Common Manufacturing Process

Abstract

The main goal of the manufacturing process is to generate the defined geometry of a chosen material for construction. In order to achieve the successful development and manufacturing of a biomedical device, all the material properties, manufacturing processes, and shape features of the device should be considered altogether with optimized performance and compatibility in mind. Any factors that might contradict with each other should be eliminated or replaced before starting the manufacturing process. In this chapter, we go through the common manufacturing processes for metals, polymers, and ceramics, classified into primary, secondary, and tertiary processes. The process compatibility between different materials and manufacturing processes is also summarized.

Problems

1.1 Problem 6.1

Consider the injection molding operation of pre-cured silicone (viscosity, 100 Pa·s, and density, 965 kg/m³) to continuously manufacture a container as shown in the Fig. 6.P1.

Fig. 6.P1

A manufactured silicone container

Here, we first focus on the cylindrical nozzle (shown below) in the machine with a diameter of 3 mm and 1 cm in length.

• (a) Calculate the required flow rate of silicone such that the Reynolds number of the silicone flowing along the nozzle is ~10.

• (b) Based on the flow rate calculated in (a), please estimate the pressure drop along the nozzle.

• (c) Imagine an untrained worker accidentally turned off the machine, and the molded container was very hard to remove manually from the mold afterward. Can you guess possible reasons why? Do you have any suggestions on the product design in order to eliminate such problems?

1.2 Problem 6.2

The metal die casting operation of titanium was applied to manufacture the bone fixation plate at a temperature of ~1900 K (the viscosity of liquid titanium as a function of temperature is shown in the left of Fig. 6.P2). Here, we first consider that there was one cylindrical nozzle (right of Fig. 6.P2) in the die with a diameter of 5 mm and 1 cm in length. This nozzle has the highest fluidic resistance along the transmission path of molten titanium during the process. Calculate the required flow rate of liquid titanium such that the Reynolds number of the flow along the nozzle is ~10. What should the minimum gauge pressure of this process be?

Fig. 6.P2

Viscosity of titanium against temperature (left) and die casting of titanium

1.3 Problem 6.3

• (a) The patient is a 68 kg man who is momentarily subjected to a force which is five times his weight on one of his legs. Determine the average normal stress developed in the tibia T of his leg at the mid-section a-a (Fig. 6.P3). The cross section can be assumed to be circular with an outer diameter of 4.5 cm and an inner diameter of 2.5 cm (please note that a bone structure should be a hollow shape). Assume the fibula F does not support a load.

• (b) Consider the tibia of the patient is being fixed by an external bone plate as shown in Fig. 6.P4 for which L is 35 cm and the radii of the four supporting rods (in gray color) are identical at 3 mm. Please estimate the shearing force shared by each rod under the external force P.

Fig. 6.P3

Momentary force acting on a leg

Fig. 6.P4

Configuration and key parameters of external bone fixation

• (c) Given a final shape of the fixation plate as shown in Fig. 6.P5, can you design the die? Please further mention the possible positions and modes of defects if you think there are any.

Fig. 6.P5

A bone fixation plate

• (d) The thickness of this bone fixation plate was 2 mm, and the multiple holes each had a diameter of 5 mm. The long hole located at the center was 5 cm in its total length (L). Based on the shear stress-shear strain curve (Fig. 6.P6), estimate the forces required to punch the different holes on the fixation plate.

Fig. 6.P6

Shear stress versus shear stain for a material used in a bone fixation plate

1.4 Problem 6.4

Refer to Fig. 6.P7. Use average yield strength Y = 400 N/mm², h₀ = 2 mm, h₁ = 1.4 mm, v₀ = 10 m/s, σ_x = 180 N/mm², sheet width w = 1000 mm, and R = 250 mm.

• (a) In a stress-strain test of the material before the rolling process, the specimen, with an initial diameter d₀ = 20 mm, fractured with a diameter d_f = 12 mm. The engineering stress at fracture was determined as S = 400 N/mm². Determine the true strain ε_f and true stress σ_f (N/mm²) at fracture.

• (b) By assuming the Poisson’s ratio of the material is 0.4 and the material deformation in the out-of-plane direction of Fig. 6.P7 is neglected, determine the exiting sheet speed v₁ (m/s), the length of compression zone L (mm), the compressive force F (N), and the torque on each roller T(Nm).

• (c) Based on your results in (a), determine the total power P (kW), by assuming the average speed v = (v₀ + v₁)/2 and the temperature increase ΔT (°C) of the work following the material property: density × specific heat of capacity = 3.7 N/mm² °C.

Fig. 6.P7

Key parameters during rolling

1.5 Problem 6.5

Consider a drawing process as referring to Fig. 6.P8 and neglecting friction.

Fig. 6.P8

Key parameters during drawing

Let us consider the material yield strength Y is a function of strain ε, with the relation Y = Y₀ + Kε = 280 + 320ε (N/mm²). Also, d₀ = 11 mm, d₁ = 6 mm, v_d = 4 m/s, density × specific heat of capacity = 3.7 N/mm² °C. Determine ε₁, Y₀ (N/mm²), Y₁ (N/mm²), F_d (N), the drawing power P (kW), the increase of the work temperature, and the maximum possible ratio of d₀/d₁.

1.6 Problem 6.6

Consider a drawing process as referring to Fig. 6.P9 and neglecting friction.

Fig. 6.P9

Key parameters during drawing

It is given that the material yield strength Y is a function of strain ε, with the relation Y = Y₀ + Kε = 250 + 300ε (N/mm²), d₀ = 6.5 mm, and d1 = 4 mm.

• (a) Determine ε₁, Y₁ (N/mm²), σ_d (N/mm²), and f_d.

• (b) Determine the pressure p₀ and p₁. Write out the yield criterion of the axisymmetric case as a relation between σ_x and p.

1.7 Problem 6.7

Please reconsider Figs. 6.P8 and 6.P9 as an extrusion process, with the parameters d₀ = 18 mm and d₁ = 10 mm. The yield strength of the material is Y = 200 + 150ε (N/mm²). Determine the extrusion stress σ_ex (N/mm²) and pressure between work and die, i.e., p₀ and p₁ (N/mm²).

1.8 Problem 6.8

A thin sheet of material is subjected to a biaxial stress field in the xy-plane, where z is the sheet thickness direction. The shear strains are zero and σ_x = 9 MPa, σ_y = 6 MPa, and σ_z = 0 MPa. If Young’s modulus E of the material is 3 GPa and its Poisson’s ratio ν = 0.3, calculate the extensional strains ε_x, ε_y, and ε_z.

1.9 Problem 6.9

Consider a radial drawing process, a cylindrical cup of thickness h = 1.0 mm is being formed for an initial sheet diameter of D_o to a cylindrical cup diameter of D_draw. The material is non-strain-hardening, with a yield strength of Y = 450 MPa.

• (a) Determine the radial stress σ₁ (MPa) in the flange at four radii: r = D_o/2 = 10 cm, r = 8.5 cm, r = 6.5 cm, and r = D_draw/2 = 5 cm for the initial position of the blank: r₀ = D_o/2.

• (b) Determine the drawing stress σ_d (MPa) at the position r = D_draw/2 = 5 cm and the drawing force F_d (kN) required as the munch moves downward from its initial position to four subsequent positions of the blank: r₀ = 9, 8, 7, and 6 cm.

• (c) (Optional) Repeat (a) and (b) by reconsidering the material with strain-hardening yield strength: Y = 450 + 450ε^0.3 (MPa).

1.10 Problem 6.10

Consider a shell of plastic material during the blow molding process. The material behaves as a neo-Hookean solid with an elastic modulus of 1.2 MPa. If the plastic after extrusion has a roughly spherical shell shape with a diameter of 2 cm and wall thickness 1 mm, before an additional pressure is applied, calculate the gauge pressure inside the plastic “balloon” during its expansion instantly up to a diameter of 2.2, 2.5, 3.5, and 10 cm.