Finite Element Simulation of Residual stress Formation in cold Rolling Process


Balraj Singh1, Gurinder Singh Brar2*

1MTech Student, Guru Nanak Dev Engineering College, Ludhiana, Punjab, INDIA 141006

2Department of Mechanical Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, INDIA 141006




Rolling is the most important metal deforming operation in industries. The metal is plastically deformed when it is passed through the combination of the rolls. By virtue of plastic deformation and the thermal gradient during cooling of rolled member residual stresses are developed. During, cold rolling residual stresses was evoked. Residual stresses are known as stresses which exist within the material without the employment of the external load. Residual stress cause the stress erosion, brittle fracture, fatigue and buckling. Effect of the residual stresses is favorable or detrimental which is determined by the nature and magnitude of the stresses. Finite element analysis was performed to ascertain the residual stresses in cold rolling with the aid of MSC-MARC software. A 3D finite element model of rolling process was developed to perform the structural analysis. Nature of residual stresses in longitudinal, transverse and along the thickness was studied. The longitudinal residual stress distribution was non-uniform that causes the defects in rolled member. It was found that irregular transverse strain distribution and temperature gradient along the width induces longitudinal residual stresses.


KEYWORDS:Cold rolling, Residual stresses, Finite element analysis, Longitudinal stress, Transverse stress.




In metal forming, rolling operation can produce the element with high precision and production rate. As the evolution in automobile, aerospace and nuclear plant, it is vital that rolling element should be manufactured with superior mechanical properties and without defects. During cold rolling residual stresses are evoked. Residual stresses are known as stresses which exist within the material without the employment of the external load. These stresses are self-stabilizing within the material. Residual stresses in rolled member will execute a prominent character in stress erosion, brittle fracture, fatigue and buckling. The existence of the residual stresses is favorable or detrimental which is determined by the nature and magnitude of the stresses.


The favorable impacts of the compressive residual stresses in manufacturing are, under the cyclic loading it appreciate the fatigue strength of the part and depreciate the stress corrosion and brittle fracture. The tensile residual stresses amply effects the fatigue failure and crack propagation can also be noticed. Intermittently, compressive residual stresses are inserted to the component through the method of the shot peening and deep rolling.


Accordingly, the determination of magnitude and distribution of residual stresses in rolled member are of great relevance. The presence of residual stresses is due to asymmetrical cooling of the rolled member. The parts that cool rapidly resist shortening as solidified, meanwhile the other remaining hot part tend to be shorten as the time elapsed. The section that cools rapidly has residual compressive stresses, although the remaining sections have residual tensile stresses.


Residual stresses may be ascertained analytically, computationally and experimentally. The experimental methods that are used to find the residual stresses are classified as destructive and non destructive. The experimental methods include hole drill method, layer removal method, sectioning method and X-ray diffraction method. The experimental methods are destructive and have some other limitation like in X-ray diffraction method residual stress is measured up to limited thickness. In order to cover up these limitations computer are widely used for the simulation of residual stresses. Finite element approach is employed for the investigation of the residual stresses. This is the one of the most powerful and famous approach for the simulation.  Finite element method provides accurate results in short time if the input related to material and boundary conditions are accurately predicted.


Vallellano et al. (2007) used ABACUS software for carrying out finite element analysis of flat rolling of a wire. Stresses and deformations were estimated at different reductions to recognize the influence of homogeneity in deformation of wire. Ismail et al. (2013) developed 3D finite element model of repeated rolling contact of rigid hemisphere on the rough surface. The von misses residual stress and plastic strain distributions were studied. Effect of increasing contact load on the residual stress was also predicted. Residual stresses were changed in first two rolling cycle and small plastic strain was accessed on rough surface. Yamanaka (2014) studied the effect of residual stresses on the metallic glass bolts manufactured by CNC cold thread rolling. By the Heyn Bauer method residual stress was calculated in axial direction. Compressive residual stress in axial direction was measured near bolt surface by Heyn Bauer method, which was validated by finite element method. Nguyen et al. (2014) used finite element approach to analyze the cold roll dimpling process. Tensile and bending tests were conducted experimentally after the dimpling operation. These tests were validated by finite element method in MSC-MARC software. Effect of friction on plastic deformation was also studied. Plastic strain distribution, bending test and tensile test of plate have good agreement with experiment and finite element method. Rout et al. (2016) ascertained stress, strain and temperature distribution in AISI 304 stainless steel induced during unidirectional and cross hot rolling process. DEFORM 3D software was used for finite element simulation. Effect of changing the rolling velocity and temperature were studied for both the operations. Plate contained higher strain at the centre and higher stress at the surface. With increase in roll speed, high temperature obtained at centre of plate. Experimental method that can be used to determine residual stresses are destructive, take too much time, laborious, expensive and difficult to carry out for complex geometries. In this study, Finite element approach is used to predict the magnitude and distribution of residual stress in cold rolling process.



In the present study, C45 steel grade was considered. The mechanical properties of C45 steel are summarized in Table 1. These properties were obtained by tensile testing.


Table 1 Mechanical properties of C45 steel grade

Young’s Modulus


Yield strength

457 MPa

Ultimate Tensile strength

654 MPa

Poisson ratio


Percentage elongation




A billet having cross section 125 mm ×125 mm and length 1000mm was cold rolled. The gap between the rollers was maintained at 90mm, such that 35 mm of reduction can be achieved. The rollers were rotated with 2.31 rad/s in opposite direction (i.e. clockwise and anticlockwise) having the diameter of 432mm. The feed rate for the material to pass through the rolls was 0.5m/s. The details of geometry are shown in Fig. 1.


Fig. 1 Detail of the geometry


MSC-MARC 2016 software was used for the simulation of the rolling operation. Both the sets of rollers are designed as rigid bodies and billet (work piece) was designed as deformable body. The deformable body was meshed with 3Dsolid tetrahedral, 10 noded element. Work piece after meshing comprised of 9428 element and 2251 nodes. Fig. 2 shows the meshed billet that is to be rolled. The contact between the rollers and deformable work piece was modeled. There is touch contact between the rollers and work piece and glue contact between the back plate and work piece. During contact definition various parameters were defined like axis of rotation of rollers (z-z axis), angular velocity of the rollers with direction, and linear velocity with direction of movement (along x-x axis) of the deformable body. Friction is another important parameter which was mentioned during contact definition. Friction of coefficient between the rollers and work piece was considered as 0.5.


Fig. 2 Meshed billet (work piece) with backup plate


As the work piece passes through the roller, mesh will break and a new formation will be created. Due to this, remeshing of present meshing has to be done. Patran tetra 3D solid remeshing type with incremental criteria and maximum strain change 0.2 was used in this analysis. The static structural type load case with adaptive multi criteria was used. The loaded time was chosen by hit and trail method by reducing time step. In adaptive stepping initial fraction of loading time of 0.001sec and maximum fraction of loading time of 0.005sec was applied to manipulate the simulation.



Residual stresses in longitudinal, transversal and along the thickness of billet were obtained by finite element simulation.  Fig. 3 shows the formation of the transverse residual stress along the width during cold rolling process. Fig. 4 shows variation of the magnitude of transverse residual stress in transverse direction. Along the width maximum residual stress is 348.2MPa at the centre of the plate and at the edges stress value reduces. This effect is due to free flow of the material in transversal direction at the edges and because of symmetrical condition at centre impedes the flow of material along width. Consequently, high stresses were obtained in centre and larger strains at the edges.


Fig. 3 Formation of transverse residual stresses


Fig. 5 shows the residual stresses distribution along the thickness. Compressive residual stresses were obtained throughout the thickness. As the material passes through the roll gap, rollers restrict the flow of material along thickness and induce the compressive stresses. Fig. 6 depicts the maximum residual stress along the thickness was at the centre part having value of -446.7MPa.Longitudinal residual stress is the prominent character which originates the defect in the rolling. The irregular distribution of longitudinal stress along the width is shown in Fig. 7 which causes the buckling in the plate.


Fig. 4 Residual stress variation along width


Fig. 5 Residual stress distribution along thickness


Due to temperature gradient and irregular deformation along the width longitudinal residual stresses will originated. The pattern of the deformation at the centre and edges was different. At the edges reduction is more than the central part because of that there is large flow of material at edges in longitudinal direction than centre. After passing through the gap, due to rigid motion of plate the part that extended more encounter longitudinal compressive residual stress and shorter part consist of tensile residual stresses to reach stable length and equal exit and entry velocities.


Fig. 6 Variation of transverse residual stress along thickness



Fig.7 Longitudinal residual stress distribution


Temperature varies along the width of plate as it is cool. At edge of the plate temperature falls rapidly as compared to centre of the plate. Thus asymmetrical cooling occurs along the width which induces compressive residual stress at the edge having magnitude -300MPa and tensile residual stress at the central region with 291.4MPa. Fig. 8 shows the longitudinal stress variation along the width.


Fig. 9 shows longitudinal stress along the rolling direction. In the roll gap compressive stress are predicted and after passing through the roll gap tensile longitudinal stress are obtained. Flow of material in transverse direction is more at the edges. Due to that longitudinal flow of material at the edges impede and flow of material at the centre along the rolling direction is larger. As a result compressive stresses are developed at centre where transversal flow was low. After passing through roll gap compressive stress changes to tensile stress due to non uniform velocity distribution at exit along the transverse direction.


Fig.8 Longitudinal residual stress along width


Fig. 9 Longitudinal stress variation along the rolling direction




In this study, residual stress distribution in flat cold rolling was studied with the aid of finite element method. The following conclusions can be drawn from the study:

1.      The compressive residual stress was predicted along the thickness and tensile residual stress along the width.

2.      The irregular transversal strain distribution and temperature gradient along the width induces longitudinal residual stresses.

3.      The edge buckling in the plate is due to non uniform distribution of longitudinal stress along the transverse direction. Compressive stress at the edges and tensile stress at the central part along the width causes buckling in the plate.



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Received on 04.07.2017                             Accepted on 05.09.2017

©A&V Publications all right reserved

Research J. Engineering and Tech. 2017; 8(4): 338-342. 

DOI: 10.5958/2321-581X.2017.00058.7