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Deformation analysis of flange curved edge in rectangular box drawing of pure copper sheet

Abstract: as part of the experimental study of rectangular box drawing, the measurement results of photoetching lattice deformation in the forming process are analyzed, and it is pointed out that in the flange curved edge deformation, the radial tensile deformation near the die opening on the angular symmetry line increases with the increase of rectangular box angular radius RC, but the circumferential compression deformation is almost independent of RC. And there is a region of radial compression deformation on the angular symmetry line, which helps to reduce the inflow resistance of curved material

key words: rectangular box drawing flange curved edge radial tensile deformation circumferential compression deformation

0 preface

in rectangular box drawing, the flange deformation on the blank pressing surface and the corresponding side wall load are non-uniform distribution, the straight and curved edge material deformation inflow speed is uneven [1], deformation constraints and other phenomena are comprehensively affected by many forming conditions, giving theoretical analysis of plastic deformation Numerical calculation and corresponding finite element simulation experiments bring great difficulties, and the analysis and Research on the deformation of curved edges are still insufficient. Through a large number of actual drawing test results, this paper investigates the deformation phenomenon of flange flange flange in rectangular box drawing, and makes a preliminary analysis of stress and strain for specific parts of flange, which provides some experimental analysis basis for further understanding and mastering the deformation essence of non rotational symmetric drawing

1 test conditions

test material: cold rolled pure copper sheet with thickness t0=0.2 mm. Test mold: rectangular punch L × w=36 mm × 72 mm, corner radius rc=1 mm, 3 mm, 9 mm, punch and die shoulder fillet radius rp=rd=1.5 mm, punch and die clearance δ= 0.3 mm。 Drawing test equipment: 500 kn single acting oil press, forming speed 0.3 mm/s. Material pressing device: the 63 MPa hydraulic pump controls four hydraulic cylinders to adjust the synchronous material pressing, and the ejection pressure p=4 × 70 Mpa。 Graphite mixture is used as a conventional lubricant (about 2000 deep drawing tests have been completed in Nagoya industry, Japan, with the advantages of high integration, stable performance, convenient adjustment, etc.)

2 experimental analysis

2.1 flow deformation of the material on the outer edge of the flange curve

in the deep drawing of rectangular box, the deformation rigidity of the long and short sides of the flange is different, and the resistance to the curve deformation is different. Therefore, the deformation mitigation effect of curved materials is different. The measurement results of flange outer edge deformation during rectangular box drawing are shown in Figure 1. It can be seen from the figure that with the increase of drawing stroke, the slab angular symmetry line gradually offsets to the long side direction, and the larger the angular radius RC, the greater the offset. According to the ratio of deformation area of flange curve and long side:

, the larger the RC is, the larger the asymmetric drawing deformation area of flange curve is, that is, the larger the ratio of deformation area of curve and straight side is, therefore, the extrusion amount of curve material to straight side increases. Although the angular symmetry line shifts to the long side, according to the comparative relationship between inflow and absorption area, the inflow of curved material has a greater impact on the short side. The joint end of the short and curved edges is squeezed into the place of 1/3 of the total length of the short edge, and there is a strong compressive force acting along the peripheral direction of the outer edge. Among them, the top 25 companies account for 75%; In 2008, six American and British companies: the joint action of the compressive force in the thickness direction of DePuy increased the inflow resistance of the short side material towards the die mouth. Therefore, the larger the punch shape parameter rc/w, the more severe the deformation of the short edge of the flange, and the weakening effect on the deformation of the curved edge [2], which has become an important reason affecting the improvement of the forming limit

Fig. 1 change of flange outer edge in deep drawing

2.2 deformation tendency of flange curved edge

deformation of flange curved edge the formability of left and right rectangular box deep drawing, but because the main direction of stress and strain at all points in the area changes instantaneously with the drawing stroke, it is very difficult to measure and calculate the deformation. In order to understand the deformation state of the curved edge during deep drawing, concentric circles and radius lines with the center of the punch angle as the center are engraved on the slab by photolithography corrosion method, and then the change ratio of chord length s/s0 and the change ratio of interval of concentric circles l/l0 before and after deformation are measured. Let the symmetry line of the curved corner before deformation be θ= 0 °, the intersection line of straight and curved edges is θ= 45 °, the change ratio l/l0 and s/s0 when the drawing stroke h=9 mm are shown in Figure 2

Figure 2 deformation distribution of flange curved edge

near the die opening, compression deformation occurs in the circumferential direction, and the larger the RC, the greater the deformation. However, the position with larger circumferential compression deformation is not on the angular symmetry line, but near the intersection line of straight and curved edges, and the position with larger radial tensile deformation is also near the intersection line of straight and curved edges. This is due to the rapid flow of straight edge material to the die opening during forming, and the reason why the curved edge material must squeeze into the straight edge with less deformation resistance. When rc=9 mm, the difference of circumferential shrinkage deformation due to position is relatively small, but near the die opening, the radial tensile deformation on the angular symmetry line is also smaller than that near the intersection line of straight and curved edges. In addition, the circumferential compressive deformation and radial tensile deformation near the boundary of short and curved edges are slightly larger than that of long and curved edges

2.3 strain analysis on the symmetrical line of flange angle

according to the test results before and after the deformation of the photoetching grid on the slab, in the cylindrical coordinate (R, θ） In, the following formula is used to approximate the circumferential strain on the line proposed by the central city work conference εθ And radial strain ε r:

Where s, S0 - the circumferential gauge distance of the lattice before and after deformation

r, R0 - Radial gauge distance of lattice before and after deformation

strain value to be obtained ε R and εθ Place it at the position after deformation: R ≈ r-uc, as shown in Figure 3 (R is the distance between the measured point on the slab and the punch angle center before deformation; UC is the rigid displacement of the measured point)

Figure 3 circumferential strain and radial strain of the symmetrical line of the flange angle

in the flange corner where the material almost moves rigidly, "deformation dead zone", ε r≈ εθ ≈ 0, this area gradually decreases with the increase of RC [3]. From a certain position in front of the die mouth, circumferential compression deformation occurs first εθ＜ 0, while radial tensile deformation ε The occurrence of R> 0 lags significantly, and this tendency increases with the decrease of RC. Near the fillet of die shoulder (ri=rc+c+rd)| εθ| and ε R increases rapidly, and the maximum tensile strain ε The value of Rmax increases with the increase of RC, but the maximum circumferential compressive strain| εθ| The max value is approximately close to 0.3

if the deformation of the material near the angular symmetry line is approximately regarded as cylinder drawing, according to

εθ= Ln[r/(r+uc)] (3)

calculated near the die opening εθ rc1=-1.03； εθ rc3=-0.71； εθ rc9=-0.41。 It can be inferred that the larger the RC is, the more significant the effect of flange flange flange deep drawing deformation is

it can be seen from Figure 4 that the thickness of the rigid deformation area near the symmetrical line end of the flange angle (0 point) basically does not change ε t≈0。 Before the material is drawn to the die opening, the flange shrinkage deformation intensifies, ε T increases gradually. The closer to the die opening, the circumferential compressive deformation and the radial tensile deformation in the drawing direction increase, and| εθ|>ε r. Therefore, the plate thickness increases, ε T increases. And the smaller RC| εθ|/ε R is much larger than 1, so, ε The larger t is. The plate located at the fillet of the punch shoulder is subject to tensile deformation in the drawing direction and bending deformation at the same time, ε T ＜ 0, the plate thickness is reduced. In particular, the plate near the convex and concave gap during initial deep drawing has hardly been deformed and hardened, and it has been thinned rapidly from t0 [4]. This part of the material is strongly stretched and deformed at the shoulder of the punch and flows to the wall| ε T | sharp increase. The shoulder material located at the fillet of the punch, as the load support part to transmit the deformation resistance of the flange curve, is subject to two-dimensional unequal tension and bending deformation at the fillet of the shoulder, and the maximum plate thickness strain is generated with the increase of the surface area| ε T | max, deep drawing cracks often occur near this place

plate thickness strain distribution on the angular symmetry line in Figure 4

although RC is small and the deformation area of flange curve edge is reduced, the circumferential shrinkage deformation is concentrated on the angular symmetry line, and the risk area of punch fillet fracture under flange deep drawing resistance is relatively reduced. So| ε T | Max is relatively large. The deformation area of the bottom corner of the punch increases with the increase of RC, and the area subject to two-way tensile deformation and participating in the outflow displacement to the side wall increases. Because the total resistance to flange flange deformation increases, RC increases, and the plate thickness thinning deformation on the symmetry line of the bottom corner of the punch leaving the fracture risk zone increases relatively, and extends along the symmetry line of the corner

2.4 stress state and formability of flange curve

in order to estimate the stress distribution according to the strain state, according to the theory of total strain ε R and εθ It is regarded as the principal stress approximately. At the measuring point nearest to the fillet of the die, the ε r/εθ=- 0.3~-0.8 shows that if the pressing stress is ignored, it is close to σ r=0、 σθ=- Y such a kind θ Directional unidirectional compression state（ ε r/εθ=- 0.5）。 Slightly away from the fillet of the die opening ε r=0、 εθ＜ Area of 0, in σ r= σθ/2 = -y/(3) 1/2 plane compressive strain state, even in the radial direction, there is compressive stress [5]. That is, with σθ＜ 0, there are σ R <0. In addition, when RC is small ε Regions with R <0 can be considered to exist σθ＜σ r＜ σθ/2. Within this scope, both exist σ r = σθ and σ R <0, also exists σθ＞ Area of 0. Adjacent to the deformation rigid body domain, there are also σθ＞ Area of 0. From the deformation of the lithography lattice, it can be judged that there is a shear strain r near the junction of the straight and curved edges of the flange θ Considerable shear stress is generated τ r θ (however, according to the yield condition, the principal stress can be considered as| σ r |、| σθ| Value is still smaller than diagonal). And near the junction of short and curved edges τ r θ The value is greater than that near the junction of long and curved edges τ r θ Value. Therefore, the flange deformation resistance tends to the short side, and reducing the deformation size of the short side of the slab can correspondingly improve the formability of rectangular box drawing

if it is considered that the flange curved edge deforms independently, the actual limit drawing ratio in the test is calculated according to the local drawing ratio of the independent deformation of the curved edge

β rc1max=21.5； β rc3max=9.0； β rc9max=3.6。 No matter the size of RC, the above drawing ratio is almost difficult to achieve for cylinder drawing. According to the analysis results of stress and strain, the reason why rectangular box deep drawing can achieve such a large local drawing ratio of curved edges is not only because of the so-called strain relaxation effect of deep drawing deformation spreading to the straight edge of the flange, the back pressure effect of curved edges caused by the prior flow deformation of straight edge materials, but also the tensile stress required in the inflow direction σ R is alleviated to a large extent, as well as the comprehensive results of many effects brought by other stress-strain states that are conducive to improving tensile formability

3 conclusion

(1) in the flange curve deformation, with the increase of the rectangular box corner radius RC, the radial tensile deformation near the die mouth on the angular symmetry line increases, but the circumferential compressive deformation is not found to be related to the change of RC. No matter the size of RC, there is a deformation region of radial compression on the angular symmetry line. Therefore, it can be considered that this strain state that reduces the inflow resistance of the curved edge material is helpful to alleviate the flange curved edge deformation and improve the deep drawing formability

(2) the material at the punch fillet is subject to two-dimensional unequal tensile deformation, and the plate thickness is thinned and deformed near the junction of the shoulder fillet and the side wall| ε T | the largest fracture occurs in this area. Because this is the force transmission area of flange drawing deformation, it is preliminarily speculated that most of the fractures in drawing are strength fractures

(3) although the circumferential deformation and radial deformation near the junction of straight and curved edges of the flange tend to be greater than that near the angular symmetry line, due to the accompanying shear

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