Abstract
This paper deals with experimental and numerical investigations of the composites damages with ductile and fragile reinforcement under quasi-static indentation loading. The main goal of the work is to increase the post-damage residual strength and ductility of thermoplastic composite. Two types of composite laminates with polypropylene (PP) matrix are tested: glass fibre laminate (GFPP) and steel fine wire mesh laminate (SWPP). The specimens are [0° 90°]2s stacking sequence and prepared by using a compression moulding technique. Quasi-static indentation tests were performed with two distinct penetration scales under low velocity (1.2 mm/min). The diameter of the hemispherical indenter is 16 mm. The failure mechanisms of composite layers were examined by the field emission scanning electron microscope (SEM). The results show that the failure mode of SWPP laminates is principally dominated by the plastic deformation component. In contrast, the GFPP laminate exhibits a fragile behaviour which is related to the fragile failure of glass fibres. In addition, the SEM shows that matrix cracking, fibre breakage, debonding and fibre pull out are the major damages observed around the indentation area. A model based on the combined use of plasticity, damage and fracture, was developed and applied to simulate quasi-static indentation behaviour and predict the resulting damage.
Introduction
Recently, there is a significant increase in the use of thermoplastic matrix laminated composite materials in many advanced engineering applications, such as aerospace, automotive, sports, etc. In addition, more formal researches considering the behaviour of these materials under low velocity impact are conducted [1, 2]. The failure mode of the laminated composite materials is still difficult to predict [3]. In fact, matrix deformation and micro-cracking, inter-facial debonding, lamina splitting, delamination, fi-bre breaking and fibre pull-out are the characteristic damage features of laminated structures under low velocity impact [4]. Damages initiate with matrix cracking and lamina splitting which lead to delami-nation, while fibre breaking is usually the last failing mechanism [5]. The study of the low-velocity impact damage could be replaced by the results of the static indentation tests [6, 7]. The response of laminates to the both types of impact and quasi-static indentation loads to low-velocity was evaluated by comparison of force-displacement diagrams as well as the extent and nature of structure degradation as a result of loads [8]. The results show that the damages mechanisms are consistent after static and dynamic tests. Significant differences were found in destruction scale in laminates. Other authors have shown that the duration of the impact strongly in-fluences the response of composite laminates under static and dynamic impacts at low velocity [9]. In addition, the quasi-static indentation tests are highly adapted to predict the dynamic impact behaviour of marine composites GRP (glass fibre reinforced) [10]. Wagih et al. [11] carried out an experimental investigation on carbon / epoxy laminates subjected to quasi-static indentation tests. The induced damage at different indenter displacements was investigated and the results showed that matrix cracking is in fact the crucial damage mechanism.
Several studies reported the assessment of the performance of woven glass-based composites with polypropylene as matrix under low velocity impact (LVI) and quasi-static indentation (QSI) [12, 13]. Other authors [14, 15] asserted the high potential of fibre metal laminates (FML) of polypropylene matrix as suitable materials for engineering applications due to their significant mechanical properties. The behaviour of these composite laminates (FML) under low velocity impact was further investigated under various energy of loading [16]. They affirmed that the interfacial fracture toughness of the impacted plates exhibit high-level absorption energy. Under low impact and quasi-static indentation test, the debonding appearance upon the lower surfaces of the FML plates decreases the peripheral strain [17]. In fact, the relevant literature offers little information on the effects of impact induced debonding on the impact response of FML. Depending on the fibre alignments in the laminate and on the location of the debonded interface, the shapes of the debond damage are something between oval, rectangular and circular [18].
The Hashin failure criterion has been used extensively for intra-laminar damage modes in industry, although it cannot accurately predict the intra-lami-nar damage initiation [19]. Recent approaches such as Cohesive Zone Model (CZM), Matzenmiller, Lubliner and Taylor (MLT) and continuum damage mechanics (CDM) were introduced to predict numerically the damage of composite laminates [20, 21]. Furthermore, various finite element models considering the three-dimensional progressive or intra and inter-laminar damage under low velocity impact were developed and could be respectively found in [22, 23].
In this present study, the low velocity indentation responses of two woven composites based on glass and steel/polypropylene laminates were investigated. A quasi-static indentation tests were performed to determine the mechanics behaviour of the two different laminates on such impact properties as the impact peak load, the absorbed energy and the morphology of the indentation damage. The mechanical results related to morphological observations from scanning electron microscopy (SEM) of fractured laminates have been studies. Furthermore, based on the experimental results, a Matzenmiller, Lubliner and Taylor (MLT) model was carried out in VUMAT subroutine program.
Experimental
Materials and Manufacture of Laminates
The composite panels used in this investigation were based on a matrix of polypropylene (PP) and reinforcement with fibre glass or stainless steel fine wire mesh. The E-glass fibre and steel wires were oriented at 0° and 90° degree in longitudinal and transverse directions, respectively. The polypropylene granules (PP) are those used for the mechanical industry with a density of 0,9 g/cm3. The melting temperature of the polypropylene (PP) occurs at 171 °C. The first used reinforcement was E-glass fibre with a density of 2.54 g/cm3, this is the most used sort of fibre glass witch stays unaffected by fire until the temperature of 830 °C from which softening and viscous flow begins; the melting occurs at 1070 °C. The second used reinforcement was stainless steel fine wire mesh with density of 7.90 g/cm3. The fibre volume fractions (vf) for the GFPP and the SWPP laminates are 48 % and 36 %, respectively.
The manufacturing of the composite panels with dimensions of 200 × 200 mm2 is performed with a mould frame, see Fig. 1. The process is based on stacking two layers of woven prepegs with different laminates. The mould containing the prepegs was placed in the air circulating oven with an adjusted internal temperature of 180 °C. The panels were then stamped with a cold press under a pressure of 0.80 N/mm2. A fast cooling is recommended to reduce as possible the crystallinity of the polypropylene matrix. When the mould's temperature is less than 55 °C, the panels were removed and carefully inspected. The thickness of the composite laminates after the compression moulding is 4,00 ± 0.10 mm. Then, the plates were naturally cooled at room temperature (23 °C, 50 % RH). More details about this manufacturing process could be found in [24, 25].
The Stacking Arrangement of the Composite and Metal Sheets in a Picture Frame Mould.
A diamond saw is used to cut the composite plates. This technique reduces drastically the surface defect and the polishing time.
The nominal dimensions of the plates are 100 × 100 × 4 mm3. Before the tests, all the specimens were left in the laboratory environment for a week.
The quasi-static indentation (QSI) tests were carried out, using a MTS universal testing machine (model criterion 41) with capacity of 50 kN load cell and displacement control with 1.2 mm/min cross-head speed. This test machine is equipped with software for programming loads and acquisition frequencies via programs called Templates. The mounting device shown on Fig. 2a can be fitted to the test machine was specially designed for indentation testing to scale macro.
Experimental Setup of the OSI Test: (a) A Cross Section at the Centre of the Testing Device and (b) the Specimen under Indentation Test.
As seen on Fig. 2b, the test device consists of a hemispherical tip indenter with a diameter of 16 mm and two square metal plates of size 200 × 200 × 10 mm3, which hold in place the tested composite plate. These fixing plates have a circular hole at their centre of 70 mm in diameter which allows the indent-er/composite contact and thus enable penetration deformation. Using this device a good alignment was applied to ensure that the plate is loaded in the testing machine centre. This installation has been specially designed and could easily fit to the MTS machine. All tests were done at room temperature without environmental conditioning. The imposed displacement was controlled and applied at velocity of 1.2 mm/min.
The indentation test was achieved at two penetration scales. Initially, the indenter is positioned at a distance of 4 mm from the specimen. At first, the in-denter is going down until a distance of H1 = 7 mm from the upper surface of the composite laminates. Then, it goes back to the initial position. After that, the process is repeated for a second load to attain the second penetration scale limited to H2 = 15 mm.
For each type of laminate, five indentation tests were performed and the indentation energies were chosen so that the first tests were performed just before the break and the others until the complete penetration of the indenter. The load-penetration average curves for GFPP and SWPP laminates are represented in Fig. 3. The curves begin with a linear part and then from a certain threshold the damage appears, that could be identified by a rigidity decrease which was caused by the fibre/matrix debonding and the matrix fracture. The laminate will suffer significant damage once it has reached a high level of indentation (maximum load). From the standpoint of resistance to indentation, the two parameters that define the behaviour of the composite are the maximum load supported and the energy absorbed. The latter can be determined from the area under the load-penetration curve to the total penetration.
Load/Displacement Curves for a Static Indentation: (a) GFPP Laminate and (b) SWPP Laminates.
The absorption energies for the SWPP laminates are found to be 21.30 Joules and 22.10 Joules, and for the GFPP laminates, they are 15.10 Joules and 16.50 Joules. From these results, it was found that the SWPP laminates were stronger and dissipated more energy (51, 90 Joules) than GFPP laminates (38, 85 Joules). This higher load capacity in the steel wire laminates can be explained by the higher deformation of the layers at the upper and lower contact surfaces of the laminate. The layers were able to with stand higher deformations before breaking and have prevented the spread of damage to the sides, thus increasing the maximum load capacity. Another dif-ficulty is related to the viscosity matrix, which has significant effects on the total rupture.
Comparison of the hysteresis curves for the GFPP and SWPP laminates indicates that the SWPP laminate dissipated more energy due to the plastic deformation of the steel wires. Therefore, the energy was absorbed in form of elastic deformation, plastic deformation and through formation of new surface during failure. In the case of the GFPP laminate, there was little or no plastic deformation due to the brittle behaviour of the glass fibres. After breaking some fibres of the contact surface, the load is carried by the neighbouringfibres and was decreasing with the depth of penetration until complete perforation was reached. The outcomes are in accordance with the results of Simeoli et al. [4]. The authors showed that the broad interface of composites based on PP and glass fibre reinforcement failure and slipping act as crack blocker, preserve the integrity of fibres.
The Scanning Electron Microscope (SEM) images of the fracture surface for the GFPP and SWPP composite specimens after the quasi-static indentation test are shown in Fig 4. The breaking mechanisms of glass fibres and steel wires are different. Fig. 4a shows a brittle failure with less of glass fibre pull-out; their breaks depend on the intrinsic strength of the fibres and the shear cell. Damage accumulation is located first in the polypropylene matrix before cracks of the fibres. In the Fig. 4b, steel wires are more flexible and break at the level of accumulated deformation. Failure of SWPP after QSI test has a complex nature. Polypropylene matrix is separated of steel wire, due to the plastic deformation of the wires. This can effectively alleviate the stress concentration at the interface and then prevent the cracks from rapid propagation [4]. Some delaminations at the Steel/PP interface are caused by plastic deformation of the steel fibres and by the presence of substantial shearing stress.
SEM Images of Fracture Surface for (a) GFPP Laminate, (b) SWPP Laminate.
Matrix-fibre debonding is also an important mechanism which often exists in the thermoplastic composites whose interface bonding is not strong, and would decrease the resistance of material [8 14].
Constitutive Model and Failure Criteria
The damage progression in composite plates GFPP and SWPP are different. Fig. 5 shows compression test curve for the laminates SWPP where three zones distinct can be observed; (i) the elastic undamaged zone, (ii) the second zone begins by the rigidity decrease, this progressive decrease of the modulus is obtained by the load-unload compression test. The cumulative damage D defined as
Damage Evaluation Model Due to Combined Damage Variables diA and diB of the S/PP Laminates
Where G_i is the stiffness, calculated from the linear region for each loop and G_0 is the initial Young's modulus [26]. The last zone corresponds to the failure of the reinforced composite. These observations highlight two simultaneous mechanisms: damage and plasticity.
Matzenmiller et al. [27] developed a damage model called “MLT model” for non-linear analysis of the composite laminates. They constructed the model using damage variables with respect to the individual failure mode in the material principal directions. The evolution of these internal variables depends upon values of stresses in Hashin's failure criteria, which are expressed in terms of stress invariants for a transversely isotropic body and the strength parameters for the composite [19]. In addition, when one of Hashin's failure criteria is satisfied at a point in a composite structure, damage ensues at that point and it can be characterized by introducing internal variables for fibre breakage in tension and compression, matrix cracking in tension and compression, and crushing.
In this work, the MLT model was extended to take into account the plasticity that appears in the SWPP laminate, which developed a ductile behaviour comparatively to the GFPP laminate that give a brittle behaviour. The plasticity and damage have been considered in the longitudinal and transverse directions. The last zone corresponds to the failure of the reinforced composite. The Hashin (1980) failure criteria are used to predict the behaviour of composite plates in a complex state of stress [19]. Damage affects the warp, weft and shear directions. However, the laminate's stress-strain is assumed elastic ortho-tropic; the relationship takes the form:
Where ∊ and σ are the strain and stress components. The two parameters (K, n) are determined experimentally. E_D^’ is the damaged stiffness matrix for an orthotopic lamina and is defined as:
With
E1 and E2are the elastic modulus in the longitudinal and transverse directions, respectively. G12 is the shear modulus.v12 and v21 are the major and minor poisson's ratio. d1 is associated with longitudinal (warp) fracture, d2is associated with transverse (weft) fracture and d3is associated with shear (fibre-matrix) failure.
The damage variables d1 are quite favourable to describe the damage part (non-linear curve softening) due to the effect of gradual micro-cracking formation. The softening behaviour of the laminates can be predicted by this MLT model (exponential function):
Eiiis the young's modulus. ∊ii i=l, 2 is the strain related to the progressive damage direction. σi, f i=l, 2 is assumed to be identical for compression to (Xc, Yc) and compression with bucking to (Xp, Yp), respectively. m is Weibull modulus and e is the natural log basis. The di, A damage variable in compression is commanded by m parameters that dictate the damage accumulation behaviour. The m parameters are defined from the strain at maximum stress and Young's modulus E.
The damage variables di, B are used to predict the failure part (strain-softening) of Steel-wire/PP laminates [20, 28]. The damage evolution is therefore expressed as:
Where he is the characteristic length of the element and Gf is the fracture energy per unit area. ∊f, i is the strain at maximum stress and (2G_f)/(h_e σ_(f, i)) is the strain value ∊ult when the specimen are totally damaged [26]. dA + dB= 1 at complete failure.
Quasi-static indentation tests were modelled and simulated using the explicit finite element software ABAQUS/Explicit and a user subroutine VUMAT that was implemented in this software. This developed model allows simulating the real behaviour of laminates. The composite laminate plate of 4 mm thickness was modelled by bonding 4 plies (each 1 mm) with an interface between every two plies, defined by normal and shear stress in order to simulate the continuity of the deformations; delamination was not considered in these simulations. Ortho-tropic elastic material model were assigned to the composite plates to simulate anisotropic nature of the material. Orthotropic post-damage and post-failure features are used with the material strain failure criteria in order to detect the damage and failure during the simulation.
The laminates were meshed with conventional shell elements (S4R). The mesh of laminates has to be refined adequately enough to have a fine mesh in the areas where there are high stress gradients (Fig. 6). For this purpose, a refined mesh was created in the vicinity of the indenter, convergence calculation was conducted to ensure that the mesh refinement in glass/pp and steel/pp laminates was sufficiently fine enough to capture the stresses and damage with a good precision. The hemispherical steel indenter with diameter of 16 mm was modelled as rigid body. According to the observations of the experiments, the parts of the plate that are outside the boundary of the central hole are not affected by damage. Thus, in order to increase time efficiency of simulations, only the central part of the plate is modelled for the quasi-static indentation simulations. The indenter was placed 0.1 mm above the top surface of the laminate. During the indentation simulation, the indent-er engages with the plate and bounces back when the indenter reaches the imposed load, the simulation was terminated after the indenter returned to its original position.
The Numerical Finite Element Model for Quasi-Static Indentation Tests.
A comparison of experimental and numerical analysis results for GFPP and SWPP laminates is represented in Fig. 7. It was observed that the proposed numerical model describes quite well the trend of the experimental curves for the studied laminates. The numerical and experimental curves overlap on the non-linear part before the laminate failure and the maximum of the compression strength limits are similar.
Experimental and Numerical Results for (a) E-Glass/PP Laminate and (b) Steel-Wire/PP Laminate.
In the failure zone, the obtained numerical values by the model are slightly inferior to the ones obtained experimentally for the failure stress, see Fig. 8.
Fracture Surfaces for E-Glass/PP Specimen Subjected to Indentation Loadings (Back Face) for (a) Experimental test and (b) modelled test.
In the GFPP laminate, primary cracks appear and tend to orient about 45° (Diagonal Tear). During the growth of this primary crack, secondary cracks appear. During the increase of indentation depth into the specimen thickness, one tip of the primary crack split into three cracks and the cracked area was bending outward. Then, the cracks orientation continues along the fibres directions (0° and 90°), especially when the sizes of the cracks are important (Fig. 8a and 8b). This cross failure (Fig. 8b) is same form as the one observed after the test (Fig. 8a).
Fig. 9 shows the crack propagation of back face of SWPP laminate, which represents the (semi-ellipse shape). This semi-ellipse failure is also noticed in the modelling (Fig. 9b) and it has the same form as the one observed after the test (Fig. 9a). Different to the first failure type (case of GFPP laminate), the crack passes through along the circular direction. It shows that the cracks of the back face are oriented along two opposite directions, which is justified by localized forces induced at the contact zone. The in-denter contact zone is confined into a circular dent of 16 mm diameter, called diffuse damage.
Fracture Surfaces for Steel-Wire/PP Specimen Subjected to Indentation Loadings (Back Face) for (a) Experimental Test and (b) Modelled Test
This work deals with the experimental and numerical investigation of the response and the damage process of laminates plates subjected to low-velocity quasi-static indentation (QSI) test. Composite laminates based on polypropylene and glass or steel fibres have been prepared using the compression moulding technique. The used numerical model (MLT) was found to be in good agreement with the experiment.
The quasi-static indentation tests at low velocity showed that the Steel/PP offer a higher strength than that of the Glass/PP thermoplastic composite. The Steel/PP laminates were capable of absorbing sig-nificant energy through extensive plastic deformation in the steel and composite layers.
The perforation threshold of SWPP composite is approximately 24 % higher than that of the GFPP composite.
The SWPP laminates showed the best performance in terms of dissipated energy, which was approximately 33.60 % higher with respect to Glass/ PP plates.
Damage behaviour of the two kinds of laminates looks different as seen from cross sectional views of damaged samples with microscopic investigation and compared with damage area.
The damage area was found to distribute centro-symmetrically around the indentation point in the SWPP plates while the GFPP generated crack which extended in transverse direction when the load was up to the maximum force.
Matrix cracking and some delamination were observed on SWPP plate while there were only matrix breaks on GFPP surface of impacted opposite side of specimens. However, as the indentation load increased, the observed fibres failure constitutes the dominant damage mode.
The numerical predictions using MLT model are successfully validated by comparing with results obtained experimentally. In the GFPP laminate, cracks tend to be oriented along 0° and 90° of the fibre directions, especially when the sizes of the cracks are important. The crack propagation of back face of SWPP laminate, which represents the semi-ellipse shape and different to the first failure type. These failures are same form as the one observed after the test. Future research is needed to investigate a number of issues, including the influence of the thickness, velocity, fibre orientation.