How Small Can the Diameter of a Wire Get When Drawn Through a Die?

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In summary, a linearly strain-hardening material is being drawn into a wire with a true-stress-true-strain curve given by σ = 34.5 + 172.4 ε. The minimum possible diameter at the exit of the die can be found by solving the equation d = 0.635 cm / (1 + (34.5 + 172.4(ε_s + 0.15ε_s))/(172.4)). Using a numerical solver, the minimum possible diameter is approximately 0.1067 cm.
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A linearly strain-hardening material with a true-stress-true-strain curve given by σ = 34.5 + 172.4 ε is being drawn into a wire. If the original diameter of the wire is 0.635 cm, what is
the minimum possible diameter at the exit of the die? Assume that there is no redundant work and that frictional work is 15% of the ideal work of deformation. (Hint: the yield stress of the exiting wire is the point on the true-stress-true-strain curve that corresponds to the total strain the material has undergone).
 
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Let ε_s be the strain at the exit of the die. The total strain experienced by the material is then (ε_s + 0.15ε_s). The yield stress of the exiting wire is σ_y = 34.5 + 172.4(ε_s + 0.15ε_s).The diameter of the wire at the exit of the die is given by d = 0.635 cm / (1 + ε_s + 0.15ε_s).Substituting the expression for the yield stress in the expression for the diameter gives:d = 0.635 cm / (1 + (34.5 + 172.4(ε_s + 0.15ε_s))/(172.4))This equation can be solved numerically to find the minimum possible diameter at the exit of the die. Using a numerical solver, the minimum possible diameter is approximately 0.1067 cm.
 

1. What is deformation and forging?

Deformation is the process of changing the shape or size of a material, while forging is a specific type of deformation that involves shaping the material by applying compressive forces. This is typically done at high temperatures to make the material more malleable.

2. What are the benefits of forging?

Forging offers several advantages, including increased strength and durability of the material. It also allows for precise shaping and improved grain structure, resulting in better mechanical properties. Additionally, forging can reduce material waste and produce a more uniform product.

3. What are the different types of forging?

There are several types of forging, including open die forging, closed die forging, and roll forging. Open die forging involves shaping the material between flat or shaped dies, while closed die forging uses shaped dies to compress the material into a specific shape. Roll forging uses rollers to shape the material between two or more dies.

4. What materials can be forged?

Forging can be done on a variety of materials, including metals such as steel, aluminum, and copper. It can also be used on some non-metallic materials like ceramics and plastics. The type of material and its properties will determine the specific forging processes that can be used.

5. What industries use forging?

Forging is used in a wide range of industries, including automotive, aerospace, construction, and oil and gas. It is also commonly used in the production of tools, machinery, and other industrial equipment. Any industry that requires strong and durable components can benefit from the use of forging.

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