A numerical and experimental investigation to the

MATERIAUX 2006 13-17 Novembre 2006 – Dijon, France

A numerical and experimental investigation to the optimization of the thermoplastic reinforced sheet deep drawing A.Agahi a, M.Shirani a, S.A.Sadough a, F.R.Biglari a, A.Alikhani b [email protected] a

Mechanical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic) Tehran, Iran b TAM of Iran Khodro Company (IKCO)

Abstract: Process design in thermoplastic reinforced sheet deep drawing involves many areas, such as determination of die design, selection of process parameters and initial blank shape design. Initial blank design in the composite sheet deep drawing refers to the design of blank initial geometry and it can help the produced part to be fabricated without defects such as earing which means the flange with varying length, and also it can reduce material consumption in addition to improving the formability. In this study for numerical investigations, a computational program based on finite element (FE) analysis, which is performed using ABAQUS/Explicit, that uses sensitivity analysis for design of initial blank configuration in deep drawing process has been constructed. The sensitivity approach modifies the position of the boundary nodes in initial blank with the aid of desired target shape, to make the boundary contour of deformed sheet coincide with the target contour. For experimental studies, a mold has been constructed to produce a part with a hemispherical dome which has a flat flange around. By assuming the target drawn sheet be with a uniform flange in length, the initial blank shape is designed using developed program. Finally a thermoplastic reinforced blank with designed shape prepared and deformed in the constructed mold with a hemispherical punch. The deformed blank had acceptable flange length uniformity and there was a good agreement between FE analysis and experimental results. Keywords: Thermoplastic reinforced sheet; Deep drawing; Experimental results; Sensitivity analysis

1. Introduction Woven fabric reinforced composites have been widely used in the aerospace, automotive, and sporting goods industries due to a number of advantages such as high strength to weight ratio, ease of handling, and well developed weaving technology. For the design of automated manufacturing processes, which will replace the hand shaping of woven fabrics, the use of accurate numerical tools for simulating the deformation behaviour of performs becomes very important. The solid mechanics analysis of the draping of fabrics by using finite element methodology takes into account the mechanical properties of the fabric and, hence, describes the physical process of draping. The fabric is considered as a continuum and the analysis of the draping of fabrics is essentially an extension of the deep drawing or diaphragm forming simulation of metal forming processes [1–7]. In current research we have used discrete layers of woven and viscous materials to model the thermoplastic reinforced composite sheet. Each ply of the viscous material is modelled as a transversely isotropic incompressible Newtonian fluid, also we have used the experimental results and non-orthogonal constitutive model that developed by Peng and


Cao [8] to model each ply of the woven material. The developed constitutive equations were implemented into the ABAQUS/Explicit code using the user material subroutine VUMAT [9, 10]. 2. OPTIMAL BLANK DESIGN IN DEEP DRAWING PROCESSES The numerical simulations of the deep drawing process are used extensively for the analysis and design of industrial parts to avoid long and expensive experimental try-out procedures. Together with non-Linearity of materials, the other important factors such as the unsteady nature of the process, large elastic-plastic involved, and the complexity of contact and frictional effects make the study of drawing process so complex that their analysis justifies the use of sophisticated numerically algorithm and usually leads to large scale computer requirements [11-14]. The deep drawing simulation enables us to optimize the process parameters such as blank holder pressure/force, die geometry, friction coefficient (lubricant), etc. One of desired subjects in deep drawing process is optimal blank design. Traditionally the optimal blank is referred to an initial blank shape which produces a net shape part. The net shape means that the trimming process is eliminated completely in deep drawing process. But deep drawing without trimming is very difficult although not impossible since even small variation of process parameters such friction and material properties can result in defects. If the optimal blank is supposed to be referred to an initial blank shape to produce a desired shape which allows trimming after deep drawing, the process design to deep drawing becomes easy to handle. Optimal blank has many advantages. The optimal blank not only improves formability but also reduces material cost, number of trials in the try out phase. But it must be noted it is not easy to find optimal blank shape due to complexity of deformation behavior especially in the case of composite sheets which are not isotropic. Since the optimal blank design was an attractive subject for sheet metal engineers, they have developed several methods which computes optimal blank shape analytically(for simple parts) or numerically such as geometric mapping method[15,16],analogy method[17,18], slip line field method[19-23], trial and error method based on FEM[2426],INOV method[27].In this paper we have applied one of this methods which is called sensitivity method[28] to the composite blanks deep drawing process. So first we have introduced thermoplastic reinforced composite sheet to ABAQUS/Explicit using user material subroutine VUMAT [9, 10] and after predicting part boundary contour, using sensitivity analysis of boundary nodes, optimal blank is designed. In this method a couple of deformation analysis, with the original and the offset blank, is required to calculate sensitivity coefficients in boundary nodes. 3. BASIS OF THE SENSITIVITY ANALYSIS With the initial blank defined by X, the deep drawing process is analyzed using FE code, ABAQUS/Explicit. X represents a position vector of a material point located in the boundary of initial blank in initial configuration. After deformation the node moves to the boundary of blank in the deformed configuration. x represents a position vector of the material point located in the boundary of deformed blank. Figure 1 shows the movement path of the boundary node during deformation. The real path is a nonlinear curve, so it is approximated with linear paths for each step (increment) of deformation in sensitivity analysis.


Figure 1: movement path of a boundary node After deformation analysis if a boundary node does not locate in the target contour, its initial position X should be modified to make the deformed contour x coincide with the target contour xT .This position modification is done using shape sensitivity which is computed numerically for every boundary nodes by considering two blanks, the original and the offset blank. The offset blank is determined from initial blank deformation analysis using eq. (1): Χδ = Χ + δ Ν (1) Where Xδ represents the position vector of a boundary node of an offset blank in initial configuration. N is the unit vector in the deformation direction at the first step and δ is the amount of offset [28]. The shape sensitivity for every boundary nodes is computed using eq. (2): Χδ − Χ S= xδ − x (2) Deformation process is analyzed using offset blank and xδ represents the position of material point located in the boundary of offset blank after deformation analysis. Unless x for a boundary node lies on the target contour, its initial coordinates X should be modified using eq. (3): Χ i = Χ i −1 − ε S N (3) Where ε is the vector of position error for a boundary node and is a distance between xT and x which is calculated using target position and final position in the deformed configuration. Superscript i in eq. (3) indicates the number of iteration. After modification of the blank shape, the deformation process is analyzed again until ε reaches a specified allowance at every boundary node. The allowable ε is selected 2mm in this paper. 4. NUMERICAL RESULTS FOR A HEMISPHERICAL CUP In this study sensitivity analysis is applied for the initial blank of a hemispherical cup. The deep drawing analysis is performed using tools which are shown in Figure 2. We modelled a punch, die and a fixed blank holder as rigid because their deformation is negligible. The blank also locates between die and the fixed blank holder. It must be noted that the target shape is a cup with a hemispherical dome and a square flange profile of 15 mm length.


Figure 2: Geometrical representation of forming tools. The blank material is a composite sheet with 1mm in thickness and the blank is meshed using 625 linear 4-node shell elements. 5.1. Deformation analysis using initial rectangular blank The first simulation was done using user material subroutine VUMAT [9, 10], to assign property of composite sheet to the blank, with a 120 * 120 mm 2 rectangular initial blank (Figure3). The depth of cup is 27mm so the punch moves 27mm through the die. Using the initial blank deformation is analyzed when punch velocity was 1mm/sec.

Figure3: Rectangular initial blank (dimensions in meter) The result of deformation is shown in Figure4 which clearly shows that rectangular blank is not suitable for target cup production.


Figure 4: Ddeformed rectangular blank with punch velocity of 1mm/sec After deformation the boundary nodes coordinates during deformation were accessible and were used to determine boundary contour of offset blank, which will be used to calculate shape sensitivity at each boundary node. 5.2. Offset blank determination and shape sensitivity, S, calculation Using information obtained in sec.5.1, the boundary of offset blank is determined by eq.1. In this study δ considered 2 mm for all boundary nodes and N is the unit vector in the deformation direction at the first step. Computed offset blank is shown in Figure5.

Figure 5: Offset blank when amount of offset is 2mm Deformation of offset blank is analyzed again and the deep drawing conditions are as considered before. Finally shape sensitivity S for all of boundary nodes is calculated using eq.2, by deformation information obtained in sec.5.1 and 5.2. 5.3. Error modification and optimal blank design After calculating modification factor, S, Firstly shape error ε at each boundary node is computed, using final position of boundary nodes in deformed blank and the target contour. Then using shape error and shape sensitivity blank shape is modified by eq. (3) which is shown in Figure6.


Figure 6: Optimized blank (dimensions in meter) Deformation process is analyzed using modified blank, Figure 7, and shape error at each boundary node is computed. Shape error in boundary nodes is less than 2mm, so the modified blank is selected as optimal blank and there is no need for more iteration.

Figure7: Deformed shape of optimal blank. 6. Experimental validation In this study the base material was from polypropylene, which was reinforced with woven glass fibers. Figure8-a,b show base and woven reinforcement utilized in the current research, respectively.

(a) (b) Figure 8: (a) Thermoplastic sheet (base material); (b) Woven glass fabric (reinforcement);


Then a woven reinforced thermoplastic sheet, was made from one layer of woven glass fiber and two layers of polypropylene. For this sheet a good consolidation was achieved by applying 2000(N) for 5 minutes. It must be noted that consolidation temperature was set to 210 ºC and also the heating time was about 100 minutes. Figure 9 shows the produced thermoplastic reinforced composite sheet.

Figure 9: Produced thermoplastic reinforced composite sheet Optimal blank shape (Figure6) was employed and the optimal blank was cut from square produced composite sheet, as it is shown in Figure 10. Then optimal blank preheated in 180 ºC for 80 minutes, and carried immediately to the die.

Figure 10: Optimal thermoplastic composite sheet reinforced with woven glass fiber Hemispherical punch diameter was 27 millimeters and matrix diameter was 30 millimeter. Figure 11-a,b show the die and tools set up that has been used for deep drawing process, respectively.

(a) (b) Figure 11: (a) hemispherical deep drawing die (die radius=4mm); (b) tool set for deep drawing process


The punch speed was set to 1 mm/sec. and punch penetrated 27 mm through die cavity. At the end of forming process, pressure remained (5 minutes in this study) until work piece cold down and let thermoplastic material to strength suitably. Finally the punch translated upward and deep drawn part exited from the die cavity. Deep drawn composite sheet is shown in figure 12.

Figure 12: Final part obtained from deep drawing of optimal blank 7. Results and discussion Flange contours of drawn cups using optimal blank are shown in Figure 13 for both experimental and simulated parts. In addition boundary profile of deformed rectangular blank is represented in Figure 13 to be compared with deformed optimal blank contours. It must be noted that due to symmetry only one fourth of contours are shown. As it is shown FE simulation has predicted optimal blank with an acceptable error. Also there is a good agreement between numerical and experimental results in the profile of deformed optimal blank. Furthermore, Figure 13 shows that deep drawing using optimal blank earing defect is deleted and it helps us to save material significantly due to trimming deletion. 0.08

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Figure 13: Flange contours of the optimal blank and rectangular blank


8. Conclusion Using a VUMAT user material subroutine, thermoplastic reinforced composite sheet is defined in ABAQUS/Explicit. Then a program of optimal blank design based on sensitivity analysis for deep drawing process has been developed. Using developed program optimal blank shape for a hemispherical hat with a square flange calculated. A thermoplastic reinforced composite sheet prepared from polypropylene (base) and woven glass fiber (reinforcement). The optimal blank shape was cut from square prepared blank. Using the optimal blank an experimental test was carried out, considering suitable consolidation temperature and time. When deformation process is performed using the optimal blank we can see that earing defect (deformed shape with a varying flange in length, e.g. Figure 4) is eliminated, therefore there will be no need for additional operations such as trimming. In order to compare FE and experimental results, boundary contours obtained are represented, and a good agreement between FE and experimental observations in deformed blank contour observed.

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