavior of composites. For instance, MTM modeling could couple with finite-element calculations [START_REF] Stupkiewicz | Fundamentals of micromechanics BT -micromechanics of contact and interphase layers[END_REF]. In SMC manufacturing process, the anisotropy is very important. The orientation distribution functions (ODFs) for SMC composites should involve information about the plane of distributed bundles (i.e. in-plane angle) [START_REF] Anagnostou | Hierarchical micromechanical modeling of the viscoelastic behavior coupled to damage in SMC and SMC-hybrid composites[END_REF]. One can conclude that to perform the design calculation, it is necessary to have the best experimental information under different types of loadings conditions [START_REF] Fitoussi | Experimental methodology for high strain-rates tensile behaviour analysis of polymer matrix composites[END_REF].

In the present work, an experimental study is conducted for understanding the mechanical and multi-scale damage behavior of A-SMC Fig. 7. Jaw and grips components in shear test. composite under tension, compression, and shear loadings. The effect of loading type, fiber orientation, and strain rate have been studied. The damage mechanisms under different loading conditions and loading rates were also reported. Two types of plates have been provided by Plastic Omnium Auto Exterior: Randomly Oriented (RO) and Highly Oriented (HO) plates. In the case of Highly Oriented (HO) plate two fiber orientation configurations of HO-0 • (parallel to loading direction) and HO-90 • (perpendicular to loading direction) are considered. Firstly, the microstructure of A-SMC using SEM, ultrasonic test, and X-ray microtomography is investigated. Then, the set-ups of tension, compression and shear tests are described. An advanced tensile-base shear setup is introduced to serve pure shear test on A-SMC composite, which shear theory and the optimized specimen via ABAQUS FE code are properly explored. In the second part of this study, the effects of fiber orientation on tension, compression and shear tests are presented. In addition, different types of damage mechanisms are introduced. In part three, strain rate dependency of mechanical properties for the three types of loading are probed and an interesting comparison is made specially for the shear test to underline the influence of local damage mechanisms on the overall response of materials. Finally, to sum up the mechanisms of damage, fractography of failed A-SMC composite is observed.

Materials and experimental procedure

Advanced sheet molding compound (A-SMC) composites

A-SMC is a new generation of high strength-to-weight ratio thermoset composites that is used in automotive industry, particularly for security parts. A-SMC composites are glass fiber-rich compounds, with 50% in mass corresponding to 38.5% in volume compared to the other types of SMC composites (Table 1). Moreover, they are vinyl-ester resinbased that reinforced via chopped bundles of glass fibers with a length of 25 mm. The mass production and time-efficient process of A-SMC composite is well-known and grabbed the industry's attention. In the first step, flexible and rolled raw materials cut to sheets with respect to the mold dimension and, subsequently, are stacked various layers into the molds. At the temperature of 150 • C and pressure of 60-120 kg cm -2 (low viscosity and cavity filling of the mold is achieved), thermocompression process is applied. Then, materials are kept in no special reticulation for short time. Finally, consolidation phase had occurred where reticulation time included.

Two types of A-SMC plates have been prepared: Randomly Oriented (RO) and Highly Oriented (HO) plates. For HO plate, two tensile directions were chosen: HO-0 • (parallel to the Mold Flow Direction (MFD))) and HO-90 • (perpendicular to the MFD).

Microstructure characterization methods

Scanning Electron Microscopy (SEM) observation

For microstructure observation and image analysis in terms of fiber orientation and qualitative investigation of fracture mechanisms, the model of HITACHI 4800 SEM was applied.

X-ray micro-computed tomography (μCT)

This technique includes an X-Ray source, a rotating table, and an Xray detector (EasyTom nano setup). The sample with a standard dimension (1 × 1 × 3 cm 3 ) was placed between the X-ray beam and the CCD camera detector. The μCT technique respects Beer-Lambert law (I=I 0 e -μx ) which showed logarithmic dependence between the initial intensity of photons "I 0 " and the intensity of the transmitted photons "I" across a traveled distance "x". The attenuation coefficient "μ" describes the fraction of an X-ray beam that is absorbed or scattered per unit thickness of the sample. For a heterogeneous sample, different "μ" yields to a different intensity of the transmitted photons. Finally, the radiograph was obtained by a projection of the attenuation data along with the path of the photons. For instance, the attenuation coefficient was for selecting a radiation energy that produced the most contrast between particular materials in radiograph. For three-dimensional visualization of the materials, "μCT" combines information that provided by many radiographs, each being made from a different angle of the sample regarding the X-ray source and detector that remain fixed.

Ultrasonic measurement

The main purpose of establishing this technique is to better understand fiber orientation and distribution [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF][START_REF] Schladitz | Nondestructive characterization of fiber orientation in reinforced SMC as input for simulation based design[END_REF]. This measurement was taken in immersion with ultrasonic apparatus including two probes (diameter of 10 mm) of transmitting (E) and receiving (R) separated at a constant distance of "d". Moreover, the specimen was located at the angle of 45 • regards to incident ultrasonic wave to create specified shear wave direction with respect to the Snell-Descart law [START_REF] Dupertuis | Generalization of complex snell-descartes and fresnel laws[END_REF]. In this method, the first stage is to measure initial velocity of ultrasonic waves in the liquid via oscilloscope for providing the flight time between two probes with the portion of distance/velocity. Then, the sample with a special thickness was perpendicularly placed between the two probes (Fig. (1-a)). Afterward, for having shear OT-wave (transversal wave), the OL-wave (longitudinal wave) should be removed that this demand The procedure of ultrasonic measurement in detail has been presented in Ref. [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF]. RO and HO plates with about 3 mm of thickness have been analyzed where the surface of each sample was 60 × 60 mm 2 .

Mechanical characterizations

To understand the global mechanical behavior and related damage mechanisms of A-SMC composites, three loading configurations of tension, compression and shear in different strain rate were applied.

Quasi-static tensile test

The testing device was applied upon a servo-hydraulic machine manufactured via Schenk Hydropuls VHS 5020. This test could serve the crosshead speed changing from quasi-static (10 -4 m s -1 ) to 20 m s -1 . Moreover, a piezoelectric crystal load cell having a capacity of a 50 kN used to measure load level. In this investigation, different level of strainrates was performed until failure of A-SMC composite. Fig. (2) represents an optimized device for using high strain rate tensile test that involved load cell, composite specimen, fixing system, sliding bar, hydraulic jack, damping joint (nitrile), and displacement direction [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF]. Moreover, the specimen schematic illustrated in Fig. (3) that is a rectangular shape to identify damage mechanisms and progressively loss stiffness occurring during dynamic loading in macro-and micro-scale observation on gauge length (i.e. 20 mm) surface. One can note that the strain was followed by a contactless technique using high-speed camera [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF].

Table 2

Visualization and quantitative analysis of RO-A-SMC and HO-A-SMC composites.

Quasi-static compression test

In this case, the testing instruments were obtained with the Instron 5881 machine (Elancourt, France) and generally contained load cell and specimen that the former part could serve 50 kN loading and velocity of 1 mm min -1 with respect to the NF ISO 6239 standard. In parallel, any local deformations that occurred were determined by using a camera with a capacity of 25 pictures per second. Additionally, in Fig. [START_REF] Yalcin | 5 -hollow glass microspheres in sheet molding compounds[END_REF], the details of jaw and its parts illustrated. Moreover, the geometry of the specimen depicted in Fig. [START_REF] Shirinbayan | Coupled effect of loading frequency and amplitude on the fatigue behavior of advanced sheet molding compound (A-SMC)[END_REF].

Shear test from quasi-static to high strain rates

The details of shear test set-up showed in Fig. [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF] that was obtained from a servo-hydraulic test machine (Schenk Hydropuls VHS5020) in order to perform shear test by means of tensile test machine. A camera (FASTCAM-APX RS with capacity 250,000 frames per second) was placed in front of the set-up to strain measurement. For the first time in this study, a novel version of jaw (Fig. [START_REF] Jacob | Energy absorption in polymer composites for automotive crashworthiness[END_REF]) and specimen were designed to better investigate the mechanisms of failure in A-SMC composite with shear test at different strain rates. Specimen dimensions illustrated in Fig. [START_REF] Abbasnezhad | Influence of loading conditions on the overall mechanical behavior of polyetherether-ketone (PEEK)[END_REF] and will be explained in more details in the following sections.

Characteristics of the novel shear test method.

Based on Fig. [START_REF] Baste | Evaluation of anisotropic damage in composite materials[END_REF], the forces and gliding planes well-demonstrated that help to define basically deformation with homogenous relative glide of parallel planes normal to the OX 2 axis along with the shear direction OX 1 . The shear amount was gained via the ratio γ = x/h which "x" is relative displacement of the parallelepiped oppose faces and "h" is the sheared width of the sample. Moreover, for providing constant shear rate, it is necessary that the opposite faces displace in a constant velocity (i.e. Ẋ = hγ). In this model, the shear stress is defined as τ = F/L.e and the related parameters were well-described in the schematic at ambient temperature [START_REF] Paupler | Mechanical metallurgy[END_REF]. The optimized geometry of sample was basically identified via ABAQUS FE code that will be talked more in the following sections. By the way, the main advantages of this method are simpler boundary condition, applicable for high strain rate shear test and much homogenized shear strain.

Moreover, upper jaw was fixed that allows to avoid much unwanted stress in different axes. This method, also, provides more real outcomes in shear strength evaluation due to the much volumetric engaged specimen. Indeed, more Representative Volume Elementary (RVE) were subjected to the stress, means including more defects and inhomogeneities in mechanical investigation of the composite that were made due to the unwanted production manner's error. As illustrated in Fig. [START_REF] Baste | Evaluation of anisotropic damage in composite materials[END_REF], the fixtures and moving jaw frame were attributed to do pure injection of the stresses into the preferential sample representative volume.

Finite element (FE) optimization of specimen geometry.

ABAQUS FE optimization was used to propose the best fitted sample geometry and dimensions for shear test to reduce perturbation and disturbance wave's impact on sample, obtaining homogenous strain flowing and rapid stabilization of strain rate in the sample gauge part during the first stage of applying load by the machine. Following our previous researches [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF][START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF], for the tensile test, the same optimization procedure was used (Fig. [START_REF] Jendli | Anisotropic strain rate effects on the fibre-matrix interface decohesion in sheet moulding compound composites[END_REF]). Finally, the geometry dimension was proposed that is much suitable for A-SMC composite.

In terms of shear test, like above-mentioned procedures, the composite assumed to be such an elastic anisotropic solid, and the results indicated the suitable dimensions in Fig. [START_REF] Abbasnezhad | Influence of loading conditions on the overall mechanical behavior of polyetherether-ketone (PEEK)[END_REF]. Four stages of geometry optimization illustrated briefly in Fig. [START_REF] Jendli | Anisotropic strain rate effects on the fibre-matrix interface decohesion in sheet moulding compound composites[END_REF]:

• Damping joint and t r determination: Damping joint was placed between the sliding and hydraulic jack that could limit shock effects, which caused to a part of total imposed displacement at the beginning of the loading. This process has been activated until the end of total elastic deformation. Then, at rise time (t r = 1 × 10 -3 s), applied strain rate changes to a constant value and subsequently, at onward It is clear that the imposed value is raised linearly up to "t r " . • Dimensional and geometrical optimization: As shown in Fig. (11-c), the aim was to optimize the specimen to serve a homogenous stress and strain field with constant strain rate within the interested zone of sample. Different width and length were analyzed that finally the dimensions presented in Fig. [START_REF] Abbasnezhad | Influence of loading conditions on the overall mechanical behavior of polyetherether-ketone (PEEK)[END_REF] proposed as an optimal dimension. • Validation of optimization: Experimental results with numerical simulation were compared and validated the proposed dimension that will be discussed in the next section.

Associated measurement.

Regarding to our last investigation [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF] of high strain rate tensile test of A-SMC composite, for experimental evaluation of strain-time measurement, 6 points were marked on the face of sample for defining the initial gauge in shear test, and then changes were monitored via high-speed camera. Subsequently, image analysis was used to observe a displacement of centroid of each marked point to show the strain between the two points. Regarding the simulation and experimental results, it was proved that after damping stage, strain rate became constant that consequently could be measured from the slope of the linear part of curve in Fig. [START_REF] Dumont | Compression moulding of SMC: in situ experiments, modelling and simulation[END_REF], which is a confirmation of the chosen boundary conditions in accordance with ABAQUS FE simulation (Fig. [START_REF] Asadi | Basalt fibers as a sustainable and cost-effective alternative to glass fibers in sheet molding compound (SMC)[END_REF]). Fig. [START_REF] Kim | Optimisation of location and dimension of SMC precharge in compression moulding process[END_REF] illustrates shear stress-strain curves for HO-A-SMC composite calculated from three points of γ 1 , γ 2 and γ 3 . The curves almost overlapped each other which indicates homogeneity of shear tests in addition to mentioned ABAQUS simulation in previous part (Fig. 11).

Results and discussion

Microstructural analysis

SEM observation

In this study, the A-SMC composite plates were prepared by Plastic Omnium Auto Exterior for doing tensile, compression and shear tests. Fig. [START_REF] Kim | Experimental investigation and numerical simulation of SMC in compression molding[END_REF] illustrates SEM observation of the RO-A-SMC microstructure that shows clearly randomly distribution of the fiber bundles (the length and number of fibers in each bundle are, respectively, 25 mm and 250) in matrix specially on polished cross-sectional view (view B) [START_REF] Shirinbayan | Multi-scale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates[END_REF]. The microstructure of HO-A-SMC has been presented in Ref. [START_REF] Shirinbayan | Multi-scale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates[END_REF].

X-ray micro-tomography

Table [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF] illustrates μCT of RO-A-SMC microstructure in terms of skin, shell and core configuration and quantitative analysis. It is clear that in RO-A-SMC composite layers, the upper and lower specimen surfaces are slightly random in fiber orientation. In contrast, for HO-A-SMC composite, the fibers were more organized according to a special direction. Moreover, in terms of porosity, RO-A-SMC composite with 0.3% of porosity is more compact than HO-A-SMC composite, but porosity distributions are more homogenized in HO-A-SMC.

Ultrasonic analysis

Ultrasonic results were obtained in a methodology that described above. The main factor in this technique is velocity of ultrasonic wave propagation, which is totally depends on mechanical properties and fiber orientation of sample. A parameter called acoustical birefringence (K%) was defined as:

K(%) = V OTmax -V OTmin V OTavarage × 100 (1)
The parameter of V OT is the velocity of the shear waves for a given relative orientation θ of the composite. This coefficient represents orientation intensity, that higher amount means more oriented fibers in the matrix. The polar diagrams of velocity for RO and HO plates given in Figs. (15 and 16). As can be seen, in Fig. [START_REF] Park | A study on fiber orientation in the compression molding of fiber reinforced polymer composite material [J][END_REF], high portion of the diagrams show special direction that there are preferred direction fibers for HO-A-SMC. However, in Fig. 16, most of the diagrams are circular that are indicating there is no preferred direction of reinforcements. Moreover, it could be understood that there is no attention-grabbing dispersion in the fiber volume fraction. Moreover, the materials seem to be an isotropic one which the characteristics of ρ (kg.m -3 ), K (%), C 11 (GPa), V OT (m.s -1 ) and V OL (m.s -1 ) were measured to complete the characteristics.

Quasi-static tension, compression, and shear loadings: effect of fiber orientations

For understanding the influence of fiber orientation, HO-90 • , RO, and HO-0 • configurations were subjected to the tension, compression, and shear loadings in quasi-static at room temperature. According to Fig. 17, nonlinearity in stress-strain curves is obvious. In Fig. (17-a), generally, the ultimate tensile strength of HO-0 • outweighed the other types and HO-90 • showed lowest tensile strength. Moreover, the Young's modulus for three fiber directions of HO-90 • , RO, and HO-0 • were measured roughly 12.5, 14.5 and 18.5 GPa. One can note that in HO-90 • most of fiber were oriented perpendicular to the loading direction. Fiber-matrix decohesion can occur when a combination of a local ultimate normal and shear stress reach on the interface of fiber/ matrix. In fact, fiber-matrix interface of oriented fibers to 90 • direction was failed under a pure normal stress. However, 45 • oriented fibers were submitted to higher interfacial shear stress and RO configuration presented tensile strength between HO-90 • and HO-0 • . In Fig. (17-b) the stress-strain behavior related to the three fiber orientations under compression loading illustrated. Similar to the tension behavior, the ultimate compression strength and strain values are higher for HO-0 • than for RO and HO-90 • . Moreover, the Young's modulus for three fiber directions of HO-90 • , RO and HO-0 • were measured roughly 16, 16 and 20 GPa. These values confirm that Youngs' modulus of A-SMC under compression loading is slightly higher than the tensile modulus. One can notice that a compression force is one that squeezes composite together. In compression loading, when fibers orientation is more in 90 • to the loading direction, fiber/matrix debonding is initiated and damage is followed by matrix micro-cracking until failure. Compressive behavior of RO and HO-90 • samples showed the same regime until just before failure. One can note that for RO samples, the fibers that are more parallel to the loading direction (i.e. fiber orientation ≪45 • ) can participate to the composite failure mechanism in addition to the decohesion of the fiber/matrix interface and matrix micro-cracking.

In Fig. (17-c), in contrast to the tension and compression, the ultimate shear strength of HO-90 • is higher than HO-0 • . Moreover, the Young's modulus for three fiber directions of HO-90 • , RO and HO-0 • are measured roughly 3.8, 3 and 1.5 GPa. This difference is for this fact that in shear test, by applying the load in HO-0 • configuration, as described before, circumferential surface of fibers was subjected to the parallelepipedal deformation and consequently shear forces caused a harsh fiber/matrix debonding. Moreover, the ultimate strain for HO-0 • is higher than the others. It can be because of the role of matrix and consequently more matrix cracking until final failure. Additionally, for HO-0 • configuration, the curvature reached the ultimate shear strength more smoothly than HO-90 • and RO configurations. However, in the case with the fiber orientation of 90 • to the loading direction, the stress was tolerated by the fibers, where the fibers resist for the high applied stress, the ultimate strength is higher for this type of orientation. In addition, fiber crack terminates the final failure and results in low strain compared to the other configurations.

The tension and compression behavior of RO-A-SMC were compared in Fig. 18 under quasi-static loading at room temperature. As can be seen, in terms of ultimate stress and failure strain, tensile values outweighed compression values by around more than 12% and 40%, respectively. Furthermore, compression modulus (about 16 GPa) is higher than tensile modulus (about 14.5 GPa). Generally, in tension test the curvature was reached the ultimate strength smoothly compared to the other one. This analysis must be completed after multi-scale damage study to understand the mechanisms under tension and compression loadings.

Effect of strain rate on shear loading

For understanding the effect of strain rate on shear behavior of RO-A-SMC, stress-strain curves in different rates from 0.25 s -1 to 10 s -1 were plotted (Fig. [START_REF] Astm | 3165-07: standard test method for strength properties of adhesives in shear by tension loading of single-lap-joint laminated assemblies[END_REF]). These curves, in general, could be divided into three sections of linear elastic behavior, damage initiation (i.e. beginning of Fig. 20. Effect of strain rate on the (a) shear modulus, (b) maximum shear stress (τ r ) and threshold shear stress (τ y ), and (c) shear strain at maximum shear stress (γ r ) and threshold shear strain (γ y ) for RO-A-SMC composite. nonlinear behavior) and damage propagation until rupture. One can observe that shear behavior of RO-A-SMC composite is strain rate dependent that by increasing the strain rate, shear modulus and ultimate shear strength are increased. For instance, under strain rate of 0.25 s -1 , the ultimate strain is roughly 14% which is more compared to ultimate strain under strain rate of 10 s -1 . Moreover, strain hardening could be observed but not as much as in high strain rate tensile test [START_REF] Shokrieh | Investigation of strain rate effects on in-plane shear properties of glass/epoxy composites[END_REF][START_REF] Anderson | Fracture mechanics: fundamentals and applications[END_REF].

Effect of strain rate on material characteristics in shear loading

Here, materials characteristics define as shear modulus (G), shear damage thresholds related to the first non-linearity (τ threshold , γ threshold ), ultimate stress and strain (τ ultimate , γ ultimate ) which presented in Figs. (20 and 21). The definition of ultimate characteristic is corresponding to the maximum stress level that was happened before delamination. As illustrated in Fig. [START_REF] Astm D | /D2344M-00 standard test method for short-beam strength of polymer matrix composite materials and their laminates[END_REF], shear modulus (G) is strain rate independent until shear strain rate of about 5 s -1 . More than this strain rates, the shear modulus drastically was increased. Moreover, other characteristics are changing with strain rate altering. Fig. [START_REF]Luft-und Raumfahrt_-Kohlenstoffaserverstärkte Kunststoffe_-Unidirektionale Laminate; Bestimmung der scheinbaren interlaminaren Scherfestigkeit[END_REF] indicates that by increasing the strain rate, the values of the maximum shear stress and threshold stress were increased. On the other hand, the visco-damageable behavior of RO-A-SMC is clear in shear loading. This notion has been well explained in the previous works [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF][START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF][START_REF] Shirinbayan | Multi-scale damage and mechanical behavior of sheet molding compound composites subjected to fatigue , dynamic , and post-fatigue dynamic[END_REF].

As demonstrated in Fig. [START_REF] Astm D | /D2344M-00 standard test method for short-beam strength of polymer matrix composite materials and their laminates[END_REF] for the samples of RO-A-SMC composite, the mechanical behavior under the shear test is more strain rate dependent compared to the tensile test, especially in terms of modulus, threshold and maximum stress. The strain rate of 5 s -1 was known as a critical strain rate. -a) confirms modulus values under tension is higher than shear one for different strain rates (about 14.5 GPa and 4 GPa, respectively). However, the tension and shear modulus variation show the same regime until around 5 s -1 but after that, shear modulus value increases dramatically until 6.5 GPa for the strain rate of 10 s -1 . Moreover, Fig. (21-b andc) compared threshold stress values (raised from 125 GPa to 175 GPa and around 75 GPa to around 100 GPa for shear and tension loadings, respectively) and threshold strain values (increased from approximately 2%-3.5% and from 0.5% to roughly 1%, for shear and tension loadings, respectively). The slope of the threshold strain/stress increasing, for shear test are respectively 4.5 and 1.3 times more than those of tensile test. Similarly, in Fig. (21-d), the same tendency can be observed. Strain at maximum stress reveals dropping regime after the strain rate of 5 s -1 for shear test compared to tension test, however, for the tension test this value is increased by strain rate increasing (Fig. (21e)).

Multi-scale damage and fractography analysis: tensile, compression and shear loadings

A wide verity of damage mechanisms of fiber-reinforced composites were reported in Refs. [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF][START_REF] Anderson | Fracture mechanics: fundamentals and applications[END_REF] which are fiber pull-out, fiber bridging, fiber/matrix debonding, fiber failure, matrix cracking, delamination, pseudo-delamination, micro-buckling and buckling delamination (Fig. [START_REF] Botelho | Mechanical behavior of carbon fiber reinforced polyamide composites[END_REF]). Fiber orientation, composition of composites and reinforcements, loading type, strain rate and temperature are important factors for initiation of each type of damage.

However, for understanding the types of mentioned damage mechanisms in A-SMC composites and the reasons for material characteristics respond, microstructural analysis with supplement to theoretical aspects of damage phenomenon are needed to discover. The damage threshold, type and sequence of damage stages are totally depending on sort of applied load, strain rate and fiber distribution in the matrix. As a result, multi-scale damage analysis of A-SMC composite under quasi-static tensile, compression and shear loadings were studied.

Tensile loading

Damage mechanisms related to the high strain rate effects on A-SMC composite were well-reported in our last researches [START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF][START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF][START_REF] Shirinbayan | Multi-scale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates[END_REF]. It was concluded that depends on the fiber orientation, two main mechanisms are in competition which are fiber/matrix debonding and pseudo-delamination alongside with matrix micro-cracking based on the strain rate (Fig. [START_REF] Sell | Application of the plane simple shear test for determination of the plastic behaviour of solid polymers at large strains[END_REF]). As can be seen, fiber-matrix interface failure and matrix micro-cracking were obviously propagated by increasing the force under tension. In the first non-linearity stage, the fiber/matrix debonding has occurred which gradually propagated through the composite by increasing the force under tension. The later caused to the several transverse cracking of the matrix. It was proved that the decohesion at the interface of fiber/matrix is the predominant damage mechanism in RO-A-SMC under tension. Matrix breakage and pseudo-delamination can also appear for higher stress levels. subjected to the quasi-static and dynamic tensile loadings. The results of high strain rate tensile tests have been presented in previous work [START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF].

Both in quasi-static and dynamic fracture surface, fibers were still attached to the matrix that sum up the fact of strong fiber-matrix bonding. Moreover, in pseudo-delamination mechanisms, fibers were pulled out from each other in parallel with matrix surrounding breakage.

Compression loading

For damage investigation of RO-A-SMC composite, in Fig. [START_REF] Holmes | Development of an S-specimen geometry for shear testing of woven thermoplastic composites[END_REF], the sequence of damage evolution in compression with microstructural observation has been plotted from interrupted compression tests. In the first stage fiber/matrix interface micro-cracking was happened in fiber zone, especially in more 90 • oriented to the loading direction and consequently caused crack propagation with increasing the and subsequently pseudo-delamination observed in the final stage. It could be observed that the same scenario of damage under tension and compression loadings were come up. However, the lower values in terms of failure stress and strain under compression test are related to the test setup and limitation of deformation under compression test.

Also, the macroscopic pictures presented in Fig. [START_REF] Jia | Shear properties of polyurethane ductile adhesive at low temperatures under high strain rate conditions[END_REF] show the fractography under compression loading. As can be seen, pseudodelamination was created which for HO-0 • is more noticeable than the other types due to the fiber direction regarding the loading forces. However, RO-A-SMC composite behaved a moderate damage regime.

Shear loading

Same as other loading types, in shear test, the main damage mechanisms are fiber/matrix interface debonding and pseudo-delamination with fiber pull-out and also fiber bundle rotation which is due to the in-plane shear forces [START_REF] Shokrieh | Investigation of strain rate effects on in-plane shear properties of glass/epoxy composites[END_REF]. Figs. (27 and 28) illustrate these damage mechanisms of RO-A-SMC composite from interrupted shear tests. First, crack-growth happened in circumferential surface of fibers in particular for the fibers in 0 • to the load direction, which is due to the parallelepipedal deformation mechanisms in shear forces that cause the formation of local stresses on fiber/matrix bonding. Then, the cracks start to grow normal to the load direction through the matrix until the final failure with pseudo-delamination mechanism.

However, in dynamic loading (Fig. ( 29)), pseudo-delamination damage was more obvious which could be a reason for proving high absorption energy and good crashworthiness capability of RO-A-SMC composite. Additionally, much portion of the fibers were attached to the matrix even in high strain rate because of excellent fiber/matrix bonding (Fig. 30). However, Fig. 29, provides a high magnification of the high strain rate fracture for showing that in final stage of fracture, matrix was a high percentage disjointed and needle-shaped fibers cause the brittle failure. It could be concluded that shear properties were clearly depended on strain rate.

Conclusion

Advanced sheet molding compound (A-SMC) composites are a new generation of SMC composite in terms of increased glass fibers more than 50% weight content, attracted the automobile manufacturers' interest to replace steel compounds in automobiles. The plates of Randomly Oriented (RO) and Highly Oriented (HO) with two configurations of 90 • (perpendicular to MFD) and 0 • (parallel to MFD) were prepared and subjected to the tension, compression, and shear loadings to understand that besides of loading types, what are the effects of fiber orientation on multi-mechanical evaluations. Moreover, different strain rates were applied to investigate the strain rate dependency of A-SMC composite according to the loading types. In terms of shear loading, a new methodology for investigation of A-SMC shear properties has been adopted. After sample optimization via ABAQUS, the samples were applied at different strain rates and compared in terms of strain rate dependency and damage mechanisms for different fiber orientations. Finally, the major conclusions are listed below:

Fig. 1 .

 1 Fig. 1. A schematic of the ultrasonic method; (a) configuration of sample and probes, and (b) sample rotation for removing OL wave and appearing OT wave.

Fig. 3 .

 3 Fig. 3. Dimensions of specimen for tensile test.

Fig. 4 .

 4 Fig. 4. Schematic of testing set-up of compression jaw.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Dimension of the specimen in the compression test.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Geometrical characteristics and dimensions of the specimen in shear test.

Fig. 10 .

 10 Fig. 10. Optimization steps via ABAQUS FE.

Fig. 11 .

 11 Fig. 11. Methodology of optimization in accordance with experiments and FE simulation of double rectangular gauge parts; (a) experimental data, (b) boundary conditions, (c) FE computation optimization of specimen geometry.

Fig. 12 .

 12 Fig. 12. Contactless strain measurement of RO-A-SMC at different strain rates in shear test.

Fig. 13 .

 13 Fig. 13. Shear stress-strain curves for HO-A-SMC composite: monitoring the 6 points.

Fig. 14 .

 14 Fig. 14. Microstructure observation of RO-A-SMC composite.

Fig. 15 .

 15 Fig. 15. Polar diagrams, main direction of fiber and table of characteristics in HO-A-SMC (A-E: vertical sample location and 1-5: horizontal sample location).

Fig. 16 .

 16 Fig. 16. Polar diagrams, main directions of fiber and the table of the characteristics in RO-A-SMC (A-C: vertical sample location and 1-4: horizontal sample location).

Fig. 17 .

 17 Fig. 17. Stress-strain curves for (a) tension, (b) compression and (c) shear behavior of A-SMC composite with respect to the fiber orientation under quasi-static loading (i.e. 0.01 s -1 ).

Fig. 18 .Fig. 19 .

 1819 Fig. 18. Tension and compression stress-strain curves for RO-A-SMC composite. Fig. 19. Shear stress-strain curves of RO-A-SMC at different strain rates.

Fig. 21 .

 21 Fig. 21. Comparison of a) modulus, b) ultimate strain, c) ultimate stress, d) threshold stress, e) threshold strain after performing tensile and shear tests at different strain rates for RO-A-SMC composite.

Fig. ( 21

 21 Fig.(21-a) confirms modulus values under tension is higher than shear one for different strain rates (about 14.5 GPa and 4 GPa, respectively). However, the tension and shear modulus variation show the same regime until around 5 s -1 but after that, shear modulus value increases dramatically until 6.5 GPa for the strain rate of 10 s -1 . Moreover, Fig.(21-b and c) compared threshold stress values (raised from 125 GPa to 175 GPa and around 75 GPa to around 100 GPa for shear and tension loadings, respectively) and threshold strain values (increased from approximately 2%-3.5% and from 0.5% to roughly 1%, for shear and tension loadings, respectively). The slope of the threshold strain/stress increasing, for shear test are respectively 4.5 and 1.3 times more than those of tensile test. Similarly, in Fig.(21-d), the same tendency can be observed. Strain at maximum stress reveals dropping regime after the strain rate of 5 s -1 for shear test compared to tension test, however, for

Fig. ( 24 )Fig. 22 .

 2422 Fig. 22. Schematic of damage mechanisms in fiber-reinforced composites; (a) in-plane damage, (b) buckling delamination, (c) micro-buckling, (d) pseudodelamination and (e) delamination [6,40].

Fig. 23 .

 23 Fig. 23. Quasi-static tensile tests for RO-A-SMC composite coupled to the microstructure observation; (1): fiber/matrix debonding, (2): fiber/matrix debonding propagation and matrix micro-cracking, (3), (4) and (5): matrix micro-cracking and pseudo-delamination mechanisms[START_REF] Shirinbayan | Mechanical characterization of a low density sheet molding compound (LD-SMC): multi-scale damage analysis and strain rate effect[END_REF][START_REF] Shirinbayan | High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension[END_REF][START_REF] Shirinbayan | Multi-scale experimental investigation of the viscous nature of damage in Advanced Sheet Molding Compound (A-SMC) submitted to high strain rates[END_REF].

Fig. 24 .

 24 Fig. 24. Fracture surfaces in RO-A-SMC composite for quasi-static and dynamic tensile loadings [2,6,42].

Fig. 25 .

 25 Fig. 25. Quasi-static compression test of RO-A-SMC coupled to the microstructure observation;(1) decohesion at the fiber/matrix interface, (2), (3) crack propagation and (4) pseudo-delamination.

Fig. 26 .

 26 Fig. 26. Macroscopic fracture behavior of HO-A-SMC and RO-A-SMC composites under quasi-static compression loading.

Fig. 27 .Fig. 28 .

 2728 Fig. 27. Quasi-static shear test of RO-A-SMC composite coupled to the microstructure observation; (1) fiber/matrix debonding, (2), (3) crack propagation and (4) pseudo-delamination.

Fig. 29 .

 29 Fig. 29. Fractography of RO-A-SMC composite under quasi-static and dynamic shear loading.

Fig. 30 .

 30 Fig. 30. Pseudo-delamination of high strain shear test in RO-A-SMC.

Availability of data and materials

The authors declare that the data and the materials of this study are available within the article.

• Shear setup and specimen dimension were properly designed and optimized by comparing ABAQUS FE codes and experimental results with a damping time of 1 × 10 -3 • Different damage mechanisms of A-SMC composites are fiber pullout, fiber failure, pseudo-delamination, fiber/matrix debonding, buckling, etc. Among them, based on the strain rate and loading types, fiber/matrix debonding, matrix cracking and pseudodelamination were competing. • The effect of fiber orientation on global mechanical behavior showed that in tension and compression tests, HO-0 • A-SMC composite represented higher strength but HO-90 • configuration presented higher shear strength compared to the HO-0 • and RO composite due to the parallelepipedal deformation. • For strain rate effects on tension, compression and shear tests, the dependency of mechanical properties (i.e. ultimate strength and ultimate strain) was well-proved. Although Young modulus was not strain rate sensitive. Shear modulus (G) was strain rate-independent until shear strain rate of about 5 s -1 . More than this strain rate value, the shear modulus drastically was increased. • In fractography by SEM observation, it was presented that by increasing strain rate (for instance in shear test: from 0.25 s -1 to 2.37s -1 ), matrix in high percentage was disjointed and fiber brittle failure was happened.

Declarations

• Consent to participate: Not applicable.

• Consent to publish: Not applicable.

• Conflict of interest: The authors declare that they have no conflicts of interest.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.