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Characterisation experiments have been conducted on a woven self-reinforced polypropylene composite (SRPP) including uniaxial and bias extension tests. Outcomes of these experiments were employed to develop a non-linear orthotropic material model within an incremental deformation framework. The material model of the woven composite was implemented into a finite element simulation to predict stretch forming behaviour of SRPP specimens. The predicted strain paths at the pole of specimens were verified against experimental outcomes. It was shown that specimens possessing different aspect ratios deform under a wide range of deformation modes from uniaxial extension to biaxial stretch modes. Finally, the effect of different forming parameters on the strain path evolution of the woven composite was elucidated through numerical simulations. It was shown that the aspect ratio of the samples plays an important role in forming behaviour of woven composites. Development of a reliable and accurate numerical model for predicting forming behaviour of woven composites and understanding their main forming mechanisms promote and encourage the extensive application of these materials systems in a wide range of mass producing industries. Adopting woven composites in manufacturing industrial components facilitates addressing environmental concerns such as recyclability and sustainability issues.

Key criteria in developing new products include sustainability, recyclability and weight reduction. Published data [_{2} emission and fuel consumptions. Thus, weight reduction in vehicles is regarded as one of the major priorities in the mass production industries such as automotive industry [

Woven Thermoplastic Composite Materials (WTPCMs) have shown great potential to be employed in the automotive industry due to their attractive properties including high specific strength, excellent impact energy absorption and balanced in-plane thermomechanical properties [

Formability of unconsolidated woven composites (prepregs) has been studied extensively [

The pre-consolidated sheets of a multilayered 2/2 twill weave self-reinforced composite (SRPP) employed in the current study was manufactured by OCV reinforcements Co. [^{3} volumetric density. Both reinforcements and the matrix were manufactured from a highly oriented semi-crystalline polypropylene polymer, making the final product to be completely recyclable. The woven fabric is manufactured from PP copolymers, made of two structurally different concentric cylinders of PP: a core made of α-PP polymer covered by b-PP polymer as the skin, in which the former has significantly higher melting temperature than the latter. Applying sufficient pressure and heat to the composite prepregs melts the skin of PP copolymer and constructs the matrix by embedding the unmelted b-PP reinforcement (selectively melting process). After cooling period, the consolidated multilayered SRPP composite sheets are produced.

In the current study, SRPP specimens with different aspect ratios (width-to-length ratios) were employed to characterise the woven composite and to study its forming behaviour at room temperature through two different sets of experiments:

1) Characterisation specimens: rectangular SRPP samples possessing 200 mm ´ 20 mm ´ 1 mm (length, width and thickness) dimensions were employed to characterise the composite material through uniaxial extension and bias extension tests. The test procedure followed ASTM D3039 standard as the standard test procedure for characterisation of polymer matrix composites. Specimens possessing [0˚, 90˚] fibre orientations were used in uniaxial extension tests to calculate longitudinal stiffness (Young’s modulus or E) and Poisson’s ratio (PR) of SRPP and samples with [−45˚, +45˚] fibre orientations were employed to measure the shear stiffness (G) of the SRPP composite through the bias extension test.

2) Stretch forming specimens: These specimens were cut-out from initially circular specimens of 200 mm in diameter. The samples’ widths (W in

Two different experiments were conducted to develop a nonlinear material model and to evaluate the accuracy of the numerical model in predicting the stretch forming behaviour of SRPP composite:

1) Characterisation experiments: Two sets of experiments were conducted to characterise the SRPP composite including uniaxial and bias extension tests. The former was employed to characterise composite mechanical response to unidirectional loadings along the fibres, to calculate modulus of elasticity as a function of longitudinal strain and to evaluate Poisson’s ratio (PR) of the woven composite. The latter was designed to characterise the shear stiffness of the material by uniaxially extending [−45˚, +45˚] SRPP specimens in a bias extension test. The equipment included a universal testing machine (INSTRON 8874) to extend SRPP samples and to measure the force by a load cell and a CCD camera for recording deformations and calculating strains during deformations.

2) Stretch forming experiments: This set of experiment was designed and conducted on a variety of [0˚, 90˚] specimens to study their forming behaviours under different forming paths specified by the ratio of minor to major strains. Forming equipment included: a custom-built press with 300 kN capacity, a hemispherical punch, an open die with a built-in lock ring to enforce boundary conditions, a blank holder system, and two CCD cameras installed beneath the open die to measure strains and their evolutions during forming. The configuration of stretch forming equipment is shown in

The characterisation experiments conducted on [0˚, 90˚] and [−45˚, +45˚] SRPP specimens revealed the nonlinear response of the woven composite to external loadings. The full characterisation of the woven SRPP required the definition of three different stress and strain dependencies: correlation between longitudinal stress and strain, longitudinal to transverse strains dependency and shear stress-strain behaviour. The outcomes of charac-

terisation experiments are depicted by the following equations:

In the above equations, the parameters are defined as follows: A = −18.5E6, B = −25.2, c = 14188.75, d = 0.00841, F = 18.5E6, M = 0.052, N = 0.0043, p = 1.08, q = 0.009, L = −0.056, R = 117.8, S = −11.6, t = 28.35 and H = 11.6. The highly nonlinear nature of these relations necessitates application of an incremental deformation theory to effectively capture complex forming behaviour of SRPP as follows:

These equations yield the following material properties for the SRPP woven composite:

Subsequently, the stress and strain tensors can be coupled together through the following plane stress orthotropic material model:

In this equation, s_{1}, s_{2} and s_{12} depict different components of the Cauchy’s stress tensor including normal stress along 1 and 2 axes and in-plane shear stress. e_{1}, e_{2} and e_{12} represent normal strains along 1, 2 and in-plane shear, respectively. E_{1} and E_{2} depict Young’s modulus along 1 and 2 axes, while n_{12} and n_{21} are the two Poisson’s ratios of the SRPP caused by stretching the specimen along the first axis depicted by the first subscript on the induced strain along the transverse axis, shown by the second subscript. The stiffness matrix of the woven composite was considered asymmetrical based on the following reasons: 1) E and n are both functions of strain. During each increment, the induced strains in 1 and 2 axes are not necessarily identical (depending on the width of the sample and enforced boundary conditions). Therefore, E and n along these two directions possess different values during different stages of deformation. 2) Existence of a strain potential function during a linear, small deformation process guarantees symmetrical properties of the material’s stiffness matrix. However, during stretch forming of a SRPP composite, large, non-linear deformations occur.

A total of 16 different SRPP specimens with different aspect ratios were stretch formed by the hemispherical punch until they fractured. The induced strains on the surface of SRPP samples were measured by the ARAMIS system. Principal strains were continuously calculated during each deformation increment. The ratio of minor to major strains (SR) was calculated to determine the induced deformation modes at the pole of specimens (The intersection of the two symmetry axes of the specimen). These deformation modes varied between the following regions: SR = −0.5 depicting uniaxial extension mode, SR = 0 exhibiting plane stress deformation and SR = +1 showing biaxial stretch.

Stretch forming simulations was conducted by the ABAQUS/implicit solver. The developed orthotropic material model was implemented into the ABAQUS by considering the plane stress condition governing stretch forming of thin SRPP blanks. Geometrical modelling of stretch forming experiment was accomplished through the ABAQUS Graphical User Interface. Four main parts were modelled within the ABAQUS/CAE (

This type of shell element enforces Kirchhoff’s thin shells theory during forming of the composite. A total of 5000 to 10000 elements were used to discretise the blanks depending on their size. The numerical simulation was accomplished through three general steps: 1: The blank was positioned on the die and a normal traction force was applied to the semi-circular edges of specimens (

The friction coefficient between blank holder-blank, die-blank and punch-blank pairs was set between 0.3 - 0.5. The contact between contact pairs was established through the master-slave approach with a surface-to- surface contact reinforcement. A linear penalty method was reinforced to the normal contact condition to prevent penetration of the contact pairs into each other. A general stabilisation procedure was enforced to address convergence issues during contact. To minimise the numerical errors, the ratio of the dissipated energy during contact and the overall energy required for forming was kept below a critical value.

The nonlinear strain path, evident in all specimens except for W200, is caused by different phenomena: 1) fixing merely the circular edges of specimens in the lock-ring causes a stretch and a contraction along the length and the width of the specimen due to Poisson’s effect, respectively 2) Establishment of initial contact between punch and the blank causes a local biaxial stretch in the pole of samples 3) Increase of forming depth changes biaxial stretch mode to another deformation mode governed by the aspect ratio of the sample 4) Gradual conformation of the blank to the punch geometry causes evolution of friction condition by variation of normal pressure and an asymmetrical contact surface along warp and weft directions (or along principal directions).

The FEA predictions demonstrate a similar trend with experimental outcomes during all stages of deformation. These results prove the high accuracy and reliability of the implemented numerical model for a woven composite during stretch forming condition. Both experiment and numerical simulations show the dependency of strain path to the aspect ratio of specimens: W25 and W50 demonstrate uniaxial and plain strain deformation modes, respectively. Increase of the specimens’ widths causes the deformation mode to shift toward biaxial stretch until W200 which exhibits SR of +0.95. The small deviation of W200 strain ratio from a complete biaxial stretch is due to the friction between the sample and the punch.

Experimental and analytical investigation on stamp forming of woven composites is complicated, time consuming and challenging due to the highly complex nature of contact condition between the punch and the blank, nonlinear mechanical response of woven composites to external loadings and complex coupling between different forming parameters. Employing a macro-mechanical numerical model facilitates analysis of different parameters on the formability of the woven SRPP efficiently by avoiding incorporation of complex interactions within the weave structure of the composite. Three specimens are selected (W25, W100, W150 with [0˚, 90˚] fibre orientations) and the effect of different mechanical properties and contact conditions on the strain path are studied.

The effect of friction condition on forming behaviour of a woven composite is elucidated in

the strain path to shift toward the plane strain by counteracting Poisson’s effect and hampering development of the negative minor strain. Friction condition only affects maximum induced strain during stretch forming of wide specimens but results in a major shift of the strain path in narrower samples due to non-proportional contact surface along warp and weft directions.

material differs by 30% compared to the original SRPP Young’s modulus. In narrow specimen, the effect of this change on the induced deformation mode is negligible. However, in wider specimens, the increase of stiffness causes a shift toward plane strain deformation mode with a decrease in principal strains for an identical forming depth. The noticeable effect of changing stiffness in different specimens is the length of pre-stretch deformation stage. This stage of forming process is a force-control process in contrast to other stages with a more displacement-control nature. Generally, changing the Young’s modulus within the realistic range of SRPP elasticity modulus does not show a prominent effect on the strain path of specimens, specifically in narrower specimens. Increasing the stiffness in wide specimens shows some local effects on the strain path, although the final gradient of the strain path seems to be identical.

Effect of shear stiffness on the strain path of woven composites, as shown in

noticeable, yet non-intuitive phenomenon during stretch forming of a woven composite with [0˚, 90˚] fibre orientations. Intuitively, the shear stiffness should not have a remarkable impact on the deformation of a [0˚, 90˚] specimen during stretch forming, due to the fact that shear strain in these specimens should be very low. The numerical results show the validity of this hypothesis in narrow specimens. However, the forming results on wider specimens elucidate the significant impact of shear stiffness on the strain history. Decrease of shear strain shifts the strain path toward plane strain deformation mode, while increase of shear stiffness results in a more biaxial stretch deformation mode. Decreasing the shear stiffness causes a more uniform strain distribution on the surface of specimens in lower forming depths:

For the same forming depth, the maximum principal strain at the pole decreases, delaying onset of failure in the woven composite.

and the punch increases simultaneously. The blank starts to conform to the punch geometry further once the shear strains at ±45˚ areas increases. This is highlighted by a change in the strain path of the sample. During the final stages of deformation, the maximum strain moves completely from the pole to ward areas located along ±45˚ directions, the shear strain increases significantly and the blank conforms completely to the punch surface (Figures 9(c-c) & 9(c-d)).

Characterisation experiments were conducted on a pre-consolidated woven self-reinforced polypropylene composite (SRPP) to elucidate in-plane material properties including Young’s modulus, Poisson’s ratio and shear stiffness. These data were employed to construct an asymmetric orthotropic material model employed in a numerical simulation to predict stretch forming behaviour of the composite. Subsequently, stretch forming experiments were conducted on different SRPP specimens by a hemispherical punch. The induced strains during forming were continuously measured to elucidate forming behaviour of the SRPP under different forming modes. The match between the numerical simulation results and the experimental outcomes on the strain path at the pole of specimens were satisfactory. Then, the developed finite element model was employed to investigate the effect of different parameters on the forming behaviour of woven composites. All major variables showed sensitivity to the aspect ratio of the samples in changing strain path at the pole. These variables included material properties and friction condition. It was elucidated that in narrow specimens, the Poisson’s ratio and friction coefficient are the most influential parameters on the strain path and therefore on the formability of the woven composites. In wide specimens, the shear stiffness and Young’s modulus are more effective parameters in the formability of the composite than others. It was revealed that the shear stiffness of a [0˚, 90˚] woven composite

has a significant effect on developing a more uniform surface strain and therefore the enhanced formability of the woven composite.

N. A. Zanjani,S. Kalyanasundaram, (2015) Stretch Forming Simulation of Woven Composites Based on an Orthotropic Non-Linear Material Model. Journal of Materials Science and Chemical Engineering,03,168-179. doi: 10.4236/msce.2015.37023