The kinematics of the deep rolling tool, contact stress, and induced residual stress in the near-surface material of a flat Ti-6Al-4V alloy plate are numerically investigated. The deep rolling tool is under multiaxis nonlinear motion in the process. Unlike available deep rolling simulations in the open literature, the roller motion investigated in this study includes penetrative and slightly translational motions. A three-dimensional finite element model with dynamic explicit technique is developed to simulate the instantaneous complex roller motions during the deep rolling process. The initial motion of the rollers followed by the penetration motion to apply the load and perform the deep rolling process, the load releasing, and material recovery steps is sequentially simulated. This model is able to capture the transient characteristics of the kinematics on the roller and contacts between the roller and the plate due to variations of roller motion. The predictions show that the magnitude of roller reaction force in the penetration direction starts to decrease with time when the roller motion changes to the deep rolling step and the residual stress distributions in the near-surface material after the material recovery step varies considerably along the roller path.

Deep rolling is a mechanical surface treatment method in which the workpiece surface is exposed to high local mechanical load using a spherical or cylindrical type tool to induce work hardening and compressive residual stress in the near-surface material. Depending upon the controlling parameters, this process alters the mechanical behavior of the material by cold working and enhances stability of the near-surface structure when the workpiece is exposed to a high temperature condition (exceeding 450°C). The high temperature fatigue resistance is due to the formation of a near-surface work hardened layer with a nanoscale microstructure during the deep rolling of the surface [

Deep rolling provides deeper case of compressive residual stress and a work hardened microstructure as well as a relatively smoother surface finish [

A large number of numerical simulations have been conducted using a spherical or cylindrical type of rolling tools to understand the contact stress distributions and deformation patterns during the near-rolling process, as well as residual stress profiles after the process. Yen et al. [

Sartkulvanich et al. [

Ali and Pan [

Other similar numerical investigation into this subject can be found in Guagliano and Vergani [

Schematic of deep rolling process on a relatively larger plate under complex roller path.

As mentioned in the introduction, the main challenge in treating the deep rolling process is the multiplicity of paths that the roller involves. Thus, a holistic three-dimensional finite element model is proposed in the present paper. The model of deep rolling consists of a rigid mandrel, a rigid cylindrical roller, and a relatively larger elastic-plastic flat plate as shown in Figure

The multiple paths of the roller are depicted in Figure

Multiple paths of the roller. (a) Initial step, (b) penetration step, (c) deep rolling step, and (d) recovery step with the left-hand column of plots being front views and the right-hand column of plots being right views.

The Cartesian coordinate system is used in the FE model. The selection of the sizes of the finite elements to simulate the multiple paths of roller motion follows the guidelines that are established in Ali and Pan [

In addition to multiple paths of roller motion, an important factor that influences the deep rolling analysis is the material model. The material model, which can adequately represent the deformation response during loading and unloading, must account for strain hardening or softening during the process. Several models have been developed, with varying degrees of accuracy, to predict the deformation response of materials. Among these models, the Johnson-Cook (JC) material model is the most widely used. The JC model has been proven to represent the plastic behavior of the material very well and has been extensively used to predict material behavior (flow) under high strain and strain rate as a function of the operating temperature. JC material model can be expressed as

In this section, a deep rolling process that consists of a smooth cylindrical roller and a smooth relatively larger elastic-plastic flat plate will be used as an illustrative example. Simulation results for multiple paths of roller motion will be presented to

demonstrate the effectiveness of the FE model in handling multiple paths in the deep rolling process,

highlight the difference between the proposed multiple paths model and the single indentation or single rolling ones,

present the residual stress distributions in the near-surface material after the material recovery vary along the roller path.

Figure

Three-dimensional finite element mesh of deep rolling.

The material constitutive constants for the JC model have been introduced into the finite element code in ABAQUS. The elastic-plastic flat plate considered in the present paper is Ti-6Al-4V alloy. This alloy offers a combination of high strength, light weight, formability and corrosion resistance which have made it a world standard in various applications such as aerospace, automotive, and marine equipment. The material properties of Ti-6Al-4V are listed in Table ^{3} s^{−1} and temperature up to 600°C [

Material properties of Ti-6Al-4V, [

Density | 4430 kg/m^{3} |

Young’s modulus | 110 GPa |

Poisson’s ratio | 0.342 |

Parameters of Johnson-Cook material model for Ti-6Al-4V [

Yield strength, |
968 MPa |

Strain hardening coefficient, |
380 MPa |

Strain rate coefficient, |
0.0197 |

Strain hardening exponent, |
0.421 |

Thermal softening exponent, |
0.577 |

Melting point, |
1605°C |

Stress-strain curve of Ti-6Al-4V from J-C model predictions at room temperature.

The FE model has been validated through two ways. First, in an elastic contact condition—that is, the boundary conditions, element type, and mesh size-by comparison with the analytical solution of Hertzian line contact for an indentation simulation between the cylinder and flat plate surface when the contact is still in the elastic deformation stage, that is, for very low loads. The difference between the Hertz theory and the FE model for the contact band width, pressure, and von Mises stress was found to be smaller than 5%. The difference between the FE and analytical solution in the elastic deformation stage can be explained by the boundary conditions of the FE model that differ slightly from the half-space assumption in Hertz theory. Second, in a simple loading path of deep rolling process, details are shown in the Appendix of the present paper.

Figures

Displacements of the reference point on the rigid roller for the complex roller path in the deep rolling process. (a) Translational and (b) rotational.

As mentioned previously in this section, an appropriate mass scaling has to be employed in the present FE analysis to enable a time-efficient simulation of the process. The appropriateness of mass scaling means that the artificial mass is added to the system without adulterating the global solution. One way to check the appropriateness of mass scaling is to compare the kinetic energy to the internal energy. Figure

Model internal energy (ALLIE) and kinematic energy (ALLKE), showing insignificant inertia effects.

Figure

Reaction forces of the roller for the complex roller path in the deep rolling process.

The historical displacement component

Figure

Figures

Mises stress distributions on the plate upper surface (top-view in the left-hand column) and in the plate (cut-view in the right-hand column) when the roller spins (a) 0.5-revolution, (b) 1.5-revolution, (c) 2.5-revolution, and (d) the roller is at the end of recovery step. Note that the roller is removed from the figure in order to see the stress distribution completely and all units are in Pa.

It is interesting to compare the Mises contour shape in the plastic zone. Figure

Mises contours with a cutoff of minimum stress limit at 862 MPa, the yield strength of Ti-6Al-4V on the

Figure

Contact pressure distributions at different steps.

Figure

Residual stress distributions within the rolling track at (a) 12 o’clock, (b) 9 o’clock, (c) 6 o’clock, (d) 3 o’clock position when the roller is at the end of recovery step, and (e) the positions for paths of residual stress.

In Figure

Contours of residual stress on the plate top surface at the end of recovery step: (a)

There is little information available in the literature regarding these tensile residual stresses near the inner and outer boundaries of the roller track since most of the deep rolling processes are simulated by using simplified 2D models. However, the authors in the present paper find that these positive stress regions could be generated by the combination of microslip and small translational motion of roller for the complex roller paths specified in the present paper. The microslip phenomenon was first observed by Heathcote [

Although the tensile stress appears in some regions in the roller track, the authors find that the neighboring surfaces surrounding the inner and outer track boundaries tend to have significant compressive stress levels, especially in

Residual stress distributions in the material neighboring the outer track at the 3 o’clock position shown in Figure

So far, there is no documented experimental result using a cylindrical roller under complex roller path. There are, however, limited numbers of well-documented experimental studies available in the literature for the deep rolling process under simple roller path using a ball tool with limited normal load due to the usage of hydraulic pressure system. All of the experimental measurements used the ball tools to deep roll the specimen on a bar-stock or plate structure. Among these experimental measurements, Nalla et al. [

Comparison of the predicted residual stress

It should be noted that Figure

A comprehensive 3D finite element dynamic analysis with considering a complex roller path is conducted to simulate the deep rolling process. In this analysis, the roller is modeled as a rigid body and is in contact with a relatively larger plate under highly lubricated condition. The plate material is modeled as an elastic-plastic material by using the JC material model for the strain hardening and deformation response in the process. The results can be summarized as follows.

The magnitude of resultant resistant force on the plate surface is approximately 10% of the loading force, which consists of 5% of the loading force on the prescribed interfacial friction and 5% of loading force on the material penetration in front of the roller. This helps a designer in implementing the high speed spindle tool design.

The magnitude of loading force in the penetration direction (depth direction) starts to decrease with time when the roller path changes to the deep rolling step and the residual stress distributions in the near-surface material after the material recovery step vary along the roller path.

With a specified roller displacement, the subsurface material reaches its saturated stress state after two or three times of deep rolls. The residual strain will not increase if no deeper roller displacement is performed.

The contact pressure distributions are no longer in semiellipsoidal shape or elastic Hertzian pressure distribution when the plate is in the deep rolling process.

The residual stress components

The residual stress components

The microslip and small translational motion of the roller can cause regional tensile stress on the plate top surface near the roller edges in the roller track.

The residual stress distributions in the neighboring subsurface material surrounding the inner and outer track boundaries are quite different from those within the deep rolling track. Significant compressive residual stresses are found on these surfaces.

While the proposed FE model is shown to have significantly higher compressive residual stress compared to the published experiments representing simple roller path conditions, its qualitative aspects have not been validated directly. The model must be validated further in the future for its capability in predicting residual stress in the complex roll path conditions.

To validate the material model, a three-dimensional finite element model was built to simulate the deep rolling on Ti-6Al-4V workpiece under simple loading path. The workpiece has a dimension of 10 × 10 × 80 mm. The roller is in spherical shape as a common tool for the deep rolling under simple loading path. The diameter of roller is 6 mm. The Johnson-Cook material model and constitutive parameters for Ti-6Al-4V described previously in the present paper was employed to simulate the material behavior under loading and unload conditions. The roller was assumed to be rigid to reduce the computational time since the roller is much harder than the workpiece. The model is designed to be symmetric in the later direction to simplify the simulation process and decrease the computational time. Eight-node linear brick finite elements with reduced integration and hourglass control (C3D8R) were used for the workpiece.

The simulation consists of three steps. Initially, the roller sits on the starting position of the workpiece. The first step is to load the roller at its center to penetrate the workpience with a depth of 40

Figure

Predicted distribution of residual stresses

Predicted reaction force on the roller for the simple roller path.

Predicted near-surface compressive residual stress for the simple roller path.

Comparison of the predicted residual stress

Translational displacements in the

Rotational displacements along the

Reaction forces in the

Normal stresses in the

Equivalent to shear stresses

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to thank United Technologies Research Center for permission to publish this paper.