Exponentially fitted two-derivative DIRK methods for oscillatory differential equations

As ultrasonic rolling mainly affects the residual stress and surface morphology of Ti6Al4V, it is of great significance to study different process parameters, such as amplitude, static pressure, time, and step length, thereby improving the performance of Ti6Al4V. However, unstable bouncing caused by the elastic relationship between the indenter and the sample is inevitable. Based on finite-element analysis and Hertz contact theory, the concept of critical damping was proposed to quickly stabilize the system. Therefore, a three-dimensional finite-element model was established using the ABAQUS software, after which the ultrasonic-rolling process was simulated by applying static pressure on the sample surface using a spring. Then, the distribution of residual stress under different amplitudes, static pressures, times, and step lengths was analyzed. Based on simulation and experimental results showed that the maximum residual stress of −689.802 MPa was obtained when the amplitude, static pressure, and time were 10 µm, 600 N, and 0.064 s, respectively. When the step length was 1/2 of the indentation width, the surface stress concentration was obvious, convex defects were large, and surface roughness Ra increased to 1.076 µm. Investigations also revealed that when the step length was 1/8, Ra decreased by 39.68% compared with that when the step length was 1/2, the thickness of the plastic-deformation layer reached 56.07 µm. When the step length was 1/10, the maximum compressive residual stress reached −888.007 MPa and Ra increased. On the basis of the abovementioned optimization parameters, the influence of step length on the properties of Ti6Al4V alloy was further explored, and direction for the strengthening process of Ti6Al4V alloy by studying the pattern of surface strengthening was presented.

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“…This model also used the ode45 function in MATLAB to solve the vibration differential equation. 47–49 The results are shown in Figure 7.…”

Section: Methodsmentioning

confidence: 99%

“…This model also used the ode45 function in MATLAB to solve the vibration differential equation. [47][48][49] The results are shown in Figure 7. Finally, the system's natural frequency was calculated, after which different damping values were used in plotting.…”

Section: Finite-element Simulationmentioning

confidence: 99%