Determination of the Position of the Strain Neutral Layer of Bending Parts
The strain neutral layer of a bent part refers to the fiber layer that remains constant during bending, neither stretched nor compressed. It serves as the benchmark for calculating the length of the bent part blank. During bending, the outer material layer stretches and the inner material compresses, shortening it. The neutral layer lies between the tension and compression zones, and its position varies with the degree of bending deformation. Accurately determining the location of the neutral layer is crucial for ensuring dimensional accuracy in bent parts. Errors in its position can lead to inaccurate blank length calculations, resulting in dimensional deviations after bending.
The location of the strain neutral layer is typically expressed as the neutral layer radius, r, which is the distance from the neutral layer to the center of the bend. The calculation formula is: r = r + kt, where r is the inner radius of the bend, t is the material thickness, and k is the neutral layer displacement coefficient, reflecting the degree of inward displacement of the neutral layer. The value of k depends on the relative bend radius (r/t). The smaller the r/t, the more severe the bending deformation, the greater the inward displacement of the neutral layer, and the smaller the k value. The larger the r/t, the gentler the deformation, the closer the neutral layer is to the center of the material, and the k value is closer to 0.5. For example, when r/t = 0.1, k ≈ 0.2; when r/t = 1, k ≈ 0.35; when r/t = 5, k ≈ 0.48; and when r/t = 10, k ≈ 0.5.
Experimental data and empirical formulas are the primary basis for determining the k value. Through numerous bending tests, the position of the neutral layer at various r/t values was measured, and a k-r/t relationship curve or empirical formula was developed. Commonly used empirical formulas include: when r/t ≤ 1, k = 0.32 + 0.08 × (r/t); when 1 < r/t ≤ 5, k = 0.36 + 0.04 × (r/t); and when r/t > 5, k = 0.5. For example, if r = 2 mm and t = 1 mm (r/t = 2), substituting this into the formula yields k = 0.36 + 0.04 × 2 = 0.44, which translates to r = 2 + 0.44 × 1 = 2.44 mm. These empirical formulas are applicable to common materials such as mild steel and brass. For specialized materials like high-strength steel, the k value should be reduced by 5%-10%.
Material properties have a certain influence on the location of the neutral layer. Materials with good plasticity (such as aluminum alloys and copper) deform more evenly during bending, with less neutral layer deflection and k values 5%-10% higher than those with less plasticity. Brittle materials (such as high-carbon steel and stainless steel) deform more concentratedly, with more pronounced neutral layer deflection and smaller k values. For example, under the same r/t=2 ratio, k for aluminum alloy is ≈0.46, while k for stainless steel is ≈0.42. Furthermore, the rolling direction of the material also affects the location of the neutral layer. Bending along the rolling direction results in greater plasticity and a slightly higher k value; bending perpendicular to the rolling direction results in a slightly lower k value, with the difference typically ranging from 0.02 to 0.05.
The bending method and die structure also affect the position of the neutral layer. During correction bending, due to the greater correction force, the material deforms more fully, resulting in less neutral layer offset than in free bending, and the k value increases by 0.03-0.08. For example, for a mild steel part with free bending at r/t = 2, k is approximately 0.42, while during correction bending, k is approximately 0.47. Bending dies with a hold-down device can reduce material slippage and wrinkling, resulting in more uniform deformation, a more stable neutral layer position, and less k value fluctuation (±0.02). Without a hold-down device, the k value fluctuates more, requiring an appropriate increase in the safety factor.
Determining the location of the neutral layer requires a combination of theoretical calculation and experimental verification. For bent parts requiring high precision, the actual neutral layer location can be measured experimentally. The experimental method is to draw evenly spaced parallel lines (1-2 mm apart) along the length of the blank. After bending, measure the change in spacing between the outer and inner parallel lines. Find the fiber layer where the spacing remains constant, which is the neutral layer. Then, calculate r mid . For example, in a test of a brass bent part (r = 5 mm, t = 2 mm), it was found that the spacing between the parallel lines at 2.9 mm from the inner side remained unchanged. Therefore, r mid = 5 + 2.9 – 2 = 5.9 mm (since the distance from the inner side to the material surface is t = 2 mm), and k = (5.9 – 5)/2 = 0.45, which is consistent with the results calculated using the empirical formula.
With the advancement of CAE simulation technology, finite element software (such as ABAQUS and Dynaform) can accurately simulate the strain distribution during bending, directly determining the location of the neutral layer. The simulation inputs include the material’s stress-strain curve and mold parameters. By analyzing the strain contour, the fiber layer with zero strain is identified, representing the neutral layer, with an accuracy of ±0.01mm. For example, a Dynaform simulation of a bent mild steel part with r = 3mm and t = 1mm yielded a neutral layer radius of 3.45mm and k = 0.45, which agrees well with experimental results. CAE simulation not only determines the location of the neutral layer but also analyzes the impact of different process parameters on it, providing a basis for optimizing the bending process.
In short, the determination of the strain neutral layer position of the bent part needs to comprehensively consider factors such as the relative bending radius, material properties, and bending method. It should be determined through empirical formulas, experimental measurements, or CAE simulations to ensure accurate calculation of the blank length and the dimensional accuracy of the bent part.
