# Curvature Design Principles for Stretch Forming Workpieces

The key technology of the stretch bending forming process is that the arc design principle of the stretch bending workpiece is to not exceed the elongation rate of the material. During stretch forming, forming defects such as thinning of the profile wall thickness, fracture, wrinkling, and cross-sectional distortion will occur. These forming defects are related to Factors such as the mechanical properties, cross-sectional shape, and bending process parameters of the profile are closely related.

## Two Key Considerations

During the stretch-forming process, the stress state of each part of the material deformation zone is different. The material outside the neutral layer is subject to tensile stress, and the material within the neutral zone (fitting with the stretch-forming mold) is subject to compressive stress. In order to prevent the material from being subjected to compressive stress If wrinkling occurs, the pre-stretching force must be sufficient to cause the material to yield and stretch. The metal outside the corresponding neutral layer will be subject to greater tensile force, resulting in thinning of the wall thickness and a tendency to fracture. Therefore, how to balance the material without wrinkling and the metal outside the neutral layer without fracture, and avoid excessive deformation of the profile cross-section, are two key considerations in determining the stretch forming process parameters.

## Stretch Forming Calculations And Formulas

Stretch forming involves the controlled stretching of a material to achieve a desired shape. While there isn’t a single universal formula for stretch forming due to the complexity of the process and the variability in materials and shapes, there are several key parameters and equations that can be used to calculate specific aspects of the process.

• Stretch Ratio (λ): The stretch ratio is the ratio of the final length (L_f) to the initial length (L_i) of the material. It is calculated as follows:
λ = L_f / L_i
• Strain (ε): Strain measures the deformation of the material during stretching and is defined as the change in length (ΔL) divided by the original length (L_i):
ε = ΔL / L_i
• Forming Force (F): The forming force required for stretch forming depends on factors like material properties, stretch ratio, and the shape being formed. The specific equation for calculating forming force can be complex and often requires experimental data or finite element analysis (FEA).
• Blank Size (B): The initial blank size can be calculated based on the desired final dimensions and the stretch ratio. The relationship between the initial blank size, final size, and stretch ratio is not a simple linear equation and may require iterative calculations.
• Die and Tooling Design: The design of the die and tooling involves considerations of the part’s geometry, material properties, and desired deformation. Calculations for die radius, die opening, and clamping force can be derived based on specific design requirements.
• Material Selection: Material selection involves assessing material properties such as ductility, yield strength, and elongation to determine its suitability for stretch forming. The choice of material can significantly impact the stretching process.

### Euler-Bernoulli Theory Calculations And Formulas

In general, the Euler-Bernoulli theory can be used to calculate the tensile and bending stress of the profile.

The tensile bending stress σ can be calculated by the following formula: σ = M * y / I
Among them, M is the bending moment, y is the distance from a certain point on the cross-section of the profile to the neutral axis, and I is the cross-sectional moment of inertia of the profile.

In addition, the section moment of inertia I of the profile can be calculated by the following formula:
I = (b * h^3) / 12
Among them, b is the width of the profile, and h is the height of the profile.

## Three Factors Need To Be Considered

When calculating the forming force of stretch-bent profiles, three factors need to be considered during the project’s technical capability review:

• Whether the jaw distance of the equipment meets the tensile length of the material;
• Whether the jaw size meets the cross-section size clamping requirements;
• The most critical point in stretch bending is to calculate the maximum tensile force required by the material.

To calculate the forming capacity of the stretch-bending workpiece, the material yield strength value takes a safety factor of 1.25 times to ensure that the equipment does not work under the maximum tensile load. The maximum tensile force of the equipment is greater than the required tensile force value of the material calculated by the formula, indicating that the tensile capacity of the equipment meets the material requirements. Bending force requirements.