Discussion on weakening temperature extraction parameters of weakened springs
Residual stress acts in conjunction with the stress experienced by the spring during operation. When a spring is stretched or compressed, the wire undergoes torsion and shear due to an axial load. However, under normal conditions, the shear force is relatively small, so it is typically only the torque that is considered. The maximum shear stress from torsion occurs at the outer surface of the wire, while the maximum residual stress, as shown in figure b), occurs near the center of the wire. Therefore, the maximum residual stress is the most critical factor, and future discussions will focus on this value.
The removal of low-temperature annealing residual stress is achieved through controlled cold working and heat treatment before winding the spring. This process imparts the necessary mechanical properties to the material. Subsequent low-temperature annealing helps eliminate residual stresses without altering the pre-treated characteristics. Current heat treatment parameters are set at 190–350°C for 20–40 minutes for phosphor bronze and 350–450°C for 1 hour for stainless steel.
The objective of this study is to reduce the processing time required for this step. Unfortunately, there are very few published reports on this topic, and most references only discuss improvements in furnace design <6>. Additionally, the changes in stress during annealing and the extent of stress removal remain poorly understood. The only existing analysis <7> focuses solely on temperature distribution during the annealing process.
Research into low-temperature annealing technology draws from several key studies [8–14], which suggest that the removal of residual stress is closely related to metal stress relaxation. To preserve the material's previously imparted properties while eliminating stress, annealing must occur below the recrystallization temperature. During this process, no structural changes take place in the metal. Furthermore, this stress relaxation is also a form of metal recovery. Recovery refers to changes in physical and mechanical properties without altering grain shape or crystal orientation, occurring before recrystallization. From the perspective of atomic dislocation theory, this can be interpreted as the disappearance of dislocation movement or point defects, although no consensus has been reached yet.
Low-temperature annealing and creep both involve stress reduction over time, but they differ in their application. Creep is a phenomenon where deformation increases under constant stress at high temperatures, while stress relaxation is a subset of creep, referring to the decrease in stress when deformation remains constant. Stress relaxation can also be viewed as a recovery process <15>. Although stress relaxation and annealing are similar, the latter specifically refers to the process after cold working. For creep, various phenomena, experiences, and physical models can be explored based on the material’s high-temperature strength and plasticity <15–16>.
Creep is generally divided into three stages: transient creep, uniform creep, and tertiary creep. Among these, uniform creep dominates the overall behavior, and multiple physical models have been proposed. This paper aims to focus on dislocation motion to quantitatively explain the creep rate, providing a basis for optimizing low-temperature annealing treatments.
In terms of quantifying the low-temperature annealing process, the creep velocity formula is extended to derive the annealing speed equation. The creep rate formula relates creep velocity to temperature and follows an activated heat formula <12, 15–16>. Here, RT represents the average vibrational energy of an atom, Q is the activation energy needed for atomic rearrangement, and exp(-Q/RT) indicates the probability of atoms having sufficient energy to cause creep. The relationship between stress and uniform creep can be described using the Dorn velocity formula.
To summarize, the general creep velocity formula is given as <15–18>: dE/dt = A * n * exp(-Q/RT) (3) where A is a constant. For low-temperature annealing, it is assumed that the above creep velocity formula can also apply. Further, assuming that the stress removal process follows Hooke’s law (equation 4), and that the longitudinal elastic modulus E is independent of temperature, low-temperature annealing can be explained as a recovery process.
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