Stress and strain of blank during cylindrical drawing
The stress and strain state of the blank during cylindrical drawing deformation is complex and changes dynamically with the deformation process. There are significant differences in the stress and strain distribution in different regions, which directly affects the plastic flow of the material and the quality of the drawn part. A deep understanding of the stress-strain state of the blank helps optimize process parameters and mold structure to avoid defects such as wrinkling and cracking. During the drawing process, the blank is mainly subjected to radial tensile stress, tangential compressive stress and through-thickness stress, which correspondingly produce radial elongation strain, tangential shortening strain and through-thickness strain. The interaction of these stresses and strains determines the deformation behavior of the material.
The flange area is the most complex region of stress and strain in the blank, primarily subject to radial tensile stress (σr) and tangential compressive stress (σθ), while through-thickness stress (σt) is negligible. Radial tensile stress, generated by the drawing force provided by the punch, causes the material to flow toward the center; tangential compressive stress, generated by the tangential contraction of the material, is the primary cause of flange wrinkling. Strain in the flange area manifests as radial elongation strain (εr > 0), tangential shortening strain (εθ < 0), and through-thickness strain (εt > 0). This means the material is elongated radially and compressed tangentially, resulting in a slight increase in thickness. For example, the flange area of a low-carbon steel blank can experience radial tensile stresses of 200-300 MPa, tangential compressive stresses of 150-250 MPa, radial elongation strains of approximately 20%-30%, tangential shortening strains of approximately -20% to -30%, and through-thickness strains of approximately 1%-3%. The stress and strain in the flange area gradually change from the outer edge to the radius of the die. The tangential compressive stress and shortening strain at the outer edge are the largest, making it most prone to wrinkling.
The stress-strain state in the die corner is more complex. As the material passes through the die corner, it is subjected to a combination of radial tensile stress, tangential compressive stress, and bending stress, with additional stress generated by friction. Radial tensile stress causes the material to flow toward the center, bending stress causes the material to bend, and frictional stress hinders material flow. The strains in the die corner include radial elongation, tangential shortening, and bending strain. The thickness decreases slightly due to bending and friction (εt < 0). For example, radial tensile stress in the die corner can reach 300-400 MPa, bending stress can reach 100-150 MPa, radial elongation strain is approximately 10%-15%, tangential shortening strain is approximately -10% to -15%, and thickness strain is approximately -0.5% to -1%. The smaller the die corner radius, the greater the bending and frictional stresses, the more significant the reduction in material thickness, and the greater the susceptibility to surface scratches or cracks.
The barrel wall primarily experiences radial tensile stress (σr), transmitted from the punch, to overcome deformation resistance and frictional resistance in the flange and die radius areas. The stress state in the barrel wall is approximately uniaxial tension, with relatively small tangential stresses (σθ) and thickness stresses (σt). The corresponding strains manifest as radial elongation (εr>0), thickness shortening (εt<0), and tangential strain (εθ≈0). For example, radial tensile stress in the barrel wall can reach 350-450 MPa, approaching the material's tensile strength. Radial elongation strain is approximately 15%-25%, and thickness shortening strain is approximately -1% to -2%. Stress and strain in the barrel wall gradually decrease from top to bottom, with the highest stress and strain in the upper portion, making it the most susceptible to cracking.
The punch radius is subject to radial tensile stress, bending stress, and frictional stress. The material bends here, transitioning from the wall to the bottom. Radial tensile stress stretches the material, bending stress causes it to bend around the punch radius, and frictional stress hinders material flow. The strains in the punch radius include radial elongation, bending, and through-thickness strains. The thickness decreases slightly due to bending and stretching (εt < 0). For example, radial tensile stress in the punch radius can reach 300-400 MPa, bending stress 100-200 MPa, radial elongation strain approximately 5%-10%, and through-thickness shortening strain approximately -0.5% to -1%. The smaller the punch radius, the greater the bending stress, the more severe the stress concentration, and the greater the risk of material cracking.
The bottom zone, located at the punch tip, undergoes virtually no plastic deformation. It primarily bears radial tensile stress transmitted from the barrel wall. The stress is low (typically < 100 MPa), and the strain is also very small (εr ≈ 0, εθ ≈ 0, εt ≈ 0). The material properties in the bottom zone essentially remain unchanged, and thickness changes are negligible. For example, the radial tensile stress in the bottom zone is approximately 50-80 MPa, and the strain in all directions is < 0.5%, making it the region with the least deformation in the drawn part.
The stress and strain distribution of a cylindrical blank during deep drawing changes dynamically as the drawing process progresses. Initially (when the flange area is large), tangential compressive stress dominates, leading to wrinkling. As drawing progresses, the flange area decreases, radial tensile stress increases, and tensile stress in the wall area becomes dominant, making cracking more likely. This uneven stress and strain distribution leads to varying degrees of work hardening in different parts of the drawn part. The wall and flange areas are significantly harder than the base area. For example, the wall of a low-carbon steel drawn part is 20%-30% harder than the base. By optimizing parameters such as blank holder force, die corner radius, and clearance, the stress and strain distribution can be improved, non-uniformity reduced, and the quality of the drawn part enhanced. For example, increasing the blank holder force reduces tangential compressive stress and prevents wrinkling; increasing the die corner radius reduces bending and friction stresses, mitigating material thinning; and a reasonable punch-die clearance ensures uniform material flow and reduces stress concentration.
Numerical simulation techniques (such as finite element analysis) can visually demonstrate the stress and strain distribution of the blank during the drawing process. This simulation can predict areas prone to wrinkling and cracking, providing a basis for process optimization. For example, a Dynaform simulation revealed that during the deep drawing of a cylindrical part, the tangential compressive stress at the outer edge of the flange reached 250 MPa, posing a risk of wrinkling. However, increasing the blank holder force to 15 kN reduced the tangential compressive stress to 200 MPa, and the wrinkling disappeared. Understanding and controlling the stress and strain state of the blank is key to achieving high-quality deep-drawn cylindrical parts.
